With the aim of characterizing the thermal conductivity for nanometer-scale thermoelectric materials, we have constructed a new measurement system based on ac calorimetry. Analysis of the obtained data requires time-evolution of temperature distribution in nanometer-scale material under periodic heating. In this study, we made a simulation using a C#-program for time-dependent temperature distribution, based on 2-dimensional heat-diffusion equation including the influence of heat emission from material edges. The simulation was applied to AlN with millimeter-scale dimensions for confirming the validity and accuracy. The simulated thermal diffusivity for 10×75-mm2-area AlN was 1.3×10-4 m2/s, which was larger than the value set in the heat-diffusion equation. This overestimation was also observed in the experiment. Therefore, our simulation can reproduce the unsteady heat conduction and be used for analyzing the ac calorimetry experiment.

Contact resistance is caused by constriction resistance and film resistance through contact layers. It is well known that a surface film causes non-linear voltage and current characteristics. The origin of non-linearity is caused by tunneling electron through thin insulation barrier or jumping over the thick barrier (Shottky barrier) on the contact surface. In this paper, a new idea causing nonlinear property by only current constriction which flows through very small contact spot area, if there is no film layer, is proposed by the two dimensional contact model. The contact model, used in this paper, is a two dimensional type narrow path of contact area (short bridge) made by thin copper foil of 0.035 mm on a glass epoxy resin board. The contact part is made by scraping with an electric drill as a single bridge shape of 0.1 mm wide and 0.3 mm long on the centre of a board (100 mm100 mm). The 3rd harmonic distortion voltage was measured by using a Component Linearity Test Equipment (Type CLT1 made by Radiometer Electronics Company) which the system supplies a pure sine wave current of 10 kHz and detects a distortion voltage of 30 kHz by a narrow band pass filter circuit. The sensitivity of the Component Linearity Test Equipment (CLT1) is under a 10-9 volt. Four bridge samples were examined for the comparison of nonlinear distortion voltage. The distortion voltage of a sample (A) (0.1 mm wide, 0.3 mm long) is too larger than the one of the sample (B) (0.2 mm wide, 0.3 mm long) at the same applied voltage which resistance is not so different each other. It seems that current constriction to the spot (A) may heat up higher and cool down lower than (B). It would be also guessed that the power dissipation of 20 kHz cause temperature oscillation of 20 kHz, then it causes a component of contact resistance of 20 kHz, and therefore the product of 10 kHz current and 20 kHz resistance component cause 30 kHz component distortion voltage.