A semi analytical description of the hole band structure in inversion layers for the physically based modelling of pMOS transistors

This paper presents a new semianalytical model for the energy dispersion of the holes in the inversion layer of pMOS transistors. The wave vector dependence of the energy inside the 2-D subbands is described with an analytical, nonparabolic, and anisotropic expression. The procedure to extract the parameters of the model is transparent and simple, and we have used the band structure obtained with the k·p method to calibrate the model for silicon MOSFETs with different crystal orientations. The model is validated by calculating several transport-related quantities in the inversion layer of a heavily doped pMOSFET and by systematically comparing the results to the corresponding k·p calculations. Finally, we have used the newly developed band-structure model to calculate the effective mobility of pMOS transistors and compare the results with the experimental data. The overall computational complexity of our model is dramatically smaller compared to a fully numerical treatment (such as the k·p method); hence, our approach opens new possibilities for the physically based modeling of pMOS transistors.