Oscillatory bistability of real-space transfer in semiconductor heterostructures

Charge transport parallel to the layers of a modulation-doped GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructure is studied theoretically. The heating of electrons by the applied electric field leads to real-space transfer of electrons from the GaAs into the adjacent ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As layer. For sufficiently large dc bias, spontaneous periodic 100-GHz current oscillations, and bistability and hysteretic switching transitions between oscillatory and stationary states are predicted. We present a detailed investigation of complex bifurcation scenarios as a function of the bias voltage ${\mathit{U}}_0$ and the load resistance ${\mathit{R}}_{\mathit{L}}$. For large ${\mathit{R}}_{\mathit{L}}$ subcritical Hopf bifurcations and global bifurcations of limit cycles are displayed.