Realizing Broadbands of Strong Nonlinear Coupling in Nanoelectromechanical Electron Shuttles

We demonstrate the transition of a coupled electron shuttle from a stable to a strongly nonlinear response at room temperature. Within this transition we observe the coupled shuttle’s response to change from Coulomb controlled to conventional field emission. This parametric process is fully reversible and occurs within a broad frequency range. In combination, the large current and wide frequency band enable energy harvesting applications. The experimental data and the numerical calculations both indicate that the source of the nonlinearity is given by the electromechanical coupling of electron shuttling.

Figure 1

(a) Two coupled nanomechanical shuttles: the metallic islands on top provide the conduction path for the electrons between source $S$ and drain $D$ contacts. (b) The flexural modes drive a mechanically assisted direct current—the shuttling current—where the center of mass remains at rest. (c) Circuit diagram with the mechanically tunable tunneling barriers between the leads and electron islands (see text for details).

Figure 2

(a) Output current with external rf signal of 0, 5, 10, and 15 dBm. (b) $IV$ characteristics at three different frequencies 68 MHz (square), 72 MHz (dot), and 92 MHz (triangle). The inset shows a steplike current in the low bias limit due to the mechanically enhanced Coulomb blockade (see text).

Figure 3

Output direct currents with different external rf signal powers: (a) 3.1, 4, and 5.4 dBm superimposed on a bias voltage of $-100\mathrm{mV}$. (b) The conventional periodic responses are recovered above a certain rf signal power level of $\sim 6\mathrm{dBm}$. (c) Color-scale graph of output current via coupled nanoscale pendula in the frequency domain with continuous ac power $P$ increase. Thin dashed lines indicate the line plots shown in (a) and (b). Note that the scale is logarithmic for direct current larger than 10 pA, and linear otherwise.

Figure 4

Bifurcation diagram showing unstable regions where self-sustained oscillations are expected. The two upper insets show corresponding phase portraits: In the pitchfork bifurcation (red or dark gray) the origin is unstable, whereas in the green (gray) region, the attractor at the origin coexists with another two nontrivial stable nodes. The lower inset shows the amplitude $x_m$ of the relative deflection for the stable solution along the black broken trace, $\alpha \simeq 3\times {10}^{-3}$.