A new discretization strategy of the semiconductor equations comprising momentum and energy balance

A discretization scheme is applied to the hydrodynamic model for semiconductor devices that generalizes the Scharfetter-Gummel method to both the momentum-conservation and the energy-conservation equations. The major advantages of the scheme are: (1) the discretization is carried out without neglecting any terms, thus providing a satisfactory description of such effects as velocity overshoot and carrier heating; and (2) the resulting equations lend themselves to a self-consistent solution procedure similar to those currently used to solve the simpler drift-diffusion equations. Two-dimensional steady-state simulations of an n-channel MOSFET and of an n-p-n BJT (bipolar junction transistor) have been carried out by means of an improved version of the program HFIELDS. Carrier-temperature plots have been obtained with a reasonable computational effort, demonstrating the efficiency of this technique. The results have been compared with those obtained with the standard drift-diffusion model and significant differences in the electron concentration have been found, especially at the drain end of the MOSFET channel