Ion-implanted threshold tailoring for insulated gate field-effect transistors

This paper develops a general threshold equation for long-channel insulated gate field-effect transistors which accounts for the effects of ion-implant profiles used in threshold tailoring. Although any integrable function used to describe the nonuniform doping will yield an analytical expression for threshold, a Gaussian function is chosen because it accurately describes the implanted profile following proper annealing, regardless of subsequent high-temperature steps during fabrication. Most profiles of interest are quasi-neutral, i.e., the spatial dependence of the majority carriers in the undepleted bulk is adequately described by the doping profile, but the threshold equation is shown to be an excellent approximation for non quasi-neutral profiles as well. Comparison with experimental results show the analytical expression to be in good agreement with data over a wide range of implant conditions and starting substrate resistivity.