Comparison of density functionals for nitrogen impurities in ZnO

Abstract

Hybrid functionals and empirical correction schemes are compared to conventional semi-local density functional theory (DFT) calculations in order to assess the predictive power of these methods concerning the formation energy and the charge transfer level of impurities in the wide-gap semiconductor ZnO. While the generalized gradient approximation fails to describe the electronic structure of the N impurity in ZnO correctly, methods that widen the band gap of ZnO by introducing additional non-local potentials yield the formation energy and charge transfer level of the impurity in reasonable agreement with hybrid functional calculations. Summarizing the results obtained with different methods, we corroborate earlier findings that the formation of substitutional N impurities at the oxygen site in ZnO from N atoms is most likely slightly endothermic under oxygen-rich preparation conditions, and introduces a deep level more than 1 eV above the valence band edge of ZnO. Moreover, the comparison of methods elucidates subtle differences in the predicted electronic structure, e.g., concerning the orientation of unoccupied orbitals in the crystal field and the stability of the charged triplet state of the N impurity. Further experimental or theoretical analysis of these features could provide useful tests for validating the performance of DFT methods in their application to defects in wide-gap materials.

ComprehensiveAb InitioStudy of Doping in Bulk ZnO with Group-V Elements

“…1). At variance, Lyons et al 9 and Sakong et al 29 find a transition energy of 1.3 and 1.46, respectively, setting α = 0.36. This is in agreement with the result of Gallino et al 11 , which, however, is obtained with the B3LYP hybrid functional 30 , making the comparison less straightforward.…”

Fixed-node diffusion Monte Carlo description of nitrogen defects in zinc oxide

“…Standard DFT calculations based on PBE obtain only small, symmetric relaxations of atoms around N 0 O . On the other hand, hybrid calculations for suitably large supercells find a symmetry broken configuration to be more favorable 12,13 , and EPR measurements are also consistent with the presence of a distorted, deep state 29 . The distorted state corresponds to an asymmetric elongation along the c direction N-Zn bond shown in Fig.…”

“…The CTLs according to Ref. [13] obtained within PBE0 are reported as 1.1-1.2 eV from 72 atom supercells, but include an ≈0.2 eV estimate of the charged defect image interaction, so the direct comparison is 0.9-1.1 eV 37 . Likewise, the CTLs according to Ref.…”

“…Meanwhile early computational results based on conventional density functional methods (LDA, GGA) predicted the charge transition level to occur at (0/ − 1) ≈ 0.4 eV above the valence band edge 9 . However, subsequent reproducibility of the experiments has proven to be challenging, and more recent computational results based on hybrid functional DFT 10,11 , a generalized Koopman's framework 12 , and a comprehensive DFT study using different exchange-correlation functionals 13 suggest instead a deep nature but with (0/−) reported in a wide range 1.0 -2.1 eV above the VBM. Recent experiments based on photoluminescence spectroscopy find the N acceptor level to lie 1.4 eV above the VBM 2,14,15 .…”

First-principles study of uniaxial strained and bent ZnO wires

“…A major question, however, is still open about the value of U to be used. On one hand there are electronic structure calculations reported with values of U in the range of 7.5 eV [41] and 9 eV [42] on d orbitals of Zn. On the other hand, U is also been applied on p orbitals of O [43,44] and both on s and d orbitals of Zn in order to describe the thermochemistry of O vacancy in ZnO [45].…”