Low-Temperature Properties of Evaporated Lead Films

Abstract

Lead films have been deposited onto room-temperature substrates having low thermal expansion coefficients and the residual mechanical stresses present in these films have been determined as a function of film thickness and film purity. At room temperature no measurable stress (<5×107 dyn/cm2) was present in any film. At 78° and 4.2°K the stress σ was given by σ=α+β/d, where α is a constant dependent on temperature and d is the film thickness. A model involving surface pinning of dislocations predicts an equation of this form, but the experimental values for the stress were found to be appreciably larger than values calculated on the basis of bulk data. The experimental values were substantiated by superconducting critical temperature measurements on films of various thicknesses. Localized crystalline growth was observed in lead films after cooling to 4°K. The film material around these micron-size crystals exhibiting five- and sixfold rotational symmetry was thinned to the point that physical holes were evident in the thinner films. In addition, with repeated temperature cycling, extensive cross slip was observed.

Superconducting Pb as material for coplanar waveguide resonators on GaAs substrates

“…Pb is known to suffer from high thermal stress when cooled to liquid He temperatures which manifests in the formation of crystallites going hand in hand with a thinning of the surrounding material [14,15]. This was also observed here and necessitates a metal thickness higher than the standard value of 200 nm.…”

Hillock formation in lead films by grain boundary sliding

“…Lahiri (1970) suggested that hillock growth may be due to grain boundary sliding and diffusion creep. Chaudhari (1974) proposed that hillock growth is a result of local stress relaxation, possibly by dislocation slip or twinning. The potential gradient resulting from differential relaxation causes a mass flow along the interface between the film and substrate.…”

The Thermodynamics and Kinetics of film agglomeration

“…Combining the capillary and elastic contribution to the change in energy associated with forming a hole in an otherwise continuous film is given by G = nr 2 h jC' ) -2mh j 2 c.oa + nr2y s + 2mhj "I fv (13) where "Is = Y fs + "If v -Y sv ' The equilibrium island shape may be found by minimizing this equation with respect to r /hj for fixed island volume V = nr 2 hj. Performing this minimization, the equilibrium island shape is given by the solution to the following equation:…”