Analytical Approximation for the Surface Potential in n-Channel MOSFETs Considering Quantum–Mechanical Effects

A physics-based analytical model for the surface potential in n-channel MOSFETs considering quantum-mechanical effects in the inversion region is presented. The model is continuous from the accumulation to strong inversion regions of operation. The results from the model show excellent agreement with the values obtained from a self-consistent solution of the Schrödinger and Poisson equations. The transconductance and current-voltage characteristics of MOSFETs obtained using the surface-potential values calculated from our model also agree very well with those obtained from numerical methods and reported data.