Geometrical quasi-ballistic effects on thermal transport in nanostructured devices
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k Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA Department of electrical and computer engineering, Purdue University, West Lafayette, Indiana 47907, USA 3 Department of physics, Universitat Autònoma de Barcelona, Bellaterra 08193, Catalonia, Spain 4 Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5 R&D Staff Scientist, Imaging, Signals and Machine Learning, Tennessee 37831, USA § Sami Alajlouni and Albert Beardo contributed equally to this work. 2
© Tsinghua University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Received: 6 July 2020 / Revised: 17 September 2020 / Accepted: 21 September 2020
ABSTRACT We employ thermoreflectance thermal imaging to directly measure the steady-state two-dimensional (2D) temperature field generated by nanostructured heat sources deposited on silicon substrate with different geometrical configurations and characteristic sizes down to 400nm. The analysis of the results using Fourier’s law not only breaks down as size scales down, but it also fails to capture the impact of the geometry of the heat source. The substrate effective Fourier thermal conductivities fitted to wire-shaped and circular-shaped structures with identical characteristic lengths are found to display up to 40% mismatch. Remarkably, a hydrodynamic heat transport model reproduces the observed temperature fields for all device sizes and shapes using just intrinsic Si parameters, i.e., a geometry and size-independent thermal conductivity and nonlocal length scale. The hydrodynamic model provides insight into the observed thermal response and of the contradictory Fourier predictions. We discuss the substantial Silicon hydrodynamic behavior at room temperature and contrast it to InGaAs, which shows less hydrodynamic effects due to dominant phonon-impurity scattering.
KEYWORDS phonon hydrodynamics, nanoscale heat transfer, quasi-ballistic transport, silicon
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Introduction
Thermal conduction at the macroscale is well-explained by Fourier’s law. However, at the nanoscale, the diffusive prediction collapses [1–4]. In recent years, several experimental observations have reported such a situation for samples heated in regions with characteristic sizes in the submicron and nanoscale [5–10]. Due to its technological relevance, a typical case of study consists of metallic nanostructures deposited on a semiconductor substrate [2, 11, 12]. In this configuration, the metal regions are heated, and the temperature is measured while heat is released to the substrate. Some approaches use an anisotropic substrate thermal conductivity [8, 13] or add an effective thermal boundary resistance (TBR) between the heat source and the substrate [2, 11] to account for the non-diffusive transport displayed by these experiments. Such methods usually lead to unrealistic values for substrate anisotropy or TBR values that typically need to be modified for different heater sizes [11, 14]. The natural conclusion is that Fourier’s law is not suitable to describe thermal transport at the
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