study of transport properties in strained mosfets: multi-scale approach
DESCRIPTION
Study of Transport Properties in strained MOSFETs: Multi-scale Approach . Maxime FERAILLE June, the 17 th 2009 CIFRE Thesis prepared with collaboration of Institut des nanotechnologies de Lyon and STMicroelectronics SupervisorPr. Alain PONCET (INSA) - PowerPoint PPT PresentationTRANSCRIPT
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Study of Transport Propertiesin 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 Pr. Alain PONCET (INSA)Co-supervisor Dr. Denis RIDEAU (STM)
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2 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 2 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
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
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3 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 3 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Outline
Introduction– Context– Relation between strain and transport
Bandstructure Calculations
Transport in Strained nMOSFETs
Transport in Confined Systems
Experimental validation
Conclusions
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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4 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
<100>
<010
>
<110>
<-11
0>
From wafer to transistorIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Transistor MOSFET
Wafer
300mm
Severalten nm
Si crystal
G DS
<110>
<1-10> ezz eyy
exx
<001
>
<100>
<110>
65nm technology nodeWafer tilted → <100>-channel Transport direction
45°
Influence of stress vs.transport orientation
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5 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Technology MotivationDoping vs. Scaling
Needs of technology boosters formobility improvement
Lower mobilityLower performance!
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Increase doping to limit short channel effects
Increasing doping leadsto higher effective field
Mobility degradation
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6 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Performance Enhancement Process
… stress engineering
CESL SMT
S. Ito IEDM’00
K. OtaIEDM’02
C. Le CamVLSI’06
STI
Uniaxial stress<110> / <100> impact ?
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Parasitic stress…
Uniaxial Stress
W Large
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7 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 7 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Transport simulation under stressIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Drift-diffusionm, vsat → constant
First investigation
Piezoresistance model
Monte CarloKubo-Greenwood
m → v(k), t(k)
Empirical model
Indu
stria
lA
dvan
ced
stress
stressMicroscopic model
Bandstructure calculationIncluding strain effects
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8 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 8 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Mobility variation: piezoresitance model Empirical Model:
Piezoresistance tensor with only 3 coefficients
p11, p12 and p44
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
stressMobility variation
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9 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 9 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
σ<110>σ<110> G
DS
Mobility variation: piezoresitance modelIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
σ<110>
G
DS
σ<110>
Coefficients measured using wafer Bending setup
Channel <110>
σ<100>
G
D
S
σ<100>
σ<010>
G
D
S
σ<010>
Thomson et al., 2006Gallon, et al., 2003
Thomson et al., 2006
Setup A Setup B Channel <100>
p11+p12+p44
2p11+p12-p44
2p11 p12
Uniaxial Stress
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10 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 10 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
a C. M. Smith, PR 94, 42 (1954)b K. Matsuda et al., JAP 73, 1838 (1993)
d C. Gallon et al., SSE 48 , 561 (2004)
Hole piezoresistance coefficients
ChannelStresspL
[10-11.Pa-1]Bulk Si Inversion
Layer in Si
<110>
<110>(p11+p12+p44)/2
71.8a, 53.5b
71.7c
60d
<100>(p11+p12)/2
2.8a, -2.5b
18.9c,10.6d
<-110>(p11+p12-p44)/2
-66.3a, -58.5b
-33.8c, -38.8d
p44138.1a,
112b 105.5c
<100> <100>p11
6.6a, -6b 9.1c
<010> <100>p12
-1.1a, 1b -6.2c + & /2
1.45
≠
needs understanding
c S. E. Thompson et al., TED 53, 1010 (2006)
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Setup A
Setup B
Deduced
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11 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 11 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
transport simulation under stressIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Drift-diffusionm, vsat → constant
Transport investigation
Piezoresistance model
Monte CarloKubo-Greenwood
m → m*, v, t
Empirical model
Indu
stria
lA
dvan
ced
stress
stressMicroscopic model
Bandstructure calculationIncluding strain effects
New measurements
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12 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 12 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Relaxed Si buffer: bandstructure basicsC
ondu
ctio
nB
ands
(ele
ctro
ns)
Vale
nce
Ban
ds(h
oles
) Si ∆-valleys → {100}
Kx(108.m-1)
Kx(108.m-1)
Kx(108.m-1)
Kz(108.m-1)
Kz(108.m-1)
Kz(108.m-1)
Ky(108.m-1)
Ky(108.m-1)
Ky(108.m-1)
Γ-valleys at [000]
Gap
40 meV
50 meV
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Dx, Dy, Dz equienergy
hh and lh degenerancy at G
010 0.5 1
0
0.5
1
kx [2p/a units]
ky [2p/a units]
kz [2
p/a
units
]
-1-1
-0.5
-0.5
-1
N
X
GU
KW
L
First Brillouin Zone
Relation dispersion
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13 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 13 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
ezz eyy
exx
Physical relation between strain and mobilitySi
licon
Latti
cee┴ e ║
(2)
e║(1)
Rec
ipro
cal
spac
e
Dispersion relation
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Phononsinteractions
Mob
ility
Stress
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14 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 14 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Outline Introduction
Bandstructure Calculations– Methods– Relaxed buffer– Strain introduction– Impact of uniaxial strain
Transport in Strained nMOSFETs
Transport in Confined Systems
Experimental validation
Conclusions
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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15 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Bandstructure calculation methodsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Schrödinger
Development Plane waves Centered-Bloch function
Methods Ab initio (DFT+LDA)- Kohn-Sham
equation- GW correction
Semi-empirical
EPM 30-bands k.pPseudo-potential Coupling terms (P,Q,..)
Solvingwww.abinit.org UTOX (In-house ST code)
Self-consistent Matrix diagonalization
Bloch function
Time Very slow fast very fast
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16 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 16 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Relaxed buffers bandstructures Ab initio calculations as relevant bandstructures
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
GWEPMk.p
Si Ge k.p 30 bands method parameters fitted according to a least square
optimization on energies and curvature masses at several k-points
Ener
gy [e
V]
Ener
gy [e
V]
D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)
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17 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 17 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Face-centered cubic Oh
New interpolation Non local pseudo-potential
Strain introductionIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Ab initio
EPM
30-bands k.p
Methods Parameters impacted
Lattice node(continuum mecanics)
Shear strain →Internal displacement
Si on [111]-Ge
Ato
ms
posi
tion
Perturbative theory approach
Symmetry broken
Supplementary coupling parameters (l ,m ,n , ..)
e┴e║
(1) e ║(2)
Pseu
do-p
oten
tiall
[Ry]
(Symbol) Relaxed
SiGe
G2
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18 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 18 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Bandstructure of Bulk Si under stress k.p 30 bands method parameters fitted according to a least square
optimization at several k-points
GWEPMk.p
Ener
gy [e
V]
10 Gpa uniaxial stress along <110>
Ener
gy [e
V]
Shear component strain involves large bandstructure modification
D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Conduction and valence valleys shifts
Same calculations with
[0.0277 0.0277 -0.0214 0 0 0]ε xx εyy εzz εyz εxz εxy
uniaxial Shear
[0.0277 0.0277 -0.0214 0 0 0.0314]
L
Relaxed
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19 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Stress [MPa]
Rel
ativ
e m
ass
[r. u
.]
Str. <110>
Uniaxial stress <110>: Conduction bandsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
GW
k.pEPM
Ban
dsdi
spla
cem
ent
Mas
ses
Varia
tions
stressstress
D x, D y Valleys
Dz Valleys ε=[0.55 0.55 -0.47 0 0 0.63]
Dz –valleys couplingProportional to εxy
Z-point
1BZ 2BZ
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20 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Uniaxial stress <110>: Valence bandsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Ener
gy [e
V] GW
k.pEPM
hhlh
so
Stress <110> [GPa]
Stress-500 → 0 MPa
Ban
dsdi
spla
cem
ent
Mas
ses
Varia
tions HH valence
Isoenergy surface (25meV)
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21 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
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
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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22 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 22 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Transport in strained nMOSIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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
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23 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Monte-Carlo Methods
Drain currentestimation
Poissonequation
SPARTA (ISE): Simple Particule
Qpart=Qtot
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental ValidationPr
inci
ple
1 particle
Statistical solving of the Master Boltzmann Transport Equation
met
hods
FIonized impurity
phonons
Surface roughness
Quantum-basedInteractions
Monte CarloTransport
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24 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Structure SINANOIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
nMOSFET High performance transistor of 65nm technology node
Tox:16Ǻ
Ngrid:1,0 .1020 cm-3 Nldd:1,0 .1020 cm-3
Lgate: 32 nm
Ngrid
Tox
NlddNldd NchLgate 50 nm50 nm
Nch:3,0 .1018 cm-3
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25 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Bandstructure inclusion in Monte-Carlo methodsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Dispersionrelation
Scatteringrates
Ban
dstr
uctu
re
Meshing in k-space
Sparta
Full-bandMonte-Carlosimulators
Unstrained (1/48) General strain (1/2)
30-bands k.p methods
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26 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Strained nMOSFET: current variationIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
200 MPa
Ion → Vd= 1V
Ilin → Vd=0.1V
SPARTA
Vg-Vth=1V
Drain current
VdVs=0V
Vb=0V
Str <110> Str <100>
Variation reduction high-field transport regimC
urre
nt v
aria
tion
(%)
<100>-channel
Ilin Ilon Ilin Ilon
32 nm gate length
Tens
ileC
ompr
essi
ve
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27 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Strained nMOSFET: Variation summarizeIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Variation trends with shorter nMOSFETs
Variation trends with high-field transport regim
<110>-Oriented channel: variation between Stress
<100>-oriented channel: Larger variation for Stress <100>
G DS
<110>
<-110>
<100>
<-110>
<100><110>
Drain current
→ Transport re-oriented along <100>
Non-equilibrium effects
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28 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 28 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Electron: Monte Carlo 3Dk vs. p-modelnMOSFET 32 nm channel length Monte Carlo simulation
Ch. <110> Ch. <100>
Electron p44 coefficients is associated to the Dz curvature mass modification along <110>
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Ilin Vd=0.1V Ilin Vd=0.1V
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29 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 29 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
New electron p-coefficients determination
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Electrons inversion layer π-coefficients
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30 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 30 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Extracted electron coefficients vs. literature
ChannelStresspL
[10-11.Pa-1]
Bulk Si
Inversion Layer in Si
<110>
<110>(p11+p12+p44)/2
-31.2a, -26b
-35.5c,d, -48.5e,-37.7f
<100>(p11+p12)/2
-24.4a, -19.0b
-25c,d,g, -34.9e,g, -22.4f
<-110>(p11+p12-p44)/2
-17.6a, -12b
-14.5c,d, -21.2e,-7.1f
p44-13.6a,
-14b-21c,d,g, -27.2e,g,
-30.6g
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 from Wafer Bendingg Deduced from <110> and <-110> stress measurements
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Deduced
Measured
Our measurements are consistent vs. Literature
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31 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
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
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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32 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
OutlineIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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
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33 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 33 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Confinement introduction Confinement appear for Lsystem < Lbroglie
Translation symmetry broken in the confinement direction
→ First Brillouin zone reduction to 2D
→ Sub-bands structure
L
X
U
W K
Y
Z
X’ K’Y’
3D crystal
2D system
D4
D2
E3’
E2’
E1’
E0’
E3
E2
E1
E0
Unstrained Strained bulk
Strained MOSFETInversion layer
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Z’
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34 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Methods for confined states
Hamiltonian
Met
hods
k.p 30-bands k.p 6-bandsEnvelop function
ConfinedSystem
(e.g SOI MOSFET)Valence band
Conduction band
z
V(z)LQW
oxide SubstratChannel
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Effective Mass Approximation
LA
Plane waves
: quantization mass
curvature mass along the confinementdirection
Vb
Vc
Si-oxVb: 0.4Vc: 0.3
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35 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Conduction sub-bands in relaxed QWIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
5 nm
First sub-bands energy map
Good adequation between k.p 30 bandsand EMA methods: isolated D-valleys
EMA30-bands k.p
LQW
Energy shifts
<001> confinement orientation
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36 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 36 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Valence sub-bands in relaxed Quantum-WellIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
[eV]
First sub-bands energy map
<001> confinement orientation
Dispersion relation
30-bands k.p
6-bands k.p
5 nm
E0
E1
E2
E0’
E1’
E2’
<110><100>
Coupling between hh and conductionBands doesn’t exist k.p 6 bands
Discrepancies Increase between 6 and 30 bands k.p methods results with layer width reduction
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37 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Stress impact on subbandsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Con
duct
ion
Subb
ands
Vale
nce
Subb
ands
Dz Isocontours10 meV-spaced
Stress <110> Relaxed
k.p methods
First sub-bandIsocontour
40 meV-spaced
<001> confinement orientation
mass modification
5 nmStr <110>
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38 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 38 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Dz sub-band masses vs. stress <110>Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
<001> confinement orientation
2Dk vs. 3Dk Simulation expected to be in good agreements for weakly confinedsystem
30-bands k.p
Curvature mass <110>
D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008).
Strain
Strain+Confinement
Bulk-like
LQW Str <110>
Dz is the lowest sub-bands
Enhanced variation
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39 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 39 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Valence subbands vs. strain <110>Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
<001> confinement orientation
5 nmStr <110>
F=1MV/cm
Relaxed
Str <110>: 500 Mpa
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40 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 40 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Holes Transport in inversion layerIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
k.p-Poisson (1D)-Schrödinger solving
Kubo-GreenwoodTransport formula
Inversion layer linear transport
Self-consistent bandstructure calculations
Stat
ic
prop
ertie
sTr
ansp
ort
prop
ertie
s
BandstructureDensity
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41 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
k.p-Poisson-Schrödinger self-consistent calculationsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Poisson
6-bands k.p-SchrödingerEigenvalues , Eigenvectors
Bandstructure calculation
V(z)Confinement potential
-predictor-corrector iteration scheme
-k-points mesh
-Matrix eigenvalues: Lanczos + spectral transformation
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42 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 42 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Kubo-Greenwood solvers transport formula coming from Boltzmann equation
linearization
Density Bandstructure
− Elastic acoustic− Inelastic nonpolar Optical
Phonon relaxation time
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Stress <110>-500 Mpa → 0 MPa
Three topmost sub-bands energies
hh bandsisoenergy
3Dk 2Dk
Wang et al., TED 53, 1840 (2006)
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43 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 43 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
3Dk vs. 2Dk Kubo-Greenwood solversIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Kubo-Greenwood mobility
Crystal 3Dk bandstructure Self-consistent k.p-poissonInversion layer 2Dk bandstructure
Low-field Monte Carlo simulations equivalent
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44 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
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
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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45 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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
Outline
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46 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 46 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Strain: setup 1Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
<110>
<110>
<001>
σ<100>
σ<100>
G
DS
σ<110>σ<110> G
DS
σ<110>
G
DS
σ<110>
p11+p12+p44
2
Dμμ = σ. p11+p12
2
Dμμ = σ. p11+p12-p44
2
Dμμ = σ.
Unusual
130nm technology node
<110>-oriented channel
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47 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 47 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Strain: setup 2Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
G
D
S
σ<100>
σ<100>
σ<100>
<110>
<110>
<001>
G
D
S
σ<100>
<100> and <010>-oriented channel
p11Dμμ = σ. p12
Dμμ = σ.
Our wafer bending experimentsallows a complete determination of p-coefficients
130nm technology node
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48 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
mobility variation extractionIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Mobility variation extracted from drain current ratiobetween relaxed and strained devices
<110>
<100> <-110>
Vd=0.1V
Vd=0.1V
Vd=0.1V
Linear transport properties
K. HUET, M. FERAILLE et al., Proc. IEEE. ESSDERC, p. 234 (2008)Channel <110>
Device B
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49 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Holes inversion layer π-coefficientsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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)
Device B
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50 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 50 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Extracted hole coefficients vs. LiteratureIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
ChannelStresspL
[10-11.Pa-1]Bulk Si Inversion
Layer in Si
<110>
<110>(p11+p12+p44)/2
71.8a, 53.5b
71.7c,d, 60e, 78.5f
<100>(p11+p12)/2
2.8a, -2.5b
18.9c,d,g, 10.6e,g, 14.5f
<-110>(p11+p12-p44)/2
-66.3a, -58.5b
-33.8c,d, -38.8e,-49.5f
p44138.1a,
112b 105.5c,d,h, 128g
<100> <100>p11
6.6a, -6b 9.1c,d, 6f
<010> <100>p12
-1.1a, 1b -6.2c,d, 23f
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 New measurements
g Cefficients deduced from <110> and <-110> stress measurements
Difference
Setup 1
Setup 2
Coherent
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51 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 51 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Hole: Kubo-Greenwood 3Dk vs. Exp.Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Kubo-Greenwood 3Dk fail to reproduce experiments
K. HUET, M. FERAILLE,et al., Proc. IEEE. ESSDERC, p. 234 (2008)
Device B
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52 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 52 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Hole: Kubo-Greenwood 2Dk vs. Exp.Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Quantization effect must be taken into accountTo study transport properties in hole inversion layer under stress
K. HUET, M. FERAILLE,et al., Proc. IEEE. ESSDERC, p. 234 (2008)
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53 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 53 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Theorical hole p-coefficient extraction
ChannelStrainpL
[10-11.Pa-1]
Bulk Si Inversion Layer in Si
Exp. Exp. Theo. h
<110>
<110>(p11+p12+p44)/2
71.8a, 53.5b
71.7c,d, 60e, 78.5f 69.5
<100>(p11+p12)/2
2.8a, -2.5b
18.9c,d,h, 10.9e,h, 14.5f 19.5
<-110>(p11+p12-p44)/2
-66.3a, -58.5b
-33.8c,d, -38.3e,-49.5f
-30.5
p44138.1a,
112b105.5c,d,h,
128g 100
<100> <100>p11
6.6a, -6b 9.1c,d, 6f 10.5
<010> <100>p12
-1.1a, 1b -6.2c,d, 23f 28.5
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)
f New measurements
g Cefficients deduced from <110> and <-110> stress measurements
h 2Dk Kubo-Greenwood simulations
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
New complete and Consistent p-coefficients
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54 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 54 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Key ideas on experiments vs. simulationsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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
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55 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 55 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
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
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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56 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
PerspectivesIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
3Dk transport properties analysis considering non uniformly stress.
Transport in inversion layer should be examined using k.p-Poisson-Schrödinger calculations on the conduction bands
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
65nm CESL Stress c artographyMax
Min
Stre
ss
Uniax. StressChannel
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57 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 57 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
PublicationsJournal
[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).
ConferenceTalk
[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 EPMBandstructure”M. FERAILLE, D. RIDEAU, A. GHETTI, A. PONCET, C. TAVERNIER, and H. JAOUEN, Proc. IEEE SISPAD, p. 264 (2006).
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58 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 58 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
QUESTIONS ?
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59 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 59 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
− Gap & m*
− Piezoresistance coefficients
Multi-scale Approach (crystal)
Ab initio
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Semi-empirical− EPM (Empirical pseudo-potentiel method)
− k.p
Ban
dstr
uctu
re
− Monte Carlo 3Dk
− Kubo-Greenwood 3Dk
Tran
spor
t
Referencecalculation
Parameters fitting
Advanced simulations Drift-Diffusion
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60 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 60 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
− k.p envelop function
− EMA (effective mass approximation)
Piezoresistance coefficients
Multi-scale Approach (inversion layer)Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Ban
dstr
uctu
re
Kubo-Greenwood
Tran
spor
t 2Dk
Si
Advanced simulations
Confinement effect
Drift-Diffusion
Parameters fitting
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61 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 61 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
MethodologyIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Strain e
Bandstructurescalculations
Transportcalculations
-Energies E (k)-Scattering Rates t(k)
Piezoresistancecoefficients
Thesiswork
Relation
Experiments
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62 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
k.p-Poisson-Schrödinger self-consistent calculationsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Poisson
6-bands k.p-SchrödingerEigenvalues , Eigenvectors
Bandstructure calculation
V(z)Confinement potential
Profiles
Isocontour 1rst subbands& Fermi distribution
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63 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 63 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Biaxial stress impact on 3Dk hole mobility
t variation
pMOSFET Bulk planarDegenerancy lift
Scattering time variation
hh
lh
so
hhlh
so
biaxial Stress 648MPa
RelaxedK. HUET, M. FERAILLE, et al., Proc. IEEE. ESSDERC, p. 234 (2008)
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
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64 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Biaxial stress impact on 2Dk hole mobilityStrain-confinement effects
compensationhh
lh
so
Relaxed5 nm
F=1MV/cmhh
lh
so
biaxial Stress 648MPa
compensation
hh
lh
so
Curvature modificationScattering time variation
m* modification t variation
pMOSFET Bulk planar
K. HUET, M. FERAILLE,et al., Proc. IEEE. ESSDERC, p. 234 (2008)
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65 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 65 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Impact of uniaxial stress on 2Dk hole mobility Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Tens
ileC
ompr
essi
veStr <110> Str < 100> Str <-110>
Str <110>: Decrease of the mobility vs. stressStr <-110>: Increase of the mobility vs. stress
200 MPa
pMOSFET Bulk planar
Mob
ility
Var
iatio
n (%
)
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66 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 66 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
3Dk vs 2Dk Kubo-Greenwood simulationsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Str < 100>
Str <100> tens.: Behaviour divergence from 2Dk and 3Dk simulations
200 MPa
pMOSFET Bulk planar
Tens
ileC
ompr
essi
ve
Mob
ility
Var
iatio
n (%
)
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67 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 67 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Unstrained nMOSFETs: profilesIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Concentration VelocityPresence of non-equilibrium thermodynamic effects
in short channel MOSFETs
25 nm gate lenth, Vg=1V, Vd=1V
Carrier densityspreading
VelocityOvershoot
Channel25 nm
Bulk Vsat
1 Å cut1Å cut from from Si/SiO2 interfaceSiO2
Si
Using 30-bands k.p
Using 30-bands k.p
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68 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Unstrained nMOSFETs: characteristicsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
IdVd IdVg
Vg
Drain current
VdVs=0V
Vb=0V
Using 30-bands k.p methods Using 30-bands k.p methods
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69 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Unstrained nMOSFETs: Ion vs. Gate length Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Differents Monte Carlo treatments of the ionized impurity scattering time and access resistance (see Fiegna et al, SISPAD 2007)
Difference increase
Resistance access contribution increase with gate length reduction
Vg=1V Vg=1V
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70 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 70 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Valence sub-bands and masses vs. QW lengthIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
Coupling between hh and conductionBands doesn’t exist k.p 6 bands
Mass variation vs. confinement strengthnot reproduced by EMA methods
DiscrepanciesBetween k.p methods
LQW
Energy shifts Curvature mass <100>
D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008)
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71 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Conduction sub-bands and masses vs. QW lengthIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
<001> confinement orientation
Good adequation between k.p 30 bandsand EMA methods: isolated D-valleys
Mass variation vs. confinement strengthnot reproduced by EMA methods
EMA30-bands k.p
30-bands k.p
LQW
Energy shifts Curvature mass <110>
D. RIDEAU, M. FERAILLE, et al., Solid- State Electronics 53, p.452 (2008)
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72 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 72 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Devices measured
Device A Device B
Type nMOSpMOS pMOS
Technology 130 nm
Oxide type GO2 GO1
Tox (Ǻ) 85 21
Channelorientation
<110> <100>, <010> and <110>
StrainOrientation
<110>, <100> and <110>
<100>, <110> and <110>
Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
σ<100>
σ<100>
<110>
<110>
<001>
G
D
S
G
DS
σ<100>
σ<100>
<110>
<110>
<001>
σ<110>σ<110>
σ<100>
σ<100>σ<110>
σ<110>
G
DS
G
DS
G
DS
Device A Device B
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73 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree 73 June 17th 2009 – Defense of M. FERAILLE’s thesis to obtain the Ph.D degree
Wafer Bending experimentsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation
e thickness
R curvature
Stress estimation:
: Young’s modulus
Well-defined stressST Rousset-Crolles collaboration