Quasi-two-dimensional analytical solution of Poisson equation in arbitrarily doped short-channel MOSFET

The potential distribution in a short-channel nonuniformly doped MOSFET is strictly two-dimensional and so far has been treated only numerically. In the letter an analytical solution of this problem resulting in an explicit expression for the potential distribution is presented. In order to test its validity this expression was used for threshold voltage calculation for a typical H-MOS transistor and has shown a good agreement with experimental results.