Time-Resolved Photoluminescence and Microwave Conductivity at Semiconductor Electrodes: Depletion Layer Effects

Abstract

Analytical expressions which include depletion layer effects on low-injection carrier relaxation are being presented for the first time here. Starting from the continuity equation for the minority carriers, we derive expressions for the output signal pertinent to time-resolved microwave and luminescence experiments. These are valid for the time domain that usually overlaps with the time scales of surface processes, such as charge transfer and trapping. Apart from the usual pulse form of illumination, theoretical expressions pertaining to other forms of illumination such as switch-on and switch-off transient modes, a periodic mode, and a steady state and their various inter-relationships are derived here. The expressions obtained are seen to be generalizations of existing flat-band low-injection results in the limit of early or initial band bendings. The importance of the depletion layer as an experimental parameter is clearly seen in the limit of larger band bendings wherein it is shown, unlike the flat-band case, to exhibit pure exponential forms of carrier relaxation. Our results are consistent with the main conclusions of the numerical and experimental work published recently. Furthermore, this work provides the actual functional relationships between the applied potential and observed carrier decay. This should enable one to extract the surface kinetic parameters, after deciding on the dominant mode of carrier relaxation at the interface, whether charge transfer or trapping, by studying the potential dependence of the rate of relaxation.

Surface Recombination Kinetics at the GaAs/Electrolyte Interface via Photoluminescence Efficiency Measurements

“…Surface recombination via midgap states is often assumed to be a facile process which is independent of system parameters such as excitation power and applied potential. − Under these circumstances, the surface is a sink for minority carriers, and band unbending is difficult to achieve because the facile loss mechanism increases the required injection rate even further. Yet this picture is inconsistent with recent studies of the GaAs/electrolyte interface, ,− which suggest that the detailed kinetics of surface recombination has a significant influence on carrier dynamics near the GaAs/electrolyte surface.…”

“…[18][19][20] Under these circumstances, the surface is a sink for minority carriers, and band unbending is difficult to achieve because the facile loss mechanism increases the required injection rate even further. Yet this picture is inconsistent with recent studies of the GaAs/ electrolyte interface, 16, [21][22][23][24][25][26][27][28][29] which suggest that the detailed kinetics of surface recombination has a significant influence on carrier dynamics near the GaAs/electrolyte surface.…”

Self-Absorption and Focusing Effects in Carrier Relaxation Dynamics under Depletion Conditions

“…It has been found that, owing to paucity of carriers at moderate depletion, the pure exponential decay terms are no longer dominant and the depletion field drives the system to K f ∞, thus almost skipping an important potential window discussed previously. 1 The previous model 1 can be said to overestimate the loss of carriers by radiative recombination within the space charge region.…”

“…The presence of a finite numerical aperture is seen to alter the source only via a parametric integration and whose integrand's spatial dependence remains as earlier. 1 Thus utilizing the results of ref 1, we obtain expressions in the Laplace plane, relating to a general time-dependent source of illumination, which now includes the effect of a numerical aperture in the presence of a depletion layer. The various limiting cases of surface kinetics and the two potential windows are briefly analyzed before the work is concluded.…”

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

“…To address these issues, we have performed an extensive series of digital simulations of the decay dynamics of photoexcited charge carriers at a semiconductor/liquid interface using the two-dimensional simulation code ToSCA, which self-consistently solves Poisson's equation within the van Roosbroeck generation, recombination, and drift-diffusion model. , The principal intent of performing these simulations was to identify conditions with respect to excitation intensity and applied potential where the rate constants for charge transfer and surface recombination can be unambiguously extracted from experimental photoluminescence decay data. While the steady-state dead-layer model helped pioneer, both pedagogically and quantitatively, the understanding of semiconductor/liquid contacts in general, , and illuminated semiconductor/liquid contacts in particular, − this work will summarize the photoluminescence simulations for a semiconductor/liquid contact under transient injection conditions and will reveal significant differences in the fitting of the decay dynamics relative to those produced by earlier models. ,− The sources of these discrepancies involve the fundamental expressions used to describe the competition between surface recombination and interfacial charge transfer at a solid/liquid interface, as well as factors related to the use of a two-dimensional treatment of the transport and excitation processes in such a system. One of ToSCA's advantages over other existing simulations is that it treats electron and hole carrier capture processes separately and does not combine them into a single effective surface recombination velocity parameter. ,− It will be shown that overestimating effective surface recombination velocities can lead to overestimates in interfacial charge-transfer rate constants under many important experimental conditions.…”