Thermal Transport in Rough Silicon Nanowires for Thermoelectric Applications
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1166-N04-07
Thermal Transport in Rough Silicon Nanowires for Thermoelectric Applications Sanjiv Sinha1, Bair Budhaev2 and Arun Majumdar2,3,4 1
Mechanical Science & Engineering, University of Illinois, Urbana, IL 61801, USA Mechanical Engineering, University of California, Berkeley, CA 94720, USA 3 Materials Sciences Division and 4Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
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ABSTRACT The coefficient of merit, ZT of nanostructured thermoelectric materials increases with reduction in thermal conductivity through phonon scattering. The ideal thermoelectric is considered to be an electron crystal and a phonon glass. This paper explores such a material concept by developing a theory for phonon localization in rough nanowires with crystalline cores. Results based on this theory suggest that the reported hundredfold decrease in thermal conductivity of rough silicon nanowires arises due to multiply scattered and localized phonons. Phonon localization presents a new direction to further enhance ZT through nanostructuring. INTRODUCTION Recently reported data on electrolessly etched rough silicon nanowires [1] suggest a hundredfold increase in ZT due to reduction in thermal conductivity of the same order. However, no known theoretical model for thermal conductivity of crystalline dielectrics predicts such reduction. Further, the observed linear increase in thermal conductivity with temperature in nanowires with diameters approaching 50 nm defies the widely-accepted Klemens-Callaway [2] model of thermal conductivity for silicon. Here we discuss a new model that considers the wave-like transmission of acoustic phonons through the wire. We show that such a nanowire behaves in essence, like a waveguide with the resulting wave dispersion becoming size and roughness dependent. Considering a twodimensional analogue of the wire problem, we solve the Helmholtz wave equation for acoustic waves in a rough film [3]. We show that roughness leads to a coupling of different modes and also the conversion of propagating modes to evanescent modes. This conversion to evanescence localizes phonons in wires with lengths approximately greater than a micrometer. We compute the resulting thermal conductivity of rough Si nanowires and show good comparison with experimental data for diameters less than 100 nm. THEORY OF PHONON LOCALIZATION IN NANOWIRES The objective of this paper is to understand the influence of a rough surface on phonon transport. A Boltzmann equation based transport is able to describe the reduction in thermal conductivity of smooth silicon nanowires [4] after accounting for the proper dispersion in such wires and boundary scattering along the lines of the Klemens-Callaway model. However, this approach fails to predict a nearly amorphous-like thermal conductivity in rough silicon
nanowires. Instead of the typical Boltzmann picture, we adopt a wave description of phonon transport in this paper. The principal difference is that we need to account for phase in the wa
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