A simple and efficient model for quantization effects of hole inversion layers in MOS devices

A simple and efficient model is introduced to study the hole quantization effects in the inversion layer of p-MOS devices. It is based on a six-band effective mass equation and a zigzag potential. The strong mixing between the heavy, light, and split-off hole bands is emphasized and quantitatively assessed. All subband dispersions are found to be anisotropic, far from parabolic, and electric field dependent. In addition, there are camel-back structures at some subband minima. The density of states (DOS) profiles show strong deviations from the step-like functions and one or two peaks may appear at the subband minima of the DOS, corresponding to the camel-back band structures. The traditional one-band effective mass approximation (EMA) using effective mass values extracted from bulk Si underestimates and oversimplifies the subband DOS. We justify this model by applying it to the capacitance of hole inversion layer and the threshold voltage shifts due to quantum mechanical (QM) effect. The model simulation shows good agreement with experimental results, demonstrating the accuracy of this model. The model and the characterization of the band structure of Si valence hole quantization lay the ground work in routine simulation of deep submicrometer MOS devices.