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 (Rc) 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 (Rshe) is negligible compared with that of the object (Rsho), such as Si. However, this assumption may be problematic because the Rsho of Ga-based liquid metals (LMs) is close to the Rshe. 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 Rshe cannot be ignored for galinstan, and the measured resistance in the contact area (RcTotal) included <10% of the Rc component when current was applied to the outer electrodes. In contrast, RcTotal included the entire Rc component when current was applied to each electrode. Furthermore, we found that the volume resistances of the object and electrode included in RcTotal cannot be ignored. Therefore, for accurate measurement, current must be applied to each electrode, and Rc must be determined from the intersections of the measured and simulated RcTotal. The obtained contact resistivity (ρc), 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 ρc of the solders (≥10-1 mΩ·mm2) with the lowest ρc among the electrical interface materials between the electronic components and wiring. This study provides valuable insight into the Rc measurement of LMs, along with new opportunities for the development of stretchable electronics using LMs.
Keywords: contact resistance; finite-element method; galinstan; stretchable electronics; transfer length method.