Showing papers on "Einstein relation published in 1992"

Transition densities for Brownian motion on the Sierpinski carpet

Abstract: Upper and lower bounds are obtained for the transition densitiesp(t, x, y) of Brownian motion on the Sierpinski carpet. These are of the same form as those which hold for the Sierpinski gasket. In addition, the joint continuity ofp(t, x, y) is proved, the existence of the spectral dimension is established, and the Einstein relation, connecting the spectral dimension, the Hausdorff dimension and the resistance exponent, is shown to hold.

Electronic transport in a model tetraphenylbenzidine main-chain polymer: Direct comparison of time-of-flight hole drift mobility and electrochemical determinations of hole diffusion.

Abstract: Electronic transport behavior is analyzed in a model polytetraphenylbenzidine (PTPB) hole transport polymer in which electroactive tetraphenylbenzidine sites are covalently bonded within the polymer main chain. Time-of-flight (TOF) techniques are used to measure the hole drift mobility as a function of electric field and temperature. The TOF data are parametrized using the phenomenological model originally proposed by Gill. For comparative purposes, the disorder model developed by the Marburg group is also used to analyze the data. Transport of holes in PTPB is demonstrated to occur via hopping among the TPB functional units. A pattern of convoluted field and temperature-dependent features, now known to be shared by a broad class of disordered molecular materials, is revealed by the TOF data. Thin solid film electrochemical techniques are applied in parallel with the TOF technique to independently obtain hole diffusion coefficients (${\mathit{D}}_{\mathit{h}}$) in thin films of PTPB. As a unique consequence of this comparison, it is established that mobilities, computed from solid-state hole diffusion data using the Einstein relation, converge with zero-field extrapolated TOF mobilities over a wide temperature range when the extrapolation is computed from log \ensuremath{\mu} vs ${\mathit{E}}^{1/2}$ plots. Therefore, the functional dependence of the logarithm of the drift mobility on the square root of field, a much discussed general feature of electronic transport in disordered molecular materials, is demonstrated to persist through the critical low-field limit. At the same time it is demonstrated that the contribution of thermally driven diffusive broadening, which can now be calculated directly from the independently determined electrochemical hole diffusion coefficients, makes an insignificant contribution to the experimentally observed width of the time-of-flight transit pulse. A comparison of the PTPB data with analogous TOF data on solid solutions of TPD (the functional unit in PTPB) dispersed in polycarbonate is described. The observation that hole drift mobilities in PTPB are an order of magnitude smaller than those in the corresponding TPD-polycarbonate solid solution is discussed in terms of disorder and steric constraints.

Long-time self-diffusion coefficients of suspensions.

Abstract: We present a theory for calculation of the long-time self-diffusion coefficient of suspensions of interacting colloidal particles without hydrodynamic interactions. The theory follows the idea put forward in the preceding paper [Jan A. Leegwater and Grzegorz Szamel, Phys. Rev. A 46, 4999 (1992)]: The self-friction coefficient is calculated approximately and the self-diffusion coefficient can be obtained using the Einstein relation. To calculate the friction coefficient, we retain the part of the three-particle dynamical correlations that can be expressed in terms of the two-particle dynamical correlations. In this way we renormalize the two-particle dynamics. To get explicit results for hard spheres, we introduce a decoupling approximation for the long-time contributions to the friction coefficient. For intermediate densities the predictions of our theory agree very well with Brownian-dynamics simulation.

A novel technique for the simultaneous measurement of ambipolar carrier lifetime and diffusion coefficient in silicon

Abstract: Using the classical semiconductor continuity equation, a new method for the simultaneous extraction of the ambipolar carrier lifetime and the ambipolar diffusion coefficient for high injection levels is developed. The method uses carrier decay measurements based on the free-carrier absorption (FCA) technique. The measurements are performed in the base of p-i-n type diodes, where the middle region is a lightly n-doped base region. By varying the forward bias, the ambipolar lifetime and diffusion coefficients are studied for different excess-carrier concentrations ranging approx. 2–4 decades above the base doping. Both the lifetime and diffusion coefficients agree well with theoretical models. The theoretical ambipolar diffusion coefficients agree well with theoretical models. The theoretical ambipolar diffusion coefficient is calculated using the values of Dn and Dp, which, in turn, are determined from mobility models and the Einstein relation. The mobility models used include carrier-carrier scattering effects which are important in the explanation of high-injection dependence.

The diffusivity-mobility ratio in nonparabolic materials

Abstract: An attempt is made to study the Einstein relation for the diffusivity mobility ratio of the carriers in III–V, II–VI, IV–VI materials and Bi by formulating the respective expressions in accordance with the Kane, Hopfield, Cohen, and McClure and Choi models, respectively, which have been stated in the literature as to be the best models in describing the carrier energy spectra in these nonparabolic materials. It is found, by taking various types of aforementioned samples and Bi, that the above ratio increases with increasing electron concentration in different manners and the rates of variations are totally band structure dependent. We have also suggested an experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion laws. In addition, the corresponding well‐known results for relatively wide band gap materials have also been obtained as special cases of our generalized formulations.

Ambipolar Diffusion of Electron–Hole Pairs in β-Rhombohedral Boron

Abstract: In β-rhombohedral boron the electronic transport is essentially determined by deep electron traps of different bonding energies The ambipolar diffusion of optically excited electron–hole pairs on diffusion paths of up to 537 mm length was investigated The diffusion length at stationary conditions is 21 mm and the mean diffusion velocity is 58 × 10−6 m s−1 From these data a lifetime of 3620 s results By Fick's second law the diffusion coefficient was determined to increase from about 5 × 10−3 to 101 cm2 s−1 with the diffusion velocity increasing from 10−5 to 10−1 m s−1 The Einstein relation yields the corresponding mobilities, which increase accordingly from about 02 to about 50 cm2 V−1 s−1 These mobilities are mean values for electrons and holes The relaxation of the excited state of the sample into the thermal equilibrium is determined by five relaxation times (66, 50, 514, 5650, 14700 s), which are immediately related to the thermal excitation of the electrons from the traps with the bond energies 018, 037, 058, 077, and 089 eV

The Einstein relation for degenerate semiconductors with nonuniform band structures

Abstract: Modification of the Einstein equation for semiconductors with nonparabolic energy bands and doped nonuniformly with impurity atoms is suggested. The suggestion is based on a new approximation of the Fermi-Dirac integral of order 1/2, namely, F/sub 1/2/( eta /sub n/), where eta /sub n/ is the reduced Fermi level for electrons. The relation reduces to that for semiconductors with parabolic energy bands and doped uniformly with impurity atoms under appropriate boundary conditions. A comparison of the calculated and exact results for F/sub 1/2/( eta ) is found to be very encouraging. >

Influence-functional theory for a heavy particle in a Fermi gas.

Abstract: We use Feynman's influence-functional theory to study the quantum dynamics of a heavy particle moving in a free Fermi gas with arbitrary average velocity. A semiclassical expansion yields a nonlinear Langevin equation with the exact friction coefficient as derived in an earlier publication. The fluctuations around a steady state far from equilibrium are due to a nonclassical state-dependent noise term and can be described by a diffusion constant. In the limit of zero average velocity, the Einstein relation is fulfilled for arbitrary temperatures

The Diffusivity-Mobilitt Ratio Under Strong Magnetic Field in III-V Superlattices with Graded Structures

Abstract: In this paper we have studied the Einstein relation for the diffusivity-mobility ratio in III–V superlattices with graded structures under magnetic quantization by formulating a new dispersion law. It is found, taking InAs/GaSb an example that the diffusivity mobility ratio increases in an oscillatory way with increasing carrier degeneracy as a consequence - SdH effect. The Einstein relation in III-V superlattice is greater than that of the same for the constituent materials. Besides the theoretical results are in agreement with the suggested experimental method of determining the same ratio in degenerate materials having arbitrary dispersion laws.

The Einstein relation in zero-gap semiconductors

Abstract: The Einstein relation for the diffusivity-mobility ratio of the carriers in zero-gap semiconductors, taking n-HgTe as an example is studied. It is found, that this ratio increases with increasing electron concentration and is in close agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors with arbitrary dispersion laws. In addition, the corresponding well-known results for isotropic parabolic energy bands have also been obtained from our generalized expressions under certain limiting conditions.

Variations of energy-band-diagrams with forward bias voltages for step-like separate-confinement-heterostructure for single-quantum-well lasers

Abstract: The variations of energy-band-diagrams with forward bias voltages for step separate-confinement-heterostructure single quantum-well lasers are investigated by numerically solving the semiconductor device equations with two band parameters described by the generalized Einstein relation and various position-dependent parameters for the materials. The effects of bandgap shrinkage are included. By examining band diagrams, it was found that the potential profiles of the quantum wells with respect to the centers of the wells are: (1) symmetric at high injection; (2) tilted at low injection; and (3) almost flat with reasonable injection. In the intrinsic regions, the difference of the quasi-Fermi potentials can be well approximated by the applied voltage. >

The Einstein Relation in Superlattices OP Wide-Band Gap Semiconductors Onder Cross-Field Configuration

Abstract: in this paper we study the Einstein relation in superlattices of wide-band gap semiconductors under crossfield configuration and the for.-ning materials incorporating spin and broadening of Landau levels, it is found, taking GaAs/AAAs superlattice as an example that the diffusivity-mobility ratio increases with increasing electron concentration and oscillates with inverse quantizing magnetic field due to SdH effect. Thetheoretical analysis is in agreement with the suggested experimental method of determining the same ratio in degenerate materials having arbitrary dispersion laws.

Nonlocal Einstein relation.

Abstract: I derive accurate nonlocal relations between the conductivity and diffusion (the Einstein formula), between the current density and local voltage, and between the local voltage and total current. These relations provide a complete description of charge transfer. Their nonlocality is shown to arise only through the density-density correlation function.

Influence of cross-field configuration on the einstein relation in quantum wires of tetragonal semiconductors

Abstract: An attempt is made to study the Einstein relation for the diffusivity-mobility ratio of the electrons is quantum wires of tetragonal semiconductors in the presence of crossed electric and magnetic fields on the basis of a newly derived electron energy spectrum considering all types of anisotropies in the band parameters. It is found taking n-Cd3As2 as an example that the same ratio increases with electron concentration in an oscillatory way. Besides, it decreases with increasing thickness and the crystal field splitting influences significantly the ratio in the whole range of the variables considered. We have also suggested an experimental method of determining the Einstein relation in degenerate materials having arbitrary dispersion laws. The results for quantum wires of parabolic semiconductors have been also obtained from our generalized expressions in the absence of cross-field configuration under certain limiting conditions.