Special methods for the solution of the Boltzmann Transport Equation

A detailed analysis of high-energy phenomena in semiconductors often requires the adoption of solution methods for the Boltzmann Transport Equation that are of a higher order than the drift-diffusion or hydrodynamic ones. M. R. has contributed to a research activity focused on the spherical-harmonics expansion of the distribution function. This approach provides the dependence of the distribution funtion on position and microscopic energy, with a computational load substantially lower than the Monte Carlo method. Other advantages are the possibility of accounting for the full-band structure of the semiconductor, and for the most important scattering mechanisms calculated by a first-principle procedure. The method can thus be exploited to directly calculate the distribution function in real space and energy, whence the details of the carrier transport [52,54,96,143]. In addition, it lends itself to calculate, e.g., the coefficients of lower-order models as functions of temperature and doping concentration [51,58,115,119], and the degradation of carrier mobility due to surface effects [53,104,112]. M. R. and coworkers have presented the first application of the spherical-harmonics approach to the carrier transport within silicon dioxide, showing fair agreement with the experimental data in the low-energy case [59,121]. In order to extend this investigation to higher energies, a systematic calculation of the band structure of the most common polymorphs of silicon dioxide has been tackled, based on the Hartree-Fock and density-funtional techniques [60].