Band Discontinuities at
Si/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)
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
Outline
1. Motivation
2. Electronic Structure Calculations
3. Mesoscopic Methods
1. Vacuum Level Alignment
2. Branch Point Energy Alignment
4. Comparison of Results
5. Si/In2O3: Interface Model Alignment
6. Summary
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
1. Motivation: Why Si/TCO Interfaces?
• 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 Sibased solar cells
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
1. Motivation: Electronic Properties of Interfaces
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Benjamin Höffling et al.
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School on Nanophotonics and
Photovoltaics 2010
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1. Motivation: Electronic Properties of Interfaces
Type I
Benjamin Höffling et al.
Type II
School on Nanophotonics and
Photovoltaics 2010
Type III
2. Electronic Structure Calculations
•
•
Spatially non-local XC-potential
HSE03 used for zeroth
approximation of XC self-energy
QP wave functions used to
compute QP shifts using manybody pertubation theory in the
G0W0 approach.
-> QP band structure of bulk
materials
F. Fuchs et al., Phys. Rev. B 76, 115109 (2007)
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
3. Methods: Electronic Properties of Interfaces
• Si and TCO have
–
–
–
Different bond types
Different lattice constants
Different lattice structures
-> Construction of structural
interface model highly nontrivial
• Mesoscopic methods that
don‘t require detailed
knowledge of interface
geometries can help.
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
Si lattice
ZnO lattice
3.1 The Vacuum Alignment Method
R.L. Anderson, Solid State Electron. 5, 341 (1962)
•
requires: ionization energy I=Evac-Ev
electron affinity A=Evac-Ec
with QP bandgap Eg=I-A
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
3.1 The Vacuum Alignment Method
•
•
•
•
Electrostatic potential at surface
obtained by DFT-LDA repeatedslab 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
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
CBM
VBM
I A
3.1. The Vacuum Alignment Method
•
•
•
ΔEv=I1-I2
ΔEc=A1-A2
We obtain Type II and Type III
heterostructures (exception:
SnO2)
-> good charge carrier
separation
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
School on Nanophotonics and
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3.2 Branch Point Alignment Method: Fundamentals
Basic concept: Virtual gap
states (ViGS)
•
V. Heine, SS 2, 1 (1964); PR A 138, 1689 (1965)
•
E BP 
EBP is the energy at
which the character
changes from donor- to
acceptor-like behavior
We use QP energies to
approximate the BZaverage of the midgap
energy
1
2Nk

k
 1

 N CB
CB

i
ci
(k ) 
1
N VB

  v (k ) 
i

VB
A. Schleife et al., APL 94, 012104 (2009)
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
i
3.2 Branch Point Alignment Method: Consequences
•
•
•
•
Surface/Interface induces
ViGS and pinns Fermi level
at EBP
We use QP energies to
approximate the BZaverage 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)
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
3.2 Branch Point Alignment Method
•
•
•
•
•
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 rule
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
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
•
•
•
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
Good agreement
between the two
methods
Exception: SnO2
Possible reason: no
surface states at this
orientation
5. Si/In2O3: Interface Model Alignment
•
•
Band offsets via averaged
electrostatic potential:
ΔEc= -1.07 eV
ΔEv= 2.95 eV
Shift due to charge transferinduced dipole moment?
  ( x )   IF ( x )  (  Si ( x )   In 2 O 3 ( x ))
•
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
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
6. Summary
•
•
•
•
•
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
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010
Thank you for your attention!
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)
Benjamin Höffling et al.
School on Nanophotonics and
Photovoltaics 2010