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Atomistic implementation
of defect diffusion and
interdiffusion in SiGe
heterostructures
P. Castrillo, M. Jaraiz, R. Pinacho, J. E. Rubio
University of Valladolid
Spain
Atomistic implementation of defect diffusion and
interdiffusion in SiGe heterostructures
Outline
• Motivation
• Physical models
• Simulation scheme
• Simulation results
• Conclusions
Castrillo et al (University of Valladolid), EMRS 2009
Strain for CMOS performance
“Since introduction at the 90nm node, strain has
become a central performance enhancement
element for the standard CMOS flow”
• mobility ↑
• drive currents ↑
45 nm technology: Si1-xGex with x ∼0.3 in embedded S/D
Ge for post-Si technologies?
• Higher carrier mobilities make Ge a potential candidate
SiGe: alloys, strain and more
• A new degree of freedom : from Si to Ge, from 0 to ±4.2%
• The vast world of semiconductor heterostructures…
Authin
et process
al., Intel Tech.
Journal (2008)
• And new issues
technologies
Castrillo et al (University of Valladolid), EMRS 2009
Simulation of SiGe processing
• Some of the new issues:
– Composition dependence of diffusivities
– Si-Ge interdiffusion
– Strain-induced diffusion anisotropy
No just a
– Modification of band structure
recalibration
– Dopant segregation
– Alloy inhomogeneities
• Drawbacks for continuum simulators:
– Many equations (many mechanisms, 3D…)
– Parameters (difficult correlation with microscopic
properties)
Castrillo et al (University of Valladolid), EMRS 2009
Atomistic Process Simulators
• Based on non-lattice Kinetic Monte Carlo approach
• Atomistic description of defects and dopants.
• Can handle sizes and times for device processing.
• Direct plug of ab-initio or basic experimental data.
• Inherently 3D.
• Computation time increases moderately with
number of mechanisms.
• More advantageous for deep submicron, far from
equilibrium,…
• Our simulator: DADOS.
Jaraiz et al, IEDM (2007)
Castrillo et al (University of Valladolid), EMRS 2009
Outline
• Motivation
• Physical models
• Simulation scheme
Self-diffusion
Strain effects
Interdiffusion
Dopant diffusion
• Simulation results
• Conclusions
Castrillo et al (University of Valladolid), EMRS 2009
Diffusion events in SiGe
Point-defect
diffusion
Si and Ge
self-diffusion
Interdiffusion
Dopant
diffusion
Si
I
B
Ge
V
Si
Ge
• Diffusion activated by Vs and Is.
• Transport capacities: DCV and DCI
• Charge states (V0, V-,V=,I0,..) : DCV = ∑ DCVq
Castrillo et al (University of Valladolid), EMRS 2009
Self-diffusion in Si and Ge
1.E-11
1.E-12
1.E-13
D (cm2/s)
1.E-14
Lines: model
1.E-15
Symbols: experimental
1.E-16
Ge in Si
Bracht et al, PRL (1998)
Ge self-diff
Si self-diff
1.E-17
Ural et al, PRL (1999)
Si in Ge
1.E-18
Shimizu et al, PRL (2007)
Werner et al, PRB (1985)
1.E-19
Vogel et al, JPC (1983)
1.E-20
Strohm, PhD thesis (2002)
1.E-21
Huger et al, APL (2008)
6
7
8
9
10
11
12
1e4/T
13
14
Zangenberet al, PRL (2001)
Silvestri et al, SST (2006)
• In general, DSi ≠ DGe
Castrillo et al (University of Valladolid), EMRS 2009
Self-diffusion in SiGe
• Defects could move differently Si and Ge atoms
• Different self-diffusivities in Si1-xGex:
Castrillo et al (University of Valladolid), EMRS 2009
Dependence on Ge content:
Ge
Si
(-/=) (0/-)
(0/-)
(+/0)
1.05
0.6
V
1.0
0.35
I
Approximation:
energies and entropies
linear with Ge content
(0/-)
(-/=)
(0/-) (+/0)
0.4
0.2
V
0.6
0.0
I
Castrillo et al (University of Valladolid), EMRS 2009
Ge and Si self-diffusion in SiGe
Experimental:
Bracht PRL (1998)
Ural PRL (1999)
Werner PRB (1985)
Vogel JPC (1983)
Strohm, Thesis (2002)
Zangenber, PRL (2001)
Silvestri SST (2006)
Castrillo et al (University of Valladolid), EMRS 2009
DGe in SiGe: effective Eact and prefactor
Is at high T
Vs at low T
Only Vs
• Multiple components:
⇒ Effective values of
Eact and prefactor
⇒ Prefactor
dependence on x
Experimental:
Strohm , PhD thesis (2002)
Zangenber et al, PRL (2001)
Castrillo et al (University of Valladolid), EMRS 2009
DGe/DSi ratio
Comparison with experimental results
for different Si1-xGex compositions
Symbols: Kube et al MSSP (2008). Dotted: fit to data for x=1
Castrillo et al (University of Valladolid), EMRS 2009
Extrinsic self-diffusion
• For Ge, extrinsic effect attributed to V=
Dotted line: estimated from Naganawa et al, APL (2008)
Symbols: Werner et al, PRB (1985)
Castrillo et al (University of Valladolid), EMRS 2009
Strain
• Biaxial strain
Example: SiGe on Si
Relaxed Si1-xGex
a0 > 0.543nm
Biaxially
compressed
Si1-xGex
Strain: ε
(compressive ε<0)
Stress: σ = Y·ε
a0
Relaxed Silicon
a0 = 0.543nm
a0
Castrillo et al (University of Valladolid), EMRS 2009
Strain effects on diffusion
• Biaxial compression
Eform(V) ↓ ⇒ DCV ↑
Eform (I) ↑ ⇒ DCI ↓
• Diffusion jump anisotropy
growth direction
For neutral defects
in plane direction
• Changes in charge levels ⇒ ∆DC
q
− Band changes: hydrostatic + band splitting
− Charge level assumed to scale as the hydrostatic ∆Egap
Castrillo et al (University of Valladolid), EMRS 2009
Strain effects on diffusion
Activation
volumes
Si0.9Ge0.1
(0.21%)
Cfr.: Aziz et al, PRB (2006);
Daw et al, PRB (2001);
Diebel, IEDM (2003)
(0.21%)
Experiments: Zangenberg et al, PRL (2001)
Castrillo et al (University of Valladolid), EMRS 2009
Interdiffusion
• Si and Ge diffusion ⇒ interdiffusion
• Relation between
DSi, DGe and Dinter:
Ge fraction
Nernst-Planck equation
0.16
as-grown
870ºC, 1.5h
DADOS sim
0.12
0.08
0.04
x→0 (Si) ⇒ Dinter ≈ Dge
x→1 (Ge)⇒ Dinter ≈ Dsi
Si0.5Ge0.5 ⇒ limited by
the slowest
0
10
20
30
40
50
Depth (nm)
Cfr.: Aubertine et al, JAP (2003)
Castrillo et al (University of Valladolid), EMRS 2009
Effect of strain on interdiffusion
Dependence of Dinter with composition (T=800 ºC)
substrate: Silicon
DCV
substrate: Si0.44Ge0.56
DCV
Dinter
Dinter
DCI
substrate
DCI
substrate
• Slope change due to strain-induced DCI-DCV crossing
Castrillo et al (University of Valladolid), EMRS 2009
Interdiffusion
Comparison with experiments in SiGe superlattices
Average SL
composition
Pseudosubstrate
composition
Experiments: Meduna et al, SST(2007); Ozguven et al, APL (2007,2008)
Castrillo et al (University of Valladolid), EMRS 2009
Dopants
Example: Boron
• Diffusion:
D B ≈ D 0Bi
[BI0 ]
[ B- ]
Ediff(B) ≈ Eform (I0) + Em(BI0) - Eb(BI-) + (e(BI-)-Ei) + (Ei - EF)
composition and strain
“extrinsic”
• Segregation:
Eform(B-) = Eform(B0) + (e(B-) - Ei) + (Ei - EF)
composition and strain “extrinsic”
• No need for B-Ge pair model assumption,
ready for other dopants.
Castrillo et al (University of Valladolid), EMRS 2009
Dopant in unstrained diffusion Si1-xGex
Antimony
Boron
Experimental data: Kringhøj et al, PRL (1996); Laitinen (2004); Fair (1981);
Kuo et al, APL (1995); Uppal et al, JAP (2004)
• Quadratic dependence of Ediff with Ge content
Castrillo et al (University of Valladolid), EMRS 2009
Outline
• Motivation
• Physical models
• Simulation scheme
• Simulation results
• Conclusions
Castrillo et al (University of Valladolid), EMRS 2009
Atomistic diffusion scheme
• Atomistic handling of defects and dopants: particles
• Continuum handling of
Fermi level and strain: boxes
nGe1
nGe2
• Ge atom counters per box
• Particle properties depend on
box properties: x (within a radius),
strain, Fermi level (if charged)…
• Jump rate (may be anisotropic)
drift
• Charge state updated every jump
• Jump probability rejection as a function of ∆(Eform+Em)
• Boxes (x, strain and Fermi level) updated from time to time
Cfr: Martin-Bragado et al, JAP (2005)
Castrillo et al (University of Valladolid), EMRS 2009
Charged defects in heterostructures
• Correct formulation of the forces on
charged defects in heterostructures
drift
Castrillo et al (University of Valladolid), EMRS 2009
1019 cm-3 uniformly
B-doped
Si/ Si0.7Ge0.3 abrupt structure
at T = 900ºC.
• Effect of band-bending on
extrinsic diffusivity
E nergy (eV)
• Si/SiGe heterostructure
bands at process
temperatures
0.6
0.4
EC
eBi(0,-)
0.2
Ei
0.0
EF
-0.2
EV
-0.4
0
D iffus ivity (cm2/s )
Band-offsets and
extrinsic diffusivity
10
1E -14
x (nm)
20
30
1E -15
1E -16
1E -17
0
10
20
x (nm)
30
Castrillo et al (University of Valladolid), EMRS 2009
Interdiffusion scheme
• Driven by Is & Vs
• Example. I: box1  box2
1
2
⇒
⇒
(and analogous for Is)
Nernst-Planck equation
by components (Vs or Is)
• Small modification of α coming from strain relaxation
Castrillo et al (University of Valladolid), EMRS 2009
Outline
• Motivation
• Physical models
• Simulation scheme
• Simulation results
• Conclusions
Castrillo et al (University of Valladolid), EMRS 2009
KMC simulations
0.5
0.25
0.4
0.2
Ge fraction
Ge fraction
Interdiffusion
0.3
0.2
as-grown
920ºC, 1h
DADOS sim
0.1
0.15
0.1
0.05
0
as-grown
annealed 845ºC, 9h
DADOS sim
0
0
10
20
30
Depth (nm)
40
50
00
10
10
20
20
30
30
40
40
50
50
Depth (nm)
Depth
(nm)
Experiments: Xia et al, JAP 2007; Aubertine et al, JAP 2005
Castrillo et al (University of Valladolid), EMRS 2009
KMC simulations: Interdiffusion
0.2
0.1
0
0.2
0.1
0
0
10
20
30
40
relaxed
0.3
0
10
20
30
40
Depth (nm)
Si0.7Ge0.3 on Si0.7Ge0.3
Ge fraction
tensed
0.3
Ge fraction
0.3
Ge fraction
Si0.7Ge0.3 on Si0.44Ge0.56
Si0.7Ge0.3 on Si
compressed
880ºC, 90min
as-grown
annealed
DADOS sim
0.2
0.1
Experiments: Xia et al, APL
(2006); JAP (2007)
0
0
10
20
30
40
Depth (nm)
Castrillo et al (University of Valladolid), EMRS 2009
KMC simulations
Interdiffusion
800ºC, 120min
Experiments: Xia et al, JAP (2007)
0.6
0.6
0.5
0.5
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
Depth (nm)
40
Ge fraction
0.6
Ge fraction
Ge fraction
as-grown
annealed
DADOS sim
0.4
0.3
0.2
0.4
0.3
0.2
0.1
0.1
0
50 0
0
50 0
10
20
30
Depth (nm)
40
10
20
30
40
50
Depth (nm)
Castrillo et al (University of Valladolid), EMRS 2009
Simulation results
Boron diffusion: Si vs. SiGe
Initial
Experiment
Simulation
T = 860ºC, t = 30 min Experiment: Kuo et al, APL (1993)
Unstrained Silicon
Strained Si0.83Ge0.17
• Retarded by both Ge content and compressive strain
Castrillo et al (University of Valladolid), EMRS 2009
KMC simulations
Boron segregation to SiGe
96 hours
850ºC
Strained
Si0.9Ge0.1
Dots: Experiment: Lever et al, JAP (1998); Lines: simulation
Castrillo et al (University of Valladolid), EMRS 2009
Conclusions
• Comprehensive description of diffusion in SiGe
• From point defects to self-, inter- and dopant diffusion
• Connection of the basic microscopic phenomenology with
measurable magnitudes
• Parameter calibration with a wide range of experimental
conditions and ab-initio calculations
• KMC implementation in the atomistic DADOS simulator
• Good agreement between simulated profiles and
experiments
Castrillo et al (University of Valladolid), EMRS 2009