Numerical simulation for direct tunneling current in poly-Si-gate MOS capacitors

To provide adequate control of short channel effects, gate-oxide thickness of MOSFETs is reduced nearly in proportional to channel length. For sub-100 nm channel lengths, an oxide thickness, t/sub ox/, of less than a few nm is needed. In such a device, gate current is significant even for low gate bias region due to direct tunneling of electrons through the oxide. To simulate direct tunneling current, quantum effects, such as (1) tunneling transition rate and (2) standoff distance due to the quantum confinement of electrons in the channel region, should be properly taken into account. For poly-Si-gate devices, (3) a depletion-layer in the gate region should also be taken into account. Recently, Price (2004) demonstrated that the Gamow formulation can be applied to analysis of the escape of electrons from the channel region into the gate. In the present study, we have numerically simulated direct tunneling current in poly-Si-gate MOS capacitors by integrating the Gamow method into a Schrodinger-Poisson solver. We especially focus on the boundary condition for the confined states that gives natural results.