Plasma-Wave Amplification in Bismuth

The amplification properties of Bi at 4.2°K with parallel applied current and magnetic field are demontrated experimentally and compared with theory. The threshold for low-frequency wave propagation requires a minimum critical ratio of current to magnetic field corresponding to a waveguide cutoff independent of frequency. A parameter $\Delta$, based on the average difference of hole- and electron-mobility anisotropy, affects the spatial growth of these waves in direct proportion to $\left|\Delta \right|$. For samples oriented to minimize $\left|\Delta \right|$, studies of waveguide cutoff show that collision damping in the body of the guide, as expressed by the dielectric tensor derived by Misawa, is sufficient to account for the observed details, and that simple metallic boundary conditions appear to be sufficient to account for the boundary field matching. Crystal orientations for optimum gain (maximum $\left|\Delta \right|$), namely, 8° off the $Z$ axis along a $-Y$ direction, exhibit gain in approximate quantitative agreement with theory. Also predicted and observed is an absolute instability oscillation occurring at currents greater than twice waveguide cutoff. In the following, three side effects are also described: (1) a depressing effect on the gain by the azimuthal magnetic field of the current and a curved current-voltage relation resulting from self-magnetoresistance; (2) additional pronounced nonlinearities of the current-voltage relation due to phonon emission when the electron-drift velocity exceeds the lattice-sound velocity, and an accompanying enhancement of amplification by a mechanism that can be made plausible; (3) feedback oscillation exhibiting the properties of the gain mechanism. The maximum frequency for amplification was about 100 kHz. Higher frequency limits have been explored, but only by extrapolation of the theory for Bi, because the high carrier mobilities make that material about the best available.