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 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)  VBM E AY = CBM  E  E AX core VBM E /AYAX AY AX g  AY, core  E - - (AY/AX) = VBM E , E - core VBM core  E AX E E core  E VBM  AY core , VBM E AX, core  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, (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. AB Reference: Yu and Cardona, Fundamentals of Semiconductors. A BABAB Type I Type II Type III

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

Point No. 2 : Common-Anion rule has been repealed ( because different cations do make a difference) Point No. 2 : Common-Anion rule has been repealed ( because different cations do make a difference) The Rule: The band offset between AX/BX with common anion X will be ~ zero Why: Because in tight-binding the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,B, d Te Cd /Hg Zn/Hg Zn/CdX SSe M g/ZnX Ga/InY Al/Ga Al/InY SbAsPN 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 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 Band offsets a predictors of Dopability

CuIn5Se8CuInSe2 E CuAlSe2 (n) pin (p) E CuGaSe2CuInTe2CuInS2ZnSZnSeZnTeCdSCdSeCdTeZnO M/D C/D M/D 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, CuInSe 2, InAs, InP Poor n-type: ZnS, CuGaSe 2, CuAlSe 2 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  H(V Cation )=0 (O-poor) 2–2–  H(V Anion )=0 (O-rich) 2+ E F n,pin E F p,pin

Band offsets as predictors of Impurity level positions Band offsets as predictors of Impurity level positions

Why is the isolated N level higher in GaAs than in GaP : Because of CBM lineup VBM  1c X1c GaPGaAs -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 doping A 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  H of charged acceptors (electron killers) is lowered Concentration of electron killers rises E F is pinned at a critical value ; doping stops CuInSe 2

Testing the Rule via ab-initio : III-V and II-VI  F is bounded by  pin and  pin Calculate H(killer,Ef)= 0 and find Ef. Note:  pin ’s line up in a given material class (p) (n)

Absolute Deformation Potential Hydrostatic deformation potential is the angular average of the polar deformation potential P(r) = ∑ C v K v (r), where K v is the lattice harmonics Li, Gong & Wei, Phys. Rev. B 73, ; Appl. Phys. Lett. 88, (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, (R) (2005). Y. –H. Li, et al., Appl. Phys. Lett. 94, (2009).  E(GaN/InN)=1.0 eV  E(GaN/InN)=1.1 eV