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Register a new userImpact ionization rates for Si, GaAs, InAs, ZnS, and GaN in the $GW$ approximation
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We present first-principles calculations of the impact ionization rate (IIR) in the $GW$ approximation ($GW$A) for semiconductors. The IIR is calculated from the quasiparticle (QP) width in the $GW$A, since it can be identified as the decay rate of a QP into lower energy QP plus an independent electron-hole pair. The quasiparticle self-consistent $GW$ method was used to generate the noninteracting hamiltonian the $GW$A requires as input. Small empirical corrections were added so as to reproduce experimental band gaps. Our results are in reasonable agreement with previous work, though we observe some discrepancy. In particular we find high IIR at low energy in the narrow gap semiconductor InAs.
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A new implementation of the GW approximation (GWA) based on the all-electron Projector-Augmented-Wave method (PAW) is presented, where the screened Coulomb interaction is computed within the Random Phase Approximation (RPA) instead of the plasmon-pole model. Two different ways of computing the self-energy are reported. The method is used successfully to determine the quasiparticle energies of six semiconducting or insulating materials: Si, SiC, AlAs, InAs, NaH and KH. To illustrate the novelty of the method the real and imaginary part of the frequency-dependent self-energy together with the spectral function of silicon are computed. Finally, the GWA results are compared with other calculations, highlighting that all-electron GWA results can differ markedly from those based on pseudopotential approaches.
The $GW$ approximation is based on the neglect of vertex corrections, which appear in the exact self-energy and the exact polarizability. Here, we investigate the importance of vertex corrections in the polarizability only. We calculate the polarizability with equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD), which rigorously includes a large class of diagrammatically-defined vertex corrections beyond the random phase approximation (RPA). As is well-known, the frequency-dependent polarizability predicted by EOM-CCSD is quite different and generally more accurate than that predicted by the RPA. We evaluate the effect of these vertex corrections on a test set of 20 atoms and molecules. When using a Hartree-Fock reference, ionization potentials predicted by the $GW$ approximation with the RPA polarizability are typically overestimated with a mean absolute error of 0.3 eV. However, those predicted with a vertex-corrected polarizability are typically underestimated with an increased mean absolute error of 0.5 eV. This result suggests that vertex corrections in the self-energy cannot be neglected, at least for molecules. We also assess the behavior of eigenvalue self-consistency in vertex-corrected $GW$ calculations, finding a further worsening of the predicted ionization potentials.
The electronic structures of substitutional rare-earth (RE) impurities in GaAs and cubic GaN are calculated. The total energy is evaluated with the self-interaction corrected local spin density approximation, by which several configurations of the open 4f shell of the rare-earth ion may be investigated. The defects are modelled by supercells of type REGa$_{n-1}$As$_n$, for n=4, 8 and 16. The preferred defect is the rare-earth substituting Ga, for which case the rare-earth valency in intrinsic material is found to be trivalent in all cases except Ce and Pr in GaN. The 3+ --> 2+ f-level is found above the theoretical conduction band edge in all cases and within the experimental gap only for Eu, Tm and Yb in GaAs and for Eu in GaN. The exchange interaction of the rare-earth impurity with the states at both the valence band maximum and the conduction band minimum is weak, one to two orders of magnitude smaller than that of Mn impurities. Hence the coupling strength is insufficient to allow for ferromagnetic ordering of dilute impurities, except at very low temperatures.
The quasiparticle band structures of 3d transition metals, ferromagnetic Fe, Ni and paramagnetic Cu, are calculated by the GW approximation. The width of occupied 3d valence band, which is overestimated in the LSDA, is in good agreement with experimental observation. However the exchange splitting and satellite in spectra are not reproduced and it is required to go beyond the GW approximation. The effects of static screening and dynamical correlation are discussed in detail in comparison with the results of the static COHSEX approximation. The dynamical screening effects are important for band width narrowing.
The spin relaxation time of electrons in GaAs and GaN are determined with a model that includes momentum scattering by phonons and ionized impurities, and spin scattering by the Elliot-Yafet, Dyakonov-Perel, and Bir-Aronov-Pikus mechanisms. Accurate bands generated using a long-range tight-binding Hamiltonian obtained from empirical pseudopotentials are used. The inferred temperature-dependence of the spin relaxation lifetime agrees well with measured values in GaAs. We further show that the spin lifetimes decrease rapidly with injected electrons energy and reach a local maximum at the longitudinal optical phonon energy. Our calculation predicts that electron spin lifetime in pure GaN is about 3 orders of magnitude longer than in GaAs at all temperatures, primarily as a result of the lower spin-orbit interaction and higher conduction band density of states.
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