Direct Measurement of the Effect of Strain on Tc in Thin Films

Abstract

Direct measurements have been made of the effect of strain on the critical temperature of tin, aluminum, and indium films. The films (<1000 Å) were vacuum deposited onto glass and mylar substrates at room temperature and were then strained by mechanically bending the substrate in liquid helium. Tc depended linearly on the strain over the range of observation, ∼10−3, for both tensile and compressive bending. The slopes of the Tc vs strain curves were 8.7° and 9.1°K per unit strain, respectively for tin and aluminum films on glass substrates and 4.9° and 3.8°K per unit strain for tin and indium films on mylar substrates. Earlier measurements1,2 have indicated considerable variation in the Tc dependence on strain from film to film, but our data are quite reproducible and do not seem to depend markedly on the evaporation conditions. For an isotropic material or an anisotropic material for which the relative orientation of the strain axis and the axes of crystal symmetry are known it is possible to relate the change in Tc to a corresponding volume change. On this basis one can compare the results on thin films with strain and pressure measurements on bulk samples. Comparing d ln Tc/d ln V for thin films and bulk samples3 we find that the values for aluminum agree within five percent, those for tin films on glass are lower by thirty percent, and those for indium films are higher by a factor of three. The change in Tc due solely to a change in sample volume can be calculated as a function of the Debye temperature on the basis of the McMillan theory1 by using the Gruneisen relation and taking λ, the phonon-mediated electron interaction, to be inversely proportional to the square of the Debye temperature. Comparing experimental results with these calculations we find that the experimental results for dTc/dθD lie within the limits imposed by μ* = 0.1 to 0.2 for bulk aluminum, tin, and indium and thin-film aluminum and tin. (Materials for which the Coulomb pseudopotential, μ*, has been measured lie within these limits.)