The motion and persistence of inhomogeneous electronic distributions
are central to the electronic technologies based on semiconductors.
Recently a broader category of possible disturbances, namely those
involving inhomogeneous spin distributions in doped semiconductors,
have been shown to exhibit long lifetimes (>100 ns) and anomalously
high diffusion rates. In addition to allowing new probes of nonequilibrium
phase coherence, this behavior indicates the potential of a new
electronic technology relying on spin. A crucial requirement of
this new technology, however, is the clarification of the transport
properties of inhomogeneous spin distributions.
A full understanding is also desirable of the relationship between the physical effects driving semiconductor spin electronics and those driving the mature area of metallic spin electronics, which has produced advances in magnetic read heads and non-volatile memory.
We have considered the properties of doped and undoped semiconductors which are unpolarized in equilibrium but have a localized perturbation of spin-polarized carriers. Ineffective screening in semiconductors requires local variations in the conduction electron density (Dn(x)) to be balanced by a local change in the valence hole density (Dp(x)). Exceptions require large space-charge fields, such as occur when donor or acceptor concentrations vary substantially. In metals, by contrast, local charge density variations are screened out on length scales of Angstroms. Shown below is an example of the space-charge field generated during packet motion.
In the presence of the space charge field, both the electrons and the holes move. Because this is an n-doped system, however, the conductivity of the electrons greatly exceeds the conductivity of the holes. Thus the electrons move much more towards the holes than vice versa. As a result the packet moves in the direction the external electric field pulls the holes (or electrons in a p-doped system). Below are shown charge and spin packets in undoped systems. in order to satisfy the approximate local charge neutrality, the packets must incorporate both electrons and holes.
In a doped semiconductor, however, there is a substantial background of conduction electrons. Thus one can create a spin packet through a spin imbalance in the conduction band (shown on the right below). This single-band spin packet does not drag a local inhomogeneous hole density with it, and thus its mobility and diffusion properties are very different from those of a spin packet in the undoped semiconductor, and also very different from those of a charge packet in the doped semiconductor.
Shown below is the ratio of the diffusion constant to the mobility for spin packets in doped GaAs versus that ratio for charge packets. The enhancement of the diffusion constant for spin packets at these low densities occurs because the electrons become degenerate at very low density at this temperature. The factor of 12 enhancement at a carrier density of 1016 cm-3 corresponds roughly to that seen by Kikkawa and Awschalom [Nature 397, 139 (1999)].
We have also described spin diffusion in spin-polarized semiconductors. The diffusion and mobility of spin packets are found to differ by orders of magnitude depending on whether they are polarized parallel or antiparallel to the spin polarization of the equlibrium carriers. This work may assist in understanding spin transport within metallic ferromagnetic semiconductors, such as GaMnAs, and semimagnetic semiconductors, such as BeMnZnSe. Both the p-doped GaMnAs and the n-doped BeMnZnSe have been used in spin-dependent devices. Below are shown spin packets polarized parallel and antiparallel to the polarized background in BeMnZnSe. The antiparallel spin packet is a single-band majority carrier (electron) packet, whereas the parallel spin packet involves both electrons and holes.
The parallel packet will have a mobility characterized by the holes, whereas the antiparallel packet will have a mobility characterized by the electrons (differing by over an order of magnitude). Below are shown the ratio of the diffusion to the mobility for parallel and antiparallel packets in BeMnZnSe
These differences in diffusion and mobility are expected to play a major role in the dynamics of spin populations in semiconductor materials. In particular they should play a role in the behavior of carrier motion in the presence of inhomogeneous spin populations. These inhomogeneous spin populations will also involve inhomogeneous charge distributions, and thus space charge fields.