Comparative study of spin injection into metals and semiconductors

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* /m(e))(3/2)(kT/E-F)(1/2)e(epsilonD/kT). Moreover, the injected spin current at the interface is reduced by the factor (m*/m(e))(3/2)(kT/E-F)(gamma(S)/gamma(F))e(epsilonD/kT), where gamma for a particular material is the square root of its momentum scattering to spin-flip scattering ratio, m* and in, are the effective and free masses, respectively, and epsilon(D) 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 l(SD)/lambda hence much greater than1.