Thermal Properties of Metallic Films at Room Conditions by the Heating Slope

Abstract

An analytical model and a methodology for determining the thermal diffusivity and the thermal conductivity of metallic thin films at room conditions are proposed. The analytical model is based on the one-dimensional heat transfer equation, which allows estimation of the thermal conductivity and thermal diffusivity through the initial heating slope value. The thermal conductivity and thermal diffusivity values of gold and aluminum films from 20 to 200 nm thicknesses, determined from the initial slope of the measured heating profiles, and their comparison with the analytical ones are discussed. Results show that thermal diffusivity increases from 30 6 × 10 −6 m 2 ∕s to 127 12 × 10 −6 m 2 ∕s for gold films, and it increases from 15 7 × 10 −6 m 2 ∕s to 95 10 × 10 −6 m 2 ∕s for aluminum films; although thermal conductivity increases from (132 35) to 306 48 W∕m · K for gold films and from (58 30) to 243 39 W∕m · K for aluminum films, when the film thickness increases. Nomenclature A = area of the film or substrate, m 2 C f = heat capacity of the film, J∕kg · K C p = specific heat at constant pressure of the film, J∕kg · K D f = thermal diffusivity of the film, m 2 ∕s d f = thin-film thickness, m d s = substrate thickness, m h = convection coefficient, W∕m 2 · K k f = thermal conductivity of the film, W∕m · K k s = thermal conductivity of the substrate, W∕m · K L = length of thin film, m m f = mass of the film, kg P 0 = applied power on the film, mW Q c = conduction heat of the substrate, mW Q hf = convection heat of the film, mW Q rf = radiation heat of the film, mW Q sf = sensible heat of the film, mW R film = electrical resistance of the film, Ω R film·f = final electrical resistance of the film, Ω R film·i = initial electrical resistance of the film, Ω R ref = electrical resistance of reference, Ω T f = temperature of the film, K T s = temperature of the substrate, K T 0 = room temperature, K t c = time of the applied pulse, s W out = transfer function, V w = width of thin film, m α f = resistance-temperature coefficient of the film, K −1 ΔR = change of electrical resistance of the film, Ω ΔT = lineal change of temperature of the film, K ΔT f = changes of temperature of the film, K ΔT f ∕Δt = initial heating slope of the film, K∕s ΔT ftr = changes of temperature of the film in the transitory regime, K ΔT s = changes of temperature of the substrate, K ε f = emissivity of the film σ = Stefan-Boltzman´s constant; 5.6704×10 −8 W∕m 2 K 4 Subscripts Au = gold samples Al = aluminum samples bulk = bulk values of the materials f = thin film s = substrate 0 = reference state

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