comments on band offsets alex zunger university of colorado, boulder, colorado s.h. wei, nrel
DESCRIPTION
Experimental Approach: X-ray Photoemission SpectraTRANSCRIPT
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Comments on Band Offsets
Alex Zunger University of Colorado, Boulder, Colorado
S.H. Wei, NREL
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Point No. 1 :
Band Offsets can be calculated from First-Principles
with useful accuracy
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Experimental Approach: X-ray Photoemission Spectra
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Theoretical Approach: an XPS Analog ( 25 th anniversary)
D VBM E
AY
= CBM D E D E
AX
core
core
VBM
VBM
E
/AY AX
AY
AY
AX
AX
g
D
AY
, coreD
E
-
-
(AY/AX) = VBM
E
D , VBM E
-
core
VBM
coreD E
AX
E E
coreD E
VBM D
AYcoreD , VBM E
AX
, coreD E VBM
E
E
The key assumption in this approach is that the
localized core level has negligible deformation
potentials!
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Calculated Band Offsets 1998
• Using all-electron (LAPW) calculations with core-level alignment. Agreements
with experimental XPS data are good.
• Establishes transitivity: (A|C) can be determined from (A|B) and (B|C).
Absolute valence band position is a well defined bulk property.
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Deformation Potentials
Q. Is it true that the reference energy level has zero deformation potential?
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Predicted Band-Offsets with core level corrections (Walsh et al 2009)
Li, Walsh, Chen, Yin, Yang, Li, Da Silva, Gong & Wei, Appl. Phys. Lett. 94, 212109 (2009).
The predicted chemical trend are similar to previous calculated results, but not the absolute values, especially for system
with large size mismatch.
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Classifications of offset types
Type I: Electrons and holes confined in one layer (A).
Type II: ‘Spatially Indirect’. Electron at A and hole at B.
Type III: Effective ‘Zero gap’. Electron transfer from B to A.
A B
Reference: Yu and Cardona, Fundamentals of Semiconductors.
A B A B A B
Type I Type II Type III
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Band Lineup Predictions - binariesR. Magri, H. Kroemer, Alex Zunger J.Appl.Phys
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Point No. 2 :
Common-Anion rule has been repealed
(because different cations do make a difference)
The Rule: The band offset between AX/BX with common anion X will be ~ zero
Why: Because in tight-binding the VBM of AX or BX are just X-like
[1] W. A. Harrison, J. Vac. Sci. Tech. 14, 1016 (1977)
[2] C. G. Van de Walle, Phys. Rev. B 39, 1871 (1989
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X, p
v
v
E (BX)
E (AX)
X, p
A, d
B, d
Te
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
1. 2
-0.2
Cd/HgZn/Hg
Zn/CdX
S Se
Mg/ZnX
Ga/InY
Al/G a
Al/InY
SbAsPN
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
1. 2
-0.2
II-VI systems III-V systems
Chemical trends of the valence band offsets: Common-anion
The
(1) VB offsets of most common-anion pairs are NON-ZERO
(2) The Reason: d orbitals of CATIONS push the individual VBM’s by different amounts
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Point No. 3
Band offsets have become central not only for
modeling electronic devices, but also because they
Predict
Dopability
Deep level positions
Water splitting ability
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Band offsets a predictors of Dopability
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CuIn5Se8CuInSe2
E
CuAlSe2
(n) pin
pin (p)
E
CuGaSe2CuInTe2CuInS2ZnS ZnSe ZnTe CdS CdSe CdTeZnO
3.74
3.20
3.52
2.70
1.19
1.73
1.23
2.48
0.53
0.18
0.60
1.170.95 0.97
2.20
2.60
2.27
2.74
3.64
2.87
0.81
0.00
-1.00
1.26M/D
C/D C/D
C/D C/D M/D M/D
2.092.27
II-VI Binaries Cu- III-VI2 Ternaries
S. B. Zhang, S.-H. Wei, and A. Zunger, J. Appl. Phys. 83, 3192 (1998).
Doping limit rule:
Material in which the CBM is much higher than E ( pin, n) can not be doped n-
type
Materials in which the VBM is much lower than E(pin, p) can not be doped p-
type
.
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• Good n-type: ZnO, ZnSe, CdS, CdSe ,CdTe,
CuInSe2, InAs, InP
• Poor n-type: ZnS, CuGaSe2, CuAlSe2
• Good p-type: ZnTe, CdTe, GaSb, InSb
• Poor p-type: ZnO, ZnS, ZnSe, CdS, CdSe
This rule explains known Doping Trends
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Recall : An interesting Puzzle
ZnO Can be doped almost exclusively N-Type
NiO Can be doped only p-Type
MgO can not be doped
Approach : Calculate the position of the Fermi level where the intrinsic compensating defect forms
spontaneously
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Dopability Trends: ZnO, NiO, MgO
Electron-dopable
Hole-dopable
DH(VCation)=0
(O-poor)
2–
DH(VAnion)=0
(O-rich)
2+
EFn,pin
EFp,pin
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Band offsets as predictors of Impurity level positions
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Why is the isolated N level higher in GaAs than in GaP : Because of CBM lineup
2.86
2.32
1.83
0.31
0.00
2.29
VBM
G1c
X1c
GaP GaAs
-30 meV
+180 meV
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Thank You
National Renewable Energy Laboratory Innovation for Our Energy Future
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Extra Slides for Discussion
National Renewable Energy Laboratory Innovation for Our Energy Future
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Le Chatelier’s principle for dopingA perturbation of a system at equilibrium shifts the thermodynamic variables into a direction that counteracts the perturbation
Dope n-type (add donors)
EF rises in the band gap and n increases
DH of charged acceptors (electron killers)
is lowered
Concentration of electron killers rises
EF is pinned at a critical value ; doping stops
CuInSe2
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Testing the Rule via ab-initio : III-V and II-VI
• eF is bounded by epin and epin
•
Calculate H(killer,Ef)= 0 and find Ef .
• Note: epin’s line up in a given material class
(p) (n)
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Absolute Deformation PotentialHydrostatic deformation potential is the angular average of the polar deformation potential P(r) = ∑ CvKv(r), where Kv is the
lattice harmonics
Li, Gong & Wei, Phys. Rev. B 73, 245206; Appl. Phys. Lett. 88, 042104 (2006).
Core level deformation potential is not negligible!
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New Approach: More ‘Natural’
The last two terms becomes more important the larger the lattice mismatch between AX and BY. Accounting for this
deformation, improves experimental agreement for a number of III-V systems.
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Comparison with Experiment
S. X. Li et al., Phys. Rev. B 71, 161201(R) (2005).Y. –H. Li, et al., Appl. Phys. Lett. 94, 212109 (2009).
DE(GaN/InN)=1.0 eVDE(GaN/InN)=1.1 eV
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1.47
1.04
1.94
-0.06
How to select a window material?
CBM
VBM
1.37
-0.81
1.04 0.97
2.51
1.97
2.29
Low CBM (e on CBM of window)
Absorber AbsorberWindow
Conclusion: CdS and ZnO are relatively good
Needs for good window material:
Are there other good choice of window material?
2
Low VBM (h on VBM of absorber)
Good lattice and chemical match with absorber
-0.01
1.18
CuGa In Se0.3 0.7
-1.23
ZnO
Large band gap ( > 2 eV)
ZnMnSe
0.03
-1.05
-0.63
0.00
-2.23
-0.70
2 CdTeCdSeCdSZnTe