The residual stress found in PVD films is due to differences in the coefficient of expansion of the film and substrate giving stress on cool-down from the deposition temperature, and the growth of the film not allowing adatoms to condense in their least energetic association with one another ("growth" or "quenched-in" stresses). In the case of tensile stresses, the atoms are farther apart than they would be in the annealed state, and in the case of compressive stresses, the atoms are closer together than they would be in the annealed state. These residual stresses are stored energy that can be released in subsequent processing or with time in storage or in service. Total film stress is a function of film thickness, elastic modulus, and the morphology and the density of the film. The film stress can easily reach the level where plastic deformation of the material can occur. For high-modulus materials such as chromium, tungsten, or metal oxides, very high stresses can be attained with a great deal of stored energy. For low-modulus materials such as gold or silver, plastic deformation will relieve the stresses before high stress levels are attained. The stresses may not be uniform through the film thickness (i.e., a stress gradient in the deposit) if the growth mode and film density change with thickness and/or if some region has been annealed more than others during the deposition process. If the stress is not uniform through the film thickness, the film will curl when separated from the substrate—if uniform, the separated film will lie flat.

Films under compression will try to expand, and if the substrate is thin, the film will bow the substrate with the film being on the convex side. If the film has a tensile stress, the film will try to contract bowing the substrate so the film is on the concave side. Tensile stress will relieve itself by microcracking of the film and the peeling of the cracked surface from the substrate. Compressive stress will relieve itself by buckling. The stress distribution in a film may be anisotropic and will give cracking or buckling patterns that depend on the stress distribution. Figure 1 shows some of the failure patterns that can be observed with stressed films.

 

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Figure 1

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The most common technique for measuring the total film stress is by measuring the deflection (bowing) of a thin substrate (beam or disk) on which the film has been deposited. By knowing the mechanical properties of the substrate and film material, the film thickness, and the deflection, the film stress can be calculated. Beam deflection can be measured by optical interferometry, laser beam reflection (optical lever arm), or the change of electrical capacitance between two surfaces. The stress due to atom displacement (strain) in a lattice can also be measured by X-ray techniques, but this technique does not take into account film morphology effects nor the effect of a high concentration of lattice defects and grain boundaries.

The most simple case is the deflection of a long, narrow, and thin substrate beam. The narrow width minimizes the "angle-iron stiffening" effect and the thin substrate allows the deflection to be easily determined. In some cases it may be necessary to determine the modulus of the film material independently. This can be done by loading the coated beam with a known stress and measuring the deflection.

One equation for calculating the film stress distribution, and the counteracting substrate stress distribution, is given by:

 

Figure 2 shows a sample calculation of the film stress that appears in the film, at the interface (both sides) and in the substrate. In this case a molybdenum film (6 microns thick, 47 x 106 psi modulus) was deposited on a thin glass beam (Corning microsheet 0211, 2 mils thick, 10.7 x 106 psi modulus) and there was a deflection of the beam equivalent to a radius of curvature equal to 6.31 inches.

High total residual film stresses are often the cause of adhesion failure (deadhesion), particularly when the film is a high-modulus material and the film thickness is large. For example, if one uses several thousand angstroms of chromium on a glass substrate, the film stress should be controlled, since a high total stress can cause adhesion failure at the interface or in the glass material. If the film thickness is less than 500 angstroms, the total film stress will be too low to cause failure in the glass. High film stress can also cause voids to form in the film (tensile stresses) or the film to form "hillocks" (compressive stress) when the film has good adherance to the substrate.

Film stresses can be controlled by changing the deposition parameters or by altering the growth mode of the film. For example, the sputtering pressure in sputter deposition (i.e., concurrent bombardment by reflected-high-energy neutrals) and the amount of energy deposited by concurrent bombardment in ion plating have important effects on the resulting film stress.

Reference:

"Measurement of Residual Stress in Films of Unknown Elastic Modulus," R.E. Cuthrell, F.P. Gerstile, Jr., and D.M. Mattox, Rev Sci Instrum 60(6) 1018, 1989.

"Stress Determination for Coatings," J.A. Sue and G.S. Schajer p. 647, Surface Engineering Vol. 5 ASM Handbook, ASM International, 1994.

"Atomistic Film Growth and Some Growth-related Film Properties," Chapter 9 and "Adhesion and Deadhesion," Chapter 11 in Handbook of Physical Vapor Deposition (PVD) Processing, Donald M. Mattox, William Andrew Publishing/Noyes Publications, 1998.