中文摘要：

给出了3ω法测试系统中描述薄膜表面加热／测温膜中温度波动的级数形式解，并将复数温度波动的实部和虚部分开表示．利用该解分析了交流加热频率、加热膜宽度和材料热物性的组合参数对加热膜温度波动幅度的影响．并根据此解对测量原理的数学模型进行了修正，建立了相应的3ω测试系统。首先测定了厚度为500nm SiO2薄膜的导热系数，验证了实验系统的合理性．加大了测试频率，利用级数模型在高频段直接得到SiO2薄膜的导热系数，结合低频段的数据同时确定了Si基体的导热系数．利用级数解分析测试了激光晶体Nd：YAG（111）面上多层ZrO2／SiO2增透膜的导热系数，测试的ZrO2薄膜的导热系数比体材料小．进行了不确定度分析．结果表明，提出的分析方法可以有效研究微器件表面薄膜结构的导热性能．

英文摘要：

Analytical solution in terms of series for temperature oscillation in the heater/thermometer film is derived for 3ω measurements. The complex temperature solution is seperated into the real and imaginary parts. Analysis is performed to show the effect of the combined parameters of ac frequency, heater width and sample thermal properties on the temperature oscillation. The mathematical model for the measurement is corrected based on the solution. Accordingly, a 3ω setup is developed to determine thermal conductivity of 500 nm-thick thin film on Si substrate. Uncertainty analysis and comparison with the results of differential-3ω methods and published values are made, the results show good mutual agreement. The thermal conductivities of SiO2 film and Si substrate are determined simultaneously with the series solution and by extension to high frequency. The method is also employed to measure the thermal conductivity of the multi-layer antireflective coating of ZrO2/SiO2 deposited on Nd：YAG surface. The ZrO2 film has a thermal conductivity smaller than the volume value. The established 3ω setup and analytical method can he applied to investigate the thermal performance of thin film-substrate structures for use with micro-systems such MEMS.