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Simple analytical valence band structure including warping and non-parabolicity to investigate hole transport in Si and Ge

This work proposes an analytical modelling of non-parabolicity for the valence bands of Si and Ge. With this aim, we obtained piecewise functions that enabled analytical evaluation of the energy after a free flight under drift, avoiding iterative procedures. In addition, particular attention was devoted to solving the problem of discontinuities in the density of states in bulk semiconductors, a shortcoming that had emerged in earlier approaches. Using our analytical functions, we were able to evaluate the mean hole energies at equilibrium and compare them with previous studies based on the pseudopotential method, obtaining an excellent agreement. We also used our analytical expressions in a single-particle Monte Carlo simulator to obtain the drift velocity under an external electric field and ohmic mobilities in pure Si and Ge. These results were compared with the experimental data and showed satisfactory agreement in all cases.