This report describes how the Boltzmann Transport Equation for carrier transport in s~~miconductocrasn be formulated in a manner suit able for numerical simulation. It arose from an effort to generalise earlier work which used pre-computed scattering matrices to solve the Boltzmann Transport Equation. It also generalises the formulation used to treat neutron transport so that energy band-structure, scattering in semiconductors and electric fields can be treated. We present two different, but relat, ed formulations here. One is a first-order formulation in terrns of directed fluxes in 3 dirnensional space and the other is a second-order form which can be written as a generalised drift-diffusion equation. This work is a part of Ms. Kausar Banoo's prol~osal for Ph.D. thesis research. In this report, we present the formulation by itself. In the Epilogue, we summarise the key results and discuss possible applications. A more complete discussion of the applications being explored and preliminary numerical results can be found in Ms. Banoo's thesis proposal.

Date of this Version

April 1998