Two-level model of longitudinal magnetic field-induced current instability and chaos inn-GaAs

Abstract

We extend our previous application of the two-impurity-level model to interpret the cross-over current instability for a $n$-GaAs semiconductor with planar ohmic contacts under an external magnetic field $B$ longitudinal to the applied dc bias. The previous assumption of spatial homogeneity in current flow direction as well as previous considerations of the Landau level shifts for the conduction band electrons and the electron mobility with the field and the carrier electron temperature dependence are all retained. In addition, we further add in a phenomenological effective magnetoresistance $h$ factor from the generation-annihilation dynamic of the filamentary current and the carrier temperature dependence of the impact ionization coefficient from the ground level ${X}_{1}$ and that of the capture coefficient ${T}_{1}^{s}$ in the generation-recombination processes. Increasing the magnetic field above a critical magnitude in the post-breakdown region of the S-shaped current density-field characteristic, we are able to find the system bifurcating to chaos via several period-doubling routes at various bias voltages. Our numerical results are consistent with those observed experimentally by Aoki, Kawase, Yamamoto, and Mugibayahi [J. Phys. Soc. Jpn. 59, 20 (1990)].