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].