Analytical framework for interpreting thermoreflectance measurements of nanoline gratings under finite spot illumination
Abstract
A frequency-domain thermoreflectance (FDTR)-based technique is presented to measure the effective thermal properties of a material stack whose surface is patterned with metallic nanoline gratings that are heated and probed by lasers. An analytical heat diffusion model is derived for predicting the FDTR phase response that incorporates a finite laser spot radius with a Gaussian intensity profile for the pump and probe lasers, as well as the dimensions of the nanoline grating. The model is validated by comparing with measurements of Au nanoline gratings, with widths ranging from 100 to 1000 nm, fabricated on a-SiO2 and c-sapphire substrates. Due to the short phonon mean free paths (MFPs) in these substrates, thermal transport remains in the diffusive regime for the whole range of nanoline widths. The model and the measurement show excellent agreement across different laser spot radii and nanoline widths, with a bulk thermal conductivity value of c-sapphire and the thermal boundary conductances at the Au-Cr/a-SiO2 and Au-Cr/c-sapphire interfaces comparable to our prior measurements and the literature. The validated model will serve as a robust baseline for extending this method to measure effective thermal conductivity as a function of the heater size. This approach is particularly relevant for materials where non-diffusive thermal transport regimes enable probing phonon MFP dependent contributions to the thermal conductivity.
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BibTeX
@misc{pathak2026analytical,
title = {{Analytical framework for interpreting thermoreflectance measurements of nanoline gratings under finite spot illumination}},
author = {Abhishek Pathak and Seungwon Park and Shubham Deshmukh and Alan J. H. McGaughey and Jonathan A. Malen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37957},
eprint = {2610.37957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37957},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytical framework for interpreting thermoreflectance measurements of nanoline gratings under finite spot illumination
AU - Abhishek Pathak
AU - Seungwon Park
AU - Shubham Deshmukh
AU - Alan J. H. McGaughey
AU - Jonathan A. Malen
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37957
UR - https://arxiv.org/abs/2610.37957
AB - A frequency-domain thermoreflectance (FDTR)-based technique is presented to measure the effective thermal properties of a material stack whose surface is patterned with metallic nanoline gratings that are heated and probed by lasers. An analytical heat diffusion model is derived for predicting the FDTR phase response that incorporates a finite laser spot radius with a Gaussian intensity profile for the pump and probe lasers, as well as the dimensions of the nanoline grating. The model is validated by comparing with measurements of Au nanoline gratings, with widths ranging from 100 to 1000 nm, fabricated on a-SiO_2 and c-sapphire substrates. Due to the short phonon mean free paths (MFPs) in these substrates, thermal transport remains in the diffusive regime for the whole range of nanoline widths. The model and the measurement show excellent agreement across different laser spot radii and nanoline widths, with a bulk thermal conductivity value of c-sapphire and the thermal boundary conductances at the Au-Cr/a-SiO_2 and Au-Cr/c-sapphire interfaces comparable to our prior measurements and the literature. The validated model will serve as a robust baseline for extending this method to measure effective thermal conductivity as a function of the heater size. This approach is particularly relevant for materials where non-diffusive thermal transport regimes enable probing phonon MFP dependent contributions to the thermal conductivity.
ER -