After picking up an EGaIn droplet, electrical contact is made by approaching the probe onto the SAM surface with a low applied force, typically 5-10 nN. We estimated the geometric contact area of the junction a by first measuring the droplet radius R with an optical microscope and applying Equation 4 in the main text, i.e., a = πR 2 sin 2 θ ≈ 0.69R 2 , and using the average value of θ = 152 • as reported in Supporting Table . The current density J can then be calculated by dividing I by a. We did not directly measure a under the microscope, because a is smaller than the diffraction limit of the microscope for some of the droplets.