An accurate, analytical, and technology-mapped definition of the surface potential at threshold and a new postulate for the threshold voltage of MOSFETs

摘要

A novel approach of defining the threshold voltage for long channel MOSFETs has been presented in this paper, where it has been proposed that it corresponds to the gate-to-source voltage for which the drift and diffusion components of the total drain current become equal to each other. In order to avoid the greater computation time associated with the numerical solution of these two components, an analytical expression of the surface potential, corresponding to the threshold condition, is given here, which has the same functional form as the one proposed by Tsividis. The fuzzy parameter n, appearing in this expression of the surface potential, is expressed as a function of the substrate doping density (N_A) and the oxide thickness (t_(ox)). The threshold voltage values, obtained analytically from the relation between the surface potential at the threshold condition and the closed-form technology-mapped expression of the fuzzy parameter n, show an excellent match with those obtained from SILVACO simulations for a wide range of N_A and t_(ox), with the maximum error being only about 4%. The comparison of the percent error values of the threshold voltage obtained from this proposed model with those obtained from the other two recently proposed methods, all with respect to SILVACO simulation results, further verifies the validity of our completely analytical, mathematically simple, and straight-forward approach, proposed in this work here.