Current Instability and Plasma Wave Generation in Ungated Two Dimensional Electron Layers

We show that the steady state with a dc current in ungated 2D electron gas might exhibit an instability related to asymmetrical boundary conditions, which is similar to the "shallow water" instability in the gated 2D electron gas. The mathematics of the problem corresponds to "deep water" solutions for plasma waves. In the ideal case, the boundary conditions should correspond to zero ac voltage at the source and zero ac current at the drain, similar to the conditions for instability in a field effect transistor. Such boundary conditions can be realized using several different device configurations. For similar device dimensions, the plasma wave generated in an ungated 2D device will have much higher frequency compared to that in gated devices.