Investigating Thermal Transport in β-Ta: A Combined Noise and COMSOL Study Open Access

Abstract

This work investigates the thermal transport behavior of β-phase tantalum (β-Ta) at cryogenic temperatures, focusing on the distinct roles of the metallic leads and the substrate in heat dissipation. Using differential noise measurements, a low temperature thermal conductivity model of the form κ(T ) = aT + bT^3 was developed, capturing the combined electron and phonon contribution of heat into the leads. Importantly, we restricted our analysis to the thermal broadening region, where voltage bias VB is less than crossover voltage Vth, allowing us to treat all measured noise as thermal noise. However, the simple model for thermal conductivity through the leads breaks down at 2µm length scale, so exploring thermal transport through insulating substrate led us to COMSOL Simulation. To visualize dissipation pathways within the substrate, a COMSOL model incorporating Joule heating was implemented to compute the temperature distribution across the β-Ta strip, copper leads, and sapphire substrate. We further highlight the discrepancy between the simulated thermal noise and experimental value to discuss thermal transport within a bad metal β-Ta at nanoscale.

Table of Contents

1. Introduction

1.1 Motivation ...................................................... 1

1.2 Background .................................................... 2

1.2.1 Bad Metal ................................................ 2

1.2.2 Johnson-Nyquist Noise .......................... 3

1.2.3 Heat Conduction ................................... 5

1.2.4 Heat Dissipation ................................... 6

2. Experimental Work

2.1 Methods ........................................................ 8

2.2 Results and Discussion ................................. 10

3. COMSOL Simulation

3.1 Motivation .................................................... 13

3.2 Methods ...................................................... 14

3.3 Results and Discussion ................................. 15

3.3.1 Thermal Boundary Resistance .............. 15

3.3.2 COMSOL Simulation ............................ 15

3.3.3 Limitations and Future Work ................. 17

4. Conclusion 

A. Appendix

A.1 Full Derivation of Thermal Conductivity .............. 21

A.2 Processing LabVIEW Output for Noise Analysis .... 23

A.3 Thermal Conductivity Fitting Results for All Lengths .... 26

A.4 COMSOL Simulation ......................................... 27

Bibliography 

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Physics, Condensed Matter
Keyword	beta-Ta Noise Measurement COMSOL Nanowires Thermal Transport Bad Metal
Committee Chair / Thesis Advisor	Sergei Urazhdin, Emory University
Committee Members	Erin Bonning, Emory University Jed Brody, Emory University

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