A simple and closed-form expression for the threshold voltage of non-uniformly doped submicron MOSFET is developed. The main features of this model are: (1) non-equipotential surface of the device which includes the non-uniformity effect along the channel; (2) charge screening effects to explain the weak substrate bias dependence for short channel devices; and (3) total gate capacitance of MOS structures (the geometric capacitance and the fringing capacitance which is calculated using the conformal transformation considering the effects of electrode thickness and lateral gate dimensions). Comparisons between the present model and experimental data show good agreement for a wide range of channel lengths and applied substrate biases.
Maneesha, Khanna, M. K., Hadlar, S., & Gupta, R. S. (1996). An empirical fringing capacitance dependent threshold voltage model for non-uniformly doped submicron MOSFETs. Solid-State Electronics, 39(11), 1687–1691. https://doi.org/10.1016/0038-1101(96)00080-9