Understanding localized states in the band tails of amorphous semiconductors exemplified by a -Si:H from the perspective of excess delocalized charges

In this paper, we use a perturbation strategy to show that the band tails in the density of states (DOS) distribution of amorphous semiconductors form due to the existence of excess delocalized charges. These charges satisfy a Gaussian distribution with a mean of zero and vary slowly in space due to the short- and medium-range order of amorphous materials. The charges exist due to the bond angle and bond length distortion. They induce an extra potential energy distribution that leads to energy band fluctuation in the energy-space diagram and consequently gives rise to localized states. A 150×150×7.5 nm large-scale finite-element excess charge model for hydrogenated amorphous silicon (a-Si:H) is developed using a moving average smoothing that filters a Gaussian array of random charge values. Thanks to the analytical and computational simplicity of the theory in this paper (compared with conventional approaches considering atomistic details and complex electron-electron interactions), this large-scale model is calculated in only 90 s and reproduces the typical exponential and linear features found in the conduction band tail of a-Si:H and other amorphous semiconductors. Through a satisfactory fitting to experimental a-Si:H DOS data in the literature, model parameters are semiquantitatively determined. Unlike previous analytical and computational efforts, this large-scale model is physically unambiguous, computationally tractable, and satisfactorily accurate. The large-scale modeling capability allows reliable insights into the geometric features of localized and extended states, which are visualized in a nonschematic manner. This further leads to reinvestigations of several established concepts and conclusions. First, calculations in this paper challenge the description that the wave function envelope of a localized state decays away from its center in an exponential manner and that the spread of this exponential decay varies with energy in a power-law manner. Second, impurity states and/or extended states are critical to enable band tail hopping. Third, low-energy states are spatially included inside high-energy states, so the existing concept of average spatial separation of localized states is meaningless. Fourth, the mobility edge obtained from conductivity activation energy measurements turns out to be higher than the actual critical energy Ect that demarcates extended states from localized states; this judgment is supported by the electron mobility-energy relation that is inferred from the geometry of states, which validates a continuous increase of energy-specific mobility as electron energy increases from Ect. Published by the American Physical Society 2024