Quantum effects upon drain current in a biased MOSFET

In the past, classical device simulators have been modified to incorporate quantum effects using a quantum mechanical (QM) threshold-shift correction. In this way, it is hoped to retain accuracy without greatly complicating the simulation by incorporation of a coupled Schrodinger equation solver. In this work, the accuracy of this approach is checked for some specific examples. The drain current of heavily doped MOSFET's is found using a one-dimensional (1-D) Schrodinger-Poisson solver combined with a gradual channel model. Numerical results are compared to classical calculations augmented by the commonly proposed channel-current invariant QM threshold correction. Comparison of the two root I-d(sat) versus V-GS curves shows the same threshold shifts, but different slopes, The slope discrepancies are independent of substrate doping, and are largest for thin oxides. These differences are shown to be due to QM effects upon the surface potential gradient, a variation neglected in previous studies. To simplify device simulations, two simple quantum-effect corrections are proposed that show great improvement in accuracy when compared to the earlier QM correction based on a channel-current invariant V-G-shift.