Diffraction phase microscopy imaging and multi-physics modeling of the nanoscale thermal expansion of a suspended resistor

Xiaozhen Wang,Jian-Ming Jin,Xin Yu,Lynford L Goddard,Tianjian Lu

doi:10.1038/s41598-017-04803-5

Abstract

We studied the nanoscale thermal expansion of a suspended resistor both theoretically and experimentally and obtained consistent results. In the theoretical analysis, we used a three-dimensional coupled electrical-thermal-mechanical simulation and obtained the temperature and displacement field of the suspended resistor under a direct current (DC) input voltage. In the experiment, we recorded a sequence of images of the axial thermal expansion of the central bridge region of the suspended resistor at a rate of 1.8 frames/s by using epi-illumination diffraction phase microscopy (epi-DPM). This method accurately measured nanometer level relative height changes of the resistor in a temporally and spatially resolved manner. Upon application of a 2 V step in voltage, the resistor exhibited a steady-state increase in resistance of 1.14 Ω and in relative height of 3.5 nm, which agreed reasonably well with the predicted values of 1.08 Ω and 4.4 nm, respectively.

Highlights

The dynamics of thermal-mechanical systems has received much attention in many different fields, such as physics, chemistry, and engineering
Huber and co-workers investigated a 15 nm transient thermal expansion of a scanning tunneling microscope (STM) tip based on a combination of an atomic force microscope (AFM) and a laser as an external heating source[12]
A group led by Meriles and Riedo used a nitrogen-vacancy center in diamond attached to the apex of a silicon thermal tip as a local scanning temperature sensor[13]

Summary

Introduction

The dynamics of thermal-mechanical systems has received much attention in many different fields, such as physics, chemistry, and engineering. A group led by Meriles and Riedo used a nitrogen-vacancy center in diamond attached to the apex of a silicon thermal tip as a local scanning temperature sensor[13] They obtained nanometer-resolved thermal conductivity maps by combining magnetic resonance and AFM. We applied epi-DPM to characterize a suspended metal resistive bridge undergoing thermal expansion, with nanometer height measurement accuracy. This particular structure is interesting because of its application as a heating element for non-contact tuning of photonic membrane devices[26, 27] and for actuating MEMS devices[28, 29]. Despite the 96 GB of RAM available on our workstation, we were unsuccessful in performing the simulation using COMSOL Multiphysics because of the problem size

Methods

Results

Conclusion