Review of the Thermal Conductivity of Thin Films

Abstract

The thermal conductivity of thin e lms (0.01 ‐ 100 mm) governs the heat transfer characteristics and affects the performance and reliability of the microelectronic devices in which they are used. To measure the thermal conductivity of these e lms, several different steady-state and transient techniques have been developed, some involving the use of lasers. New methods of thin-e lm deposition have also been developed. This paper reviews experimental and analytical techniques and the thermal conductivity results obtained. It is shown that that the results obtained by these different measurement techniques and deposition methods vary signie cantly. This emphasizes the importance of measuring the thermal conductivity of thin-e lm materials that closely resemble those being used in specie c applications. Nomenclature A = cross-sectional area a = radius of e lm b = width C = specie c heat d = diameter of metal line E = exponential function e = electrical charge ef = thermal diffusivity f = frequency G = conductance g = ratio of e lm to substrate effusivity I = electrical current K = thermal conductivity k = Boltzmann constant L = location of e lm edge Lo = Lorentz constant l = length of line N = number of slabs of coating material q = power output ‐ input length R = resistance T = temperature t = time W = width X = location of sensor z = layer of thickness a = thermal diffusivity a9 = thermal conductivity of microcracks b = size of microcracks g = fraction cross-sectional area covered by microcracks, g < 1 D = difference « = emissivity l = mean free path of phonons n = velocity of sound r = density s = electrical conductivity t = time constant v = frequency