arXiv2023
We study the electrothermal actuation of nanomechanical motion using a combination of numerical simulations and analytical solutions. The nanoelectrothermal actuator structure is a u-shaped gold nanoresistor that is patterned on the anchor of a doubly-clamped nanomechanical beam or a microcantilever resonator. This design has been used in recent experiments successfully. In our finite-element analysis (FEA) based model, our input is an ac current; we first calculate the temperature oscillations due to Joule heating using Ohm's Law and the heat equation; we then determine the thermally induced bending moment and the displacement profile of the beam by coupling the temperature field to Euler-Bernoulli beam theory with tension. Our model efficiently combines transient and frequency-domain analyses: we compute the temperature field using a transient approach and then impose this temperature field as a harmonic perturbation for determining the mechanical response in the frequency domain. This unique modeling method offers lower computational complexity and improved accuracy, and is faster than a fully transient FEA approach. Our dynamical model computes the temperature and displacement fields in time domain over a broad range of actuation frequencies and amplitudes. We validate the numerical results by directly comparing them with experimentally measured displacement amplitudes of NEMS beams around their eigenmodes in vacuum. Our model predicts a thermal time constant of 1.9 ns in vacuum for our particular structures, indicating that electrothermal actuation is efficient up to ~80 MHz. We also investigate the thermal response of the actuator when immersed in a variety of fluids.