Analytical solutions for threshold voltage calculations in ion-implanted IGFETs

Analytical expressions for threshold voltages are obtained for ion-implanted IGFETs having Gaussian impurity profiles. The results are based on a closed-form solution of the static Poisson's equation in the depletion layer. The subtrate bias dependence of the threshold voltage has been derived. A comparison of the results from the present calculations to the previously published data for profiles centered near the SiSiO ₂ interface shows excellent agreement with some changes in the doping parameters. Modelling of threshold voltages for short channel devices is presented by defining an equivalent box profile. These results will be quite useful in the design of implanted devices for VLSI applications where it is expected that highly nonlinear charge profiles will be obtained by the use of very shallow ion implants and minimal high temperature processing.