Modified ballistic–diffusive equations for obtaining phonon mean free path spectrum from ballistic thermal resistance: I. Introduction and validation of the equations

References

• G. Chen, “Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles,” J. Heat Transfer., vol. 118, no. 3, pp. 539–545, Aug. 1996. DOI: 10.1115/1.2822665.
   Web of Science ®Google Scholar
• S. Chu and A. Majumdar, “Opportunities and challenges for a sustainable energy future,” (in English),” Nature, vol. 488, no. 7411, pp. 294–303, Aug. 16 2012. DOI: 10.1038/nature11475.
   PubMed Web of Science ®Google Scholar
• M. N. Luckyanova, “Coherent phonon heat conduction in superlattices,” Science, vol. 338, pp. 936–939, 2012. DOI:10.1126/science.1225549.
   PubMed Web of Science ®Google Scholar
• C. Dames, “Thermal materials: pulling together to control heat flow,” Nat. Nanotech., vol. 7, pp. 82–83, 2012. DOI:10.1038/nnano.2012.4.
   PubMed Web of Science ®Google Scholar
• D. J. Singh, “Nanostructuring and more,” Nat. Mater., vol. 7, pp. 616–617, 2008. DOI:10.1038/nmat2243.
   PubMed Web of Science ®Google Scholar
• E. Pop, “Energy dissipation and transport in nanoscale devices,” Nano Res, vol. 3, no. 3, pp. 147–169, Mar. 2010. DOI: 10.1007/s12274-010-1019-z.
   Web of Science ®Google Scholar
• E. Pop, S. Sinha, and K. E. Goodson, “Heat generation and transport in nanometer-scale transistors,” Proc. IEEE., vol. 94, pp. 1587–1601, 2006. DOI:10.1109/JPROC.2006.879794.
   Web of Science ®Google Scholar
• R. J. Mehta, “A new class of doped nanobulk high-figure-of-merit thermoelectrics by scalable bottom-up assembly,” Nat. Mater., vol. 11, no. 3, pp. 233–240, Mar. 2012. DOI: 10.1038/nmat3213.
   PubMed Web of Science ®Google Scholar
• A. Majumdar, “Materials science. Thermoelectricity in semiconductor nanostructures,” Science, vol. 303, pp. 777–778, 2004. DOI:10.1126/science.1093164.
   PubMed Web of Science ®Google Scholar
• L. E. Bell, “Cooling, heating, generating power, and recovering waste heat with thermoelectric systems,” Science, vol. 321, pp. 1457–1461, 2008. DOI:10.1126/science.1158899.
   PubMed Web of Science ®Google Scholar
• B. Poudel, “High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys,” Science, vol. 320, pp. 634–638, 2008. DOI:10.1126/science.1156446.
   PubMed Web of Science ®Google Scholar
• K. Biswas, “High-performance bulk thermoelectrics with all-scale hierarchical architectures,” Nature, vol. 489, pp. 414–418, 2012. DOI:10.1038/nature11439.
   PubMed Web of Science ®Google Scholar
• A. I. Boukai, “Silicon nanowires as efficient thermoelectric materials,” Nature, vol. 451, pp. 168–171, 2008. DOI:10.1038/nature06458.
   PubMed Web of Science ®Google Scholar
• M. S. Dresselhaus, “New directions for low-dimensional thermoelectric materials,” Adv. Mater., vol. 19, pp. 1043–1053, 2007. DOI:10.1002/adma.200600527.
   Web of Science ®Google Scholar
• J. P. Heremans, M. S. Dresselhaus, L. E. Bell, and D. T. Morelli, “When thermoelectrics reached the nanoscale,” Nat. Nanotech., vol. 8, pp. 471–473, 2013. DOI:10.1038/nnano.2013.129.
   PubMed Web of Science ®Google Scholar
• D. Kraemer, “High-performance flat-panel solar thermoelectric generators with high thermal concentration,” Nat. Mater., vol. 10, pp. 532–538, 2011. DOI:10.1038/nmat3013.
   PubMed Web of Science ®Google Scholar
• A. I. Hochbaum, et al. “Enhanced thermoelectric performance of rough silicon nanowires,” Nature, vol. 451, no. 7175, pp. 163–U5, Jan 10 2008. DOI:10.1038/nature06381.
   PubMed Web of Science ®Google Scholar
• Y. Hu, L. Zeng, A. J. Minnich, M. S. Dresselhaus, and G. Chen. “Spectral mapping of thermal conductivity through nanoscale ballistic transport,” Nat. Nano., vol. 10, no. 8, pp. 701–706, 08//print 2015. DOI:10.1038/nnano.2015.109.
   PubMed Web of Science ®Google Scholar
• A. J. Minnich, et al. “Thermal conductivity spectroscopy technique to measure phonon mean free paths,” Phys. Rev. Lett., vol. 107, no. 9, pp. Art. no. 095901. Aug 25 2011. DOI:10.1103/PhysRevLett.107.095901.
   PubMed Web of Science ®Google Scholar
• M. E. Siemens, “Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams,” Nat. Mater., vol. 9, pp. 26–30, 2009. DOI:10.1038/nmat2568.
   PubMed Web of Science ®Google Scholar
• F. Yang and C. Dames, “Mean free path spectra as a tool to understand thermal conductivity in bulk and nanostructures,” Phys. Rev. B., vol. 87, pp. 035437, 2013. DOI:10.1103/PhysRevB.87.035437.
   Web of Science ®Google Scholar
• A. J. Minnich, “Determining phonon mean free paths from observations of quasiballistic thermal transport,” Phys. Rev. Lett., vol. 109, pp. 205901, 2012. DOI:10.1103/PhysRevLett.109.205901.
   PubMed Web of Science ®Google Scholar
• A. J. Minnich, “Thermal conductivity spectroscopy technique to measure phonon mean free paths,” Phys. Rev. Lett., vol. 107, pp. 095901, 2011. DOI:10.1103/PhysRevLett.107.095901.
   PubMed Web of Science ®Google Scholar
• C. Dames, and G. Chen, “Thermal Conductivity Of Nanostructured Thermoelectric Materials,” in Thermoelectrics Handbook: Macro to Nano, D. M. Rowe, Ed.. CRC press, 2005
   Google Scholar
• J. Lee, et al. “Investigation of phonon coherence and backscattering using silicon nanomeshes,” Nat Commun, vol. 8, pp. 14054, 2017. DOI: 10.1038/ncomms14054.
   PubMed Web of Science ®Google Scholar
• G. Chen, “Ballistic-diffusive equations for transient heat conduction from nano to macroscales,” (in English). J. Heat Transfer., vol. 124, no. 2, pp. 320–328, Apr. 2002. DOI: 10.1115/1.1447938.
   Web of Science ®Google Scholar
• G. Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Mit-Pappalardo Series in Mechanical Engineering). Oxford; New York: Oxford University Press, 2005, pp. xxiii, 531.
   Google Scholar
• O. Kwon, G. Wehmeyer, and C. Dames. Modified Ballistic-Diffusive Equations to Obtain Phonon Mean Free Path Spectrum from Ballistic Thermal Resistance: II. Derivation of Intergral Equation Based on Ballistic Thermal Resistance.
   Google Scholar
• G. Chen, “Ballistic-diffusive heat-conduction equations,” (in English) Phys. Rev. Lett., vol. 86, no. 11, pp. 2297–2300, Mar. 12 2001. DOI: 10.1103/PhysRevLett.86.2297.
   PubMed Web of Science ®Google Scholar
• R. G. Yang, G. Chen, M. Laroche, and Y. Taur, “Simulation of nanoscale multidimensional transient heat conduction problems using ballistic-diffusive equations and phonon Boltzmann equation,” (in English) J. Heat Transfer., vol. 127, no. 3, pp. 298–306, Mar. 2005. DOI: 10.1115/1.1857941.
   Web of Science ®Google Scholar
• J. R. Howell, M. P. Menguc, and R. Siegel. Thermal Radiation Heat Transfer. CRC press, 2010.
   Google Scholar