Analysis of fluctuations in semiconductor devices through self-consistent Poisson-Schrödinger computations

The effects of random doping and random oxide thickness fluctuations in metal-oxide-semiconductor field-effect transistors are analyzed by using self-consistent Poisson-Schrödinger computations. The Poisson and Schrödinger equations are solved by using the Newton iteration technique in which the Jacobian matrix is computed through first-order perturbation theory in quantum mechanics. A very fast technique based on linearization of the transport equations is presented for the computation of threshold voltage fluctuations. This technique is computationally much more efficient than the traditional Monte Carlo approach and it yields information on the sensitivity of threshold voltage fluctuations to the locations of doping and oxide thickness fluctuations. Hence, it can be used in the design of fluctuation resistant structures of semiconductor devices. Sample simulation results obtained by using this linearization technique are reported and compared with those obtained by using the Monte Carlo technique.