The electron and hole effective masses associated with hydrogenated amorphous silicon

Through a direct fit with some hydrogenated amorphous silicon density-of-states experimental data sets, Malik and O’Leary (2005) found that the electron and hole density-of-states effective masses associated with this material greatly exceed those found for the case of crystalline silicon. Earlier work by Abeles and Tiedje (1983), however, interpreted the optical gap shifts observed in hydrogenated amorphous silicon-based superlattices as arising from quantum mechanical confinement, the effective mass of both carriers instead being set to the free electron mass. This naturally leads to the question: why the discordance in these effective mass selections? Through the development of a robust means of determining the optical gap shifts within such superlattices we perform linear fits of the optical gap’s dependence on the reciprocal of the square of the width of the confined layers. Developing a complementary theoretical framework, we are able to demonstrate that the electron and hole effective mass selections of Malik and O’Leary lead to slopes (corresponding to the optical gap’s dependence on the reciprocal of the square of the width of the confined layers) that are closer to that found through our linear fits than that obtained through the free electron mass selections suggested earlier by Abeles and Tiedje. With these results in mind, a qualitative explanation for hydrogenated amorphous silicon’s heavier electron and hole effective masses is provided. A dimensionless solution to the one-dimensional finite-depth potential well problem is offered as a coda to this analysis.