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

Using the fixed-node diffusion Monte Carlo (FN-DMC) method, we evaluate the formation energies and charge transition levels of substitutional nitrogen defects in the wide-band-gap semiconductor zinc oxide. The use of a direct-solution, many-body approach inherently secures a good description of electron-electron interactions, achieving high accuracy without adjustable parameters. According to FN-DMC nitrogen is a deep acceptor with a charge transition level 1.0(3) eV above the valence-band maximum when 72-atom supercells are used. This result falls on the lower end of typically reported hybrid density functional results for the same size supercells, which range from 1.0 to 1.8 eV. Further, residual finite-size effects due to charged defect image interactions in the 72-atom supercells are estimated by supercell extrapolation within hybrid density functional theory. When the finite-size correction is included, we obtain a deep acceptor at 1.6(3) eV. This result is in good agreement with recent experimental measurements. We also analyze the local compressibility of charge according to FN-DMC and common density functionals and find that the use of hybrid functionals obtains compressibilities in better agreement with the many-body theory. Our work illustrates the application of the FN-DMC method to a challenging point defect problem, demonstrating that uncertainties and approximations can be well controlled.

Figure 1

Bond length between neutral N (blue) and Zn (gray) in a supercell. $\mathrm{\Delta }{E}_{\mathrm{rel}}$ refers to the relative total energy of FN-DMC between two given neutral geometries.

Figure 2

Supercell extrapolations carried out with DFT-PBE0 that show the finite-size effect (FSE) corrections for (a) the ionization potential and (b) electrostatic image interactions between ionized nitrogen defects. The $x$ axis indicates $1/L$, where $L\times L\times L$ is the number of unit cells in the supercell. The $y$ axis is the FSE correction for a given supercell; in the limit of an infinite-size supercell, the FSE corrections go to zero. In (a) the DMC values with the finite-size correction applied are within statistical error (0.1 eV).

Figure 3

Defect formation energies and charge transition levels for nitrogen in zinc oxide. The experimental ionization level [15] is shown as a black solid line. The gray lines indicate stochastic error bars around the computed quantities.

Figure 4

Charge fluctuations of each spin on the site of Zn, O, and N atoms in the 72-atom supercell. Stochastic uncertainties are smaller than the symbols. Here, $\uparrow$ denotes the majority spin, and $\downarrow$ denotes the minority spin.