Study of Transport Properties
in strained MOSFETs: Multi-scale Approach
Maxime FERAILLE
June, the 17th 2009
CIFRE Thesis prepared with collaboration of
Institut des nanotechnologies de Lyon and STMicroelectronics
Supervisor
Co-supervisor
Pr. Alain PONCET (INSA)
Dr. Denis RIDEAU (STM)
Study of Transport Properties in Strained
MOSFETs: Multi-scale Approach
 Introduction
 Bandstructure Calculations
 Transport in Strained nMOSFETs
 Transport in Strained and Confined Systems
 Experimental Validation for holes
 Conclusions
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
2
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Outline
 Introduction
– Context
– Relation between strain and transport
 Bandstructure Calculations
 Transport in Strained nMOSFETs
 Transport in Confined Systems
 Experimental validation
 Conclusions
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
3
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
From wafer to transistor
45°
<010>
<-110>
Wafer
S
G D
Transistor
MOSFET
<110>
<110>
<100>
Several
ten nm
<1-10>
65nm technology node
Wafer tilted → <100>-channel
Influence of stress vs.
transport orientation
<001>
300mm
ezz
eyy
<110>
exx
<100>
Transport direction
Si crystal
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
4
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Technology Motivation
Doping vs. Scaling
Increasing doping leads
to higher effective field
Increase doping
to limit short channel effects
Mobility degradation
Lower mobility
Lower performance!
Needs of technology boosters for
mobility improvement
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
5
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Performance Enhancement Process
STI
C. Le Cam
VLSI’06
Parasitic stress…
CESL
SMT
S. Ito
IEDM’00
K. Ota
IEDM’02
… stress engineering
W Large
Uniaxial stress
<110> / <100> impact ?
Uniaxial Stress
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
6
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Industrial
Transport simulation under stress
Drift-diffusion
m, vsat → constant
stress
Empirical model
Piezoresistance model
Advanced
First investigation
Monte Carlo
Kubo-Greenwood
m → v(k), t(k)
Microscopic model
stress
Bandstructure calculation
Including strain effects
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
7
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Mobility variation: piezoresitance model
 Empirical Model:
Mobility variation
stress
Piezoresistance tensor
with only 3 coefficients
p11, p12 and p44
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
8
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Mobility variation: piezoresitance model
 Coefficients measured using wafer Bending setup
Uniaxial Stress
Setup A Channel <110>
Thomson et al., 2006
Gallon, et al., 2003
σ<110>
G +p
p11+p
12
44
S
2
D
σ<110>
Setup B Channel <100>
σ<110>
p11+pG12-p44
S
2
D
σ<110>
σ<100>
Thomson et al., 2006 σ<010>
p11
p12
σ<100>
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
σ<010>
9
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Hole piezoresistance coefficients
a
C. M. Smith, PR 94, 42 (1954)
b
K. Matsuda et al., JAP 73, 1838 (1993)
c
S. E. Thompson et al., TED 53, 1010 (2006)
d C.
Channel
Gallon et al., SSE 48 , 561 (2004)
Stress
pL
[10-11.Pa-1]
Bulk Si
Inversion
Layer in Si
<110>
71.8a,
53.5b
71.7c
60d
2.8a,
-2.5b
18.9c,
10.6d
-66.3a,
-58.5b
-33.8c,
-38.8d
138.1a,
112b
105.5c
<100>
6.6a, -6b
9.1c
<100>
-1.1a,
-6.2c
(p11+p12+p44)/2
<100>
Setup A
<110>
(p11+p12)/2
<-110>
(p11+p12-p44)/2
p44
<100>
Setup B
<010>
p11
p12
≠
Deduced
+ & /2
1b
1.45
needs understanding
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
10
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Industrial
transport simulation under stress
Drift-diffusion
m, vsat → constant
stress
Empirical model
Piezoresistance model
Advanced
New measurements
Monte Carlo
Kubo-Greenwood
m → m*, v, t
Microscopic model
stress
Bandstructure calculation
Including strain effects
Transport investigation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
11
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Conduction
Bands
(electrons)
Relaxed Si buffer: bandstructure basics
40 meV
hh and lh degenerancy
Dx, Dy, Dz
at G
equienergy
Gap
Valence
Bands
(holes)
Si ∆-valleys → {100}
Kz(108.m-1)
Ky(108.m-1)
50 meV
Kx(108.m-1)
kz [2p /a units]
Kz(108.m-1)
1
Relation dispersion
0.5
Ky(108.m-1)
0
-0.5
-1
-1
Kx(108.m-1)
Kz(108.m-1)
-1
-0.5 0
0.5
ky [2p/a units]
0
kx [2p/a units]
11
Γ-valleys at [000]
First Brillouin Zone
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Ky(108.m-1)
Kx(108.m-1)
12
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Physical relation between strain and mobility
Lattice
ezz
e┴
eyy (2)
e║
e║xx(1)
Phonons
interactions
Reciprocal
Mobility
space
Silicon
Stress
Dispersion relation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
13
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Outline
 Introduction
 Bandstructure Calculations
–
–
–
–
Methods
Relaxed buffer
Strain introduction
Impact of uniaxial strain
 Transport in Strained nMOSFETs
 Transport in Confined Systems
 Experimental validation
 Conclusions
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
14
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Bandstructure calculation methods
Schrödinger
Bloch function
Development
Methods
Solving
Time
Plane waves
Ab initio (DFT+LDA)
- Kohn-Sham equation
- GW correction
www.abinit.org
Self-consistent
Very slow
Centered-Bloch function
Semi-empirical
EPM
Pseudo-potential
30-bands k.p
Coupling terms (P,Q,..)
UTOX (In-house ST code)
Matrix diagonalization
fast
very fast
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
15
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Relaxed buffers bandstructures
GW
EPM
k.p
Si
Energy [eV]
Energy [eV]
 Ab initio calculations as relevant bandstructures
Ge
 k.p 30 bands method parameters fitted according to a least square
optimization on energies and curvature masses at several k-points
D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
16
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Strain introduction
Si on [111]-Ge
e
(2)
║
e║(1)
e┴
Lattice node
(continuum mecanics)
Shear strain →
Internal displacement
EPM
Pseudo-potentiall [Ry]
Atoms
position
Ab initio
Si
Ge
New interpolation Non
local pseudo-potential
(Symbol) Relaxed
G2
30-bands k.p
Symmetry broken
Face-centered cubic Oh
Perturbative theory approach
Supplementary coupling parameters
Methods
(l ,m ,n , ..)
Parameters impacted
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
17
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Bandstructure of Bulk Si under stress
Energy [eV]
 k.p 30 bands method parameters fitted according to a least square
optimization at several k-points
Conduction and valence
valleys shifts
GW
EPM
k.p
Same calculations with
L
10 Gpa uniaxial Relaxed
stress along <110>
[0.0277 0.0277 -0.0214 0 0 0]
[0.0277 0.0277 -0.0214 0 0 0.0314]
ε xx εyy εzz εyz εxz εxy
Shear
Shear component strain involves
large bandstructure modification
Energy [eV]
uniaxial
D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
18
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Uniaxial stress <110>: Conduction bands
Bands
displacement
1BZ
ε=[0.55 0.55 -0.47 0 0 0.63]
Dz –valleys coupling
Proportional to εxy
stress
stress
2BZ
Relative mass [r. u.]
Masses
Variations
Z-point
GW
EPM
k.p
Str. <110>
Stress [MPa]
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
19
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
hh
lh
Energy [eV]
Bands
displacement
Uniaxial stress <110>: Valence bands
so
GW
EPM
k.p
Masses
Variations
Stress <110> [GPa]
HH valence
Isoenergy surface (25meV)
Stress
-500 → 0 MPa
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
20
Introduction
Bandstructure Calculations Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Key ideas on bandstructure calculations
Semi-classical methods fits well Ab initio results but
the computational cost is much lower
Dz-valley transverse mass variation due to <110>uniaxial stress
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
21
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Transport in strained nMOS
 Introduction
 Bandstructure Calculations
 Transport in Strained nMOSFETs
– Monte-Carlo methods
– Bandstructure inclusion in Monte-Carlo Simulations
– Strained nMOSFETs simulations
 Transport in Confined Systems
 Experimental validation
 Conclusions
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
22
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Principle
Monte-Carlo Methods
Statistical solving of the Master
Boltzmann Transport Equation
Poisson
equation
Surface
roughness
Monte Carlo
Transport
phonons
Ionized impurity
Drain current
estimation
F
methods
Quantum-based
Interactions
SPARTA (ISE): Simple Particule
1 particle
Qpart=Qtot
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
23
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Structure SINANO
nMOSFET
High performance transistor of 65nm technology node
Ngrid
Tox
Nldd
50 nm
Lgate
Tox:16Ǻ
Nch
50 nm
Nldd
Nch:3,0 .1018 cm-3
Ngrid:1,0 .1020 cm-3
Nldd:1,0 .1020 cm-3
Lgate: 32 nm
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
24
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Bandstructure
Bandstructure inclusion in Monte-Carlo methods
Scattering
rates
Full-band
Monte-Carlo
simulators
Dispersion
relation
30-bands k.p methods
Sparta
Unstrained (1/48)
General strain (1/2)
Meshing in k-space
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
25
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Strained nMOSFET: current variation
Tensile
Ilin
Compressive
Current variation (%)
Str <100>
Str <110>
200 MPa
Ilon
Ilin
Variation reduction
high-field transport regim
Ilon
<100>-channel
Vg-Vth=1V
Ilin → Vd=0.1V
Ion → Vd= 1V
Vs=0V
Vd
Vb=0V
Drain current
32 nm gate length
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
SPARTA
26
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Strained nMOSFET: Variation summarize
 Variation
trends with high-field transport regim
Drain current
 Variation
trends with shorter nMOSFETs
Non-equilibrium effects
S
G
D
<110>
<100>
 <110>-Oriented channel: variation
between Stress
<-110>
<110>
<100>
 <100>-oriented channel: Larger variation for Stress <100>
<-110>
→ Transport re-oriented along <100>
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
27
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Electron: Monte Carlo 3Dk vs. p-model
nMOSFET 32 nm channel length Monte Carlo simulation
Ilin Vd=0.1V
Ilin Vd=0.1V
Ch. <110>
Ch. <100>
Electron p44 coefficients is associated
to the Dz curvature mass modification along <110>
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
28
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Electrons inversion layer π-coefficients
New electron p-coefficients determination
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
29
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Extracted electron coefficients vs. literature
Channel
Stress
pL
[10-11.Pa-1]
Bulk
Si
Inversion Layer
in Si
<110>
-31.2a,
-26b
-35.5c,d, -48.5e,
-37.7f
-24.4a,
-19.0b
-25c,d,g, -34.9e,g,
-22.4f
-17.6a,
-12b
-14.5c,d, -21.2e,
-7.1f
-13.6a,
-14b
-21c,d,g, -27.2e,g,
-30.6g
(p11+p12+p44)/2
<100>
(p11+p12)/2
<110>
<-110>
(p11+p12-p44)/2
p44
a
C. M. Smith, PR 94, 42 (1954)
b
K. Matsuda et al., JAP 73, 1838 (1993)
c
S. E. Thompson et al., TED 53, 1010 (2006)
d S.
E. Thompson et al., IEDM , 415 (2006)
e C.
Gallon et al., SSE 48 , 561 (2004)
f Measured
Measured
Deduced
from Wafer Bending
g Deduced
from <110> and <-110> stress
measurements
Our measurements are consistent
vs. Literature
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
30
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Key ideas on transport in strained nMOS
Experimental mobility variation is well reproduced with
Monte carlo simulation
p44 coefficient is related to the curvature modification of
Dz valley
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
31
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Outline
 Introduction
 Bandstructure Calculations
 Transport in Strained nMOSFETs
 Transport in Confined Systems
–
–
–
–
Confinement introduction
Bandstructure in a relaxed Quantum Well
Bandstructure in a strained Quantum Well
Holes transport in confined systems
 Experimental validation
 Conclusions
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
32
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Confinement introduction
 Confinement appear for Lsystem < Lbroglie
 Translation symmetry broken in the confinement direction
3D crystal
Z
L
U
Y
→ First Brillouin zone reduction to 2D
X
W
2D system
K
Z’
X’
Y’
K’
E3’
E3
E2’
E2
E1’
E1
E0’
→ Sub-bands structure
D4
Unstrained
D2
Strained
bulk
E0
Strained MOSFET
Inversion layer
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
33
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Methods for confined states
oxide
Confined
System
Conduction
band
Channel
LQW
Si-ox
Substrat
V(z)
Vc
z
(e.g SOI MOSFET)
Vb: 0.4
Vc: 0.3
Vb
Valence band
LA
Hamiltonian
Methods
k.p 30-bands
k.p 6-bands
Envelop function
Effective Mass Approximation
Plane waves
: quantization mass
curvature mass along the confinement
direction
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
34
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Conduction sub-bands in relaxed QW
5 nm
LQW
EMA
30-bands k.p
First sub-bands energy map
Energy shifts
Good adequation between k.p 30 bands
and EMA methods: isolated D-valleys
<001> confinement orientation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
35
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Valence sub-bands in relaxed Quantum-Well
<001> confinement orientation
5 nm
E0
[eV]
E1
E2
<100> <110>
E0’
30-bands k.p
6-bands k.p
E1’
E2’
First sub-bands energy map
Dispersion relation
Discrepancies Increase between 6 and 30 bands k.p methods results
with layer width reduction
Coupling between hh and conduction
Bands doesn’t exist k.p 6 bands
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
36
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Conduction
Subbands
Stress impact on subbands
Dz Isocontours
10 meV-spaced
k.p methods
Valence
Subbands
Stress <110>
Relaxed
mass modification
First sub-band
Isocontour
40 meV-spaced
5 nm
Str <110>
<001> confinement orientation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
37
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Dz sub-band masses vs. stress <110>
LQW
Str <110>
Dz is the lowest sub-bands
Bulk-like
Strain
Strain+
Confinement
Enhanced
variation
30-bands k.p
Curvature mass <110>
2Dk vs. 3Dk Simulation expected to be
in good agreements for weakly confined
system
D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008).
<001> confinement orientation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
38
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Valence subbands vs. strain <110>
Str <110>
5 nm
F=1MV/cm
Relaxed
Str <110>: 500 Mpa
<001> confinement orientation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
39
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Static
properties
Holes Transport in inversion layer
Self-consistent bandstructure calculations
k.p-Poisson (1D)-Schrödinger solving
Transport
properties
Bandstructure
Density
Inversion layer linear transport
Kubo-Greenwood
Transport formula
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
40
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
k.p-Poisson-Schrödinger self-consistent calculations
Poisson
6-bands k.p-Schrödinger
Eigenvalues
, Eigenvectors
-k-points mesh
V(z)
Confinement potential
-predictor-corrector iteration scheme
-Matrix eigenvalues:
Lanczos + spectral transformation
Bandstructure calculation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
41
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Kubo-Greenwood solvers
 transport formula coming from Boltzmann equation
linearization
Density
Phonon relaxation time
Bandstructure
3Dk
2Dk
− Elastic acoustic
− Inelastic nonpolar Optical
Wang et al., TED 53, 1840 (2006)
hh bands
Stress <110>
isoenergy -500 Mpa → 0 MPa
Three topmost
sub-bands energies
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
42
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
3Dk vs. 2Dk Kubo-Greenwood solvers
Crystal 3Dk bandstructure
Self-consistent k.p-poisson
Inversion layer 2Dk bandstructure
Low-field Monte Carlo
simulations equivalent
Kubo-Greenwood mobility
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
43
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Key ideas on transport in confined system
Electrons <110>-curvature mass modification similar in
2Dk and 3Dk systems
Confinement involves strong impact on hole
bandstructure variation vs. Stress
k.p-poison-schrödinger used in transport properties
studied in hole inversion layer
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
44
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Outline
 Introduction
 Bandstructure Calculations
 Transport in Strained nMOSFETs
 Transport in Confined Systems
 Experimental validation for holes
–
–
–
–
Wafer Bending experiments
Holes mobility extraction
Hole piezoresistance coefficients determination
Advanced transport simulations validation
 Conclusions
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
45
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Strain: setup 1
Conclusions
σ<110>
130nm technology node
σ<100>
σ<110>
σ<110>
G
S
G
G
D
S
S
D
D
σ<100>
<110>
σ<110>
<110>
<001>
Unusual
<110>-oriented channel
Dμ
μ
=
p11+p12+p44
2
. σ
Dμ
μ
=
p11+p12 .
σ
2
Dμ
μ
=
p11+p12-p44
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
2
. σ
46
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Strain: setup 2
130nm technology node
σ<100>
σ<100>
<110>
<110>
<001>
σ<100>
σ<100>
<100> and <010>-oriented channel
Dμ
μ
=
p11
. σ
Dμ
μ
=
p12 . σ
Our wafer bending experiments
allows a complete determination of p-coefficients
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
47
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
mobility variation extraction
Linear transport properties
Vd=0.1V
<110>
Vd=0.1V
<100>
Device B
Vd=0.1V
Channel <110>
<-110>
Mobility variation extracted from drain current ratio
between relaxed and strained devices
K. HUET, M. FERAILLE et al., Proc. IEEE. ESSDERC, p. 234 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
48
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Holes inversion layer π-coefficients
Device B
 Bulk values are not satifactory to adjust mobility variation
p-coefficients must be fitted
 Experimental determination done.
K. HUET, M. FERAILLE et al., Proc. IEEE. ESSDERC, p. 234 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
49
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Extracted hole coefficients vs. Literature
Channel
Stress
pL
[10-11.Pa-1]
Bulk Si
Inversion
Layer in Si
<110>
71.8a,
53.5b
71.7c,d, 60e,
78.5f
(p11+p12)/2
2.8a,
-2.5b
18.9c,d,g,
10.6e,g, 14.5f
<-110>
-66.3a,
(p11+p12-p44)/2
-58.5b
p44
138.1a,
112b
105.5c,d,h,
128g
<100>
6.6a, -6b
9.1c,d, 6f
f
<100>
-1.1a, 1b
-6.2c,d, 23f
g
(p11+p12+p44)/2
<100>
Setup 1
<110>
<100>
Setup 2
<010>
p11
p12
-33.8c,d,
-38.8e,
-49.5f
Coherent
a
C. M. Smith, PR 94, 42 (1954)
b
K. Matsuda et al., JAP 73, 1838 (1993)
c
S. E. Thompson et al., TED 53, 1010 (2006)
d S.
E. Thompson et al., IEDM , 415 (2006)
e C.
Gallon et al., SSE 48 , 561 (2004)
New measurements
Cefficients deduced from <110> and
<-110> stress measurements
Difference
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
50
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Hole: Kubo-Greenwood 3Dk vs. Exp.
Device B
Kubo-Greenwood 3Dk fail to reproduce experiments
K. HUET, M. FERAILLE,et al., Proc. IEEE. ESSDERC, p. 234 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
51
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Hole: Kubo-Greenwood 2Dk vs. Exp.
Quantization effect must be taken into account
To study transport properties in hole inversion layer under stress
K. HUET, M. FERAILLE,et al., Proc. IEEE. ESSDERC, p. 234 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
52
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Theorical hole p-coefficient extraction
Channel
Bulk Si
Exp.
Exp.
Theo. h
<110>
71.8a,
53.5b
71.7c,d, 60e,
78.5f
69.5
2.8a,
-2.5b
18.9c,d,h,
10.9e,h, 14.5f
(p11+p12+p44)/2
<100>
(p11+p12)/2
<110>
<-110>
(p11+p12-p44)/2
p44
<100>
<010>
Inversion
Layer in Si
Strain
pL
[10-11.Pa-1]
-66.3a,
-58.5b
138.1a,
112b
<100>
6.6a,
<100>
-1.1a, 1b
p11
p12
-6b
19.5
a
C. M. Smith, PR 94, 42 (1954)
b
K. Matsuda et al., JAP 73, 1838 (1993)
c
S. E. Thompson et al., TED 53, 1010 (2006)
d S.
E. Thompson et al., IEDM , 415 (2006)
e C.
Gallon et al., SSE 48 , 561 (2004)
-33.8c,d,
-38.3e,
-49.5f
105.5c,d,h,
128g
9.1c,d,
6f
-6.2c,d, 23f
-30.5
f New
measurements
g Cefficients
100
10.5
28.5
deduced from <110>
and <-110> stress measurements
h 2Dk
Kubo-Greenwood
simulations
New complete and
Consistent p-coefficients
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
53
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Key ideas on experiments vs. simulations
Presentation of new experimental data of mobility
variation in strained pMOSFETs
Determination of New piezoresistance coefficients values
Quantization effects must accounted for in the hole
inversion layer transport properties
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
54
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Conclusions
 Development and benchmark of bandstructure calculations tools
of bulk material under stress
 3Dk transport properties analysis on nMOSFETs
− Monte Carlo reproduce experimental hole mobility variation
− p44 coefficient related to the Dz curvature modification under stress
 Transport properties studies in hole inversion layer
− Development of self-consistent k.p Poisson-schrödinger calculations
− Divergence between 2Dk and 3Dk Kubo-Greenwood transport solutions
 New Wafer Bending experiments
− Consistent and complete piezoresistant coefficients determined
− Quantization effects modelling are mandatory in the strained p-MOSFETs
transport study
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
55
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Perspectives 65nm CESL Stress cartography
 3Dk transport properties analysis considering non
uniformly stress.
Stress
Max
Min
Channel
 Transport in inversion layer should be examined
using k.p-Poisson-Schrödinger calculations on the
conduction bands
Uniax.
Stress
 Confinement impact in the high-field transport
properties of short channel MOSFET structure must
be studied
 Confrontation of measurements and advanced
transport solvers solutions must be performed at
high stress level
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
56
Publications
Journal
[1] “On the Validity of the Effective Mass Approximation and the Luttinger k.p Model in Fully Depleted SOI MOSFETs”
D. RIDEAU, M. FERAILLE, M. MICHAILLAT, Y. M. NIQUET, C. TAVERNIER, and H. JAOUEN, Solid- State Electronics 53, p.452 (2008).
[2] “Strained Si, Ge, and Si1-xGex alloys modeled with a first-principles-optimized full-zone k.p method”
D. RIDEAU, M. FERAILLE, L.CIAMPOLINI, M. MINONDO, C. TAVERNIER, and H. JAOUEN, Phys. Rev. B 74, p. 195208 (2006).
Conference
Talk
[1] “Experimental and Theoretical Analysis of Hole Transport in Uniaxially Strained pMOSFETS”
K. HUET, M. FERAILLE, D. RIDEAU, R. DELAMARE, V. AUBRY-FORTUNA, and M.KASBARI, S. BLAYAC, C. RIVERO, A. BOURNEL,
C. TAVERNIER, P. DOLLFUS, and H. JAOUEN, Proc. IEEE. ESSDERC, p. 234 (2008).
[2] “Transport Masses in Strained Silicon MOSFETs with Different Channel Orientations”
D. RIDEAU, M. FERAILLE, M. MICHAILLAT, C. TAVERNIER, and H. JAOUEN, Proc. IEEE. SISPAD, p. 106 (2008).
[3] “On the validity of the Effective Mass Approximation and the Luttinger k.p Model in Confined and Strained 2D-Holes-Systems”
D. RIDEAU, M. FERAILLE, M. SZCZAP, C. TAVERNIER, and H. JAOUEN, Proc. IEEE ULIS, p. 63 (2008).
[4] “Electronic bandstructure of two dimensional strained semiconductors”
M. FERAILLE and D. RIDEAU, GDR Nano, Journées - Simulation et Caractérisation -, les 19 et 20 octobre 2006, Grenoble (2006).
Poster
[1] “Low-Field Mobility in Strained Silicon with Full Band Monte Carlo Simulation using k.p and EPM
Bandstructure”
M. FERAILLE, D. RIDEAU, A. GHETTI, A. PONCET, C. TAVERNIER, and H. JAOUEN, Proc. IEEE SISPAD, p. 264 (2006).
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
57
QUESTIONS ?
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
58
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Transport
Bandstructure
Multi-scale Approach (crystal)
Semi-empirical
− EPM (Empirical pseudo-potentiel method)
Ab initio
− k.p
Reference
calculation
Parameters fitting
− Monte Carlo 3Dk
− Gap & m*
− Kubo-Greenwood 3Dk
− Piezoresistance
coefficients
Advanced simulations
Drift-Diffusion
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
59
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Transport
Bandstructure
Multi-scale Approach (inversion layer)
− k.p envelop function
Confinement effect
Si
− EMA (effective mass approximation)
Parameters fitting
2Dk
Piezoresistance
coefficients
Advanced simulations
Drift-Diffusion
Kubo-Greenwood
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
60
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Methodology
Strain e
Bandstructures
calculations
Experiments
Thesis
work
Relation
-Energies E (k)
-Scattering Rates t(k)
Piezoresistance
coefficients
Transport
calculations
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
61
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
k.p-Poisson-Schrödinger self-consistent calculations
Poisson
6-bands k.p-Schrödinger
Eigenvalues
, Eigenvectors
Confinement potential
V(z)
Isocontour 1rst subbands
& Fermi distribution
Profiles
Bandstructure calculation
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
62
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Biaxial stress impact on 3Dk hole mobility
pMOSFET Bulk planar
Degenerancy lift
hh
t variation
lh
so
biaxial Stress 648MPa
Scattering time variation
hh
lh
so
Relaxed
K. HUET, M. FERAILLE, et al., Proc. IEEE. ESSDERC, p. 234 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
63
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Biaxial stress impact on 2Dk hole mobility
pMOSFET Bulk planar
Strain-confinement effects
compensation
hh
lh
so
m* modification
t variation
Relaxed
biaxial Stress 648MPa
hh
hh
lh
lh
so
compensation
so
5 nm
F=1MV/cm
Curvature modification
Scattering time variation
K. HUET, M. FERAILLE,et al., Proc. IEEE.
ESSDERC, p. 234 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
64
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Impact of uniaxial stress on 2Dk hole mobility
Str <110>
Str < 100>
Str <-110>
Tensile
Compressive
Mobility Variation (%)
200 MPa
pMOSFET Bulk planar
Str <110>: Decrease of the mobility vs. stress
Str <-110>: Increase of the mobility vs. stress
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
65
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
3Dk vs 2Dk Kubo-Greenwood simulations
Str < 100>
Tensile
Compressive
Mobility Variation (%)
200 MPa
pMOSFET Bulk planar
Str <100> tens.: Behaviour divergence from 2Dk and 3Dk simulations
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
66
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Unstrained nMOSFETs: profiles
25 nm gate lenth, Vg=1V, Vd=1V
1Å cut from from Si/SiO2 interface
SiO2
1 Å cut
Si
Channel
25 nm
Using 30-bands k.p
Velocity
Overshoot
Carrier density
spreading
Bulk Vsat
Using 30-bands k.p
Concentration
Velocity
Presence of non-equilibrium thermodynamic effects
in short channel MOSFETs
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
67
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Unstrained nMOSFETs: characteristics
Vg
Vs=0V
Vd
Vb=0V
Using 30-bands k.p methods
IdVd
Drain current
Using 30-bands k.p methods
IdVg
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
68
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Unstrained nMOSFETs: Ion vs. Gate length
Difference
increase
Vg=1V
Vg=1V
Resistance access contribution increase with gate length reduction
Differents Monte Carlo treatments of the ionized impurity scattering time and
access resistance (see Fiegna et al, SISPAD 2007)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
69
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Valence sub-bands and masses vs. QW length
LQW
Discrepancies
Between k.p methods
Curvature mass <100>
Energy shifts
Coupling between hh and conduction
Bands doesn’t exist k.p 6 bands
Mass variation vs. confinement strength
not reproduced by EMA methods
D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
70
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Conduction sub-bands and masses vs. QW length
<001> confinement orientation
LQW
30-bands k.p
EMA
30-bands k.p
Curvature mass <110>
Energy shifts
Good adequation between k.p 30 bands
and EMA methods: isolated D-valleys
Mass variation vs. confinement strength
not reproduced by EMA methods
D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008)
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
71
Introduction
Bandstructure Calculations
σ<110>
G
S
<110>
σ<100>
<110>
<001>
G
σ<110>
G
D
Conclusions
Device B
Type
Device A
Device B
nMOS
pMOS
pMOS
<110>
<001>
130 nm
Technology
<110>
σ<100>
D
σ<100>
S
Experimental Validation
σ<100>
D
S
Transport in confined Systems
Devices measured
Device A
σ<110>
Transport in Strained nMOS
Oxide type
GO2
GO1
Tox (Ǻ)
85
21
Channel
orientation
<110>
<100>, <010>
and <110>
Strain
Orientation
<110>, <100>
and <110>
<100>, <110>
and <110>
σ<100>
σ<100>
σ<110>
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
72
Introduction
Bandstructure Calculations
Transport in Strained nMOS
Transport in confined Systems
Experimental Validation
Conclusions
Wafer Bending experiments
R curvature
e thickness
Stress estimation:
: Young’s modulus
ST Rousset-Crolles collaboration
Well-defined stress
June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
73