Optical beam induced minority carrier distribution in semiconductors

Wilson, Tony; Pester, P. D.

doi:10.1002/pssa.2210970132

Cited by 20 publications

(5 citation statements)

References 13 publications

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“…Optical coordinates have also been introduced, given by where sin ϑ is the numerical aperture of the objective lens. The time-resolved PMC signals will now be found to be proportional to a volume integral over the minority carrier concentration, say N , given by The symmetry of the problem suggests that we may use the Fourier−Bessel transform of n ( r , z ) to solve the problem. , Accordingly The continuity equation now bocomes, in terms of ñ , where κ 2 = D n ν 2 + 1/τ. It is important to note that the boundary conditions that applied to n of eq 29 viz…”

Section: Model and Analysis Of The Effects Of Focusingmentioning

confidence: 99%

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

Ramakrishna

Rangarajan

1996

J. Phys. Chem.

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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. 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.

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Section: Model and Analysis Of The Effects Of Focusingmentioning

confidence: 99%

“…The time-resolved PMC signals will now be found to be proportional to a volume integral over the minority carrier concentration, say N, given by The symmetry of the problem suggests that we may use the Fourier-Bessel transform of n(r,z) to solve the problem. 12,13 Accordingly…”

Section: Model and Analysis Of The Effects Of Focusingmentioning

confidence: 99%

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

Ramakrishna

Rangarajan

1996

J. Phys. Chem.

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“…The symmetry of our problem suggests that the solution is most easily obtained in a cylindrical coordinate system [19]. It will be useful to introduce the Fourier-Bessel…”

Section: The Photoluminescence Image Of a Defectmentioning

confidence: 99%

“…It has already been shown [20] that the presence of a point like defect may be taken into account, to the first Born approximation, by modifying the generation term to where the defect of strengthy is located a t (yo, a ) and po(r, z ) is the solution of (7) in the absence of the defect. An appropriate form for the optical generation function is [19] where go is a constant which takes into account the surface reflectivity, 01 is the intensity absorption coefficient and c is the half-width of the probe beam. We may find p(0, z ) most easily by taking the Fourier-Bessel transform of ( 7 ) with g(r, z ) replaced by g'(r, 2).…”

Section: The Photoluminescence Image Of a Defectmentioning

confidence: 99%

Photoluminescence and Optical Beam Induced Current Images of Defects in Semiconductors

Wilson

McCabe

1987

Phys. Stat. Sol. (a)

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The photoluminescence images of defects in semiconductors are calculated and the factors discussed which affect the resolution. In the special case of a Schottky barrier being present on the surface of the semiconductor it is shown that the optical beam induced current resolution and the photoluminescence resolution are identical. It is further shown that by considering the ratio of the contrasts in the two cases that the depth of a point defect may be calculated.

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“…Schematic diagram of Schottky barrier 'ohmic coniaciThe cyclindrical symmetry[5,9] of the problem suggests that it may be most easily solved by introducing the Fourier-Bessel (or Hankel) transform of n(r, z , t ) defined as m G(v, z, t ) = J n(r, z, t ) Jo(vr) r dr ,…”

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confidence: 99%

An analysis of the photocurrent induced in a semi-infinite schottky barrier by a time varying focussed laser beam

Pester

Wilson

1988

Phys. Stat. Sol. (a)

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General expressions are derived for the photocurrent induced in a semi-infinite Schottky barrier diode due t o excitation by a focussed convergent light beam. A simple repeated transform technique using the Hankel and Laplace transformations is used to solve the diffusion equation. Special cases are considered where the excitation can be described by 8-functions, step functions, and harmonic modulation of the beam. The effects of beam focusing and cases where a simpler treatment may be used are discussed. Es werden allgemeine Ausdrucke fur den Photostrom abgeleitet, der in einer halbunendlichen Schottkybarrierendiode durch Anregung mit einem fokussierten konvergenten Lichtstrahl induziert wird. Eine einfache wiederholte Transformationskinetik mit Hankel-und Laplace-Transformationen wird benutzt, um die Diffusionsgleichung zu losen. Speziell der Fall wird beobachtet, wo die Anregung durch %-Funktionen, Stufenfunktionen und harmonische Modulation des Strahls beschrieben werden kann. Die Einflusse von Strahlenfokussierung und Falle, wo eine einfachere Behandlung benutzt werden kann, werden diskutiert.

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Optical beam induced minority carrier distribution in semiconductors

Cited by 20 publications

References 13 publications

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

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

Photoluminescence and Optical Beam Induced Current Images of Defects in Semiconductors

An analysis of the photocurrent induced in a semi-infinite schottky barrier by a time varying focussed laser beam

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