Direct Study of Thermal Conductivity of Aluminum Nanowires
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Direct Study of Thermal Conductivity of Aluminum Nanowires N. Stojanovic1,2, D. H. S. Maithripala3, J. M. Berg1,2 and M. Holtz1,4 1 Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 2 Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409 3 Department of Mechanical Engineering, University of Peradeniya, Peradeniya, KY20400, Sri Lanka 4 Department of Physics, Texas Tech University, Lubbock, Texas 79409 ABSTRACT Thermal conductivity and electrical resistivity of 1 μm long aluminum nanowires, 75, 100, and 150nm in width and 100nm thick, were measured at room temperature. The method consists of microfabricated electrothermal test devices and a model-based data processing approach using finite-element analysis (FEA). The electrical and thermal properties of the nanowires differ significantly from bulk values while electrical resistivity agrees well with theoretical prediction. Electron transport equation models, which adequately describe the resistivity data, consistently underestimate the thermal conductivity. Incorporating a phonon contribution of ~ 21 W/m·K to the total thermal conductivity is found to accurately describe the measured values. INTRODUCTION Electrical and thermal conductivities of structures with submicron dimensions differ significantly from that of the bulk counterparts of the same material [1]. This is generally attributed to reduced grain size [2] and increased influence of surface scattering [3]. Fabrication of nanowires and direct measurement of their electrical resistivity (ρ = 1/σ) has been reported for a number of technologically important materials [4,5] and found to increase rapidly for structures below several hundred nanometers in thickness (t) and width (w) due to greater impact of surfaces and grains. Thermal conductivity (κ) is important in densely packed devices where thermal management is a limiting factor in performance. Several studies have established that κ decreases in metallic thin films relative to the bulk values [6,7]. While electrical properties of metals on this scale are well studied, direct measurement of thermal conductivity is much less common since thin films and wires are generally supported by a substrate so that parasitic losses are significant relative to the conductance through the structure. One approach is to produce suspended nanowires [5,8]. Few studies have taken this approach due to fabrication difficulties. Alternatively, one may measure σ of the metal nanowire and assume validity of the WiedemannFranz (W-F) law, which requires identical electron transport mechanisms for electrical current and heat flow, resulting in a simple relation κ/σ = LT with L the Lorenz number and T absolute temperature. At constant T, W-F implies the so-called electrical-thermal transport analogy (ETTA) κ/κ bulk = σ/σbulk. Here, we stress that W-F law just considers the electronic contribution to κ, making W-F applicable for calculating the total thermal conductivity only when thermal conduction by lattice is negligible in compari
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