⊥ c Zn i V Zn First-principles modeling of defects and hydrogen in oxides Chris G. Van de Walle Materials Department, University of California, Santa Barbara, USA with 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/~vandewalle First-principles calculations Density functional theory, many-body perturbation theory Hydrogen as a fuel Oxides • Transparent • Kinetics conductors • Complex hydrides • Dielectrics • Metal hydrides • Thermal barriers • Proton conductors • Complex oxides Nitrides Quantum • Doping Ga computing • Surfaces • Interfaces N N with defects • Efficiency, loss • Qubits • Single photon emitters
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 or surface/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]=N O exp(-E f /kT) 1 − + + − + V O 2 Al 2 O 3 ½ O 2 Al 2 O 3 : V O O chemical potential
Defect Formation Energy Determine defect concentrations: [D]=N O exp(-E f /kT) ε F 1 + − + + − + + V O 2 e - e − @ ε F Al 2 O 3 ½ O 2 Al 2 O 3 : V O O chemical potential
Defect Formation Energy Determine defect concentrations: [D]=N O exp(-E f /kT) ε F - 1 − + + − − + V O 2 e - e − @ ε F Al 2 O 3 ½ O 2 Al 2 O 3 : V O O 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).
Defect Formation Energies example: V O • Plotted for extreme Al-rich and O-rich limits • Very wide range given by Formation Energy (eV) O-Rich Δ H f (Al 2 O 3 )= -17.36 eV • Actual chemical potential is Al-Rich somewhere in between • Slope indicates charge • Kinks: charge transition levels • Information used to study fixed charge and defect levels Fermi level (eV)
Native point defects in α -Al 2 O 3 Al i Formation Energy (eV) V O O i V Al Al-Rich O-Rich Fermi level (eV) Fermi level (eV)
Defect level positions in α -Al 2 O 3 Conduction band (0/-) (+/0) (3+/+) Energy (eV) V Al V O Al i O i (0/2-) (+/0) (2+/+) (2-/3-) (-/2-) (0/-) Valence band
Local geometry and charge densities O Al i V O Al 0 V O Al i 0 e − O i V Al V Al 0 h + 0 O i
Defect levels in κ - and α -Al 2 O 3 V Al V O Al i O i V O V Al O i O Al Al O Al i Energy (eV) κ -Al 2 O 3 ** α -Al 2 O 3 GaN 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).
Hydrogen in Al 2 O 3 Formation Energy (eV) H i H O Al-rich O-rich μ O = -0.65 eV Fermi level (eV) O 2 gas @ 270 o C and 1 Torr
Hydrogen in Al 2 O 3 • Hydrogen can easily incorporate α -Al 2 O 3 H O 8 into Al 2 O 3 Formation Energy (eV) +1 -1 6 • Hydrogen occupies the interstitial site (H i ) 4 • (+/-) impurity level near mid-gap 2 +1 -1 H i • Low migration energy 0 • H i can interact with native -2 defects or impurities in Al 2 O 3 -4 μ O = − 0.65 eV -6 0 2 4 6 8 O 2 gas @ 270 o C Fermi level (eV) and 1 Torr
H complexes with Al vacancy in Al 2 O 3 • Al vacancy: V Al 8 − 3 charge state over most of Al 2 O 3 Formation Energy (eV) V Al +H 6 band gap 4 negative fixed-charge center 2 • H captured by Al vacancy: H i V Al +2H 0 • V Al + n H ( n =1,3) complexes lower V Al +3H the electrical charge of V Al -2 • V Al +3H complex is electrically -4 inactive κ -Al 2 O 3 -6 0 2 4 6 Fermi level (eV)
Local geometry and charge density 0 0 Ga Al N O Ga N 0 0 C Al H i C H
Gallium in Al 2 O 3 Formation Energy (eV) Ga i Ga O Ga Al Ga-rich O-rich μ O = -0.65 eV O 2 gas @ 270 o C Fermi level (eV) and 1 Torr
Nitrogen in Al 2 O 3 N Al Formation Energy (eV) N i N O Al-rich O-rich μ O = -0.65 eV O 2 gas @ 270 o C Fermi level (eV) and 1 Torr
Carbon in Al 2 O 3 C Al Formation Energy (eV) C i C O Al-rich O-rich μ O = -0.65 eV O 2 gas @ 270 o C Fermi level (eV) and 1 Torr
Impurity Levels in Al 2 O 3 Ga i N i C i H i H O Ga Al Ga O N Al N O C Al C O (0/-1) (+1/-1) (+1/-1) (-1/-3) Energy (eV) (0/-1) (0/-1) (-1/-2) (+1/-1) (+1/0) (-1/-2) (+3/+1) E Fermi (0/-1) (+1/0) (0/-1) (+2/0) (0/-1) (+1/-1) (0/-1) (+3/+2) (+3/0) (+3/+1) (+1/0) (+4/+3) (+4/+3) (0/+1) (+2/+1) (+2/+1) GaN (+3/+2) (+4/+3) Al 2 O 3
Diffusion of point defects • Relevant for … Top View – growth » Defects ‘frozen in’ or not – Ion implantation » Anneal damage – Degradation Side View – Irradiation • Zinc interstitial: – E m =0.57 eV
Annealing temperature of point defects − E b 1 − Γ ≈ − Γ = Γ Γ ≈ 1 13 1 s exp 10 s 0 0 kT E b (eV) T annealing (K) 2+ Zn i 0.57 219 2- V Zn 1.40 539 2+ 1.70 655 V O 0 2.36 909 V O 0 (split) O i 0.87 335 2- (oct) O i 1.14 439 A. Janotti and C. G. Van de Walle, Phys. Rev. B 76 , 165202 (2007).
Summary • First-principles calculations provide qualitative insights and quantitative details for point defects • Native defects and impurities in Al 2 O 3 • 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 -Al 2 O 3 : J. R. Weber, A. Janotti, and C. G. Van de Walle, J. Appl. Phys. 109 , • 033715 (2011). α -Al 2 O 3 : 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).
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