IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

First Principle Calculations of Band Offsets ofSiO2 and ZrSiO4 with Silicon

R. Shaltaf

Université Catholique de Louvain - Louvain-la-Neuve, Belgium

11th Nanoquanta Workshop on Electronic ExcitationsHouffalize

22/09/2006

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

Collaborators

Université catholique deLouvain

J. Bouchet

G.-M. Rignanese

X. Gonze

Polytechnique Fédérale deLausanne, Switzerland.

F. Giustino

A. Pasquarello

École Polytechnique, France.

F. Bruneval

L. Reining

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

Outline

1 IntroductionMotivationsTheoretical basis

2 Si/Sio2 InterfaceLDA levelGW correctionsGWΓ

3 ZrSiO4/Si interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Outline

1 IntroductionMotivationsTheoretical basis

2 Si/Sio2 InterfaceLDA levelGW correctionsGWΓ

3 ZrSiO4/Si interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

What are the band-offsets at the interface of oxide material withsilicon?

Technical requirement

VBO and CBO > 1.0-1.5 eVto avoid e− or h+ injectionfrom Si to the oxide

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Why bother?!

Problem

When MOSFET size reaches acritical size, high leakagecurrents

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Why bother?!

Problem

When MOSFET size reaches acritical size, high leakagecurrents

Solutionusing higher κ-material

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Outline

1 IntroductionMotivationsTheoretical basis

2 Si/Sio2 InterfaceLDA levelGW correctionsGWΓ

3 ZrSiO4/Si interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Question

How to calculate the band offsets?

Van de Walle-Martin method1

VBO = ∆E1V − ∆E2

V − ∆V

CBO = ∆E1C − ∆E2

C − ∆V

1G. Van de Walle and R. M. Martin, Phys. Rev. B 35, 8154 1987Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Band diagram

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Band diagram

DFT fails to give thecorrect gap

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

Band diagram

DFT fails to give thecorrect gap

GW corrections is neededto correct the position ofthe bands

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

GW calculation

The many body corrections will be calculated using GWapproximation

ǫqp = ǫDFT+ < φDFTnk |Σ(r , r ′, ǫDFT)|φDFT

nk >

Σ = iGW

G will be approximated by the independent particle one G0

W = vε−1

RPA approximation will be used for the calculation of ǫ

ε = δ − vP0

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

MotivationsTheoretical basis

GW calculation II

To calculate the dynamic screening we will use plasmonpole approximationDifferent procedures exist for evaluating the parameters ofthe model:

Hybertsen-Louie 2

von Linden and Horsch3

Godby-Needs 4

Engle-Farid 5

The energies in W will be updated using scissor-operatorshift

2Hybertsen and Louie, Phys. Rev. B 34, 5390 (1986)3W. von der Linden nd P. Horsch, Phys. Rev. B 37, 8351, (1987)4Godby and Needs,Phys. Rev. Lett. 62, 1169, (1989)5G. E. Engel and B. Farid, Phys. Rev. B 47, 15931 (1993)

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Outline

1 IntroductionMotivationsTheoretical basis

2 Si/Sio2 InterfaceLDA levelGW correctionsGWΓ

3 ZrSiO4/Si interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Si/SiO2 interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

interface model

0 Lalong z direction

-15

-10

-5

ener

gy (

eV)

Γ L X Γ-20

-10

0

10

Ene

rgy

(eV

)

KS structure β-cristobalite SiO2

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Band offsets on DFT level

CBO=1.75 eV VBO=2.91eV Other DFTcalculations

VBO=2.90 eV a

VBO=3.05 eV b

aPantelides et al, IEEE,Trans. Nucl. Sci, 47, 2262,2000

bTuttle, Phys. Rev. B 67,155324 (2003)

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Outline

1 IntroductionMotivationsTheoretical basis

2 Si/Sio2 InterfaceLDA levelGW correctionsGWΓ

3 ZrSiO4/Si interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

different plasmon pole,different correction

Si that is not simple

∆Eg ∆Ev ∆Ec

GN +0.65 eV -0.44 eV +0.21 eV

HL +0.67 eV -0.66 eV +0.01 eV

EF +0.70 eV -0.65 eV +0.05 eV

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

different plasmon pole,different correction

Si that is not simple

∆Eg ∆Ev ∆Ec

GN +0.65 eV -0.44 eV +0.21 eV

HL +0.67 eV -0.66 eV +0.01 eV

EF +0.70 eV -0.65 eV +0.05 eV

NI +0.67 eV -0.47 eV +0.20 eV

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

different plasmon pole, different correction II

∆Eg ∆Ev ∆Ec ∆VBO ∆CBO

GN +3.10 eV -1.80 eV +1.30 eV 1.36 1.12

LH +3.51 eV -2.33 eV +1.18 eV 1.67 1.17

EF +3.33 eV -2.11 eV +1.21 eV 1.40 1.18

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

different plasmon pole, different correction II

∆Eg ∆Ev ∆Ec ∆VBO ∆CBO

GN +3.10 eV -1.80 eV +1.30 eV 1.36 1.12

LH +3.51 eV -2.33 eV +1.18 eV 1.67 1.17

EF +3.33 eV -2.11 eV +1.21 eV 1.40 1.18

NI +3.08 eV -1.78 eV +1.30 eV 1.31 1.10

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

GW corrections for SiO2

LDA G0W0 G0W

VB (Γ) 0.00 -1.80 -2.17

CB (Γ) 5.24 6.54(1.30) 6.76(1.52)

Gap 5.24 8.34 8.93

Experimental Eg=9.00 eV, see Tuttle, Phys. Rev. B 67, 155324(2003)

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Band offsets results including many body corrections

LDA G0W0 G0W

VBO 2.91 4.27 4.64

CBO 1.75 2.61 3.07

LDA G0W0 G0W

VBO 2.19 3.22 3.60

CBO 2.12 3.25 3.47

can we enhancethe results furtherwhat aboutincluding vertexcorrections

Expt.: VBO 4.2-4.8, CBO 3.2-3.5 6

6see Tuttle, Phys. Rev. B 67, 155324 (2003)Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Outline

1 IntroductionMotivationsTheoretical basis

2 Si/Sio2 InterfaceLDA levelGW correctionsGWΓ

3 ZrSiO4/Si interface

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

GW Γ I

This GW approximation may, in principle, be improved using anapproximate vertex correction Γ. For instance, Γ has beenestimated using the LDA7

ǫLDA = δ − (v − Kxc)P0

7Del Sole, Reining, and Godby, Phys. Rev. B 49, 8024 (1994)Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

GWΓ I

Results for Silicon

∆Eg ∆Ev ∆Ec

G0W0Γ[present] +0.71 eV -0.02 eV +0.69 eV

G0WΓ[present] +0.74 eV -0.01 eV +0.73 eV

Del Sole et al.8 +0.66 eV +0.01 eV +0.67 eV

Fleszar Hanke 9 +0.57 eV -0.06 eV +0.63 eV

The corrections are mainly in the conduction band giving somecredit to the use of a simple scissor operator...

8Del Sole, Reining, and Godby, Phys. Rev. B 49, 8024 (1994)9Fleszar and Hanke, Phys. Rev. B 56, 10228 (1997)

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

results for SiO2

Eg ∆Ev ∆Ec

G0W0 8.34 eV -1.80 eV +1.30 eV

G0W 8.93 eV -2.17 eV +1.52 eV

G0W0Γ 8.20 eV -1.27 eV +1.69 eV

G0WΓ 8.79 eV -1.66 eV +1.89 eV

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

LDA levelGW correctionsGWΓ

Bands Offets

LDA G0W0 G0W

VBO 2.91 4.27 4.64

CBO 1.75 2.61 3.07

LDA G0W0Γ G0WΓ

VBO 2.91 4.16 4.56

CBO 1.75 2.75 2.91

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

ZrSiO4/Si interface structure

-20

-10

0

10

strained ZrSiO4

Γ X M Γ H-60

-40

-20

-10

0

10

ZrSiO4

Γ X M Γ H-60

-40

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

BO results

Table: Quasiparticle BO in (eV) ZrSiO4

LDA G0W0 G0W

VBO 1.05 1.29 1.56

CBO 3.51 5.03 5.27

Table: Quasiparticle BO in (eV) s-ZrSiO4

LDA G0W0 G0W

VBO 1.86 2.06 2.33

CBO 1.53 2.71 2.85

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

remarks

Care must be taken when doing band offsets calculationswith plasmon pole models

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

remarks

Care must be taken when doing band offsets calculationswith plasmon pole models

GW and GWΓ give similar results for the band offsets

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with

IntroductionSi/Sio2 Interface

ZrSiO4/Si interface

remarks

Care must be taken when doing band offsets calculationswith plasmon pole models

GW and GWΓ give similar results for the band offsets

BO of ZrSiO4/Si indicate thats it can be promising materialin MOSFET technology

Shaltaf First Principle Calculations of Band Offsets of SiO2 and ZrSiO4 with