Considering that Bi \(_2\) Sr \(_2\) CaCu \(_2\) O \(_{8+\delta }\) (Bi2212) intrinsic Josephson junctions have a body-centered tetragonal structure, and we adjusted a directional tunneling matrix element in the effective density of states. Using the d-wave Eliashberg equations, tunneling spectra of overdoped Bi2212 intrinsic Josephson junction are well reproduced in a wide temperature range below the critical temperature \(T_c\) . From which we obtained the pairing glue spectral function \(\alpha ^2F(\Omega )\) , which is composed of a low-energy resonance peak and a high-energy broad spectrum. These two parts have different effects on the tunneling spectra: the low-energy resonance peak controls the entire shape of the tunneling spectra, and the high-energy broad spectrum maintains a certain electron-boson coupling constant \(\lambda \) . Some interesting and important rules in the fitting process are summarized. The dip of tunneling spectra gradually disappears with increasing temperature, which can be fitted using a simple Dynes’ form of density of states, where the energy gap is energy-independent. As the temperature rises to \(T_c\) , the main peak position of the density of states of the sample still remains a finite value, that is, the energy gap is not closed when the superconductivity disappears, which provides an angle to investigate the pseudogap phenomenon in high- \(T_c\) superconductors.
