IEEE Transactions on Electron Devices, Vol. 54, No. 1, pp. 169-172, Jan. 2007
(Manuscript received May 19, 2006; revised  September 14, 2006.)

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We present a rigorously derived analytical Poisson solution for undoped semiconductors and apply the general solution to the generic MOSFETs with two gates, unifying different types such as silicon-on-insulator (SOI), symmetric and asymmetric double gate (s-DG, a-DG) structures.  The Newton-Raphson (NR) method is used to solve the surface-potential equations resulting from the application of the boundary conditions to the general Poisson solution, with an initial guess 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 for benchmark tests.  The results demonstrate unification of surface-potential solutions  having an accuracy of 10^-15 V for SOI, a-DG, and s-DG MOSFETs, achieved with 2 to 6 iterations., Furthermore, the explicit solution yields less than 3.5% error for back-to-front gate oxide thickness ratios larger than 25.

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