Investigation on a nanomechanical transistor

Abstract

In this paper, we propose the mathematical model of a novel device, the nanomechanical transistor, able to control a current through a small drive voltage. The novelty of the device relies in its mechanical working principle where nanopillars vibrate between electrodes under a self-excitation regime which provides a continuative electric charge transportation. The dynamics of the investigated system involves electromechanical phenomena with the addition of quantum effects due to the electron tunneling of charges from pillars to electrodes. The theory here presented is an attempt to build a general model for those multiphysics phenomena (electrical-mechanical with presence of quantum effects) frequently met in nanotechnology that do not fit yet into a systematic frame.

Appendix

The quantum tunneling occurring between two electrodes at nanometer distance can be estimated by introducing an equivalent, non-linear conductance term G _t . Different closed-form relations exist in literature to calculate G _t . In general, given the geometry of the system, the tunneling conductance depends on both the distance d and the potential difference V between the electrodes. In this article we use the Simmons formulae [16], referred to a rectangular barrier with image forces included. Therefore:

(29)

where S=40 nm² is the surface exposed to tunnel, φ ₀=5 eV the conductor working function, m _el the electron mass, and:

Notice that (29) is valid when the potential barrier is above the Fermi level. When the distance between electrodes is reduced over a certain threshold, the current flows unimpeded in the conduction band of the insulator. To include this condition in the model for G _t , we used the saturation value G _c =γ _c S, with γ _c =10¹¹ S/m², representing the contact conductance. Consequently, the model used in this article takes into account both charge transfer mechanisms: quantum tunneling and contact conduction. Application of Eq. (29) to the present model produces:

$$ \everymath{\displaystyle} \begin{array}{@{}llll} G_{dp}=G_{t}(g-r+x,V_{d}-V_{p}) \cr\noalign{\vspace{3pt}} G_{ps}=G_{t}(g-r-x,V_{p}-V_{s}) \cr\noalign{\vspace{3pt}} G_{ds}=G_{t}(2g,V_{d}-V_{s}) \end{array} $$

(30)