Quantum mechanical effects on random oxide thickness and random doping induced fluctuations in ultrasmall semiconductor devices

Quantum mechanical effects on fluctuations in ultrasmall semiconductor devices are studied. Quantum mechanical effects are included in the analysis by using the density gradient model, for which the main parameters (effective masses) are identified through the two-dimensional Schrödinger equation. A very fast technique for the computation of threshold voltage fluctuations induced by random oxide thickness and doping variations is proposed. This technique is based on linearization of the transport equations with respect to the fluctuating quantities. This technique is computationally very efficient because it avoids numerous simulations for various doping and oxide realizations (as in the case of Monte Carlo techniques). At the same time, it provides information about the sensitivity of threshold voltage to the fluctuations of oxide thicknesses and doping at different locations. Sample simulation results are reported and compared with those previously published and good agreement is observed.