Transient photocurrent and optical absorption of disordered thin-film semiconductors: in-depth injection and nonlinear response

The time-of-flight method is a fundamental approach for characterizing the transport properties of semiconductors. Recently, the transient photocurrent and optical absorption kinetics have been simultaneously measured for thin films; pulsed-light excitation of thin films should give rise to non-negligible in-depth carrier injection. Yet, the effects of in-depth carrier injection on the transient currents and optical absorption have not yet been elucidated theoretically. Here, by considering the in-depth carrier injection in simulations, we found a 1/t^{1-alpha/2} initial time (t) dependence rather than the conventional $1/t^{1-alpha}$ dependence under a weak external electric field, where alpha<1 is the index of dispersive diffusion.The asymptotic transient currents are not influenced by the initial in-depth carrier injection and follow the conventional 1/t^{1+alpha} time dependence. We also present the relation between the field-dependent mobility coefficient and the diffusion coefficient when the transport is dispersive. The field dependence of the transport coefficients influences the transit time in the photocurrent kinetics dividing two power-law decay regimes. The classical Scher--Montroll theory predicts a_1+a_2=2 when the initial photocurrent decay is given by 1/t^{a_1} and the asymptotic photocurrent decay is given by 1/t^{a_2}. The results shed light on the interpretation of the power-law exponent of 1/t^{a_1} when a_1+a_2neq 2.