High-field transport in semiconductors based on eigenvalue solution to Boltzmann equation

The Boltzmann equation is solved by expanding the distribution function in terms of a finite number of basis functions. The zero eigenvalue of the resulting matrix is solved for the hot-electron distribution. This method arrives at the solution at least two orders of magnitude faster than the commonly used Monte Carlo method. Using the scattering rates due to ionized impurities, phonons, alloy disorder, and intervalley scattering calculated from a realistic band structure, we obtain velocity-field curves for various semiconductor alloys and compounds without any adjustable parameters. The results are in good agreement with experiments.