Hole quantization and hole direct tunneling in deep submicron p-MOSFETs

Hole quantization is studied by a simple and efficient model based on the six-band effective mass approximation (EMA). Due to the valence band mixing effect, the traditional one-band EMA using effective mass values extracted from bulk Si underestimates the density of states and gives inaccurate results on the energy quantization. Furthermore, an improved one-band EMA, where effective mass values of energy quantization and density of states are empirically determined from the numerical results of six-band EMA (they are 0.29/1.16, 0.23/0.70, 0.23/0.60 m₀), is proposed. In addition, its practical application to the modeling of quantum mechanical effects is also justified. Based on the hole quantization and using a Freeman-Dahlke hole dispersion in oxide band gap, the hole direct tunneling (DT) is also calculated and the results are in good agreement with the experiments.