Analysis of photoluminescence generated in a semi-infinite semiconductor slab by a time-varying focused laser beam

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.

Section: Discussionmentioning

confidence: 58%

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

Ramakrishna¹,

Rangarajan²

1995

“…When this premultiplying factor is plotted as a function of λz, 9 it is clear that its value is close to unity for a low numerical aperture. Moreover, these authors have drawn attention to the fact that under conditions where eq 37 is given by e -Rz , the actual lateral form of the excitation is immaterial.…”

Section: Model and Analysis Of The Effects Of Focusingmentioning

confidence: 91%

“…9 However, we shall introduce a one-dimensional potential in this problem which varies along the z-direction only. This may be expressed as where As usual, D n and τ are the diffusion constant and the bulk lifetime of the minority carriers, respectively.…”

Section: Model and Analysis Of The Effects Of Focusingmentioning

confidence: 99%

“…The Fourier-Bessel transform of the source term which is given by eq 30 reduces to 9 where λ ) R sin 2 Θ/2.…”

Section: Model and Analysis Of The Effects Of Focusingmentioning

confidence: 99%

“…reduction of the 3-D problem to a 1-D problem is the same here as was achieved in a previous work, 9 since the potential is assumed to vary only in the direction (z-axis) perpendicular to the surface.…”

mentioning

confidence: 92%

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

Ramakrishna

Rangarajan

1996

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. Selfabsorption, 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 FourierBessel 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.

Computer simulation of the photoluminescence decay at the GaAs-electrolyte junction. 1. The influence of the excitation intensity at the flat band condition

Krueger¹,

Jung²,

Gajewski³

1994

The influence of excitation intensity, surface recombination velocity, and photocunent on the time-resolved photoluminescence (PL) at the nlGaAs-electrolyte junction under flat band conditions was investigated using computer simulations. The mathematical background of the two-dimensional semiconductor analysis package (TOSCA) will be presented. We will show that the effects may be characterized qualitatively by exponential fit function(s), although in most cases the simulated PL decay is nonexponential. For a free carrier concentration no = 5 x 1017 cmP3, under the conditions of low injection density (pi) and with flat bands, both the surface recombination and the photocurrent lead to a remarkable decrease in the PL decay time either for surface recombination velocities SO > lo3 cm/s or for exchange photocurrent densities j@,O > lo-'' A/cm2. Under the conditions chosen in this work, the PL decay time approximated by the monoexponential decay time T decreases to a minimum value in Tfin = 1.64 ns when SO I lo6 cm/s or jph,O L lov8 A/cm2. This minimum indicates that the diffusion of the minority carriers toward the surface where they immediately nonradiatively vanish by means of surface recombination and/or charge transfer, respectively, is limited by the thermal velocity. In both cases, diffusion competes effectively against bulk recombination. For injection levels (p,/no) > 0.1, the PL decay time decreases with increasing injection density because the quadratic recombination process dominates. At high injection densities, the surface recombination velocity may not remain constant during the PL decay, but instead varies as a function of time S(t); S may decrease from its maximum value (SO) by up to 1 order of magnitude during the PL decay. The results will be discussed in relation to experimental results published previously by other groups.