⊥cZni
VZn

First-principles modeling of defects
and hydrogen in oxides
Chris G. Van de Walle
Materials Department, University of California, Santa Barbara, USAwith Minseok Choi (Inha U., South Korea), Justin Weber (Intel),Anderson Janotti (U. Delaware), John Lyons (NRL)
Supported by ONR and SRC
International Workshop on Models and Data for Plasma-Material Interaction in Fusion Devices(MoD -PMI 2019)
National Institute for Fusion Science, Tajimi, Japan
June 18-20, 2019

Van de Walle Computational Materials Group
www.mrl.ucsb.edu/~vandewalleFirst-principles calculations

Density functional theory, many-body perturbation theoryOxides• Transparentconductors• Dielectrics• Thermal barriers• Complex oxides

Quantum
computingwith defects• Qubits• Single photon emitters

Hydrogen as a fuel• Kinetics• Complex hydrides• Metal hydrides• Proton conductors

Nitrides• Doping• Surfaces• Interfaces• Efficiency, lossGaNN

Computational Approach• Traditional density functional theory approach– Local or semi-local density approximation• Hard to interpret due to band-gap problem• Major problem when addressing defects orsurface/interface states• Our approach: Hybrid functional calculations– The HSE hybrid functional• A fraction of screened Hartree-Fock exchange• Accurate band gaps and defect levels• 120-atom supercell, 400 eV cutoff energy,
2x2x1 k-point mesh
J. Heyd, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys 118, 8207 (2003).

Defect Formation Energy

Determine defect concentrations: [D]=NO exp(-Ef/kT)

VO

Al2O3: VO−+Al2O3

12½ O2
O chemical potential

Defect Formation Energy

Determine defect concentrations: [D]=NO exp(-Ef/kT)

VO+Al2O3: VO−+Al2O3

12+e-e − @ εF
½ O2O chemical potentialεF

Defect Formation Energy

Determine defect concentrations: [D]=NO exp(-Ef/kT)

VO-Al2O3: VO−+Al2O3

12−e-e − @ εF
½ O2O chemical potential“First-principles calculations for point defects in solids”,
C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse,
A. Janotti, and C. G. Van de Walle, Rev. Mod. Phys. 86, 253 (2014).

εFDefect Formation Energiesexample: VOFormation Energy (eV)• Plotted for extreme Al-rich andO-rich limits
O-RichAl-Rich• Very wide range given by
ΔHf (Al2O3)= -17.36 eV•Actual chemical potential issomewhere in between• Slope indicates charge• Kinks: charge transition levels• Information used to study fixedcharge and defect levels
Fermi level (eV)Native point defects in α-Al2O3
Formation Energy (eV)

Ali
VOOi
VAl
O-RichFermi level (eV)Al-RichFermi level (eV)Defect level positions in α-Al2O3
Conduction band(0/-)(+/0)

Energy (eV)(3+/+)

VAlVOAli(+/0)(2+/+)(2-/3-)(-/2-)(0/-)

Valence bandOi(0/2-)

Local geometry and charge densities
VOOAli
AlVO0Ali0e−Oi

VAlVAl0h+Oi0

Defect levels in κ- and α-Al2O3Energy (eV)VO VAl Oi Ali OAl AlO

VAl VO Ali Oi

GaN

κ-Al2O3 **α-Al2O3

κ: J. R. Weber, A. Janotti, and C. G. Van de Walle, J. Appl. Phys. 109, 033715 (2011).
α: M. Choi, A. Janotti, and C. G. Van de Walle, J. Appl. Phys. 113, 044501 (2013).

Formation Energy (eV)Hydrogen in Al2O3HiHOAl-richO-richFermi level (eV)μO = -0.65 eVO2 gas @ 270 oC
and 1 Torr

Hydrogen in Al2O3Formation Energy (eV)8 α-Al2O3-1-1• (+/-) impurity level near mid-gap

HO+16• Hydrogen can easily incorporate
into Al2O3• Hydrogen occupies theinterstitial site (Hi)

42+1

Hi

0-2-4

• Low migration energy• Hi can interact with nativedefects or impurities in Al2O3

μO = −0.65 eV-602684Fermi level (eV)O2 gas @ 270 oCand 1 TorrH complexes with Al vacancy in Al2O3Formation Energy (eV)86

• Al vacancy:

VAl−3 charge state over most of Al2O3band gap

VAl+H

negative fixed-charge center

420

VAl+2HHiVAl+3H-2-4-6

κ-Al2O30 2 4 6Fermi level (eV)

• H captured by Al vacancy:• VAl+nH (n=1,3) complexes lower
the electrical charge of VAl• VAl+3H complex is electricallyinactiveLocal geometry and charge density
GaAl0NO0GaCAl0NHi0CH

Formation Energy (eV)Gallium in Al2O3Gai
GaOGaAlGa-richO-richFermi level (eV)μO = -0.65 eVO2 gas @ 270 oC
and 1 Torr

Nitrogen in Al2O3
Formation Energy (eV)NAlNi

NOAl-richO-richμO = -0.65 eV

Fermi level (eV)O2 gas @ 270 oC
and 1 Torr

Formation Energy (eV)

Carbon in Al2O3
CAlCi

COAl-richO-richμO = -0.65 eV

Fermi level (eV)O2 gas @ 270 oC
and 1 Torr

Impurity Levels in Al2O3
GaAl GaO Gai NAl NO Ni

CAl CO Ci

Hi HO(0/-1)(+1/-1)

Energy (eV)(-1/-3) (+1/-1)(0/-1)(0/-1)(-1/-2)(+1/0) (+3/+1)(+1/0)(0/-1)(0/-1)(0/-1)(0/-1)(+1/-1)(+3/0)(+2/0)(+3/+2)(+3/+1)(+1/0)(0/+1)(+2/+1)GaN(-1/-2)(+4/+3) (+4/+3)(+2/+1)(+3/+2)(+4/+3)

Al2O3(+1/-1)

EFermiDiffusion of point defects
TopView• Relevant for …
– growth» Defects ‘frozen in’ or not– Ion implantation» Anneal damage
SideView– Degradation– Irradiation• Zinc interstitial:– Em=0.57 eV

Annealing temperature of point defects
 Eb Γ = Γ0 exp  −
 kT 

Γ0 ≈ 1013 s −1

Γ ≈ 1s −1

Eb (eV)T annealing (K)Zni2+

0.57219

VZn2-

1.40

539

VO2+

1.70

655

VO0

2.36

909

Oi0(split)

0.87

335

Oi2-(oct)

1.14439

A. Janotti and C. G. Van de Walle, Phys. Rev. B 76, 165202 (2007).

Summary• First-principles calculations provide qualitative insights andquantitative details for point defects• Native defects and impurities in Al2O3• References• Defects: C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse,A. Janotti, and C. G. Van de Walle, Rev. Mod. Phys. 86, 253 (2014).
• κ-Al2O3: J. R. Weber, A. Janotti, and C. G. Van de Walle, J. Appl. Phys. 109,033715 (2011).
• α-Al2O3: M. Choi, A. Janotti, and C. G. Van de Walle, J. Appl. Phys. 113,044501 (2013).
• ZnO: J. L. Lyons, J. B. Varley, D. Steiauf, A. Janotti and C. G. Van de Walle, J.
Appl. Phys. 122, 035704 (2017).
• GaN: J. L. Lyons and C. G. Van de Walle, NPJ Comput. Mater. 3, 12 (2017).