The space charge capacitance of non-degenerate semiconductors with shallow and deep impurity levels

Abstract

The formation of a space charge layer in non-degenerate n-type semiconductors with both shallow and deep impurity levels in the forbidden zone is described theoretically utilizing the exact expression for the charge density in the depletion layer. The impedance of n-type semiconductors with shallow and deep impurities can be modelled with an equivalent circuit comprising two capacitances in parallel. These two capacitances represent the space charge due to the response of electrons in the conduction band, and the response of the deep donors, respectively. At high frequencies only the former response contributes to the differential space charge capacitance, whereas at low frequencies the former as well as the latter response contributes. The dependence of both capacitances on dc bias approximately follows the Mott-Schottky behaviour in certain potential intervals and from the C −2 vs. V plots the shallow as well as the deep donor density together with the position of the deep donors in the forbidden zone can be derived. Numerical simulations illustrate the behaviour of the capacitances as a function of the dc bias and provide insight into the accuracy of low-frequency impedance spectroscopy.