Thermally-Stimulated Currents in Thin-Film Semiconductors: Analysis and Modelling
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Thermally-Stimulated Currents in Thin-Film Semiconductors: Analysis and Modelling Charles Main1, Nacera Souffi2, Steve Reynolds3, Zdravka Aneva4, Rudi Brüggemann2, and Mervyn Rose1 1 Electronic Engineering and Physics, University of Dundee, Dundee, United Kingdom 2 Institut für Physik, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany 3 Institut für Photovoltaik, Forschungszentrum Jülich, Jülich, Germany 4 Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria ABSTRACT This paper investigates the robustness of the thermally stimulated current technique as a method to determine the density of states distribution in thin film semiconductors under a wide range of conditions. Numerical simulation is used to solve the non-linear time-dependent rate equations for free and trapped charge in systems with continuous and structured DOS profiles. We explore the derivation of energy and density scales from temperature and conductivity data. We examine for these systems the limits of the method’s apparent immunity to varying conditions of strong and weak retrapping, and investigate the corrections required for variations in carrier lifetime with temperature. INTRODUCTION Thermally stimulated conductivity (TSC) is an experimental technique widely used to investigate the distribution of electronic states (DOS) in semiconductor materials. The experimental method involves cooling a sample to low temperature, a period of illumination to reach a steady state, in which gap states are occupied by excess charge carriers, and then after a short relaxation time in the dark, heating at a constant rate β Ks-1. Trapped charge thermally excited as the temperature rises contributes to an excess free carrier density e.g. for electrons ntsc, and excess conductivity σtsc. As the temperature is raised, a narrow range of states around a gradually sinking energy Em(T) provide the greatest contribution to the thermal excitation rate at a given temperature T, and hence to σtsc. As Em sweeps downward toward the equilibrium Fermi energy EF, measurement of σtsc can give information on the DOS, g(E). Here, and below, for clarity we restrict the treatment to that of excess electrons. There are two limiting cases for this process, commonly termed ‘weak’ and ‘strong’ retrapping. In the former, the recombination time τR, for a free electron is shorter than the retrapping time τtm in states ‘around’ Em, so in a quasi-static approximation (small dntsc dt ), the instantaneous free electron density is determined only by the rates of emission at Em and recombination. In the latter case, τtm
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