1

Dopant and Self-Diffusion in Semiconductors:

A Tutorial

Eugene Haller and Hughes Silvestri

MS&E, UCB and LBNL

FLCC Tutorial

1/26/04

FLCC

2

Outline

• Motivation

• Background – Fick’s Laws

– Diffusion Mechanisms

• Experimental Techniques for Solid State Diffusion

• Diffusion with Stable Isotope Structures

• Conclusions

3

Motivation

• Why diffusion is important for feature level control of device processing

– Nanometer size feature control: - any extraneous diffusion of dopant atoms may result in device performance degradation

• Source/drain extensions

– Accurate models of diffusion are required for dimensional control on the nanometer scale

4

Semiconductor Technology Roadmap

2001 2002 2003 2004 2005 2006 2007

(International Technology Roadmap for Semiconductors, 2001)

Thermal & Thin-film, Doping and Etching Technology Requirements, Near-Term

5

Fick’s Laws (1855)

Diffusion equation does not take into account interactions with defects!

CS

t

x

DS

CS

x

only valid for pure interstitial diffusion

JinJout

+GS

-RS

As V AV

RAV kr AV

CAV

t

x

DAV

CAV

x

kr AV k f AS V

GAV k f AS V Example: Vacancy Mechanism

2nd Law

Jin Jout

dx

J DCS

x

Fick’s 1st Law: Flux of atoms

6

Analytical Solutions to Fick’s Equations

D = constant

- Finite source of diffusing species:

CS

t

x

DS

CS

x

DS

2CS

x 2

Solution: Gaussian -

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

No

rma

lize

d C

on

cen

tra

tion

Depth

C x,t S

Dte

x 2

4 Dt

- Infinite source of diffusing species:Solution:

Complementary error function -

C x, t Co 12

ez 2

0

y dz

, y

x

2 Dt 0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1N

orm

aliz

ed

Co

nce

ntr

atio

n

Depth

7

Solutions to Fick’s Equations (cont.)D = f (C) Diffusion coefficient as a function of concentration

Concentration dependence can generate various profile shapes and penetration depths

8

Solid-State Diffusion ProfilesExperimentally determined profiles can be much more complicated - no analytical solution

B implant and anneal in Si with and without Ge implant

Kennel, H.W.; Cea, S.M.; Lilak, A.D.; Keys, P.H.; Giles, M.D.; Hwang, J.; Sandford, J.S.; Corcoran, S.; Electron Devices Meeting, 2002. IEDM '02, 8-11 Dec. 2002

9

Direct Diffusion Mechanisms in Crystalline Solids

Pure interstitial

Direct exchange

Elements in Si: Li, H, 3d transition metals

No experimental evidenceHigh activation energy

(no native defects required)

10

Vacancy-assisted Diffusion Mechanisms

As V

AV

Dissociative mechanism

As

Ai V

Vacancy mechanism

(Sb in Si)

(Cu in Ge)

(native defects required)

11

Interstitial-assisted Diffusion Mechanisms

Interstitialcy mechanism

Kick-out mechanism

As I

AI

As I

Ai

(P in Si)

(B in Si)

(native defects required)

12

Why are Diffusion Mechanisms Important?

• Device processing can create non-equilibrium native defect concentrations– Implantation: excess interstitials

– Oxidation: excess interstitials

– Nitridation: excess vacancies

– High doping: Fermi level shift

13

Oxidation Effects on Diffusion

• Oxidation of Si surface causes injection of interstitials into Si bulk

• Increase in interstitial concentration causes enhanced diffusion of B, As, but retarded Sb diffusion

• Nitridation (vacancy injection) causes retarded B, P diffusion, enhanced Sb diffusion

(Fahey, et al., Rev. Mod. Phys. 61 289 (1989).)

Oxidation during device processing can lead to non-equilibrium diffusion

14

Implantation Effects on Diffusion• Transient Enhanced Diffusion (TED) - Eaglesham, et al.

• Implantation damage generates excess interstitials– Enhance the diffusion of dopants diffusing via interstitially-

assisted mechanisms– Transient effect - defect concentrations return to equilibrium

values

• TED can be reduced by implantation into an amorphous layer or by carbon incorporation into Si surface layer

– Substitutional carbon acts as an interstitial sink

Eaglesham, et al., Appl. Phys. Lett. 65(18) 2305 (1994).

(Stolk, et al., Appl. Phys. Lett. 66 1371 (1995).)

15

Doping Effects on DiffusionHeavily doped semiconductors - extrinsic at diffusion temperatures

– Fermi level moves from mid-gap to near conduction (n-type) or valence (p-type) band.

– Fermi level shift changes the formation enthalpy, HF, of the charged native defect

– Increase of CI,V affects Si self-diffusion and dopant diffusion

CV ,Ieq CSi

o expSV ,I

F

kB

exp

HV ,IF

kBT

, H

V F H

V o

F EF EV

Ec

Ev

V--/-

V-/o

V+/++

Vo/+

Io/+

0.11 eV

0.57 eV

0.35 eV

0.13 eV0.05 eV

V states (review by Watkins, 1986)

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Doping Effects on DiffusionFermi level shift lowers the formation enthalpy, HF, of the charged native defect

– Increase of CI,V affects Si self-diffusion and dopant diffusion

CV ,Ieq CSi

o expSV ,I

F

kB

exp

HV ,IF

kBT

, H

V F H

V o

F EF EV

Numerical example: If EF moves up by 100 meV at 1000 °C, the change in the native defect concentration is:

Cexteq

Cinteq

e

H intF H ext

F

kBT

~ 3Native defect concentration is 3 times larger

for a Fermi level shift of only 100 meV

Ec

Ev

V--/-

V-/o

V+/++

Vo/+

Io/+

0.11 eV

0.57 eV

0.35 eV

0.13 eV0.05 eV

EF (int)

EF (ext)100 meV

17

Doping Effects on Diffusion

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86

D (

cm2s-1

)

1000/T (1000/K)

DSi

(ni)

DSi

(ext)

DAs

(ni)

DAs

(ext)

D ni D ext ni

CAseq

The change in native defect concentration with Fermi level position causes an increase in the self- and dopant diffusion coefficients

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Experimental Techniques for DiffusionCreation of the Source

- Diffusion from surface- Ion implantation- Sputter deposition- Buried layer (grown by MBE)

Annealing

Analysis of the Profile

- Radioactivity (sectioning)- SIMS- Neutron Activation Analysis- Spreading resistance- Electro-Chemical C/Voltage

Modeling of the Profile- Analytical fit- Coupled differential eq.

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Primary Experimental Approaches

• Radiotracer Diffusion– Implantation or diffusion from surface– Mechanical sectioning– Radioactivity analysis

• Stable Isotope Multilayers– Diffusion from buried enriched isotope layer– Secondary Ion Mass Spectrometry (SIMS)– Dopant and self-diffusion

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Radiotracer diffusion• Diffusion using radiotracers was first technique available

to measure self-diffusion– Limited by existence of radioactive isotope

– Limited by isotope half-life (e.g. - 31Si: t1/2 = 2.6 h)

– Limited by sensitivity– Radioactivity measurement

– Width of sections

Application of radio-isotopes to surface

annealing

Mechanical/Chemical sectioning

Measure radioactivity of each section

Depth (m)

Con

cen

trat

ion

(cm

-3)

Generate depth profile

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Diffusion Prior to Stable IsotopesWhat was known about Si, B, P, and As diffusion in Si

Si: self-diffusion: interstitials + vacanciesknown: interstitialcy + vacancy mechanism, QSD ~ 4.7 eVunknown: contributions of native defect charge states

B: interstitial mediated: from oxidation experiments known: diffusion coefficient unknown: interstitialcy or kick-out mechanism

P: interstitial mediated: from oxidation experiments known: diffusion coefficient unknown: mechanism for vacancy contribution

As: interstitial + vacancy mediated: from oxidation + nitridation experiments known: diffusion coefficient unknown: native defect charge states and mechanisms

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Stable Isotope Multilayers• Diffusion using stable isotope structures allows

for simultaneous measurements of self- and dopant diffusion– No half-life issues

– Ion beam sputtering rather than mechanical sectioning

– Mass spectrometry rather than radioactivity measurement

28Si enriched

FZ Si substrate

nat. Si

a-Si cap

1017

1018

1019

1020

1021

1022

0 500 1000 1500

con

cen

tra

tio

n (

cm-3

)

Depth (nm)

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Stable Isotope Multilayers

28Si enriched

FZ Si substrate

nat. Si

a-Si cap

1017

1018

1019

1020

1021

1022

0 500 1000 1500co

nce

ntr

ati

on

(cm

-3)

Depth (nm)

Multilayers of enriched and natural Si enable measurement of dopant diffusion from cap and self-diffusion between layers simultaneously

Secondary Ion Mass Spectrometry (SIMS) yields concentration profiles of Si and dopant

Simultaneous dopant and self-diffusion analysis allows for determination of native defect contributions to diffusion.

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Secondary Ion Mass Spectrometry• Incident ion beam sputters sample surface - Cs+, O+

– Beam energy: ~1 kV

• Secondary ions ejected from surface (~10 eV) are mass analyzed using mass spectrometer– Detection limit: ~1012 - 1016 cm-3

• Depth profile - ion detector counts vs. time – Depth resolution: 2 - 30 nm

Ion gun

Mass spectrometer

Ion detector

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Diffusion Parameters found via Stable Isotope Heterostructures

• Charge states of dopant and native defects involved in diffusion

• Contributions of native defects to self-diffusion

• Enhancement of dopant and self-diffusion under extrinsic conditions

• Mechanisms of diffusion which mediate self- and dopant diffusion

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Si Self-Diffusion• Enriched layer of 28Si epitaxially grown

on natural Si• Diffusion of 30Si monitored via SIMS

from the natural substrate into the enriched cap (depleted of 30Si)

• 855 ºC < T < 1388 ºC– Previous work limited to short

times and high T due to radiotracers• Accurate value of self-diffusion

coefficient over wide temperature range:

(Bracht, et al., PRL 81 1998)

DSi 560 170240 exp

4.76 0.04 eV

kBT

1095 ºC, 54.5 hrs

1153 ºC, 19.5 hrs

Tk

eVD

BSi

04.076.4exp560 240

170

27

1017

1018

1019

1020

1021

0 200 400 600 800 1000 1200 1400 1600

co

nce

ntr

ati

on

(cm-3)

Depth (nm)

Si and Dopant DiffusionArsenic doped sample annealed 950 ˚C for 122 hrs

AsV o Ass V

Vacancy mechanismAsI o Ass

Io eInterstitialcy mechanism

ni

extrinsic intrinsic

- Vo

- V-

- V--

28

1017

1018

1019

1020

1021

0 200 400 600 800 1000 1200 1400 1600

co

nce

ntr

ati

on

(cm

-3)

Depth (nm)

Si and Dopant Diffusion

AsV o Ass V

Vacancy mechanismAsI o Ass

Io eInterstitialcy mechanism

Arsenic doped sample annealed 950 ˚C for 122 hrs

ni- Vo

- V-

- V--

29

1017

1018

1019

1020

1021

0 200 400 600 800 1000 1200 1400 1600

co

nce

ntr

ati

on

(cm

-3)

Depth (nm)

Si and Dopant Diffusion

AsV o Ass V

Vacancy mechanismAsI o Ass

Io eInterstitialcy mechanism

Arsenic doped sample annealed 950 ˚C for 122 hrs

ni- Vo

- V-

- V--

30

Native Defect Contributions to Si Diffusion

Diffusion coefficients of individual components add up accurately:

DSi(ni )tot fIo CI

o DIo fI

CI DI

fV CV DV

DSi(ni )

(Bracht, et al., 1998)

(B diffusion) (As diffusion)(As diffusion)

10-19

10-18

10-17

10-16

10-15

10-14

0.7 0.8 0.9

D (

cm2s-1

)

1000/T (1000/K)

DSi

(V-)

DSi

(I+)

DSi

(Io)

DSi

(Io+I++V-)

DSi

(ni)

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GaSb Self-Diffusion using Stable Isotopes“as-grown structure”

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GaSb Self-Diffusion using Stable Isotopes

Annealed 650 °C for 7 hours

1020

1021

1022

1023

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

GaSb Isotope Heterostructure

(annealed at 670 oC for 7 hrs)

Iso

top

e C

on

ce

ntr

ati

on

s (

cm

-3)

Depth (microns)

123 Sb 121 Sb

71 Ga 69 Ga

nat GaSb (cap) 69 Ga121 Sb 71 Ga123 Sb nat GaSb

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GaSb Self-Diffusion using Stable IsotopesSimultaneous isotope diffusion experiments revealed that Ga and Sb

self-diffusion coefficients in GaSb differ by 3 orders of magnitude

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GaAs Self-Diffusion using Stable Isotopes

Temperature dependence of Ga self-diffusion in GaAs under intrinsic (x), p-type Be doping (), and n-type Si doping ().

Ga self-diffusion is retarded under p-type doping and enhanced under n-type doping due to Fermi level effect on Ga self-interstitials

Bracht, et al., Solid State Comm.112 301 (1999)

35

Diffusion in AlGaAs/GaAs Isotope Structure

Ga self-diffusion coefficient in AlGaAs found to decrease with increasing Al content.

Activation energy for Ga self-diffusion - 3.6 ± 0.1 eV

Bracht, et al., Appl. Phys. Lett. 74 49 (1999).

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Diffusion in Ge Stable Isotope StructureAnnealed 586 °C for 55.55 hours

Fuchs, et al., Phys. Rev B 51 1687 (1995)

Ge self-diffusion coefficient determined from 74Ge/70Ge isotope structure

Tk

eVscmD

BGe

05.00.3exp102.1 123

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Diffusion in GaP Stable Isotope Structure

Annealed 1111 °C for 231 min

Ga self-diffusion coefficient in GaP determined from 69GaP/71GaP isotope structure

Tk

eVscmD

BGa

5.4exp0.2 12

Wang, et al., Appl. Phys. Lett. 70 1831 (1997).

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Diffusion in Si1-xGex

• SiGe will be used as “next generation” material for electronic devices– Will face same device diffusion issues as Si

– Currently, limited knowledge of diffusion properties

SiGe HBTs with cut-off frequency of 350 GHzRieh, J.-S.; Jagannathan, B.; Chen, H.; Schonenberg, K.T.; Angell, D.; Chinthakindi, A.; Florkey, J.; Golan, F.; Greenberg, D.; Jeng, S.-J.; Khater, M.; Pagette, F.; Schnabel, C.; Smith, P.; Stricker, A.; Vaed, K.; Volant, R.; Ahlgren, D.; Freeman, G.; Intl. Electron Devices Meeting, 2002. IEDM '02. Digest. International , 8-11 Dec. 2002, Page(s): 771 –774

39

Previous Results on Diffusion in Si1-xGex

McVay and DuCharme (1975) 71Ge diffusion in poly-SiGe alloys

Strohm, et al., (2001)71Ge diffusion in SiGe alloys

40

Stable Isotope Diffusion in Si1-xGex

1017

1018

1019

1020

1021

1022

0 100 200 300 400 500 600 700 800

Si0.75

Ge0.25

(900C 2days) simulation

30Si Conc.76Ge Conc.

Con

cent

ratio

n (c

m-3)

Depth (nm)

• Use isotope heterostructure technique to study Si and Ge self-diffusion in relaxed Si1-xGex alloys. (0.05 ≤ x ≤ 0.85) – No reported measurements of simultaneous Si

and Ge diffusion in Si1-xGex alloys

Simulation result of simultaneous

Si and Ge self-diffusion

Si substrate

SiGe graded buffer layer

200 nm nat. Si1-xGex

200 nm nat. Si1-xGex

400 nm 28Si1-x70Gex

Fitting of SIMS diffusion profile to simulation result of simultaneous Si and Ge self-diffusion will yield self-diffusion coefficients of Si and Ge

41

Conclusions

• Diffusion in semiconductors is increasingly important to device design as feature level size decreases.

• Device processing can lead to non-equilibrium conditions which affect diffusion.

• Diffusion using stable isotopes yields important diffusion parameters which previously could not be determined experimentally.