Effect of a Magnetic Field on the Diffusion of an Electron-Hole Plasma in Germanium

The diffusion of an optically injected electron-hole plasma parallel and perpendicular to an applied magnetic field has been studied in germanium. The density gradient within the crystal has been measured directly by an infrared-beam-absorption technique. Diffusion measurements made parallel to the magnetic field are adequately explained by the theory. For values of ${\omega }_c\tau >3.5\mathrm{}$ (where ${\omega }_c$ is the electron cyclotron frequency and $\tau$ is the electron scattering time with the lattice), the diffusion across the magnetic field is more rapid than that predicted by a theory that takes into account the anisotropic magnetoconductive properties of germanium. If we express the observed diffusion coefficient as the sum of the computed collisional coefficient plus a term $D_{\mathrm{excess}}$ representing the additional diffusion, we find that at the largest achievable values of ${\omega }_c\tau$, $D_{\mathrm{excess}}$ is within a factor of 2 of the Bohm value $\frac{\mathrm{kT}}{16eB}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$.