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

Abstract

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/t1-α/2 initial time ( t) dependence rather than the conventional 1/t1-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/t1+α time dependence. <p>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 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.

Origin of the Delayed Fluorescence by Triplet–Triplet Annihilation in Solids with a Power Law Exponent of between −1/2 and −1

“…α = k B T/E 0 for dispersive diffusion, where E 0 represents the energy characterizing the exponential density of states. [34][35][36]40,41 If TTA occurs between mobile excitons under the good mixing condition, then the fluorescence decay is proportional to 1/t 2 as shown in eq 54 even though α < 1. an exponent of 2. At an intermediate temperature, the powerlaw decay with an exponent of 1 − α/2 will become a powerlaw decay with an exponent of 2.…”

“…The detrapping rate with activation energy E can be expressed as γ( E ) = 2Γ exp[− E /( k B T )], where the factor of 2 indicates two hopping directions in one-dimensional systems. The waiting-time distribution for the detrapping is given by − ,, ψ false( t false) = ∫ 0 ∞ d E ⁡ g false( E false) ⁡ γ false( E false) ⁡ exp false( prefix− γ ( E ) t false) ≈ α Γ false( α + 1 false) ( 2 Γ rw ) α t α + 1 where ⁡ α ≡ k B T / E 0 α = k B T / E 0 is a key quantity called the dispersion parameter. The dispersion parameter is the ratio of the thermal energy to the characteristic energy of trap states.…”

“…α = 1 for normal diffusion. α = k B T / E 0 for dispersive diffusion, where E 0 represents the energy characterizing the exponential density of states. − ,, If TTA occurs between mobile excitons under the good mixing condition, then the fluorescence decay is proportional to 1/ t 2 as shown in eq even though α < 1.…”

“…where the factor of 2 indicates two hopping directions in one-dimensional systems. The waiting-time distribution for the detrapping is given by [34][35][36]40,41 α is less than unity. When α is small, detrapping assisted by thermal energy is suppressed.…”

Fluctuation relation in continuous-time random walks driven by an external field

“…Under an applied field, the transition rate in the field direction and that in the opposite direction are denoted by γ rp (F ) and γ rm (F ), respectively. By considering the Arrhenius law, these two transition rates can be expressed as [34]…”