A consistent gate and substrate current model for submicron MOSFET's by considering energy transport

Accurate modeling of the hot electron induced gate and substrate currents is of considerable importance for submicron MOS devices. In this paper, a new approach based on the simplified two-dimensional energy balance equations by incorporating the effect of transversal electric field and energy-dependent saturation velocity and relaxation time is presented. Substrate current characteristics can be predicted from the calculated energy dependent impact ionization rate. A consistent gate current is also obtained by using the same set of parameter values. Results of the gate and substrate currents present very good agreement with the experiment for a wide range of biases and channel lengths. Moreover, the conventional drift-diffusion approach tends to overestimate the calculated substrate current, while the new approach has solved the problem without difficulty.