Band Discontinuities at Si/Transparent Conducting Oxide Heterostructures from ab-initio Quasiparticle Calculations B. Höffling, A. Schleife, F. Fuchs,

Band Discontinuities atSi/Transparent Conducting Oxide

Heterostructures from ab-initio Quasiparticle Calculations

B. Höffling, A. Schleife, F. Fuchs,

C. Rödl, and F. Bechstedt

Institut für Festkörpertheorie und –optik

Friedrich-Schiller-Universität Jena

and

European Theoretical Spectroscopy

Facility (ETSF)

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

School on Nanophotonics and Photovoltaics 2010

1. Motivation2. Electronic Structure Calculations3. Mesoscopic Methods

1. Vacuum Level Alignment2. Branch Point Energy Alignment

4. Comparison of Results5. Si/In2O3: Interface Model Alignment

6. Summary

Outline

Benjamin Höffling et al.


• Transparent Conducting Oxides like ITO and ZnO are used as transparent electrodes in photovoltaic and optoelectric devices.

• Key properties such as ionization energy, electron affinity, charge neutrality level and work function are poorly known.

• Electronic properties of Si/TCO heterojunctions determine the efficiency of Si-based solar cells

1. Motivation: Why Si/TCO Interfaces?



1. Motivation: Electronic Properties of Interfaces

+ ++

- - -

- - -



1. Motivation: Electronic Properties of Interfaces

Type I Type II Type III



• Spatially non-local XC-potential HSE03 used for zeroth approximation of XC self-energy

• QP wave functions used to compute QP shifts using many-body pertubation theory in the G0W0 approach.

-> QP band structure of bulk materials

F. Fuchs et al., Phys. Rev. B 76, 115109 (2007)

2. Electronic Structure Calculations



• Si and TCO have– Different bond types– Different lattice constants– Different lattice structures

-> Construction of structural interface model highly non-trivial

• Mesoscopic methods that don‘t require detailed knowledge of interface geometries can help.

3. Methods: Electronic Properties of Interfaces

Si lattice

ZnO lattice Benjamin Höffling et al.


• requires: ionization energy I=Evac-Ev

electron affinity A=Evac-Ec

with QP bandgap Eg=I-A

3.1 The Vacuum Alignment Method

R.L. Anderson, Solid State Electron. 5, 341 (1962)



• Electrostatic potential at surface obtained by DFT-LDA repeated-slab supercell calculations

• Plane averaged electrostatic potential with bulk oscilations and vacuum plateau

• QP-CBM and VBM relative to electrostatic bulk oscillations known

• Alignment yields ionization energy and electron affinity

3.1 The Vacuum Alignment Method

CBM

VBM

AI



• ΔEv=I1-I2

• ΔEc=A1-A2

• We obtain Type II and Type III heterostructures (exception: SnO2)

-> good charge carrier separation

3.1. The Vacuum Alignment Method

Crystal Eg I A ΔEc ΔEv

rh-In2O3 3.31(3.02)a

6.11 9.41 -1.57 3.58

bcc-In2O3 3.15(2.93)a

5.95(4.1-5.0)f

9.10(7.7-8.6)f

-1.42 3.27

wz-ZnO 3.21(3.38)b

5.07(4.25-4.95)g

8.28(7.82, 8.35)g,h

-0.53 2.34

rt-SnO2 3.64(3.6)c

4.10(4.44)i

7.73(8.04)i

0.44 1.38


• EBP is the energy at which the character changes from donor- to acceptor-like behavior

• We use QP energies to approximate the BZ-average of the midgap energy

A. Schleife et al., APL 94, 012104 (2009)

3.2 Branch Point Alignment Method: Fundamentals

k CBk

kkN

1 CB

i

VB

iv

VB

cBP )(N

1)(

N2

1E

ii

Basic concept: Virtual gap states (ViGS)V. Heine, SS 2, 1 (1964); PR A 138, 1689 (1965)



• Surface/Interface induces ViGS and pinns Fermi level at EBP

• We use QP energies to approximate the BZ-average of the midgap energy

• EBP >CBM creates creates charge accumulation layer near oxide surface

• confirmed for ZnO: M. W. Allen et al., Phys. Rev. B 81, 075211 (2010)

3.2 Branch Point Alignment Method: Consequences



3.2 Branch Point Alignment MethodCrystal Eg EBP ΔEc ΔEv

rh-In2O3 3.31(3.02)a

3.79(3.50)a

-1.48 3.50

bcc-In2O3 3.15(2.93)a

3.50(3.58)a

-1.35 3.23

wz-ZnO 3.21(3.38)b

3.40(3.2, 3.78)d,e

-1.17 3.09

rt-SnO2 3.64(3.6)c

3.82 -1.19 3.53

• Type II and Type III heterostructures• Branch point in good agreement with experiments• EBP> Eg in all TCOs• SnO2 now Type II heterostructure• Similar values for ΔEv: Common anion rule



• Good agreement between the two methods

• Exception: SnO2

• Possible reason: no surface states at this orientation

4. Comparison of Results: Band Lineup

Si Interface with

via EBP via I and A

ΔEc ΔEv ΔEc ΔEv

rh-In2O3 -1.48 3.50 -1.57 3.58

bcc-In2O3 -1.35 3.23 -1.42 3.27

wz-ZnO -1.17 3.09 -0.53 2.34

rt-SnO2 -1.19 3.53 0.44 1.38



• Band offsets via averaged electrostatic potential:ΔEc= -1.07 eV

ΔEv= 2.95 eV• Shift due to charge transfer-

induced dipole moment?

• Integration shows a transfer of 3 electrons into the oxide. But: only about 0.5 electrons into the slab.-> ionic component in Si-O bonding

5. Si/In2O3: Interface Model Alignment

))()(()()(32xxxx OInSiIF



• We calculated branch point levels, ionization energies and electron affinities for Si, In2O3, SnO2, and ZnO.

• Band offsets for Si/TCO interfaces determined by two different alignment methods in good agreement with each other (exception: SnO2)

• Branch Point Energy Alignment and Vacuum Energy Alignment are usefull tools for the efficient calculation of band discontinuities that don‘t require detailed structural interface models

• Interface Model Alignment confirms predictions.• For Si/TCO heterostructures a tendency for Type II or

misaligned Type III heterostructures is observed -> Good charge carrier separation

6. Summary



B. Höffling et al., APL 97, 032116 (2010)

a P.D.C. King et al., Phys. Rev. Lett. 101, 116808 (2008), P.D.C. King et al., Phys. Rev. B 79, 205211 (2009)b W. Martienssen and H. Warlimont eds., Handbook of Condensed Matter and Materials Data, (Springer, Berlin, 2005)c K. Reimann and M. Steube, Solid State Commun. 105, 649 (1998)d W. Walukiewicz, Physica B 302-303, 123 (2001)e P.D.C.King et al., Phys. Rev. B 80, 081201 (2009)f A. Klein, Appl. Phys. Lett. 77, 2009 (2000)g K. Jacobi et al. Surf. Sci. 141, 109 (1984)h W. Mönch, Semiconductor Surfaces and Interfaces, (Springer, Berlin, 2001)i C. Kiliç and A. Zunger, Appl. Phys. Lett. 81, 73 (2002)

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Band Discontinuities at Si/Transparent Conducting Oxide Heterostructures from ab-initio Quasiparticle Calculations B. Höffling, A. Schleife, F. Fuchs,