Tuned and screened range-separated hybrid density functional theory for describing electronic and optical properties of defective gallium nitride

D. Kirk Lewis, Ashwin Ramasubramaniam, and Sahar Sharifzadeh

Phys. Rev. Materials 4, 063803 – Published 18 June 2020

Abstract

We apply a hybrid density functional theory approach, based on a tuned and screened range-separated hybrid (SRSH) exchange-correlation functional, to describe the optoelectronic properties of defective gallium nitride (GaN). SRSH and time-dependent SRSH (TDSRSH) are tuned to produce accurate energetics for the pristine material and applied to the study of a series of point defects in bulk GaN, a blue light-emitting material that degrades in the presence of defects. We first establish the accuracy of the method by comparing the predicted quasiparticle gap and low-energy excitation spectra of (TD)SRSH and many-body perturbation theory for both pristine GaN and GaN containing a single nitrogen vacancy. Aided by the reduced computational cost of (TD)SRSH, we then report on three additional technologically relevant point defects and defect complexes in GaN: the gallium vacancy, the carbon interstitial, and the carbon-silicon complex. We compute the low-energy optical absorption spectra for these defects and show the presence of defect-centered transitions. Furthermore, by estimating the Stokes shift, we predict, in agreement with previous studies, that the carbon substitutional defect is a candidate for the detrimental yellow luminescence in GaN. This study indicates that TDSRSH is a promising and computationally feasible approach for quantitatively accurate, first-principles modeling of defective semiconductors.

Received 27 March 2020
Accepted 11 May 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.063803

Physics Subject Headings (PhySH)

Electronic structure Point defects

Nitrides

Density functional approximations Density functional theory Time-dependent DFT

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Kirk Lewis¹, Ashwin Ramasubramaniam ², and Sahar Sharifzadeh ^1,3,*

¹Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA
²Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
³Division of Materials Science and Engineering, Boston University, Boston, Massachusetts 02215, USA

^*ssharifz@bu.edu

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Vol. 4, Iss. 6 — June 2020

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Images

Figure 1
The structure of bulk wurtzite GaN. (a) Shows the pristine unit cell and (b) the $4 \times 4 \times 3$ 192-atom supercell for defect studies.
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Figure 2
(a) Band structure within $G W$ , DFT-HSE, and DFT-SRSH and (b) imaginary component of the dielectric function within $G W / BSE$ , TDHSE, and TDSRSH for pristine GaN. In (a) the band structure path for a hexagonal lattice from Ref. [119] was used. For (b) a broadening of 0.25 eV was applied to the theoretical results to mimic experimental broadening and the spectra were normalized such that the highest peak position is at 1. The experimental dielectric function is taken from Ref. [118].
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Figure 3
Predicted imaginary component of the dielectric function for GaN containing one $V_{N}^{1 +}$ defect for BSE, TDSRSH, and TDHSE. For these calculations, no electrostatic correction has been applied to defect-state energies.
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Figure 4
Band diagram for GaN in the presence of the (a) $V_{N}^{1 +}$ , (b) $V_{Ga}^{3 -}$ , (c) $C_{N}^{1 -}$ , and (d) $C_{N} − {Si}_{Ga}$ point defect. Blue (red) color corresponds to occupied (unoccupied) states with the blue (red) shaded region corresponding to the pristine valence (conduction) band. Localized (defect) states are shown with dashed lines. Band diagrams are on the same energy scale and aligned with respect to their valence band maxima for ease of comparison. The lowest-energy transition between occupied and unoccupied states is shown. The $\sim 0.1$ eV variation in the bulk band gap between different defects is due to the introduction of the defect. (e) The imaginary part of the dielectric function for pristine GaN and GaN in the presence of the $V_{N}^{1 +}, V_{Ga}^{3 -}, C_{N}^{1 -}$ , and $C_{N} − {Si}_{Ga}$ defects. A Gaussian broadening of 0.1 eV was applied and the spectra are normalized such that the highest peak in the energy window was set to 1. In the case of charged defects an electrostatic correction was applied to localized defect states as described in the text.
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Figure 5
The hole and electron density associated with the lowest-energy excited-state transition calculated within TDSRSH for the (a) $V_{N}^{1 +}$ , (b) $V_{Ga}^{3 -}$ , (c) $C_{N}^{1 -}$ , and (d) $C_{N} − {Si}_{Ga}$ defects. The density is calculated as a weighted combination of transitions from Kohn-Sham orbitals. The lower plot shows the occupied hole state while the upper plot shows the unoccupied electron state. All isosurfaces enclose 30% of the respective charge distribution's total charge.
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Figure 6
A schematic of the configuration coordinate diagram showing the processes of photoabsorption and luminescence. Starting with a defect in the ground state $D^{q}$ , in charge state $q$ (bottom curve), an incident photon excites the material to state $D^{q + 1}$ (top curve) that has the same geometry as the ground state but a different defect charge state $q + 1$ , where the electron is now in the conduction band. The vertical shift in energy between the two systems is $E_{opt}$ and is followed by a relaxation of the atoms to the minimum energy of $D^{q + 1}$ , shifted by the amount of the Stokes shift $E_{S}$ . The transition back to the initial ground state occurs either without phonons at the energy of the zero-phonon line (ZPL) or via the multistep process involving return to state $D^{q}$ and emission of a photon with energy $E_{PL}$ followed by relaxation back to the equilibrium ground-state system, with energy change given by the anti-Stokes shift $E_{A S}$ .
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