Study of applicability of Boltzmann-statistics and two mobility models for organic semiconductors

The organic semiconductors are treated as non-degenerate based on recent experiment on validity of classical Einstein relationship. The expression of density of holes is analytically derived by using the Boltzmann statistics. The mobility model of Pasveer et al. and the exponential model of Pai modified by Blom et al. are combined to solve drift-diffusion equations to extract information about the mobility and effective density of state. The results show that the mobility model of Pasveer et al. can not well fit the experimental $J$–$V$ data for a rubrene single crystal from Krellner et al. both at low and high voltages, and some of the parameters extracted show inconsistent temperature dependence which should be constants in the theoretical framework of Pasveer et al. Whereas the exponential model gives satisfactory fit for experimental $J$–$V$ data at all voltage ranges, and the extracted parameters show correct temperature dependence. The temperature dependence of parameters contained in the exponential model of mobility can be well fitted by using simple expressions proposed by Blom et al. And the temperature dependence of effective density of state derived from the non-degenerate Boltzmann statistics is verified. The distribution of potential, electric field and density of holes are calculated as analyzed.