High-Accuracy Contact Resistance Measurement Method for Liquid Metal by Considering Current-Density Distribution in...

Liquid metals (LMs) are used as stretchable conductors in various stretchable electronic devices. Moreover, such devices using Ga-based LMs have attracted considerable attention. Herein, we propose a method for accurately determining the contact resistance (R_c) between galinstan and Cu electrodes by considering the current-density distribution in transfer length method (TLM) measurement. Conventional TLM measurements assume that the sheet resistance of the metal electrode (R_she) is negligible compared with that of the object (R_sho), such as Si. However, this assumption may be problematic because the R_sho of Ga-based liquid metals (LMs) is close to the R_she. Therefore, we developed a method of applying current to each measuring electrode and compared it with the conventional method of applying current to the outer electrodes. Simulation results indicated that R_she cannot be ignored for galinstan, and the measured resistance in the contact area (R_c^Total) included <10% of the R_c component when current was applied to the outer electrodes. In contrast, R_c^Total included the entire R_c component when current was applied to each electrode. Furthermore, we found that the volume resistances of the object and electrode included in R_c^Total cannot be ignored. Therefore, for accurate measurement, current must be applied to each electrode, and R_c must be determined from the intersections of the measured and simulated R_c^Total. The obtained contact resistivity (ρ_c), i.e., the contact resistance per unit contact area, was 0.115 mΩ·mm². The maximum error was 0.085 mΩ·mm², which was lower than the ρ_c of the solders (≥10^-1 mΩ·mm²) with the lowest ρ_c among the electrical interface materials between the electronic components and wiring. This study provides valuable insight into the R_c measurement of LMs, along with new opportunities for the development of stretchable electronics using LMs.