Quasiballistic heat conduction, in which some phonons propagate ballisticallyover a thermal gradient, has recently become of intense interest. Most worksreport that the thermal resistance associated with nanoscale heat sources isfar larger than predicted by Fourier's law, however, recent experiments showthat in certain cases the difference is negligible despite the heaters beingfar smaller than phonon mean free paths. In this work, we examine how thermalresistance depends on the heater geometry using analytical solutions of theBoltzmann equation. We show that the spatial frequencies of the heater patternplay the key role in setting the thermal resistance rather than any singlegeometric parameter, and that for many geometries the thermal resistance in thequasiballistic regime is no different than the Fourier prediction. We alsodemonstrate that the spectral distribution of the heat source also plays amajor role in the resulting transport, unlike in the diffusion regime. Our workprovides an intuitive link between the heater geometry, spectral heatingdistribution, and the effective thermal resistance in the quasiballisticregime, a finding that could impact strategies for thermal management inelectronics and other applications.
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