The realization of scattering matrix approach to transport modeling through spherical harmonics

摘要

The spherical harmonics are applied to realize the scattering matrix method of carrier transport modeling. Using the spherical harmonics has the advantage of reducing the matrix by approximately a factor of 10 less than the previous discrete basis approach. To realize the approach, new spherical harmonic functions are defined to overcome difficulties associated with orthogonality. The scattering matrix is calculated using Monte-Carlo techniques to populate the new basis functions. As an initialstep towards demonstrating the accuracy of the new mathematical formulation, we calculate the electron energy distribution function in silicon for various homogeneous electric fields, and excellent agreement with both Monte Carlo and discrete basissimulations is obtained.