We discuss a possible mechanism of the current instability in multi-gated structures with periodic modulation of the electron density in the device channel. In such structures, the plasma wave velocity is periodically modulated as well, and the stationary electric current may become unstable with respect to generation of the plasma oscillations. In the simplest model of periodically alternating stripes of the electron density with plasma wave velocities sa and sb, respectively (sa < sb), the instability occurs when the electron drift velocity approaches sa. For typical parameters, the plasma oscillation frequency can be tuned to be in the terahertz range of frequencies.
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At the first glance, a more simple realization of the device is possible. One can deplete the channel in regions a in such a way that u = Va = sa. In this case, the drift velocities in the sections b will be different and correspond to Va < sa in the sections with odd numbers (counted from the source) and Va > sa in the even sections. One can show, however, that the condition u < u* needed for instability is not satisfied for such a device.
Strictly speaking, the wave vector of a plasma wave (proportional to Ω/(sc – Vc)) diverges at the points, corresponding to Vc = sc = u. However, this singularity is cured by accounting for diffusion or finite viscosity, neglected in our theory. Here, for simplicity, we assume that the diffusion length (or analogous length related to finite viscosity) is larger than Lc. This assumption (together with assumption ) guarantees that regions c do not affect the BC between a and b.
