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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