Analytical solution to space charge limited currents with exponentially distributed traps

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An analytic solution to space charge limited currents with exponentially distributed traps is developed. While early theoretical work predicts a power law relation between current and voltage, our analytic solution predicts a voltage dependent slope and much higher current magnitudes than the conventional solution because of the contribution of background carriers. Fitting the experimental data to the model suggests a much higher value for the parameter l=Tc/T=30, indicating a broad exponential trap distribution in tris(8-hydroxyquinoline)aluminum. Data fitting strategies and possible misleading fits are discussed.