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The impact ionization rate in silicon is numerically derived from wave functions and energy band structure based on an empirical pseudopotential method. The calculated impact ionization rate is well fitted to an analytical formula with a power exponent of 4.6, indicating soft threshold of impact ionization rate, which originates from the complexity of the Si band structure. The calculated impact ionization rate shows strong anisotropy at low electron energy (ε<3 eV), while it becomes isotropic at higher energy. Numerical calculation also reveals that the average energy of secondary generated carriers depends linearly on the primary electron energy at the moment of their generation. A full band Monte Carlo simulation using the newly derived impact ionization rate demonstrates that calculated quantum yield and ionization coefficient agree well with reported experimental data.

The physics of electron transport in bulk silicon is investigated by using a newly developed Monte Carlo simulator which improves the state-of-the-art treatment of hot carrier transport. (1) The full band structure of the semiconductor was computed by using an empirical-pseudopotential method. (2) A phonon dispersion curve was obtained from an adiabatic bond-charge model. (3) Electron-phonon scattering was computed by using a rigid pseudo-ion model. The calculated scattering rate is consistent with the full band structure and the phonon dispersion curve of silicon, thus leaving no adjustable parameters such as deformation potential coefficients. (4) The impact-ionization rate was calculated by using Fermi’s golden rule directly from the full band structure. We took into account the dielectric function depending on both wave vector and transition energy in the numerical calculation of the rate. The impact-ionization rate obtained in the present study strongly depends on both wave vector and band index of the conduction electron, which is ignored by the traditional Keldysh formula. (5) In the simulator, the final state of a scattering electron is determined in such a way as to conserve both energy and momentum in scattering processes. The simulated results, under the steady-state conditions as well as under the nonequilibrium conditions, are presented and compared with experimental results. Special attention is focused on anisotropic transport during velocity overshoot. Quantitative agreement between calculated and experimental results confirms the validity of the newly developed Monte Carlo simulator and the physical models that were used.

The rate of impact ionization due to the primary hole in silicon is numerically derived from pseudo-wave-functions and realistic energy band structure based on a nonlocal empirical pseudopotential method including the spin-orbit interaction. The calculated impact-ionization rate SII [s−1] is well fitted to an analytical formula with a power exponent of 3.4, indicating a soft threshold of the impact ionization rate: SII [s−1]=1.14×1012 [s−1 eV−3.4]×(ε [eV]−1. 49 [eV])3.4, where ε [eV] is the energy of the primary hole relative to the valence band edge. The soft threshold originates from the complexity of the silicon band structure. The calculated impact-ionization rate shows strong anisotropy at low hole energies (ε<3 eV), while it becomes isotropic at high hole energies, indicating the isotropy of the joint density of states at high energies. Numerical calculation also makes it clear that average energies of secondary generated carriers ε̄ depend linearly on primary hole energies at the moment of their generation. The calculated average energies of secondary generated holes ε̄(hole) [eV] and electrons ε̄(electron) [eV] are well fitted to linear functions of primary hole energy ε [eV]: ε̄(hole) [eV]=3.75×10−1 ε [eV]−4.76×10−1 [eV],ε̄(electr on) [eV]=−3.14×10−1 ε [eV]−8.60×10−1 [eV]. The standard deviations of secondary generated carriers are also presented.