Proton irradiation of both n-type and semi-insulating bulk samples of β-Ga₂O₃ leads to the formation of two paramagnetic defects with spin S = 1/2 and monoclinic point symmetry. Their high introduction rates indicate them to be primary irradiation induced defects. The first electron spin resonance (EPR1) has a g-tensor with principal values of g_b = 2.0313, g_c = 2.0079, and g_a^* = 2.0025 and quasi-isotropic superhyperfine interaction of 13G with two equivalent Ga neighbors. Under low temperature photoexcitation, this defect is quenched and replaced by a different metastable spin S = 1/2 center of comparable intensity. This second defect (EPR2) has similar principal g-values of g_b = 2.0064, g_c = 2.0464, and g_a^* = 2.0024 and shows equally superhyperfine interaction with two equivalent Ga atoms. This EPR2 defect is stable up to T = 100 K, whereas for T > 100 K the initial defect is recovered. Density functional theory calculations of the spin Hamiltonian parameters of various intrinsic defects are carried out using the gauge including projector augmented wave method in order to determine the microscopic structure of these defects. The intuitive models of undistorted gallium monovacancies or self-trapped hole centers are not compatible with neither of these two defects.

We develop a first-principles theory for Schottky barrier physics. The Poisson equation is solved self-consistently with the electrostatic charge density over the entire barrier using the density functional theory (DFT) electronic structure converged locally, allowing computation of a Schottky barrier entirely from DFT involving thousands of atomic layers in the semiconductor (SC). The induced charge in the bulk consists of conduction and valence band charges from doping and band bending, as well as charge from the evanescent states in the gap of the SC. The Schottky barrier height (SBH) is determined when the induced charge density and the induced electrostatic potential reach self-consistency. Tests on the GaAs-graphene and Si/Al heterostructures yield SBH, width, along with depletion and inversion layers obtained self-consistently as functions of temperature and bulk doping.

A combined experimental/theoretical study of the electron paramagnetic resonance (EPR) centers in irradiated β-Ga₂O₃ is presented. Four EPR spectra, two S = 1/2 and two S = 1, are observed after high-energy proton or electron irradiation. Three of them have been reported before in neutron irradiated samples. One of the S = 1/2 spectra (EPR1) can be observed at room temperature and below and is characterized by the spin Hamiltonian parameters g_b = 2.0313, g_c = 2.0079, and g_a* = 2.0025 and a quasi-isotropic hyperfine interaction with two equivalent Ga neighbors of ∼14 G on ⁶⁹Ga and correspondingly ∼18 G on ⁷¹Ga in their natural abundances. The second (EPR2) is observed after photoexcitation (with a threshold of 2.8 eV) at low temperature and is characterized by g_b = 2.0064, g_c = 2.0464, and g_a* = 2.0024 and a quasi-isotropic hyperfine interaction with two equivalent Ga neighbors of 10 G (for ⁶⁹Ga). A spin S = 1 spectrum with a similar g-tensor and a 50% reduced hyperfine splitting accompanies each of these, which is indicative of a defect of two weakly coupled S = 1/2 centers. Density functional theory calculations of the magnetic resonance fingerprint (g-tensor and hyperfine interaction) of a wide variety of native defect models and their complexes are carried out to identify these EPR centers in terms of specific defect configurations. The EPR1 center is proposed to correspond to a complex of two tetrahedral V_Ga1 with an interstitial Ga in between them and oriented in a specific direction in the crystal. This model was previously shown to have lower energy than the simple tetrahedral Ga vacancy and has a 2−/3− transition level higher than other V_Ga related models, which would explain why the other ones are already in their diamagnetic 3− state and are thus not observed if the Fermi level is pinned approximately at this level. The EPR2 spectra (S = 1/2 as well as the related S = 1) are proposed to correspond to the octahedral V_Ga2 in which the spin is located on an oxygen off the defect’s mirror plane and has a tilted spin density. Models based on self-trapped holes and oxygen interstitials are ruled out because they would have hyperfine interaction with more than two Ga nuclei and because they cannot support a corresponding S = 1 center.

A computational study within the framework of density functional theory in the local density approximation (LDA) is presented for native defects and doping in ${\mathrm{ZnGeN}}_2$. Gap corrections are taken into account using an LDA+$U$ approach and finite size corrections for charged defects are evaluated in terms of an effective charge model, introduced in this paper. The donor or acceptor characteristics of each of the cation and N vacancies and the two cation antisite defects are determined as well as their energies of formation under different chemical potential conditions. These are then used to determine defect concentrations and Fermi level pinning self-consistently. The cation antisite defects are found to have significantly lower formation energy than the cation vacancies. At a typical growth temperature of 1200 K, the charge neutrality condition pins the Fermi level close to the crossing of the formation energies of the ${\mathrm{Zn}}_{\mathrm{Ge}}^{-1}$ acceptor with the ${\mathrm{Ge}}_{\mathrm{Zn}}^{2+}$ shallow donor. Since this point lies closer to the valence-band maximum (VBM), intrinsic $p$-type doping would result at the growth temperature and will persist at room temperature if the defect concentrations are frozen in. It is the highest and of order ${10}^{16}{\mathrm{cm}}^{-3}$ for the most Ge-poor condition. On the other hand, for the most Ge-poor condition, it drops to ${10}^{13}{\mathrm{cm}}^{-3}$ at 1200 K and to almost zero at 300 K because then the Fermi level is too close to the middle of the gap. Oxygen impurities are found to strongly prefer the ${\mathrm{O}}_{\mathrm{N}}$ substitutional site and are found to be shallow donors with a very low energy of formation. It can only be suppressed by strongly reducing the oxygen partial pressure relative to that of nitrogen. At high temperatures, however, introduction of oxygen will be accompanied by compensating ${\mathrm{Zn}}_{\mathrm{Ge}}^{-2}$ acceptors and would lead to negligible net doping. The prospects for Ga base $p$-type doping are evaluated. While good solubility is expected, site competition between Zn and Ge sites is found to lead to a compensation problem similar to that of the two antisites and leads to $p$-type doping of the same level of ${10}^{16}{\mathrm{cm}}^{-3}$.

The role of exchange defects on the band structure of ${\mathrm{ZnGeN}}_2$ is investigated. Exchange defects are defined through the exchange of cations Zn and Ge starting from the ideal $Pna{2}_1$ crystal structure, which obeys the local octet rule. Each such exchange creates several nitrogen-centered tetrahedra which violate the local octet rule, although overall charge neutrality is preserved. We study several distributions of exchange defects, some with all antisites making up the exchange defect close to each other and with increasing numbers of exchange defects, and others where the two types of antisites ${\mathrm{Zn}}_{\mathrm{Ge}}$ and ${\mathrm{Ge}}_{\mathrm{Zn}}$ are kept separated from each other. We also compare the results for these models with a fully random distribution of Zn and Ge on the cation sites. We show that for a single-nearest-neighbor exchange defect, the band gap is narrowed by about 0.5 eV due to two effects: (1) the ${\mathrm{Zn}}_{\mathrm{Ge}}$ antisites form filled acceptor states just above and merging with the valence-band maximum (VBM) of perfect crystal ${\mathrm{ZnGeN}}_2$ and (2) the ${\mathrm{Ge}}_{\mathrm{Zn}}$ antisites form a resonance in the conduction band which lowers the conduction-band minimum (CBM). When more exchange defects are created, these acceptor states broaden into bands which can lower the gap further. When tetrahedra occur surrounded completely by four Zn atoms, states even deeper in the gap are found localized all near these tetrahedra, forming a separate intermediate band. Finally, for phase-segregated ${\mathrm{Zn}}_{\mathrm{Ge}}$ and ${\mathrm{Ge}}_{\mathrm{Zn}}$, the gap is significantly more reduced, but no separate band is found to occur. The ${\mathrm{Zn}}_{\mathrm{Ge}}$ acceptorlike states now form a percolating defect band which is significantly wider and hence reaches deeper into the gap. In all cases, the wave functions near the top of the new VBM remain, to some extent, localized near the ${\mathrm{Zn}}_{\mathrm{Ge}}$ sites. For a fully random case, the gap is even more severely reduced by almost 3 eV. The total energy of the system increases with the number of octet-rule-violating tetrahedra and the energy cost per exchange defect of order 2 eV is quite high.