Mobility of electrons in a quantized silicon inversion layer due to phonon scattering

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Abstract
A theory for the mobility limited by lattice scattering in a quantized silicon inversion layer is developed in this paper. The expression for the relaxation time for scattering of a degenerate two-dimensional electron gas by a nonpolar optic phonon is derived from the Boltzmann equation and is found to differ from those given by other workers. The wave vectors of different phonons participating in the intersubband and intervalley transitions in a (100)-oriented silicon surface are then estimated by following a geometrical construction and considering the lowest three subbands. The dispersion curves for bulk phonons are used to determine the phonon temperatures. By taking an acoustic phonon and an averaged low-energy and an averaged high-energy phonon, the mobility is calculated by using both the nondegenerate and degenerate statistics. It is found that the mobility values are different for the two cases even at 300 K.