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; Patrick E Hopkins

doi:10.1038/s41467-024-53441-9

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

Nat Commun. 2024 Oct 24;15(1):9167. doi: 10.1038/s41467-024-53441-9.

Authors

Md Rafiqul Islam¹, Pravin Karna², John A Tomko³, Eric R Hoglund^{3

4}, Daniel M Hirt¹, Md Shafkat Bin Hoque¹, Saman Zare¹, Kiumars Aryana¹, Thomas W Pfeifer¹, Christopher Jezewski⁵, Ashutosh Giri², Colin D Landon⁶, Sean W King⁷, Patrick E Hopkins^{8

9

10}

Affiliations

¹ Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, 22904, USA.
² Department of Mechanical Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, 02881, USA.
³ Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA, 22904, USA.
⁴ Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, 37830, USA.
⁵ Components Research, Intel Corporation, Hillsboro, Oregon, OR, 97124, USA.
⁶ Logic Technology Development, Intel Corporation, Hillsboro, Oregon, OR, 97124, USA.
⁷ Supplier, Technology, and Industry Development, Intel Corporation, Hillsboro, Oregon, OR, 97124, USA.
⁸ Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, 22904, USA. phopkins@virginia.edu.
⁹ Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA, 22904, USA. phopkins@virginia.edu.
¹⁰ Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA. phopkins@virginia.edu.

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.

Abstract

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