From the point of view of optical coatings, the importance of the mechanical properties of thin films lies primarily in their relation to coating stability, that is, the extent to which coatings will continue to behave as they did when removed from the coating chamber, even when subjected to disturbances of an environmental and/or mechanical nature.
There are many factors involved in stability, many of which are neither easy to define nor measure, and there are still great difficulties to be overcome. The approach used in quality assurance in manufacture is entirely empirical.
Tests are devised that reproduce, in as controlled a fashion as possible, the disturbances to which the coating will be subjected in practice, and samples are then subjected to these tests and inspected for signs of damage. Sometimes the tests are deliberately made more severe than those expected in use. Coating performance specifications are normally written in terms of such test levels.
Stress is normally measured by depositing the material on a thin, flexible substrate that deforms under the stress applied to it by a deposited film. The deformation is measured, and the value of stress necessary to cause it is calculated.
The substrate may be of any suitable material; glass, mica, silica, and metal, for example, have all been used. The form of the substrate is often a thin strip, supported so that part of it can deflect. Then, either the deflection is measured in some way, or a restoring force is applied to restore the strip to its original position.
Usually, the deflection or the restoring force is measured continuously during deposition. Optical microscopes, capacitance gauges, piezoelectric devices, and interferometric techniques are some of the successful methods. A useful survey of the field of stress measurement in thin films in general is given by Hoffman. A particularly useful paper that deals solely with dielectric films for optical coatings is that by Ennos.
Ennos used a thin strip of fused silica as a substrate, simply supported at each end on ball bearings so that the center of the strip was free to move. An interferometric technique with a helium-neon laser as the light source was used to measure the movement of the strip. The strip formed one mirror of a Michelson interferometer of novel design, shown in Figure 11.28.
Since the laser light was linearly polarized, the upper surface of the prism was set at the Brewster angle to eliminate losses by reflection of the emergent beam. Apart from the more obvious advantages of large coherence length and high collimation, the laser beam made it possible to line up the interferometer with the bell jar of the machine in the raised position (see Figure 11.28b).
No high-quality window in the machine was necessary, as the glass jar of quite poor optical quality proved adequate. To complete the arrangement, the laser light was also directed onto a test flat for the optical monitoring of film thickness. A typical record obtained with the apparatus is also shown in Figure 11.28c.
The calibration of the fused-silica strip was determined both by calculation and by measurement of deflection under a known applied load. Curves plotted for a wide range of materials show the variation of stress in the films during the actual growth as a function both of film thickness and evaporation conditions, with some examples included in the paper (see Figure 11.29).
It is of particular interest to note the frequent drop in stress when the films are exposed to the atmosphere. This is principally due to the adsorption of water vapor, an effect to be considered further toward the end of this tutorial.
The interferometric technique has been further improved by Roll and Hoffman. Ledger and Bastien took the Michelson interferometer of Ennos and replaced it with a cat’s-eye interferometer, using circular disks as sensitive elements that are far less temperature-sensitive.
This innovation has enabled the measurement of stress levels in optical films over a wide range of substrate temperatures. Examination of differences in thermally induced stress for identical films on different substrate materials, as substrate temperature varies after deposition, has permitted the measurement of the elastic moduli and thermal expansion coefficients of the thin-film materials.
Although the measured value of the expansion coefficient for bulk thorium fluoride crystals is small and negative, the values for thorium fluoride thin films were consistently large and positive, varying from \( 11.1 \times 10^{-6} \) to \( 18.1 \times 10^{-6} \, ^\circ \mathrm{C}^{-1} \). Young’s modulus for the same samples varies from \( 3.9 \times 10^5 \) to \( 6.8 \times 10^5 \, \mathrm{kg} \, \mathrm{cm}^{-2} \) (i.e., \( 3.9 \times 10^{10} \) to \( 6.8 \times 10^{10} \, \mathrm{Pa} \)).
Ledger and Bastien arranged the interferometer so that fringes were counted as they were generated at the center of the interferometer during the deposition of the film. An asymmetric fringe shape allowed the distinction between a fringe appearing and a fringe disappearing. This meant that the stress level would be lost if the fringe count failed at any stage.
A group at the Optical Sciences Center modified the interferometer to view a sufficiently large field that included a number of fringes. The fringe pattern was then interpreted as an interferogram to give the form of the surface of the deformable substrate. This effectively decoupled each measurement from all others and permitted the stress to be determined unambiguously at any stage, even if some intervening measurements were missed or skipped.
The interferometer was used in a detailed study of titanium dioxide films deposited by thermal evaporation with or without ion assist. Thermally evaporated films usually exhibit a tensile stress that is a consequence of the disorder frozen into the film, as freshly arriving material covers what already exists. An increase in the rate of deposition gives less time for the material on the surface to reorganize itself and therefore should lead to an increase in tensile stress. This is clearly seen in Figure 11.30.
Under bombardment, the tighter packing of the films leads to an increase in compressive stress because of the transfer of momentum to the growing film (Figure 11.31). In fact, it is possible by careful control of the bombardment to achieve extremely low values. Unfortunately, not all materials exhibit such a simple relationship.
Pulker [78] has studied the relationship between stress levels and the microstructure of optical thin films, developing further some ideas of Hoffman. The work is surveyed elsewhere. Good agreement between measured levels of stress and those calculated from the model has been achieved, but perhaps the most spectacular feature has been the demonstration, in accord with the theory, that small amounts of impurity can have a major effect on stress.
The impurities congregate at the boundaries of the columnar grains of the films and reduce the forces of attraction between neighboring grains, thus reducing stress. Small amounts of calcium fluoride in magnesium fluoride, around 4 mol%, reduce tensile stress by some 50%.
Pellicori has shown the beneficial effect of mixtures of fluorides in reducing cracking in low-index films for the infrared. Windischmann has discussed and modeled the stresses in ion-beam sputtered thin films. He identifies momentum transfer as the important parameter, aligning with conclusions regarding ion-assisted deposition. The results of Figure 11.31 agree with the Windischmann model. Strauss has recently reviewed mechanical stress in optical coatings.
Abrasion Resistance:
Abrasion resistance is another mechanical property that is of considerable importance and yet extremely difficult to define in any terms other than empirical. The problem is that abrasion resistance is not a single fundamental property but rather a combination of factors such as adhesion, hardness, friction, packing density, and so on.
Various ways of specifying abrasion resistance exist, but all depend on arbitrary empirical standards. The standard sometimes involves a pad made from rubber, which may be loaded with a particular grade of emery. The pad is drawn over the surface of the film under a controlled load for a given number of strokes.
Signs of visible damage show that the coating has failed the test. Because the pad in early versions of the test was a simple eraser, the test is sometimes known as the eraser test. Similar standard tests may be based on the use of cheesecloth or even of steel wool. Wiper blades and sand slurries have also been used to attempt to reproduce the kind of abrasion that results from wiping in the presence of mud.
Most of the tests suffer from the fact that they do not give a measure of the degree of abrasion resistance but are merely of a go/no-go nature. There is a modification of the test which does permit a measure of abrasion resistance to be derived from the extent of the damage caused by a controlled amount of abrasion.
This is still probably the best arrangement yet devised, but even here the results vary considerably with film thickness and coating design so that it is far from an absolute measure of a fundamental thin-film property. The scratch test, described shortly, is sometimes used to derive an alternative measure of abrasion resistance. Abrasion resistance is, therefore, primarily a quality-control tool.
Adhesion:
Adhesion is another important mechanical property that presents difficulties in measurement. What we usually think of as adhesion is the magnitude of the force necessary to detach a unit area of the film from the substrate or from a neighboring film in a multilayer. However, accurate measures of this type are impossible. Quality-control testing is, as for many of the other mechanical properties, of a go/no-go nature. A strip of adhesive tape is stuck to the film and removed. The film fails if it delaminates along with the tape.
Jacobsson and Kruse have studied the application of a direct-pull technique to optical thin films. In principle, the adhesive forces between film and substrate can be measured simply by applying a pull to a portion of the film until it breaks away.
This is a technique used for other types of coatings, such as paint films. The test technique is straightforward and consists of cementing the flat end of a small cylinder to the film, then pulling the cylinder, along with the portion of the film under it, off the substrate in as near-normal a direction as possible.
The force required to accomplish this is the measure of the force of adhesion. Great attention to detail is required. The end of the cylinder must be true, must be cemented to the film so that the thickness of cement is constant and so that the axis of the cylinder is vertical.
The pull applied to the cylinder must have its line of action along the cylinder axis, normal to the film surface. The precautions to be taken, and the tolerances that must be held, are considered by Jacobsson and Kruse.
Their cylindrical blocks were optically polished at the ends, and, to ensure a pull normal to the surface, the film and substrate were cemented between two cylinders, the axes of which were collinear. The mean value of the force of adhesion between 250-nm-thick ZnS films and a glass substrate was found to be \( 2.3 \times 10^7 \, \mathrm{Pa} \), which rose to \( 4.3 \times 10^7 \, \mathrm{Pa} \) when the glass substrate was subjected to 20 minutes of ion bombardment before coating. Zinc sulfide films evaporated onto a layer of SiO, some 150 nm thick, gave still higher adhesion figures of \( 5.4 \times 10^7 \, \mathrm{Pa} \).
The increases in adhesion due to ion bombardment and the SiO layer were consistent, and the scatter in successive measures of adhesion was small, some 30% in the worst case. An alternative method of measuring the force of adhesion is the scratch test, devised by Heavens and improved and studied in detail by Benjamin and Weaver, who applied it to a range of metal films.
The test is straightforward but complex to interpret. A round-ended stylus is drawn across the film-coated substrate under increasing loads, and the point at which the film under the stylus is removed from the surface is a measure of the adhesion of the film.
Benjamin and Weaver were able to show that plastic deformation of the substrate under the stylus subjected the interface between the film and the substrate to a shear force, directly related to the load on the stylus by the expression:
\[
F = \frac{a r – a P}{(2a^2)^{1/2}}
\]
where:
– \( a = \sqrt{\frac{W}{\pi P}} \)
– \( P \) is the indentation hardness of the substrate,
– \( r \) is the radius of the stylus point,
– \( a \) is the radius of the circle of contact,
– \( W \) is the load on the stylus, and
– \( F \) is the shear force.
The shear force is roughly proportional to the square root of the load on the stylus. For the film to be removed by drawing the stylus across it, the shear force must be great enough to break the adhesive bonds.
Using this apparatus, Benjamin and Weaver confirmed quantitatively what had been qualitatively observed before: the adhesion of aluminum deposited at pressures around \( 10^{-5} \, \text{Torr} \) (\( 1.3 \times 10^{-5} \, \text{mbar} \) or \( 1.3 \times 10^{-3} \, \text{Pa} \)) on glass was initially poor, with values similar to van der Waals forces.
However, after approximately 200 hours, it improved to values consistent with chemical bonding. Aluminum deposited at higher pressures, around \( 10^{-3} \, \text{Torr} \) (\( 1.3 \times 10^{-3} \, \text{mbar} \) or \( 0.13 \, \text{Pa} \)), exhibited consistently high bonding immediately after deposition.
This was attributed to the formation of an oxide bonding layer between aluminum and glass. Additional experiments demonstrated the importance of such oxide layers in other metal films on glass. On alkali halide crystals, the initial bonding at van der Waals levels showed no subsequent improvement with time.
More recently, the scratch test has been studied by Laugier, who included the effects of friction during the scratching action in the analysis. Zinc sulfide has been shown to exhibit unusual aging behavior, occurring in two well-defined stages.
After 18–24 hours following deposition, adhesion increases by a factor of four from an initially low value. After three days, adhesion begins to increase further, reaching a maximum after seven days, which can be 20 times the initial value.
This is attributed to zinc oxide formation at the interface, with free zinc at the interface first combining with oxygen diffusing through the layer from the outer surface, followed by zinc diffusing to the boundary from within the layer.
Commercial instruments for these tests are now available and help to standardize the procedures as far as possible. Unfortunately, none of these adhesion tests is entirely satisfactory. Some difficulties relate to measurement consistency, but the greatest challenge lies in the nature of adhesion itself. The forces attaching a film to a substrate or one film to another are typically very large (often greater than \( 100 \, \text{ton in}^{-2} \), or \( 10^9 \, \text{Pa} \)) but are also very short-range. These forces are principally between individual atoms, leading to two major consequences:
- The forces can be blocked by a single atom or molecule of contaminant, making adhesion highly susceptible to even slight contamination. A monomolecular layer of contaminant is sufficient to destroy adhesion entirely, and even a fraction of such a layer can adversely affect it.
- While the adhesion force is large, the work required to detach the coating—the product of the force and its range—can be quite small. Coatings typically fail progressively rather than suddenly across a significant area.
This progressive failure emphasizes the importance of the work of adhesion, which encompasses the surface energy required to expose new surfaces during adhesion failure, along with any energy lost to plastic deformation of the film or substrate.
Some metal films, particularly those on plastics, exhibit evidence of an electrostatic double layer forming over time, contributing positively to adhesion. For tape tests, adhesive forces are comparatively weak but act over a relatively large area. Thus, a film is unlikely to be detached unless it is very weakly bonded or contains stress concentrators that initiate delamination.
In the direct-pull technique, progressive failure can result from uneven adhesive thickness or off-center pulls, reducing the measured force. Even with meticulous precautions, the true adhesion force is difficult to obtain, making this method more suitable as a quality-control tool. Poor adhesion typically results in significantly reduced measured forces.
The scratch test suffers additional issues. Many films used in optical coatings shatter under high loads before delamination occurs. Such shattering dissipates additional energy, introducing film hardness and brittleness into the results.
Rarely do dielectric materials produce clean scratches, making this test more useful for comparing coatings rather than obtaining absolute measures. Goldstein and DeLong achieved some success assessing dielectric films using microhardness testers for scratching.
Most commercial scratch testers include a microscope for visual examination of failures. Some also incorporate sensitive acoustic detectors to identify damage onset. A stylus skidding over a surface generates less noise than one plowing through and shattering the material.
Chemical Resistance:
The chemical resistance of a film is significant, especially concerning atmospheric moisture effects, which are discussed later. Bulk material solubility provides a useful guide, but in thin-film form, the surface-area-to-volume ratio is extremely large, magnifying any solubility tendencies. Thin-film chemical behavior depends heavily on thickness, multilayer interactions, deposition conditions, and test methods. Materials can be broadly categorized into:
- Moisture-resistant: e.g., titanium oxide, silicon oxide, zirconium oxide.
- Slightly affected: e.g., zinc sulfide.
- Badly affected: e.g., sodium fluoride.
