Modes of Charge Transfer at an Illuminated Semiconductor Electrode, a Digital Simulation

Laser, Daniel

doi:10.1149/1.2129165

Cited by 14 publications

(13 citation statements)

References 12 publications

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“…This can be supported by the results of photocurrent rise time calculations given in Ref. (13), being in the order of magnitude of 10-~-lO -~ sec. The characteristic decay time presented here, and ascribed to surface processes, is at least one order of magnitude longer.…”

Section: Theorysupporting

confidence: 61%

“…Just after the photocurrent jump a decay portion is expected 9 The initial slope of the transients for model A is djA'/d$ ~ --jh " kr' [10] which is seen to be independent of Cred. For model B, however, one finds djB'/dt ~ --Jh " k/ 9 (1 --~) = --jh" kr' 9 ka/(kiCred + ]Ca) [11] Introducing the notation [12] one finds for model A the expression 9 A ----1/kr' [13] whereas the same time constant for model B is 9 B --(1/kr') (1 + kiCred/ka) [14] If the modulation depth is very small, that is, hi << I hence ~Ja << Jh ~ then the average value of j' under modulated illumination can be considered to be the same as that under constant illumination, that is, j; is' so the average excess photocurrent for model A can be calculated as 1/jA' -= (1/jh ~ (1 + kr'/kiCred)~ l/is' [15] for model B,-f is given by…”

Section: [9]mentioning

confidence: 99%

“…A number of kinetic models can be formulated for steady state leading to Eq. [1] (11)(12)(13)(14). The surface processes invclved in these models can be summarized as follows:…”

Section: Theorymentioning

confidence: 99%

See 2 more Smart Citations

Mechanism of Hole Injection on Ferric Oxide Photoelectrodes

Pajkossy

1983

J. Electrochem. Soc.

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Section: Theorysupporting

confidence: 61%

Section: [9]mentioning

confidence: 99%

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Mechanism of Hole Injection on Ferric Oxide Photoelectrodes

Pajkossy

1983

J. Electrochem. Soc.

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“…fp,n (i) = fa Fie -~y df~ [31] Mp,. (i, j) = fa Fi Fj dr2 [32] Np.n (i, j) = -~ faaF,_N" VFk 6~ F~ d/+ fa VF~.…”

Section: Methods Of Solution--thementioning

confidence: 99%

Modeling of Charge Carrier Transport in Photoetching of Gallium Arsenide

Mannheim

Alkire

Sani

1994

J. Electrochem. Soc.

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Wet photoelectrochemical etching of GaAs was investigated with the use of a numerical model that calculated electron, hole, and potential distributions in a selectively illuminated semiconductor. The Galerkin finite element method was used to solve the Poisson equation for the potential and the species transport equations for holes, and electrons in two dimensions. The transport equations included generation, recombination, diffusion, and migration terms. A technique was developed for examining the sensitivity of the distribution of holes, electrons, and the potential to the parameters of the system including the surface reaction rate constant, diffusion coefficients, doping concentration, light intensity, wavelength, and the recombination length. The sensitivity analysis technique facilitated identification of parameters for which the behavior of this complex, nonlinearly coupled system is most sensitive.Anisotropic etching is essential for creating the closely spaced fine patterns needed for microelectronic devices. In the case of semiconductors, anisotropic etching of high-aspect trenches having vertical sidewalls may be accomplished by using a combination of wet etching in conjunction with selective illumination of the region to be etched. In such cases, interesting questions arise concerning the difference in etch rates between the illuminated and the dark regions of the surface, as well as the sharpness with which the boundary between the two regions may be achieved. In the present investigation, a numerical simulation 1 was carried out on the reaction and transport phenomena at the edge of the illuminated region during photoetching of n-GaAs in an electrolytic solution.When an n-type semiconductor is immersed in an electrolytic solution, the energy bands bend to establish equilibrium between the semiconductor and the solution. Band bending produces a potential gradient, or space-charge layer, near the surface. Illumination decreases band bending by producing a photovoltage 2 and a change in surface potential 3 which may be experimentally measured by electrolyte electroreflectance and photoreflectance techniques. 4 A result of surface illumination is a non-uniform potential distribution along the surface, the illuminated regions being less negative than the dark regions.Selective photoetching of semiconductors in an electrolytic solution may thus be accomplished by illuminating specific regions of the surface by light having an energy greater than the bandgap energy. Anisotropic maskless photoetching of GaAs, InP, InGaAs, and HgCdTe using a focused laser has been demonstrated in the fabrication of various grating profiles, grooves, trenches, and throughholes. ~-12In a semiconductor the distribution of etch rate is controlled by the distribution of potential and of carrier concentration. These distributions are affected by illumination wavelength and intensity, doping concentration, surface reaction processes, rate of recombination, surface potential, and diffusion coefficients. Several mathematical models h...

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“…Use of a digital computer in the numerical solution of the governing equations eliminates the need for restrictive assumptions. Such mathematical models of semiconductors (MacDonald, 1962;DeMari, 1968a, b;Choo, 1971Choo, , 1972Laser and Bard, 1976a, b, c;Sutherland and Hauser, 1977;Laser, 1979;Orazem and Newman, 1984a, b) generally lack a satisfactory expression for activity coefficients. This has limited their application to semiconductors with low electron and hole concentrations as compared to the maximum concentration of electrons or holes allowed in the respective energy level.…”

Section: Introductionmentioning

confidence: 99%

Electron and hole transport in degenerate semiconductors

Orazem

1986

AIChE Journal

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Concentration-dependent activity coefficients were used in conjunction with dilute-solution transport equations to show the effect of degeneracy on the apparent physical properties of semiconductors and on the performance of photovoltaic cells. The approach presented here allows convenient treatment of degenerate semiconductors in a manner that is both thermodynamically consistent and consistent with the Fermi-Dirac distribution for electrons. These calculations show that neglect of the concentration dependency of the activity coefficients has a large effect on the calculated values for local concentrations in a photovoltaic device, but affects the calculated values of power density and cell potential only slightly. Neglect of the concentration dependency of the activity coefficients does have a significant effect on the calculation of the resistivity of the semiconductor. M. E. Orazem Department of Chemical EngineeringUniversity of Virginia Charlottesville, VA 22901 SCOPEDilute-solution transport equations with constant activity coefficients are commonly used to model semiconductors. These equations are consistent with a Boltzmann distribution and are therefore invalid for degenerate semiconductors for which the Boltzmann distribution does not adequately describe electron or hole concentrations. Concentration-dependent activity coefficients were used in conjunction with dilute-solution transport equations to show the effect of degeneracy on the performance of photovoltaic cells and on the apparent physical properties of semiconductors. The approach presented here allows convenient treatment of degenerate semiconductors in a manner that is both thermodynamically consistent and consistent with the Fermi-Durac distribution for electrons. This approach is compared to the alternative treatment of degeneracy by modification of the Nernst-Einstein relationship between mobility and diffusivity. CONCLUSIONS AND SIGNIFICANCEA one-dimensional mathematical model of photovoltaic devices is presented that accounts explicitly for the influence of degeneracy. Macroscopic transport equations for electrons and holes in semiconducting materials were made consistent with Fermi-Durac statistics by inclusion of a concentration-dependent activity coefficient. These equations allow modeling of degenerate semiconductors for which the electron and hole concentrations are less than their respective effective energy band site densities and for which the effective conduction and valence band site densities are greater than the dopant concentration. Calculations are presented for a Shottky-barrier photovoltaic device and a photoelectrochemical cell modeled under the assumption of constant activity coefficients and with concentration-dependent activity coefficients. Comparisons among the results of these calculations show that neglect of the concentration dependency of the activity coefficients has a large effect on the calculated values for local concentrations. The values of power density and cell potential obtained from these calculations,...

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Modes of Charge Transfer at an Illuminated Semiconductor Electrode, a Digital Simulation

Cited by 14 publications

References 12 publications

Mechanism of Hole Injection on Ferric Oxide Photoelectrodes

Mechanism of Hole Injection on Ferric Oxide Photoelectrodes

Modeling of Charge Carrier Transport in Photoetching of Gallium Arsenide

Electron and hole transport in degenerate semiconductors

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