Numerical Simulation on Self-heating for Interlayer Tunneling Spectroscopy in $Bi_2Sr_2CaCu_2O_{8+x}$

For interlayer tunneling spectroscopy using a small stack of $Bi_2Sr_2CaCu_2O_{8+x}$ (Bi-2212) intrinsic junctions in a high-bias range, large self-heating takes place due to the poor thermal conductivity of Bi-2212. In this study, we numerically estimate the self-heating around a Bi-2212 sample stack for I-V or dI/dV-V measurements. Our results show that the temperature discrepancy between the Bi-2212 sample stack and top Au electrodes due to bias-induced self-heating is small enough along the c-axis direction of Bi-2212. On the other hand, the lateral temperature discrepancy between the sample stack and the Bi-2212 on-chip thermometer stack can be as large as ${\sim}20\;K$ for the highest bias required to observe the pseudogap hump structure. We thus suggest a new in-situ ac thermometry, employing the Au current-bias electrode itself deposited on top of the sample stack as the resistive thermometer layer, which is supposed to allow safe temperature measurements for the interlayer tunneling spectroscopy.