Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of p-Si:B)

A moderately doped semiconductor is considered on the insulator side of the insulator-metal phase transition, where the acceptors in (-1), (0), and (+1) charge states form A(O) and A(+) bands. The expressions are derived for the Debye-Huckel and Schottky-Mott screening lengths of an external electrostatic field for the case of hopping transport of holes via acceptors. The quasistatic capacitance of a semiconductor is calculated in the temperature region where hopping hole conductances in the A(O) and A(+) bands are approximately equal. It is shown that the Debye-Huckel screening length can be determined using the measurements of quasistatic capacitance even in the high-field regime, i.e., in the Schottky-Mott approximation. The frequency of an electric signal in the measurements of quasistatic semiconductor capacitance in a metal-insulator-semiconductor structure must be much lower than the average frequency of hole hopping via acceptors (boron atoms in silicon).