Theory of spin-polarized transport in ferromagnet-semiconductor structures: Unified description of ballistic and diffusive transport

A theory of spin-polarized electron transport in ferromagnet-semiconductor heterostructures, based on a unified semiclassical description of ballistic and diffusive transport in semiconductors, is outlined. The aim is to provide a framework for studying the interplay of spin relaxation and transport mechanism in spintronic devices. Transport inside the (nondegenerate) semiconductor is described in terms of a thermoballistic current, in which electrons move ballistically in the electric field arising from internal and external electrostatic potentials, and are thermalized at randomly distributed equilibration points. Spin relaxation is allowed to take place during the ballistic motion. For arbitrary potential profile and arbitrary values of the momentum and spin relaxation lengths, an integral equation for a spin transport function determining the spin polarization in the semiconductor is derived. For field-driven transport in a homogeneous semiconductor, the integral equation can be converted into a second-order differential equation that generalizes the spin drift-diffusion equation. The spin-polarization in ferromagnet semiconductor structures is obtained by matching the spin-resolved chemical potentials at the interfaces, with allowance for spin-selective interface resistances. Illustrative examples are considered.Comment: 11 pages, 4 figures; to appear in Materials Science and Engineering

Thermoballistic spin-polarized electron transport in paramagnetic semiconductors

Spin-polarized electron transport in diluted magnetic semiconductors (DMS) in the paramagnetic phase is described within the thermoballistic transport model. In this (semiclassical) model, the ballistic and diffusive transport mechanisms are unified in terms of a thermoballistic current in which electrons move ballistically across intervals enclosed between arbitrarily distributed points of local thermal equilibrium. The contribution of each interval to the current is governed by the momentum relaxation length. Spin relaxation is assumed to take place during the ballistic electron motion. In paramagnetic DMS exposed to an external magnetic field, the conduction band is spin-split due to the giant Zeeman effect. In order to deal with this situation, we extend our previous formulation of thermoballistic spin-polarized transport so as to take into account an arbitrary (position-dependent) spin splitting of the conduction band. The current and density spin polarizations as well as the magnetoresistance are each obtained as the sum of an equilibrium term determined by the spin-relaxed chemical potential, and an off-equilibrium contribution expressed in terms of a spin transport function that is related to the splitting of the spin-resolved chemical potentials. The procedures for the calculation of the spin-relaxed chemical potential and of the spin transport function are outlined. As an illustrative example, we apply the thermoballistic description to spin-polarized transport in DMS/NMS/DMS heterostructures formed of a nonmagnetic semiconducting sample (NMS) sandwiched between two DMS layers. We evaluate the current spin polarization and the magnetoresistance for this case and, in the limit of small momentum relaxation length, find our results to agree with those of the standard drift-diffusion approch to electron transport.Comment: Minor corrections; 3 references added; changed to single-column forma

Barrier-controlled carrier transport in microcrystalline semiconducting materials: Description within a unified model

A recently developed model that unifies the ballistic and diffusive transport mechanisms is applied in a theoretical study of carrier transport across potential barriers at grain boundaries in microcrystalline semiconducting materials. In the unified model, the conductance depends on the detailed structure of the band edge profile and in a nonlinear way on the carrier mean free path. Equilibrium band edge profiles are calculated within the trapping model for samples made up of a linear chain of identical grains. Quantum corrections allowing for tunneling are included in the calculation of electron mobilities. The dependence of the mobilities on carrier mean free path, grain length, number of grains, and temperature is examined, and appreciable departures from the results of the thermionic-field-emission model are found. Specifically, the unified model is applied in an analysis of Hall mobility data for n-type microcrystalline Si thin films in the range of thermally activated transport. Owing mainly to the effect of tunneling, potential barrier heights derived from the data are substantially larger than the activation energies of the Hall mobilities. The specific features of the unified model, however, cannot be resolved within the rather large uncertainties of the analysis.Comment: REVTex, 19 pages, 9 figures; to appear in J. Appl. Phy

Unified description of ballistic and diffusive carrier transport in semiconductor structures

A unified theoretical description of ballistic and diffusive carrier transport in parallel-plane semiconductor structures is developed within the semiclassical model. The approach is based on the introduction of a thermo-ballistic current consisting of carriers which move ballistically in the electric field provided by the band edge potential, and are thermalized at certain randomly distributed equilibration points by coupling to the background of impurity atoms and carriers in equilibrium. The sum of the thermo-ballistic and background currents is conserved, and is identified with the physical current. The current-voltage characteristic for nondegenerate systems and the zero-bias conductance for degenerate systems are expressed in terms of a reduced resistance. For arbitrary mean free path and arbitrary shape of the band edge potential profile, this quantity is determined from the solution of an integral equation, which also provides the quasi-Fermi level and the thermo-ballistic current. To illustrate the formalism, a number of simple examples are considered explicitly. The present work is compared with previous attempts towards a unified description of ballistic and diffusive transport.Comment: 23 pages, 10 figures, REVTEX

Complete determination of the reflection coefficient in neutron specular reflection by absorptive non-magnetic media

An experimental method is proposed which allows the complete determination of the complex reflection coefficient for absorptive media for positive and negative values of the momenta. It makes use of magnetic reference layers and is a modification of a recently proposed technique for phase determination based on polarization measurements. The complex reflection coefficient resulting from a simulated application of the method is used for a reconstruction of the scattering density profiles of absorptive non-magnetic media by inversion.Comment: 14 pages, 4 figures, reformulation of abstract, ref.12 added, typographical correction

Spin-polarized electron transport in ferromagnet/semiconductor heterostructures: Unification of ballistic and diffusive transport

A theory of spin-polarized electron transport in ferromagnet/semiconductor heterostructures, based on a unified semiclassical description of ballistic and diffusive transport in semiconductor structures, is developed. The aim is to provide a framework for studying the interplay of spin relaxation and transport mechanism in spintronic devices. A key element of the unified description of transport inside a (nondegenerate) semiconductor is the thermoballistic current consisting of electrons which move ballistically in the electric field arising from internal and external electrostatic potentials, and which are thermalized at randomly distributed equilibration points. The ballistic component in the unified description gives rise to discontinuities in the chemical potential at the boundaries of the semiconductor, which are related to the Sharvin interface conductance. By allowing spin relaxation to occur during the ballistic motion between the equilibration points, a thermoballistic spin-polarized current and density are constructed in terms of a spin transport function. An integral equation for this function is derived for arbitrary values of the momentum and spin relaxation lengths. For field-driven transport in a homogeneous semiconductor, the integral equation can be converted into a second-order differential equation that generalizes the standard spin drift-diffusion equation. The spin polarization in ferromagnet/semiconductor heterostructures is obtained by invoking continuity of the current spin polarization and matching the spin-resolved chemical potentials on the ferromagnet sides of the interfaces. Allowance is made for spin-selective interface resistances. Examples are considered which illustrate the effects of transport mechanism and electric field.Comment: 23 pages, 8 figures, REVTEX 4; minor corrections introduced; to appear in Phys. Rev.

Unbound exotic nuclei studied by transfer to the continuum reactions

In this paper we show that the theory of transfer reactions from bound to continuum states is well suited to extract structure information from data obtained by performing "spectroscopy in the continuum". The low energy unbound states of nuclei such as $^{10}$Li and $^{5}$He can be analyzed and the neutron-core interaction, necessary to describe the corresponding borromean nuclei $^{11}$Li and $^{6}$He can be determined in a semi-phenomenological way. An application to the study of $^{10}$Li is then discussed and it is shown that the scattering length for s-states at threshold can be obtained from the ratio of experimental and theoretical cross sections. The scattering single particle states of the system n+$^{9}$Li are obtained in a potential model. The corresponding S-matrix is used to calculate the transfer cross section as a function of the neutron continuum energy with respect to $^{9}$Li. Three different reactions are calculated $^{9}Li(d,p)^{10}Li$, $^{9}Li(^{9}Be,^{8}Be)^{10}Li$, $^{9}Li(^{13}C,^{12}C)^{10}Li$, to check the sensitivity of the results to the target used and in particular to the transfer matching conditions. Thus the sensitivity of the structure information extracted from experimental data on the reaction mechanism is assessed.Comment: 21 pages, 5 ps figures, accepted for publication on Nucl. Phys.

Generalized Drude model: Unification of ballistic and diffusive electron transport

For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean free path and arbitrary shape of the conduction band edge profile. Universal formulas are obtained for the current-voltage characteristic in the nondegenerate case and for the zero-bias conductance in the degenerate case, which describe in a transparent manner the interplay of ballistic and diffusive transport. The semiclassical approach is adopted, but quantum corrections allowing for tunneling are included. Examples are considered, in particular the case of chains of grains in polycrystalline or microcrystalline semiconductors with grain size comparable to, or smaller than, the mean free path. Substantial deviations of the results of the unified model from those of the ballistic thermionic-emission model and of the drift-diffusion model are found. The formulation of the model is one-dimensional, but it is argued that its results should not differ substantially from those of a fully three-dimensional treatment.Comment: 14 pages, 5 figures, REVTEX file, to appear in J. Phys.: Condens. Matte