Defecte in OxiziZnO

8/11/2019 Defecte in OxiziZnO

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FirstFirst--principles simulations of defectsprinciples simulations of defects

Chris G. Van de WalleMaterials Department, UCSB

A. Janotti, J. Lyons, J. Varley, J. Weber (UCSB)P. Rinke (FHI), M. Scheffler (UCSB, FHI Berlin)G. Kresse (U. Vienna)

. reyso , . euge auer sse or NSF, DOE

School on Computational Modeling of Materials

December 2-3, 2010Antwerp, Belgium


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Why study defects?Why study defects? Defects Vacancy

dislocations Point defects:

Native defects Impurities

Defects often determineInterstitial

the properties of materials Doping and its limitations

Device degradation Diffusion

Mediated b oint defects

Antisite


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Technological significanceTechnological significance Semiconductors

c eve g er op ng eve s p-type doping of AlN would allow UV lasers

Controllabl do e materials -t e andn-t e Oxides

Photovoltaics

CuInxGa1-xSe2 Hydrogen storage materials

Kinetics of hydrogen release in NaAlH4 Embrittlement of structural metals


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Links to experimentLinks to experiment Secondary Ion Mass Spectrometry (SIMS) Impurity concentrations (to within factor of 2)

os ron ann a on spec roscopy Most sensitive to negatively charged vacancy(-like) defects

EXAFS (extended x-ray absorption fine structure) Microscopic structure, atomic relaxations

Electron paramagnetic resonance + ENDOR Hyperfine parameters (wave functions, atomic positions)

Vibrational spectroscopy (Raman, FTIR) Local vibrational modes; sensitive to atomic positions

Deep level transient spectroscopy Electronic transition levels

Total-energy differences, not Kohn-Sham levels Photoluminescence (PL), PL excitation

Optical transition levels


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Defect calculations: geometryDefect calculations: geometry Greens functions

mp emen a on cu Non-intuitive

Surface effects

Supercells "

R. P. Messmer and G. D. Watkins, inRadiation Damage and Defects in Semiconductors(Inst. of Phys. London, 1972), No. 16, p. 255.


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Defect Formation EnergiesDefect Formation EnergiesExample: VO

+VO +2

oxide: VO oxide O2


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Defect Formation EnergiesDefect Formation EnergiesExample: VO

Fe +VO +

2

oxide: VO oxide O2 reservoir

e @ F(electronreservoir)


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FormalismFormalism Eform : formation energy

Concentration of defects or impurities:C = Nsites exp [ Eform/kT]

Example: oxygen vacancy in ZnO+ = + + +

O: energy of oxygen in reservoir, i.e.,oxygen chemical potential

EF: energy of electron in its reservoir, i.e., the Fermi level enera express onE form(Dq) = E tot(Dq) E tot(bulk)+ n i i + qE F

n i: num er o a oms e ng exc ange o orm e e ec


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Formation energyFormation energy V in ZnO

Zn-rich conditions:Zn=E tot(bulk Zn)

O=E tot(O2)+ Hf (ZnO)


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Transition levelsTransition levels Char e-state

transition levels+/0CB

VB(+/0)(2+ /+)

2+/0


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Issues...Issues... Band a roblem

DFT (LDA, GGA) Affects formationenergies and

transition levels Even for neutral chargestates, if defect-inducedKohn-Sham states are occupied with electrons

DFT/LDA band gap


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BandBand--gap corrections: Empirical correctionsgap corrections: Empirical corrections Ad hoc corrections Scissors operator

gap eve s ase on con uc on- vs. va ence- an c arac er

Delta-function(-like) term added to potential, shiftss states N. E. Christensen, Phys. Rev. B30, 5753 (1984).

D. Segev, A. Janotti, and C. G. VdW, Phys. Rev. B75, 035201 (2007). Issues

Hard to control May have unintended consequences (indirectvs . direct gaps, )

Extrapolations based on calculations that yielddifferent gaps

eren p ane-wave cu o s Different exchange-correlation functionals

. , . , . , . . , . Issue: different choices of parameter not only produce different gap,

but also different levels of accuracy for description of defect


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BandBand--gap corrections: SIC and LDA+gap corrections: SIC and LDA+ UU Physically meaningful improvements Self-interaction corrections

J. P. Perdew and A. Zunger, Phys. Rev. B23, 5048 (1981). Difficult to implement in self-consistent calculations for solids Incorporate in pseudopotentials

. , . , . ,Phys. Rev. B 52, 14316 (1995).

n n +

0.37Ec LDA+U approach

0.34

. 1.51Ev

. . . ,Appl. Phys. Lett.87, 122102(2005).

S. Lany and A. Zunger,

7.16Zn3d-band

.. . , .

Issues: Determination of U .

How to extrapolate to theexperimental gap?


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Oxygen vacancy in ZnOOxygen vacancy in ZnO

orrec e


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BandBand--gap corrections: Beyond DFTgap corrections: Beyond DFT Quasiparticle calculations

Combine DFT andG 0W0 : goo or s ruc ura proper es G 0W0: many-body perturbationtheory for defects: accurate

electron affinities in solids P. Rinke, A. Janotti, M. Scheffler,

and C. G. Van de Walle, Phys.Rev. Lett.102, 026402 (2009).

Quantum Monte Carlo Richard Hennig


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DeepDeep vs.vs. shallow defectsshallow defects

CB

VBVB

Note: dispersion Due to finite su ercell size Energetics taken care of by special-point sampling Make sure correct occupation of states


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DeepDeep vs.vs. shallow defectsshallow defects

CB

VBVB

DeepLocalized wave function

ShallowDefect-induced state is

Level (usually) far from bandedges

resonance in VB or CBNear VB or CB: only small

perturbationEffective mass state


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Alignment of Fermi levelAlignment of Fermi level

Charges are exchanged with E F, referenced to E vq = q orm tot tot

Presence of defect in supercell shifts average electrostaticpotential with respect to bulk

defect bulk

V


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Supercell size effectsSupercell size effects Neutral defects:

atomic relaxations are included, and overlap ofwave functions is small enough

Charged defects: Inbalance in electronic and

Coulomb divergence Neutralizing background

G=0 term calculatedfor neutral system


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Supercell size effectsSupercell size effects Neutralization leads to unintended terms in

Interactions with neutralizing background and

Makov-Payne correctionE L = E 2/ L C 2/L3 + O L-5

G. Makov and M.C. Payne, Phys. Rev. B51, 4014 (1995). Correct in vacuum

Effect of solid: dielectric constant


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Supercell size effectsSupercell size effects Explicit studies as a function of supercell size have

Fits to 1/L and 1/L3 terms In some cases, Makov-Payne correction satisfactory In other cases: Makov-Payne

correction makes things

significantly worse Example: V+ in diamond Shim, Lee, Lee, and Nieminen,

Phys. Rev. B 71, 035206 (2005).

With MP

MP


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Supercell size effectsSupercell size effects Need rigorous analysis of electrostatic interactions

C. Freysoldt, J. Neugebauer, and C. G. Van de Walle,Phys. Rev. Lett.102, 106402 (2009).

Coefficient of 1/L3 (quadrupole) term

Alignment term ows es ng w e erpoint charge correction(Makov-Payne) suffices or not Fails if defect state decays slowly; point-charge model

overcorrects Prescri tion for addressin this roblem


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Native point defects in ZnONative point defects in ZnO VO, VZn dominate

A. Janotti and C. G. Van de WalleZn-rich Appl. Phys. Lett.87, 122102 (2005).

S. B. Zhanget al. , Phys. Rev. B 63,075205 (2001). F. Oba et al. Ph s. Rev. B 77

245202 (2008).

VO: deep donor Also hi h formation ener in

n-type ZnO VZn: deep acceptor

Cause of reen luminescence A. F. Kohan, G. Ceder,D. Morgan, C. G. Van de Walle,

Phys. Rev. B 61, 15019 (2000)


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Native defectsNative defectsvsvs

. impurities. impurities Native defects cannot explain n -type doping

Impurities: donors?


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Interstitial Hydrogen in ZnOInterstitial Hydrogen in ZnO

2

3

( e

V )

0

1

+H

a t i o n e n

e r g

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-1 F o r

EF (eV)

H+ is the only stable charge state hydrogen acts as shallow donor Unexpected! In other semiconductors hydrogen reduces the conductivity

C. G. Van de Walle, Phys. Rev. Lett.85, 1012 (2000).y y u

But: highly mobileM. G. Wardle, J. P. Goss and P. R. Briddon, Phys. Rev. Lett. 96, 205504 (2006).

unstable at temperatures where n -type conductivity is known topersist (>500 oC)Also cannot explain dependence of conductivity on oxygen partial pressure


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Substitutional h dro en in ZnOSubstitutional h dro en in ZnO Forced to reconsider the role ofhydrogen...

new physics/chemistry emerged! Substitutional hydrogen VO HO Formation energy:low

Ionization energy: small;shallow donor

i

ons s en y exp a ns epen ence on -type conductivity on oxygen partialpressure Zn

g [ X ] [n ] g [ X ] [n ][n ]

HO [Hi]

l o

[V O]

[HO][Hi][Hi]

l o

[V O][V O]

[HO][HO]

pO 21/2pO 21/2


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pp --type doping of ZnOtype doping of ZnO Nitrogen is often regarded as most suitable

hole dopant Shallow acceptor in ZnSe

Numerous reports of p -type ZnO crystals - , ,

Reliability? Reproducibility?

C.H. Park, S.B. Zhang, and S.-H. Wei, PRB 66, 073202 (2002).


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BandBand--gap corrections: Hybridgap corrections: Hybrid functionalsfunctionals Mixing of Hartree-Fock (exact exchange) and DFT

A. D. Becke, J. Chem. Phys.98, 1372 (1993). unc ona s m x n ~ o exac exc ange PBE0 J. P. Perdew, K. Burke, and M. Ernzerhof,

. . . , . J. P. Perdew, M. Ernzerhof, and K. Burke,

J. Chem. Phys. 105, 9982 (1996).

HSE Exact exchange only for short-range interactions J. Heyd, G. E. Scuseria and M. Enzernhof,

J. Chem. Phys. 118 , 8207 (2003).

a n very goo escr p on o many proper es Band gaps close to experiment


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HSE calculations forHSE calculations for ZnOZnO Hybrid functionals

include a portion ofexact exchange,correct band gap . , . . ,

and M. Ernzerhof, J. Chem.Phys. 118, 8207 (2003).

=0.36 VASP code (ver. 5.1)


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Nitrogen acceptor inNitrogen acceptor in ZnOZnO Deep acceptor Lar e ionization ener : 1.3 eV Low formation energy undern-type

conditions Localized wavefunction

NOJ. L. Lyons, A. Janotti, and C. G. Van de

Walle, Appl. Phys. Lett.95, 252105 (2009).x a on = .Planar bonds = 1.94


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Test case:Test case: NN SeSe inin ZnSeZnSe

Similar semiconductor N known shallow

Zn-rich(0/-)

acceptor in ZnSe Effective p -type dopant NSe Results agrees well with

experimental values Theor : E = 150 meV Exp.: EA = 110-130 meV


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NNOO acceptor: Experimentacceptor: Experiment

coordinate diagram Absorption:2.4 eV 1.7 eV

NO0 to CB 2.4 eV = 520 nm Zero honon line at2.1 eV

Emission:electron falling from

o O eve 1.7 eV = 730 nm


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NNOO acceptor: experimentacceptor: experiment

Localization on N atom

Directed towards axial zincneighbor

W.E. Carlos, E.R. Glaser, and D.C., , . N. Y. Garces, N. C. Giles, L. E.

Halliburton, G. Cantwell, D. B. Eason,D. C. Reynolds, and D. C. Look,

Spin density of nitrogen state(Isosurface is 5% of maximum

density)

pp . ys. e . , .

Why nitrogen cannot lead to p-type conductivity in ZnO, J. L. Lyons, A. Janotti, and C.G. Van de Walle, Appl. Phys. Lett.95, 252105 (2009).


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TiOTiO22 in GGAin GGA--PBEPBE

Rutile

- p s a esCBM - Ti d states


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Hybrid functional calculations for TiOHybrid functional calculations for TiO22

HSE functional Heyd, Scuseria, & Ernzerhof, J. Chem. Phys.118 , 8207 (2003); erratum: J. Chem. Phys.124, 219906 (2006)

H-F mixing parameter 0.20;screenin arameter = 0.2 -1 PAW, VASP 5.1

72 atom-supercell -po n s: , , . , . , . ; es e or x x cutoff: tested for up to 400 eV

A. Janotti, J. B. Varley, P. Rinke, N. Umezawa, G. Kresse, andC. G. Van de Walle, Phys. Rev. B 81, 085212 (2010).

TiOTiO l il i


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TiOTiO22 -- structural propertiesstructural properties

PBE versus H EPBE versus H E Rutile


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Band structure of TiOBand structure of TiO 22

HSE can be tuned to reproduce the exp. band gap value

Eff t f HSE l b dEff t f HSE l b d


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Effects of HSE on valence bandEffects of HSE on valence band

versus conduction bandversus conduction band(determined from surface calculations)(determined from surface calculations)

HSE lowers the VBM by 0.6 eV and raises the CBM by 0.7 eV


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SingleSingle--particle states ofparticle states of VVOO in TiOin TiO22

unrelaxed vacancy induced single-particle states are in the gap


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SingleSingle--particle states ofparticle states of VVOO in TiOin TiO22re axe versus unre axe vacancyre axe versus unre axe vacancy

GGA cannot describe relaxed vacancy in 0 and +1 charge statesoccupied states above the CBM


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SingleSingle--particle states ofparticle states of VVOO in TiOin TiO22 versus y r unc onaversus y r unc ona

relaxed VO0

and VO+

can be described in HSE

Formation energies ofFormation energies of


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Formation energies ofFormation energies ofVV in TiOin TiO22unrelaxed

formation energy of +2 and +are lowered, consistent with thean a gnmen

Fermi level (eV)

Formation energies ofFormation energies of


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Formation energies ofFormation energies ofVV in TiOin TiO22unrelaxed

formation energy of +2 and +are lowered, consistent with the

relaxed

an a gnmen

relaxation energies for +2 aresimilar in PBE and HSE

transition levels (+2/0) and (+/0)are near the CBM

Fermi level (eV)


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Oxygen vacancy in TiOOxygen vacancy in TiO 22

shallow donor - can cause conductivity

low formation energy in O-poor conditions


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Summary and OutlookSummary and Outlook The field of defects in materials is active with

direct applications for many technologicallyimportant systems Much broader than merely point defects in semiconductors

been made on crucial issues: DFT band-gap errors

Still need for deeper physicalunderstanding

e erences verv ews J. Neugebauer and C. G. Van de Walle,J. Appl. Phys.95, 3851 (2004).

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Defecte in OxiziZnO

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