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

Abstract

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 ${\ensuremath{\omega}}_{c}\ensuremath{\tau}>3.5$ (where ${\ensuremath{\omega}}_{c}$ is the electron cyclotron frequency and $\ensuremath{\tau}$ 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 ${\ensuremath{\omega}}_{c}\ensuremath{\tau}$, ${D}_{\mathrm{excess}}$ is within a factor of 2 of the Bohm value $\frac{\mathrm{kT}}{16eB}$ ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.