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−α/2 initial time (t) dependence rather than the conventional 1/t^1−α dependence under a weak external electric field, where α < 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+α 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 that a₁ + a₂ = 2 when the initial photocurrent decay is given by $1/ta1$ and the asymptotic photocurrent decay is given by $1/ta2$⁠. The results shed light on the interpretation of the power-law exponent of $1/ta1$ when a₁ + a₂ ≠ 2.