Surface-Potential Solution for Generic Undoped MOSFETs With Two Gates

We present a rigorously derived analytical Poisson solution for undoped semiconductors and apply the general solution to generic MOSFETs with two gates, unifying different types such as silicon-on-insulator (SOI) and symmetric and asymmetric double gate (s-DG and a-DG) structures. The Newton-Raphson method is used to solve surface-potential equations resulting from the application of boundary conditions to the general Poisson solution, with an initial guess that is very close to the exact solution. The universal initial guess can be used as an approximate explicit solution for fast evaluation, while the iterative solution can be used for benchmark tests. The results demonstrate the unification of surface-potential solutions having an accuracy of 10^-15 V for SOI, a-DG, and s-DG MOSFETs, which are achieved within two to six iterations. Furthermore, the explicit solution yields less than 3.5% error for back-to-front-gate oxide thickness ratios larger than 25