Analysis of the steady-state photocarrier grating method for the determination of the density of states in semiconductors

In this paper we present a complete theoretical analysis of the steady-state photocarrier grating (SSPG) method, starting from the generalized equations that describe charge transport and recombination under grating conditions. The analytical solution of these equations and the application of simplifying assumptions leads to a very simple formula relating the density of states (DOS) at the quasi-Fermi level for trapped electrons to the SSPG signal at large grating periods. By means of numerical calculations reproducing the experimental SSPG curves we test our method for DOS determination. We examine previous theoretical descriptions of the SSPG experiment, illustrating the case when measurements are performed at different illumination intensities. We propose a procedure to estimate the minority-carriers mobility-lifetime product from SSPG curves, introducing a correction to the commonly applied formula. We illustrate the usefulness of our technique for determining the DOS in the gap of intrinsic semiconductors, and we underline its limitations when applied to hydrogenated amorphous silicon. We propose an experimental procedure that improves the accuracy of the SSPG-DOS reconstruction. Finally, we test experimentally this new method by comparing the DOS obtained from SSPG and modulated photocurrent measurements performed on the same samples. The experimental DOS obtained from both methods are in very good agreement.