One of the most significant features of optical thin films is the way in which their properties and behavior differ from those of identical materials in bulk form. This is, of course, also true for thin films in areas other than optics.
Almost always, the performance of the film is poorer than that of the corresponding bulk material. Refractive index is usually lower, although, very occasionally, for some semiconductor materials, it can be slightly higher with greater losses, less durability, and inferior stability. There is also sensitivity to deposition conditions, especially substrate temperature.
Heitmann has studied the influence of parameters such as the residual gas pressure within the chamber and the rate of deposition on the refractive indices of cryolite and thorium fluoride. Raising the residual gas (nitrogen) pressure from \(4 \times 10^{-6} \, \text{Torr}\) (\(5.3 \times 10^{-6} \, \text{mbar}\) or \(5.3 \times 10^{-4} \, \text{Pa}\)) in one case, and \(2 \times 10^{-6} \, \text{Torr}\) (\(2.6 \times 10^{-6} \, \text{mbar}\) or \(2.6 \times 10^{-4} \, \text{Pa}\)) in another, to \(2 \times 10^{-5} \, \text{Torr}\) (\(2.6 \times 10^{-5} \, \text{mbar}\) or \(2.6 \times 10^{-3} \, \text{Pa}\)) had no measurable effect, within the accuracy of the experiment (±0.1% for thorium fluoride and ±0.3% for cryolite).
However, a further increase in residual pressure to \(2 \times 10^{-4} \, \text{Torr}\) (\(2.6 \times 10^{-4} \, \text{mbar}\) or \(2.6 \times 10^{-2} \, \text{Pa}\)) gave a drop in the refractive index of 1.5% for cryolite and 1.4% for thorium fluoride.
At this higher pressure, the mean free path of the nitrogen molecules was less than the distance between the boat and the substrate, and the decrease in refractive index was probably caused by increased porosity of the layers. This tends to confirm that the mean free path of the residual gas molecules should be kept longer than the source–substrate distance, but that any further increases in mean free path beyond this have little effect.
Heitmann concluded that the mean free path of the molecules is the important parameter, not the ratio of the numbers of evaporant molecules to residual gas molecules impinging on the substrate in unit time, which appeared to have no effect on refractive index.
He also found that changes in the rate of deposition, from a quarter-wave in 0.5 minutes (measured at 632.8 nm) to a quarter-wave in 1.5 minutes, caused a decrease in refractive index of 0.6% in both cases, but that a further decrease to a quarter-wave in 5 minutes produced only slight variations. Heitmann’s results are probably best interpreted in terms of slight changes in film microstructure, induced by the variations in deposition conditions.
Layer microstructure is, in fact, the most significant factor in determining the properties of optical thin films and the way in which they differ from the same material in bulk form. During the past two decades, there has been an increasing interest in the microstructure of, and microstructural effects in, optical thin films.
A useful technique for the study of thin-film structure, which immediately yielded important results, is electron microscopy. Its use in the examination of thin-film coatings has involved the development of techniques for fracturing multilayers and for replicating the exposed sections.
Pearson, Lissberger, Pulker, and Guenther have all made substantial contributions in this area, and their results show that the layers in optical coatings have, almost invariably, a pronounced columnar structure, with the columns running across the films normal to the interfaces. To their investigations, we can add those of Movchan and Demchishin and then Thornton, who investigated the effects of substrate temperature and, in Thornton’s case, also residual gas pressure, on the microstructure of evaporated and sputtered films.
This showed that a critical parameter in the vacuum deposition of thin films is the ratio of the temperature of the substrate \(T_{\text{sub}}\) to the melting temperature \(T_{\text{melt}}\) of the evaporant. For values of this ratio lower than around 0.5, the structure of the layers is intensely columnar, the columns running along the direction of growth.
Increased gas pressure forces the growth into a more pronounced columnar mode even for slightly higher values of substrate temperature. Because the most useful materials in optical thin films are all of high melting point, substrate temperatures can never be higher than a small fraction of the evaporant melting temperature, and so the structure of thin films is almost invariably a columnar one, with the columns running along the direction of growth, normal to the film interfaces.
The columns are several tens of nanometers across and roughly cylindrical in shape. They are packed in an approximately hexagonal fashion with gaps in between the columns, which take the form of pores running completely across the film. There are large areas of column surface that define the pores and are exposed to the surrounding atmosphere. The columnar structure of a film of zinc sulfide is shown in Figure 12.1.
Packing density, \( p \), defined as:
\[
p = \frac{\text{Volume of solid part of film (i.e., columns)}}{\text{Total volume of film (i.e., pores plus columns)}}
\]
is a very important parameter. It is usually in the range 0.75–1.0 for optical thin films. For thermally evaporated thin films, it is most often 0.8–0.95 and seldom as great as unity. A packing density that is less than unity reduces the refractive index below that of the solid material of the columns.
A useful expression that is reasonably accurate for films of low index connects the index of the film, \( n_f \), that of the solid part of the film, \( n_s \), and the voids, \( n_\nu \), with the packing density, \( p \):
\[
n_f = p n_s + (1 – p) n_\nu \tag{12.1}
\]
The behavior of films of higher index, 2.0 and above, can be more complicated, but in many cases, a linear law as in Equation 12.1 is sufficiently accurate and is, therefore, often used. If the value of packing density has been derived from optical measurements by using Equation 12.1, as is frequently the case, then the expression can, and should, be used.
In any event, it gives an indication of the correct trend. For an alternative expression that is more complicated and can give a better fit in many of the more complex cases, although still not always ideal, the paper by Harris and colleagues can be consulted.
Packing density is a function of substrate temperature, usually (but not always) increasing with substrate temperature, and of residual gas pressure, decreasing with rising pressure. Film refractive index, therefore, is also affected by substrate temperature and residual gas pressure. The columns can vary in cross-sectional area as they grow outward from the substrate surface, which is one cause of film inhomogeneity.
Substrate temperature is a difficult parameter to measure and control, so consistency in technique—heating for the same period each batch, identical rates of deposition, pumping for the same period before commencing deposition, and so on—is of major importance in ensuring a stable and reproducible process.
Changing the substrate dimensions, especially substrate thickness, from one run to the next can cause appreciable changes in film properties. Such changes are even more marked in the case of reactive processes where the residual gas pressure is raised and where a reaction between evaporant and residual atmosphere takes place at the growing surface of the film. Thus, it should not be surprising that a high proportion of test runs are required in any manufacturing sequence.
Various modeling studies have confirmed that the columnar growth results from the limited mobility of the material on the surface of the growing film. It diffuses over the surface under thermal excitation until it is buried by arriving material. Diffusion through the bulk of the material is not significant. Thus, lower substrate temperature and higher rates of deposition lead to more pronounced columns and reduced packing density.
The energetic processes involve an element of bombardment of the growing films. The transfer of momentum drives the material deeper into the film and, although the columnar structure may persist to some extent, squeezes out the voids.
The packing density is normally close to or equal to unity. The results of the higher packing density are almost all favorable. The consequences of the columnar microstructure are all less serious in the energetically deposited films (Figure 12.2).
A second level of microstructure in thin films is their crystalline state. Although this is less well understood, considerable progress has been made. Optical thin films are deposited from vapor that has been derived from sources at comparatively very high temperature.
The substrates on which the films grow are at relatively low temperature. There is, therefore, a great lack of equilibrium between the growing film and the arriving vapor. The film material is rapidly cooled or quenched, and this not only influences the formation of the columnar microstructure but also affects the crystalline order.
The material condensing will attempt to reach the equilibrium form appropriate to the temperature of the substrate, but the correct rearrangement of the molecules takes time, and the film will tend to pass through the higher-temperature forms during this rearrangement.
If the rate of cooling is greater than the rate of crystallization, then a higher-temperature form will be frozen into the layer. The very rapid cooling rate normally existing in thin films implies the presence of quite high-temperature forms, and there are often mixtures of phases. This explains an, at first sight, curious behavior of thin films.
Frequently, there is an inversion in the crystalline structure in that at low substrate temperatures a predominance of high-temperature crystalline forms is found, whereas at high substrate temperatures, more low-temperature material appears to form. The low substrate temperature leads to a higher quench rate, and the rest follows.
Amorphous forms, corresponding to a quite high temperature, can often be frozen by very rapid cooling, and are enhanced by a higher temperature of the arriving species. For example, sputtering, where additional kinetic energy is possessed by the arriving molecules, often gives amorphous films. The low-voltage ion-plating technique, again with high incident energy, appears virtually invariably to give amorphous films.
The high-temperature forms are often only metastable and may change their structure at quite low temperatures, leading to problems of various kinds. Some films deposited in amorphous form by sputtering may sometimes be induced to recrystallize, in a manner described as explosive, by a slight mechanical disturbance, such as a scratch, or by laser irradiation.
Samarium fluoride has two principal crystalline forms, a hexagonal high-temperature form and an orthorhombic low-temperature form. Table 12.1 shows the results of thermal evaporation and ion-assisted deposition, which both lead to this apparently inverted structure.
Zirconia has three principal structures—monoclinic, tetragonal, and cubic—in ascending temperature. Klinger and Carniglia found that very thin zirconia shows a cubic structure but becomes monoclinic when thicker than a quarter-wave at 600 nm. This behavior can be explained by a lower rate of quenching when the film is thicker and less thermally conducting.
Alumina, normally amorphous in thin-film form, can recrystallize in the electron microscope when subjected to the electron bombardment necessary for viewing. Amorphous zirconia, which can occur when films are very thin, has been shown to exhibit similar behavior.
Thin films, therefore, are complicated mixtures of different crystalline phases, some being high-temperature metastable states. Such behavior is clearly very material and process-dependent, and each specific system requires individual study.
What is a good structure for one application may not be so for another. The low scattering of the amorphous phases makes them attractive for certain applications, but their high-temperature or high-flux behavior may not be as satisfactory. Much more needs to be done in attempting to improve our understanding.
The columnar structure and the crystalline structure can be considered as essentially regular intrinsic features of film microstructure. Then, in addition, there are defects that can be thought of as local disturbances of the intrinsic features.
A principal and very important class of defect is the nodule. Nodules are inverted conical growths that propagate through the film or multilayer. They can occur in all processes. They start at a seed that is usually a very small defect or irregularity, and it appears that virtually any irregularity, even minute ones, may act as a seed.
Scratches on the substrate, pits, dust, contamination, material particles ejected from the source, loose accumulations of material in the vapor phase, perhaps even local electric charges, can all cause nodules to start growing.
Once the nodule starts, it continues to grow until it forms a domed protrusion at the outer surface of the multilayer. The nodule itself is very much larger than the defect that causes it. It is not, in itself, a contaminant. It is made up of exactly the material of the remainder of the coating. It is simply growing in a different way.
The outer surface of the nodule is a quite sharp boundary between it and the remainder of the coating. This sharp boundary is a region of weakness, and there is frequently a fissure around the nodule, either partially or completely, and the nodule may sometimes be detached from the coating completely, leaving a hole behind.
Nodules are present in almost all coatings. The only way of suppressing them appears to be a move toward perfection in the substrate, its surface and its preparation, and in the coating deposition. The incidence of nodules over superpolished substrates, for example, is much reduced compared with conventional substrates. A typical nodule is shown in Figure 12.3, and the hole left by a detached nodule is shown in Figure 12.4.
Variation in refractive index is not the only feature of film behavior associated with the columnar structure. The pores between the columns permit the penetration of atmospheric moisture into the film, where, at low relative humidity, it forms an adsorbed layer over the surfaces of the columns, and at medium relative humidity, actually fills the pores with liquid water due to capillary condensation. Moisture adsorption has been the subject of considerable study by Ogura, who used the variation in adsorption with relative humidity to derive information on the pore structure of the films.
The moisture, since it has a different refractive index (around 1.33) from the 1.0 of the air that it displaces from the voids, causes an increase in the refractive index of the films. Since the geometrical thickness of the film does not change, the increase of film index during adsorption is accompanied by a corresponding increase in optical thickness. Exposure of a film to the atmosphere, therefore, usually results in a shift of the film characteristic to a longer wavelength. Such shifts in narrowband filters have been the subject of considerable study.
Schildt et al. found that for freshly prepared filters of zinc sulfide and magnesium fluoride, constructed for the region 400–500 nm, the variation in peak wavelength could be expressed as:
\[
\Delta\lambda = q \log_{10} P
\]
where \( q \) is a constant varying from around 1.4 for filters that had aged to around 8.3 for freshly prepared filters, and \( P \) is the partial pressure of water vapor measured in Torr (\( P \) should be replaced by \( 0.75 \times P \) if \( P \) is measured in mbar or \( 0.0075 \times P \) if \( P \) is measured in Pa), and \( \Delta\lambda \) is measured in nm. \( \Delta\lambda \) was arbitrarily chosen as zero when the pressure was 1 Torr (1.3 mbar or 133 Pa). This relationship was found to hold good for the pressure range 1 to approximately 20 Torr (1.3–26 mbar or 133–2660 Pa).
The filters settled down to the new values of peak wavelength some 10–20 minutes after exposure to a new level of humidity began. They found that the shifted values of peak wavelength could be stabilized by cementing cover slips over the layers using an epoxy resin.
Koch showed that the characteristics of narrowband filters became quite unstable during adsorption until the filters reached an equilibrium state. Macleod and Richmond, Richmond, and Lee have made detailed studies of the effects of adsorption on the characteristics of narrowband filters. The results are applicable to all types of multilayer coatings.
The shifts in the characteristics are due, as we have seen, to the filling of the pores of the film with liquid water. In multilayers, the pores of one film are not always directly connected with the pores of the next, and the penetration of atmospheric moisture is frequently a slow and complex process in which a limited number of penetration pores take part, from which the moisture spreads across the coating in increasing circular patches. The primary entry points for the moisture are thought to be nodules where capillary condensation can take place in the fissures that often surround them.
The coating may take several weeks to reach equilibrium and, afterwards, will exhibit some instability should the environmental conditions change. The patches, which can sometimes be seen with the naked eye as a flecked or mottled appearance, can be made more visible if the coating is viewed in monochromatic light, at or near a wavelength for which there is a rapid variation of transmittance (Figure 12.7).
The edge of an edge filter or the passband of a narrowband filter is especially suitable. Wet patches show a shift in wavelength that changes them from high to low transmittance, or vice versa, and they can be readily photographed as was done in Figure 12.8 and Figure 12.9.
The drift of the filters toward longer wavelengths, which occurs on exposure to the atmosphere, varies considerably in magnitude with both the materials and the spectral region, and there is frequently considerable hysteresis on desorption.
In the infrared, the layers are thick, and many of the semiconductor materials used as high-index layers have high packing density. This means that moisture-induced drift is less of a general problem than it is in the visible and ultraviolet regions of the spectrum, although it is important in some applications.
In the visible region, drifts can be as high as 10 nm, and sometimes greater, toward longer wavelengths. The gradual stabilization of the coating as it reaches equilibrium is frequently referred to as aging or settling.
The energetic processes can usually suppress completely the moisture-induced drifts and have been almost universally adopted for suitable coatings. It should be noted, however, that not all materials respond well to the brutal bombardment characteristic of the energetic processes. Metals suffer from the inevitable implantation of the bombarding species.
Their optical properties are degraded by the scattering of conduction electrons that result. Fluorides lose fluorine, so the bombardment must be strictly limited; otherwise, the concentration of vacancy defects becomes too great. Oxygen tends to fill the vacancies and form oxyfluorides that are neither as rugged as the original fluorides nor as useful in the ultraviolet.
It is not simply in generating optical shifts that moisture is a problem for coatings. It has major mechanical and sometimes chemical effects as well. The stress in the coating is transmitted across the gaps between the columns by short-range forces. These forces can be very easily blocked by water molecules.
An alternative explanation is that the moisture, which coats the surfaces of the columns, reduces the surface energy to something approaching that of liquid water. Since the surface energy is an important factor in the stress/strain balance in the film, the result of the moisture adsorption is a change in the stress level. The stress is usually tensile, and the moisture reduces it, often significantly.
Adhesion is also affected by moisture. The materials used for thin films typically have very high surface energies, and the work of adhesion is correspondingly high. The presence of liquid water in a film can cause a reduction in the surface energy of the exposed surfaces by at least an order of magnitude.
If water is present at the site of an adhesion failure and can take part in a process of bond transfer rather than bond rupture followed by adsorption, it will reduce the work of adhesion, and it is more likely that the failure will propagate.
There is frequently enough strain energy in a film to supply the required work. The penetration sites for the moisture patches are probably associated with defects that may act as stress concentrators, where adhesion failures driven by the internal strain energy in the films may originate.
Blistering is a similar form of adhesion failure frequently associated with moisture penetration sites and a compressively strained film. Uniform strain in a film is translated into a shear stress across its interface that is zero in the center and a maximum at the edge. Thus, the edges of a coating are particularly vulnerable.
Defects at the edge act as stress concentrators, and if the forces are sufficiently high, delamination can begin and gradually propagate from the edge across the film. The presence of moisture encourages such failures. It is important, therefore, that defects at the edge of a coating should be kept to an absolute minimum. Great care should be taken with the fixtures that hold the substrates in place during the coating operation. These should be designed to avoid any small scratches or other damage to the edges of the substrates.
We have already mentioned that changes in temperature cause changes in the spectral characteristics of coatings, with narrowband filters being the most sensitive to such alterations. We must divide the coatings into those that have been simply thermally evaporated and those produced by an energetic process.
For small temperature changes, the principal effect is a simple shift toward longer wavelengths with increasing temperature. For the materials commonly used in the visible region of the spectrum, the shift is of the order of 0.003% °C⁻¹, while for infrared filters it can be greater, and a useful figure is 0.005% °C⁻¹, although it can be as high as 0.0125% °C⁻¹.
It must be emphasized that these figures depend strongly on the particular materials used. Filters of lead telluride and zinc sulfide can actually have negative coefficients greater than 0.01% °C⁻¹, and using these materials, it is even possible to design a filter that has a zero temperature coefficient.
With greater positive changes of, say, 60 °C or more, it is usual for any moisture in the filter to desorb partially, causing an abrupt shift toward shorter wavelengths (Figure 12.10). This shift is not recovered immediately upon cooling to room temperature, and so considerable hysteresis is apparent in the behavior.
Subsequent temperature cycling, before readsorption of any moisture, will then exhibit no hysteresis. Eventually, if maintained at room temperature, the filter will readsorb moisture and drift gradually back to its initial wavelength.
Exposure to higher temperatures still, over 100 °C, can cause permanent changes that appear to be related to minute alterations in the structure of the layers, altering the adsorption behavior so that some materials become less ready to adsorb moisture while others show more rapid adsorption.
A frequently applied empirical treatment involves baking filters at elevated temperatures, usually several hundred degrees Celsius, for some hours. The baking process reduces residual absorption, particularly in reactively deposited oxide films, and improves the subsequent stability of the coatings.
Part of the baking process appears to involve the opening up of the pores in the films, by smoothing out restrictions, so that moisture adsorption processes are more rapid and the films reach equilibrium in normal atmospheres much more quickly.
Films deposited by energetic processes usually exhibit lower temperature coefficients than thermally evaporated films, even when the effects of moisture desorption and adsorption in conventional films are eliminated.
This is, at first sight, a surprising result. However, the explanation appears to lie in the microstructure. The lateral thermal expansion of the loosely packed columns in thermally evaporated films enhances the drifts due to temperature changes.
In energetically deposited films, the material is virtually bulk-like in that there are no voids between any residual columns, and the material exhibits bulk-like properties. The change in characteristics with temperature changes now corresponds to what would be expected from bulk materials.
Indeed, Takahashi has shown that for multiple-cavity narrowband filters, once the design and materials are chosen, the expansion coefficient of the substrate dominates the behavior and can even change the direction of the induced spectral shift.
The stress induced in the coating by the differential lateral expansion and contraction of substrate and coating is translated by Poisson’s ratio into swelling or reduction normal to the film surfaces.
As a result of this modeling and improved understanding, temperature coefficients of peak wavelength shift at 1550 nm of 3 pm °C⁻¹ (pm is picometre, i.e., 0.001 nm, so that 3 pm °C⁻¹ at 1550 nm represents 0.0002% °C⁻¹) have routinely been achieved in energetically deposited tantala/silica filters for communication purposes, and shifts even lower than 1 pm °C⁻¹ are possible. The Takahashi model has been further elaborated by Kim and Hwangbo.
Coatings subjected to very low temperatures usually shift toward shorter wavelengths, consistent with their behavior at elevated temperatures. The actual coatings are not usually affected mechanically, but the substrates tend to be more vulnerable. Laminated components, in particular, run the risk of breaking because of differential contraction and/or expansion.
There are losses associated with all layers, which can be divided into scattering and absorption. In absorption, the energy lost from the primary beam is dissipated within the coating and usually appears as heat. In scattering, the flux lost is deflected and either re-emerges from the coating in a different direction or is trapped beyond the critical angle within the coating or substrate.
Absorption is a material property that may be intrinsic or due to impurities. A deficiency of oxygen, for example, can cause absorption in most of the refractory oxide materials. Scattering is usually due to defects in the coating, which can be classified into volume or surface defects.
Surface defects are simply departures from the smooth, flat surfaces of the ideal film. Such departures can result from roughness of the substrate surface that tends to be reproduced at each interface in a multilayer or from the columnar structure of the layers, which results in a nodular appearance of the film boundaries. Volume defects are local variations of optical constants and are usually caused by dust particles, pinholes, or fissures in the coating.
Losses in thin films are of particular importance in the laser field, where they determine the limiting performance of multilayers. A major problem in the production of high-quality laser coatings is dust that emanates from the sources and from the powdery deposit that forms on the cold walls of the chamber.
If this dust can be eliminated, only possible if the strictest attention is paid to detail and the most involved precautions are taken, then the remaining source of scattering loss is the roughness of the interfaces between the layers and between the multilayer and substrate.
If great care is exercised, then, in the visible and near-infrared regions, the total losses (absorption and scattering) can be reduced below 0.001% (for some very special applications, losses toward one-tenth of this figure have been achieved). The power-handling capability of the coatings can reach about 5 J/cm² for pulses of 1 ns or less at 1.06 μm.
Useful surveys of scattering in thin-film systems have been written by Duparré and by Amra. Laser damage remains a very active research topic. The best bulk crystals can exhibit intrinsic damage thresholds ultimately connected with multiphoton events causing the raising of electrons into the conduction band. Damage in thin-film systems, on the other hand, is dominated by defects in the films so that the intrinsic level is not reached.
In continuous wave applications, particularly in the infrared, thermal effects associated with absorption, either local or general, appear to be the principal source of damage, with small defects being less significant. In most other cases, local defects are the problem.
The particular nature of the defects may vary considerably, from inclusions to cracks or fissures. Significant attention has recently been paid to nodules that tend to grow through the films from any substrate imperfections. These nodules are poorly connected thermally to the film, which is suspected to be an important factor in the initiation of damage.
In spectral regions where water absorbs strongly, considerable importance is attached to the presence of liquid water within the films. In other parts of the spectrum, its role is less clear, but it may still play a part. Laser damage has been surveyed recently by Koslowski and by Stolz and Génin.
