Exploring the validity and limitations of the Mott-Gurney law for charge-carrier mobility determination of semiconducting thin-films

Using drift-diffusion simulations, we investigate the voltage dependence of the dark current in single carrier devices typically used to determine charge-carrier mobilities. For both low and high voltages, the current increases linearly with the applied voltage. Whereas the linear current at low voltages is mainly due to space charge in the middle of the device, the linear current at high voltage is caused by charge-carrier saturation due to a high degree of injection. As a consequence, the current density at these voltages does not follow the classical square law derived by Mott and Gurney, and we show that for trap-free devices, only for intermediate voltages, a space-charge-limited drift current can be observed with a slope that approaches a value of two. We show that, depending on the thickness of the semiconductor layer and the size of the injection barriers, the two linear current-voltage regimes can dominate the whole voltage range, and the intermediate Mott-Gurney regime can shrink or disappear. In this case, which will especially occur for thicknesses and injection barriers typical of single-carrier devices used to probe organic semiconductors, a meaningful analysis using the Mott-Gurney law will become unachievable, because a square-law fit can no longer be achieved, resulting in the mobility being substantially underestimated. General criteria for when to expect deviations from the Mott-Gurney law when used for analysis of intrinsic semiconductors are discussed.