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

The spherical harmonics are applied to realize the scattering matrix method of carrier transport modeling. Using the spherical harmonics has the advan tage of reducing the matrix by approximately a factor of 10 less than the p revious discrete basis approach. To realize the approach, new spherical har monic functions are defined to overcome difficulties associated with orthog onality. The scattering matrix is calculated using Monte-Carlo techniques t o populate the new basis functions. As an initial step towards demonstratin g the accuracy of the new mathematical formulation, we calculate the electr on energy distribution function in silicon for various homogeneous electric fields, and excellent agreement with both Monte Carlo and discrete basis s imulations is obtained. (C) 1999 Published by Elsevier Science Ltd. All rig hts reserved.