Comparative full-band Monte Carlo study of Si and Ge with screened pseudopotential-based phonon scattering rates

摘要

In a previous article J. Appl. Phys. 92, 5359 (2002), we presented a combination of a full-band Monte Carlo method using an advanced band structure and a variable Brillouin zone discretization, with phonon scattering rates based on the screened pseudopotential considering the positions of the atoms in the elementary cell. To make the method suitable for sufficiently fast applications, such as device simulations, the simplest wave number dependent approximation was introduced. It contains an average of the cell structure factor, and only two fit parameters: The acoustic and the optical deformation potentials. As the pseudopotential, the Ashcroft model potential is chosen, and screening is taken into account using the Lindhard dielectric function. In the present article, based on the study of the influence of the two deformation potentials on the electron and hole drift velocities in Si and Ge, we show how to select the deformation potentials. Depending on the targeted agreement with experimental results, the pairs of deformation potentials for electrons and holes can be used uniformly for a wide temperature range or separately for different temperatures. For Ge, we achieve remarkable quantitative agreement with the temperature, field, and orientation dependencies of experimental electron and hole drift velocities in the wide temperature range from 77 to 300 K with a single set of the two deformations potentials for each carrier type. A detailed comparative simulation of the transport properties in Ge and Si at different temperatures is presented which is comprised of the steady-state dependence of the drift velocity on the electric field, the low-field mobility, and transient transport. Peculiarities of the drift velocity-field dependencies, such as the anisotropy, and a negative differential mobility are discussed in terms of the different band structures in connection with the field dependence of the simulated distribution functions. For doped materials, ionized impurity scattering is included. The resulting dependencies on the doping level are consistent with experimental values.