A physical compact model for direct tunneling from NMOS inversion layers

This paper presents a physically based, analytical, circuit simulation model for direct tunneling from NMOS inversion layers in a MOS structure. The model takes account of the effect of quantization on surface potential in the silicon, the supply of carriers for tunneling and the oxide transmission probability. The inclusion of quantum effects is based on a variational approach to THE solution of the Poisson and Schrödinger equations in the silicon inversion layer [Rev Modern Phys 54 (1982) 437]. Usually the variational approach requires iterative solution of equations which is computationally prohibitive in a circuit simulation environment. In this paper, it is shown that by considering the dominant effects in weak and strong inversion, it is possible to formulate a set of equations which give all required quantities for the calculation of quantization in the inversion layer, without the requirement for iterative solution. The tunneling model is based on the concept of transparency. Improved formul ae for the transparency and the escape frequency are used. Comparisons with coupled Poisson and Schrödinger simulations and with measurements are demonstrated.