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

Interesting features of the modulated photocurrent experiment have bee n emphasized in a recent paper where we have shown that, if the locali zed 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 capt ure cross section and the absolute value of the density of these state s by means of this experiment. In the present paper, we extend the cal culation of the dc and ac photocurrent to the case where distributions of correlated states associated with the well-known dangling bonds (D B) are present in the material. This calculation includes the contribu tions of both holes and electrons and takes into account the interacti ons 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, th e correlation energy being either positive or negative. We first deriv e the variations with respect to energy of the occupation functions of any distribution of DB states for both signs of the correlation energ y under steady-state conditions. We show that the concept of quasi-Fer mi-levels for trapped carriers introduced by Simmons and Taylor for mo novalent states has to be reconsidered for the correlated states and w e 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 th e correct expressions of the electron and hole lifetimes related to th ese 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 mo dulated photocurrent. Simplified expressions of the modulus of the mod ulated photocurrent and of its phase shift with reference to the ac ex citation light are given in two cases: a recombination-limited regime and a trapping- and release-limited regime. The behaviors of the modul ated photocurrent related to the presence of DB states are also underl ined in both regimes by means of a numerical simulation. It is shown t hat a distribution of DB centers exhibiting a positive correlation ene rgy roughly behaves as two distributions of monovalent states whereas a distribution of DB centers with a negative correlation energy roughl y behaves as a single distribution of monovalent states. An important property of the DB states with a positive correlation energy is that t hey can give a significant response in the trapping- and release-limit ed regime even if their ground-energy level is below the Fermi level. It is also shown that if there are both monovalent- and correlated-sta te distributions in the gap, it is possible to derive an order of magn itude of the lowest capture cross sections from the transition between the recombination-limited and trapping- and release-limited regimes.