Evaluating size effects on the thermal conductivity and electron-phonon scattering rates of copper thin films for experimental validation of Matthiessen’s rule

Md. Rafiqul Islam, Pravin Karna, John A. Tomko, Eric R. Hoglund, Daniel M. Hirt, Md Shafkat Bin Hoque, Saman Zare, Kiumars Aryana, Thomas W. Pfeifer, Christopher Jezewski, Ashutosh Giri, Colin D. Landon, Sean W. King and Patrick E. Hopkins ()
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Md. Rafiqul Islam: University of Virginia
Pravin Karna: University of Rhode Island
John A. Tomko: University of Virginia
Eric R. Hoglund: University of Virginia
Daniel M. Hirt: University of Virginia
Md Shafkat Bin Hoque: University of Virginia
Saman Zare: University of Virginia
Kiumars Aryana: University of Virginia
Thomas W. Pfeifer: University of Virginia
Christopher Jezewski: Hillsboro
Ashutosh Giri: University of Rhode Island
Colin D. Landon: Hillsboro
Sean W. King: Hillsboro
Patrick E. Hopkins: University of Virginia

Nature Communications, 2024, vol. 15, issue 1, 1-9

Abstract: Abstract As metallic nanostructures shrink towards the size of the electronic mean free path, thermal conductivity decreases due to increased electronic scattering rates. Matthiessen’s rule is commonly applied to assess changes in electron scattering rates, although this rule has not been validated experimentally at typical operating temperatures for most of the electronic systems (e.g., near room temperature). In this study, we experimentally evaluate the validity of Matthiessen’s rule in determining the thermal conductivity of thin metal films by measuring the in-plane thermal conductivity and electronic scattering rates of copper (Cu) films with varying thicknesses (27 nm — 5 µm), microstructures, and grain boundary segregation. Comparing total electron scattering rates measured with infrared ellipsometry to infrared ultrafast pump-probe measurements, we find that the electron-phonon coupling factor is independent of film thickness, whereas the total electronic scattering rate increases with decreasing film thickness. Our findings provide experimental validation of Matthiessen’s rule for electron transport in thin metal films at room temperature and also introduce an approach to discern critical heat transfer processes in thin metal interconnects, which holds significance for the advancement of future CMOS technology.

Date: 2024
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DOI: 10.1038/s41467-024-53441-9

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