Monte Carlo simulations of electron transport properties of diamond in high electric fields using full band structure

Abstract

Electron transport properties in diamond under high electric fields (⩽5×106 V/cm) have been investigated by means of Monte Carlo simulations which include a full band structure, a wave-vector- and frequency-dependent dielectric function, phonon scattering rates with phonon dispersion relations, and impact ionization rates. The full band structure of diamond was calculated using an empirical pseudopotential method with an expansion of 113 plane waves, and was utilized to evaluate the dielectric function using the Lindhard method while suitable deformation potential coefficients were chosen in an adiabatic bond-charge model. Calculated results such as transition energies at the main points of symmetry and lines in the Brillouin zone as well as phonon dispersions were in good agreement with corresponding experimental data previously reported. The impact ionization rates of electrons in diamond were then evaluated from Fermi’s golden rule using the full band structure and dielectric function. The electric field (F) dependence of the electron drift velocity obtained reproduced experimental results previously reported on hot electron effects well and was fitted well by an analytical equation. It is found that the impact ionization probability rapidly increases with F⩾1×106 V/cm so that an electron in the diamond conduction band can yield electron-hole pair production for 1 μm travel on average at ≈1.5×106 V/cm. The F dependence of the impact ionization probabilities obtained is discussed in relation to energy (E) distributions of hot electrons created in high F on the order of 106 V/cm which are represented well by a Gaussian function, exp[−(E–Egap)2/wF2], for E≈7 eV, where Egap is the band gap energy and wF is a F-dependent constant corresponding to energy spread of ≈4 eV.