Post on 01-Jan-2017
Defects and doping in oxides: What we have learned so farAnderson JanottiMaterials Department, University of California Santa Barbara
Tuesday, February 23, 2010
Collaborators
J. Varley, J. Lyons, J. Weber, C. G. Van de Walle (Materials Dept., UCSB)P. Rinke, M. Scheffler (MPI-Berlin, UCSB)S. Limpijumnong, P. Reunchan (Suranaree Univ. of Tech. Thailand)G. Kresse, University of ViennaT. Ive, O. Bierwagen, J. Speck (Materials Dept., UCSB)M. McCluskey (Washington State University)G. D. Watkins (Lehigh University) L. Halliburton (West Virginia University)S. Chambers (Pacific Northwestern Nat. Lab)
Tuesday, February 23, 2010
Variety of crystal structures and band gaps
Material Crystal structutre Band gap (eV)ZnO wurtzite 3.4TiO2 Anatase, rutile 3.0 - 3.4SnO2 rutile 3.6In2O3 bixbyte 2.7
ZnO-based “Invisible” electronics
Available as large single crystals
2-inch ZnO wafer grown by Eagle-Picher Technologies
Diebold, Surf. Sci. Rep. (2003)
Transparent transistors, Wager, Science (2003)
Murai et al, phys. stat. sol. (2007)
ZnO transparent electrode: Mega cone
Possible applications• light emitting diodes and laser diodes• transparent electronics• electronic “noses” (gas sensors)• photocatalysis, water splitting• transparent electrodes, smart widows
Oxide semiconductors
ZnO TiO2
Tuesday, February 23, 2010
Major problem: controlling the conductivityVision
Tuesday, February 23, 2010
Controlling the conductivity is a major problem
• High levels of unintentional n-type conductivity– traditionally attributed to native point defects: oxygen
vacancies and/or cation interstitials
– conductivity varies inversely with oxygen partial pressure
• Difficult to make p-type– valence band is low in energy in an absolute scale
– stability and reproducibility are main issues (p-ZnO)
Kroger, The Chemistry of imperfect crystals, (North-Holland Publishing Co., Amsterdam, 1964)Tomlins, Routbort, and Mason, J. Appl. Phys. Rev. 87, 117 (2000)Look, et al., Phys. Rev. Lett. 82, 2552 (1999), Phys. Rev. Lett. 95, 225502 (2005)Hartnagel and Dawar, Semiconducting Transparent Thin Films, (IOP, Bristol, 1995)
Goal: understand the effects of native defects and impurities by performing first-principles calculations (DFT-LDA and beyond)
Tuesday, February 23, 2010
Ef(V q
O) = Et(V
qO)− Et(ZnO) +
1
2Et(O2) + µO + q�F
µZn + µO = ∆Hf (ZnO)
c = N0e−βEf
�VBM ≤ �F ≤ �CBM
First-principles formalism
Ex.: Oxygen vacancy in ZnO
Determine concentra7ons/solubility
O-‐rich, Zn-‐rich condi7ons
p-‐type, n-‐type
Transition levels (shallow/deep donor/acceptor) Migration barriers (stability) Optical transitions - configuration coordinate diagrams Frequencies of local vibration modes
Formation energies
VASP: periodic boundary condi7ons, plane-‐wave basis set, special k points, projector augmented poten7als (PAW)
Tuesday, February 23, 2010
Oxygen vacancy in ZnO cannot be described by DFT-LDA
Electrically active - introduces levels in the gap Possible charge states: 0, +1, +2, Optically active - sub band-gap transitions Cannot be described in DFT-LDA/GGA ?
LDA/GGA
VBM
CBM
0.8 eV
Zn dbs
The band gap is drastically underestimated in DFT-LDA/GGA0.8 eV (LDA/GGA) vs. 3.4 eV (Expt.)
Tuesday, February 23, 2010
Approaches to overcome the band gap problemLDA+U
U applied to semicore d states ➙ partial correction of band gaps extrapolation from LDA and LDA+U calculations ex: ZnO, InN, GaN, SnO2, In2O3
Screened hybrid functional (Heyd, Scuseria, Einzernhof)
mix of Hartree-Fock and GGA/LDA exchange ➙ removes self-interaction band gaps in agreement with experiments (by tuning mixing parameter)
more general, can be applied to any semiconductor/material ex: ZnO, InN, TiO2, SrTiO3
GW correct band gaps
combined with LDA ➙ correct formation energies and transition levels ex: Si, MgO
Tuesday, February 23, 2010
Combining LDA and LDA+U to overcome theband gap problemLDA+U
U applied to semicore d states ➙ partial correction of band gaps extrapolation from LDA and LDA+U calculations ex: ZnO, InN, GaN, SnO2, In2O3
p-d repulsion
gap
d states
VBM (O p states)
CBM (Zn s states)
LDA+U: d bands are lowered with respect to VBMThe band gap is partially corrected: LDA: 0.8; LDA+U 1.5; Exp. 3.4 eV
Tuesday, February 23, 2010
Combining LDA and LDA+U to overcome theband gap problemLDA+U
U applied to semicore d states ➙ partial correction of band gaps extrapolation from LDA and LDA+U calculations ex: ZnO, InN, GaN, SnO2, In2O3
p-d repulsion
gap
d states
VBM (O p states)
CBM (Zn s states)
LDA+U: affects both valence band and conduction band
Tuesday, February 23, 2010
Correcting transition levels and formation energies based on LDA/LDA+U calculations
Appl. Phys. Lett. 87, 122102 (2005)
!(q/q!) =!(q/q!)LDA+U
! !(q/q!)LDA
ELDA+Ug ! ELDA
g
(Eexpg ! ELDA+U
g ) + !(q/q!)LDA+U
Take into account valence vs. conduction band character of the defect state in the gap
Tuesday, February 23, 2010
Deep donor (2+/0) at 1 eV below CBMcannot cause conductivity
+1 charge state unstable EPR active, need light excitation to see +1
High formation energy in n-typeLow concentrations in equilibrium conditionsIn agreement with Watkins & Vlasenko Phys. Rev. B 71, 125210 (2005): +1 only observed after irradiation
Zn-rich
Form
atio
n en
ergy
(eV
)Oxygen vacancy in ZnO
Tuesday, February 23, 2010
Oxygen vacancy in ZnOElectronic proper7es strongly coupled with local laLce relaxa7ons
Tuesday, February 23, 2010
VO in ZnO: comparison with experiment
Ea! Ee!
�F @CBM
Vlasenko & Watkins, Phys. Rev. B 71, 125210 (2005).
Tuesday, February 23, 2010
• VO, VZn: dominant defects– Janotti and Van de Walle,Phys. Rev. B 76, 165202 (2007)– Zhang et al., Phys. Rev. B 63, 075205 (2001)– Oba et al., Phys. Rev. B 77, 245202 (2008).
• VO: deep donor– Also high formation energy inn-type ZnO
• VZn: deep acceptor– Cause of green luminescence– Kohan, et al. Phys. Rev. B 61, 15019 (2000)– Janotti and Van de Walle, Phys. Rev. B 76, 165202 (2007)
• Zni: high formatio energyunstable, migration barrier 0.57 eV
Native point defects in ZnO
Tuesday, February 23, 2010
Native defects vs. impurities
• Native defects cannot explain n-type doping• Impurities: donors?
Tuesday, February 23, 2010
Interstitial hydrogen in ZnO
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Substitutional hydrogen in ZnO
Tuesday, February 23, 2010
Diffusion of substitutional hydrogen
How does HO move?
Dissociation:HO+ → Hi+ + VO0 costs 3.8 eV!
Tuesday, February 23, 2010
Diffusion of substitutional hydrogen
2.5 eV
How does HO move?
Dissociation:HO+ → Hi+ + VO0 costs 3.8 eV!
Migration:– Concerted exchange of H and neighboring O– Barrier: 2.5 eV⇒ becomes mobile above 500 ºC
• Consistent with experimentalobservations– Shi et al., Phys. Rev. B 72,195211 (2005)– Jokela and McCluskey, Phys. Rev. B 72, 113201 (2005)
Tuesday, February 23, 2010
Hydrogen multicenter bonds
Tuesday, February 23, 2010
Nitrogen doping in ZnO
In principle, the most promising p-type dopant in ZnO
Experimental results are highly controversial
Stability and reproducibility are main issues
Tuesday, February 23, 2010
ZnO: Hybrid functional calculations
ZnO band structure
Tuesday, February 23, 2010
NO in ZnO
Lyons, Janotti, and Van de Walle, Appl. Phys. Lett. 95, 252105 (2009)
Deep acceptor
Will not lead to p-type conductivity
Tuesday, February 23, 2010
NO in ZnO – theory vs. experiment
Lyons, JanoL, and Van de Walle, Appl. Phys. LeO. 95, 252105 (2009)
Annealed in air
Garces et al., Appl. Phys. LeO. 80, 1334 (2002)
Tuesday, February 23, 2010
NO in ZnO: theory vs. experiment
Lyons, JanoL, and Van de Walle, Appl. Phys. LeO. 95, 252105 (2009)
Anisotropy in the spin density
Tuesday, February 23, 2010
Oxygen vacancy in TiO2
LDA/GGA functionals can describe only +2 charge state Electrons from 0 and +1 charge states go to the conduction band
LDA/GGALDA/GGA
?
LDA/GGA
Is DFT-LDA/GGA enough?
Tuesday, February 23, 2010
Ru7le
TiO2:Hybrid functional calculations
Tuesday, February 23, 2010
TiO2: GGA vs. Hybrid functional (HSE)
Phys. Rev. B 81, 085212 (2010)Tuesday, February 23, 2010
relaxed VO0 and VO+ can be described in HSE
VO in TiO2: GGA vs. HSE
Phys. Rev. B 81, 085212 (2010)Tuesday, February 23, 2010
gap states have strong contributions from the two out-of-plane Ti atoms
VO0 and VO+ charge distributions
spin=0 spin=1/2, paramagne7c
Phys. Rev. B 81, 085212 (2010)Tuesday, February 23, 2010
shallow donor - can cause conductivity low formation energy only in extreme O-poor conditions
VO in TiO2: HSE results
Phys. Rev. B 81, 085212 (2010)Tuesday, February 23, 2010
Summary
LDA/LDA+U scheme • Limited to systems with semicore d states• Computationally inexpensive, large systems (>200 atoms)
Hybrid functionals (HSE)• Mixing parameter and screening length• Can be applied to any semiconductor • Computationally demanding (~100 atoms, few k-points)
Tuesday, February 23, 2010
SummaryZnO
Native defects are not the cause of unintentional n-type conductivity
Impurities are the likely cause (hydrogen) Nitrogen doping not lead to p-type ZnO
TiO2
Oxygen vacancy is a shallow donor Low formation energy only in extreme O-poor Need to relate µO to realistic conditions
Tuesday, February 23, 2010
Tuesday, February 23, 2010
Janotti & Van de Walle PRB 76, 165202 (2007)
Oba et al., PRB 77, 245202 (2008)
LDA/LDA+U vs. HSE
Tuesday, February 23, 2010
Diffusion of point defects
Tuesday, February 23, 2010
Annealing temperature of point defects
Tuesday, February 23, 2010
Si and Ge in ZnO
Phys. Rev. B 80, 205113 (2009)• Si and Ge are shallow donors• [Si] of up to 10E17 cm-3 observed in as grown single crystals McCluskey and Jokela, Physica B 401-402, 355 (2007)
Tuesday, February 23, 2010