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.