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

An alternative approach of using a distributed transmission line analogy for solving transport equations for ballistic nanostructures is applied for solving the three-dimensional problem of electron transport in gated ballistic nanostructures with periodically changing width. The structures with varying width allow for modulation of the electron drift velocity while keeping the plasma velocity constant. We predict that in such structures biased by a constant current, a periodic modulation of the electron drift velocity due to the varying width results in the instability of the plasma waves if the electron drift 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, in the periodically modulated structures, this analog of the sonic boom is repeated many times leading to a larger increment of the instability. The constant plasma velocity in the sections of different width leads to resonant excitation of the unstable plasma modes with varying bias current. This effect (that we refer to as the superplasmonic boom condition) results in a strong enhancement of the instability. The predicted instability involves the oscillating dipole charge carried by the plasma waves. The plasmons can be efficiently coupled to the terahertz electromagnetic radiation due to the periodic geometry of the gated structure. Our estimates show that the analyzed instability should enable powerful tunable terahertz electronic sources.

Figure 1

Schematic diagram of the 2D transistor structure with modulated width.

Figure 2

First three quantized plasmonic levels in the noninteracting plasma cavities formed in strips 1 (${\omega }_{0,p}^{\left(1\right)}$, red lines) and strips 2 (${\omega }_{0,m}^{\left(2\right)}$, blue lines) as a function of the electron drift velocity in strips 1. Open (solid) circles indicate stable (unstable) transparency points. Vertical dashed lines marked with red arrow correspond to the super-resonance condition.

Figure 3

Energy band spectrum of the drifting plasmonic crystal when the electron drift velocity in both strips 1 and 2 is less than the plasma wave velocity: $v_{01},v_{02}<v_p$. Here $v_{01}=0.43v_p,v_{02}=0.1v_{01}$. The two lowest stable plasmonic bands formed due to the resonant coupling of the quantized plasmonic levels in strips 1 (${\omega }_m^{\left(1\right)}$) and strips 2 (${\omega }_m^{\left(2\right)}$) are shown. Stable bands ${\omega }_{00}^{(\pm )}$ correspond to the lattice acoustic plasmon as described in the text.

Figure 4

Energy band spectrum of the drifting plasmonic crystal when the electron drift velocity is within the instability range: $v_{02}<v_p<v_{01}$. Here $v_{01}=1.12v_p,v_{02}=0.1v_{01}$. (a) Plasmonic band frequencies in the stable bands (${\omega }_m^{\left(1\right)}$, solid black lines) and unstable bands (${\omega }_{mp}^{(\pm )}$, red circles and blue squares); (b) instability increments in the unstable plasmonic bands.

Figure 5

Totally unstable energy band spectrum of the drifting plasmonic crystal at $v_{01}=1.41v_p,v_{02}=0.1v_{01}$ corresponding to the resonant coupling of all quantized plasmonic levels in strips 1 and 2. The first four unstable bands are shown. (a) Plasmonic band frequencies; (b) instability increments.

Figure 6

Energy band spectrum of the drifting plasmonic crystal at the electron drift velocity within the instability range: $v_{01}=1.71v_p,v_{02}=0.1v_{01}$. (a) Plasmonic band frequencies in the stable bands (solid black lines) and unstable bands (red circles and blue squares); (b) Instability increments in the unstable bands. Inset: the ${\omega }_{12}^{(\pm )}$ unstable band at $v_{01}=1.65v_p$ showing the evolution of the unstable band with the changing drift velocity as described in the text.