Interface Stress in Artificial Multilayers
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INTERFACE STRESS IN ARTIFICIAL MULTILAYERS J.A. RUUD, A. WITVROUW AND F. Division of Applied Sciences,
SPAEPEN Harvard University,
Cambridge,
MA 01238
ABSTRACT A new method for measuring interface stress is presented. The curvature of substrates coated with artificial multilayers is measured as a function of bilayer repeat length. The interface stress is determined from the slope of the curvature plotted versus inverse repeat length. As an example, the2 (111) Au/amorphous A1 20 3 interface stress was determined to be 1.13+0.06 J/m (compressive) . X-ray and TEM observations allowed the possibility of interfacial phases to be ruled out as possible alternative sources of the stress. INTRODUCTION The surface stress is the work required to deform elastically a unit area of surface by a unit strain. The interface stress, correspondingly, is the work required to deform elastically a unit area of interface (1] [2] . Direct measurements of interface stresses have not been made. Cammarata and Sieradzki (3] have pointed out that the surface stress can cause perceptible changes in the lattice parameters of ultra-fine microstructures, such as artificial multilayers. They appeal to this effect to explain the enhancement of the biaxial modulus observed in some multilayers. In this paper we describe a new method for determining the interface stress in multilayers that makes use of the curvature these stresses cause in the substrate of a thin film. A similar method has been used before for measuring surface stresses of semiconductor surfaces [4) (5]. THEORY A thin hemispherical
film on a substrate under a biaxial stress, a, bends cap with principal radii R, according to the equation [6]:
0._1 6
E d (1-v) df R
as
a
(1)
where E, V, and d, are, respectively Young's modulus, Poisson's ratio, and the thickness of the substrate and d. is the thickness of the film. This equation is valid for d«
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