Abstract
We predict instability of the steady state with a direct current for an ungated two-dimensional (2D) electron layer. This instability caused by the current flow is similar to the "shallow water" instability in the gated 2D electron gas [see M. Dyakonov and M. S. Shur, Phys. Rev. Lett. 71, 2465 (1993)]. The mathematics of the problem correspond to "deep water" solutions for plasma waves. Just like in the "shallow water" case, this instability occurs when the boundary conditions correspond to zero ac voltage at the source and zero ac current at the drain. Such boundary conditions can be realized using either an external circuit or a depleted region at the drain. For the same device dimensions and electron mobility, the plasma wave generated in an ungated 2D device has a much higher frequency and, as a consequence, a much higher resonance quality factor, which makes the ungated devices promising for applications in resonant terahertz detectors.