Analytical expressions for the static MOS transistor characteristics based on the gradual channel model

Analytical solutions are derived from Pao and Sah's double integral formula for the theoretical static I- V characteristics of MOS transistors including both the diffusion and drift currents based on the gradual channel model. Expressions for the entire saturation, non-saturation and low level current regions are given, while the specific importance of the theory is seen in the cross-over region between low level and normal operation. Reddi and Sah's formula for channel shrinkage is modified and included to account for the small drain conductance in the saturation region by taking the drain avalanche breakdown voltage into consideration. The solutions are compared with experimental data, and the effectiveness and the limit of the theory is quickly examined.