Convergence of the Legendre polynomial expansion of the Boltzmann equation for nanoscale devices

The convergence of the Legendre polynomial expansion of the Boltzmann equation is investigated for the first time for devices. It is shown that in nanoscale devices a rather larger number of polynomials are required. But even in the case of larger devices an expansion at least up to the 3rd order is necessary to avoid large truncation errors. The resultant large system of linear equations can be memory and CPU efficiently solved by the numerical package ILUPACK1.1.