The effect of the minority carrier distribution on the threshold voltage of a MOSFET

Abstract

Based upon the concept of minority carrier transverse diffusion within the surface space charge region and its resultant quasi-Fermi level distribution, a simple one-dimensional theory of the threshold voltage for both long- and short-channel MOSFETs is developed. In the new model, the non-uniform distribution of the quasi-Fermi level for minority carriers with respect to that for majority carriers is characterized by introducing an effective diffusion length and is averaged over all the channel length. The non-uniformity in the quasi-Fermi level for minority carriers results in a non-uniform bulk charge density which is averaged similarly. Using the above averaged values and considering the charge-sharing effect, the threshold voltage for a MOSFET is expressed. Numerical results are obtained which show the strong dependence of threshold voltage on the effective diffusion length, which can not be overlooked especially when the device is scaled down. The theoretical calculations are also compared to the experimental data for the fabricated NMOS and PMOS. The good agreement supports the correctness of the developed theory.