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

Abstract

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 m/square to 1 /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 /square to 0.5 /square. The results of this study are of potential value for characterizing the conductive thin films in micro/nano fabrication and relevant areas.