Comments on Band Offsets

Alex Zunger University of Colorado, Boulder, Colorado

S.H. Wei, NREL

Point No. 1 :

Band Offsets can be calculated from First-Principles

with useful accuracy

Experimental Approach: X-ray Photoemission Spectra

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!

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.

Deformation Potentials

Q. Is it true that the reference energy level has zero deformation potential?

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.

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

Band Lineup Predictions - binariesR. Magri, H. Kroemer, Alex Zunger J.Appl.Phys

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Common-Anion rule has been repealed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

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

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

Band offsets a predictors of Dopability

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

.

• 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

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

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

Band offsets as predictors of Impurity level positions

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

Thank You

National Renewable Energy Laboratory Innovation for Our Energy Future

Extra Slides for Discussion

National Renewable Energy Laboratory Innovation for Our Energy Future

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

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)

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!

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.

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

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