page 1 phys 661 - baski diffraction techniques topic #7: diffraction techniques introductory...

$: Page 1 Phys 661 - Baski Diffraction Techniques Topic #7: Diffraction Techniques Introductory Material –Wave-like nature of electrons, diffraction/interference$
Phys 661 - Baski Diffraction Techniques Page 1

Topic #7: Diffraction Techniques• Introductory Material

– Wave-like nature of electrons, diffraction/interference of waves

– Reciprocal space

• LEED = Low Energy Electron Diffraction

– Incoming electron beam (< 100 eV) is perpendicular to sample.

– Undistorted reciprocal unit cell, but no real-time data collection.

• RHEED = Reflection High Energy Electron Diffraction

– Incoming electron beam (~keV) has glancing angle to sample.

– Real-time data collection, but observe distorted unit cell.

• XRD = X-ray Diffraction (3D)


Electron Scattering: Elastic (Diffraction) & Inelastic

LEEDRHEED

TED

Auger, SEM


Intro: Wave-like Behavior of Electrons

• De Broglie wavelength for an electron is given by:

212

2

for an accelerated electron beam using

2 2

2

1240 eV nm 1.23nm

2 0.511 MeV

o o

oK o

oo

h h h hc

p mv eV mc eVmm

eVwhere v E mv eV

m

VeV

• For accelerating voltage Vo = 100 V, = 0.12 nm (atomic spacing).


Intro: Wave Interference

(path length difference) Maxim sin: a dn

d = slit spacing

Incoming Wave

Intensity on Screen

2 where sincos

dI

sind


Intro: Real vs. (Reciprocal, Diffraction, or k) Space

k-Space (i.e. spacing of diffraction spots in nm–1)

Real Space (i.e. spacing of surface atoms in nm)

larger real-space smaller k-space

2G

a

a


LEED: History

• Low Energy Electron Diffraction (LEED) = e– in, e– out (elastic)

• 1924: Discovered accidentally by Davisson and Kunsman during study of electron emission from a Ni crystal.

• 1927: Davisson and Germer found diffraction maxima for:

– n = D sin where D = surface spacing, = electron wavelength

• 1934: Fluorescent screen developed by Ehrenburg for data imaging.

• 1960: UHV technology enabled LEED of clean surfaces.


LEED: Front-view Apparatus

Sample

Grid 1: retarding voltage(selects only elastic electrons)

Grid 2: accelerating voltage(creates fluorescence on screen)

Fluorescent Screen


k-Space: Bragg Scattering vs. LEED Equation

X-ray Diffraction

Derive LEED equation using Bragg’s Law for X-ray diffraction, where appropriate angles are substituted and is for the electron wavelength.

elec sinn D 2 sin cos

sin 2

n D

n D

ki kfD

Angle ki

kf

xray 2 sinn d

dd

ElectronDiffraction


k-Space: Ewald Sphere for LEED

sample

LEED spots Diffractede-beams

EwaldSphere

ReciprocalLattice Rods

eleci

2 pk

//2 n

ka

Incoming e-beam ik

fk

2

a


k-Space: Square Lattice Reconstructions

Real space LEED


LEED: Si(111)7x7

35 eV 65 eV

• Larger D spacings give closer LEED spots (smaller ).

• Higher energy electrons give closer spots.

Bulk 1x spacing

Surface 7x spacing

sinn D Real Space: Si surface atoms

7× bulk spacing


LEED: Data Analysis

SampleElectron Gun

R

LEED spot

xSpacing D

1.227sin , where nm, sin

1.227nm where 66 mm in lab

o

o

xn D

RV

RD R

xV


RHEED: Schematic of Technique

• RHEED has higher energy (keV) and lower angle (2°) vs. LEED.

• Real-time data acquisition possible, but diffraction pattern is distorted.

k-Space

Real Space

ik

LEED


k-Space: Ewald Sphere for RHEED

Incoming e-beam

Diffractede-beams

sample

ReciprocalLattice Rods

EwaldSphere

RHEED spots

k

ik

fk


RHEED: Si(111)7x7

k-Space: Larger period e-beam

k-Space: Smaller period e-beam

E-beam

Real Space: Smaller period e-beam

Real Space: Larger period e-beam


RHEED: AlN

• Surface periodicity given by spacing between peaks.

• Surface quality given by full-width at half-max of peaks.In

tens

ity

RHEED image of AlN Line profile of AlN <1120>

FWHM

Slide courtesy of Lei He - 2004


X-ray Diffraction (XRD)

• Bragg’s Law and Ewald Construction

• Types of Scans:

– Theta/2Theta (/2)

– Rocking Curve

– Diffraction-Space Map

• Philips Materials ResearchDiffractometer


XRD: Diffraction Condition

Ewald Construction

2 sin

2where

hkln d

k

d

k

ik

ik

fk

k

fk

Bragg’s Law


XRD: (/2) Scan or “Gonio” on MRD

• Vary MAGNITUDE of k while maintaining its orientation relative to sample normal.HOW? Usually rotate sample and detector with respect to x-ray beam.

• Resulting data of Intensity vs. 2 shows peaks at the detector (kf) for

k values satisfying the diffraction condition.

• Detects periodicity of planes parallel to surface.

ikfk

ksmaller k


XRD: /2 Example

• Polycrystalline sample has a number of peaks due to mixture of crystal orientations.

10 20 30 40 50 60 70 80 90 1000

2000

4000

6000Polycrystalline Silicon Powder

Inte

nsity

(co

unts

/sec

)


XRD: “Rocking” Curve Scan

• Vary ORIENTATION of k relative to sample normal while maintaining its magnitude.How? “Rock” sample over a very small angular range.

• Resulting data of Intensity vs. Omega (sample angle) shows detailed structure of diffraction peak being investigated.

ikfk

k

“Rock” Sample

kSample normal


XRD: Rocking Curve Example

• Rocking curve of single crystal GaN around (002) diffraction peak showing its detailed structure.

16.995 17.195 17.395 17.595 17.7950

8000

16000

GaN Thin Film(002) Reflection

Inte

nsity

(C

ount

s/s)

Omega (deg)


XRD: Diffraction-Space Map

• Vary Orientation and Magnitude of k.

• Diffraction-Space map of GaN film on AlN buffer shows peaks of each film.

/2

GaN(002) AlN


XRD: X-ray Tube (non-monochromatic)

mino

hc

eV

min

Bremsstrahlung

Characteristic Spectrum

(target dependent)

Max. X-ray energy = Max. electron energy

• Characteristic SpectrumK-series radiation created via incoming electron beam.

• BremsstrahlungBroad spectrum of “braking” radiation due to decelerating electrons.

K

K

ELECTRON IN PHOTON OUT

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