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Dopant and Self-Diffusion in Semiconductors:
A Tutorial
Eugene Haller and Hughes SilvestriMS&E, UCB and LBNL
FLCC Tutorial1/26/04
FLCC
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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
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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
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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--
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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 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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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.