基于微波透射法的金属薄膜方块电阻测量理论及其应用

Theory and verification of a microwave transmission method of measuring sheet resistance of metallic thin film

依据矩形波导基模的场分布表达式和电磁边界条件,解析推导了插入金属薄膜后的矩形波导透射系数,建立了考虑介质衬底影响的金属纳米薄膜微波透射系数仿真计算方法及其方块电阻的微波测量方法.运用全波电磁仿真方法对金属纳米薄膜方块电阻的微波测量装置进行了仿真验证,结果表明透射系数幅度与方块电阻的对数之间呈线性关系.采用磁控溅射工艺分别在高阻硅和玻璃两种介质衬底表面制备了不同方块电阻值的银薄膜,并测量其微波透射系数.实测结果表明,提出的方法适用于方块电阻阻值为0.05—0.5?/square的金属薄膜.研究结果对于微纳制造领域的导电薄膜方块电阻表征具有参考价值.

Metallic thin films deposited on non-conductive substrates are widely used in areas like microwave absorbers,photovoltaic, packaging, electromagnetic shielding, and integrated circuits. From scientific and engineering point of view, measuring sheet resistance of metallic thin films is important. In this study, we develop a theory of evaluating sheet resistance by using transmission coefficient of a rectangular waveguide（RG） and verify it with sputtered silver films of various thickness values. According to the field distribution of RG working under the fundamental mode and corresponding electromagnetic boundary conditions, we first analytically derive the transmission coefficient of an RG with the metallic thin film exactly occupying its cross section. Comparing existing theory, we take the effect of the non-conductive substrate supporting the metallic thin film into consideration. According to this derivation, we establish a method to calculate the sheet resistance of metallic thin films from the amplitude of RG transmission coefficient.To verify our derivation, we also conduct full-wave simulations of a standard WR-75 RG used for characterizing the metallic thin film at 13.65 GHz. Both the analytical derivations and full-wave simulations show that the amplitude of the transmission coefficient depends on the logarithm of the sheet resistance in a linear manner. It is also demonstrated that the substrate effect may not be ignored. To facilitate measurement, we propose a sandwiched structure by placing the metallic thin film between two waveguide flanges. This modification removes the stringent requirements for sample preparation. Simulations of this sandwiched structure indicate that it is possible to realize non-contact measurement if the air gap between metallic thin film and waveguide flange is below 0.1 mm. Through full-wave simulations, we also show the feasibility of metallic thin film evaluation by using such transmission lines as dielectric filled RG, circular waveguide, and coaxial line. Finally, we prepare various silver films with sheet resistances ranging from 20 mΩ/square to 1 Ω/square（measured by the four-point probe technique） on the top of high resistance silicon and glass substrates,respectively. We measure the amplitudes of transmission coefficient of these metal films in RG by using vector network analyzer. The obtained experimental results are well consistent with the derivation and simulation results, thereby verifying the proposed method. It is recommended that the proposed method is suitable for conductive films with sheet resistances ranging from 0.05 Ω/square to 0.5 Ω/square. The results of this study are of potential value for characterizing the conductive thin films in micro/nano fabrication and relevant areas.