Multi-Dimensional Quantum Tunneling and Transport Using the Density-Gradient Model

We show that quantum effects are likely to significantly degrade the performance of MOSFETs (metal oxide semiconductor field effect transistor) as these devices are scaled below 100 nm channel length and 2 nm oxide thickness over the next decade. A general and computationally efficient electronic device model including quantum effects would allow us to monitor and mitigate these effects. Full quantum models are too expensive in multi-dimensions. Using a general but efficient PDE solver called PROPHET, we implemented the density-gradient (DG) quantum correction to the industry-dominant classical drift-diffusion (DD) model. The DG model efficiently includes quantum carrier profile smoothing and tunneling in multi-dimensions and for any electronic device structure. We show that the DG model reduces DD model error from as much as 50% down to a few percent in comparison to thin oxide MOS capacitance measurements. We also show the first DG simulations of gate oxide tunneling and transverse current flow in ultra-scaled MOSFETs. The advantages of rapid model implementation using the PDE solver approach will be demonstrated, as well as the applicability of the DG model to any electronic device structure.