General analytical Poisson solution for undoped generic two-gated
metal-oxide-semiconductor field-effect transistors

W. Z. Shangguan, T. C. Au Yeung, Z. M. Zhu, and X. Zhou

Applied Physics Letters, Vol. 90, No. 1, 012110, 1 January 2007
(Manuscript received 7 September 2006; accepted 29 November 2006; published online 3 January 2007.)

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We present a general analytical solution to the Poisson equation for undoped semi-conductors. This general Poisson solution is then applied to generic dual-gate metal-oxide- semiconductor field-effect transistors (MOSFETs), unifying different types including silicon-on-insulator, and symmetric andasymmetric double-gate MOSFETs. Newton-Raphson (NR) algorithm is called to solve the resultingsurface-potential equation. An exact solution is proposed making the NR algorithm computationally very efficient. While the universal initial guess can be used as an approximate solution for fast evaluation, the iterative results by NR algorithm are useful for benchmark tests.