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A new approach of using distributed transmission line analogy for solvingtransport equations for ballistic nanostructures is applied for solving thethree dimensional problem of the electron transport in gated ballisticnanostructures with periodically changing width. The structures with thevarying width allow for modulation of the electron drift velocity while keepingthe plasma velocity constant. We predict that in such structures biased by aconstant current, a periodic modulation of the electron drift velocity due thevarying width results in the instability of the plasma waves if the electrondrift velocity to plasma wave velocity ratio changes from below to above unity.The physics of such instability is similar to that of the sonic boom, but, inthe periodically modulated structures, this analog of the sonic boom isrepeated many times leading to a larger increment of the instability. Theconstant plasma velocity in the sections of different width leads to theresonant excitation of the unstable plasma modes with the varying bias current.This effect (that we refer to as the super plasmonic boom condition) results ina strong enhancement of the instability. The predicted instability involves theoscillating dipole charge carried by the plasma waves. The plasmons can beefficiently coupled to the terahertz (THz) electromagnetic radiation due to theperiodic geometry of the gated structure. Our estimates show that the analyzedinstability should enable powerful tunable terahertz electronic sources.

Current driven "plasmonic boom" instability in three-dimensional gated periodic ballistic nanostructures