Specific Heat of Granular Aluminum Films

Abstract

The specific heat of granular Al-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ films with ${T}_{c}\ensuremath{\cong}2\ifmmode^\circ\else\textdegree\fi{}$K has been measured between 1.3 and 8\ifmmode^\circ\else\textdegree\fi{}K. The results show that the enhancement of ${T}_{c}$ is a bulk effect. Within experimental accuracy the electron density of states at the Fermi surface is the same as that of pure Al. The lattice heat capacity is increased in the granular films such that the measured ${\ensuremath{\Theta}}_{D}$ is 28% less than that of pure Al. This result indicates that the phonon density of states is greatly enhanced at low frequencies and seems to confirm the tunneling data of Klein and Leger. The experimental methods used to measure the small (\ensuremath{\sim} 0.5 erg/\ifmmode^\circ\else\textdegree\fi{}K) heat capacity of the films are discussed. The thermal conductivity of Au+7-at.%-Cu wire and the heat capacity of silicon (\ensuremath{\sim} 50 mg) were measured to test the capability and accurancy of the experimental techniques.