A critical examination of the assumptions underlying macroscopic transport equations for silicon devices

Assumptions used to derive macroscopic transport equations for silicon devices are critically examined. The position- and momentum-dependent distribution function for a silicon n-i-n diode is obtained from a rigorous solution to the Boltzmann equation, and various macroscopic quantities, such as the electron temperature tensor, energy and heat fluxes, and mobility, are rigorously evaluated and compared with widely used approximations. The common approximation of the heat flux by Fourier´s law is shown to differ substantially from the actual heat flux. The results also show that at a given energy, the mobility within a submicrometer device can be much different than that for electrons at the same energy in bulk silicon