Vibrational properties of amorphous silicon-germanium alloys and ...
Dopant and Self-Diffusion in Silicon and Silicon Germanium
description
Transcript of Dopant and Self-Diffusion in Silicon and Silicon Germanium
FLCC
Dopant and Self-Diffusion in Silicon and Silicon Germanium
Eugene Haller, Hughes Silvestri, and Chris Liao
MS&E, UCB and LBNL
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Outline• Motivation
• Background – Fick’s Laws– Diffusion Mechanisms
• Experimental Techniques for Solid State Diffusion
• Diffusion of Si in Stable Isotope Structures
• Future Work: Diffusion of SiGe in 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
• Drain extension Xj < 10 nm by 2008*• Extension lateral abruptness < 3 nm/decade by 2008*
– Accurate models of diffusion are required for dimensional control on the nanometer scale
*International Technology Roadmap for Semiconductors, 2004 Update
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Semiconductor Technology Roadmap(International Technology Roadmap for Semiconductors, 2004 Update)
Difficult Challenges ≥ 45nm Through 2010 Summary of Issues
Front-end Process modeling for nanometer structures
Diffusion/activation/damage models and parameters including SPE and low thermal budget processes in Si-based substrate, i.e., Si, SiGe:C, Ge (incl. strain), SOI, and ultra-thin body devices
Characterization tools/methodologies for these ultra shallow geometries/junctions and low dopant levels
Modeling hierarchy from atomistic to continuum for dopants and defects in bulk and at interfaces
Front-end processing impact on reliability
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MOSFET Scaling
Substrate
Gate
Source Drain
Substrate
Gate
Source DrainLeff
Nsub
Xj
LgTox
Planar Bulk-Si Structure Thin-Body Structure
So
urc
e
Dra
in
Gate 2Gate 2
Fin Width Wfin = TSi
Fin Height = Hfin = W
Gate Length = Lg
Current Flow
Gate 1Gate 1
So
urc
e
Dra
in
Gate 2Gate 2
Fin Width Wfin = TSi
Fin Height = Hfin = W
Gate Length = Lg
Current Flow
Gate 1Gate 1
scaling to Lg < 20nm
Si1-xGex in the S/D regions will be needed for thin-body PMOSFETs in order to
• enhance mobility via strain • lower parasitic resistance
– S/D series resistance– contact resistance
Si and Ge interdiffusion, as well as B diffusion in Si1-xGex and Si must be well understood and characterized
Silicon Substrate
Source Drain
SiO2
SOI
GateGate
Silicon Substrate
Source Drain
SiO2
SOI
GateGate
Courtesy of Pankaj Kalra and Prof. Tsu-Jae King
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Fick’s Laws (1855)
Diffusion equation does not take into account interactions with defects!
CS
tx
DS
CS
x
JinJout
+GS
-RS
As V AV
RAV kr AV
CAV
tx
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
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Analytical Solutions to Fick’s Equations
D = constant
- Finite source of diffusing species:
CS
tx
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 1
No
rma
lize
d C
on
cen
tra
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 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
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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 → unlikely
(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 Mechanisms
Interstitialcy 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 DiffusionTransient Enhanced Diffusion (TED) - Eaglesham, et al., Appl. Phys. Lett. 65(18) 2305 (1994).
• 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
– 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 expSV ,I
F
kB
exp
HV ,IF
kBT
, H
V F H
V oF EF E
V
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 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 Diffusion
Creation 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 – new approach– 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 Isotope Multilayer StucturesWhat 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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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 in diffusion
• Contributions of native defects to self-diffusion
• Enhancement of extrinsic dopant and self-diffusion
• Mechanisms 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)
1095 ºC, 54.5 hrs
1153 ºC, 19.5 hrs
DSi 560 170240 exp
4.760.04 eV
kBT
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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
Arsenic doped sample annealed 950 ˚C for 122 hrs
AsV o Ass V o e
Vacancy mechanism
AsI o Ass I
Interstitialcy mechanism
ni
extrinsic intrinsic
Io
I-
I--
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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
Arsenic doped sample annealed 950 ˚C for 122 hrs
niIoI-I--
AsV o Ass V o e
Vacancy mechanism
AsI o Ass I
Interstitialcy mechanism
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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
Arsenic doped sample annealed 950 ˚C for 122 hrs
ni
IoI-I--
AsV o Ass V o e
Vacancy mechanism
AsI o Ass I
Interstitialcy mechanism
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Si and Dopant DiffusionSupersaturation of Io, I+ due to B diffusion
Io and I+ mediate Si and B diffusion
Enhancement due to Fermi level effectDiffusion mechanism: Kick-out
– Bi0 Bs
- + I 0 + h
– Bi0 Bs
- + I +
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Si and Dopant DiffusionPhosphorus Diffusion Model:Interstitialcy or Kick-out mechanism – Io, I-
Pair assisted recombination or dissociative mechanism – V0
PI0(Pi0) Ps
I0 e
PI0(Pi0) Ps
I
PI0(Pi0)V 0 Ps
e
PI(Pi) Ps
I0
PI(Pi)V 0 Ps
1016
1017
1018
1019
1020
1021
500 1000 1500
Co
nce
ntr
atio
n (
cm-3
)
Depth (nm)
Annealed 1100 ˚C for 30 min
1264.023.0P scm
kT
eV)11.033.3(exp36.0D
1240.32
8.3SD
Iscm
kT
eV)24.040.5(exp103.4D
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Native Defect Contributions to Si Diffusion
Diffusion coefficients of individual components add up accurately:
DSi(ni )tot fIo CI
o DIo fI
CI DI
fI CI DI DSi(ni )
(Bracht, et al., 1998)
(B diffusion) (As, P diffusion)(B, P 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
(I-)
DSi
(I+)
DSi
(Io)
DSi
(Io+I++I-)
DSi
(ni)
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Diffusion in Ge Stable Isotope Structure
Annealed 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
DGe 1.210 3 exp 3.00.05 eV
kBT
cm2s 1
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Diffusion in Si1-xGex
• SiGe is used as new material to enhance electronic devices– Will face same device diffusion issues as Si
– Currently, limited knowledge of diffusion properties
compressive strain 30% Idsat increase
Intel’s 90nm CMOS TechnologySi1-xGex in PMOS S/D regions to enhance on-state drive current without increasing off-state leakage
Si1-xGex in the S/D regions will be needed for thin-body PMOSFETs in order to
• enhance mobility via strain • lower parasitic resistance
– S/D series resistance– contact resistance
Si and Ge interdiffusion, as well as B diffusion in Si1-xGex and Si must be well understood and characterized
Silicon Substrate
Source Drain
SiO2
SOI
GateGate
Silicon Substrate
Source Drain
SiO2
SOI
GateGate
T. Ghani et al., 2003 IEDM Technical Digest
Courtesy of Pankaj Kalra and Prof. Tsu-Jae King
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Diffusion in SiGe Isotope Structures
• Diffusion of Si in pure Ge
• Si and Ge self-diffusion in relaxed Si1-xGex structures
• Si and Ge self-diffusion in strained Si1-xGex structures
• Simultaneous Si and Ge dopant and self-diffusion
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Si Diffusion in Pure Ge
• Before determination of Si and Ge self-diffusion in SiGe can be made must determine Si diffusion in Ge and Ge diffusion in Si– Large amounts of data on Ge diffusion in Si - used as a tracer for Si self-
diffusion due to longer half-life– Much less data on Si diffusion in Ge
• MBE grown Ge layer– 100 nm spike of Si (1020 cm-3)
Ge substrate
Ge epilayer
~ 1020 cm-3 Si
1017
1018
1019
1020
0 100 200 300 400 500 600 700 800
Con
cent
ratio
n (c
m-3
)
Depth (nm)
[Si] [C] - - -
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Si Diffusion in Pure Ge
1017
1018
1019
1020
150 200 250 300 350 400 450
Si C
on
cen
tra
tion
(cm
-3)
Depth (nm)
10-19
10-18
10-17
10-16
10-15
10-14
10-13
0.00085 0.00095 0.00105 0.00115
550650750850950
DS
i (cm
-3)
1/T (1/K)
[Strohm, 2002]
[Uppal, 2003]
[Södervall, 1997]
[Räisänen, 1981]
[Current Work]
T (°C)
DSi 38 27.471.5 exp
(3.320.1)eV
kT
cm2s 1
Annealed at 550 °C for 30 days
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Si and Ge Self-DiffusionRelaxed Si1-xGex Structures
• 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
• Proposed isotope heterostructure:– MBE grown - Group of Prof. Arne Nylandsted Larsen, Univ. of Aarhus, Denmark
Si substrate
SiGe graded buffer layer
200 nm nat. Si1-xGex
200 nm nat. Si1-xGex
400 nm 28Si1-x70Gex
1017
1018
1019
1020
1021
1022
0 100 200 300 400 500 600 700 800
Si0.95
Ge0.05
(850C 30days) simulation
30Si Conc.76 Ge Conc.
Con
cent
ratio
n (c
m-3
)
Depth (nm)
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Si and Ge Self-DiffusionStrained Si1-xGex Structures
• Study Si and Ge self-diffusion in strained Si1-xGex alloys. – 0.15 ≤ x ≤ 0.75
• Vary composition between layers to generate: – Compressive strain (x - y < 0)
– Tensile strain (x - y > 0) x - y≈ 0.05
Si substrate
SiGe graded buffer layer
100 nm nat. Si1-yGey
100 nm nat. Si1-yGey
200 nm 28Si1-x70Gex
Proposed isotope heterostructure: MBE grown - Group of Prof. Arne Nylandsted Larsen
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Simultaneous Dopant and Self-Diffusion Si1-xGex Multilayer Structures
• Five alternating 28Si1-x70Gex (0.05 ≤ x ≤ 1) and natural Si1-xGex
layers with amorphous cap• Implant dopants (B, P, As) into amorphous cap • Simultaneous Si and Ge self-diffusion and dopant diffusion
amorphous Si cap
Si substrate
SiGe graded buffer layer
100 nm nat. Si1-xGex
100 nm 28Si1-x70Gex
Proposed isotope heterostructure: MBE grown - Group of Prof. Arne Nylandsted Larsen
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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.
• Technique will be extended to SiGe alloys with variation of composition, strain and doping level.