TRAPPING AND RECOMBINATION VIA DANGLING BONDS IN AMORPHOUS AND GLASSY SEMICONDUCTORS UNDER STEADY-STATE CONDITIONS - APPLICATION TO THE MODULATED PHOTOCURRENT EXPERIMENT

Interesting features of the modulated photocurrent experiment have been emphasized in a recent paper where we have shown that, if the localized states in the gap belong to the same species of monovalent centers, then it is possible to deduce both an order of magnitude of the capture cross section and the absolute value of the density of these states by means of this experiment. In the present paper, we extend the calculation of the dc and ac photocurrent to the case where distributions of correlated states associated with the well-known dangling bonds (DB) are present in the material. This calculation includes the contributions of both holes and electrons and takes into account the interactions of both types of carriers with distributions of monovalent as well as correlated states in the gap of a semiconductor. We concentrate in particular on the signature of the DB states in the data analysis, the correlation energy being either positive or negative. We first derive the variations with respect to energy of the occupation functions of any distribution of DB states for both signs of the correlation energy under steady-state conditions. We show that the concept of quasi-Fermi-levels for trapped carriers introduced by Simmons and Taylor for monovalent states has to be reconsidered for the correlated states and we underline the differences between the cases of positive and negative correlation energies. We give a clear and comprehensive scheme of the different recombination paths for the correlated states and derive the correct expressions of the electron and hole lifetimes related to these kinds of states. The results of the steady-state-regime study are then used in a second part to identify how the DB states modify the modulated photocurrent. Simplified expressions of the modulus of the modulated photocurrent and of its phase shift with reference to the ac excitation light are given in two cases: a recombination-limited regime and a trapping- and release-limited regime. The behaviors of the modulated photocurrent related to the presence of DB states are also underlined in both regimes by means of a numerical simulation. It is shown that a distribution of DB centers exhibiting a positive correlation energy roughly behaves as two distributions of monovalent states whereas a distribution of DB centers with a negative correlation energy roughly behaves as a single distribution of monovalent states. An important property of the DB states with a positive correlation energy is that they can give a significant response in the trapping- and release-limited regime even if their ground-energy level is below the Fermi level. It is also shown that if there are both monovalent- and correlated-state distributions in the gap, it is possible to derive an order of magnitude of the lowest capture cross sections from the transition between the recombination-limited and trapping- and release-limited regimes.