On the Integral Representations of Electrical Characteristics in Si Devices

It is shown that the 1D hydrodynamic model of the fundamental transport equations in differential form can be transformed into an equivalent integral representation. The advantage of this procedure lies in the fact that integrals are generally easier to evaluate than the corresponding differential equations. The technique of the integral representations is applied to two examples. In case of a MOSFET, a closed form analytical expression for the carrier concentration and the velocity is obtained. In case the electric field is a step-function with a strong discontinuity, the influence of the diffusion effect as well as the mobility model on the steady state velocity overshoot is analysed without the need for a dedicated numerical solver.