Quantized thermal transport across mechanical contacts of rough surfaces

The heater temperature was calibrated using the measurement of the electrical resistance of the heater using the circuitry shown in Fig. S2 a. During the experiments a constant bias, Vtot is applied. The electrical resistance is measured from the voltage drop across the heater. The resulting current–voltage diagram is shown in Fig. S2 b. The electrical resistance changes as a function of the power dissipated in the heater due to the temperature dependence of the electrical resistivity of the silicon. To determine the electrical resistance Rel of the heater as a function of temperature, we exploit the fact that the maximum electrical resistance occurs at a temperature determined by the doping level in the heater. For the cantilevers used here this occurs at 550 ◦C, see Fig. S2 c. For other temperatures, we assume that the dissipated electrical power is proportional to the temperature rise in the heater. The temperature calculation using this method has been shown to have an uncertainty of less than 30% and is thereby comparable to the uncertainty of other methods used to measure temperatures in microscale structures. The calibration process and the underlying assumptions were described in detail by Menges et al. [2].