1

Dopant and Self-Diffusion in Semiconductors:

A Tutorial

Eugene Haller and Hughes SilvestriMS&E, UCB and LBNL

FLCC Tutorial1/26/04

FLCC

2

Outline

• Motivation

• Background – Fick’s Laws– Diffusion Mechanisms

• Experimental Techniques for Solid State Diffusion

• Diffusion with Stable Isotope Structures

• Conclusions

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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

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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

Jin Jout

+GS-RS

As + V ⇔ AVRAV = 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 = −D ∂CS

∂x

Fick’s 1st Law: Flux of atoms

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Analytical Solutions to Fick’s EquationsD = 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

Nor

mal

ized

Con

cent

ratio

n

Depth

C x,t( )=S

πDte

−x 2

4 Dt

- Infinite source of diffusing species:Solution:

Complementary error function -C x, t( )= Co 1−

2π

ez 2

0

y∫ dz

, y =

x2 Dt 0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1N

orm

aliz

ed C

once

ntra

tion

Depth

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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 implantKennel, 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

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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)

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Vacancy-assisted Diffusion Mechanisms

As + V ⇔ AVDissociative mechanism

As ⇔ Ai + V

Vacancy mechanism

(Sb in Si)

(Cu in Ge)

(native defects required)

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Interstitial-assisted Diffusion MechanismsInterstitialcy mechanism

Kick-out mechanism

As + I ⇔ AI

As + I ⇔ Ai

(P in Si)

(B in Si)

(native defects required)

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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

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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

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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).)

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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 exp SV ,IF

kB

exp −

HV ,IF

kBT

, H

V −F = H

V oF − EF − E

V −( )

Dopant charge state Native defect charge stateextrinsic n-type As

+ I-, V-

extrinsic p-type As- I+, V+

Ec

Ev

V--/-

V-/o

V+/++Vo/+

Io/+

0.11 eV

0.57 eV

0.35 eV0.13 eV

0.05 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 exp SV ,IF

kB

exp −

HV ,IF

kBT

, H

V −F = H

V oF − EF − E

V −( )

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 − Hext

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 eV0.13 eV

0.05 eV

EF (int)EF (ext)

100 meV

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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 (c

m2s-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 (µm)

Con

cent

ratio

n (c

m-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

10 17

10 18

10 19

10 20

10 21

10 22

0 500 1000 1500

conc

entra

tion

(cm

-3)

Depth (nm)

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Stable Isotope Multilayers

28Si enriched

FZ Si substrate

nat. Si

a-Si cap

10 17

10 18

10 19

10 20

10 21

10 22

0 500 1000 1500co

ncen

tratio

n (c

m-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 = 560−170+240( )exp −

4.76 ± 0.04( )eVkBT

1095 ºC, 54.5 hrs

1153 ºC, 19.5 hrs

( ) ( )

±−= +

− TkeVD

BSi

04.076.4exp560 240170

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10 17

10 18

10 19

10 20

10 21

0 200 400 600 800 1000 1200 1400 1600

conc

entra

tion

(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 + e−Interstitialcy mechanism

ni

extrinsic intrinsic

- Vo

- V-

- V--

28

10 17

10 18

10 19

10 20

10 21

0 200 400 600 800 1000 1200 1400 1600

conc

entra

tion

(cm

-3)

Depth (nm)

Si and Dopant Diffusion

AsV( )o ↔ Ass+ + V−

Vacancy mechanismAsI( )o ↔ Ass

+ + Io + e−Interstitialcy mechanism

Arsenic doped sample annealed 950 ˚C for 122 hrs

ni- Vo

- V-

- V--

29

10 17

10 18

10 19

10 20

10 21

0 200 400 600 800 1000 1200 1400 1600

conc

entra

tion

(cm

-3)

Depth (nm)

Si and Dopant Diffusion

AsV( )o ↔ Ass+ + V−

Vacancy mechanismAsI( )o ↔ Ass

+ + Io + e−Interstitialcy mechanism

Arsenic doped sample annealed 950 ˚C for 122 hrs

ni- Vo

- V-

- V--

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Native Defect Contributions to Si Diffusion

Diffusion coefficients of individual components add up accurately:DSi(ni )tot = fIo CI o DI o + 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 (c

m2s-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

Isot

ope

Con

cent

ratio

ns (c

m-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 IsotopesTemperature 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 enhancedunder n-type doping due to Fermi level effect on Ga self-interstitials

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

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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

( ) ( )

±−×= −−

TkeVscmD

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

( )

−= −

TkeVscmD

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

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Previous Results on Diffusion in Si1-xGexMcVay and DuCharme (1975) 71Ge diffusion in poly-SiGe alloys

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

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Stable Isotope Diffusion in Si1-xGex

10 17

10 18

10 19

10 20

10 21

10 22

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-xGexalloys. (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 layer200 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

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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.