Simulation of Near Zero Field Magnetoresistance Contributions from Vacancies in GaN as a Probe of Radiation Damage

Radiation-intensive environments create native defects in gallium nitride (GaN) devices [1], which negatively impact performance. Despite ongoing research, many defects in GaN remain unidentified [1,2]. Traditionally, electrically detected magnetic resonance (EDMR) and electron nuclear double resonance (ENDOR) have been essential for identifying defects in group-IV materials, where the low abundances of nuclei with non-zero spins produce clear hyperfine resonances. However, in GaN, all gallium and nitrogen nuclei possess non-zero nuclear spins, leading to strong coupling between defects and numerous nuclei, which results in complex and often unresolvable hyperfine interactions [2]. A variation of EDMR, operated at near-zero magnetic field (NZFMR) [3], offers increased sensitivity to the nuclear hyperfine environment and may provide a more effective method for defect identification. We use a two-step process to theoretically simulate the NZFMR response for two common native defects in GaN, V_N and V_Ga. First, we calculate the defect wave function and corresponding hyperfine tensor using multiband real-space Green’s functions to exactly solve the Dyson equation for a localized perturbation in bulk. This approach avoids periodicity and finite volume effects. From the inhomogeneous Green’s function solution, we extract the defect wave function and the hyperfine couplings for nearby nuclei. In the second step, these hyperfine parameters are used to simulate the spin dynamics of the defect in an open quantum system using the Lindbladian formalism. Due to the large number of spin-active neighbors, a fully quantum mechanical treatment of the nuclear bath is not feasible, as the memory requirement scales as (2I + 1)^N. To address this, we model the nuclear bath using a classical nuclear hyperfine averaging method, reducing the (2I + 1)^N subspace to a sum of ∑_j(2I_j + 1) classical fields. We then compute a multiplicity-weighted average to produce a single NZFMR signal.

Acknowledgments: This material is based upon work supported by the Air Force Office of Scientific Research
under award number FA9550-22-1-0308.
[1]S. J. Pearton and F. Ren, E. Patrick, M. E. Law and A. Y. Polyakov, ECS J. Solid State Sci. Technol. 5,Q35
(2015)
[2]H. J. von Bardeleben et al, Phys. Rev. Lett., 109, 20 206402 (2012)
[3]P. M. Lenahan et al. IEEE Xplore doi: 10.1109/IRPS48203.2023.10118053