Modelling and Measurements of the Thermal Diffusivity of Diamond Thin Film Samples
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MODELLING AND MEASUREMENTS OF THE THERMAL DIFFUSIVITY OF DIAMOND THIN FILM SAMPLES Tan Hong Siang, Hui Ping, Jaeshin Ahn and Tan Fong Hock Nanyang Technological University, School of Electrical & Electronic Engineering, Singapore 2263 ABSTRACT A new method for the modelling and measurement of the thermal diffusivity of very thin films is proposed, and is applied to diamond thin film samples grown by chemical vapor deposition using a mixture of methane and hydrogen. This method is based on a two-dimensional model of the heat conduction process in a thin film to which a delta-function heat pulse is applied as a line source. The mathematical solution is specialized to obtain expressions for the temperature pulse propagating through the plane of the film. With suitable approximations, it is shown that the thermal diffusivity of the film can be deduced directly from a measurement of the temperature excursion with time at various points on the films. The advantages and difficulties of the measurement using this method will be discussed.
INTRODUCTION In recent years there has been an increasing volume of research on the deposition of diamond thin films (DTF) and diamond-like-carbon (DLC) films, motivated by the many potential applications of such films because of their attractive properties. Some of these useful and, in some cases, unique properties include their hardness figures, wide energy band-gap, large carrier mobility, high refractive index, good transparency to visible and infra-red, high temperature and radiation damage resistance, large breakdown voltage and high thermal conductivity. The methods used for growing these DTF and DLC samples from hydrocarbon gases include chemical vapor deposition methods based on plasma-enhancement techniques using photo ionization (Hg discharge lamp, excimer laser, hydrogen discharge lamp, synchrotron radiation) or by plasma-enhancement using electron-cyclotronresonance (ECR), microwave-plasma, hot filament activated plasma, AC and DC plasmas. Several methods have been used to measure the thermal conductivity, k, and diffusivity, a, of the diamond films. One of these is the thermal wave technique [1] which uses the mirage effect to measure a. A modulated laser beam is directed at a spot on the film to be measured, heating the film which in turn heats up the surrounding air and causes a modulated change in its refractive index. This is used to deflect another laser beam which is directed close to and parallel to the plane of the film near the heated spot. The thermal diffusivity a is deduced from the amplitude and phase of the thermal waves produced by the heated film. Another measurement technique is a quasi static method [2] using a free-standing DTF or DLC film coated with black paint and clamped between two heated electrodes in vacuum. The steady Mat. Res. Soc. Symp. Proc. Vol. 270. Q1992 Materials Research Society
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state temperature distribution on the film is measured with a thermograph. The thermal conductivity, k, is deduced from the balance between the heat supplie
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