Study of Transport Properties in strained MOSFETs: Multi-scale Approach

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)

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


Outline

Introduction– Context– Relation between strain and transport



Transport in Confined Systems

Experimental validation

Conclusions

Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

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>

<01

0>

<110>

<-1

10>

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

<00

1>

<100>

<110>

65nm technology nodeWafer tilted → <100>-channel Transport direction

45°

Influence of stress vs.transport orientation


Technology MotivationDoping vs. Scaling

Needs of technology boosters formobility improvement

Lower mobilityLower performance!


Increase doping to limit short channel effects

Increasing doping leadsto higher effective field

Mobility degradation


Performance Enhancement Process

… stress engineering

CESL SMT

S. Ito IEDM’00

K. OtaIEDM’02

C. Le CamVLSI’06

STI

Uniaxial stress<110> / <100> impact ?


Parasitic stress…

Uniaxial Stress

W Large


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

Ind

us

tria

lA

dv

anc

ed

stress

stress

Microscopic model

Bandstructure calculationIncluding strain effects


Mobility variation: piezoresitance model

Empirical Model:

Piezoresistance tensor with only 3 coefficients

p11, p12 and p44


stressMobility variation


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


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)


Setup A

Setup B

Deduced


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

Ind

us

tria

lA

dv

anc

ed

stress

stress

Microscopic model

Bandstructure calculationIncluding strain effects

New measurements


Relaxed Si buffer: bandstructure basicsC

on

du

ctio

nB

and

s(e

lect

ron

s)

Val

ence

Ban

ds

(ho

les)

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


Dx, Dy, Dz equienergy

hh and lh degenerancy at G

0

10 0.5 1

0

0.5

1

kx [2p/a units]

ky [2p/a units]

kz [

2p/a

un

its]

-1-1

-0.5

-0.5

-1

N

X

GU

KW

L

First Brillouin Zone

Relation dispersion


ezz eyy

exx

Physical relation between strain and mobilityS

ilic

on

Lat

tice

e┴e ║

(2)

e║(1)

Rec

ipro

cal

spac

e

Dispersion relation


Phononsinteractions

Mo

bil

ity

Stress


Outline Introduction

Bandstructure Calculations– Methods– Relaxed buffer– Strain introduction– Impact of uniaxial strain




Conclusions



Bandstructure calculation methodsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

Schrödinger

Development Plane waves Centered-Bloch function

MethodsAb initio (DFT+LDA)

- Kohn-Sham

equation- GW correction

Semi-empirical

EPM 30-bands k.pPseudo-potential Coupling terms (P,Q,..)

Solving

www.abinit.org UTOX (In-house ST code)

Self-consistent Matrix diagonalization

Bloch function

Time Very slow fast very fast


Relaxed buffers bandstructures Ab initio calculations as relevant bandstructures


GW

EPMk.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

En

erg

y [e

V]

En

erg

y [e

V]

D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)


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

po

siti

on

Perturbative theory approach

Symmetry broken

Supplementary coupling parameters (l ,m ,n , ..)

e┴

e║(1) e ║

(2)

Pse

ud

o-p

ote

nti

all

[Ry]

(Symbol) Relaxed

SiGe

G2


Bandstructure of Bulk Si under stress k.p 30 bands method parameters fitted according to a least square

optimization at several k-points

GW

EPMk.p

En

erg

y [e

V]

10 Gpa uniaxial stress along <110>

En

erg

y [e

V]

Shear component strain involves large bandstructure modification

D. RIDEAU, M. FERAILLE, et al., Phys. Rev. B 74, p. 195208 (2006)


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


Stress [MPa]

Rel

ati

ve

mas

s [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

ds

dis

pla

cem

ent

Mas

ses

Var

iati

on

s

stressstress

Dx, Dy

Valleys

Dz Valleys ε=[0.55 0.55 -0.47 0 0 0.63]

Dz –valleys couplingProportional to εxy

Z-point

1BZ 2BZ


Uniaxial stress <110>: Valence bandsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

En

erg

y [e

V] GW

k.pEPM

hhlh

so

Stress <110> [GPa]

Stress-500 → 0 MPa

Ban

ds

dis

pla

cem

ent

Mas

ses

Var

iati

on

s HH valenceIsoenergy surface (25meV)


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



Transport in strained nMOSIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

Introduction


Transport in Strained nMOSFETs– Monte-Carlo methods– Bandstructure inclusion in Monte-Carlo Simulations– Strained nMOSFETs simulations



Conclusions


Monte-Carlo Methods

Drain currentestimation

Poissonequation

SPARTA (ISE): Simple Particule

Qpart=Qtot

Introduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental ValidationP

rin

cip

le

1 particle

Statistical solving of the Master Boltzmann Transport Equation

met

ho

ds

FIonized impurity

phonons

Surface roughness

Quantum-basedInteractions

Monte CarloTransport


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 Nch

Lgate50 nm50 nm

Nch:3,0 .1018 cm-3


Bandstructure inclusion in Monte-Carlo methods


Dispersionrelation

Scatteringrates

Ban

dst

ruct

ure

Meshing in k-space

Sparta

Full-bandMonte-Carlosimulators

Unstrained (1/48) General strain (1/2)

30-bands k.p methods


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 regim

Cu

rren

t va

riat

ion

(%

)

<100>-channel

Ilin Ilon Ilin Ilon

32 nm gate length

Ten

sile

Co

mp

ress

ive


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


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>


Ilin Vd=0.1V Ilin Vd=0.1V


New electron p-coefficients determination


Electrons inversion layer π-coefficients


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


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


Deduced

Measured

Our measurements are consistent vs. Literature


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



OutlineIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

Introduction



Transport in Confined Systems– Confinement introduction– Bandstructure in a relaxed Quantum Well– Bandstructure in a strained Quantum Well– Holes transport in confined systems


Conclusions


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

WK

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


Z’


Methods for confined states

Hamiltonian

Met

ho

ds

k.p 30-bands k.p 6-bandsEnvelop function

ConfinedSystem

(e.g SOI MOSFET)Valence band

Conduction band

z

V(z)LQW

oxide SubstratChannel


Effective Mass Approximation

LA

Plane waves

: quantization mass

curvature mass along the confinementdirection

Vb

Vc

Si-oxVb: 0.4

Vc: 0.3


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


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


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


Stress impact on subbandsIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

Co

nd

uct

ion

Su

bb

and

sV

alen

ceS

ub

ban

ds

Dz Isocontours10 meV-spaced

Stress <110> Relaxed

k.p methods

First sub-bandIsocontour

40 meV-spaced


mass modification

5 nmStr <110>


Dz sub-band masses vs. stress <110>



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


Valence subbands vs. strain <110>



5 nmStr <110>

F=1MV/cm

Relaxed

Str <110>: 500 Mpa


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

Sta

tic

pro

per

ties

Tran

spo

rt

pro

per

ties

BandstructureDensity


k.p-Poisson-Schrödinger self-consistent calculations


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


Kubo-Greenwood solvers transport formula coming from Boltzmann equation

linearization

Density Bandstructure

− Elastic acoustic− Inelastic nonpolar Optical

Phonon relaxation time


Stress <110>-500 Mpa → 0 MPa

Three topmost sub-bands energies

hh bandsisoenergy

3Dk 2Dk

Wang et al., TED 53, 1840 (2006)


3Dk vs. 2Dk Kubo-Greenwood solversIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

Kubo-Greenwood mobility

Crystal 3Dk bandstructureSelf-consistent k.p-poisson

Inversion layer 2Dk bandstructure

Low-field Monte Carlo simulations equivalent


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




Experimental validation for holes– Wafer Bending experiments– Holes mobility extraction– Hole piezoresistance coefficients determination– Advanced transport simulations validation

Conclusions

Outline


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

Dμ

μ= σ.

p11+p12

2

Dμ

μ= σ. p11+p12-p44

2

Dμ

μ= σ.

Unusual

130nm technology node

<110>-oriented channel


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

p11

Dμ

μ= σ. p12

Dμ

μ= σ.

Our wafer bending experimentsallows a complete determination of p-coefficients

130nm technology node


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


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


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




f New measurements

g Cefficients deduced from <110> and <-110> stress measurements

Difference

Setup 1

Setup 2

Coherent


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


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



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,

112b

105.5c,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




f New measurements

g Cefficients deduced from <110> and <-110> stress measurements

h 2Dk Kubo-Greenwood simulations


New complete and Consistent p-coefficients


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


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



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

Str

ess

Uniax. StressChannel


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).


QUESTIONS ?


− Gap & m*

− Piezoresistance coefficients

Multi-scale Approach (crystal)

Ab initio


Semi-empirical− EPM (Empirical pseudo-potentiel method)

− k.p

Ban

dst

ruct

ure

− Monte Carlo 3Dk

− Kubo-Greenwood 3Dk

Tran

spo

rt

Referencecalculation

Parameters fitting

Advanced simulations Drift-Diffusion


− 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

dst

ruct

ure

Kubo-Greenwood

Tran

spo

rt 2Dk

Si

Advanced simulations

Confinement effect

Drift-Diffusion

Parameters fitting


Methodology


Strain e

Bandstructurescalculations

Transportcalculations

-Energies E (k)-Scattering Rates t(k)

Piezoresistancecoefficients

Thesiswork

Relation

Experiments


k.p-Poisson-Schrödinger self-consistent calculations


Poisson

6-bands k.p-SchrödingerEigenvalues , Eigenvectors

Bandstructure calculation

V(z)

Confinement potential

Profiles

Isocontour 1rst subbands& Fermi distribution


Biaxial stress impact on 3Dk hole mobility

t variation

pMOSFET Bulk planar

Degenerancy lift

Scattering time variation

hh

lh

so

hh

lh

so

biaxial Stress 648MPa

RelaxedK. HUET, M. FERAILLE, et al., Proc. IEEE. ESSDERC, p. 234 (2008)




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 modification

Scattering time variation

m* modification t variation

pMOSFET Bulk planar



Impact of uniaxial stress on 2Dk hole mobility


Ten

sile

Co

mp

ress

ive

Str <110> Str < 100> Str <-110>

Str <110>: Decrease of the mobility vs. stress

Str <-110>: Increase of the mobility vs. stress

200 MPa

pMOSFET Bulk planar

Mo

bil

ity

Var

iati

on

(%

)


3Dk vs 2Dk Kubo-Greenwood simulations


Str < 100>

Str <100> tens.: Behaviour divergence from 2Dk and 3Dk simulations

200 MPa

pMOSFET Bulk planar

Ten

sile

Co

mp

ress

ive

Mo

bil

ity

Var

iati

on

(%

)


Unstrained nMOSFETs: profilesIntroduction Bandstructure Calculations Transport in Strained nMOS Transport in confined Systems ConclusionsExperimental Validation

Concentration Velocity

Presence 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


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


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


Valence sub-bands and masses vs. QW length


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)


Conduction sub-bands and masses vs. QW length



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)


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>


σ<100>

σ<100>

<110>

<110>

<001>

G

D

S

G

D

S

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


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

Study of Transport Properties in strained MOSFETs: Multi-scale Approach

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