Activity Coefficients of Electrons and Holes in Semiconductors with a Parabolic Density of States

Bonham, D. Bivings; Orazem, Mark E.

doi:10.1149/1.2108344

Cited by 5 publications

(3 citation statements)

References 25 publications

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“…In the simulations presented below the Fermi level is limited to increase up to 0.25 eV below the conduction band, to avoid the free electrons entering degenerate statistics. In degeneration the activity coefficient of electrons departs markedly from γ n ) 1, [45][46][47] so the thermodynamic factor should become large. This effect may be eventually significant for measurements of the diffusion coefficient in highly doped nanostructured semiconductors.…”

Section: Diffusion Of Freementioning

confidence: 99%

Chemical Diffusion Coefficient of Electrons in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells

2004

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The properties and physical interpretation of the electron diffusion coefficient, D n , observed in nanostructured semiconductors and dye-sensitized solar cells by small perturbation electrical and electrooptical techniques are investigated. The chemical diffusion coefficient is defined as the product of a thermodynamic factor (that accounts for the effect of nonideal statistics in a gradient of chemical potential) and a jump diffusion coefficient (that depends on average hopping distances and rates). The thermodynamic and kinetic similarities, as well as the differences, between interacting ions in the lattice and electrons in nanostructured semiconductors are discussed. From these considerations, the chemical diffusion coefficient of electrons for multiple trapping transport in nanoporous dye solar cells can be calculated indirectly, and the results are in agreement with the reduction of the kinetic-transport equations in the quasistatic approximation. The chemical diffusion coefficient in several models for electrons is discussed: for a wide but stationary distribution of sites energies, giving the Fermi-level dependent D n [Fisher et al. J. Phys. Chem. B 2000, 104, 949] and for the enhancement of the diffusivity by effect of electrostatic shift of energy levels [Vanmaekelbergh et al. J. Phys. Chem. B 1999, 103, 747]. This last model is shown to correspond to the mean-field approximation to interaction in a lattice gas. A general expression containing all of these cases is provided, and several important consequences of the distinction between macroscopic diffusion and single particle random walk are pointed out.

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Section: Diffusion Of Freementioning

confidence: 99%

Chemical Diffusion Coefficient of Electrons in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells

2004

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“…For hEg= 0, Eq. [13] and [14] reduce to the conventional (uniform) results. The extra terms in addition to the conventional results are due to the nonideal behavior of the carriers and will be related to the activity coefficients of the carriers as shown below.…”

Section: Energy Bands In Nonuniform Semiconductorsmentioning

confidence: 83%

“…So, both hEg and A are positive quantities, hEg is called the effective bandgap shrinkage, and A, called the effective asymmetry factor (12), measures the change in the conduction bandedge (A x) and density of states, 0 -< A -< 1. It is noted that a different choice of the reference state for the electrostatic potential leads to different expressions for carrier densities.-For example, if we [ J kT [14] where bEg and A are the same expressions defined by Eq. [11] and [12], respectively.…”

Section: Energy Bands In Nonuniform Semiconductorsmentioning

confidence: 99%

Activity Coefficients of Electrons and Holes in Semiconductors with Nonuniform Composition: I . Nondegenerate

Chang

1988

J. Electrochem. Soc.

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A simple formalism for the calculation of the equilibrium activity coefficients of electrons and holes in a nondegenerate semiconductor with nonuniform composition is presented. These activity coefficients are functions of bandgap, electron affinity, and the density of states which vary with position. The calculation of carrier activity coefficients requires the selection of chemical potential and electrostatic potential references. The choice of these reference states is addressed. The relations between purely thermodynamic quantities and parameters of the band theory are also presented. It is shown that the intrinsic level is a purely thermodynamic property of the intrinsic bulk semiconductor. The approach presented here allows convenient treatment of nonuniform semiconductors in a manner that is both thermodynamically consistent and consistent with the Poisson-Boltzmann equation for the electrostatic potential.

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Photoelectrochemical Devices for Solar Energy Conversion

Orazem

Newman

1986

Reviews of Physiology, Biochemistry and Pharmacology

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Activity Coefficients of Electrons and Holes in Semiconductors with a Parabolic Density of States

Cited by 5 publications

References 25 publications

Chemical Diffusion Coefficient of Electrons in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells

Chemical Diffusion Coefficient of Electrons in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells

Activity Coefficients of Electrons and Holes in Semiconductors with Nonuniform Composition: I . Nondegenerate

Photoelectrochemical Devices for Solar Energy Conversion

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