Theoretical study of the quasistatic capacitance of metal–insulator–semiconductor structures in amorphous semiconductors

Abstract

We present the theoretical analysis of the quasistatic capacitance of metal–insulator–semiconductor structures for the case of amorphous semiconductors. The contribution of the bulk of the semiconductor is emphasized. We show that the semiconductor bulk capacitance is simply given by the ratio, taken at the insulator/semiconductor interface, of the space-charge density to the electric field. From the explicit expressions of these quantities as a function of the surface potential, a numerical calculation of the capacitance versus bias curves is performed. This is used to discuss the ability of the capacitance to reproduce the underlying structures of the density of states (DOS) in the gap. We derive also approximate analytical expressions of this capacitance in the case of exponentially distributed band-tail states. Moreover, we show that it is possible to reconstruct the DOS of the amorphous semiconductor from the bias dependence of the semiconductor capacitance using simple approximate analytical expressions. In particular, the square of the bulk semiconductor capacitance can lead in most cases to a reasonable DOS reconstruction. Using the capacitance versus bias curves derived from the numerical simulation, the accuracy of the reconstruction is then checked on DOS examples consisting of two exponential band tails and a Gaussian deep defect density, which can be representative of typical amorphous semiconductors such as hydrogenated amorphous silicon (a-Si:H). We emphasize the influence on the deep gap states reconstruction of the bulk Fermi-level position, whether it is located in a DOS minimum or not. We also discuss the influence of the characteristic temperature in the case of an exponential band tail which should be met in the accumulation bias regime. As this was done in the crystalline case to develop the metal–oxide–semiconductor technology, the method proposed can be used as a characterization tool to investigate metastability phenomena and to optimize technological processes related to amorphous semiconductor field-effect devices.