Conditions under which heterogeneous charge-transfer rate constants can be extracted from transient photoluminescence decay data of semiconductor/liquid contacts as determined by two-dimensional transport modeling

An extensive series of digital simulations of the decay dynamics of photoexcited charge carriers at a semiconductor/liquid interface has been performed using the two-dimensional simulation code ToSCA, ToSCA treats majority and minority carrier capture processes separately and incorporates field-dependent carrier mobility terms. These features produce dramatic differences in the output parameters obtained when fitting experimental data with ToSCA relative to those obtained by fitting such data with prior, less complete, simulations. The simulations revealed that for a typical (n-type in our example) InP electrode in contact with outer-sphere redox reagents dissolved in the liquid phase the photoluminescence decays were generally insensitive to the value of the minority carrier charge-transfer rate constant, k(ht). Instead, diffusion and drift-induced separation of photogenerated carriers in the space-charge layer of the semiconductor dominated the time decay of the observed luminescence signal under most experimentally accessible conditions. Values of k(ht) and of the minority carrier low-level surface recombination velocity, S-p, could be obtained from an analysis of the photoluminescence decays only when the following restricted sets of conditions were satisfied simultaneously: 10(1) cm s(-1) less than or equal to S-p less than or equal to 10(5) cm s(-1), 10(-18) cm(4) s(-1) less than or equal to k(ht) less than or equal to 10(-15) cm(4) s(-1), and the electrode potential, E, was in the region 0 < E < +0.15 V relative to the flat-band potential of the n-type semiconductor/liquid interface. The simulations demonstrated that it was not possible to extract a "field dependence" of the charge-transfer rate constant when the semiconductor/liquid contact was maintained in reverse bias (E greater than or equal to +0.15 V vs the flat-band potential) and was subjected to light pulses that produced low or moderate carrier injection levels. Under such conditions, the photoluminescence decay dynamics were dominated by drift-induced charge separation in the space-charge layer of the semiconductor. Under high-level injection conditions, no "field dependence" could be observed because the majority of the photoluminescence decay dynamics occurred near the flat-band condition, so the value of the band bending in the semiconductor under dark, equilibrium conditions had negligible influence on the luminescence transients produced by a high-intensity laser pulse. Additionally, comparison between one-dimensional and two-dimensional simulations showed that use of one-dimensional simulation routines to extract S-p and k(ht) values from experimental data obtained using focused laser beam excitation can lead to severe overestimates of interfacial charge-transfer rates.