Impact of Transduction Scaling Laws on Nanoelectromechanical Systems

We study the electromechanical transduction in nanoelectromechanical actuators and show that the differences in scaling laws for electrical and mechanical effects lead to an overall nontrivial miniaturization behavior. In particular, the previously neglected fringing fields considerably increase electrical forces and improve the stability of nanoscale actuators. This shows that electrostatics does not pose any limitations to the miniaturization of electromechanical systems; in fact, in several respects, nanosystems outperform their microscale counterparts. As a specific example, we consider in-plane actuation of ultrathin slabs and show that devices consisting of a few layers of graphene are feasible, implying that electromechanical resonators operating beyond 40 GHz are possible with currently available technology.

Figure 1

3D geometries and 2D electric fields of NEMS electrostatic actuators. Electrostatic actuators consisting of (a) rigid and (b) elastic beams exhibit (c) electric field lines, which combine the characteristics of the fields of a (d) parallel plate and (e) coplanar strips. (f) The displacement of elastic beams calculated with the full electric field (solid) is significantly larger than in the parallel-plate approximation (dashed).

Figure 2

Displacement and instability in parallel-beams transduction. (a) Normalised pull-in displacement of a rigid parallel-beam actuator [Fig. 1] for different ratios of height to initial gap. The parallel-plate approximation is valid for electrostatic actuators with high aspect ratios and the normalized pull-in distance $y_p/g_0$ approaches $1/3$ for large beam heights. Inset: Pull-in voltage for different height to gap and width to gap ratios. The spring constant is $k=0.5{\text{Nm}}^{-1}$ for all widths and heights. The beam width has a significant contribution to the pull-in voltage. (b) Stable (solid) and unstable (dashed) equilibrium curves for different ratios of height to initial gap, $h/g_0$, and $w=g_0$.

Figure 3

Normalised pull-in displacement of a coplanar strip actuator for different ratios of width to initial gap. The system corresponds to a parallel-beam actuator of zero height with a cross section shown in Fig. 1. Inset: stable (solid) and unstable (dashed) equilibrium curves for different strip width to initial gap ratios. The actuation range is greater than that of a parallel-plate actuator due to the scaling of the fringing forces.

Figure 4

Electric fields and capacitances of comb-drive actuators. (a) Illustration of a comb-drive actuator. (b) Selected field lines for a unit cell. (c) Capacitance of a unit cell as a function of finger overlap for a near unity aspect ratio ($h=260\mathrm{nm}$) as well as for nearly flat slabs ($h=5\mathrm{nm}$). The full 3D capacitance is higher than its 2D approximation as it includes the extra capacitance of the tip fields $E_f$ and the global fields $E_g$, but it has a lower slope because this extra capacitance has a negative contribution to the force. This capacitance does not change the linear behavior of the actuator that persists in the ultrathin membrane regime.