Comparative study of spin injection into metals and semiconductors

Abstract

We present an analysis of spin injection efficiency that is of general application and relevant to a wide range of spin-electronic devices. By applying simple band structure ideas to a single interface between a metallic ferromagnet and a three-dimensional semiconductor, two conflicting figures of merit are identified - spin accumulation and polarization of injected current - and their validity to the analysis of different device types is discussed. The injected spin accumulation is smaller than the all-metal injection case by a factor (m*/me)3/2(kT/EF)1/2e^εD/kT. Moreover, the injected spin current at the interface is reduced by the factor (m*/me)3/2(kT/EF)(γS/γF) e^εD/kT, where γ for a particular material is the square root of its momentum scattering to spin-flip scattering ratio, m* and me are the effective and free masses, respectively, and εD is the donor binding energy. These results are consequent on the boundary condition that the spin channel electrochemical potentials are continuous at the interface. By inserting an insulating tunnel barrier between the ferromagnet and the semiconductor, not only is this boundary condition removed and the spin polarization of the injected current restored to the all-metal magnitude, but also the spin accumulations in the metal and the semiconductor even have opposite signs. This implies that thin or discontinuous tunnel barriers have the worst spin injection efficiency of any configuration. We finally note that for injected spin current into metals with polarization approaching 100%, the Fermi surface is polarized to a depth which exceeds the equilibrium carrier depth by a factor lSD/λ, hence >>1.

Spin electronics a review

“…Recent theories conclude that spin-tunnel injection is efficient because it releases us from having to satisfy the boundary conditions on electrochemical potential continuity and, in so doing, completely changes the physics of the problem. However, in contrast to popular thinking, Borges et al [91] point out that, in certain circumstances, the tunnelling configuration is capable of delivering the worst spin injection of all due to the reversal of the chemical potential divergences either side of the tunnel barrier. This situation arises for the case of very thin or discontinuous tunnel barriers which is precisely the case expected if realization of a metal semiconductor direct contact is marred by oxidation or other surface contamination.…”

“…Experiments have been performed which purport to show spin injection into two-dimensional semiconductors [86] though their interpretation is considered ambiguous in some quarters [87][88][89]. More recently, theoretical work has appeared [90,91] which explains why direct injection into two-dimensional semiconductors is expected to be disappointing.…”

“…The fundamental problem is seen in figure 24 where in the absence of interface scattering the electrochemical potentials (and hence µ) are continuous at the interface. This means that the spin-accumulation density (which scales as the pseudodensity of states [91]) is very small in the semiconductor: hence also is the spin-polarized current through the interface which feeds it.…”

Silicon spin diffusion transistor: materials, physics and device characteristics

“…Nonoptimal electrode geometry: Recent modelling [28][29][30] indicates that the emitter efficiency can be dramatically improved by implementing spin injection into a base with length (distance between the collector and base contacts) much greater than the thickness (distance between the emitter and collector contacts) and also by interposing the collector between the emitter and base contact. Tuning of the barrier resistances to optimise conduction in the region of positive current gain is necessary.…”

The discovery, development and future of GMR: The Nobel Prize 2007

“…The difficulties arise principally because most ferromagnetic material are metals with a considerably lower electrical resistance than a semiconductor. There are various materials solutions to this problem: develop a room temperature magnetic semiconductor thereby removing the material missmatch [132][133][134]; use a ferromagnetic oxide material such as Fe 3 O 4 as the ferromagnetic material, thereby reducing the impedance missmatch [135,136] or insert a Schottky or tunnel barrier at the interface between the ferromagnet and the semiconductor [137][138][139]. All these approaches have their merits and are being actively pursued.…”