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The effect of a one-dimensional field (1) on the self-absorption characteristics and (2) when we have a finite numerical aperture for the objective lens that focuses the laser beam on the solid are considered here. Self-absorption, in particular its manifestation as an inner filter for the emitted signal, has been observed in luminescence experiments. Models for this effect exist and have been analyzed, but only in the absence of space charge. Using our previous results on minority carrier relaxation in the presence of a field, we obtain expressions incorporating inner filter effects. Focusing of a light beam on the sample, by an objective lens, results in a three-dimensional source and consequently a three-dimensional continuity equation to be solved for the minority carrier concentration. Assuming a one-dimensional electric field and employing Fourier-Bessel transforms, we recast the problem of carrier relaxation and solve the same via an identity that relates it to solutions obtained in the absence of focusing effects. The inner filter effect as well as focusing introduces new time scales in the problem of carrier relaxation. The interplay between the electric field and the parameters which characterize these effects and the consequent modulation of the intensity and time scales of carrier decay signals are analyzed and discussed.

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 fate of relaxation.

A model Hamiltonian to describe adsorbate-mediated electron transfer is proposed and analyzed for the (electrochem.) currents. This Hamiltonian differs fundamentally from the ones used earlier (cf. Schmickler 1980, 1982). Three situations are treated, viz., (1) a lone adsorbate picture; (2) presence of an inactive neighboring adsorbate; and (3) electrostatic effects due to an adsorbate lattice. In all 3 cases, the mediation is via a single adsorbate only. Several limiting cases are considered and related to the earlier results of Marcus and Schmickler.

The theoretical analysis of chemisorption involving two adsorbates is taken up to obtain expressions for "indirect interactions", distortions in charge-transfer processes (as compared with the lone adsorbate problem), etc. This is achieved by constructing an appropriate model Hamiltonian and deriving analytical expressions for single-particle fermion Green's functions (GFs) as well as higher order Fermion and boson GFs required for evaluating the energies involved beyond the Hartree-Fock and mean-field limits.

The problem of electron transfer mediated by the chemisorbed layer with random occupancy on a 2-dimensional lattice is taken up. The anal. employs linear response formalism and CPA for evaluating the current. Two cases referring to (1) the delocalized and (2) the localized electronic states in the chemisorbed layer are treated.