AN EFFICIENT DETERMINISTIC SOLUTION OF THE SPACE-DEPENDENT BOLTZMANN TRANSPORT-EQUATION FOR SILICON

The space-dependent nonequilibrium distribution function is obtained by directly solving the Boltzmann transport equation for Si. Legendre polynomials are used to express the Boltzmann equation in an analytical form which incorporates the effects of a nonparabolic band structure, inelastic phonon scattering, as well as spatial variation. The resulting linear difference/differential equation is discretized and solved using sparse-matrix methods in the energy domain, and iterative methods in the real-space domain. Values for average electron energy and electron drift velocity calculated from the resulting distribution function are in good agreement with those obtained from Monte-Carlo calculations. This method should prove to be useful in CAD tools for semiconductor devices.