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.

1. Motivation2. Electronic Structure Calculations3. Mesoscopic Methods

1. Vacuum Level Alignment2. Branch Point Energy Alignment

4. Comparison of Results5. Si/In2O3: Interface Model Alignment6. Summary

OutlineOutline

School on Nanophotonics and Photovoltaics 2010Benjamin 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: Why Si/TCO Interfaces?

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

1. Motivation: Electronic Properties of Interfaces1. Motivation: Electronic Properties of Interfaces

School on Nanophotonics and Photovoltaics 2010

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Benjamin Höffling et al.

1. Motivation: Electronic Properties of Interfaces1. Motivation: Electronic Properties of Interfaces

School on Nanophotonics and Photovoltaics 2010

Type I Type II Type III

Benjamin Höffling et al.

• 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 Calculations2. Electronic Structure Calculations

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

• 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 Interfaces3. Methods: Electronic Properties of Interfaces

Si lattice

ZnO lattice School on Nanophotonics and Photovoltaics 2010Benjamin 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 Method3.1 The Vacuum Alignment Method

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

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

• 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 Method3.1 The Vacuum Alignment Method

CBM

VBM

AI

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

• 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 Method3.1. The Vacuum Alignment Method

School on Nanophotonics and Photovoltaics 2010

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: Fundamentals3.2 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)

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

• 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: Consequences3.2 Branch Point Alignment Method: Consequences

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

3.2 Branch Point Alignment Method3.2 Branch Point Alignment Method

School on Nanophotonics and Photovoltaics 2010

Crystal 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 ruleBenjamin Höffling et al.

• Good agreement between the two methods

• Exception: SnO2

• Possible reason: no surface states at this orientation

4. Comparison of Results: Band Lineup4. Comparison of Results: Band Lineup

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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

Benjamin Höffling et al.

• 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/In5. Si/In22OO33: Interface Model Alignment: Interface Model Alignment

School on Nanophotonics and Photovoltaics 2010

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

Benjamin Höffling et al.

• 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. Summary6. Summary

School on Nanophotonics and Photovoltaics 2010Benjamin Höffling et al.

School on Nanophotonics and Photovoltaics 2010

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)

Thank you for your attention!

Benjamin Höffling et al.