Heating Effects in Interlayer Tunneling Spectroscopy of Bi$_{2.1}$Sr$_{1.4}$Ca$_{1.5}$Cu$_{2}$O$_{8+\delta }$ as Inferred from Single Junction Methods

In order to study Joule-heating effects on small intrinsic Josephson junction (IJJ) stacks or mesas, we compare their current-voltage curves, I(V), with those of single junctions, both using Bi$_{2.1}$Sr$_{1.4}$Ca$_{1.5}$Cu$_{2}$O$_{8+\delta }$ (Ca-Bi2212) intercalated by HgBr$_{2}$. Even for small volume stacks with reduced dissipation by intercalation, there can be self-heating despite the absence of the commonly seen backbending of I(V). This conclusion is based on distinctive features of I(V) of intermediate size mesas which were absent in single junctions.