ion beam induced pattern formation on si and ge surfaces€¦ · semiconductors [17-32], and other...

Ion Beam Induced Pattern Formation on Si and Ge Surfaces

Von der Fakultät für Physik und Geowissenschaften

der Universität Leipzig

genehmigte

DISSERTATION

zur Erlangung des akademischen Grades

Doctor rerum naturalium

Dr. rer. nat.

vorgelegt

von M.Sc. Bashkim Ziberi

geboren am 11. September 1974 in Radiovce (Mazedonien)

Gutachter:

Prof. Dr. B. Rauschenbach (IOM Leipzig und Universität Leipzig)

Prof. Dr. Michael J. Aziz (Harvard University)

Prof. Dr. S. Linz (Westfälische Wilhelms-Universität Münster)

Tag der Verleihung 19.12.2006

Diese Arbeit wurde im Zeitraum Mai 2002 bis Juni 2006 am Leibniz-Institut für

Oberflächenmodifizierung e. V. Leipzig angefertigt.

This work was prepared from May 2002 until June 2006 at the Leibniz-Institut für

Oberflächenmodifizierung e. V. Leipzig.

Betreuer / Supervisors: Prof. Dr. B. Rauschenbach / Dr. F. Frost

Bibliographische Beschreibung

Ziberi, Bashkim

Ion Beam Induced Pattern Formation on Si and Ge Surfaces

Universität Leipzig, Dissertation

135 S., 148 Lit., 79 Abb., 9 Tab.

Referat:

Die vorliegende Arbeit beschäftigt sich mit systematischen Untersuchungen zur

Ionenstrahlerosion von Si- und Ge-Oberflächen. Im Mittelpunkt standen dabei die

Aufklärung von Selbstorganisationsprozessen, die beim Beschuss mit Ne+-, Ar

+-, Kr

+-, und

Xe+-Ionen mit eine Energie zwischen 500 eV bis 2000 eV auftreten. Besonderes Interesse

galt dabei den entstehenden hoch-geordneten Ripple- und Punktmustern, mit Dimensionen

der Einzelstrukturen deutlich kleiner als 100 nm. In diesem Zusammenhang wurde der

Einfluss verschiedener Prozessparameter, wie Ionenenergie, Ioneneinfallswinkel, und

Ionenfluenz und -fluss, auf die Strukturbildung im Detail untersucht. Ein weiteres

Hauptaugenmerk lag auf dem Einfluss zusätzlicher sekundärer Ionenstrahlparameter, und

dabei speziell der Winkelverteilung der Ionen im Breitstrahl. Weiterhin wurde der

Zusammenhang zwischen verschiedenen Prozessparametern und der Größe sowie dem

Ordnungsverhalten untersucht. Dazu wurde u. a. das Skalierungsverhalten

unterschiedlicher Rauhigkeitskenngrößen mit den oben genannten Parameter bestimmt.

Bei Einstellung geeigneter Prozessparameter können die entstehenden Strukturen einen

sehr hohen Ordnungsgrad aufweisen. Bei Verwendung geeigneter Breitstrahlionenquellen

bietet das hier untersuchte Verfahren einen alternativen und kosteneffizienten Ansatz zur

Realisierung großflächig nanostrukturierter Oberflächen für unterschiedlichste

Anwendungen.

Zur Charakterisierung der Oberflächentopographie und der oberflächennahen Bereiche

wurden die Rasterkraftmikroskopie (AFM), die Rasterelektronenmikroskopie (REM),

Transmissions-Elektronenmikroskopie (TEM) sowie die Röntgen-Kleinwinkelstreuung

(GISAXS) und Röntgenbeugung unter streifendem Einfall (GID) eingesetzt.

Table of Contents

1 Introduction 3

2 Basics of Ion Beam Sputtering 7

2.1 Ion-Target Interaction.................................................................................... 7

2.2 Ion Range and Energy Distribution............................................................... 9

2.3 Sigmund's Sputtering Theory ........................................................................12

3 Continuum Theory of Pattern Formation 15

3.1 Linear Continuum Model ..............................................................................16

3.2 Nonlinearities in the Continuum Model ........................................................22

3.3 Damped Kuramoto-Sivashinsky Equation ....................................................23

4 Experimental Setup and Analysis Methods 25

4.1 Ion Beam equipment......................................................................................25

4.1.1 Design of the Ion Beam Equipment ........................................................25

4.1.2 Characterization of the Broad Beam Ion Source .....................................26

4.2 Analysis Methods ..........................................................................................31

4.2.1 Scanning Force Microscopy (AFM)........................................................31

4.2.2 X-ray Scattering Techniques ...................................................................35

4.2.2.1 Grazing Incidence Small Angle X-Ray Scattering (GISAXS).......37

4.2.2.2 Grazing Incidence Diffraction (GID) .............................................38

5 General Properties of the Surface Topography on Si and Ge 41

5.1 Overview of Emerging Topographies ...........................................................41

5.2 Influence of Ion Species ................................................................................45

6 Ripple and Dot Patterns on Si and Ge Surfaces 49

1

Table of Contents

6.1 Influence of Ion Energy................................................................................. 50

6.2 Ion Fluence and Flux..................................................................................... 61

6.3 Geometrical Shape ........................................................................................ 68

6.4 GISAXS and GID.......................................................................................... 72

6.4.1 Ge ............................................................................................................ 73

6.4.2 Si.............................................................................................................. 80

7 Pattern Transitions on Si and Ge Surfaces 87

7.1 Role of Ion Incidence Angle ......................................................................... 87

7.1.1 Influence of Ion Incidence Angle on Pattern Transition on Si................ 88

7.1.2 Influence of Ion Incidence Angle on Pattern Transition on Ge .............. 90

7.1.3 Discussion ............................................................................................... 92

7.2 Role of Secondary Ion Beam Parameters on the Surface Topography ......... 94

7.2.1 Secondary Ion Beam Parameters vs. Ion Incidence Angle ..................... 95

7.2.2 Secondary Ion Beam Parameters vs. Ion Energy .................................... 98

7.2.3 Summary ................................................................................................. 98

8 Comparison of Experimental Results with Theory 101

8.1 Bradley-Harper Model and the Nonlinear Extension.................................... 101

8.2 Surface Relaxation Mechanisms ................................................................... 103

8.3 Other Models................................................................................................. 105

9 Conclusions 109

Appendices 111

A1 Details of the Continuum Equation............................................................... 111

A2 The model for GISAXS and GID Simulations.............................................. 113

List of Acronyms 115

Bibliography 116

2

Chapter 1

Introduction

The fabrication of regular nanostructures on the nanometer length scale builds the basis

for many technological applications in variety of fields. These applications range from

optics to optoelectronics, to biological optics, to templates for the deposition of functional

thin films, and to heteroepitaxial growth of quantum dots or wires [1-3]. Further

applications are in the field of data storage industry, for creating high density magnetic

media [4,5]. In general there are two approaches for the fabrication of nanostructures. One

is top-down technique that involves lithographic patterning using optical sources with a

wavelength much smaller than the visible light. This technique is time consuming and cost-

intensive. In contrary to this technique is the bottom-up approach. This technique relies on

self-assembly or self-organization processes. There are various methods like

semiconductor heteroepitaxy [6] and block copolymer lithography [7,8]. Another method

for the generation of self-organized nanostructures is the low-energy ion beam erosion of

solid surfaces. This erosion process usually known as sputtering is a widespread technique

used in many surface processing applications. It is the main tool applied in depth profiling,

surface analysis, sputter cleaning and deposition. Ion beam sputtering is also used to

modify the surface of the solid by producing different topographies. For particular

sputtering conditions, due to self-organization processes, these topographies can evolve in

well ordered nanostructures on the surface like ripples or dots. Nanostructure formation is

observed on different materials such as metals [9-16], crystalline and amorphous

semiconductors [17-32], and other materials [33,34]. During the last years, it has been

reported about the formation of dot nanostructures on III/V (InP, GaSb, InAS, InSb)

semiconductors under normal ion incidence or oblique ion incidence with sample rotation

[27,28,35]. The evolving structures revealed particular domains with hexagonal ordering.

These investigations paved the way for further intensive studies in this field, by also

including other materials for nanostructuring.

The main advantage of ion erosion method is the possibility to produce large-area

nanostructured surfaces in a one-step process. Another advantage is the easy control of

different process parameters. However, the main disadvantage is the long range lateral

ordering of nanostructures and the less control of their shape. The basics behind the ion

beam erosion method is the interaction of the incoming ions with target atoms. During this

interaction, ions transfer energy and momentum to target atoms, eventually leading to

sputtering of the surface. The process of nanostructure formation itself is a complex

interplay between sputtering that roughness the surface and different relaxation

mechanisms, that act to smooth the surface. Indeed, this interplay depends on different

sputtering parameters. Therefore, from the above discussion it is important to study the

3

Chapter 1: Introduction

influence of different process parameters on the evolution of the surface topography. This,

not only to identify the dominant mechanisms, but also to find the process parameters that

can influence evolution, size, shape, and lateral ordering of nanostructures.

This will be the task of the work presented here. Namely, to study the evolution of the

surface topography on Si and Ge surfaces and the possibility to form nanostructures with

large scale ordering, in particular the formation of ripple and dot patterns.

During studies on III/V semiconductors, it came out that it is difficult to understand the

process of pattern formation and the influence of different sputtering parameters. One

reason was that these systems were made of two components, leading to preferential

sputtering, and the enrichment of the dot nanostructures with one component, for example

with Indium or Gallium. Therefore the idea was to use simpler one component systems for

the process of pattern formation, like Si and Ge. Further, to verify if the formation of dot

nanostructures is characteristic only of III/V semiconductors, or it can be applied also on

other materials. Another reason for choosing these two systems is their importance for

applications in different fields of technology. Last but not least, the lack of a systematic

study on the evolution of the surface topography during low-energy ion beam erosion at

room temperature.

For Si, according to earlier reports on ripple formation under noble gas ion beam

erosion, two cases can be distinguished: I) The formation of ripple patterns at relatively

high ion energies (typically above 20 keV) at room temperature or below. Under these

conditions, ripples form at ion incidence angles ranging from 35 deg and 65 deg with

respect to the surface normal, with ripple wavelength above 300 nm [36-38]. Upon ion

bombardment, the target surface becomes amorphous. II) Ripple patterns are also reported

at lower ion energies (e. g., at 750 eV) but at temperatures above 400 °C [26]. In the later

case, ripples form at ion incidence angles near 67° with wavelength larger than 200 nm.

Under these erosion conditions the target surface remains crystalline. In general, it can be

stated that, independent of ion energy, ripple patterns are observed at ion incidence angles

from 40° up to 70° and with ripple wavelength > 100 nm. Dot patterns have been observed

for Si at normal ion incidence for an ion energy of 1200 eV [30], but with a low degree of

ordering.

Concerning Ge, only few reports about pattern formation during low-energy ion beam

erosion exist. Up to now ripple patterns are observed for 1000 eV Xe+ ion beam sputtering

at high temperatures (~ 300 °C) under an ion incidence angle of 55 deg [21]. The surface

of the forming ripples remains crystalline after ion bombardment with a ripple wavelength

of 200 nm.

In this work, a detailed study of the surface topography evolution for Si and Ge during

noble gas ion beam erosion, for low ion energies between 500 eV and 2000 eV will be

presented. Chapter 2 contains a short introduction of the ion beam sputtering theory. In

Chapter 3, the theory of ripple formation by presenting different relaxation mechanisms

will be given. The description of the ion beam setup used for the experiments will be given

4

in Chapter 4. In this chapter a new parameter for controlling the evolution of the surface

topography will be introduced, by discussing its influence on ion beam properties. Atomic

force microscopy and small angle X-ray scattering techniques used to characterize the

surface topography will be presented in Chapter 4.2. Chapter 5 will deal in general, with

possible topographies evolving on Si and Ge surfaces by discussing the role of ion

incidence angle and the ion mass. The influence of ion energy, erosion time and ion flux on

the size and ordering of ripple and dot nanostructures will be discussed in Chapter 6. Also

the geometrical shape of nanostructures will be addressed in this chapter. Results will be

discussed by using both characterizing methods. In Chapter 7 completely new phenomena

not observed up to now, will be addressed. Namely the transition from dots to ripples and

again to dots. During these transitions the evolving dots show an almost perfect array of

dots covering the whole sample area. In this context a new parameter for controlling the

large scale ordering of dot nanostructures will be presented. The last chapter is devoted to

the discussion of the current theory of pattern formation and its consistency with the

experimental results.

5

Chapter 2

Basics of Ion Beam Sputtering

The bombardment of solid targets with energetic particles (ions) gives rise to different

processes. For example the backscattering of incident ions, implantation of ions in to the

target, and emission of electrons and photons. Additionally, due to collision processes, an

ion penetrating the target surface will slow down by transferring its kinetic energy and

momentum to the target atoms. Depending on the transferred energy this may lead to the

displacement of atoms (creating vacancies and interstitials) causing lattice defects. If these

atoms (primary knock-on atoms) receive enough kinetic energy they will induce additional

collisions with other target atoms and hence additional atomic displacements. This

situation is referred to as a collision cascade [39,40]. If a small number of atoms is set in

motion and for an isotropic distribution of collision density one speaks of a linear collision

cascade. Such a cascade can be described by binary collisions between moving ions and

stationary atoms. On the other hand due to momentum reversal, target atoms may travel

towards the surface. If these atoms posses enough kinetic energy they can overcome the

surface binding energy barrier and will be ejected away from the surface. Under

continuous bombardment of the surface this will lead to a material erosion. A process

known as sputtering. Furthermore, the increasing number of ions will induce additional

defects in the crystalline structure, and for a high defect density this may lead to a surface

amorphisation.

For the kinetic energy loss of the incoming ion, elastic (nuclear collisions) and inelastic

processes (electronic excitation) must be considered. However, for the low-energy range

(up to 2000 eV ion energy) the energy loss of ions happens mainly through nuclear

collision processes. This nuclear collision processes determine the energy deposition and

the range of ions in the target. The amount of energy deposited by an ion and the ion range

depend on the material properties (density structure, atomic mass etc.), and the ion mass

and energy. These two sets of parameters describe completely the collision cascade

processes and are the basis for the continuum theory of pattern formation that will be

presented in Chapter 3.

2.1 Ion-Target Interactions

Ions penetrating the surface undergo different collision processes with target atoms.

During this process they transfer part of their kinetic energy to target atoms [39]. If only

the nuclear collision processes are considered, then the differential energy loss of an ion

per unit length dx is given by

7

Chapter 2: Basics of Ion Beam Sputtering

8

)(ENSdx

dEn−=

(2.1)

where N is the atomic density in the solid, and Sn(E) is the nuclear stopping cross section

(energy loss rate), E is the initial energy of an incoming ion.

The nuclear stopping cross section gives the average energy dissipated during the

collision processes. The expression for Sn(E) depends on the form of the screening

(potential) function used to describe the interaction between the ions and atoms. For low

ion energies, where the screening of the coulomb interaction is essential, the Sn(E)

according to Sigmund is given by [39,41,42]:

m

ECdTTETCTETdE

mmm

T

mmm

T

n −===

−−−−−∫∫ 1

),()(211

0

11

0

maxmax γσ (2.2) S

with

m

s

m

smm a

eZZ

M

Ma

22

21

2

12 2

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= λπ

C

ere dσ is the interaction cross section, T the energy transferred from an ion with

(2.3)

( )

.4

2

21

21

MM

MM

+=γ

H

.))((

)(10462.8)(

23.02

23.0121

21115

ZZMM

sZZMES n

n ++××= − ε

)19593.001321.0(

)1383.11ln(5.5.021226.0 εεε

0)(

εε++

+=sn

ET γ=max being the maximum energy transmitted by an elastic collision (head on

. The parameter m characterizes the power law potential used to describe the

Coulomb interaction between atoms, and

collision)

oss section and the

en

the energy loss and cross sections is the

Zie

or ≤ 30 that includes the case for low ion energy:

(2.5)

m is a dimensionless function of m that can take

values from 1 = 0.5 up to 0 ≈ 24, and as is the screening length [39]. M1, Z1 and M2, Z2 are

the mass and atomic number of the ion and target atoms, respectively.

To simplify calculations the reduced notations for the nuclear cr

ergy are introduced. In this way the problem of different ion-target combinations is

reduced into a two body collision process [43].

A rather successful approach for calculating

gler, Biersack and Littmark (ZBL) approximation. ZBL proposed a universal screening

function for the interaction potential by presenting numerical solutions for Sn(E) and sn( )

[44]. The analytical expressions for Sn(E) and sn( ) used for the fitting procedure are

(2.4)

F

2.2: Ion Range and Energy Distribution

9

.))((

)(03253.023.0

223.0

12121

2

ZZMMZZ

MeVE

++=ε

.20.08for 2/1

2.0for 3/1

≤≤=≤=

εε

m

m

(2.7)

The above model for the energy loss is also the basis for the Monte Carlo simulations

SRIM 2003) that will be used

and the reduced energy is given through

g cross section independent of the ion-target

ombination. The is the dimensionless reduced energy parameter, and it describes how

arameter m presented above depends on the value of and

later for some ion-target combinations [44]. In Fig. 2.1 the

s f

e to elastic and inelastic collision processes an ion penetrating the target will loose its

nergy until it comes at rest after a certain range. The traveling distance of the ion in the

target depends on the mass ratio of the colliding particles and on the ion energy. The range

Figure 2.1: Nuclear stopping cross section of Ne+, Ar+, Kr+ and Xe+ ions in Si and Ge targets, calculated

according to Eq. (2.4).

(2.6)

Here sn( ) is the reduced nuclear stoppin

c

energetic a collision is. The p

according to Winterbon et al.

(

stopping cross sections Sn(E) for Si and Ge calculated for an ion energy Eion = 100 eV –

000 eV are plotted. The plot ow that heavier ions loose more 2 or different ion species sh

energy per collision compared to lighter ions (see Table 2.1), i. e. they undergo fewer

collisions with target atoms until they come at rest. This means the mean penetration path

(that will be discussed in the next section) for heavier ions is shorter compared to lighter

ions.

2.2 Ion Range and Energy Distribution

Du

e

15

20

0 500 1000 1500 2000 25000

5

10

Kr+

Xe+

Ge

m]15

20

Ar+

Ne+

Sn(E

) [e

Vnm

2 /ato

ion energy Eion

[eV]

0 500 1000 1500 2000 25000

5

10

Xe+

Kr+

Ar+

Ne+

Sn(E

) [e

Vnm

2 /ato

ion energy Eion

[eV]

Si

m]


.2

1

)(

1

)(

1)(

21

0

0

m

mm

E

nE n NC

E

m

m

ES

dE

NES

dE

NE

ion

ion

−−≅=−= ∫∫ γ

Dn

R

dxxFdxxENSdE )())(( ==

Table 2.1: The energy loss per unit length in Si and Ge calculated using Eq. (2.1) for different ion species for

Eion = 2000 eV.

energy loss dE/dx (eV/nm)

Ne+ Ar+ Kr+ Xe+

Si 211 389 577 631

Ge 195 420 762 942

of an ion can be calculated by integrating the stopping cross section Sn(E) using Eq. (2.2)

[45]

educed length ρ, it follows:

(2.9)

with a0 = 0.0529 nm

In the experiments usually the projected range R accessible.

distance between the hitting point of the ion on the surface and the point where this ion

comes at rest along the direction of incidence and Rp < R. For amorphous and

polycrystalline targets and low ion energies Schiøtt [46] introduced a formula for the

rojected range that depends on the ion-target combination

ion penetration depths (for ions of the same type) one

In this case a broad statistical distribution of ion ranges

nt of energy deposited by an ion in a

primary collision over a range dx, for an elastic scattering, is given by

(2.11)

tion function. Sigmund in the context of the

lin

(2.8)

By introducing the r

221

1223.

223.

1

0

)(

8854.04)(

MM

MM

ZZ

aNR

+⎟⎟⎠

⎞⎜⎜⎝

⎛+

= περ2

being the Bohr radius.

p is Rp is defined as the

p

(2.10)

.~3/2

23/2

12p E

ZZMR ⎥

⎤⎢⎡

⎟⎟⎞

⎜⎜⎛ +

2

21

m

ZZ ⎦⎣ ⎠⎝

Due to the stochastic nature of

considers the range of many ions.

and ion range straggling is obtained.

Winterbon et al. [47] showed that the amou

with FD(x) being the energy depth distribu

ear collision cascade theory [42] derived the expression for FD(x). By introducing a set

of transport equations and using the Edgeworth expansion, it could be shown that the

average energy deposited at a point r(x,y,z) in the target by an ion traveling along the z axis

10

2.2: Ion Range and Energy Distribution

11

⎟⎟⎞

⎜⎜⎝

+−−=

2

22

222/3 22exp

)2()(

βααβπyx

FD r (2.12)

with (E) being the total energy deposited. Expression (2.12) has a Gaussian form and is

va

.2). The parameters a, α and depend on the ion

en

ion function depend

on the stopping cross section function. This means the distribution of the deposited energy

can be calculated by studying the energy loss process using, fo

.5) and Eq. (2.6). Usually simulation programs for calculating the collision processes are

lision between the ion and target atoms as well as the collision between recoil

toms with other targ llowed until all the

cles come at rest. In this work the SRIM 2003 simu

sed to calculate the ion range and the distribution of the deposited energy in the target.

Figure 2.2: Schematic drawing of the distribution of the deposited energy of an ion in the target. Also given

are the parameters characterizing the distribution.

⎛ +− 20 )()(ν ahzE

is given by

⎠

lid for amorphous targets. The parameter a is the average depth of the deposited energy,

α and are the width of the distribution (straggling) parallel and perpendicular to the ion

beam projection, respectively (Fig. 2

ergy and on the ion-atom mass ratio, i. e. on the kinematics of the collision process. As

shown from Eq. (2.8) and Eq. (2.12) the range and the mean distribut

r example Eq. (2.4), Eq.

(2

applied. A successful software code with a very broad field of applications is the Monte

Carlo based SRIM 2003 (Stopping and Range of Ions in Matter) simulation program

developed by Ziegler et al. [44]. It is based on two body collision processes in amorphous

targets (binary collision approximation BCA). Through a detailed calculation, the history

of every col

a et atoms can be followed. These processes are fo

participating parti lation program is

u

If the energy transferred to the target atom during the collision process is higher than the

displacement energy (~ 15 eV for Si and Ge, taken from Ref. [44]) the atom will live its

lattice site creating a vacancy. If the energy of this recoil atom is smaller than the

displacement energy it will stay in the lattice, by releasing the rest of the energy as

phonons and remaining as an interstitial atom. If a moving atom hits another atom

transferring its energy by knocking it out of lattice site, and taking its place in the lattice,

one speaks of a replacement collision. In general it is not possible to deduce FD(x) directly

a

α

h

x

Ion beamz

a

α

h

x

Ion beamz


.1

)(),(),(211

m

ECNENSEFEY

mmm

InIionDion −===

−−γαΛαΛαΛα

v

vD N

ExnxF

)()()(ν

=

m SRIM simulations, but can be calculated from the number of displaced (vacancies

and replacements) atoms. According to Bolse [48]

(2.13)

with n

fro

In the low-energy regime, the collision processes are confined at the near surface

region. If the amount of ions per area and time (ion flux) hitting the target is increased, also

the number of defects will increase up to a critical point that the upper surface layer

becomes amorphous. The formation of this layer depends also on the target material and

temperature, and on the ion mass and energy. However, the dominant influence on

amorphization, at room temperature, comes from the ion fluence (ions per area). Detailed

studies about the surface damage accumulation of Ge and Si materials, at ion energies up

to 3000 eV, are performed by different groups [40,49-52]. By bombarding the Ge surface

with 3000 eV Ar+ ions Kido et al. [50] showed that at a fluence of ~ 1 × 1014 ions/cm2 an

amorphous layer is formed. Similar results were reported by Bock et al. [51] for studies on

Si and Ge surfaces using Ar+ ions (ion energy from 100 eV up to 3000 eV). Both these

showed that the amorphization and

aturation values for Si and Ge are very close to each other. The lowest ion fluence used in

urface amorphization on all samples is expected. This correlates with results presented in

ing the sample surface is observed.

v(x) being the vacancy density and Nv the total number of vacancies, and (E) is

defined in Eq. (2.12).

studies showed that the layer thickness increases with ion fluence and it saturates above ~ 15 21 × 10 ions/cm . Further increases on the layer thickness, for a given temperature, are

expected with increasing ion energy. They also

s

this work is 1.87 × 1016 ions/cm2 well above the amorphization threshold. For this reason a

s

Section 6.3 using HRTEM (high resolution transmission electron microscopy) where an

amorphous layer cover

2.3 Sigmund's Sputtering Theory

If an atom moving toward the target surface gains enough energy to overcome the

surface binding energy it will be ejected from the target. This process is characterized by

the sputter yield, Y, and gives the mean number of emitted atoms per incident ion. Most

contribution to the sputter yield comes from the recoil atoms traveling in backward

direction. According to Sigmund [39,41,42], the sputtering yield depends on the target

material, on the ion beam parameters and on the experimental (geometrical) conditions,

and is is defined as (by making use of Eq. (2.11))

(2.14)

The sputter yield has a linear dependence from the distribution of the deposited energy,

12

2.3: Sigmund's Sputtering Theory

13

i. e. the number of displaced atoms. FD(E,αion) corresponds to the depth distribution

function FD(x) and can be determined from Eq. (2.12). In Eq. (2.14) αI (for low ion

energies) is a dimensionless function of the mass ratio, and of the ion beam incidence angle

αion. Λ is the material dependent parameter given by

.)(

042.0)0,(sb

nI

E

ESEY

α=

bionion EYEY −= ))(cos0,(),( αα (2.17)

(2.15)

Esb being the surface binding energy.

ield is a function of the cosine of αion

wi

ork the sputter yield value at normal

incidence will be applied. In order to be compatible with experimental studies, for the rest

of

with 2/)( 2aC πλ= from Eq. (2.3) and

sbENC02

1

4

3

πΛ =

00 BM

The final relation of the sputter yield given by Sigmund [41], for normal ion incidence,

has the form

(2.16)

Expression (2.16) is deduced for low ion energies, near the sputtering threshold (m = 0).

However, as discussed by Sigmund in the same work, with a low uncertainty Eq. (2.16)

can be well applied also at higher ion energies where m ≥ 1/3. For oblique ion incidence

the sputter y

th the exponent b being a function of the mass ratio. However, for M2/M1 ≤ 3, b ≈ 5/3 is

independent of the mass ratio [41]. Equation (2.17) is valid for not too oblique incidence

angles (between 50 deg and 60 deg). With further increase of the incidence angle the

sputter yield will decrease due to the increased amount of reflected ions from the target

surface. For all calculations in the context of this w

the work the energy of incoming ions will be denoted by Eion.

15

Chapter 3

Continuum Theory of Pattern Formation

For describing the formation and evolution of surfaces under ion beam bombardment,

different models are proposed. These models mainly can be divided into continuum models

and microscopic models. In microscopic models, the atomic and crystalline structure of the

evolving topography on the surface is taken in consideration [53-56]. The microscopic

models are based on Monte Carlo and Molecular dynamic simulations. In contrary, in the

continuum models the surface topography is described by a continuous function, without

taking in consideration the atomic and crystalline structure of the surface. Therefore these

models are valid for amorphous materials. For the time evolution of the surface topography

at a mesoscopic scale, differential partial equations are used [57-61]. These models were

originally developed to describe rough interfaces and fractal topographies, and they posses

some specific scaling properties in the spatial and temporal evolution. Furthermore, the

continuum models have prevailed over microscopic models, for describing the evolution of

periodicities on the surface due to ion beam sputtering. The continuum models provide

quantitative predictions about the temporal evolution of the surface topography, and about

the scaling properties of the evolving structures.

The basis of these continuum equations, is Sigmund's theory of sputtering of amoprhous

targets, presented in the previous Chapter. It was shown that an ion hitting the target will

transfer it’s energy to the target atoms. Due to this energy transfer a removal of atoms from

the surface takes place. This material removal can lead to modifications on the surface

topography, usually producing rough surfaces. However, due to self-organization processes

this surface erosion process sometimes can produce well ordered nanostructures on the

surface [9,12,17,21,26-28,30-32,62-64]. The distribution of the deposited energy equation

(2.12) is given for one ion. For a flux of incoming ions that penetrate the sample

simultaneously at different points one has to integrate Eq. (2.12) over all individual events.

The erosion rate v(A) at a given point A, depends from the energy deposition of all ions in

a region around A, with a width comparable to a. The total erosion rate is given by

∫=A

D drrFrAv )()()( ΦΛ

(3.1)

with Λ given by Eq. (2.15), and Φ(r) is the ion flux J corrected for the local curvature

variations on the surface [42]. The integral is performed over the region of all points that

contribute to the energy deposited at A.

In absence of a perfectly smooth surface the distribution of the deposited energy

depends on the local spatial shape of the surface. This will result in local variations of the

sputter yield and the erosion velocity.

Chapter 3: Continuum Theory of Pattern Formation

The evolution of the surface topography during the sputtering process is a result of

complex processes taking place on the surface and near surface region. In the continuum

models usually there are two competing mechanisms: i) curvature dependent sputtering

that leads to a rough surface with time, and ii) relaxation processes acting to smooth the

surface. These relaxation processes can be of different origin like thermally activated

surface diffusion, viscous flow, or erosion related smoothing mechanisms. There are

additional processes that can influence the topography evolution like re-deposition of the

material and the re-emission of particles.

It is the competition between roughening and the smoothing mechanisms, that can result

in laterally ordered structures on the surface. This is also the basis of the continuum models

that will be presented in the next sections, together with their main properties. In general,

in the continuum model two cases can be distinguished. The evolution of the surface

topography at oblique ion incidence without sample rotation, whereupon ripple structures

evolve on the surface. In this case, there is an anisotropy present, given by the direction of

the ion incidence angle. This situation is described by the anisotropic continuum equation.

Second, the topography evolution at normal ion incidence or oblique ion incidence with

sample rotation. Due to rotational symmetry structures having isotropic distribution, like

dots, form on the surface. Hence, the isotropic version of the continuum equation is used.

3.1 Linear Continuum Model

Based on Sigmund theory of sputtering of amorphous targets Bradley and Harper (BH)

developed a model to explain the formation of ripple structures on the surface [61,65].

They showed that the variation of the sputter yield with the local surface curvature induces

a roughness on the surface, that leads to ripple structures. This surface roughness is caused

A

a) trough

C

B

b) crest

C

ion beamion beamion beamion beam

Figure 3.1: Schematic drawing of different erosion rates during ion beam sputtering. The surface at point A

(trough) is eroded faster than in B (crest). This because the average energy deposited at point A by ions

hitting the surface at point C is greater than the energy deposited at point B (the thick solid line has the same

length). The doted arrows have the same length and indicate that the ion hitting the surface has the same

distance from point A, respectively B.

16

3.1: Linear Continuum Model

17

by the different erosion rates in troughs (Fig. 31.(a)) compared with crests (Fig. 3.1(b)). By

combining the curvature dependent sputtering, with surface smoothing due to thermally

activated surface diffusion, they developed a linear continuum equation for the evolution

of the surface topography:

(3.2) .4

4

4

4

2

2

2

2

2

2'00 ⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

−∂∂

+∂∂

+∂∂

+−=∂∂

y

h

x

hD

y

hS

x

hS

x

hvv

t

h thyx

Equation (3.2) describes the temporal evolution of the surface height h(x,y,t) for an

angle αion with respect to the normal of an initial flat surface. The coordinate system axis x

and y lie parallel and perpendicular to the projection of the ion beam on to the surface,

respectively. Eq. (3.2) is valid for small slope approximation, i. e. the radius of curvature is

much larger than the mean depth a (Fig. 2.2). The first term, on the right hand side of Eq.

(3.2), represents the angle dependent erosion velocity of a flat surface. The second term,

describes the lateral movement of structures on the surface. As argued by Makeev et al.

[66], these two terms do not affect the characteristics of structures (wavelength and

amplitude), therefore they can be omitted from the surface evolution equation. The third

term describes the curvature dependent erosion rate, and the final term describes the

surface relaxation due to material transport on the surface [67,68].

The BH coefficient S depends on the ion energy, ion incidence angle and the material

properties

(3.3) .YN

JaS ionyxionyx )()( ,0, αΓα=

Here J is the flux of incoming ions, and Y0(αion) is the angle dependent sputter yield of

an initial flat surface. The Γx(αion) and Γy(αion) coefficients account for the local variations

of the sputter yield, expressed as [61]

.cos2

1)(

cos3cos2

12

sin)(

1

22

2

1

2

211

2

1

2

1

ioniony

ionionionionx

B

ACB

a

B

A

B

AC

B

A

B

B

B

A

αβαΓ

ααααΓ

⎟⎟⎠ ⎞

⎜⎜⎝

⎛+−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎠

⎞⎜⎜⎝

⎛+−=

(3.4)

These coefficients depend on the ion incidence angle and on the parameters a, α and

characterizing the distribution of the deposited energy, and can be calculated using the

simulation code SRIM 2003 introduced in Section 2.2. The coefficients A, B1, B2, C are

given in Appendix A1. In Fig. 3.2, Γx(αion) and Γy(αion) as function of ion incidence angle,

for Si using Xe+ ions with 2000 eV ion energy are plotted. The plots show that Γx(αion) can

have both positive and negative values, while Γy(αion) has always negative values. For

symmetry reasons at αion = 0 deg, Γx = Γy in this case no ripple structures are expected on

the surface.


0 20 40 60 8-0.3

0.0

0.3

0

a = 2.85 nmα = 1.83 nmβ = 1.13 nm

Γx

Γy

Γ x, Γy

ion incidence angle αion

[deg]

Figure 3.2: Coefficients Γx(αion), Γy(αion) calculated for 2000 eV Xe+ ion beam erosion of Si, according to Eq.

(3.4). The parameters a, α and are deduced from SRIM simulations.

The coefficient Dth in Eq. (3.2), describes the thermally activated surface diffusion

[67,68] related with material transport on the surface, having the form

(3.5)

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

Tk

E

Tk

NΩDD

BB

sth ∆γexp

2

with Ds being the surface diffusion constant, is the surface free energy per unit area, Ω is

the atomic volume, ∆E the activation energy for surface diffusion, kB the Boltzmann

constant, and T the surface temperature.

As stated at the introduction of this Section, it is the simultaneous acting of the third and

fourth term in Eq. (3.2) that can lead to the formation of ripple structures on the surface.

A simpler way to explain Eq. (3.2) is by taking the Fourier transform of it [69]. By

defining h(qx,qy) as the Fourier transform of the surface height, and q ≡ (qx,qy) the wave

vector, Eq. (3.2) can be written as

(3.6) ( )[ ] ).,,(d

),,(d 4422 tqqh qqDqSqSt

tqqhyxyx

thyyxx

yx +−−−=

The solution of Eq. (3.6) is

(3.7) [ ]tqRqqhtqqh yxyx )(exp)0,,(),,( =

with h(qx,qy,0) being the initial amplitude spectrum of the Fourier component and the

growth factor

(3.8)

( ). qqDqSqSqqR yx

thyyxxyx

4422),( +−−−=

18


Equation (3.7), represents the time evolution of the amplitude of the Fourier

co

n < 45 deg Γx(αion) < Γy(αion) < 0, the coefficient

S

mponents, and it increases exponentially for positive R(q) values. In this case the surface

roughens. While, for negative values of R(q) the surface smoothens. The factor R(q) has a

maximum at q* = (max|Sx,y| / 2Dth)1/2 with |Smax| being the larger in absolute value of -Sx, or

-Sy, respectively. While in Eq. (3.8) the diffusion term is always positive, the sign of R(q)

will depend on the coefficient Sx,y given in Eq. (3.3), i. e. on the parameters Γx(αion) and

Γy(αion). From Eq. (3.7) and Eq. (3.8) the amplitude with the wavenumber q* will grow

faster than all others. This will result in a periodicity with the wave number q*, that will

dominate the surface topography. The alignment of the wave vector of the periodicities

depends on the values of Sx, and Sy.

According to Fig. 3.2 for αio

)()()/( 0 ionxionYNJax αΓα= . The wave vector qx = (|Sx| / 2Dth)1/2 is aligned along the x-

jection of the ion beam on to the surface.axis and is parallel to the pro 1 For αion > 45 deg

Γy(αion) < Γx(αion) and Γy(αion) < 0, )()()/( 0 ionyiony YNJaS αα Γ= , in this case qy =

(|Sy| / 2Dth)1/2 is aligned along the y-axis, and perpendicular to the ion beam projection.

From the above discussion, the characteristic wavelength of ripples can be written as

.max

22

22/1

,,⎟⎟

⎠

⎞

⎜⎜

⎝

⎛==

yx

th

yx S

D

qππλ

9)

In following the b or certain sputtering parameters will be analyz

Concerning the ion energy Eion by using Eq. (2.8) and Eq. (2.14) it follows that

0)

ing use of Eq. (3.3) th S ~ J, i. e. ~ (1 / J)1/2 is a decreasing

function of the ion flux.

iii) d Eq.

αion (at least for not to oblique incidence).

mechani iveness decreases. Makeev et al. [70],

introduced the ion-induced effective surface diffusion ESD as the main relaxation

me

(3.

ehavior of f ed.

i)

(3.1.~2/1E

λ 1

This means the wavelength of ripples decreases with increasing ion energy.

ii) Mak e coefficient

Taking into account that Dth is independent of αion and from Fig. 3.2 an

(2.17) the coefficients Γx(αion) and Γy(αion) and Y0(αion) are increasing functions of

αion, then decreases with

iv) In Eq. (3.9) does not depend on the ion fluence, i. e. no changes of the ripple

wavelength with ion fluence are expected.

While for high temperatures thermal diffusion can be regarded as dominating relaxation

sm, with decreasing temperature its effect

chanism at low temperatures. This mechanism does not imply a real mass transport

along the surface, but is generated by preferential erosion of the target during the ion beam

1 The wave vectors qx,y are deduced from Eq. (3.8) by differentiating with respect to q.

19


sputtering. By including the ESD term, and neglecting thermal diffusion, Eq. (3.2) can be

written in the form

(3.11)

,

82

23

⎟⎠⎞

⎜⎝⎛

=

αa

cFaD ESD

yy

The last th in Eq. (3.2). The

co , and can be fully determined from the para

distribution of the deposited ener

sym

3.12)

(3.13)

with

ree terms of Eq. (3.11) are equivalent to the relaxation term

efficients meters for the ESDxxD , ESD

xyD ESDyyD

gy, from the ion flux, and the ion incidence angle. For the

metric case where α = the coefficients in Eq. (3.11) are expressed as:

(

⎟⎟⎠

⎜⎜⎝

−≡ff

ion222

exp2 βαπαβ

; ions⎞⎛ caaJE

F24Λ αsin= ; ionsc αsincos =≡ and 2

2

2

2scf

βα+= .

22 aa

m of coefficients in Eq. (3.11) will be given in Appendix A1.2.

If ESD is the main relaxation mechanism then the ripple wavelength can be calculated

as follows

(3.14)

y making use of Eq. (2.8), Eq. (3.12) and Eq. (3.13) the scaling behavior of ESD as a

fun

i. e

The general for

B

ction of Eion is given by

(3.15)

. the wavelength is increasing with ion energy.

( ) ,12463

242

22

424

4

2

3

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛++⎟

⎠⎞

⎜⎝⎛

⎟⎞

⎜⎛

=s

cascs

a

a

FaDESD

xx αα

⎠⎝α

.4

4

22

4

4

4

2

2

2

2

y

hD

yx

hD

x

hD

y

hS

x

hS

t

h ESDyy

ESDxy

ESDxxyx ∂

∂−

∂∂∂

−∂∂

−∂∂

+∂∂

=∂∂

,2

4

2222

2

2

3

⎥⎥⎦

⎤

⎢⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

= sccsa

a

FaD ESD

xy αα

,22

2222 ⎟⎠⎞

⎜⎝⎛ −−= cs

acs

FaS x α

,2

2cFa

S y −=

.max

22

2/1

,

,, ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛=

yx

ESDyyxxESD

yxS

Dπλ

,~~ 2mion

ESD Eaλ

20


21

.)(

222

0,⎟⎟

⎠

⎞

⎜⎝

=⎟⎠

=ionyionxrionyx

s

Y

Nd

Sd

αΓαΓηαγππλ

A

),(max)(max⎜⎝

IVF

22/1

⎜⎛

⎟⎞

⎜⎛ dF

( ) ,qqFqSqSR yxbyyxxb +−−−= 22)(q

lso from Eq. (3.14), it follows that ESD is independent of the ion flux and ion fluence

use

ion incidence angle.

hat can contribute

duced viscous flow (IVF) [67,68]. The viscous flow term is introduced by Mullins [68]

IVF is related with material transport

alo

range of . The term contributing to

sm

7) q = [max|Sx,y| / (2 d Fs)] and for the ripple wavelength, by

taking d = a, it follows that

(3.18)

rom Eq. (3.18) it can be concluded that is independent from the ion flux and ion

flu

elength

d. The dependence of ESD from the ion incidence angle is given by the relation between

DESD and Sx,y, that depend on

Another relaxation mechanism t to surface smoothening is the ion-

in

and Orchard [71] using Navier-Stokes equations.

ng the surface and depends on the concentration of defects created within a cascade

[72]. Concerning IVF two cases can be distinguished. In the first case proposed by Chason

et al. the bulk viscous flow is extended to the

oothening is Fb q with the coefficient Fb = / b. Here is the surface energy and b is

the bulk viscosity coefficient. Umbach et al. [29], using the model of Orchard, discussed

the other case, when viscous flow is restricted to a surface layer of thickness d. This

thickness is comparable to the ion range in the solid a, and the amplitude of structures, but

much smaller than the wavelength of structures. For this case, in the growth rate equation

the smoothening term –Fs d3 q4 is added. The surface relaxation rate coefficient Fs = / s,

with s being the surface viscosity coefficient. Mayer et al. following the suggestions by

Volkert et al. proposed a more meaningful measure of viscosity by taking r = b,s J. r is

the flux-independent viscous relaxation per ion, and 1 / r ~ κionE . The exponent describes

how strong the relaxation rate depends on the ion energy. The growth rate factor in Eq.

(3.8) for the two cases has the form

(3.16)

(3.17)

Differentiation of Eq. (3.16) does not deliver a characteristic wave vector for the

ripples. While from Eq. (3.1 3 1/2

( ). qqdFqSqSR yxsyyxxs44322)( +−−−=q

F

ence. Due to increasing values of Y0(αion) and Γx(αion) and Γy(αion) with αion, the

wavelength will decrease with ion incidence angle. For the ion energy, by approximating

≈ 1 from Ref. [72] the wav

(3.19) .~ 3mionEλ


22

⎥⎦

⎢⎣

−−=22

)(cos)(sin)(cos)(sin32

ionionionionx ααα

ααα

λ

⎤⎡ 222

222cos ion aaF α

3.2

amplitude saturation with erosion time observed

experimentally (see Section 6.2), and for the stochastic nature of the sputtering process,

Cuerno et. al. [59,60 otropic noisy Kura -Sivashinsky

0)

This is valid for Sx, < 0, Sy < 0. For positive S values the scaling properties are described

The relaxation term D may be of thermal nature, ion-induced ESD, or viscous flow. The

las

etric

case α = it follows [66]

(3.21)

e

regime is dominating the surface topography up to a crossover time tc, and (3.20) takes the

s) of

Figure 3.3: Evolution of the surface topography after Park et al. [74] for x × y > 0. Ripple patterns in a)

and b) evolve in the linear regime. a) Sy < Sx < 0, b) Sx < Sy < 0. c) Long time behaviour when non-linear

terms dominate the process. The incident beam is oriented along the y axis.

Nonlinearities in the Continuum Model

The linear BH model predicts an exponential increase of the ripple amplitude in Eq.

(3.7). However, to account for

] proposed the anis moto equation

(3.2( ) ( ) ( ) ).,,(22

2222222 tyxhhDhhhShSh yxyy

xx

yyxxt ηλλ

+∂+∂−∂+∂+∂+∂=∂

using the Kardar-Parisi-Zhang equation [73].

t term in Eq. (3.20) represents the stochastic nature of ions arriving on the surface. The

third and fourth term account for the angle dependence of the erosion velocity. The

coefficients x and y (not to be confused with the wavelength) can be calculated using

sputter parameters and the energy distribution parameters a, α and . For the symm

From Eq. (3.21) it is evident that y is negative for all incidence angles, while x can

take both positive and negative values [66]. Due to the nonlinearity of Eq. (3.20) general

analytical solutions are not possible. Through numerical integration, Park et al. have

linear

form of (3.2). In this regime the amplitude (represented through the surface roughnes

.2

)(cos2

23

ααλ

shown that Eq. (3.20) can be divided in to parts (regimes). For short times th

aF iony −=

y

x a) b) c)

3.3: Damped Kuramoto-Sivashinsky Equation

23

rip

rocess, disappear (Fig. 3.3). With further sputtering, the surface roughness exhibits kinetic

3.3 Damped Kuramoto-Sivashinsky Equation

more,

the

on is 0)

ith an additional damping term of the form –χ h introduced by Chaté et al. [78]. Although

the physical m

Figure 3.4: Evolution of the surface topography after Park et al. [74] for x × y < 0, Sx < Sy < 0 and

different times. a) t = 104, b) t = 2 × 105 and c) t = 107.

ple structures increases exponentially. After the crossover time tc, the nonlinear terms

dominate the evolution of the surface, and the amplitude saturates. While the coefficients

x and y do not influence the wavelength of ripples, their sign plays an important role in

the evolution of the surface topography in the non-linear regime. Theoretical simulations

have shown that, for x × y > 0 the surface roughness saturates and the ripple structures,

formed at short sputter times, during which the linear regime is dominating the sputter

p

roughening [74,75]. Also for x × y < 0, the surface roughness saturates and the ripples

disappear. However for prolonged sputtering a new type of rotated ripples (with respect to

linear regime ripples) is observed, with a rotation angle 2/11 )/(tan xyc λλθ −= − or

2/11 )/(tan yxc λλθ −= − (Fig. 3.4).

For normal incidence the coefficients in Eq. (3.20) are isotropic with S ≡ Sx = Sy,

≡ x = y, D ≡ Dxx = Dyy. Numerical simulations by Kahng et al. showed that for > 0

dot structures evolve on the surface, while for < 0 holes evolve on the surface [75].

For off-normal ion incidence with sample rotation, due to rotational symmetry, Eq.

(3.20) also becomes isotropic and the coefficients are expressed as S = Sx + Sy, = x + y

[65,76]. As shown by Bradley [65] this is true for fast rotating substrates with angular

velocity much larger than the ripple amplitude growth rate ω >> DSav /2 , and for Sav < 0.

The main disadvantage of the KS equation is the failure to account for dot or ripple

stabilization for long sputter times observed experimentally (see Section 6.2). Further

model can not account for the hexagonal ordering of particular domains of dot

structures. Recently, through simulations, Facsko et al. [77] using the damped KS equation

for the sputtering process, showed hexagonal ordered dots evolving on the surface similar

to those in III/V semiconductors [27,28]. The damped KS equati based on Eq. (3.2

w

eaning of the term is not yet understood, this term has an important role in

y

x a) b) c)


the

xponential increase of the surface height due to the linear term [79]. Numerical

larger than a critical value χ , hexagonally

Eq. (3.22) show that the hexagonal ordering of patterns

maintained [79] ngth of structures

ith erosion time in agreement with experimental result

:

Corresponding Fourier images showing the characteristic spatial frequencies dominating the surface (see

ection 4.2.1).

surface evolution process. It suppresses the transition to kinetic roughening during the

temporal evolution of the surface in the nonlinear regime. For normal ion incidence the

damped KS equation is given by

(3.22)

By considering only the damping term, Eq. (3.22) it gives an exponential decrease of

the surface height, during the temporal evolution. This decrease, counteracts the

e

( ) ).,,(2

242 tyxhhDhShht ηλχ +∇+∇−∇+−=∂

simulations showed that depending on the value of χ also the surface topography varies

accordingly [77,80] (Fig. 3.5). For values of χ c

ordered patterns evolve on the surface. With decreasing χ, (χ < χc), the hexagonal ordering

decreases until for even lower χ values structures with no ordering are present on the

surface. Long time simulations of

is . These simulations also demonstrated that the wavele

remains constant w s in Section 6.2.

Figure 3.5: Surface topography calculated using the DKS equation (3.22) after [77]. a) Early time regime

for χ = 0.24, b) Late time regime for χ = 0.24. c) Structures with no apparent ordering for χ = 0.15. Inset

a) b) c)

S

24

Chapter 4

Experimental Setup and Analysis Methods

In this chapter a description of the ion beam equipment and the methods used to

characterize the evolution of the surface topography will be presented. Especially the setup

of the ion source employed for sputtering experiments and the characteristics of the

extracted beam, will be discussed in Section 4.1. In the second part atomic force

microscopy as the main method applied in this work to characterize the surface topography

will be presented. In this context, a summary of the statistical quantities for characterizing

the surface topography will be given. Further, the grazing incidence small angle X-ray

scattering methods used for ex-situ studies of structures will be shortly described.

4.1 Ion Beam Equipment

4.1.1 Design of the Ion Beam Equipment

The samples investigated in this work where all treated in a home built ion beam

equipment (ISA 150). A simplified overview of the equipment is given in Fig. 4.1. The

main parts are: a) pumping system; b) gas system for supplying sputter gases; c) the load

lock for sample handling; d) Faraday cup arrays; e) sample holder, and f) the ion source.

The base pressure in the chamber is about 2 × 10-6 mbar. Depending on the gas species,

the working pressure was varying between 5 × 10-5 mbar and 1 × 10-4 mbar. In this work

four different inert gases were used Ne+, Ar+, Kr+, and Xe+. The variations on the working

pressure were necessary in order to maintain the stable operation of the beam source.

However, it is observed that pressure variations (achieved by varying the amount of gas

supplied in the chamber) do not influence the evolving topography.

The distance between the aluminum sample holder and the ion source (acceleration

grid) amounts around 400 mm, and is smaller than the mean free path length of ions

amounting around 1 m, for the working pressure given above. Therefore the extracted ions

will reach the sample without collisions that could effect their kinetic energy and lead to a

broad beam. The sample holder offers the possibility of rotating around its axis with about

12 rotations per minute. Additionally, it can be tilted from 0 deg up to 90 deg with respect

to the axis of the ion beam source. Further, to avoid thermal effects on the sample the back

side of the sample holder is water cooled. However, variations of the temperature from

room up to 60 °C did not have any influence on the evolution of the surface topography on

Si and Ge (this has been performed by measuring the water temperature on the back side of

the sample holder).

25

Chapter 4: Experimental Setup and Analysis Methods

26

Fig

e

pro

he surface topography at least for hole structures (see Chapter 5). Due

ure 4.1: Schematic view of main parts of the ion beam equipment ISA 150. The distance between the ion

source and the sample holder is about 40 cm.

The Faraday cup array is used to determine the ion current density distribution. Fiv

bes are mounted, one in the middle and four in each edge covering a radius of ~

120 mm. A deviation of up to 15 % in ion current density value between the middle and

edge probes is present, and it depends on the ion source parameters. However, as it will be

shown later the ion current density has no influence on the topography evolution.

4.1.2 Characterization of the Broad Beam Ion Source

The ion source, is a home built broad beam source of Kaufman-type [81,82] with a two

grid ion optics system (Fig. 4.2). All inner parts of the ion source are made of purified

graphite.

The ion source is equipped with a hot filament (tungsten wire) that emits electrons, by

applying an appropriate current. The electrons are then accelerated toward the anode rings

lying under positive voltage called discharge voltage Udis (in this case Udis = 100 V). The

Udis voltage controls the acceleration of emitted electrons in the filament sheath. With

increasing Udis the energy of electrons will increase also, thus increasing the number of

double charged ions. The variation of Udis between 40 V and 100 V showed no influence

on the evolution of t

6.5e-3 mbar

2.0e-6 mbar 1.0e-2 mbar2.0e-6 mbar

Faraday cup array

sample holder

ionsource

vacuum pumping system

sample rotator

gas system

ample handlingload lock for s

6.5e-3 mbar

2.0e-6 mbar 1.0e-2 mbar2.0e-6 mbar

Faraday cup array

sample holder

ionsource

vacuum pumping system

sample rotator

gas system

ample handlingload lock for s

4.1: Ion Beam Equipment

Figure 4.2: Schematic drawing of the main components of the, Kaufman type, broad-beam ion source (ISQ

150) of the ion beam equipment ISA 150.

to collisions with gas atom tion takes place, i. e.

the plasma is created. T anode rings, determined

by filame anent

ionization efficiency is increased, before they reach

e vessel walls. The ion optical system is made of two multi-aperture grids having a

18

older.

s present in the discharge vessel an ioniza

here is a discharge current flowing to the

nt heating current. Additionally, the discharge vessel is equipped with perm

magnets that makes the electrons perform spiral trajectories, performing larger travel

lengths in the vessel. In this way, the

th

0 mm diameter. The multi-aperture plane parallel grids are made of holes (for the given

diameter around 3000 holes) with a cylindrical form covering the whole grid surface. In

order to have higher transparency holes are hexagonally arranged [83]. The grid optics,

consists of the screen grid and the acceleration grid that are used to extract the ions from

Figure 4.3: Potential diagram across the different parts of the ion source and outside, up to the sample

Permanent Magnet

Hot Filament

Anode

Discharge Vessel

Acceleration GridGas Supply

Screen Grid

Ub

Uacc

Udis

Permanent Magnet

Hot Filament

Anode

Discharge Vessel

Acceleration GridGas Supply

Screen Grid

Ub

Uacc

Udis

h

27


the plasma (see the potential distribution in Fig. 4.3). The characteristics of the grid system

are: a) hole diameter of 2.5 mm each; b) The grid opening is 180 mm; c) The screen grid

has a thickness of 1 mm, while the acceleration grid is 2 mm thick. d) The distance

between grids is 2 mm.

After the plasma is created the potential of the discharge anode is determined by the

voltage applied in the screen grid Uscr. It is the anode voltage (Udis + Uscr) that determines

the ion beam energy, thereafter called beam voltage Ub. By applying an appropriate

negative voltage at the acceleration grid Uacc ions will be extracted from the plasma and

accelerated toward the second grid.

The total extraction voltage is given by the absolute values of Ub and Uacc, Uextr = Ub –

Uacc [84]. Under experimental conditions the beam and accelerator grid can take values

that vary between 100 V ≤ Ub ≤ 2000 V and -10 V ≤ Uacc ≤ -1000 V.

The ion beam is also characterized by the total current Ib transported in the beam.

resulting in a direct grid current Iacc (see plot in

Figure 4.4: Beamlet plots for Uacc = -100 V, -400 V, and -900 V at corresponding experimental conditions.

-c): Ub = 500 V and a high plasma density np = 5 × 1010 cm-3; (d-f): Ub = 1000 V and medium plasma

Furthermore, in case of improper values of the grid voltages, part of the extracted ion beam

directly hits the accelerator grid

Fig. 4.4(a)). Because of the resulting fast grid destruction and beam pollution, such an

operation mode is usually avoided (refer to other plots in Fig. 4.4). Beside of the extracted

ions also neutrals can diffuse from the plasma chamber leading to a density of neutrals

within the grid system. In a charge-exchange collision between an extracted beamlet ion

and a neutral, a secondary ion is created which could be accelerated towards the

accelerator grid. This is the origin of the unavoidable accelerator grid current Iacc which

typically amounts a few percent of the beam current [34]. It is the difference between the

total beam current Ib and Iacc that gives the real beam current density at the sample position.

Between the ion source and the sample holder an electron emitting tungsten wire is

mounted to prevent the charging of the sample.

Before discussing some characteristics of the beam it is useful to give several

-900 V-900 V

-400 V-400 V

-100 V-100 V

500 V500 V

500 V500 V

500 V500 Va)

b)

c)

-900 V-900 V

-400 V-400 V

-100 V-100 V

1000 V1000 V

1000 V1000 V

1000 V1000 Vd)

e)

f)

Plasma sheathboundary

(a

density np = 2 × 1010 cm-3. The plots are calculated using the simulation code IGUN [83,85].

28

4.1: Ion Beam Equipment

definitions. The beam extracted from one hole is defined as a beamlet. The superposition

of all beamlets yields the broad-beam, therefore the broad-beam properties are mainly

defined by the beamlet properties. Due to the diverging ion trajectories the beam broadens

with the distance from the ion source. This is usually described by the beam divergence.

Th

am trajectories extracted from one hole for different

Ua

out that the beam

bro

Figure 4.5: Angular distribution obtained from one beamlet for different acceleration voltages for two

ifferent Ub values, deduced from Fig. 4.4.

e divergence angle, is defined as the half opening angle of the beamlet cone that

contains a certain amount of the overall current (for example 75 % or 95 %) [83,86-89].

Additionally, the angular distribution of ions leaving the hole should be considered. These

beam properties will be referred as secondary ion beam parameters.

In Fig. 4.4 are plotted the ion be

cc. The simulations are performed with the computer code IGUN [90] using the

geometrical dimensions of the grid system given above. The simulations are plotted for

two different plasma density values. This is performed to point

1

adening depends on the plasma density, that influences the plasma sheath boundary.

The ion trajectories plotted in Fig. 4.4(a-c), for Ub = 500 V, show that the beam broadens

with decreasing acceleration voltage. This is the case for high plasma density np =

5 × 1010 cm-3. For medium plasma density np = 2 × 1010 cm-3 the beamlets (Fig. 4.4(d-f))

plotted for Ub = 1000 V show a broadening of the beam with increasing Uacc. This means

with increasing Uacc the beamlet divergence, i. e. broad beam divergence increases. The

last extraction conditions are valid for the experimental studies presented in this work,

when varying the Uacc.

The angular distribution of ions in the beamlets for different accelerator voltages is

quantitatively presented in Fig. 4.5. The angular distribution for Ub = 500 V and Uacc = -

100 V is affected by the direct impingement of the beamlet on the accelerator grid. The

d

1 In fact the simulations yield the beam for a half hole diameter with the supposition that the beam is

symmetric to the other half.

0.0

0.5

1.00.0

0.5

1.0

0 5 10 15 20 25 300.0

0.5

1.0U

acc= -900V

inte

nsit

y [a

.u.]

angle [deg]

Uacc

= -400V

b acc

0.0

0.5

1.0

a) U = 500 V U = -100V

1.0

0.0

0.5

0 5 10 15 20 25 300.0

0.5

1.0U

acc= -900V

inte

nsit

y [a

.u.]

angle [deg]

Uacc

= -400V

b acc

b) U = 1000 V U = -100V

29


plots for Ub = 1000 V show that the beamlet with the highest angular distribution, i. e. with

the highest beam divergence, is obtained for Uacc = -900 V. In this case most of the ions

leave the hole with an angle between 4 deg and 6 deg. With decreasing Uacc this angle

range shifts toward smaller values. The superposition of these beamlet configurations to

the number of holes, making up the grid opening, defines the broad beam properties.

Additionally to Uacc also the Ub, i. e. the ion energy, influences the secondary ion beam

parameters [83]. For the particular case the increase of Ub leads to a decrease of the beam

divergence. However, the influence is not so pronounced as for Uacc [85].

Beside the plasma conditions and the extraction voltages, the geometrical parameters of

the two grid optical system also influence the beamlet divergence (see Fig. 4.2). For

example, with increasing distance between grids the beamlet divergence decreases. An

increase of the screen grid thickness or decrease of the hole diameter leads to a decrease of

the beamlet divergence. A more detailed description of the relations between the grid

parameters and the beam characterizing properties is given by Tartz et al. [83,91,92].

These beam properties are valid for the particular ion source and ion beam conditions. The

variation of one of the above parameters could lead to results different from those

presented here.

30

4.2: Analysis Methods

4.2 Analysis Methods

4.2.1. Atomic Force Microscopy

The investigation of the surface topography in the nanometer range, requires a

characterization method with a very high resolution by still yielding a good statistics.

Especially, for structures with a low aspect ratio (ratio height to length) and dimensions

below 50 nm, presented in this work, there are only few methods that can be applied. One

of

measurements with AFM: i) contact mode, ii) non-contact mode and iii)

TappingMode™ or dynamic mode. The last mode was developed as a method to achieve

high resolution, without inducing destructive frictional forces between the sample and the

tip. With this technique, the cantilever is oscillated near its resonant frequency with

constant amplitude as it is scanned over the sample surface. As the tip is brought close to

the sample surface its amplitude will reduce. A feedback positioning unit takes care that

the distance between the tip and the sample, i. e. the oscillation amplitude, remains

constant during scanning, without getting in contact with each other.

The measurements presented in this work, were all performed using Dimension 3000

with a Nanoscope IIIa controller, in TappingMode™ from Veeco Instruments [96], and

MFP-3D ,AFM, in dynamic mode from Asylum Research [95]. Compared to Nanoscope

IIIa controller that can record up to 512 points per line, the MFP-3D offers the possibility

to perform large area scans with high resolution up to 4096 points per line. The

measurements were performed in air, using silicon tips with nominal radius smaller than

10 nm, and sidewall angles < 18 deg [99].2 During the measurements, a special attention

was paid to the tip artifacts [100-102]. Sometimes the tip-sample interaction may lead to a

deterioration of the tip. If the tip radius is too large to access the structure inter-distance,

then the measured topography will be determined by the tip shape. Such a situation is

visualized in Fig. 4.6. Therefore, for most of the data presented in this work, several

measurements using different tips for every sample were performed. In this way the tip

artifacts are kept at minimum. Other important factors to be considered are the image size,

these methods is the Atomic Force Microscopy AFM [93,94]. The developments of last

years made the AFM to one of the mostly used methods for characterizing the surface

topography on different materials. Beginning from conductive to non-conductive materials

up to biological samples [95,96]. The main advantage of AFM is its sub-nanometer

resolution and the possibility to give a direct real space image of the surface. Today there

are hand-full of books that explain the working principle of scanning probe microscopy

[97,98]. With the AFM method, one scans the surface with very sharp tip mounted on a

piezo-scanner that can be set in motion by applying a voltage on it. Usually there are three

modes used for

2 Olympus cantilevers with tetrahedral tip for standard applications where used (Typ: OMCL-AC160TS).

Additionally, ultra sharp tips (Typ: OMCL-AC160BN) were used to measure some samples, for comparison.

But, no differences on the measured surface topography were observed.

31

Chapter 4: Experimental setup and analysis methods

10

0 50 100 150 200 250 300

0

5

heig

ht [

nm]

length [nm]

.)),((1

1

2∑=

−==N

i

hyxhN

wrms

ghts around an average height, and is given by

(4.1)

Here h(x,y) represents the surface height at a given point, and

Figure 4.6: Height profile of ripple structures, and the schematic drawing of the geometrical tip shape. If the

tip radius is larger than radius of the valley between ripples, then the tip artefacts are present in the AFM

image.

the number of points one image has, and the spacing between points [103,104]. If L is the

image size, N the number of points, and d the data point spacing then L = N d. Therefore,

in order to have an accurate estimation and a better statistics, it is important that

measurements with different size and high enough resolution are performed. For example,

for a measurement with a scan size 4 µm × 4 µm with 1024 × 1024 data points, gives a

point spacing of ~ 4 nm. For structures with a mean size of 40 nm it means around 10 data

points per structure.

The most important statistical quantity used to characterize the height fluctuations of the

surface is the rms-root mean square roughness. It describes the fluctuations of the surface

hei

h - the mean height of

the surface. For quantitative analysis of the surface roughness samples with scan size of

2 µm × 2 µm and 4 µm × 4 µm were used with 512 × 512 and 1024 × 1024 data points,

respectively. This means a spacing d < 4 nm. However, a comparison with measurements

having data point spacing d < 2 nm between points, showed no difference on the rms

roughness value. This indicates that the largest contribution to the rms value comes from

structures (ripples, dots) present on the surface.

The rms value alone can not fully characterize the surface because it gives information

only along the vertical direction [105,106]. However, sometimes it is very useful to know

the positional correlation between different points on the surface. Especially on structured

sur

ed to characterize the surface

faces quantities like the wavelength, homogeneity and lateral correlation of structures

are of great importance. This is best achieved by analyzing the height profile in the

reciprocal or Fourier space. The main statistical quantity us

32


topography in the reciprocal space is the Power Spectral Density (PSD) function.

Performing the discrete two dimensional Fast Fourier Transformation 2D-FFT, of the

height profile of AFM images, it is possible to deduce the dominating spatial frequencies

present on the surface and the amplitude of the roughness. The FFT for the discrete case is

given by

(4.2)

for a square image L × L with N and d equal in x and y directions, fx, and fy are the spatiel

frequency coordinates along the x-axis and y-axis, respectively.

Two representative examples for ripple and dot structures are given in Fig. 4.7. The

moving away from the center. Due to the preferred orientation of ripples

spots (rings), the better is the lateral

ordering. In fact the position of the first spot (ring) gives the mean s

structures. For the ripples, it is assumed that the separa on between

ripple size. Due to the wavelike f

averaged PSD(f), especially for structures

wi

∑∑= =

+−=N

x

N

y

yfxfNLi

yxyxeyxh

NffFFT

1 1

)(/2

2),(

1),(

π

FFT images give information about spatial frequencies (fx,fy) ranging from –128 µm-1 to

128 µm-1. The spatial frequency has a minimum value at the center of the image and it

increases by

(Fig. 4.7(a)), in the FFT image (Fig. 4.7(c)) spots are visible. The direction of spots gives

the direction of the wave vector of ripples.

The AFM image in Fig. 4.7(b), shows dot structures emerging on the surface. The

image reveals the short range ordering of dots building domains having hexagonal

ordering. However, these domains are randomly distributed in between them, therefore, a

ring is visible in the corresponding FFT spectra (Fig. 4.7(d)).

The position of the spot (ring) determines the characteristic spatial frequency of ripples

(dots), i. e. the wavelength of structures in the real space. From the width of the spot (ring)

information about the homogeneity, and spatial correlation of periodicities can be deduced.

Additional spots (rings), are multiples of the first one, and are related to the high lateral

ordering of structures. The higher the number of

eparation between the

ripples is equal to the ti

orm of ripples, the term ripple wavelength will be used to

describe their size. This will be done with the supposition, that the separation in between

ripples is equal to their size. For dots, the mean separation is equal to the mean lateral size

by supposing that the dots are close packed to each other.

However, from the FFT images is difficult to make quantitative estimation about these

quantities. For this reason, the area or two dimensional PSD(fx,fy) function of the surface

height is introduced, by taking the square of FFT [105,107,108]. A more practical way of

evaluating the data is by introducing the angular

th an isotropic distribution [106]. This is done by performing angular averaging over all

spatial frequencies with constant distance 222yx fff += . Summarizing it follows that,

(4.3)

∑∑

==

=−=ff N

nyx

f

N

nf

ffFFTN

PSDDN

fPSD0

2

0

)),((1

21

)(

33


34

4

There are different models for describing the lateral ordering of structures. Applying the

model of Zhao et al. [106] the system correlation length can be used as quantity to

describe the lateral ordering of ripples and dots. The gives the length scal which

Figure 4.7: Typical AFM images of ripple and dot structures on, a) Si and b) Ge surfaces. (c,d) The

corresponding FFT spectra. (e,f) Angular averaged PSD spectra.

where Nf is the number of points at constant distance f [107]. The range of f values depends

on L and N and is limited by 1/L < f < N/2L.

10-3

10-2

10-1

10-1

101

The unit of angular averaged PSD spectra is (length) . For the rest of the work the

notation PSD will be used, instead. It is obvious that in the case of ripples there is an

asymmetry in the distribution of the spatial frequencies. However, by performing angular

averaging of the FFT image, the dominating spatial frequencies (the spots) will contribute

mostly to the PSD spectra compared to the rest of the Fourier spectrum. The PSD spectra

are plotted in Fig. 4.7. The position of the first peak gives a quantitative information about

the wavelength of structures.

e up to

103

105

PS

D [

nm4 ]

spatial frequency f [nm-1]

λ

FFT

z

0 nm

500 nm

ζ ~ 1/FWHM

f =

-12

8µm

-1…

128

µm-1

10-3

10-2

10-1

10-1

101

103

105

PS

D [

nm4 ]


ζ ~ 1/FWHM

λ

z = 20 nmz = 7 nm

500 nm

a) b)

FFTc) d)

e) f)

103

105

10-3

10-2

10-1

10-1

101

PS

D

z = 20 nmz = 7 nm

[nm

4 ]


λ

FFT

z

0 nm

500 nm 500 nm

a) b)

ζ ~ 1/FWHM

f =

-12

8µm

-1…

128

µm-1

10-3

10-2

10-1

10-1

101

103

105

PS

D [

nm4 ]


ζ ~ 1/FWHM

λ

FFTc) d)

e) f)λ

z = 20 nmz = 7 nm

FFT

z

0 nm

z

0 nm

500 nm500 nm 500 nm500 nm

a) b)

FFTc) d)

-1f

= -

128

µm-1

…12

8µm

ζ ~ 1/FWHM

10-3

10-2

10-1

10-1

101

103

105

PS

D [

nm4 ]


ζ ~ 1/FWHM

λe) f)


spatial correlation is present i. e. the mean domain size. It is deduced from the FWHM of

the first order PSD peak, and is inverse proportional to the FWHM, ~ 1/ FWHM.

At the end it is worth to mention that from the PSD function, by integrating over the

spatial frequency range under consideration, the square of the rms surface roughness can

be deduced which is equivalent to Eq. (4.1).

4.2.2 X-Ray Scattering Techniques

The X-ray scattering measurements were performed at the European Synchrotron

Radiation Facility (ESRF) in Grenoble, France. The ESRF is a third generation

synchrotron facility with a storage ring circumference of 844.4 m, working at an energy of

6 GeV [109]. The experiments were carried out at the ID01 beam line. The ID01 is

equipped with devices, a wiggler and an undulator, that produce synchrotron radiation of a

high brilliance [110]. Additional optical devices are used for tuning, focusing and

alignment of the X-ray beam (Fig. 4.8). A detailed description of the ESRF facility, ID01

beam line, and the experimental setup is given at the ESRF home page [110].

The samples were mounted vertically on the sample holder, fixed on a 6 axes

diffractometer. To avoid air scattering of the beam the sample was covered with a Kapton

foil filled with Helium. The scattered intensity is detected using a linear position sensitive

detector (PSD) mounted at the end of the detector arm (Fig. 4.9). All the experiments

presented in this work were performed at an energy of 8 keV corresponding to a

wavelength of 1.55 Å.

Figure 4.8: Picture view of the optics used at the ID01 for aligning focusing and tuning of the X-ray beam

source [110].

undulatorundulatorundulatorundulator

35


Figure 4.9: a) The setup used for measurements showing the outcome of the X-ray and the PSD detector with

the detector arm; b) Sample holder with the Helium filled Kapton foil [110].

For sample investigation grazing incidence X-ray techniques are used. The idea behind

thi

xx--rayray

Sample holderSample holdera) b)

s geometry is to probe near surface regions, i. e. very suitable for the investigation of

surface structures. However, the rather widely distributed intensity in the reciprocal space

and the weak signal coming from the surface structures, requires very bright and

collimated beam. This can be achieved in third generation synchrotron radiation facilities

[111]. In grazing incidence techniques the X-ray beam impinges on the substrate under a

small angle, typically several tenths of degree, and is partly specularly and partly diffusely

reflected. The small impingement angle is chosen in order that the penetration of the X-ray

beam on the substrate is only few nanometer. This ensures an enhancement of the ratio of

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.510

-8

10-6

10-4

10-2

100

αc Ge

Si

nom

rali

zed

inte

nsit

y

αi [deg]

Figure 4.10: Reflectivity curves for Si and Ge. The critical angle αc = 0.22 deg for Si and αc = 0.25 deg for

Ge is deduced from the position at which the intensity has its maxium.

36


the scattered intensity from nanostructures compared to that of the bulk. Usually the

incidence and the scattering angle are chosen in such a way, that the condition for a total

reflection of the scattered intensity is fulfilled. The critical angle for total reflection αc =

π/2 – arcsin(n), depends on the refraction index n. Typically the αc is between 0.1 deg –

0.5 deg depending on the X-ray energy, and on the material used for studying. For the

experiments presented in this work the condition for total reflection is fulfilled for αc <

0.22 deg for Si, and αc < 0.25 deg for Ge. It is deduced from the reflectivity curves

(Fig. 4.10), by performing a scan for different incoming angles αi and scattering angles αf

of the beam, i.e. by varying the depth of the impingement of the X-ray beam on the

substrate. The position where the reflectivity curve has its maximum gives the total

reflection angle. With further increase of αi and αf the scattered intensity decreases rapidly.

Below, a short description of the grazing incidence methods and their geometries used

4.2

e distribution of nanostructures (isotropic or not), and the angular distribution of ripples.

Figure 4.11: Schematic presentation of the GISAXS geometry. a) The incident X-ray is along the ripples,

attering vector in the x-y plane are

presented.

for the sample investigation will be given.

.2.1 Grazing Incidence Small Angle X-Ray Scattering

Grazing incidence small angle X-ray scattering (GISAXS) is a technique used for

scattering experiments under grazing incidence and exit angles [111-116]. By probing the

scattered intensity close to the (000) reciprocal lattice point, GISAXS is not sensitive to the

crystalline structure of the material, but only on the index of refraction i. e. electron density

variations. In Fig. 4.11 the scattering geometry for the GISAXS is given. The incidence

and the scattering angle are chosen in such a way that the condition for a total reflection of

the scattered intensity is fulfilled, i. e. αi = αf = 0.2 deg. In the GISAXS geometry 2 is the

in plane scattering angle, and ω is the azimuthal angle. The rotation of ω, allows to study

th

PSD

αi

αf

ω

2θ

PSDPSD

αi

αf

ω

2θ x

yqII

qy

qx

2θ 2θki

kf

a)b)

and the scattered intensity is collected in the PSD detector set parallel to the sample surface. b) The wave

vectors of the incident and the scattered beam together with the sc

37


In this geometry the sample is mounted in such a way that the ripples are aligned along the

)2sin(cos θα fy kq =

X-ray beam.3 Usually the scattered intensity is plotted in the reciprocal space, and is

characterized by the momentum transfer q (scattering vector), between the incident and the

scattered X-ray beam with wave vectors ki and kf, respectively. From the geometrical

sketch in Fig. 4.11(b), the momentum vector components of the reciprocal space can be

expressed by the scattering experimental angles using the relations

(4.4)

(4.5)

where

)2coscos(cos θαα fix kq −=

λπ /2=== kfi kk .

4.2.2.2 Grazing Incidence Diffraction

In comparison to GISAXS, Grazing Incidence Diffraction (GID) is usually used to

study the crystalline properties of nanostructures [111,112,115,116]. A schematic drawing

rface normal until the Bragg

co

Figure 4.12: Schematic presentation of the GID geometry. a) The PSD is set vertically to the sample surface

to collect the scattered intensity for different αf, b) The wave vectors of the incident and scattered beam

projected in the x-y plane are given. Also given are the two components of the scattered vector qrad and qang

and the two scan modes used.

is given in Fig. 4.12. The sample is rotated around the su

ndition of a particular lattice plane is fulfilled. In the GID setup, the PSD detector is set

perpendicular to the sample surface in order to measure the scattered intensity for different

αf (Fig. 4.12(a)). The GID geometry of the incident and the scattered wave vector is given

in Fig. 4.12(b). For the present studies, two scan modes in the reciprocal space were used:

3 Ripples form independent of the crystalline orientation of the sample. Therefore, no attention is paid to

the alignment of ripples with respect to the crystalline direction during the sputtering experiments.

αi

αfω

2θ

PS

D

αi

αfω

2θ

PS

DP

SD

x

yqII

2θ 2θki

kf

ωlattice plane

qang

qrad

ω-scan

ω -2θ-scana)

b)

38


i) The angular scan (ω-scan), in this case the length of the scattering vector is kept

constant,

)sin(*sin2 θωθ −= kqang

varying his length (ω-2 -scan). This makes the radial scan strain sensitive. Due to these

scan modes the scattering vector q is divided into two components usually notated with

q

by varying his direction. ii) Radial scan performed along the scattering vector by

(

ang and qrad. This reciprocal space coordinates can be derived from the experimental

scattering angles using the relations

(4.6)

4.7) ).cos(*sin2 θωθ −= kqrad

39

Chapter 5

General Properties of the Surface Topography on Si and Ge

As already mentioned in the introduction, the aim of the work is to study the evolution

of the surface topography on Si and Ge surfaces during low-energy ion beam erosion.

Especially, the capability to form large-scale ripple and dot nanostructures on the surface is

of pronounced interest. There are many parameters which play a crucial role for the

formation of nanostructures on the surface. Beginning with the geometrical parameters of

the ion-optical system, continuing with the extraction voltages applied on the grid system,

and ending with the parameters that influence the ion-target interactions. For the rest of the

work, the experimental results concerning the influence of these parameters on the

evolution of ripple and dot patterns on Si and Ge surfaces will be discussed.

At the beginning, an overview of topographies emerging on Si and Ge surfaces will be

given. In general, the role of ion incidence angle1 will be discussed. Section 5.2 will deal

with the influence of ion species on the evolution of the surface topography on both

materials.

5.1 Overview of Emerging Topographies

During low-energy ion beam erosion of Si and Ge surfaces, different topographies can

evolve on the surface. Features like holes, bumps, ripples, and dots are common. As

mentioned above, the evolution of features strongly depends on the conditions under which

the experiments are performed. An important role on the evolution of the surface

topography, at oblique ion incidence angles, exerts the rotation respectively non-rotation of

the target holder around its surface normal, Fig. 5.1 (see description of the ion beam

equipment in Section 4.1.1). From here on, “SR” denotes sample rotation and “NSR” no

sample rotation, respectively. In cases with sample rotation, due to rotational symmetry,

there is an isotropic evolution of the surface topography. This is true under the supposition

that the substrate is rotating fast enough [65]. Usually SR leads to roughness suppression,

i.e. the surface smoothens. However, as shown recently, sample rotation at oblique

incidence can lead to the formation of well-ordered dot nanostructures on the surface

[28,31,35]. For the case with NSR, there is an anisotropy present on the surface given by

the ion beam direction. In general, this results in the formation of structures (usually

ripples) with preferred spatial orientation. There are plenty of examples showing the

formation of ripples at off-normal incidence in many materials (for an overview see

1 During the experiments as ion incidence angle is taken the angle between the surface normal of the ion

source grid system and the surface normal of the sample holder.

41

Chapter 5: General Properties of the Surface Topography on Si and Ge

Target

αion

Target

Ion beam Ion beam

αion

a) b)

NSRSR

Figure 5.1: Schematic presentation of the experimental setup for the case: a) with sample rotation, and b)

without sample rotation.

Chapter 1 and Ref. [117,118]). However, as it will be shown in Chapter 7, this is not

necessarily the case. For example, although there is an anisotropy present, the dot

structures show an isotropic spatial distribution, emerging on the surface.

The samples used in this work were Si(100) and Ge(100). However, as discussed in

Chapter 2 the surface evolution processes take place inside an amorphous layer covering

the sample surface.2 The layer thickness is in the range of the ion penetration depth.

Therefore the crystallographic orientation of the sample does not influence the surface

topography. The Si substrates were epi-polished, p-type with a conductivity of 0.01 –

0.02 Ω cm, while the Ge substrates were undoped with a conductivity of > 30 Ω cm. AFM

measurements of the initial surfaces of both materials revealed a root mean square

roughness ~ 0.2 nm. All investigated samples were sputtered at room temperature.

Examples of possible topographies emerging on Si surfaces after low-energy ion beam

erosion are presented in Fig. 5.2. Si substrates were bombarded with Ar+ ions, at ion

energies Eion ≤ 2000 eV, with an ion flux of J = 1.87 × 1015 cm-2 s-1 for 3600 s,

corresponding to a total ion fluence of Φ = 6.7 × 1018 cm-2. The AFM images reveal a

complexity of different topographies on the surface by varying the ion incidence angle αion.

In the case of SR for Eion = 500 eV and αion = 0 deg, hole structures evolve on the surface

(Fig. 5.2(a)). With increasing the ion incidence angle the height of structures decreases

until at αion = 45 deg the surface smoothens (Fig. 5.2(b)). By further increase of αion at

75 deg, dot structures with isotropic distribution evolve on the surface (Fig. 5.2(c)). For

NSR, structures showing preferential orientation form on the surface (Fig. 5(d-f)). Figure

5.2(d) reveals ripple structures on the Si surface at Eion = 1500 eV for αion = 15 deg.

Ripples are aligned perpendicular to the ion beam projection. At αion = 45 deg the surface

smoothens, and at αion = 75 deg columnar structures aligned along the ion beam projection

form on the surface. The same topography is observed by using Kr+ and Xe+ ions to

bombard the Si surface. Similar results are also found on Ge surfaces using Kr+ and Xe+

2 Investigations on amorphous Si and Si(111) samples showed no difference on the evolution of the

surface topography compared to results in Si(100).

42

5.1: Overview of Emerging Topographies

500 nm

500 nm

250 nm

2 nm

0 nm

8 nm

0 nm

10 nm

0 nm

7 nm

0 nm

(a)

(b)

(c)

(d)

500 nm

200 nm

0 nm

Eion = 500 eV, αion = 0°, SR Eion = 1500 eV, αion = 15°, NSR

Eion = 500 eV, αion = 45°, SR


2 nm

0 nm

Eion = 1500 eV, αion = 45°, NSR

(e)

(f)

500 nm

500 nm500 nm500 nm

500 nm500 nm

250 nm250 nm

2 nm

0 nm

2 nm

0 nm

8 nm

0 nm

8 nm

0 nm

10 nm

0 nm

10 nm

0 nm

7 nm

0 nm

7 nm

0 nm

(a)

(b)

(c)

(d)

500 nm500 nm

200 nm

0 nm

200 nm

0 nm


Eion = 500 eV, αion = 45°, SR


2 nm

0 nm

2 nm

0 nm


(e)

(f)

500 nm500 nm

500 nm500 nm

Figure 5.2: AFM images of different topographies on Si surfaces after Ar+ ion beam erosion. The black

arrow indicates the ion beam direction.

ions, especially with NSR.3 The topography is analyzed in terms of rms surface roughness,

that can also be taken as a measure for the height fluctuations on the surface and the

amplitude of structures [106]. These results are summarized in Fig. 5.3 where the surface

roughness w is plotted as a function of αion for Si, using Ar+ ions. The graph shows that the

roughness decreases up to a minimum value with ion incidence angle. By further

increasing of the αion the w increases again. Fig. 5.3 reveals that the evolution of w with αion

is independent of the ion energy used and if there is sample rotation or not. In general,

three regions with regard to αion can be distinguished. Region I: the surface is rough for αion

between 0 deg and ~ 40 deg, and features like dots, holes, and ripples form on the surface.

Region II: smooth surfaces for αion from ~ 40 deg up to ~ 60 deg. Region III: the surface

roughens again at grazing incidence above 60 deg and features like dots or columnar

structures emerge. Analogous results are obtained using different ion species to

3 The role of ion species on the evolution of the surface topography will be discussed in Section 5.2.

43


0 15 30 45 60 75

0.1

1

10

100

IIIIIIE

ion = 500 eV

Eion

= 1500 eV

Eion

= 1800 eV

Ar+, SR

Ar+, NSR

Ar+, SR

rms

roug

hnes

s w

[nm

]


[deg]

Figure 5.3: Development of rms surface roughness with ion incidence angle for Si using Ar+ ions at different

ion energies (Φ = 6.7 × 1018 cm-2). The results are plotted for the case with and without sample rotation.

bombard the Si surface. Results for Kr+ and Xe+ ions are plotted in Fig. 5.4(a), exemplary

for Eion = 2000 eV. Figure 5.4(b) shows a similar behavior for the evolution of the surface

roughness with ion incidence angle on Ge surfaces using Kr+ and Xe+ ions.

There is a parameter region for both materials with its center at 45 deg that is always

valid independent from all the sputtering parameters treated in this work. Namely, at this

ion incidence angle the surface remains smooth with a roughness w < 0.2 nm. Hence, this

sputtering condition is very well suited for large area surface smoothing, and finds a broad

application in the field of optic manufacturing [119-121].

In this section, the evolution of the surface topography in terms of surface roughness as

a function ion incidence angle was discussed without a detailed treatment of the particular

0 15 30 45 60 750.1

1

10

100E

ion = 2000 eV

IIIIII

Xe+

Kr+

rms

roug

hnes

s w

[nm

]


[deg]

0 15 30 45 60 750.1

1

10

Eion

= 2000 eV

IIIIII

Kr+

Xe+

rms

roug

hnes

s w

[nm

]


[deg]

a) b)

Figure 5.4: Rms surface roughness w as a function of αion using Kr+ and Xe+ ions to bombard the surface (Φ

= 6.7 × 1018 cm-2, Eion = 2000 eV, without sample rotation). a) Si, b) Ge.

44

5.2: Influence of Ion Species

structures. It was shown that there is a general behaviour of the surface roughness with ion

incidence angle for different sputtering parameters. A detailed discussion especially of

region I will be given in Chapter 7. Moreover, the discussion concerning the influence of

other process parameters will be given in the next Chapters. Obviously, it is difficult and

beyond the scope of this work to study the influence of different process parameters on all

topographies presented in Fig. 5.2. Especially, as it will be shown in the topography

diagrams in Section 7.2, by varying the sputtering conditions additional structures evolve

on the surface. As discussed in Chapter 1, particular interest will be paid to ripple and dot

structures, and hence to the conditions under which these structures evolve.

5.2 Influence of Ion Species

When an ion penetrates the target surface it transfers its energy and momentum due to

collision processes to the target atoms until it comes at rest. This process of slowing down

of ions gives rise to different phenomena on the surface and near-surface region. The most

important process parameters are the range and straggling of the distribution of the

deposited energy of incoming ions. This distribution depends on the energy of incoming

ions, ion incidence angle, and the properties of the target material. Additionally, the

distribution depends on the mass of incoming ions.

Experimental results show that the evolution of the surface topography on Si and Ge

surfaces is ion species dependent. During the bombardment of Si surfaces with Ne+ ions at

ion energies 300 eV ≤ Eion ≤ 1000 eV structures evolve on the surface. For 1000 eV ≤ Eion

≤ 2000 eV the surface remains smooth.4 Using Ar+, Kr+, and Xe+ as bombarding ions the

surface roughens i. e. structures evolve. Their formation depends also on other sputtering

conditions as it will be shown later in this work. Similar dependence of the surface

topography on Si with different ion species, was observed previously by Carter for

intermediate ion energies (above 20 keV) [122].

In the case of Ge, no structures are commonly observed (the surface remains smooth)

when Ne+ and Ar+ ions are used to bombard the surface. An example of topography

evolution on Ge surfaces for different ion species is given in Fig. 5.5. The AFM images

show that in the case of Ar+ ions, the surface remains smooth, while for Kr+ and Xe+ ions a

dot like structure evolves on the surface. However, there is a region (Eion = 1300 eV –

2000 eV and αion = 0 deg – 20 deg) where dot like structures are also observed using Ar+

ions, but with no ordering and an amplitude below 1 nm.

Due to lack of experimental studies, up to now, on the influence of ion species on the

surface topography on Si and Ge, it is difficult to give an exact explanation for the above

observations. Nevertheless, two possible explanations can be propsed for the emerging

4 For ion energies 300 eV ≤ Eion ≤ 1000 eV the formation of structures depends on other sputtering

parameters, like ion incidence angle similar to the discussion in Section 5.1. Contrary to this, for 1000 eV ≤

Eion ≤ 2000 the surface remains smooth independent of ion incidence angle.

45


(a) (b) (c)3 nm

0 nm

3 nm

0 nm

500 nm500 nm 500 nm500 nm 500 nm500 nm

3 nm

0 nm

3 nm

0 nm

3 nm

0 nm

3 nm

0 nm

Ar+ Kr+ Xe+

Figure 5.5: Surface topographies on Ge after ion beam erosion with different ion species at Eion = 1200 eV,

αion = 15 deg without sample rotation.

surface topography using different ion species:

(i) It is known from the theory and experiments that the main contribution to the sputter

yield originates from atoms ejected from the uppermost surface layers [40]. This

ejection process is related to the distribution of the deposited energy just below this

surface layer, that depends on the mass of the incoming ions. In Fig. 5.6 the depth

profiles of the deposited energy FD in Si using Ne+, Ar+, Kr+, and Xe+ ions at

Eion = 2000 eV are plotted using the SRIM simulation code [123]. The profiles show

that with increasing ion mass, the mean penetration depth (Fig. 5.4(b)) and the width of

the distribution decrease. This means that for heavier ions the energy distribution

maximum is located closer to the surface region than for lighter ions, i.e. more recoils

are created in the upper surface layer for heavier ions (for comparison see energy loss

values in Table 2.1). A similar behavior of the energy distribution and the mean depth

is also observed for simulations using Ge as a target material.

(ii) In addition to the energy deposition also highly energetic sputtered target atoms as well

as backscattered projectile ions become more important for primary ions with lower ion

mass. These sputtered particles contribute to additional sputtering of peaks compared to

valleys, hence prohibiting the evolution of structures and leading to smooth surfaces

[124]. This is supported by TRIM.SP [125,126] calculations using Ne+, Ar+, and Kr+

ions. Some conclusions of these simulations are: a) For lighter projectile ions, the

number of highly energetic particles emitted at an emission angle between 0 deg and

15 deg with respect to the surface plane, is higher when Ne+ ions are used compared to

Ar+, and Kr+ ions. b) Additionally, the number of highly energetic particles emitted

under these angles increases with ion energy, for a given ion species. c) The energy of

sputtered particles increases with decreasing ion mass. d) This number increases also

with increasing ion incidence angle, that would explain for example the larger surface

roughness observed at small incidence angles and its decrease with increasing angle up

to 45 deg.

From the above discussion it is obvious that the evolution of the surface topography

depends on the ion species used. For ion species with lighter mass than the target, usually

46

5.2: Influence of Ion Species

0 5 10 15 200

40

80

120

160

a)

Ne+

Ar+

Kr+

Xe+

Fits using Eq. (2.12)

FD (

z) [

a.u.

]

mean depth a [nm]

800 1200 1600 20001

2

3

4

5

b)

Ne+

Ar+

Kr+

Xe+

power fit

mea

n de

pth

a [n

m]

ion energy Eion

[eV]

Figure 5.6: a) Depth distribution of the deposited energy on Si for different ion species (Eion = 2000 eV, at

normal incidence). The solid line is a fit using the Eq. (2.12). b) Mean depth a of the deposited energy for

different ion energies and different ion species. A power law fit of data for Ar+ ions is performed with m =

0.31 (see discussion for Fig. 6.3 in Section 6.1). All simulations were performed with SRIM code.

no structures are observed. On the other side, once these structures form, their

characteristics like mean size, lateral ordering, homogeneity, and height do not depend on

the ion species used as it will be shown in Chapter 6.

47

Chapter 6

Ripple and Dot Patterns on Si and Ge surfaces

In Section 5.1, a short introduction of different topographies evolving on Si and Ge

surfaces during low-energy ion beam erosion was given. Depending on sputtering

conditions, features like holes, ripples, dots, and smooth surfaces can evolve. However,

from particular interest, and the main subject of this work is the formation of ripple and dot

patterns. Theoretically, the process of pattern formation is related to the competition

between the curvature dependent sputtering and different relaxation processes that results

in the formation of nanostructures on the surface. The question that arises is, it is possible

to control the evolution, lateral ordering and size of structures? If yes, which parameters

are more relevant? To answer this question the influence of different process parameters

has to be addressed. Some of these parameters include the ion energy Eion, ion fluence Φ,

and ion flux J which will be discussed in detail in the next sections. Section 6.1 will show

that with increasing ion energy the wavelength of structures increases. This increase

correlates with theoretical predictions, by considering ion induced effective surface

diffusion ESD or ion-induced viscous flow IVF as a dominant relaxation mechanism.

However, there are conditions under which a completely new behavior is observed, namely

a change in orientation of the wave vector of ripples in Si, or a transition from ripples to

dots on Ge, with increasing ion energy. In Section 6.2, the role of ion fluence and ion flux

on the evolution of the surface topography and the lateral ordering of structures will be

discussed. While the wavelength of structures remains constant with ion fluence the lateral

ordering increases. The geometrical shape of ripples and dots investigated with high-

resolution transmission electron microscopy is given in Section 6.3. Additional to the AFM

method also small angle X-ray scattering techniques are used to characterize the ripple and

dot structures. These results will be discussed in Section 6.4.

Results for both materials, Si and Ge, are presented. In the case of Si, results will be

given for Ar+, Kr+, and Xe+ ions. Also, for Si two cases are distinguished, a) SR and b)

NSR. With SR the results for a grazing incidence angle of 75 deg, where dot structures

evolve on the surface, will be given [31]. For Ge only the case with NSR will be discussed.

Dot structures form also on Ge surfaces with SR. However, under experimental conditions

used in this work, they show only a vague lateral ordering, and a large size distribution

making it very difficult to deduce general statements.

49

Chapter 6: Ripple and Dot Patterns on Si and Ge surfaces

6.1 Influence of Ion Energy

Silicon

This section is devoted to the role of ion energy Eion on the formation of patterns on Si

surfaces. The Eion is varied between 500 eV and 2000 eV, which is limited by the power

supply of the ion source. The experiments were performed at room temperature with an

ion-current density jion ~ 300 µA cm-2 (corresponding to an ion flux J =

1.87 × 1015 cm-2 s-1) and a total ion fluence of Φ = 6.7 × 1018 cm-2. The ion fluence used

ensures that the evolving patterns are well above the saturation regime concerning the

surface roughness (see Section 6.2).

In Fig. 6.1, the AFM images of ripple patterns emerging on Si surfaces, at an ion

incidence angle αion = 15 deg from the surface normal, without sample rotation are given.

The Si surface is bombarded with Ar+ ions with three different Eion: a) 800 eV, b) 1500 eV,

and c) 2000 eV. In order to study the characteristic wavelength (i. e. spatial frequency) of

ripples, Fast Fourier transformation (FFT) of the AFM images is performed using Eq.

(4.2). The FFT images show clear spots in the spatial frequency spectra that correspond to

the dominating ripple wavelength in the real space. Additional spots in the FFT image

indicate the high lateral ordering of ripples. The FFT image shows that the wave vector of

ripples is parallel to the projection of the ion beam onto the surface plane. Compared to

high spatial-frequency ripples, AFM images reveal additional low spatial-frequency

corrugations on the surface with a wave vector perpendicular to the ion beam projection.

Due to a rather broad size distribution, it is difficult to determine their wavelength.

However, the amplitude of these corrugations is very small compared to that of short

wavelength ripples.1 For quantitative determination of the characteristic wavelength of

ripples, the power spectral density (PSD) function is obtained from FFT images by angular

averaging using Eq. (4.3). The corresponding PSD graphs for three different ion energies

are given in Fig. 6.2. The position of the first peak on the PSD graph gives the

characteristic spatial frequency of ripples, i. e. the ripple wavelength . From the PSD

graphs a shift of the first peak towards smaller spatial frequencies with increasing ion

energy is observed. Further, the integral over the PSD function, which can be taken also as

a measure for the rms surface roughness w, indicates an increase of w with Eion. This

means also that the mean height (amplitude) of ripples increases with ion energy. Results

about the change of the ripple wavelength , and the system correlation length with ion

energy are quantitatively summarized for Ar+ and Kr+ ions in Fig. 6.3. The graphs show an

increasing from 40 nm up to 70 nm by varying the ion energy from 500 eV up to

2000 eV. In Fig. 6.3, the system correlation length is normalized to the ripple wavelength

1 For example, by excluding the short wavelength contributions, applying a Fourier filtering, to an AFM

image with 16 × 16 µm2 scan size for Eion = 1200 eV at αion = 15 deg, a mean amplitude of the long

wavelength corrugations of ~ 0.6 nm was deduced.

50

6.1: Influence of Ion Energy

500 nm500 nm

4 nm

0 nm

4 nm

0 nm

500 nm500 nm

7 nm

0 nm

7 nm

0 nm

500 nm500 nm

10 nm

0 nm

10 nm

0 nm

a) Eion = 800 eV, αion = 15°, NSR

b) Eion = 1500 eV, αion = 15°, NSR

c) Eion = 2000 eV, αion = 15°, NSR

FFT

FFT

FFT

f = - 128 µm-1 … 128 µm-1

d)

e)

f)

Figure 6.1: AFM images of self-organized ripple patterns on Si surfaces after Ar+ ion beam erosion at Φ =

6.7 × 1018 cm-2, for different ion energies. (d-f) Corresponding Fourier images (image size ± 128 µm-1). The

arrows indicate the direction of the incoming ion beam.

/ . The ratio / , shows in how many periods a perfect lateral ordering of ripples is

present. While for Kr+ ions the ordering of ripples is independent of Eion, for Ar+ ions the

best ordering is achieved at Eion = 1200 eV. For the given sputtering conditions in the case

of Kr+ at Eion = 500 eV no ripple structures are observed.

Theoretically the scaling behavior of with Eion depends on the particular relaxation

mechanism under consideration. Under given sputtering conditions, two relaxation

mechanisms can be considered from relevance for the process of ripple formation.

i) Ion-induced ESD as presented in Section 3.1. From Eq. (3.8), (3.12), and (3.13) and by

making use Eq. (2.8) for the ion range it follows

(6.1)~~ Eaλ 2mion .

51


10-3

10-2

10-1

10-2

100

102

104

106

1st peak 800 eV

1500 eV 2000 eV

pow

er s

pect

ral d

ensi

ty P

SD

[nm

4 ]


Figure 6.2: Angular averaged PSD functions obtained from FFT images in Fig. 6.1. The first peak

corresponds to the characteristic ripple wavelength.

The wavelength is proportional to the mean penetration depth a, which scales with Eion

as . In order to compare the evolution of with EmionEa 2~ ion with the theory, a linear

( ionE∝ )λ and power-law ( )mionE 2∝λ fit of the experimental results for the case of Ar+

ions is performed. The power-law fit gives an exponent m = 0.22. This is in a reasonable

400 800 1200 1600 200020

40

60

80

0

10

20

30

40

50

ζ/λ

Ar+

Kr+

linear fit power fit

ripp

le w

avel

engt

h λ

[nm

]

ion energy Eion

[eV]

//

Figure 6.3: The dependence of the ripple wavelength and the system correlation length (normalized to )

on ion energy Eion (Φ = 6.7 × 1018 cm-2, αion = 15 deg, Ar+ and Kr+ ions) for Si. The linear fit and power fit

(with an exponent m = 0.22) of the data for Ar+ ions are also given.

52


agreement with the power-law fit of the mean depth SRIM data plotted in Fig. 5.4 for

Ar+ ions, resulting in an exponent m = 0.31.

ii) Another relaxation mechanism that can influence the process of ripple formation is the

ion-enhanced viscous flow (IVF) [29]. Here smoothing occurs by ion-induced viscous

relaxation confined to a near surface region of depth d, with d being of the order of the

ion range a, and much smaller than the ripple wavelength (a ~ d << ). Then from Eq.

(3.19) , i. e. the ripple wavelength increases with ion energy, and m = 0.15 is

deduced.

mionEa 3~

From the above discussion it seems that both mechanisms predict an increase of with

Eion similar to experimental results. However, the value of the parameter m calculated from

the experimental data should be taken with caution. In order to better distinguish between a

linear and power-law dependency the energy range would have to be extended. However,

this was not possible due to the limited range of ion energy feasible in the experiments.

A ripple wavelength increasing with ion energy is observed also by using Xe+ ions to

sputter the Si surface for Eion >1000 eV (Fig. 6.4). The results are given for three different

ion incidence angles. The graph shows also that the wavelength of ripples decreases with

increasing ion incidence angle, a fact that will be elaborated in more detail in Chapter 7.

However, there is a more complex behavior of the surface topography dependent on ion

energy in the case of Xe+ ions, which is not predicted by the continuum theory. In Fig. 6.5

AFM images of Si surfaces after sputtering with Xe+ ions, at αion = 20 deg, for different ion

energies are given. For Eion = 1200 eV ripple patterns with the wave vector parallel to the

ion beam projection form on the surface with wavelength = 46 nm (Fig. 6.5(a)). By

decreasing the ion energy to Eion = 800 eV, ripples vanish and the surface remains smooth

1200 1400 1600 1800 2000

45

60

75

5° 15° 20°

ripp

le w

avel

engt

h λ

[nm

]

ion energy Eion

[eV]

Figure 6.4: The dependence of wavelength on ion energy for ripples on Si, using Xe+ ions, for different ion

incidence angles.

53


(Fig. 6.5(b)). Further decrease of ion energy results in a new type of ripples evolving on

the surface (Fig. 6.5(c)). Now, the wave vector is oriented perpendicular to the ion beam

projection. These ripples have a mean height similar to ripples with parallel wave vector,

but with wavelength = 111 nm, which is more than two times larger. The spots in the

corresponding FFT image show a larger radial distribution of these ripples compared to

ripples with parallel wave vector.2 The parameter region of a smooth surface between these

two mode ripples depends on sputtering conditions. For example, it can be shifted toward

smaller Eion values with increasing αion. For a better presentation, the results for the

2 nm

0 nm

2 nm

0 nm

5 nm

0 nm

5 nm

0 nm

500 nm500 nm

500 nm500 nm



FFT

FFT

f = - 128 µm-1 … 128 µm-1

e)

d)

5 nm

0 nm

5 nm

0 nm

1000 nm1000 nm


FFT f)

Figure 6.5: (a-c) Surface topography on Si after Xe+ ion beam sputtering at Φ = 6.7 × 1018 cm-2 for different

Eion. (d-f) Calculated FFT images with image size ± 128 µm-1. Please note the different scale in AFM images.

2 The larger radial distribution for ripples with perpendicular wave vector is mainly due to sticking

together of ripples at some positions that contributes to the characteristic spatial frequency on the FFT.

54


0 15 30 45 60 75500

1000

1500

2000

C

B

A

ripp

les

+ d

ots

pillarstructures

parallelmoderipples

smoothsurfaces

ion

ener

gy E

ion [

eV]


[deg]

Figure 6.6: Topography diagram giving the surface topography on Si due to Xe+ ion beam erosion (Φ =

6.7 × 1018 cm-2) for different ion energies and ion incidence angles, without sample rotation. A – represents

hole structures, B – represents hillock structures, and C – the normal mode ripples. The symbols indicate the

experimental data. - smooth surfaces, - hole structures, - hillock structures, - perpendicular-mode

ripples, - parallel-mode ripples + dots, - parallel-mode ripples, - columnar structures.

evolution of the surface topography for different Eion and αion are plotted using a so-called

topography diagram TD. Such a TD is presented in Fig. 6.6. It reveals a complexity of

different topographies that depend on Eion, and αion. Obviously, the surface topography

reliance on Eion will also depend on the value of αion. The boundaries (doted lines) on the

TD are used as a guide to the eye, to distinguish between different topography regions. In

most of the cases their position is taken as a middle point between the experimental data

(symbols in Fig. 6.6) representing two different topographies.3 For explanation, as parallel-

mode ripples are meant ripples with the wave vector parallel to the projection of the ion

beam on to the surface. With ripples plus dots are meant surfaces where parallel-mode

ripples and dots coexist. Ripples with the wave vector oriented perpendicular to the ion

beam projection, are named perpendicular-mode ripples.

In the SR case (ensuring an isotropic evolution of the surface topography) at oblique ion

incidence, depending on sputtering parameters dot patterns can form on the surface. Dot

patterns form also at normal ion incidence [31], similar to those reported by other research

groups [30]. The focus here will lie on dot patterns at oblique ion incidence, because of the

larger amplitude and the much better lateral ordering compared to the dots at normal

incidence, making them more appropriate for other applications. In Fig. 6.7 an example of

3 This is done with the supposition that topographical transitions are continuous and that the transition

point lies in the middle between the experimental data.

55


f = - 128 µm-1 … 128 µm-1c) Eion = 2000 eV, αion = 75°, SR

500 nm500 nm

500 nm500 nm

a) Eion = 500 eV, αion = 75°, SR

b) Eion = 1000 eV, αion = 75°, SR

500 nm500 nm

20 nm

0 nm

20 nm

0 nm

20 nm

0 nm

20 nm

0 nm

30 nm

0 nm

30 nm

0 nm

FFT

FFT

FFT

d)

e)

f)

Figure 6.7: (a-c) Dot structures on Si after Kr+ ion beam erosion with SR at Φ = 6.7 × 1018 cm-2 for different

Eion. (d-f) Corresponding FFT images with size ± 128 µm-1.

dot patterns evolving on the Si surface during sputtering with Kr+ ions (αion = 75 deg, Φ =

6.7 × 1018 cm-2) is given. The AFM images show domains of close-packed, hexagonally

ordered dot structures evolving on the surface. These domains are randomly ordered with

respect to each other. The position of the first ring on the FFT specifies the mean lateral

size of dots . Additionally, FFT images reveal that the size of dots increases with Eion,

giving the possibility to control their size in a certain range. Similar results are observed by

using Ar+ and Xe+ ions. Quantitatively, the dependence of and (equal to the mean

domain size for dots) on Eion is summarized in Fig. 6.8. The results show an increase of the

mean dot size, from 25 nm up to 50 nm, with increasing ion energy. In the case of Ar+

ions, the mean dot size increases up to Eion = 1000 eV. For further increasing Eion, dots

overlap with each other creating conglomerates of dots with no ordering, until at Eion =

56


30

40

50

0

3

6

90

3

6

90

3

6

9

400 800 1200 1600 2000

30

40

50

ion energy Eion

[eV]

30

40

50

λ

ζ/λ

mea

n do

t siz

e/pe

riod

icit

y λ

[nm

]

(c)

(b)

(a)

Xe+

Kr+

Ar+

ζ/λ

Figure 6.8: The variation of the mean dot size and the normalized correlation length on Si with ion energy

for different ion species (αion = 75 deg, and Φ = 6.7 × 1018 cm-2).

2000 eV the surface smoothens. For Kr+ and Xe+ ions, dots form in the range 500 eV ≤ Eion

≤ 2000 eV and their size increases with Eion. The determination of the mean dot size for

Xe+ ions at Eion = 500 eV is associated with a large uncertainty due to the marginal lateral

ordering of dots. The ratio / shows that for Eion > 750 eV the lateral ordering of dot

structures remains constant. For Ar+ ions the best lateral ordering of dots is obtained at Eion

= 500 eV. A behavior similar to that of Ar+ is observed for Ne+ ions under the given

sputtering conditions. However, the uniformity and ordering of dots is much less

pronounced than for Ar+ ions.

Germanium

Analogous investigations for the surface topography with ion energy were performed on

Ge. The parameters used for the sputtering process are identical to those for Si. A

representative example of ripple patterns on Ge is given in Fig. 6.9 after Xe+ ion beam

sputtering with Eion = 2000 eV, at αion = 5 deg, and ion fluence Φ = 6.7 × 1018 cm-2. The

FFT image reveals that the wave vector of ripples is parallel with respect to the ion beam

projection. The findings on the dependence of on Eion are summarized in Fig. 6.10. The

ripple wavelength increases with ion energy, similar to Si. For the given sputter conditions,

57


500 nm500 nm


10 nm

0 nm

10 nm

0 nm

FFT

f = - 128 µm-1 … 128 µm-1

Figure 6.9: AFM image of ripple patterns on Ge surfaces after Xe+ ion beam erosion without sample

rotation, for Φ = 6.7 × 1018 cm-2.

no ripples were observed at Eion = 500 eV. The ratio / shows that for Eion > 1000 eV the

lateral ordering of ripples is improved significantly compared to Eion = 800 eV. By

considering the ESD term as the main relaxation mechanism, a power-law fit to the

experimental data yields an exponent m = 0.21. This is in a very good agreement with the

exponent m = 0.21 deduced by a power-law fit of the mean depth a from the SRIM

simulations data (Fig. 6.10). However, similar to Si, a larger Eion range would be necessary

to enable a better determination of the scaling behavior of with Eion.

By studying the surface topography with ion energy at different ion incidence angles, an

interesting effect is observed. Namely, by increasing Eion for αion = 20 deg a transition from

400 800 1200 1600 20001

2

45

60

75

0

5

10

15 λ power fit, m = 0.21 SRIM: a, m = 0.21

ζ/λ

mea

n w

avel

engt

h λ

& m

ean

dept

h a

[nm

]

ion energy Eion

[eV]

ζ/λ

Figure 6.10: The dependence of and / on Eion for Xe+ ion beam erosion of Ge (αion = 5 deg, Φ =

6.7 × 1018 cm-2). Also plotted is the mean depth a for Xe+ ions on Ge for different Eion calculated with SRIM.

The power-law fits performed for and a, give a scaling exponent m = 0.21.

58



500 nm500 nm

500 nm500 nm



500 nm500 nm

5 nm

0 nm

5 nm

0 nm

5 nm

0 nm

5 nm

0 nm

5 nm

0 nm

5 nm

0 nm

FFT

FFT

FFT

d)

e)

f)

f = - 128 µm-1 … 128 µm-1

Figure 6.11: Surface topography on Ge after Xe+ ion beam erosion with no sample rotation, for different Eion

(Φ = 6.7 × 1018 cm-2) (d-f) Corresponding FFT images. The arrows indicate the ion beam direction.

ripple to dot structures occurs. Such an example is presented in Fig. 6.11, where AFM

images of the Ge surface after sputtering with Xe+ ions for: a) Eion = 500 eV, b) Eion =

800 eV, and c) Eion = 1200 eV are depicted. At 500 eV, parallel-mode ripples, as shown in

the corresponding FFT image, form on the surface. The large angular distribution of spots

is related to the less pronounced lateral ordering of ripples. By increasing Eion, ripples and

dots evolve simultaneously on the surface. In the FFT image the spots have a more curved

form indicative of dots, but the preferential direction of ripples is still observable. At

1200 eV, the surface consists only of dot structures with particular domains showing

59


0 5 10 15 20 25 30 35500

1000

1500

2000

hill

ock

stru

ctur

es

d

ots

smooth

A

parallelmode ripples

ripples + dots

dots

ion

ener

gy E

ion [

eV]


[deg]

Figure 6.12: Topography diagram for Ge after Xe+ ion beam sputtering (Φ = 6.7 × 1018 cm-2) for different

ion energies and ion incidence angles. Region A represents perpendicular-mode ripples. The symbols

represent the experimental data: - hillock structures, - smooth surfaces, - perpendicular-mode

ripples, - parallel-mode ripples + dots, - parallel-mode ripples, - columnar structures, - dots.

hexagonal ordering. The evolution of the surface topography with ion energy for different

incidence angles is summarized in the topography diagram in Fig. 6.12. The TD gives a

complex picture of evolving topographies similar to Si. The topography depends not only

on Eion but also on the incidence angle. For αion = 5 deg a transition from perpendicular-

mode to parallel-mode ripples is observed with increasing ion energy. The same discussion

as for Si can be made concerning the boundaries between different parameter regions.

Summary

The above results for Si and Ge show that ion energy, is a key-parameter for the

formation of ripple and dot structures and for determining their wavelength. Generally, the

results evidence an increase of the wavelength of nanostructures with ion energy. This

correlates with the theoretical models that also predict an increase of with Eion by

considering ESD or IVF as relaxation mechanisms (at least for certain ion energy range).

However, there are experimental conditions under which completely new phenomena are

observed. One is the formation of a new type of ripples with the wave vector perpendicular

to the projection of the ion beam. The wavelength of these ripples is approximately two

times larger compared to the wavelength of parallel-mode ripples. Moreover, there is a

transition from ripples to dots with increasing ion energy on Ge surfaces. Both

observations are not consistent with the theoretical model presented in Chapter 3. It should

be mentioned that the role of ion incidence angle on the topographical transitions will be

discussed in Section 7.1.

60

6.2: Ion Fluence and Flux

6.2 Ion Fluence and Flux

In this chapter the temporal evolution of ripple and dot patterns on Si and Ge will be

discussed in detail. Explicitly, results about the evolution of the characteristic wavelength

of nanostructures and the surface roughness w with ion fluence Φ will be presented. The

results for different ion species will be given. The ion fluence equals the total number of

ions hitting the surface per unit area. For a given ion flux the ion fluence Φ is equivalent

with the sputter time, or with the thickness of the removed layer.

All experiments were conducted under conditions, under which well ordered ripple and

dot structures are formed.

Silicon

A representative example of evolving ripple patterns, with increasing ion fluence on Si

is given in Fig. 6.13. The surface is sputtered with Kr+ ions at Eion = 1200 eV, αion = 15 deg

and ion current density jion = 300 µA cm-2 for different ion fluences: a) Φ = 3.3 × 1017 cm-2

(sputter time 180 s), b) Φ = 2.2 × 1018 cm-2 (1200 s), c) Φ = 1.3 × 1019 cm-2 (7200 s). The

AFM image in Fig. 6.13(a) reveals ripple topography from the beginning of the sputtering

process. The first spot on the corresponding FFT image clearly indicates the characteristic

wavelength of ripples in Fig. 6.13(d). The wave vector of ripples is oriented parallel to the

ion beam projection. However, the rather broad radial and angular distribution of the first

spot, reveal that ripples have a rather poor lateral ordering (alignment) and size

homogeneity. With increasing ion fluence the ordering of ripples increases (Fig. 6.13(b,e)),

as seen from the FFT image where the radial and angular distribution of the spots

decreases. Also more high order peaks become visible (Fig. 6.13(c,f)).

The AFM images show that ripples are interrupted by defects (denoted by the circle in

Fig. 6.13(c)), producing two new ripples or coalescence of two ripples in one. The number

of defects decreases with Φ leading to almost perfectly ordered ripples with approximately

2 defects per 1 µm2, for the highest fluence shown in Fig. 6.13(c).

In Fig. 6.14 the PSD functions of the corresponding FFT images from Fig. 6.13 are

plotted. For comparison the PSD of an untreated substrate is included. The PSD graphs

show a clear distinct peak growing at a given spatial frequency. The position of the peak

does not change with ion fluence indicating independent wavelength values with Φ. In

contrast, the width of the peak decreases. These results are quantitatively summarized in

Fig. 6.15 by plotting the evolution of the ripple wavelength and the system correlation

length with ion fluence for Ar+, Kr+, and Xe+ ion species. The results are presented for

Eion = 1200 eV, and αion = 15 deg. The graphs show a ripple wavelength ~ 50 nm, that is

not varying with ion fluence. At the same time increases with ion fluence. At the

beginning (up to an ion fluence Φ = 2 × 1018 cm -2) there is a steeper increase than for

larger fluences. For a total fluence of Φ = 4 × 1019 cm-2, the extends up to 1 µm. This

61


500 nm500 nm

7 nm

0 nm

7 nm

0 nm

500 nm500 nm

7 nm

0 nm

7 nm

0 nm

500 nm500 nm

7 nm

0 nm

7 nm

0 nm

a) Φ = 3.4 x 1017 ions/cm2, NSR

b) Φ = 2.2 x 1018 ions/cm2, NSR

c) Φ = 1.3 x 1019 ions/cm2, NSR

FFT

FFT

FFT

d)

e)

f)

f = - 128 µm-1 … 128 µm-1

Figure 6.13: (a-c) Surface topography on Si after Kr+ ion beam erosion with Eion = 1200 eV, αion = 15 deg,

for different ion fluences. The solid circle in c) indicates an existing defect between ripples. (d-f)

corresponding Fourier images.

value of the system correlation length for ripples can be interpreted as the mean distance

between the defects on the AFM image.

Concerning dot structures forming at oblique ion incidence, with sample rotation,

similar behavior of and , like for ripples is observed. These results are plotted in

Fig. 6.16 for: a) Φ = 1.1 × 1017 cm-2 (sputter time 60 s), b) Φ = 2.2 × 1018 cm-2 (1200 s), c)

Φ = 1.3 × 1019 cm-2 (7200 s). The surface is bombarded with Kr+ ions at Eion = 1000 eV,

αion = 75 deg and ion current density jion = 300 µA cm-2. The images show an increase of

the lateral ordering and size homogeneity of dots with ion fluence. For prolonged

sputtering (Fig. 6.16(c)) large domains of close packed dots showing hexagonal order form

on the surface. In the corresponding FFT images the radial width of the ring decreases and

62


100

102

104

(d)

(c)

(b)

(a)


100

102

104

100

102

104

pow

er s

pect

ral d

ensi

ty P

SD

[nm

4 ]

10-3

10-2

10-1

100

102

104

Φ = 1.3 x 1019

ions/cm2

Φ = 2.2 x 1018

ions/cm2

Φ = 3.4 x 1017

ions/cm2

Φ = 0

0

300

600

900

0

300

600

900

0

300

600

900

20

40

60

80

20

40

60

80

0 5 10 40

20

40

60

80

λ

ion fluence Φ [1018

cm-2]

syst

em c

orre

lati

on le

ngth

ζ [

nm]

ripp

le w

avel

engt

h λ

[nm

]

Ar+

Kr+

Xe+

ζ

Figure 6.14: Angular averaged PSD functions

obtained from FFT images in Fig. 6.13(d-f).

For comparison the PSD function of an

untreated (not eroded) surface is given (a).

Figure 6.15: Ion fluence dependence of wavelength

and the system correlation length for ripples on

Si with Eion = 1200 eV, αion = 15 deg for different

ion species.

500 nm500 nm 500 nm500 nm 500 nm500 nm

a) Φ = 1.1 x 1017 ions/cm2, SR b) Φ = 2.2 x 1018 ions/cm2, SR c) Φ = 1.3 x 1019 ions/cm2, SR

FFT FFT FFT

5 nm

0 nm

5 nm

0 nm

20 nm

0 nm

20 nm

0 nm

20 nm

0 nm

20 nm

0 nm

d) e) f)

f =

-12

8µm

-1…

128

µm-1

Figure 6.16: (a-c) AFM images of dot structures on Si surfaces after Kr+ ion beam sputtering, with sample

rotation, at Eion = 1000 eV, αion = 75 deg for different ion fluences. (d-f) The corresponding FFT images.

63


the number of multiple rings increases. Fig. 6.17 shows the evolution of the mean size of

dots and the system correlation length with Φ. The results are given for Ar+ at Eion =

500 eV and Kr+ and Xe+ ions at Eion = 1000 eV.4 From the graphs, the mean size of dots

does not change while increases with ion fluence. For prolonged sputtering a system

correlation length up to 150 nm is observed. Also the results indicate a mean size of dots

that is independent from the ion species used.

Germanium

The evolution of and with ion fluence for structures on Ge, displays similar result

like for Si. This is shown for the case of dot patterns evolving on the Ge surface, after Xe+

ion beam sputtering with NSR, for Eion = 2000 eV and αion = 20 deg (see Fig. 6.11(c) and

Section 7.1). Results for the dependence of and / on ion fluence are plotted in Fig. 6.18.

Similar to the case of dots in Si also in Ge the mean size of dots remains constant with ion

fluence while the ordering increases with ion fluence until it saturates. The mean size

fluctuations for low ion fluences are related to the large size distribution of dots.

0

50

100

150

0

50

100

150

0

50

100

150

0 4 8 120

20

40

60 λ


cm-2]

0

20

40

60

syst

em c

orre

lati

on le

ngth

ζ [

nm]

mea

n do

t siz

e/pe

riod

icit

y λ

[nm

]

0

20

40

60

(c)

(b)

(a)

Xe+, α

ion = 75°, E

ion = 1000 eV

Kr+, α

ion = 75°, E

ion = 1000 eV

Ar+, α

ion = 75°, E

ion = 500 eV

ζ

Figure 6.17: Dependence of the mean dot size and the system correlation length on ion fluence for dots on

Si. The results are given for different ion species.

4 As shown in Fig. 6.8 for Ar+ ions dots with the best lateral ordering evolve for Eion = 500 eV.

64


0 4 8 120

20

40

60

80

2

3

4

λ

ζ/λ

mea

n do

t siz

e λ

[nm

]


cm-2]

Xe+, α

ion = 20°, E

ion = 2000 eV

ζ/λ

Figure 6.18: Evolution of mean dot size and the normalized system correlation length with ion fluence, for

dots on Ge.

Evolution of the Structure Height

Next, the evolution of the amplitude of ripple and dot structures, with ion fluence for Si

and Ge will be addressed. This will be done in terms of rms surface roughness w using Eq.

(4.1). It is known that the surface roughness depends on the length scale of the image used

to deduce w. For this reason images with scan size 2 µm × 2 µm were used for all samples.

Fig. 6.19 gives the evolution of the rms surface roughness w with ion fluence for ripples

and dots on Si. The experimental results show that for small sputtering fluences, up to

5.6 × 1017 cm-2, w seems to grow exponentially (dotted line). For Φ ~ 1 × 1018 cm-2, the

0 4 8 12 400.1

1

Ar+ α

ion = 15°, E

ion = 1200 eV

Kr+ α

ion = 15°, E

ion = 1200 eV

Xe+ α

ion = 15°, E

ion = 1200 eV

exp. growth


cm-2]

rms

roug

hnes

s w

[nm

]

0 4 8 120.1

1

Ar+, α

ion = 75°, E

ion = 500 eV

Kr+, α

ion = 75°, E

ion = 1000 eV

Xe+, α

ion = 75°, E

ion = 1000 eV

exp. growth

rms

roug

hnes

s w

[nm

]


cm-2]

a) b)

Figure 6.19: Rms surface roughness evolution with ion fluence in Si for different ion species. The dotted line

illustrates the exponential grow for the initial stage of sputtering. a) ripples, b) dots.

65


roughness, i. e. the ripple and dot amplitude, saturates and remains constant upon further

sputtering. The results in Fig. 6.19 prove also that the evolution of the amplitude with ion

fluence behaves similar for Ar+, Kr+, and Xe+ ions. The results show a similar behavior of

w with Φ for ripples and dots.

The evolution of w with Φ is investigated also for Ge. A representative example is given

in Fig. 6.20 using the same sputtering conditions like in Fig. 6.18. In this case the surface

roughness saturates at an ion fluence of Φ = 8.4 × 1016 cm-2, corresponding to an erosion

time of only 45 s.

The results for w (i. e. structure amplitude) with ion fluence for Si and Ge can be

summarized as following: (i) For small ion fluences the surface roughness seems to have

an exponential increase, (ii) with increasing ion fluence the roughness saturates and

remains constant even for prolonged sputtering (up to Φ = 4 × 1019 ions / cm-2).

Another point to be addressed in the context of ion fluence is the evolution of the

surface topography for conditions where ripples and dots evolve simultaneously (see also

discussion in Chapter 7) on Si and Ge. This is done in order to observe how stable are

these regions, and if one type of structures is dominating the other or they simply coexist.

Figure 6.21 gives an example of surface evolution on Si during Xe+ ion beam erosion at

Eion = 2000 eV, αion = 34 deg, with no sample rotation and for different ion fluences. The

AFM image in Fig. 6.21(a) shows a simultaneous formation of ripples and dots for low ion

fluences at Φ = 3.4 × 1017 ions / cm-2 (sputter time 180 s). The characteristic ring

representative for dots and additionally the peaks for ripples are present on the 120 min by

an ion flux of jion = 300 µA cm-2). The only difference is that the alignment of ripples

0 4 8 12

1

Xe+, α

ion = 20°, E

ion = 2000 eV

exp. growth

rms

roug

hnes

s w

[nm

]


cm-2]

Figure 6.20: Evolution of rms surface roughness w as function of Φ for Xe+ ion beam erosion of Ge surfaces.

The results are plotted for dots with Eion = 2000 eV, at αion = 20 deg and without sample rotation.

66


500 nm500 nm

500 nm500 nm

500 nm500 nm

3 nm

0 nm

3 nm

0 nm

4 nm

0 nm

4 nm

0 nm

4 nm

0 nm

4 nm

0 nm

a) Φ = 3.4 x 1017 ions/cm2

b) Φ = 2.2 x 1018 ions/cm2

c) Φ = 1.3 x 1019 ions/cm2

FFT

FFT

FFT

d)

e)

f)

f = - 128 µm-1 … 128 µm-1

Figure 6.21: (a-c) Surface topography on Si after Xe+ ion beam sputtering without sample rotation for

different ion fluences at Eion = 2000 eV and αion = 34 deg. (d-f) Corresponding FFT images. The solid circle

visualizes the equal radius of the rings in the FFT spectra.

increases, which influences also the ordering of dots that form along the ripples. The FFT

(Fig. 6.21(f)) reveals the quadratic ordering of dots, but still a preferred orientation is

observed along the wave vector of ripples.

Ion Flux

Here the influence of the ion flux on the evolution of ripples and dots is studied.

Experimental results for the evolution of the wavelength and surface roughness with ion

flux J are summarized in Fig. 6.22. The results are presented for ripples on Si and dots on

Ge, sputtered with 2000 eV Xe+ ions at αion = 20° and a total fluence Φ = 6.7 × 1018 cm-2.

67


0.0 0.5 1.0 1.5 2.00

20

40

60

80

0

1

2

3

4

5

rms

roug

hnes

s w

[nm

]

/ Si/Ge

wav

elen

gth

λ [n

m]

ion flux J [1015

cm2/s]

/ Si/Ge

Figure 6.22: Structure wavelength and rms surface roughness with ion flux for ripples on Si and dots on Ge

surfaces after Xe+ ion beam erosion with Eion = 2000 eV, αion = 20 deg.

The erosion time was varied so that the total amount of ions hitting the surface Φ remains

constant. In the ion flux range used for the experiments (jion was varied from 80 µA cm-2 up

to 300 µA cm-2), no variation of the wavelength is observed. Also the surface roughness

w remains constant with ion flux.

6.3 Geometrical shape

The geometrical shape of ripples and dots is studied using the cross-section profile

taken from AFM images. A better method to investigate the geometrical shape and the

surface damage on the atomic scale is the High Resolution Transmission Electron

Microscopy (HRTEM). HRTEM was performed in a 400 keV microscope possessing a

point resolution of 0.155 nm. Cross-sectional samples were prepared by gluing samples

face to face, embedding resulting sandwiches in alumina tubes, wire-saw cutting, plan-

parallel grinding, one-sided polishing, other-sided dimpling followed by polishing to a

residual thickness of about 15 µm, and Ar+-ion beam etching at 2.8 keV.

In Fig. 6.23 a magnified image of Fig. 6.13(c) for the ripple topography together with

the cross-section profile is given. The cross-section profile, taken from the solid line of the

AFM image, gives a separation of ~ 50 nm between ripples, and a height of ~ 4 nm. Also

from the profile, the site facing the ion beam is less steep than the other side with sidewall

angles varying between 8 deg and 14 deg, respectively. This asymmetry is present for

whole ion incidence angle range where ripples evolve (from 5 deg up to 25 deg). The

amount of asymmetry, i. e. the ratio of ~ 1 : 2 between the site facing the ion beam and the

opposite site, remains the same. Fig. 6.24 shows a cross section HRTEM image of the

68

6.3: Geometrical Shape

0 50 100 150 200 250 300

2.5 nm

Length [nm]

0.2 µm

0.4 µm

0.6 µm

0.8 µm

1 µm1 µ

m ~ 14° ~ 8°

(a) (b)

Figure 6.23: AFM image of ripple nanostructures on Si after Kr+ ion beam erosion (Eion = 1200 eV, αion =

15 deg). (b) Height profile along the line drawn in the AFM image showing the asymmetric form of ripples.

The arrows indicate the ion beam direction.

same sample. The HRTEM reveals very well aligned ripples having a homogenous height

of ~ 5 nm, and a separation of 50 nm in between. Also the asymmetric form of ripples

similar to the AFM cross section profile is clearly observed. Additionally the HRTEM

image reveals an amorphous layer covering the ripple surface. To this amorphous layer

contributes also an oxide layer forming due to the delay between sputtering and HRTEM

measurements. The thickness of the amorphous layer is ~ 6 nm and it depends on the ion

energy, ion incidence angle, and the ion species used. The surface amorphization is

expected because the total ion fluence used to sputter the surface is some orders of

magnitude higher than the amorphisation threshold. As reported by Gnaser for 2 keV Xe+

ions on Si, the threshold value is Φ ~ 1015 ions/cm2 [40] (details are discussed in Section

2.2).

Beneath the amorphous layer the surface is single crystalline with the corresponding

50 nm

FFT FFT

50 nm

FFT FFT

Figure 6.24: Cross-sectional HRTEM image of ripple patterns. The arrows give the direction of the ion

beam. Inset: The amorphous covering layer has a thickness of 6 nm. Also given are the FFT images

calculated from the amorphous respectively crystalline part of ripples.

69


200

nm

50 nm

100 nm

150 nm

200

nm

50 nm

100 nm

150 nm

0 50 100 150 200 250

10 nm

Length [nm]

(a) (b)

Hei

ght

[nm

]

Figure 6.25: A magnified image of dot nanostructures on Si after Kr+ ion beam erosion with Eion = 1000 eV

and αion = 75 deg. (b) Height profile along the line drawn in the AFM image showing the sinusoidal-like form

of dots. The AFM image and the cross-section profile graph have an one to one aspect ratio.

lattice parameter for Si (0.543 nm). The FFT images deduced from the inset (Fig. 6.24)

clearly show that the upper layer is amorphous, while the layer beneath reveals a

crystalline structure. Further, the HRTEM image indicates a strong correlation on the shape

of ripples between the amorphous layer a-Si and the crystalline interface c-Si.

Fig. 6.25 shows a magnified AFM image of dot nanostructures evolving on Si with

similar conditions like in Fig. 6.16(c). The cross section (solid line) displays the sinusoidal

like form of dots. The dots have an average height of up to 10 nm and a 40 nm separation

in between. The sinusoidal form of dots can be supplementary verified from the HRTEM

cross-section measurements (Fig. 6.26). The HRTEM analysis gives a separation between

dots ~ 37 nm and a dot height of ~ 9 nm. Similar to ripples the dot surface is covered with

a thin amorphous plus oxide layer. The thickness of the amorphous layer it varies from

2 nm on the valleys up to 3.5 nm on the top of dots. This depends on the variations of the

local surface angle.

HRTEM investigations on Ge structures were also performed. In Fig. 6.27 an example

for the dot structures evolving at 20 deg ion incidence (see Section 7.1.2) is given.

3.5 nm

2 nm

Figure 6.26: Cross-sectional HRTEM image of dot structures with a height of ~ 9 nm and a separation of ~

37 nm. Inset: The anisotropic distribution of the amorphous layer is highlighted.

70

6.3: Geometrical Shape

Figure 6.27: A cross-sectional HRTEM image showing the crystalline structure of a dot on Ge covered with

an amorphous layer.

Similar to Si the surface is covered with ~ 6 nm amorphous layer, and the dots have a

height of ~ 4 nm.

Additionally, the HRTEM image of ripples (shown in Fig. 6.9) reveals a homogeneous

structure with ~ 5nm height and an amorphous layer of ~ 8 nm (Fig. 6.28). The distance

between ripples is ~ 60 nm. The asymmetry of ripples is less pronounced than in the case

of Si.

Figure 6.28: Cross-sectional view of ripple structures on Ge samples. The surface is covered with an

amorphous layer.

71


72

6.4 GISAXS and GID

The main aim of GISAXS and GID investigations was to study the periodicity, ordering

and lateral correlation of nanostructures. Furthermore, the investigation of nanostructures

with GISAXS and GID provides a much better statistics compared to AFM. This because

the scattered intensity is an average over the beam spot illuminating the surface that can be

up to some millimeters in size (spot size in the experiments was 200 µm × 100 µm in width

and few millimeters along the beam spot on the sample surface). As given in Section 4.2.3,

GISAXS gives information about the size and correlation of nanostructures on the surface,

and is not sensitive to the crystalline structure. As it is known from the HRTEM

investigations, the nanostructures are composed of an amorphous layer covering the

crystalline part of nanostructures. Therefore, GID is used to deduce information about the

crystalline part of nanostructures by setting up the in plane angle to fulfill the Bragg

condition. While only the horizontal ordering of nanostructures is of interest the qy

component of the scattering vector is used for GISAXS plots. The qz component gives no

contribution for αi = αf = constant [111]. For discussing the experimental results, and

especially the lateral correlation length of nanostructures from the scattered intensity

spectra, certain theoretical models should be applied to the experimental data. Usually, in

small angle X-ray scattering the scattered intensity is given as a product (in the reciprocal

space) of the square of a form factor for a given object, and the correlation function

that describes the position of structures (i. e. the lateral ordering) [127,128].

)(qF

)(qC

)()()( 2 qqq CFI = (6.2)

For the fitting procedure the form factor of a cone is used (the expression is given in

Appendix A2). The shape of the cone can be influenced by varying the tilt angle and by

choosing a reasonable radius value comparable to the radius of structures obtained from

the HRTEM images. The ordering of ripples is described using the one-dimensional linear

paracrystal model (Eq. (A2.2)). While for dots, the hexagonal paracrystal model is used to

account also for the hexagonal arrangement of dots and for peaks having different

distances between them (Eq. (A2.4)) [127].

Theoretically, the ordering of nanostructures is generally discussed in the frame of two

models: a) The long range order (LRO) model that assumes perfect arrangement of

nanostructures inside a given domain independent of distance; b) The short range order

model (SRO) assuming a decreasing order with distance [111,116,129]. According to

Schmidbauer [111] by considering the auto-correlation function in real space the LRO

model gives equidistant intensity peaks with a constant width. For the SRO model, the

peaks are equidistant but the width increases in contrast to the intensity of peaks, which

decreases, with increasing number of peaks. In the reciprocal space the intensity profiles

6.4: GISAXS and GID

show equidistant peaks decreasing with increasing q for both models. However in the

case of LRO the peak width remains constant and can be expressed as:

(6.3)

here is the correlation length and it shows up to which length scale positional

(6.4)

ith σ being the standard deviation ean distance

ξπδ 2

=q

w

correlation of nanostructures is present. In the SRO model the peak width decreases and is

given by the relation deduced from Stangl et al. [130]

dqδ =

q 2)(σ

w of the m d between two neighboring

structures, i. e. the width of the first peak of the correlation function in real space. For

convenience with AFM studies, d will be substituted with .5 In this model for the

correlation length it follows

.2 2

3

σλξ = (6.5)

From (6.4) and (6.5) a relation between q and can be deduced

(6.6)

ll be shown from the experime d intensity plots below, the peak width

increases with peak number suggesting that the SRO model can be applied, i. e. the

ord

M. Detailed description of the

sam

.4.1 Ge

In Fig. 6.29 an example of the GISAXS spectra by varying the in-plane angle 2 for

Ge is given. The sample was sputtered with Xe+ ions using Eion = 2000 eV, at αion

=

.ξ

δ =q2 2π

As wi ntal scattere

ering of structures disappears gradually with distance.

The samples used for investigation with GISAXS and GID were previously treated in

the ion beam equipment and characterized with the AF

ples analyzed with AFM was already given in the previous sections. It should be

mentioned that, due to the time limit restrictions at the ESRF facility and well in advance

planning of the measurements, only few samples were investigated.

6

ripples in

5 deg and ion fluence Φ = 6.7 × 1018 cm-2 (Fig. 6.9). The scans are performed for two

azimuthal angles ω = 0° and 180°. The intensity spectra show multiple equidistant peaks

5 The mean separation of structures deduced from the AFM studies is denoted with λ and is equivalent

with d .

73


-0.16 -0.08 0.00 0.08 0.1610

2

104

106

108

1010

∆q

-q1 +q

1

ω = 0 ω = 180°

inte

nsit

y [a

.u.]

qy [Å

-1]

Figure 6.29: GISAXS scan of a Ge ripple sample (Eion = 2000 eV) for two azimuth angles (ω = 0° and 180°).

th(up to 8 order), appearing due to the high lateral ordering of ripples. The distance between

-1 6peaks ∆q = ± 0.0113 Å , equivalent with the position of the first order peak q1,

corresponds to a ripple wavelength q∆πλ /2= = 55 nm. The slight asymmetry in the

intensity profile between the scans at 0° and 180° is due to the slight asymmetric shape of

ripples. The high intensity of the cent a contribution of the specular beam and

the diffuse scattering coming from the lateral uncorrelated roughness, including short

spatial frequency corrugations observed on AFM images.

A comparison of GISAXS spectra, for ripples formed under different ion energies,

reveals a decreasing distance between peaks, i. e. an increa

ral peak is

se of the ripple wavelength with

increasing Eion (Fig. 6.30). However, the spectra show a slightly better ordering of ripples

with increasing Eion. A GID angular scan of samples at the vicinity of the )202( Bragg

reflection (along the ]101[ crystallographic plane) displays equivalent results compared

with GISAXS (Fig. 6.30). This indicates that surface ripples correlate quite well with the

crystalline part of rip However, in the GID spectra the number of multiple peaks

decreases more rapidly with decreasing ion energy compared to GISAXS. This means the

crystalline part of ripples at 1200 eV is less ordered compared to the ripple surface. From a

comparison of the background intensities of GISAXS and GID spectra it seems that the

interface is more homogeneous compared to the surface (the GISAXS background

intensity has a more curved form compared to GID, for clarity see the graphs for

ples.

6 For the GISAXS and GID spectra with equidistant peaks the separation between peaks is equal with the

position of the first order peak. For this reason both notations will be used in the discussion. The situation

changes when the spectra have different peak separation like in the case of dot spectra.

74

6.4: GISAXS and GID

Figure 6.30: Comparison between GISAXS spectra and angular GID spectra of the )202( Bragg reflection

for different ion energies. Also given are the simulated curves using Eq. (6.4). The dashed lines (at Eion =

2000 eV) indicate the different background intensities of GISAXS and GID.

Eion = 2000 eV in Fig. 6.30).7

A summary of inter peak distances and their width, deduced from the GISAXS and GID

. The results show an increase of the ripple wavelength, for

bo

spectra is given in Table 6.1

th GISAXS and GID data, with ion energy similar to AFM results. However the values

deduced with small angle X-ray scattering methods are about 20 % smaller compared to

AFM. Further, the peak width q decreases with ion energy indicating an improved

ordering of ripples with Eion. For comparison the peak width deduced from the PSD spectra

(using AFM images) are given. Taking in account the low statistics due to the scan

101

105

109

101

105

109

101

105

109

1013

-0.12 -0.06 0.00 0.06 0.1210

1

105

109

q [Å-1]

101

105

109

GID

: int

ensi

ty/1

0 [a

.u.]

GIS

AX

S: i

nten

sity

[a.

u.] 10

1

105

109

1013

GISAXS qy

Eion

= 2000 eV

Eion

= 1500 eV

Eion

= 1200 eV

GID: qang

at (-220)

simulations

7 The roughness on the surface is higher than in the interface.

75


Table 6.1: The inter peak distances, peak width and the corresponding ripple wavelengths for GISAXS and

GID spectra for different samples are given. Also the wavelengths of ripples and the peak width deduced 8from PSD spectra of AFM images are given for comparison.

Eion ∆q

(eV) (Å-1) (Å-1) (nm) (Å-1)

qang -1)

λGID

(nm)

λAFM

(nm)

qPSD

(Å-1) y qy λGISAXS ∆qang

(Å

1200 ± 0.00186 ± 00.0127 48 0.0133 .00317 47 56 0.0011

1500 ± 0.012 0.00168 52 ± 0.012 0.00156 52 63 0.0010

2000 ± 0.0113 0.00162 56 ± 0.0115 0.00135 55 68 0.00107

ize limit in the AFM data, qPSD given in Table 6.1 are in the range of q values from the

ISAXS and GID data.

ations are performed using the expressions for the correlation

fun

orrelation lengths using Eq. (6.7). For comparison the mean height of ripples hAFM deduced from the AFM

(eV)

(nm) (nm)

GISAXS

(nm) (nm) (nm)

GID

(nm)

Rmean

(nm)

(deg)

h

(nm)

hAFM

(nm)

s

G

Additional to the experimental data, the corresponding simulated curves are also plotted

in Fig. 6.30. The simul

ction and the form factor of cone given in Appendix A2 and the assumption that the

peaks have a Gaussian distribution [111,131]. From the simulated curves the model

reproduces quite good the distance between peaks as well as the number of multiple peaks.

However, with this model the width of the first peak is underestimated by at least an order

of magnitude. Probably the short spatial frequency corrugations, the defects of ripples and

their asymmetry should be included in the model. Beside this, by analyzing the fitting

parameters listed in Table 6.2 the model seems to be a good approximation. Thus, the

fitting parameters for the form factor, the radius Rmean (base), the height h and the angle

of the cone (Fig. A2.2) correlate very well to the results deduced from AFM and

Table 6.2: The parameters used in the fitting procedure for GISAXS and GID data and the calculated lateral

c

images is given.

E GISAXλionS

SGISAXSSσ GID

Sλ GIDSσ

1200 47 3.1 5600 45 5.1 1700 15 10 2 2.5

1500 52 2.8 8600 53 3.7 5500 15 15 4 3.4

2000 56 2.8 11200 56 2.8 11200 20 15 5.3 4.2

8 Usually for data evaluation from the X-ray scattering techniques in the reciprocal space the Å-1 as a unit

is used, which is the case also here. However, for the rest of the data (including AFM data) the unit nm will

be used.

76

6.4: GISAXS and GID

HRTEM im ples in Ge. For comparison the m

im is o giv n T .2. th rre unction the waveleng f

nanostructures (chosen to c wi e e m lu nd siz ia σ

udies is presented in Fig. 6.32 with intensity peaks in

the

ages for rip

als

ean height deduced from AFM

lation fages en i able 6 For e co th o

oincide th th xperi ental va es) a the e dev tion

are used as fitting parameters. By changing the value of the size distribution parameter σ

the number of multiple peaks and their intensity vary simultaneously, i. e. they are related

to each other. The size distribution is in the range between 5 % and 7 %. With these values,

applying Eq. (6.5), the lateral correlation length is calculated. increases with Eion and

can reach up to = 11.2 µm for 2000 eV, which seems significantly high. Another

possibility to prove the validity of the SRO model is to plot the peak widths from the

measured spectra, as a function of q. This will be done on the example of the GID data for

Eion = 2000 eV. The data are fitted with multiple Gauss profiles (Fig. 6.31(a)) to determine

the peak width. The results are plotted in Fig. 6.31(b), and show an increase of the peak

width with peak number. With a quadratic fit to the data using Eq. (6.4) a standard

deviation σ = 3.3 nm is maintained. This value is very close to σ = 2.8 nm deduced from

the simulations. In general, from the above discussion the SRO model seems a good

approximation for predicting the main features of the experimental observations although

the correlation length is quite high.

Further, a two-dimensional scan of the crystalline part of ripples in the reciprocal space

using the GID geometry is done. By performing for example ω-scan for different 2 steps.

The scattering geometry for GID st

reciprocal space. From the geometry only scans at certain directions contribute to the

spectra with distinguished intensity peaks. Fig. 6.33 shows a GID map performed for

ripples in Ge along the (220) and )202( Bragg reflections. The maps are recorded for the

sample sputtered at Eion = 1500 eV. The distance between the intensity peaks in the

reciprocal space corresponds to the ripple wavelength. By comparing the maps with the

Figure 6.31: a) Multiple Gaussian fit of the experimental data from Fig. 6.23 for Eion = 2000 eV. b) Peak

widths deduced from the Gaussian profiles as a function of qang and the fitted curve using Eq. (6.4).

-0.10 -0.05 0.00 0.05 0.1010

2

103

104

105

106

a) GID: Exp. data Gauss fit

inte

nsit

y [a

.u.]

qang

[Å-1]

-0.10 -0.05 0.00 0.05 0.10

0.000

0.005

0.010

0.015

0.020

b)

σ = 3.3 nmξ = 7.6 µm

GID: Exp. data fit using Eq. (6.4)

δq [

Å-1]

qang

[Å-1]

77


)202(

)220(

)022(

qrad

qang

x

y

Figure 6.32: Drawing of the scattering geometry in the reciprocal space. The scattered intensity is collected

using the radial scan for the )220( and the angular scan for the )202( , respectively )022( Bragg reflection.

ig. 6 arall

respectively perpendicular to

scattering geometry in F .32, the intensity peaks appear almost p el to the (220),

)202( . The misalignment of peaks by 5 deg and 85 deg,

l spectra for

the

Figure 6.33: Reciprocal space maps recorded for ripples in Ge (Eion = 1500 eV) using the GID geometry at

(220) respectively

corresponds to the misalignment of ripples with respect to the crystallographic planes. This

supports the fact that the ripple formation is dictated by processes that take place in the

surface and near surface region, and not from the crystallographic orientation.

As will be discussed in Chapter 7 dot patterns showing a large area hexagonal lateral

ordering form on Ge surfaces. Fig. 6.34 shows the GISAXS and GID radia

se dots. The GISAXS data are performed for two different azimuth angles ω = 0° and

30°. The first peak for all scans appears at ±=== °° 1rad

301y

01y qqq 0.0148 Å-1 representing the

)202( Bragg reflection. The lines are to visualize the misalignment of ripples with respect

to the crystallographic plane.

-0,04 -0,02 0,00 0,02 0,04

-0,04

-0,02

0,00

0,02

0,04

qy [Å

-1]

q x [Å

-1]

4E3

2E4

6E4

(220)

5 deg

-0,04 -0,02 0,00 0,02 0,04

-0,04

-0,02

0,00

0,02

0,04

qy [Å

-1]

q x [Å

-1]

4E3

1E4

5E4

(-220)

85 deg

78

6.4: GISAXS and GID

mean separation of dots = 43 nm which is close to = 46 nm obtained from the PSD

spectra using AFM images. The second peak, for ω = 0° scan, appears at

0.0297 Å-1 and is a multiple (double) of the first one. For ω = 30° the second peak ±=°02yq

appears at ±== °° 301y

302y q)2/3(2q

ee inset in Fig.

0.0255 Å-1 which is characteristic for a hexagonal dot

lattice (s 6.34). Furthermore, the third peak at

±== °° 301y

302y q)2/3(3q 0.0386 Å-1 is visible. The hexagonal ordering of dots is observed

Figure 6.34: Experimental and simulated data for dots on Ge (Eion = 2000 eV, αion = 20 deg) using GISAXS

at azimuth angles ω = 0° and 30° and GID at (220) Bragg reflection. Inset: schematic drawing of a

reciprocal lattice point showing the hexagonal ordering.

-0.05 0.00 0.05

103

105

107

qrad

at (220)

simulated data

q [Å-1]

104

106

108

1010 q

y at ω = 30°

simulated data]

105

107

inte

nsit

y [a

.u.

1

1011 q

y at ω = 0°

simulated data0

9

ω = 30°ω = 30°

°0y2q

°0y3q

°−0

y2q

1radq 2

radq3radq

1radq−

2radq−

3radq−

°30y1q °30

y2q °303 yq

y1q− y1q °0°0

°−30

y1q°−30

y2q

yq1

79


Table 6.3: Fitting parameters used for the simulations and the calculated S. For comparison the mean

height hAFM deduced from the AFM images is given.

GISAXS and

GID spectra

Eion

(eV)

λS

(nm)

σS

(nm) S

(nm)

Rmean

(nm)

(deg)

h

(nm)

hAFM

(nm)

qy at ω = 0° 2000 41 4.2 3829 17 16 4.8

qy at ω = 30°

qrad at (220) 2000 48 2.2 10450 17 20 5.4

4.5

also for the crystalline part of dots by performing a GID scan at (220) Bragg reflection

(Fig. 6.34).

The experimental curves are simulated using Eq. A2.4 for the correlation function and

the cone form factor (Eq. A2.3). The parameters used for the fitting procedure are given in

Table 6.3. The simulated curve for ω = 0° fits well to the experimental data by predicting

the peak position, width and the number of peaks. For ω =30° and GID scans only the first

and second peak are reproduced but not the third peak. Additionally, the width of the first

peak is underestimated. From the fitting parameters a lateral correlation of dots up to

10 µm is deduced comparable to that of ripples (Table 6.3). A large difference between

values for ω = 0° and ω = 30° is found. Probably a better model should be applied that can

predict the large area hexagonal ordering of dots.

6.4.2 Si

In Fig. 6.35(a,b) a GISAXS map of ripples on Si for two different ion energies is

presented. The samples are sputtered using Ar+ ions at αion = 15 deg and Φ =

Figu XS rippl mple gari e s red f erent ne

1200 . Th anned differ uth s ω. eaks equ nt

spacing with a) ∆q = ± 0.0141 Å and b) ∆q = ± 0.0101 Å. The central peak (white line) in the map is due to

the specular beam.

re 6.35: A GISA map of e sa s in lo thmic scal putte or diff ion e rgies a)

eV, b) 2000 eV e samples are sc for ent azim angle The p have idista

-0,060

-0, 00 0, 0,06

16

20

03 0, 03 -0,00

6 - 0, 0,06

8

16

32

0,03 0,00 03

4

8

12

qy [Å

-1]

ω [

deg]

4E3

2E5

24

ω [

1E7

deg]

4E3

2E5

2E7

a) b)

qy [Å]

80

6.4: GISAXS and GID

Tabl ce between peaks ∆q and the peak width q deduced from GISAXS and GID scans are

give e c w ngth ples r lso t lues d ed from the

PSD FM images are given.

E ∆q q λ ∆q q λ λ q

e 6.4: The distan

n together with th alculated avele of rip . For compa ison a he va educ

spectra of the A

ion

(eV) GID

(Å-1) GID

(Å-1) GID

(nm) y

(Å-1) y

(Å-1) GISAXS

(nm) AFM

(nm) PSD

(Å-1)

1200 ± 0.0142 0.00149 44 ± 0.0141 0.00186 45 47 0.00161

2000 ± 0.0103 0.00146 60 ± 0.0101 0.00165 62 64 0.00167

6.7 × 1018 cm-2. The scans are recorded for different azimuth angles ω. The intensity lines

along qy are clearly visible. The number of multiple lines proves the high lateral ordering

(alignment) of ripples. The maps indicate an improved ordering of ripples at Eion =2000 eV

compared to Eion =1200 eV, contrary to the results in Fig. 6.3. Additionally, there is an

asymmetry in the intensity distribution and the number of peaks. This confirms the

symmetric form of ripples similar to the AFM line profiles and HRTEM images. The

between intensity lines is equal to the ripple wavelength. A line profile for a

ω value (GISAXS in Fig. 6.36) gives a ripple wavelength of = 45 nm and =

62

From the map also the angular distribution of ripples can be deduced by taking a line

profile for a given qy value, and determine the FWHM of the peak (Fig. 6.36). This is done

by making a Gaussian fit to the experimental data. The angular distribution of ripples is

Fig 36: st ri for sa g a) K re

tak GI aps ven iffere uth an e nes aus of

the data.

0,9

1,2

1,5

a

distance

particular

nm, respectively. This corresponds quite good with the wavelength deduced from the

PSD spectra of AFM images (see Table 6.4).

ure 6.

en from

Angular di

SAXS m

ribution of

for a gi

pples

q

mples usin

nt azim

and b) A

gles ω. Th

r+, and c)

solid li

r+ ions. Th

are a G

e data a

sian fit y for d

0 80,0

0,3

0,6

16 24 32 40

Ar+: E

ion = 1200 eV, FWHM = 13 deg

Ar+: E


Kr+: E


Gaussian fit

nons

ity

ω [deg]

rmal

ized

inte

81


13 o 1 and de n V. Fig. 6.36 the angular

distribution, which is about 8 deg, for the sam 6.13(c), sputtered for

lar e s ed 1 m 120 , αio 15

r+ ions). A comparison of results indicates that the angular distribution of ripples

ecreases, i. e. their alignment increases, with ion fluence.

deg f r Eion = 200 eV 19 g for Eio

ple presented in Fig.

= 2000 e In

ger flu nces is al o present (Φ = .3 × 1019 c -2, Eion = 0 eV n = deg, with

K

d

Further, the crystalline part of ripples is studied for different crystallographic planes.

Examples of the measured spectra are given in Fig. 6.37 for )220( , )202( , and )022(

Bragg reflections. The scattering geometry for GID studies is presented in Fig. 6.32.

Results in Fig. 6.37 reveal no difference between the GID spectra measured at different

1010

1012

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

Figure 6.37: GID scans performed on different Bragg reflection planes for samples sputtered at different ion

energies. Also shown are GISAXS spectra deduced from Fig. 6.27 for comparison. The simulated curves are

plotted for two characteristic examples.

101

103

105

107

109

1011

qang

at (2-20)

qang

at (-220)

qang

at (-220)

inte

nsit

y [a

.u] 10

0

102

104

GISAXS

qang

at (2-20)

q [Å]

106

108

GISAXS

qrad

at (220)

qrad

at (220)

exp. data simulations

Eion

= 2000 eV

Eion

= 1200 eV exp. data simulations

82

6.4: GISAXS and GID

Table 6.5: Fitting parameters used for simulating the GID data near the )202( Bragg reflection.

Eion

(eV)

λS

(nm)

σS

(nm)

S

(nm)

Rmean

(nm)

(deg)

h

(nm)

hAFM

(nm)

1200 45 2.7 6250 20 13 3.5 2.5

2000 61 3.5 9264 22 15 5.3 5

reflection planes. In all measurements the asymmetry in the intensity distribution is visible.

The mean peak separation ∆q (for Eion = 1200 eV: ∆q = ± 0.0142 Å; Eion = 2000 eV: ∆q =

± 0.0103 Å) and the peak width coincide quite good with the GISAXS and AFM data

(Table 6.4). Using the same explanation like for Ge, the SRO model can be applied to

evaluate the experimental data. The simulations are performed on behalf of two examples

by using the experimental data of the )202( Bragg reflection for Eion = 1200 eV and

2000 eV, respectively. The fitting parameters used for the simulations are summarized in

Table 6.5. From Eq. (6.5) a lateral correlation of 6250 nm and 9264 nm is deduced,

respectively. Also the form factor fitting parameters have reasonable values compared to

the AFM height data. However the model can not predict the asymmetry of the

experimental data and the width of the first peak is narrower than the experimental one.

A question that usually rises is, if there is strain involved in the process of structure

formation? This can be addressed by analyzing the intensity contribution in GID geometry

by performing a radial scan qrad. The spectra along the (220) Bragg reflection for

Figure adial an of in Si 1200 g the rag tion cans

are per for 0 180 d

-0.2 -0.1 0.0 0.1 0.210

105

107

109

6.38: R

formed

GID sc

deg and

ripples

eg.

(Eion = eV) alon (220) B g reflec . The s

1

103

GID radial at (220) 0° 180°

sity

[a.

u.]

qrad

[Å]

Inte

n

83


ripples on Si (sputtered at Ei 1200 e plott n Fig. 6.38. The spectrum deg

indicates an asymm in the intensity peaks. If there would have been strain involved,

than by rotating the sample at 180 deg and perfor again same n one ould

rec ive the identical spectrum like for 0 deg. Obviously this is not the case. From this short

iscussion it seems that there is no strain involved in the process of structure formation

Figure 6.39: GISAXS and GID scans for Si samples sputtered for two different ion energies. GISAXS scans

performed for different azimuth angles ω. GID radial and angular scans are performed along the (400)

Bragg reflection. Also the simulated intensity curves for the GISAXS data are plotted.

on = eV) ar ed i at 0

etry

ming the sca sh

e

d

presented in this work.9

In Fig. 6.39 the GISAXS and GID spectra for dots in Si formed at αion = 75 deg are

plotted. The spectra reveal similar results for GISAXS and GID studies, i.e. the same

ordering is observed for the amorphous and the crystalline part of dots. The GISAXS

-0,06 -0,04 -0,02 0,00 0,02 0,04 0,0610

2

104

106

108

qy ω = 0 deg

qy ω = 18 deg

simulation

Eion

= 1000 eV

9 However, for a detailed investigation more experiments are needed. The best possible way would be to

perform in-situ measurements.

1010

1012

qrad

at (400)

qang

at (400)

qy ω = 0 deg

qy ω = 50 deg

simulations

Eion

= 2000 eV

qrad

at (400)

qang

at (400)10

9

1011

q [Å-1]

.]

-q2

-q1

+q2

+q1

-q2

-q1

+q2

+q1

107

inte

nsit

y [a

.u

105

84

6.4: GISAXS and GID

Table 6.6: Parameters about the mean distance between dots deduced from the experimental data using X-

ray scattering techniques and AFM are given. Also given are the parameters used for simulations.

Eion

(eV)

q1

(Å-1)

λ

(nm)

λAFM

(nm)

λS

(nm)

σS

(nm) S

(nm)

Rmean

(nm)

(deg)

h

(nm)

hAFM

(nm)

1000 ± 0.0178 35 35 34 4.6 928 15 25 7 8

2000 ± 0.0155 41 45 40 4.1 1903 17 35 11 10

scans, performed for different azimuth angles, deliver the same intensity profile indicating

the isotropic distribution of dots on the surface due to sample rotation during sputtering.

Also in the GID studies the intensity peaks are observed for both the radial and the angular

scan performed along the (400) Bragg reflection.10 The first side maximum appears at q1 =

qy = qrad = qang = ± 0.0178 Å for Eion = 1000 eV and at q1 = qy = qrad = qang = ± 0.0155 Å

for Eion = 2000 eV. The second peak position (q2 = ± 0.0288 Å for Eion = 1000 eV and q2 =

± 0.029 Å for Eion = 2000 eV) is between 12q representing a square lattice and 13q by

assuming a hexagonal lattice. This observations correlate with the AFM images where dots

are arranged in domains showing square respectively hexagonal ordering. The fitting

model used for dots on Si is applied on behalf of two examples on GISAXS data. The

model predicts the first peak position and the peak width. However, there are difficulties in

reproducing the second intensity peak. This is due to the overlap of the intensity

contributions coming from square respectively hexagonal domains of dots. The fitting

parameters together with the experimental values are summarized in Table 6.6. For

comparison also the wavelength and height from the AFM method are given. With this

model a lateral correlation length of dots up to 1.9 µm is obtained.

or dots the intensity peaks have an isotropic distribution.

10 For example, from Fig. 6.32, in the case of ripples a qang scan along the (220) Bragg reflection will not

provide intensity peaks. While f

85

Chapter 7

Pattern Transitions on Si and Ge Surfaces

Experimental results presented in Chapter 5 and Chapter 6 proved out the influence of

different ion beam parameters on the evolution of the surface topography on Si and Ge.

Particular attention was paid to the conditions were ripple and dot structures evolve. One

of the main demands on these structures is to maintain a large scale lateral ordering. As

will be shown in the next sections there are two parameters of the sputtering process that

contribute significantly to the achievement of such ordering: These are the ion incidence

angle and the secondary ion beam parameters. In Chapter 5, a general discussion of the

role of ion incidence angle on the surface topography is given. However small step

variations of αion show a completely new phenomenon present on the surface. Namely,

transition from ripples to dots. Additionally, the evolving dots have a large scale ordering.

This will be discussed in Section 7.1. Section 7.2 will deal with the role of beam

divergence and the angular distribution of ions within the ion beam on the surface

evolution. This quantity, neglected up to now in the studies for nanostructuring with ion

beam, plays a crucial role in surface evolution processes.

7.1 Role of Ion Incidence Angle

It is well known that the distribution of the deposited energy of ions hitting the surface

depends also on the incidence angle with respect to the surface normal. Consequently, the

amount of the material eroded, i. e. the sputter yield, depends on the ion incidence angle

(see Chapter 2). Therefore, it is expected that αion affects the surface topography. On the

other side, αion is important in order to compare the experimental results with the

continuum theory, describing the process of ripple formation. The results in Section 5.1

revealed that depending on αion, topographies like dots, ripples, and even smooth surfaces

are possible. The amplitude development of ripples and dots on αion was divided mainly in

three regions without discussing in detail the structures forming in these regions.

Indeed, the experimental results that will be presented below give a much more complex

picture of the surface topography with varying αion. Completely new phenomena are

observed, like transitions from ripples to dots. During this transition, there are αion values

where the evolving structures are almost perfectly laterally ordered on a large scale,

covering the entire sample. In the last part of this section the evolution of the wavelength

of ripples and dots with αion for both materials will be discussed. In this context, a

comparison with theoretical values will be performed. There will be a separate presentation

of results for Si and Ge to avoid confusion. The experiments were performed for the case

87

Chapter 7: Pattern Transitions on Si and Ge surfaces

with no sample rotation. As pointed out from the topography diagrams in Section 6.1 a

diversity of structures can evolve for different ion energies. Therefore in this section the

ion energy will be kept constant at Eion = 2000 eV (due to the higher amplitude the

structures posses at 2000 eV).

7.1.1 Influence of Ion Incidence Angle on Pattern Transition on Si

During the experiments, the Si surface is bombarded with Ar+, Kr+, Xe+ ions having an

ion energy Eion = 2000 eV, and ion fluence Φ = 6.7 × 1018 cm-2 (corresponding to 60 min

sputter time by an ion current density of jion ~ 300 µA cm-2). A summary of topographies

evolving for different αion, is given in Fig. 7.1.

(100) Si

αion

a) αion = 0°

c) αion = 23°b) αion = 5°

d) αion = 45° e) αion = 75°

500 nm500 nm

500 nm500 nm 500 nm500 nm

500 nm500 nm 1500 nm1500 nm

10 nm

0 nm

10 nm

0 nm

2 nm

0 nm

2 nm

0 nm

7 nm

0 nm

7 nm

0 nm

250 nm

0 nm

250 nm

0 nm

2 nm

0 nm

2 nm

0 nm

Figure 7.1: Surface topography on Si after Xe+ ion beam erosion without sample rotation, for different ion

incidence angles (Eion = 2000 eV, Φ = 6.7 × 1018 cm-2). The arrows indicate the ion beam direction.

88

7.1: Role of Ion Incidence Angle

At αion = 0 deg the surface is rather smooth with small hillocks.1 By changing the ion

incidence angle to 5 deg with respect to the surface normal the topography changes

completely (Fig. 7.1(b)), i. e. well ordered ripple patterns evolve on the surface. The wave

vector of ripples is parallel to the ion beam projection. By further increasing the ion

incidence angle this topography remains stable up to αion = 23 deg where a mixture of dots

and ripples is observed on the surface (Fig. 7.1(c)). This mixed topography is preserved

until at αion = 45 deg the surface smoothens (Fig. 7.1(d)). At grazing incidence of 75 deg,

columnar structures emerge on the surface. These structures form in the direction of the ion

beam, i. e. 90 deg rotated compared to ripples at near normal ion incidence, and the mean

size increases with ion fluence. However, these structures can not be identified as ripples.2

Below, the surface structures emerging around αion = 23 deg, will be analyzed in detail.

As Fig. 7.1(c) shows, at αion = 23 deg dot and ripple structures form simultaneously on the

surface. Ripples have a slightly curved form (compared to ripples at 5 deg) and are

interrupted by dots. The dots itself form mainly along the ripples, i. e. the alignment of dots

is dictated by the previous alignment of ripples. By increasing the ion incidence angle to

25 deg this coexistence of patterns is retained (Fig. 7.2). However a close look at the AFM

image reveals that ripples with different spatial orientations form on the surface. From the

AFM image three type of ripples can be distinguished. The first type are aligned

perpendicular to the ion beam projection. The other type of ripples make an angle different

500 nm500 nm

FFT8 nm

0 nm

8 nm

0 nm

αion = 25°, Eion = 2000 eV f = - 128 µm-1 … 128 µm-1

Figure 7.2: AFM image of coexisting ripple and dot structures on Si with ripples having different

orientations (Xe+, Φ = 6.7 × 1018 cm-2) (the black arrow indicates the beam projection). Also given is the

corresponding FFT image (white arrows point out the two distinct wave vectors).

1 In the case when Ar+ ions are used to bombard the surface under normal incidence (not shown here), dot

structures appear similar to those reported by Gago et al. [30,31]. 2 Detailed experimental studies show that, for low ion fluences ripples with the wave vector oriented

parallel to the ion beam projection evolve on the surface. Additional increase of ion fluence leads to gradual

formation of the columnar structures along the beam. Similar results have already been reported [132].

89


to the ion beam projection. The third type of ripples show a curved form. This is reflected

also on the corresponding FFT image showing peaks with two distinct orientations.

Additionally, the broad angular distribution of the first order spots in the FFT, that posses a

half circle form, is due to the contribution of curved ripples observed by AFM. By a further

increase of αion to 26 deg, the AFM image shows structures aligned mainly in two

directions that cross each other making an angle of 90 deg between them (in the one

direction ripples are still observed) (Fig. 7.3). It is interesting that both dominating

directions are rotated with respect to the ion beam projection. i. e. they are not

perpendicular or parallel to the ion beam projection. Along these directions dots having a

chain like form dominate the surface. The dots show an almost perfect lateral ordering,

with only few defects appearing at the same positions where previously ripple defects

existed (see Section 6.2). This is reflected on the FFT image (Fig. 7.3). The same distance

of the first order spots from the image center implies the same periodicity of dots in the

two directions. Further, the FFT indicates clearly the two wave vectors dominating the

surface with the same size, but oriented perpendicular to each other.

7.1.2 Influence of Ion Incidence Angle on Pattern Transition on Ge

The topography transition from ripples to dots is not only characteristic of Si but is also

observed on Ge. However, for increasing ion incidence angle, in Ge first there is a

transition from dots to ripples and then back from ripples to dots. Figure 7.4 shows the

surface evolution on Ge after Xe+ ion beam sputtering for different ion incidence angles

(Eion = 2000 eV, Φ = 6.7 × 1018 cm-2). The AFM image for normal incidence shows dot

structures evolving on the surface (Fig. 7.4(a)). The ring on the FFT image (in the inset),

500 nm500 nm

FFT

αion = 26°, Eion = 2000 eV f = - 128 µm-1 … 128 µm-1

Figure 7.3: An almost perfect square array of dots dominating the Si surface (Xe+, Φ = 6.7 × 1018 cm-2), the

black arrow indicates the ion beam direction. The corresponding FFT image reveals the square ordering of

dots (white arrows point out the two distinct wave vectors).

90


indicates the presence of dots with uniform size but with a rather poor lateral ordering. At

αion = 5 deg dot nanostructures disappear and well ordered ripples evolve on the surface

(Fig. 7.4(b)). The wave vector of ripples is aligned parallel to the ion beam projection. By

increasing the ion incidence angle to 10 deg ripples are still dominating the surface, but

they start to transform back into dots (Fig. 7.4(c)). Also ripples have a curved form,

reflected also in the FFT image (see inset) where the peaks posses a larger angular width.

Additionally, the FFT image shows a ring representative of dots on the surface. Further

increase of αion toward 20 deg (Fig. 7.4(d)) results in a complete transition of patterns from

ripples into dots. The dots have a hexagonal ordering covering the whole image area (in the

8 nm

0 nm

8 nm

0 nm

12 nm

0 nm

12 nm

0 nm

10 nm

0 nm

10 nm

0 nm

7 nm

0 nm

7 nm

0 nm

300 nm300 nm

400 nm

0 nm

400 nm

0 nm

2 nm

0 nm

2 nm

0 nm

a) αion = 0° b) αion = 5°

c) αion = 10° d) αion = 20°

e) αion = 45° f) αion = 75°

1000 nm1000 nm

300 nm300 nm

300 nm300 nm 300 nm300 nm

300 nm300 nm

Figure 7.4: Surface topographies on Ge after Xe+ ion beam erosion for different in incidence angles (Eion =

2000 eV, Φ = 6.7 × 1018 cm-2). The arrows give the ion beam direction. Inset: Corresponding FFT images

calculated from AFM images having 4 µm × 4 µm size.

91


FFT image six equidistant peaks are observed). Furthermore, the FFT image reveals that

ordering is more pronounced in the direction that previously ripples existed as seen from

the second order peaks observed in the direction of the incoming beam. At 45 deg the

surface remains smooth (Fig. 7.4(e)). Until at grazing incidence (αion = 75 deg) the

columnar structures form along the ion beam projection (Fig. 7.4(f)), with the same

characteristics like in Si.

A summary of surface topographies evolving for different ion incidence angles on Si

and Ge surfaces is given in Table 7.1. This Table is valid for the sputtering conditions

given in this section. By varying process parameters also the range of αion for a given

topography will change.

7.1.3 Discussion

In Section 5.1 the amplitude of structures in terms of the rms surface roughness with ion

incidence angle was discussed. Additionally, the wavelength of ripple and dot structures

with ion incidence angle can be analyzed, using the sputtering conditions presented in the

previous two sections. Experimental results concerning the wavelength of ripple and dot

nanostructures with ion incidence angle are summarized in Fig. 7.5 for Si and Ge samples.

From the plots, the wavelength decreases with αion for both Si (Fig. 7.5(a)) and Ge

(Fig. 7.5(b)). Results for different ions (Ar+, Kr+, and Xe+ for Si and Kr+ and Xe+ ions for

Ge) indicate that the wavelength evolution is independent of the ion species used. In

Fig. 7.5 the theoretical values of = (αion) are also plotted. These values are calculated by

considering ion-induced ESD and IVF as relaxation mechanisms, described in Section 3.1.

The calculated ESD values using Eq. (3.14) are an order of magnitude smaller than the

experimental data. The use of the ESD term implies an increase of wavelength with ion

incidence angle at least for Ar+ and Kr+ ions, while for Xe+ ions a marginal decrease is

observed.3 The IVF values are calculated using Eq. (3.18) by taking the surface energy

term = 1.05 J m-2 from Ref. [133] for Si and = 1.9 J m-2 from Ref. [21] for Ge. The

atomic density is equal to N = 5 × 1028 m-3 for both materials. For the thickness of the

Table 7.1: Summary of evolving topographies on Si and Ge surfaces with ion incidence angle.

Region Si (topography) Ge (topography)

I hillock (αion = 0 deg – 3 deg) dots (αion = 0 deg – 3 deg)

II ripples (αion = 4 deg – 22 deg) ripples (αion = 4 deg – 12 deg)

III ripples + dots (αion = 23 deg – 39 deg) dots (αion = 13 deg – 30 deg)

IV smooth (αion = 40 deg – 60 deg) smooth (αion = 31 deg – 60 deg)

V columns (αion = 65 deg – 75 deg) columns (αion = 65 deg – 75 deg)

3 The ESD coefficients in Eq. (3.12) depend on the ratio of the energy distribution parameters a, α and .

These parameters are deduced using the SRIM code, for Eion = 2000 eV.

92


0 20 400

3

6

9

40

60

80

100a)

ESD model

Xe+

Kr+

Ar+

/ / Ar+/Kr

+/Xe

+: exp. data

/ / IVF model: Ar+/Kr

+/Xe

+

wav

elen

gth

λ [n

m]


[deg]

0 10 20 30 400

3

6

9

40

60

80b)

Xe+: ESD model

Kr+: exp. data

Xe+: exp. data

Xe+: IVF model

wav

elen

gth

λ [n

m]


[deg]

Figure 7.5: Experimental and calculated values of as function αion using different ion species for Φ =

6.7 × 1018 cm-2, Eion = 2000 eV: a) Si, b) Ge.

amorphous layer a decreasing d with increasing ion incidence angle is expected. A

reasonable description of this decrease is by approximating the layer-thickness parameter

to a cosine function, i. e. d ~ d cos(αion). The IVF values predict quite good the

experimental data and the decrease of the wavelength with αion. Moreover, there is almost

no difference between the curves plotted for different ion species. For calculations of IVF,

the r is used as a fitting parameter. The IVF values are calculated by taking the viscous

relaxation term r = 4 × 1024 N m-2 cm-2 for Si and r = 2 × 1024 N m-2 cm-2 for Ge.4 From

these values, using the expression = r/jion with jion = 300 µA cm-2 a viscosity coefficient

Si = 2.13 × 109 N s m-2, respectively Ge = 1.07 × 109 N s m-2 is deduced. The relaxation

terms r have the same order of magnitude as the values presented in Ref. [21]. But, due to

the high fluxes used in this work, the viscosity coefficient has values that are two orders

of magnitude smaller than those reported in the same reference. The above discussion

suggests that ion induced viscous flow is more reliable to describe the evolution of the

wavelength with ion incidence angle.

In summary, the results in Section 7.1 indicate the importance of ion incidence angle on

the evolution of the surface topography. Depending on ion incidence angle a complexity of

different topographies can evolve on the surface. The most important conclusions of the

above discussion concerning ripples and dots are:

i) The ripple-dot transition for Si and dot-ripple dot transition for Ge are caused by

small variations of the ion incidence angle.

ii) The transition is continuous and there are conditions at which a coexistence of both

structures is possible. As shown in Section 6.2 this coexistence remains even for

4 The relaxation term r was used as a fitting parameter during the calculations until the IVF reached

values comparable to the experimental one.

93


large fluences, indicating that these mixed topographies are not meta-stable that

would eventually lead to the domination of one type of structures over the other.

iii) During the transition from ripples to dots, the former serve as a guide for the lateral

ordering of dots.

iv) Although there is a preferred orientation of the ion beam given by the ion incidence

angle structures having isotropic lateral distribution evolve on the surface, at least

on Ge. Additionally, the dominant directions of laterally square ordered dots on Si

are different from that of the ion beam projection.

v) Ripple structures on both materials evolve at ion incidence angles just a few

degrees off the surface normal. This is in contrast to the discussion in Ref. [134]

that implies a ripple inhibition for incidence angles up to 25 deg. Moreover, in

other studies up to now ripple formation is reported for incidence angles between

35 deg and 70 deg. Our experimental results show that exactly in this region the Si

and Ge surfaces remain smooth.

It is obvious that due to different sputtering conditions used to create structures different

results are obtained by various research groups. In this context one very important

parameter not considered up to now, is the characteristics of the ion beam itself. This will

become more clear in the next section.

7.2 Role of Secondary Ion Beam Parameters on the Surface Topography

As already discussed in Section 4.2, there is a number of ion source and beam extraction

parameters that can influence the angular distribution of ions within the ion beam and the

beam divergence [81-84,86,87,92,135,136]. One of the most important parameters that

influences the angular distribution of ions within the ion beam is the acceleration voltage

Uacc applied at the second grid of the broad beam ion source (Fig. 4.2). Throughout this

work, this parameter was kept constant at Uacc = 1000 V.5 As shown in Section 4.1.2 the

increase of Uacc results in an increase of the angular distribution of ions within the beam

and the beam divergence (Fig. 4.4(d-f).6 In this section, the specific role of Uacc on the

surface topography will be discussed in detail. Beyond this, the geometrical parameters of

the ion-optical system will be kept constant to avoid additional influence on the angular

distribution and the beam divergence.7 Eventually, the plasma will be treated as given, i. e.

without discussing plasma properties like plasma density and plasma sheath boundary.

5 This value was taken due to the higher amplitude the structures show at Uacc = 1000 V. Details will be

given below. 6 The impact of Uacc on the beam divergence is valid for the particular ion-optical system. 7 For example, experimental studies show that the transition from ripples to dots, on Si and Ge, for Uacc =

1000 V will happen for larger ion incidence angles by increasing the distance between grids.

94

7.2: Role of Secondary Ion Beam Parameters on the Surface Topography

7.2.1 Secondary Ion Beam Parameters vs. Ion Incidence Angle

Examples for the impact of Uacc on Si and Ge surfaces are given in Fig. 7.6. On Si at Uacc =

200 V dots arranged in chain like form on the surface and by increasing Uacc to 1000 V the

surface is dominated by ripples (Fig. 7.6(a,b)). For Ge, the AFM images show a transition

from smooth to a ripple surface (Fig. 7.6(c,d)). However, a thorough investigation reveals

that the influence of Uacc on the topography is much more complicated, especially if one

studies the behavior of Uacc for different ion incidence angles αion. Such an example is

presented in Fig. 7.7 for Ge. The TD shows the influence of Uacc on the surface topography

for different ion incidence angles. The samples were sputtered with Xe+ ions at Eion =

2000 eV and Φ = 6.7 × 1018 cm-2. The TD presents a complex picture of the surface

topography. In addition to the influence of ion incidence angle also by varying the Uacc a

topography transition can be obtained. This transition is, however, present only at certain

range of ion incidence angles. For example, for αion = 5 deg, topography transitions from

smooth to dots and from dots to ripples are observed with increasing Uacc. Further, for low

Uacc values and independent of αion, the surface remains smooth. Whereas with increasing

αion this parameter region increases to larger Uacc until the surface topography is not

influenced by Uacc.

The boundaries (doted lines) on the TD are guides to the eye used to distinguish

between different topography regions similar to the explanation in Section 6.1.

a) αion = 20°, Uacc = 200 eV

500 nm500 nm

3 nm

0 nm

3 nm

0 nm

7 nm

0 nm

7 nm

0 nm

500 nm500 nm

2 nm

0 nm

2 nm

0 nm

10 nm

0 nm

10 nm

0 nm

500 nm500 nm

500 nm500 nm

b) αion = 20°, Uacc = 1000 eV

c) αion = 10°, Uacc = 200 eV d) αion = 10°, Uacc = 1000 eV

Figure 7.6: Surface topography on Si and Ge surfaces for different extraction voltages during Xe+ ion beam

erosion (Eion = 2000 eV, Φ = 6.7 × 1018 cm-2) without sample rotation: Si (a,b); Ge (c,d).

95


0 5 10 15 20 25 30 35

200

400

600

800

1000

parallel mode ripples

ripples

+ dots

dots

smooth surface

acce

lera

tion

vol

tage

Uac

c [V

]


[deg]

Figure 7.7: Topography diagram for Ge surfaces for different acceleration voltages Uacc and ion incidence

angles αion. The presented results are for Xe+ ions with Eion = 2000 eV, Φ = 6.7 × 1018 cm-2, without sample

rotation. The symbols represent the experimental data. - smooth surfaces, - parallel mode ripples +

dots, - parallel mode ripples, and - dots.

Similar investigations were performed on Si surfaces using the same sputtering

conditions like for Ge. Here topographical transitions are also observed, however, the

boundary positions between different parameter regions vary compared to Ge. This can be

attributed to the differences in material properties. The TD in Fig. 7.8 shows that the

0 5 10 15 20 25 30 35 40 45

200

400

600

800

1000

smoothdots

ripples + dotsparallelmoderipples

hill

ock

feat

ures

acce

lera

tion

vol

tage

Uac

c [V

]


[deg]

Figure 7.8: Topography diagram for Si surfaces for different Uacc and αion. The results are given for Xe+ ions

at Eion = 2000 eV, Φ = 6.7 × 1018 cm-2, without sample rotation. The symbols represent the experimental

data. - smooth surfaces, - parallel mode ripples + dots, - parallel mode ripples, and - hillock

structures.

96


topography is not influenced too much by the Uacc, at least for small ion incidence angles.

However, at angles between 20 deg and 40 deg a topographical transition is present, from

(ripple + dot) to a dot structure and for lower Uacc the surface smoothens.

It is important to state that this topography transitions are continuous. Thus, between the

ripple and dot parameter regions there is an intermediate region, where ripples and dots

coexist together. By crossing over from a parameter region where structures form a smooth

one the amplitude of structures, i. e. the surface roughness, decreases gradually until the

surface remains smooth.

As next, the rms surface roughness, i. e. amplitude of structures, with Uacc is studied.

The results are plotted in Fig. 7.9 for Si and Ge surfaces, at different ion incidence angles.

In general, one observes an increase of the surface roughness with increasing Uacc for both

materials. At 45 deg the surface topography is independent of the Uacc value. In the case of

Ge, for all incidence angles the surface roughness takes the same value for Uacc = 200 V.

Further, the overall surface roughness decreases with ion incidence angle.

The influence of the acceleration voltage on the dot structures forming on Si surfaces at

grazing incidence (75 deg, SR) is also investigated. An example is given in Fig. 7.10 where

AFM images showing the surface topography after Kr+ ion beam sputtering of Si surfaces

with Uacc = 200 V and 1000 V are depicted. In this case, the Uacc has an impact on the

lateral ordering of dots, i. e. with increasing Uacc the ordering of dots is improved, visible

in the AFM image. Additionally, the long wavelength modulations are suppressed with

increasing Uacc.

7.2.2 Secondary Ion Beam Parameters vs. Ion Energy

The above results are presented for a constant value of Eion. However, if both

parameters Uacc and Eion are varied simultaneously, then the overall picture is even more

complicated. Examples of the surface topography for Ge using Xe+ ions, are given in

200 400 600 800 10000,0

0,5

1,0

1,5

2,0

2,5a) Si

αion

= 45 deg

αion

= 34 deg

αion

= 27 deg

αion

= 20 deg

αion

= 5 deg

rms

roug

hnes

s w

[nm

]

Uacc

[V]

200 400 600 800 10000,0

0,5

1,0

1,5

2,0

2,5b) Ge

αion

= 45 deg

αion

= 27 deg

αion

= 20 deg

αion

= 5 deg

rms

roug

hnes

s w

[nm

]

Uacc

[V]

Figure 7.9: The dependence of surface roughness on Uacc, deduced from the experimental data presented in

the topography diagrams. The results are plotted for different ion incidence angles: a) Si, b) Ge.

97


30 nm

0 nm

30 nm

0 nm

20 nm

0 nm

20 nm

0 nm

500 nm500 nm 500 nm500 nm

a) Uacc = 200 eV b) Uacc = 1000 eV

Figure 7.10: AFM images of Si surfaces after sputtering with Kr+ ions at Eion = 1000 eV, grazing incidence

of αion = 75 deg, Φ = 6.7 × 1018 cm-2 for different acceleration voltages.

Fig. 7.11. The TD are plotted for two ion incidence angles: a) 5 deg and b) 20 deg. From

the TD it can be seen that:

i) The dependence of the surface topography on Eion is influenced by value of Uacc, or

vice versa.

ii) There is a parameter region in which a change in orientation of ripples is observed

with increasing Eion (Fig. 7.11(a)).

iii) In Fig. 7.11(a) with increasing Uacc at αion = 5 deg a transition from dots to ripples

is evident.

iv) For αion = 20 deg the opposite transition is observed, namely from ripples to dots

with increasing Eion.

500 1000 1500 2000200

400

600

800

1000

smooth

parallelmoderipples

ripples+ dots

dots

acce

lara

tion

vol

tage

Uac

c [V

]

ion energy Eion

[eV]

500 1000 1500 2000200

400

600

800

1000

ripples + dots

perpendicular mode ripples

parallel mode ripples

dot structures

smooth surface

acce

lera

tion

vol

tage

Uac

c [V

]

ion energy Eion

[eV]

a) Ge, Xe+, αion = 5 deg b) Ge, Xe+, αion = 20 deg

Figure 7.11: Topography diagram for structures on Ge surfaces by varying Uacc for different Eion and for two

αion. The symbols indicate the experimental data. - smooth surfaces, - perpendicular mode ripples, -

parallel mode ripples + dots, - parallel mode ripples, and - dots.

98


7.2.3 Summary

The above discussion underlines the importance of the secondary ion beam parameters

on the surface topography. By varying the beam characteristics, different topographies can

form on the surface. One important conclusion from the above results is the use of Uacc as

an additional parameter during the sputtering process for controlling the resulting surface

topography. The influence of Uacc is not only characteristic of Si and Ge surfaces, also on

III/V semiconductors an influence of Uacc was found [137].

The TD plots showed that with increasing beam divergence there is a transition from

dots to ripples. Similar transitions are observed by varying the ion incidence angle. In fact,

the Uacc influences not only the angular distribution of ions but also the effective angle of

ions arriving at the sample surface. In this way the variation of Uacc can be considered as

fine adjustment of ion incidence angle.

Furthermore, the dot-ripple transition with increasing Uacc on Ge, can be compared with

the ripple-dot transition observed with increasing Eion for Ge in Fig. 6.11. This would

correlate with the statement in Section 4.1.2, namely, that the beam divergence decreases

with increasing ion energy, i. e. the opposite of Uacc. Therefore, consideration of such

effects is important in order to explain the different topographical transitions.

The observed dependence of the structure formation on the Uacc is unique to the used

ion source and its plasma and ion beam properties. Other ion sources with other extraction

system geometries probably will produce other structure properties and dependencies.

To come to a comprehensive understanding of the impact of such secondary ion beam

properties on the structure formation more detailed experimental investigations are

necessary. However, in the theoretical models up to now, the inclusion of such parameters

is missing.

At the end, it is worth to mention that the above discussion would explain the different

results obtained from different research groups (and the difficulty to reproduce these

results) for nanostructures on Si and Ge surfaces [69,138-142].

99

Chapter 8

Comparison of Experimental Results with Theory

8.1 Bradley-Harper model and the Nonlinear Extension

A successful theory should be in position to predict the experimental findings and

explain the scaling behavior of sputtering parameters to each other. This task will be

addressed in this Chapter by comparing the experimental results with the continuum theory

presented in Chapter 3. Theoretically, the process of ripple formation is based on the

Sigmund’s linear collision cascade theory of amorphous targets. Bradley and Harper

making use of this theory showed that due to local variations in the surface curvature also

the sputter yield changes locally [61]. This curvature dependent sputtering leads to surface

roughness. On the other side due to the erosion process itself and the mobility of particles

there are different relaxation processes present on the surface.

Concerning roughness, the most important parameters are the coefficients Γx(αion) and

Γy(αion) given in Eq. (3.4) which determine not only the orientation of ripples but also their

wavelength. They depend on the local surface curvature and are completely determined by

the ion incidence angle and the distribution of the deposited energy parameters a, α and .

Following the discussion in Chapter 3 and the Appendix A1.1 for small ion incidence

angles, with respect to the surface normal, Γx(αion) < Γy(αion). In this case the wave vector

of ripples is along the x-axis i. e. parallel to the ion beam projection. With increasing αion

there is a value for which Γx(αion) > Γy(αion), i. e. the ripples change their orientation and

evolve along the y-axis (perpendicular to the ion beam projection). In Fig. 8.1 the Γx and Γy

coefficients as a function of αion for Si and Ge using Xe+ ions at 2000 eV are plotted. For

both materials a change in orientation of ripples at ~ 45 deg is expected. Monte Carlo

simulations of Koponen et al. [54] confirm this change in orientation that it happens

between 30 deg and 60 deg. At near normal ion incidence theoretical predictions agree

with the experimental results presented in this work, namely, the formation of ripples with

the wave vector parallel to the ion beam projection. However, in the experiments no

change in orientation of ripples with increasing αion is observed. Furthermore, a close

investigation of Si and Ge surfaces at 75 deg shows that for small ion fluences, ripples with

the wave vector parallel to the ion beam projection evolve on the surface.

One prediction of the linear BH model is the exponential increase of the amplitude of

structures with ion fluence. This is contrary to the experimental results presented in

Fig. 6.18 and Fig. 6.19. To account for these observations the nonlinear terms where added

to the BH model (see Section 3.2) and the Kuramoto-Sivashinsky continuum equation was

introduced [59,60]. A detailed description of the continuum equation and nonlinear

101

Chapter 8: Comparison of Experimental Results with Theory

0 20 40 60 8-0,6

-0,3

0,0

0,3

0

a = 2.85 nmSi: α = 1.83 nm β = 1.13 nm

a = 2.39 nmGe: α = 1.44 nm β = 0.9 nm

Γx

Γy

Γ x, Γy [

a. u

.]


[deg]

Figure 8.1: The evolution of the coefficients Γx and Γy related to curvature dependent sputtering as a

function of αion calculated from Eq. (3.4) for Si and Ge (Xe+ ions at Eion = 2000 eV). Also given are the

energy distribution parameters determined with the SRIM code.

parameters is given by Makeev et al. [66]. It is shown that the tilt dependent sputter yield

parameters, x and y, of the nonlinear part of the KS equation, can be expressed by the

energy distribution parameters and αion. While y is always negative with αion, x can take

both positive and negative values. Numerical simulations of Park et al. [74] of Eq. (3.20)

showed that for low fluences the linear regime dominates the surface topography. In this

regime ripple structures form on the surface and the surface roughness increases. With

increasing ion fluence the nonlinear terms gain an importance and after a certain fluence

they dominate the sputtering process. This is accompanied by amplitude saturation of

ripples. Additionally, with further increasing fluence ripples disappear and either a new

type of ripples or kinetic roughening on the surface appears. This important conclusion of

the nonlinear theory is in disagreement with the experimental observations. Although the

amplitude saturation agrees with the experiments, the ripple topography remains stable for

fluences many orders larger than the amount needed for the amplitude to saturate (see

Section 6.1.2). The only difference between the evolution of ripples in the linear regime

and of the ripples in the nonlinear regime is the amplitude saturation. Furthermore, by

performing kinetic Monte Carlo simulations of Eq. (3.20) Brown et al. [132] showed that

the wave length of ripples increases with ion fluence. This is also not observed in

experimental studies.

Passing over to the ripple wavelength, given by Eq. (3.9), it is obvious that the value of

will depend on the type of the relaxation terms used to describe it. Below a summary of

these terms and their influence on will be given.

102

8.2: Surface Relaxation Mechanisms

8.2 Surface Relaxation Mechanisms

1. According to the BH model, by considering thermal diffusion as the main relaxation

mechanism, from Eq. (3.9) it follows

.~

2/1

⎟⎟⎠

⎞⎜⎜⎝

⎛Ja

D th

λ

rom Eq. (8.1) with the diffusion coefficient Dth being independent of ion flux, the

wa

urthermo

. Another relaxation mechanism is the ion induced effective surface diffusion ESD

rom (8.2) ESD is an increasing function of ion energy that agrees with the experimental

res . The scaling parameter m has a reasonable value, although

a larger energy range is needed to better determine this coefficient. Further, the flux

ind

d for Ar+, Kr+, and Xe+ ions

usi

(8.1)

F

velength is a decreasing function of the ion flux i. e. ~ 1/J1/2. This is not observed

from the experimental results, which show a rather independent of J. Concerning the ion

energy Eion, from Eq. (8.1) and making use of Eq. (2.8) we have mionE 2/1~λ , i. e. is a

decreasing function of Eion. This is also contrary to experiments. F re, no time-

dependent relaxation of ripples is observed after the ion beam is turned off. The above

discussion indicates that thermal diffusion can be ruled out as the main relaxation

mechanism for room temperature experiments presented in this work.

2

proposed by Makeev et al. [70]. It is temperature independent and can be described

completely from the energy distribution parameters (see Section 3.1 and Appendix A1.2).

By considering the symmetric case α = for simplicity,1 and assuming that the wave

vector of ripples lies along the x-axis the ripple wavelength is

(8.2)

.~~2

2 2

2/1

mion

x

xxESD Ea

S

D⎟⎟⎠

⎞⎜⎜⎝

⎛= πλ

F

ults presented in Section 6.1

ependent expression of ESD coincides with the experimental results in Fig. 6.21.

However, the value of the ripple wavelength is an order of magnitude smaller than the

experimental one. Also the ESD term, for the given sputtering conditions, predicts an

increasing wavelength with ion incidence angle as shown in Fig. 7.5 (for Ar+ and Kr+

ions). While the experiments show a decrease of with αion.

Another point to be discussed is the value of for different ion species. The

experimental results give a value of independent of used ion species, for the same

sputtering conditions. In Table 8.1 the ESD values calculate

ng Eq. (8.2) are given. The parameters a, α, and , are calculated for Eion = 1200 eV and

αion = 15 deg [48,123]. From the given values a difference up to 40 % between the

1 In the detailed discussion in Ref. [66] is concluded that there is no difference in the overall qualitative

results between the symmetric and the asymmetric case.

103


Table 8.1: Calculated wavelengths of ripples for different ion species, and for different relaxation

processes (ESD and IVF). Parameters a, α, and were calculated using the SRIM code. Coefficients x and

Dx were calculated using Eq. (A1.3) and (A1.5).

Ion a α

species (nm) (nm) (nm) x

(nm)

Dx

(nm3)

λESD

(nm)

λIVF

(nm)

Ar+ 2.5 2 1.6 -0 9 0 .45 .332 7.54 44

Kr+ 2.2 1.6 1.1 -0.29 0.107 5.4 46

Xe+ 2.1 1.4 0.8 -0.18 0.037 4.02 49

[ ] .)(),(max

22

2/1

0⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

rionyionx

IVFY

Na

ηγ

αΓαΓπλ

wavelengths for Ar+ and Xe+ ions is observed, and indeed it decreases with increasing ion

ma s.

rize as follows:

y.

3. If ion induced viscous flow IVF is considered as the main relaxation mechanism than the

ripple wavelength can be expressed as (see Section 3.1):

hing by viscous flow is restricted to a layer of thickness d comparable with the ion

range in the solid a and the amplitude of structures, but much smaller than the wavelength

[29]. This condition seems more realistic to our experimental results. Further, as shown by

Brongersma et al. [143], the viscous relaxation rate r is independent of temperature in the

s

The above discussion, assuming ESD as the dominant relaxation process, can be

summa

i) The ESD mechanism agrees with the experiments concerning the ion flux and

the ion energ

ii) It disagrees concerning the wavelength value, ion incidence angle and the ion

mass.

(8.3)

with the viscosity coefficient given by = r/J. Eq. (8.3) is applicable for the case when

smoot

range from 90 K up to 300 K (the experiments presented in this work were performed at

room temperature), i. e. IVF is independent in the given temperature range. Additionally,

IVF is independent of the ion flux. Considering the dependence of IVF on Eion from Eq.

(3.19) it follows that, mionIVF E3~λ , i. e. it is an increasing function of ion energy.

Furthermore, the ripple wavelength is predicted quite good using the IVF mechanism.

Also, as shown in Table 8.1, there are minor changes of IVF by using different ion species.

Calculations of IVF for different αion show that it decreases with ion incidence angle similar

to experimental results. Although, the decrease is not so pronounced like in the

104

8.3: Other Models

experiments. However, as discussed in Section 7.1, the IVF values are deduced by using

the r as a fitting parameter.

8.3 Other Models

Another mechanism to

),,(

22

4

2

2

2

2

tyxy

h

x

hh

y

h

x

hh

t

h ηβαγ +⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∇+

∂∂

+∂∂

+−=∂∂

(8.4)

with

be considered is the shadowing effect [144,145]. Mostly

iscussed for thin film growth processes, it implies that certain regions on the surface

pared to other regions due to the shadowing effects from the

neighboring peaks. While for growth processes this would lead to surface roughening for

etc

8.5)

A detailed d aid on

eters α, and are different from the notations

used for the rest of the work). Here,

nd tilt dependent sputtering, and is a damping parameter [77,80] (coefficients a1x and a1y

are proportional to Γx and Γy, while a3x and a3y to x and y). From Eq. (8.5) it results that

d

receive less ions com

hing processes shadowing has the role of a smoothing mechanism [146]. The effect of

shadowing is stronger at grazing incidence angles, where the shadowing of the valleys is

higher.2 This mechanism may be behind the amplitude saturation observed for dots on Si,

at grazing incidence of 75 deg. For the columnar structures (Fig. 7.1(e) and Fig. 7.4(f)))

evolving on the surface in the case without sample rotation other effects (additional to

shadowing) may be identified. First due to the anisotropy given by the direction of the ion

beam an instability is initiated on the surface. As argued by Sigmund [42] once hills form

on the surface sputtering at the top of the hills is lower compared to the hill sides and

valleys. Additionally, due to the grazing incidence angle the ions are hitting the column

walls, the particle reflection will contribute additionally to the erosion of valleys. However,

additional theoretical simulations are necessary to verify the effect of shadowing on the

formation of structures.

Considering the experimental results shown in this work, it is worth to mention that

recently an anisotropic generalized version of a damped non-local Kuramoto-Sivashinsky

equation was proposed to model ion beam erosion under oblique ion incidence [147,148].

The equation has the form

(

escription of Eq. (8.4) is given in Ref. [147]. Here attention will be p

.3

3

x

y

a

a=β,

1

1

x

y

a

a=α

param (please note that these coefficients

α, describe the anisotropy due to surface roughening

a

2 Due to the nonlocal nature of the shadowing effect only numerical solutions are possible. Numerical

simulations of Drotar et al. [146] showed indeed that shadowing for etching processes can lead to smooth

surfaces. They showed also that the surface roughness saturates with ion fluence similar to our experimental

results.

105


106

Figure 8.2: Plotted m Fig. 8.1) as a

function of ion incid e curve.

the parameter ters, and as plotted in

.

fluences

hexagonally ordered dots are observed. With decreasing α below 0.95 (this value depends

on the ion fluence used) this topography transfers into well aligned ripples. An increase of

rtly in Section 5.2. Nevertheless, the observed transition

fro

0 20 40 60 80 100-10

0

10

20

is the parameter α (taken from the ratio of Γx and Γy coefficients fro

ence angle. The inset is given for better identifying the decrease of th

α depends on the ratio of the roughening parame

Fig. 8.2 (by taking the ratio of curves in Fig. 8 1) it decreases with αion. In their simulations

30

40

Si Ge

1.0

1.1

α =

Γx/Γ

y


[deg]

0 10 20 300.8

0.9

Vogel and Linz show that by varying the parameter α different topographies can evolve on

the surface. Explicitly, for α =1 at low fluences mounds are formed, while at high

the ion incidence angle enhances the anisotropy in curvature dependent sputtering and,

therefore, facilitates the formation of hexagonal dot patterns. These transitions are similar

to experimental results by identifying the parameter α with ion incidence angle. Further,

simulations in Ref. [147] predict a saturation of the surface roughness with ion fluence,

similar to experimental results.

By studying the impact of damping parameter it is shown that with increasing the

hexagonal ordering of dot structures increases. For even larger a previously patterned

surface passes over into a smooth surface. However, the origin of the damping mechanism

is still not known. Potential candidates are re-deposition processes as already suggested

[77,79] or, alternatively, self-sputtering by atoms or particles released by the sputtering

process itself, as discussed sho

m ordered dot pattern to smooth surfaces with increasing ion incidence angle, can be

explained by an enhanced damping which dominates over surface roughening by curvature

dependent sputtering.

Additionally, the behavior of can be compared with experimental results, for example,

with the parameter Uacc. As already shown in Section 4.1, an increase of Uacc results in an

increase of the angular distribution of ions and the effective angle of ions arriving on the

8.3: Other Models

sample surface. Further, in Section 7.2 it was shown that with increasing angular

distribution, the ordering of structures is improved, and the surface roughness increases.

Therefore, it can be stated that the increase of angular distribution has a similar effect to an

increase of the damping term. However, the results of Vogel and Linz are only preliminary

one. Further investigation are needed, especially to identify the physical origin of the

parameters introduced in this section.

107

Chapter 9

Conclusions

In this work a systematic experimental study of the surface topography evolution on Si

and Ge surfaces during low-energy ion beam erosion is presented. It was demonstrated that

ion beam erosion at low ion energies up to 2000 eV is very well suited for producing

nanostructured surfaces with sizes below 100 nm. Due to self-organization processes, and

for given sputtering conditions, these nanostructures show an almost perfect lateral

ordering covering the whole sample area under treatment. In this context a particular

interest is given to the formation of ripple and dot nanostructures on the surface. For the

sputtering experiments a home built broad beam ion source is used. The major part of the

work deals with the influence of different process parameters on the evolution, amplitude,

lateral size and ordering of these nanostructures. A detailed sample characterization have

been performed by means of atomic force microscopy and small angle X-ray scattering

techniques.

During the experimental investigations it was shown that there are a large number of

process parameters that influence the evolution of the surface topography. Explicitly, a

thorough study of the role of ion incidence angle, ion energy, ion fluence, and ion flux on

the evolution of ripples and dots is performed. These patterns are analyzed in terms of

surface roughness and wavelength (mean size) of nanostructures. Ion incidence angle

investigations, for the case without sample rotation, show ripple patterns with the wave

vector parallel to the ion beam projection evolving on the surface at near normal ion

incidence, comparable to theoretical predictions. However, experimental studies indicate

no change in orientation of ripples with increasing ion incidence angle, as the theory

predicts. Further, a detailed study shows transitions between ripples and dots by varying

the ion incidence angle. This behavior is similar for both materials Si and Ge.

The wavelength (mean size) of nanostructures can be controlled up to a certain range by

varying the ion energy from 500 eV up to 2000 eV, and in fact increase with increasing ion

energy. In this way the wavelength (mean size) of nanostructures can be varied between

30 nm and 70 nm. At the same time, the nanostructures maintain their lateral ordering. This

behavior of the wavelength with ion energy agrees with the theoretical model by

considering ion enhanced surface diffusion or ion induced viscous flow as the main

relaxation mechanisms. However, there are other completely new effects not accounted for

by the continuum theory, namely, the change in orientation of ripples on Si or the

transition from ripples to dots on Ge with increasing ion energy.

Temporal investigations of the evolution of ripples and dots showed that lateral ordering

of nanostructures increases with increasing ion fluence. At the same time the wavelength

of nanostructures remains constant with ion fluence. The independence of the

109

Chapter 9: Conclusions

wavelength with ion fluence is observed at different sputtering conditions. This

observations disagree with the theoretical model as shown from the simulations [74,132].

In the context of this work also the influence of ion mass (Ne+, Ar+, Kr+ and Xe+ ions)

on the surface evolution process is investigated. In general, in order that pattern formation

occurs the incoming ion should have at least the mass of the target material. Thus, no

patterns evolve on Si using Ne+ ions and for Ge using Ne+ and Ar+ ions. However, once

ripples and dots evolve on the surface their dynamics (wavelength, height, lateral ordering)

is not influenced by the ion mass. The independence of the wavelength value from the ion

mass implies ion induced viscous flow as the main relaxation mechanism.

Similar dependencies are observed also for dot structures evolving on Si surfaces at

grazing ion incidence with sample rotation.

In this work, for the first time it was shown that additionally to the ion beam parameters

also secondary ion beam parameters are crucial for the formation of nanostructures at least

on semiconductor materials. Explicitly, the role of the acceleration voltage applied on the

second grid that influences the angular distribution of ions within the beam and the beam

divergence is studied. This parameter is important for: i) the evolution of nanostructures on

the surface, and ii) the lateral ordering of nanostructures. In this way, an additional

parameter for controlling the process of nanostructure formation is introduced.

Another important result is that by combining the secondary ion beam parameter with

the ion incidence angle, at certain sputtering conditions, parameter regions are identified

where transitions between ripples and dots, or vice versa, exist. Especially the transition

from ripples to dots is of particular importance. Due to the previous existence of ripples the

evolving dots have an almost perfect lateral ordering covering the whole sample area.

These investigations show that ion beam sputtering is very well suited as an alternative

method to produce large area nanostructures on the surface. Although the process itself is a

stochastic one the evolving topographies show a remarkably high lateral ordering. The

formation of patterns on Si and Ge surfaces and previous reports on III/V semiconductors

show that this process is a general one. However, the adjustment of the sputtering

conditions to the particular material is very important.

110

Appendices

A1. Details of the Continuum Equation

A1.1 The A, B1, B2, C coefficients presented in Eq. (3.5) can be determined through

,22

422

22

22

24

4

4

32⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛

⎟⎠

⎜⎝= c

asc

aacs

aas

a

f

Fa

S x ββαβαααα

2⎞⎛ a

The general expressions of the coefficients are

(A1.3)

(A1.4)

(A1.1) ionβ⎝

ion

ion

aaB

aA

ααα

αα

2

2

2

2

1

2

cossin

sin

⎟⎟⎠

⎞⎜⎜⎛

+⎟⎠⎞

⎜⎝⎛=

⎟⎠⎞

⎜⎝⎛=

.2

1

cos

22

2

2

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

⎟⎠⎞

⎜⎝⎛=

αβ

αα

aaC

aB ion

A1.2 Makeev et al. using the local parameters of the surface morphology gave a detailed

description of the nonlinear noisy Kuramoto-Sivashinsky continuum equation [66]

22

4

4

4

4

4

2

2

2

2

0 yx

hD

y

hD

x

hD

y

hS

x

hSv

t

hxyyyxxyx ∂∂

∂−

∂∂

−∂∂

−∂∂

+∂∂

+−=∂∂

).,,(22

22

tyxy

h

x

h yx ηλλ

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

+ (A1.2)

,2

⎟⎠

⎜⎝

−=αf

S y

22 ⎞⎛ aFac

111

Appendices

⎩⎨ )21(4)23(

2 6446284sccscs

fx βαβαβα

⎧+−++= 24

1042

1024

10 aaaFcλ

,4222

⎬⎫

− fcs)21(2

48

12

22

42

4

42

⎭−⎟⎟

⎠

⎞⎜⎜⎝

⎛+−−

as

as

af

βαβαα

,2 242242

⎭⎬

⎩⎨ fccs

fy βαβαα

226

24

24 ⎫⎧

−−+=aaaFcλ

(A1.5)

(A1.6)

(A1.7)

(A1.8)

ith

⎩⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+++−−= 4

8

82

4

422

2

224

6

632

2

2

5

3

6341224

sa

fsa

ffca

fsa

fsa

f

FaDESD

xx ααααα

,10152106222

⎭⎬⎟⎟

⎠⎜⎜⎝

++⎟⎟⎠

⎜⎜⎝

−+ sfsfs 610

46

22222

2⎫⎞⎛⎞⎛ aaaa

cααααβ

a

,3 223 β cFa

DESD =24 2αfyy

,4

6

⎥⎤

⎟⎞

s 32

21

4

2

2

2

22

2

2

22

2

22

2

32

3

⎥⎦⎟⎠

⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎠⎞

⎜⎝⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

afs

ac

aa

fsa

fca

fsa

fa

FaDESD

xy

αααβ

ααα

β

(A1.9)

w

⎟⎟⎠

⎞⎜⎜⎝

⎛−

f

ca

f

JEpa22

24

2exp

2 βαπαβ; θsin=s ; θcos≡c and 2

2

22

2

2

)(sin)(cos θβ

θα

aaf +=≡F .

112

A2: The Model for GISAXS and GID Simulations

A2. The model for GISAXS and GID Simulations

The simulations performed on the GISAXS and GID data in Chapter 6.2 are based on

some assumptions. The first assumption to be made is the form factor belonging to a single

object. Next is the correlation function that describes the positions of structures and their

correlation to each other. There are sources where a detailed description of the fitting

model is given [111,116,127,128]. According to Lazzari the scattered intensity is given as

a product (in the reciprocal space) of the square of a form factor of a certain object

and the correlation function C that describes the position of structures (i. e. the

)(qF

)(q

ordering).

ripples the ordering is described by using the correlation function of the linear

pa

(A2.2)

where D0 =

(A2.1)

For

)()()( 2 qqq CFI =

racrystal model given by

)cos(4

1exp2

2

1exp1

2

1exp1

)(

02222

22

qDqq

qqC

⎟⎠⎞

⎜⎝⎛ −−⎟

⎠⎞

⎜⎝⎛ −+

⎟⎠⎞

⎜⎝⎛ −−

=σσ

σ

d = is the mean distance between structures and σ

2R

h

z

2R

h

z

is the mean distance

factor of a cone in the cartesian frame is given by the expression [127]

2.3)

ere R = Rmean = D0/2 is the cone radius at the base, α is the tilt angle (Fig. A2.1). The

he

Figure A2.1: Schematic sketch of a cone with characteristic parameters as used for the si ulations. , h, and

2R were taken as fitting parameters.

deviation.

The form

.)exp(

)tan(

)tan(

)tan(2),,,(

1

0

2

dziqzz

Rq

RqJz

RHRqFH

−⎟⎠

⎞⎜⎝

⎛−

⎥⎦

z⎢⎣

⎟⎠

⎞⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−= ∫

α

αα

πα

⎤⎡

(A

H

ight h of the cone is calculated using the relation h = Rmeantan(α). J1 is the first order

Bessel function. The same form factor is used for ripples and for dots. However, by

varying the angle α and the radius R the shape of the cone can be influenced. In the case of

ripples α and R are chosen in such a way that the cone takes a triangle shape (Table 6.2 and

m

113

Appendices

-0.12 -0.06 0.00 0.06 0.1210

-6

10-3

100

103

108

1010

1012

1014

F(q

,R,H

,α)

a)

Eion

= 1200 eV

Eion

= 1500 eV

Eion

= 2000 eV

C

(q)

q [Å-1]

-0.12 -0.06 0.00 0.06 0.12

10-2

10-1

100

101

102

108

1010

1012

F(q

,R,H

,α)

b) Eion

= 1200 eV

Eion

= 2000 eV

C(q

)

q [Å-1]

Figure A2.2: Correlation functions and form factors used for the fitting procedure for ripples: a) Ge, b) Si.

( ) ⎟⎟⎞

⎜⎜⎛

−= qiDq2

3expexp) 0

22πσ⎠⎝

qP (1

( ) ⎟⎠⎝⎞

⎜⎛−= qiDqqP

2

1expexp)( 0

222 πσ

s

able 6.5).

ween peaks are different. The expression is given by

(A2.4)

with probability distributions:

(A2.5)

(A2.6)

s and the form factors used for ripple

nd Si are given in Fig. A2.2 and Fig. A2.3.

6.4). While for dots the truncated shape of the cone is used by choosing larger angle value

(T

For dots the correlation function of the hexagonal paracrystal is used. This because the

distances bet

⎟⎟⎞

⎜⎜⎛ +

⎟⎟⎞

⎜⎜⎛ +

=)(1

Re)(1

Re)( 21 qPqPqC

⎠⎝ −⎠⎝ − )(1)(1 21 qPqP

The correlation function and dot simulations in Ge

a

-0.06 0.00 0.06

10-2

10-1

100

101

102

108

109

1010

1011

F(q

,R,H

,α)

b) Eion

= 1000 eV

Eion

= 2000 eV

C(q

)

q [Å-1]

-0.06 0.00 0.0610

-4

10-2

100

102

108

109

1010

1011

F(q

,R,H

,α)

a) GISAXS: ω = 0° GISAXS: ω = 30° GID at (220)

C(q

)

q [Å-1]

Figure A2.3: Correlation functions and form factors used for the fitting procedure for dots. a) Ge, b) Si.

114

List of Acronyms

AFM Atomic Force Microscopy

BH Bradley-Harper

ESD Effective Surface Diffusion

FFT Fast Fourier Transformation

FWHM Full Width at Half Maximum

GID Grazing Incidence Diffraction

GISAXS Grazing Incidence Small Angle X-ray Scattering

HRTEM High Resolution Transmission Electron Microscopy

ISA Ionenstrahlätzanlage

ISQ Ionenstrahlquelle

IVF Induced Viscous Flow

KS Kuramoto-Sivashinsky

LRO Long Range Order

NSR No Sample Rotation

PSD Power Spectral Density

rms Root Mean Square

SR Sample Rotation

SRIM Stopping and Range of Ions in Matter

SRO Short Range Order

TD Topography Diagram

115

Bibliography

Bibliography

[1] G. A. Prinz, Science 282, 1660 (1998).

[2] M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, 252 (1997).

[3] L. P. Lee and R. Szema, Science 310, 1148 (2005).

[4] C. A. Ross, Annu. Rev. Mater. Res. 31, 203 (2001).

[5] B. D. Terris, T. Thomson, and G. Hu, Microsyst. Technol. (2006).

[6] C. Teichert, Phys. Rep. 365, 335 (2002).

[7] M. Park, Ch. Harrison, P. M. Chaikin, R. A. Register, and D. H. Adamson, Science 276, 1401 (1997).

[8] M. V. Meli, A. Badia, P. Grutter, and R. B. Lennox, Nano Letters 2, 131 (2002).

[9] P. Haymann, C. r. hebd. séances Acad. sci. 248, 2472 (1959).

[10] H. Behner and G. Wedler, Surf. Sci. 160, 271 (1985).

[11] G. Carter, M. J. Nobes, and J. L. Whitton, Appl. Phys. A 38, 77 (1985).

[12] S. Rusponi, C. Boragno, and U. Valbusa, Phys. Rev. Lett. 78, 2795 (1997).

[13] M. V. R. Murty, T. Curcic, A. Judy, B. H. Cooper, A. R. Woll, J. D. Brock, S. Kycia, and R. L. Headrick, Phys. Rev. Lett. 80, 4713 (1998).

[14] S. van Dijken, D. de Bruin, and B. Poelsema, Phys. Rev. Lett. 86, 4608 (2001).

[15] O. Malis, J. D. Brock, R. L. Headrick, M. S. Yi, and J. M. Pomeroy, Phys. Rev. B 66 (2002).

[16] W. L. Chan, N. Pavenayotin, and E. Chason, Phys. Rev. B 69 (2004).

[17] G. Carter, M. J. Nobes, F. Paton, J. S. Williams, and J. L. Whitton, Radiat. Eff. Defect. S. 33, 65 (1977).

[18] S. W. MacLaren, J. E. Baker, N. L. Finnegan, and C. M. Loxton, J. Vac. Sci. Technol. A 10, 468 (1992).

116

Bibliography

[19] K. Elst, W. Vandervorst, J. Alay, J. Snauwaert, and L. Hellemans, J. Vac. Sci. Technol. B 11, 1968 (1993).

[20] J. B. Malherbe, CRC Crit. Rev. Solid State Mater. Sci. 19, 55 (1994).

[21] E. Chason, T. M. Mayer, B. K. Kellerman, D. T. McIlroy, and A. J. Howard, Phys. Rev. Lett. 72, 3040 (1994).

[22] G. Carter and V. Vishnyakov, Surf. Interface Anal. 23, 514 (1995).

[23] J. J. Vajo, R. E. Doty, and E. H. Cirlin, J. Vac. Sci. Technol. A 14, 2709 (1996).

[24] K. Vijaya Sankar C. M. Demanet, J. B. Malherbe, N. G. van der Berg, R. Q. Odendaal,, Surface and Interface Analysis 24, 497 (1996).

[25] Z. X. Jiang and P. F. A. Alkemade, Appl. Phys. Lett. 73, 315 (1998).

[26] J. Erlebacher, M. J. Aziz, E. Chason, M. B. Sinclair, and J. A. Floro, Phys. Rev. Lett. 82, 2330 (1999).

[27] S. Facsko, T. Dekorsy, C. Koerdt, C. Trappe, H. Kurz, A. Vogt, and H. L. Hartnagel, Science 285, 1551 (1999).

[28] F. Frost, A. Schindler, and F. Bigl, Phys. Rev. Lett. 85, 4116 (2000).

[29] C. C. Umbach, R. L. Headrick, and K. C. Chang, Phys. Rev. Lett. 8724 (2001).

[30] R. Gago, L. Vazquez, R. Cuerno, M. Varela, C. Ballesteros, and J. M. Albella, Appl. Phys. Lett. 78, 3316 (2001).

[31] B. Ziberi, F. Frost, T. Höche, and B. Rauschenbach, Appl. Phys. Lett. 87 (2005).

[32] B. Ziberi, F. Frost, Th. Höche, and B. Rauschenbach, Phys. Rev. B 72, 235310 (2005).

[33] S. Habenicht, W. Bolse, K. P. Lieb, K. Reimann, and U. Geyer, Phys. Rev. B 60, R2200 (1999).

[34] Yuh-Renn Wu A. Datta, and Y. L. Wang, Phys. Rev. B 63, 125407 (2001) 63, 125407 (2001).

[35] F. Frost, B. Ziberi, T. Höche, and B. Rauschenbach, Nucl. Instrum. Meth. B 216, 9 (2004).

[36] G. Carter and V. Vishnyakov, Phys. Rev. B 54, 17647 (1996).

[37] T. K. Chini, M. K. Sanyal, and S. R. Bhattacharyya, Phys. Rev. B 66 (2002).

[38] S. Hazra, T. K. Chini, M. K. Sanyal, J. Grenzer, and U. Pietsch, Phys. Rev. B 70 (2004).

117

Bibliography

[39] R. Behrisch, Sputtering by Particle Bombardment (Springer Verlag, Heidelberg, 1981, 1983).

[40] H. Gnaser, Low-Energy Ion Irradiation of Solid Surfaces (Springer, Berlin, 1999).

[41] P. Sigmund, Phys. Rev. 184, 383 (1969).

[42] P. Sigmund, J. Mat. Sci. 8, 1545 (1973).

[43] J. Lindhard, V. Nielsen, and M. Scharff, Mat. Fys. Medd. Dan Vid. Selsk. 36, No. 10 (1968).

[44] J. F. Ziegler, J. B. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985).

[45] M. Nastasi, J. W. Mayer, and J. K. Hirvonen, Ion-Solid Interactions: Fundamentals and Applications (Cambridge University Press, Cambridge, 1996).

[46] H. E. Schiott, Mat. Fys. Medd. Dan Vid. Selsk. 35, 3 (1966).

[47] K. B. Winterbon, P. Sigmund, and J. P. Sanders, Mat. Fys. Medd. Dan Vid. Selsk. 37, 14 (1970).

[48] W. Bolse, Mat. Sci. Eng. R 12, 53 (1994).

[49] Z. H. Lu, D. F. Mitchell, and M. J. Graham, Appl. Phys. Lett. 65, 552 (1994).

[50] Y. Kido and H. Nakano, Surf. Sci. 239, 254 (1990).

[51] W. Bock, H. Gnaser, and H. Oechsner, Surf. Sci. 282, 333 (1993).

[52] I. Konomi, A. Kawano, and Y. Kido, Surf. Sci. 207, 427 (1989).

[53] I. Koponen, M. Hautala, and O. P. Sievanen, Phys. Rev. B 54, 13502 (1996).

[54] I. Koponen, M. Hautala, and O. P. Sievanen, Phys. Rev. Lett. 78, 2612 (1997).

[55] M. Hautala and I. Koponen, Nucl. Instrum. Meth. B 117, 95 (1996).

[56] M. V. R. Murty, Phys. Rev. B 62, 17004 (2000).

[57] G. Carter, M. J. Nobes, H. Stoere, and I. V. Katardjiev, Surf. Interface Anal. 20, 90 (1993).

[58] G. Carter, M. J. Nobes, and I. V. Katardjiev, Vacuum 44, 303 (1993).

[59] R. Cuerno and A. L. Barabasi, Phys. Rev. Lett. 74, 4746 (1995).

[60] R. Cuerno, H. A. Makse, S. Tomassone, S. T. Harrington, and H. E. Stanley, Phys. Rev. Lett. 75, 4464 (1995).

118

Bibliography

[61] R. M. Bradley and J. M. E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988).

[62] M. Navez, D. Chaperot, and C. Sella, C. r. hebd. séances Acad. sci. 254, 240 (1962).

[63] G. Carter, V. Vishnyakov, and M. J. Nobes, Nucl. Instrum. Meth. B 115, 440 (1996).

[64] B. Ziberi, F. Frost, and B. Rauschenbach, Appl. Phys. Lett. 88 (2006).

[65] R. M. Bradley, Phys. Rev. E 54, 6149 (1996).

[66] M. A. Makeev, R. Cuerno, and A. L. Barabasi, Nucl. Instrum. Meth. B 197, 185 (2002).

[67] C. Herring, J. Appl. Phys. 21, 301 (1950).

[68] W. W. Mullins, J. Appl. Phys. 30, 77 (1959).

[69] E. Chason and M. J. Aziz, Scripta Materialia 49, 953 (2003).

[70] M. A. Makeev and A. L. Barabasi, Appl. Phys. Lett. 71, 2800 (1997).

[71] S. E. Orchard, Appl. Sci. Res. 11A, 451 (1962).

[72] T. M. Mayer, E. Chason, and A. J. Howard, J. Appl. Phys. 76, 1633 (1994).

[73] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986).

[74] S. Park, B. Kahng, H. Jeong, and A. L. Barabasi, Phys. Rev. Lett. 83, 3486 (1999).

[75] B. Kahng, H. Jeong, and A. L. Barabasi, Appl. Phys. Lett. 78, 805 (2001).

[76] R. M. Bradley and E. H. Cirlin, Appl. Phys. Lett. 68, 3722 (1996).

[77] S. Facsko, T. Bobek, A. Stahl, H. Kurz, and T. Dekorsy, Phys. Rev. B 69, 153412 (2004).

[78] H. Chaté and P. Manneville, Phys. Rev. Lett. 58, 112 (1987).

[79] Th. Bobek, Selbstorganisation von periodischen Nanostrukturen & Quantenpunkten durch Ionensputtern (Shaker Verlag, Aachen, 2005).

[80] M. Paniconi and K. R. Elder, Phys. Rev. E 56, 2713 (1997).

[81] H. R. Kaufman, J. J. Cuomo, and J. M. E. Harper, J. Vac. Sci. Technol. 21, 725 (1982).

[82] H. R. Kaufman and R. S. Robinson, Aiaa Journal 20, 745 (1982).

[83] M. Tartz, Ph.D. Thesis (2003).

119

Bibliography

[84] M. Zeuner, H. Neumann, F. Scholze, D. Flamm, M. Tartz, and F. Bigl, Plasma Sources Sci. Technol. 7, 252 (1998).

[85] M. Tartz, private comunication.

[86] D. Korzec, K. Schmitz, and J. Engemann, J. Vac. Sci. Technol. B 6, 2095 (1988).

[87] M. A. Ray, S. A. Barnett, and J. E. Greene, J. Vac. Sci. Technol. A 7, 125 (1989).

[88] M. Zeuner, J. Meichsner, H. Neumann, F. Scholze, and F. Bigl, J. Appl. Phys. 80, 611 (1996).

[89] E. K. Wahlin, M. Watanabe, J. Shimonek, D. Burtner, and D. Siegfried, Appl. Phys. Lett. 83, 4722 (2003).

[90] R. Becker and W. B. Herrmannsfeldt, Rev. Sci. Instrum. 63, 2756 (1992).

[91] M. Tartz, E. Hartmann, R. Deltschew, and H. Neumann, Rev. Sci. Instrum. 71, 678 (2000).

[92] M. Tartz, E. Hartmann, R. Deltschew, and H. Neumann, Rev. Sci. Instrum. 73, 928 (2002).

[93] G. Binning, H. Rohrer, C. Gerber, and E. Weibel, Phys. Rev. Lett. 49, 57 (1982).

[94] G. Binnig, C. F. Quate, and C. Gerber, Phys. Rev. Lett. 56, 930 (1986).

[95] http://www.asylumresearch.com/Reference/Bibliography.shtml.

[96] http://www.veeco.com/appnotes/.

[97] D. Sarid, Scanning Force Microscopy with Applications to Electric Magnetic, and Atomic Forces (Oxford U. Press, New York, 1991).

[98] S. N. Maganov and M.-H. Whangbo, Surface Analysis with STM and AFM (VCH, Weinheim, 1995).

[99] http://www.atomicforce.de/Olympus_Cantilevers/olympus_cantilevers.html.

[100] K. L. Westra, A. W. Mitchell, and D. J. Thomson, J. Appl. Phys. 74, 3608 (1993).

[101] K. L. Westra and D. J. Thomson, J. Vac. Sci. Technol. B 13, 344 (1995).

[102] F. Frost, D. Hirsch, and A. Schindler, Appl. Surf. Sci. 179, 8 (2001).

[103] J. M. Bennet and L. Mattson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington D. C., 1989).

[104] H. N. Yang, Y. P. Zhao, A. Chan, T. M. Lu, and G. C. Wang, Phys. Rev. B 56, 4224 (1997).

120

Bibliography

[105] P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, Europhysics Letters 22, 717 (1993).

[106] Y. Zhao, G.-C. Wang, and T.-M. Lu, Characterization of Amorphous and Crystalline Rough Surfaces: Principles and Applications (Academic Press, San Diego, 2001).

[107] “Standard Practice for Estimating the Power Spectral Density Function and Related Finish Parameters from Spectral Profile Data” (ASTM Standard F1811-97, 748-759, 1997).

[108] A. Duparre, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, Appl. Opt. 41, 154 (2002).

[109] http://www.esrf.fr/.

[110] http://www.esrf.fr/UsersAndScience/Experiments/SurfaceScience/ID01.

[111] M. Schmidbauer, X-Ray Diffuse Scattering from Self-Organized Mesoscopic Semiconductor Structures (Springer, Berlin, 2004).

[112] T. H. Metzger, I. Kegel, R. Paniago, and J. Peisl, J. Phys. D 32, A202 (1999).

[113] J. Stangl, V. Holy, G. Springholz, G. Bauer, I. Kegel, and T. H. Metzger, Mat. Sci. Eng. C 19, 349 (2002).

[114] J. Stangl, A. Hesse, T. Roch, V. Holy, G. Bauer, T. Schuelli, and T. H. Metzger, Nucl. Instrum. Meth. B 200, 11 (2003).

[115] J. Stangl, V. Holy, and G. Bauer, Rev. Mod. Phys. 76, 725 (2004).

[116] U. Pietsch, V. Holý, and T. Baumbach, High-Resolution X-Ray Scattering: From Thin Films to Lateral Nanostructures (Springer, New York, 2004).

[117] G. Carter, J. Phys. D 34, R1 (2001).

[118] M. V. R. Murty, Surf. Sci. 500, 523 (2002).

[119] M. Wissing, M. Batzill, and K. J. Snowdon, Nanotechnology 8, 40 (1997).

[120] F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, and A. Schindler, Appl. Phys. A 78, 651 (2004).

[121] F. Frost, R. Fechner, B. Ziberi, D. Flamm, and A. Schindler, Thin Solid Films 459, 100 (2004).

[122] G. Carter, V. Vishnyakov, Y. V. Martynenko, and M. J. Nobes, J. Appl. Phys. 78, 3559 (1995).

[123] J. P. Biersack F. Ziegler, and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985).

121

Bibliography

[124] F. Frost, private comunication.

[125] J. P. Biersack and W. Eckstein, Appl. Phys. A 34, 73 (1984).

[126] W. Eckstein, Computer Simulation of Ion-Solid Interactions (Springer-Verlag, Berlin, 1991).

[127] R. Lazzari, J. Appl. Crystallogr. 35, 406 (2002).

[128] http://www.esrf.fr/computing/scientific/joint_projects/IsGISAXS/isgisaxs.htm.

[129] M. Schmidbauer, M. Hanke, and R. Kohler, Phys. Rev. B 71 (2005).

[130] J. Stangl, T. Roch, V. Holy, M. Pinczolits, G. Springholz, G. Bauer, I. Kegel, T. H. Metzger, J. Zhu, K. Brunner, G. Abstreiter, and D. Smilgies, J. Vac. Sci. Technol. B 18, 2187 (2000).

[131] I. Kegel, T. H. Metzger, J. Peisl, P. Schittenhelm, and G. Abstreiter, Appl. Phys. Lett. 74, 2978 (1999).

[132] A. D. Brown, J. Erlebacher, W. L. Chan, and E. Chason, Phys. Rev. Lett. 95 (2005).

[133] S. Hara, S. Izumi, T. Kumagai, and S. Sakai, Surf. Sci. 585, 17 (2005).

[134] G. Carter, Phys. Rev. B 59, 1669 (1999).

[135] M. Tartz, E. Hartmann, F. Scholze, and H. Neumann, Rev. Sci. Instrum. 69, 1147 (1998).

[136] C. Huth, H. C. Scheer, B. Schneemann, and H. P. Stoll, J. Vac. Sci. Technol. A 8, 4001 (1990).

[137] B. Ziberi, F. Frost, M. Tartz, H. Neumann, and B. Rauschenbach, Thin Solid Films 459, 106 (2004).

[138] W. Fan, L. Lin, L.-J. Qi, W.-Q. Li, H.-T. Sun, Ch. Gu, Y. Zhao, and M. Lu, J. Phys.-Condens. Mat. 18, 3367 (2006).

[139] R. Gago, L. Vazquez, R. Cuerno, M. Varela, C. Ballesteros, and J. M. Albella, Nanotechnology 13, 304 (2002).

[140] J. Kim, D. G. Cahill, and R. S. Averback, Phys. Rev. B 67 (2003).

[141] F. Ludwig, C. R. Eddy, O. Malis, and R. L. Headrick, Appl. Phys. Lett. 81, 2770 (2002).

[142] J. E. Van Nostrand, S. J. Chey, and D. G. Cahill, Phys. Rev. B 57, 12536 (1998).

[143] M. L. Brongersma, E. Snoeks, and A. Polman, Appl. Phys. Lett. 71, 1628 (1997).

122

Bibliography

123

[144] R. P. U. Karunasiri, R. Bruinsma, and J. Rudnick, Phys. Rev. Lett. 62, 788 (1989).

[145] C. Roland and H. Guo, Phys. Rev. Lett. 66, 2104 (1991).

[146] J. T. Drotar, Y. P. Zhao, T. M. Lu, and G. C. Wang, Phys. Rev. B 62, 2118 (2000).

[147] S. Vogel and S. J. Linz, http://arxiv.org/abs/cond-mat/0509437.

[148] S. Vogel and S. J. Linz, Phys. Rev. B 72 (2005).

Acknowledgements

There are many persons who helped and supported me during these years, to whom I owe many

thanks. I apology from the beginning in order that I forget somebody. But, I'm in a hurry to catch

the deadline for submitting the work, before summer holidays.

I'm greatly thankful to my thesis advisor, Prof. Dr. B. Rauschenbach, for his readiness to accept

me as a Ph.D. student, for the support, and for the many helpful discussions.

My special thank goes to H. Neumann, Dr. M. Tartz, Dr. B. Faust, and F. Scholze for the very

useful discussions concerning ion sources. Including the technical support for the ion grid system.

Your discussions helped me to make a step further in understanding many tricks about the ion

sources. Additional thank to Michael for performing the very valuable simulations.

I thank Dr. T. Höche for performing the HRTEM measurements and Prof. Dr. U. Gösele for his

approval to perform the measurements at the MPI Halle.

My thank goes also to D. Hirsch and Dr. D. Flamm for their technical support with the AFM

and the ISA equipment, especially at the beginning of my work.

Further, my thank goes to Teresa Lutz, for helping me performing part of the thousands of

thousands of sputtering experiments and AFM measurements.

Many thanks to Dr. T. Metzger and Dr. D. Carbone from the ESRF in Grenoble, for their

support during the measurements and for data evaluation.

I also want to thank Prof. Dr. M. J. Aziz and Prof. Dr. M. P. Brenner from the University of

Harvard, for their useful discussion concerning the process of pattern formation.

I'm grateful to Dr. J. W. Gerlach and Dr. D. Manova for their critical work through parts of the

manuscript.

My thank goes to the colleagues of the ion beam department for their warm welcome and for the

very nice moments during these years. A special thank goes to lunch table companions who helped

me to understand the German way of making jokes.

I don't want to forget Mrs. H. Beck for preparing the filament wires, and Mrs. Herold in the

Chemical lab.

Here I want to thank Dr. E. Schubert, with whom I shared the room for two years, for never

getting bored from my questions. Also, I thank Prof. Dr. M. Schubert who helped me to be here at

IOM, by introducing me to Dr. F. Frost.

I kept my special thanks for the end. I still remember the first day I came to IOM to meet

Frank (Dr. Frost), we were sitting at the seminar room. You were speaking about the project, and I

was thinking to leave the university or not. I'm very thankful to you for accompanying me during

these years. For introducing me to the world of nanotechnology and giving me the possibility to

work in such an interesting and fascinating subject. You were always there for me, even then when

your phone was ringing several times per day. I'm also very thankful to the many discussions,

suggestions and to your keen eyes for details. I'll always be in debt to you.

At the end, a want to thank my family. My two lovely daughters Fatbardha and Ndrina for

making me relax from the long stressful days. To my wife, thank you very much for the patience

during these years, and for sacrificing many holidays.

I dedicate my work to those who are the reason for me to be here were I am, to my parents.

Curriculum vitae

Name: Bashkim Ziberi

Date of birth: 11. September 1974

Place of birth: Radiovce (Macedonia)

Nationality: Albanian

Marital status: Married since January 1999

Children: Fatbardha (born July 22, 2004)

Ndrina (born April 23, 2006)

Education and scientific activities:

1981 – 1989 Primary school in Radiovce (Macedonia)

1989 – 1993 Secondary school in Tetovo (Macedonia)

1993 – 1998 Physics studies at the Univeristy of Tirana (Albania)

in the group „Special Physics“ (5 years)

Diploma thesis „Investigation of Microstructures on metal-

ceramic Cu-C-PbO samples with Electron Microscopy“

1998 – 1999 Teaching Assistant at the University of Tetovo (Macedonia)

1999 – 2001 Master of Science studies in Physics at the University of

Leipzig

07/2001 M. Sc. thesis „Ultrasound Monitoring of the Synthesis of

Zeolites in Real Time”

2001 – 2002 Scientific employee at the Faculty of Physics and Earth

Sciences, University of Leipzig

since 05/2002 Scientific employee at the Leibniz-Institut für

Oberflächenmodifizierung e. V. Leipzig and Ph. D. student at

the University of Leipzig, Institute of Experimental Physics II.

Awards:

06/2004 Young Scientist Award of the European Materials Research

Society for the work on ion beam induced self-organization on

semiconductor surfaces

06/2005 348. WE-Heraeus Seminar Poster Prize sponsored by the

“Wilhelm und Else Heraeus – Stiftung” during the Wilhelm und

Else Heraeus-Seminar on “Ions at Surfaces: Patterns and

Processes”

List of Publications

The following articles have been published in the course of this thesis, are submitted, or in

preparation for future publication

1. Ion beam assisted smoothing of optical surfaces

F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, A. Schindler

Applied Physics A 78: Materials Science & Processing, 651 (2004)

2. The shape and ordering of self-organized nanostructures by ion sputtering

F. Frost, B. Ziberi, T. Höche, B. Rauschenbach

Nuclear Instruments & Methods B 216, 9 (2004)

3. Large area smoothing of optical surfaces by low-energy ion beams

F. Frost, R. Fechner, B. Ziberi, D. Flamm, A. Schindler

Thin Solid Films 459, 100 (2004)

4. Importance of ion beam parameters on self-organized pattern formation on

semiconductor surfaces by ion beam erosion;

B. Ziberi, F. Frost, H. Neumann, B. Rauschenbach

Thin Solid Films 459, 106 (2004)

5. Highly ordered self-organized dot patterns on Si surfaces by low-energy ion beam

erosion

B. Ziberi, F. Frost, B. Rauschenbach, T. Höche

Applied Physics Letters 87, 033113 (2005)

6. Ripple pattern formation on silicon surfaces by low-energy ion-beam erosion:

Experiment and theory

B. Ziberi, F. Frost, T. Höche, B. Rauschenbach

Physical Review B 72, 235310 (2005)

7. Dot pattern formation on Si surfaces by low-energy ion beam erosion

B. Ziberi, F. Frost, T. Höche, B. Rauschenbach

in Kinetics-Driven Nanopatterning on Surfaces, edited by Eric Chason, George H.

Gilmer, Hanchen Huang, and Enge Wang (Mater. Res. Soc. Symp. Proc. 849,

Warrendale, PA , 2005), KK 6.2.

8. Pattern transitions on Ge surfaces during low-energy ion beam erosion

B. Ziberi, F. Frost, B. Rauschenbach

Applied Physics Letters 88, 173115 (2006)

9. Self-organized dot patterns on Si surfaces during noble gas ion beam erosion


Surface Science (im Druck, 2006)

10. Low-energy ion bombardment induced nanostructures on surfaces


Vacuum (im Druck, 2006)

11. Formation of large-area nanostructures on Si and Ge surfaces during low-energy ion

beam erosion


Journal of Vacuum Science & Technology A 24, 1344 (2006)

Publikations on other Subjects:

12. Ion beam sputter deposition of soft x-ray Mo/Si multilayer mirrors;

E. Schubert, F. Frost, B. Ziberi, G. Wagner, H. Neumann, B. Rauschenbach

Journal of Vacuum Science & Technology B 23, 959 (2005)

13. In situ diagnostics of zeolite crystallization by ultrasonic monitoring

R. Herrmann, W. Schwieger, O. Scharf, C. Stenzel, H. Toufar, M. Schmachtl, B. Ziberi,

W. Grill

Microporous and Mesoporous Materials 80, 1 (2005)

Selbständigkeitserklärung

Hiermit versichere ich, daß die vorliegende Arbeit ohne unzulässige Hilfe und ohne Benutzung

anderer als der angegebenen Hilfsmittel angefertigt und daß die aus fremden Quellen direkt oder

indirekt übernommenen Gedanken in der Arbeit als solche kenntlich gemacht wurden.

Ich versichere, daß alle Personen, von denen ich bei der Auswahl und Auswertung des Materials

sowie bei der Herstellung des Manuskripts Unterstützungsleistungen erhalten habe, in der

Danksagung der vorliegenden Arbeit aufgeführt sind.

Ich versichere, daß außer den in der Danksagung genannten, weitere Personen bei der geistigen

Herstellung der vorliegenden Arbeit nicht beteiligt waren, und insbesondere von mir oder in

meinem Auftrag weder unmittelbar noch mittelbar geldwerte Leistungen für Arbeiten erhalten

haben, die im Zusammenhang mit dem Inhalt der vorliegenden Dissertation stehen.

Ich versichere, daß die vorliegende Arbeit weder im Inland noch im Ausland in gleicher oder in

ähnlicher Form einer anderen Prüfungsbehörde zum Zwecke einer Promotion oder eines anderen

Prüfungsverfahrens vorgelegt und in ihrer Gesamtheit noch nicht veröffentlicht wurde.

Ich versichere, daß keine früheren erfolglosen Promotionsversuche stattgefunden haben.

Leipzig, 30.06.2006 Bashkim Ziberi

ion beam induced pattern formation on si and ge surfaces€¦ · semiconductors [17-32], and other...

Documents