In-situ comprehensive calibration of a tri-port nano-electro-mechanical device

TL;DR

This paper introduces a comprehensive in-situ calibration method for a tri-port nano-electro-mechanical device, enabling full characterization of its harmonic response and parameters through purely electrical measurements at cryogenic temperatures.

Contribution

The authors develop a novel experimental approach for in-situ calibration of a tri-port NEMS device, combining electrical, thermal, and mechanical measurements without disconnecting components.

Findings

Derived the non-linear capacitance function C(x)

Measured spring constant and mass of the mode

Validated the model with detailed electrical and thermal analysis

Abstract

We report on experiments performed in vacuum and at cryogenic temperatures on a tri-port nano-electro-mechanical (NEMS) device. One port is a very non-linear capacitive actuation, while the two others implement the magnetomotive scheme with a linear input force port and a (quasi-linear) output velocity port. We present an experimental method enabling a full characterization of the nanomechanical device harmonic response: the non-linear capacitance function $C(x)$ is derived, and the normal parameters $k$ and $m$ (spring constant and mass) of the mode under study are measured through a careful definition of the motion (in meters) and of the applied forces (in Newtons). These results are obtained with a series of purely electric measurements performed without disconnecting/reconnecting the device, and rely only on known DC properties of the circuit, making use of a thermometric property of the oscillator itself: we use the Young modulus of the coating metal as a thermometer, and the resistivity for Joule heating. The setup requires only three connecting lines without any particular matching, enabling the preservation of a high impedance NEMS environment even at MHz frequencies. The experimental data are fit to a detailed electrical and thermal model of the NEMS device, demonstrating a complete understanding of its dynamics. These methods are quite general and can be adapted (as a whole, or in parts) to a large variety of elecromechanical devices.