doi: 10.1111/cote.12301
Colour gamuts arising from absorber– dielectric–metal optical resonators Declan Oller, a,* De He,a Jin Ho Kim,b Domenico Pacifici,b Jimmy Xua,b and Gustavo E. Fernandesb
Coloration Technology
a
Department of Physics, Brown University, 182 Hope St., Providence, RI, 02912, USA Email:
[email protected]
b
School of Engineering, Brown University, 184 Hope St., Providence, RI, 02912, USA
Received: 10 February 2017; Accepted: 17 July 2017 Society of Dyers and Colourists
Structural colouration is a quickly growing field, encompassing physical and photonic processes such as interference, diffraction, and scattering. In this study, we investigated the optical effects in the visible wavelength range, and in particular, the colour gamuts achievable with absorber–dielectric–metal sandwich structures. These chemical-free layered structures are highly tunable, easily scaled, optical cavities that are capable of generating remarkable colours whose properties are determined completely by material and structural parameters. We employed experimental and numerical strategies to demonstrate that each absorber spans a unique colour gamut, i.e. a subset of the full chromaticity space. While gamut overlap is observed between different absorber types, the gamut areas unique to each absorber occur at different hues of high excitation purity. A comprehensive understanding of how these colour gamuts develop and how different materials may be combined to expand larger subsets of the chromaticity space is required in order to maximize the variety of colours achievable with this system and elevate it into a ‘structural colouration technology’.
Introduction Colours are fundamentally important to our perception of the world. They affect us in both physiological and psychological ways [1–5] and thus constitute an integral part of the human experience. Myriad ingenious colouration methods exist in nature or have arisen from human effort. The most ubiquitous technique is chemical colouration, whereby photons with energy corresponding to a molecular or atomic resonance are absorbed and removed from the light that reaches our eyes. While chemical colouration has certain advantages, e.g., it can produce very bright colours with high excitation purity, and lack of iridescence, it is also has disadvantages: the chemicals used are often environmentally unfriendly, can degrade under ultraviolet (UV) illumination or heating [6–12], and can seldom be created anew by design; a desired colour must result from a specific chemical or mixture of existing chemicals. Structural colouration (or ‘physical colouration’) is a promising alternative to chemical colouration, encompassing many mechanisms such as interference, diffraction, and scattering. Structural colouration has many advantages; notably, it does not use the same environmentally harmful materials that chemical colouration does, can have better resistance to sunlight and heat, and can be created by design, as opposed to mixing (as is often done for chemical colouration). Disadvantages (depending on the platform) often include lower saturation, more difficult fabrication, and iridescence. It is a well established, yet also a quickly growing field of research. Structural colouration has been shown to occur in nature in the form of beetle shells [13,14], bird feathers [15,16], butterfly wings [17], opals [18], and of course our familiar blue sky. A comprehensive review is given by Sun et al. [19], covering the different mechanisms giving rise to colouration in nature with examples of each. Human use of structural colouration is ancient as well, from
tempering colours of metal oxides [20,21] to use of nanoparticles in making glass [22]. More recently, the advent of modern fabrication techniques has given rise to creative colouration methods. Notable recent examples are subwavelength plasmonic colour filters [23], large-scale plasmonic pixel printing [24], actively controlled plasmonically enhanced pixels [25,26], and a photonic crystal from anodized aluminum layers of alternating indices [27]. An exciting platform for structural colouration can be created through a multilayer film structure of an absorber on top of a dielectric on top of a reflective metal (Figure 1). The mechanism by which this structure gives rise to colour is commonly explained as a Fabry-Perot cavity, an implementation of thin-film interference [28,29]. With white light incident on the structure, light of each wavelength both reflects off the initial air–absorber interface and enters into the structure, in which it undergoes further reflections off the absorber–dielectric and dielectric–metal interfaces (the metal is thick enough that it can be considered semi-infinite and thus not allowing any transmission). The extra optical path length these beams travel between reflecting interfaces, as well as phase shifts from the reflections at the interfaces, cause them to have both different phase and amplitude with respect to the initially reflected beam. When finally leaving the structure they all combine and, for a given wavelength, this sum of reflected beams either interferes constructively or destructively, in which case that wavelength is suppressed to the viewer. The distribution of reflected wavelengths (some suppressed and some not) determines the final colour. Due to its simplicity, it is inherently scalable and easy to produce, not needing any nanofabrication steps. This structure has been reported previously in various forms: Xue et al. [30] produced a wide range of colours by varying the effective refractive index of the dielectric layer, Yue et al. [29] used the structure to create high saturation colour filters, and Yang et al. [31] demonstrated that iridescence could be minimized in this
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Oller et al. Color gamuts of Fabry-Perot resonators
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Figure 1 Numerically simulated colour gamuts for three different absorber materials (Co, C, Ge) on a standard xy CIE chart. Representative points are shown (a–f) at the edges of each colour gamut, indicating the highest excitation purity achievable for these hues with this set of absorber materials. The thicknesses used to calculated these points are as follows: (a) 308 nm AAO, 40.6 nm C, (b) 33 nm AAO, 30.6 nm C, (c) 45 nm AAO, 3.6 nm Ge, (d) 220 nm AAO, 4.0 nm Ge, (e) 106 nm AAO, 5.1 nm Co, (f) 330 nm AAO, 7.4 nm Co. A schematic of the structure (not to scale) is shown as well (top)
structure. These reports and others demonstrate excellent and inventive design and characterization of this structure. However, the full colour gamut possibilities have not been reported, yet are fundamentally important for harnessing these structural colouration pathways into a novel colouration technology. Additionally, in past reports, exploration of the absorbing layer’s effect has been minimized to a role as a generic absorbing layer. However, it can also be used as another colour tuning parameter.
Experimental In this study, samples were prepared as described below. A polished Si wafer is cleaved into strips of approximately 1 cm by 5 cm, which are then sonicated sequentially in acetone and isopropyl alcohol (IPA) and dried with pressurized nitrogen. Next, a 5 nm titanium adhesion layer is deposited via electron beam (e-beam) evaporation at a rate of 1 A/s, immediately after which a 600–800 nm aluminum (Al) layer is deposited via e-beam evaporation at a rate of 5 A/s. Anodic aluminum oxide (AAO) is created by electrochemically anodizing the Al layer [32]. Anodization was performed in a 0.3 M oxalic acid electrolyte solution at 40 V and 10 °C with a typical growth rate of 100 nm/min. Anodization times were always limited such that at least 200 nm of the bottom Al layer would remain unanodized so that it would behave as a semiinfinite reflector. Because AAO is used here simply as a dielectric spacer, only a single anodization step is used, giving rise to porous but unordered AAO. No pore widening was done. For samples in which different regions were anodized for different lengths of time, nail polish was
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applied and cured to protect a given region from further anodization, after which time it was removed with acetone and IPA. Absorber materials (copper, germanium, nickel, iron, and cobalt) were then deposited via e-beam evaporation at a rate of 1 A/s on top of the AAO. Shadow masks were used to leave parts of the sample with no deposited absorber for characterization purposes. All materials deposited by e-beam evaporation were deposited at a base pressure in the 106 mTorr range. Refractive indices of all materials used (Al, AAO, absorber materials) were measured by variable angle spectroscopic ellipsometry of the material deposited on a silicon reference sample and fitted using the CompleteEase (from J. A. Woollam, USA) software (Woollam, USA). The reflectance spectra of the fabricated samples were measured using a calibrated system (QEX10) from PV Measurements, Inc. (Boulder, CO), specifically designed to measure specular reflectance, at a constant angle of 7° from normal incidence. Several calibration samples were employed to achieve wavelength- and intensity-normalized reflectance curves. All measurements given in the paper were normalized between 0 and 1 with respect to a calibrated mirror reference sample. Reflection spectra were calculated from refractive indices by using a standard Transfer Matrix Method (TMM). The numerical simulations were performed in Mathematica v10.3 (Wolfram Research, USA) via a standard TMM formulation of Maxwell’s Equations boundary-matching conditions between layers [33]. No scattering, no surface roughness, and an incident medium of vacuum (n = 1) was assumed. Reflectivity curves (calculated or measured) were then used to calculate the ‘perceived colours’, using the D65 illuminant and the CIE 1931 2° Standard Observer colour matching functions [34,35]. Calculated colours were plotted on a standard 1931 CIE xy colour space chromaticity diagram. The xy colour space is useful for presenting colour gamuts in a physically meaningful way, but unfortunately does not have a native concept of hue; the curved part of its perimeter corresponds to the perceived colour of pure wavelengths in the visible spectrum, but the straight segment of the perimeter (the ‘line of purples’) has no monochromatic equivalent. Therefore, unless otherwise explicitly stated, in this paper the word ‘hue’ is to be read as ‘angle around the white point’ for a colour. Sample photographs were taken using overhead sunlight as the illuminant, which closely approximates D65.
Results and discussion In this study, we numerically and experimentally demonstrate the total colour gamuts achievable with this highly tunable, easily scaled, optical cavity structure. Here, the dielectric layer consisted of AAO, chosen for its good optical properties, surface properties, and ease of manufacture. The full colour gamut for a given absorber material was achieved by varying two parameters: the AAO thickness (tAAO) and the absorber thickness (tAbs). By investigating the general behavior of varying these thickness parameters individually, we showed that the total range of colours this structure could produce for a given absorber material is bounded and well defined. Furthermore, we
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Oller et al. Color gamuts of Fabry-Perot resonators
showed that, due to their different indices of refraction, different absorbers give rise to different colour gamuts in which the weaknesses of one can be compensated by the strengths of another. The gamuts of three absorber materials (calculated from literature refractive indices) are overlaid on a xy CIE plot to demonstrate their common regions and differences (Figure 1). In addition, representative points were chosen for each absorber to demonstrate the highest excitation purity for a given hue which can’t be attained by the other absorber materials. The Al substrate is very reflective ( 90%) in the visible range of wavelengths ( 360–780 nm) and the AAO layer is practically lossless (n = 1.6 [36]) in this wavelength range. The absorbing layers used are lossy and optically dense, showing high values of the real and complex refractive index (n and k) within the visible range. The bulk reflectivity of each of the component materials on their own is spectrally flat and thus gray. However, inventive combinations of these in this structure give rise to brilliant colours, as seen in Figure 1. R
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It is informative to investigate the colour produced by our structure, as one thickness parameter is varied while the other is kept constant. Figure 2 illustrates the effects of experimentally varying tAAO while keeping tAbs constant. The Al substrate was anodized in steps so that the AAO thickness increased by fixed amounts. A 4.4-nm Ge layer was deposited on half of the sample as well as on a reference Si substrate. The resulting observed colours are shown in Figure 2a. The solid reflectivity curves shown in Figure 2b were calculated using the TMM and measured physical parameters, while the dashed reflectivity curves in Figure 2b were measured for each of the numbered regions in Figure 2a. These measured reflectivity curves were then used to calculate the perceived colours, which were used as background for the panels in Figure 2b, and show excellent agreement with the photographed colours of Figure 2a. This indicates that the measured material parameters are accurate and that the TMM is capable of modelling the structure with high fidelity, despite the fact that our version of the TMM does
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Figure 2 Experimental results for constant tAbs = 4.4 nm Ge and increasing tAAO (from 215 to 392 nm). (a) A photograph of the sample; the left side has only AAO on Al, displaying weak colour, while the right side shows the full structure with the absorber. (b) Material parameters measured from the sample are used to calculate the normal reflectance (solid curves), compared with measured reflectance (dashed curves). Perceived colours calculated from measured reflectivity are shown in the plot backgrounds. (c) Measured material parameters are used to calculate the colour path (dotted line) as tAAO is increased from 194 to 431 nm as well as the plotted points corresponding to the regions of the sample in (a). (d) The same path and points are also plotted in the CCP; the path goes through more than one interference order
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Figure 3 Experimental results of varying tAbs. (a) A photograph of the sample. Each row (in the direction of the arrows) is a constant tAAO and each column is a different value of tAbs. (b) The variations in tAbs for each of the three tAAO values; each point corresponds to a region of the sample in (a). As seen in (a), the colour change with increasing tAbs is highly dependent on tAAO. (c) Corresponding colour paths on CIE charts; for large tAbs the colour path returns to the gray point. Each point corresponds to a region of the sample in (a)
not account for surface roughness or scattering due to layer imperfections. The colours computed from the (calculated) spectra of Figure 2b are also plotted as points in the CIE plot shown in Figure 2c. The dashed curve connecting these points was also computed using the TMM with the measured physical parameters. tAAO was varied from 194 to 391 nm in the numerical calculation. As seen in the Cartesian Chromaticity Plot (CCP) of Figure 2d, the colour varies far more dramatically with tAAO than with tAbs. The description of this structure as a optical cavity [29,31] is pertinent to explain this behavior – to first order, the cavity length, i.e. tAAO, dictates the positions of the peaks and valleys in the reflection spectrum while the top absorbing layer affects the ratio of peak to valley intensity (i.e. the cavity’s finesse). The horizontal colour bands correspond to interference maxima for a given dominant wavelength determined by tAAO; adjacent colour bands combine to form an ‘interference order’, which repeats for increasing tAAO. The explanation for the ‘limit’ behavior as tAAO ? ∞ follows directly from this. For small cavity sizes, only one wavelength can maximally interfere; however, as the cavity gets larger, constructive interference maxima can occur at several wavelengths. The effect of this can be seen in Figure 2d: the higher orders begin to smear out and blend into each other as a given large tAAO gives rise to interference at several wavelengths at once. As tAAO gets very large, so many wavelengths are able to interfere that R is
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spectrally flat and the colour washes out to gray. This effect can also be seen in a CIE chart, in which an increasing tAAO path will spiral into the gray point for high enough tAAO. The case of tAAO = 0 is actually a special case as reported by Kats et al. [37]. However, although it also produces colour through interference, the mechanism by which it creates this interference is different; while the tAAO > 0 structure produces phase differences primarily through propagation of light in the cavity, the structure reported by Kats et al. depends on a complex phase shift at the metal–absorber interface, which is absent in the tAAO > 0 case. It is relevant to note that while we varied the thickness tAAO to change the cavity’s optical path length (nAAOtAAO), it can also be effected by altering nAAO, as Xue et al. [30] did by both widening the AAO pores and infiltrating the pores with ethanol. Because the feature size of the pores formed via our fabrication process are subwavelength, the quality of the AAO has no noticeable effect on the colour purity. While tAAO is the primary factor in determining hue, it is also interesting to explore the effect of changing tAbs with a constant tAAO. Past reports on this structure have not explored the properties of the absorber and how they can be utilized to generate different hues, using it simply as a cavity reflector/absorber and optimizing its thickness to maximize the reflectivity peak/valley ratio. However, our experiments and calculations indicate that it, in fact, also has a role in determining the colour, albeit less dramatically than tAAO. A useful parameter for analyzing the colour gamut
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Oller et al. Color gamuts of Fabry-Perot resonators
quantitatively is excitation purity (EP), which is defined as follows for a given point (colour) in the xy CIE colour space: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðx xwp Þ2 þ ðy ywp Þ2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi EPðx; yÞ ¼ ðxbd xwp Þ2 þ ðybd ywp Þ2
16 6 19 1 21 6 24 1 26 6 29 1 31 6 34 1
where the point in question is {x, y}, {xwp, ywp} is the white point, and {xbd, ybd} is the point (closer to {x, y}) where the line going through {xwp, ywp} and {x, y} intersects the colour space perimeter. It is essentially the per cent of purity of a colour and thus varies from 0 to 1. Our fabricated structure seen in Figure 3a shows three rows of different tAAO (61, 187, 217 nm), with tAbs varied from 0 to 17 nm of Ge. Earlier fabricated samples indicated that tAbs had no effect on hue, only on the EP; however, inspection of the CCP in Figure 3b shows that this colour change is not very noticeable for many values of tAAO and ranges of tAbs, which makes this effect easy to miss (e.g., the bottom row of Figure 3a). For a relatively small tAbs, the absorbing layer contributes two main effects: (1) a different front-surface reflectance; and (2) a selective absorber that maximally
absorbs the wavelengths for which the interference condition dictates a large overlap of the electric field with the absorber (e.g. in an anti-node). However, as tAbs increases, the phase change from propagating through its optical thickness becomes an important effect as it effectively increases the cavity size. This effect can be seen in Figure 3c in which a colour path is generated as tAbs is increased for a fixed tAAO – up to a point, the hue is mostly constant but increases the EP, but further increase of tAbs changes the hue. The limit behavior tAbs ? ∞ is that in which no incident light is able to fully transmit through the absorber into the cavity, and thus there are no interference effects and no reflection aside from that of the air–absorber interface. This is the same as the bulk absorber reflectivity, which is typically spectrally flat and gray. Indeed, this is what the paths in Figure 3b,c are seen to approach. One more parameter that can be varied for unique colouration production is the absorber material. In the above experimental results, Ge was used due to its good colouration and fabrication properties. However, as shown in the fabricated sample in Figure 4a, many other materials
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Hue Figure 4 (a) Photograph of single-piece sample with increasing AAO thickness and rows of different absorber materials. Top row is AAO/Al only, rows below are absorber/AAO/Al. Measured absorber thicknesses: Ge = 6 nm, Co = 10 nm, Cu = 10 nm, Fe = 10 nm, Ni = 7 nm. Measured AAO thicknesses are labeled above. (b–f) CIE plots for the five different absorber materials show the total gamut for that absorber (solid line), as well as the path (dashed arrow) for the corresponding measured tAbs and measured tAAO. The points on this path and colours inset in each CIE plot were calculated from measured parameters of this sample. (g) Calculation of excitation purity (EP) for the gamut boundary for each absorber material as a function of hue. The direction of the dashed arrows indicate the order of the absorbers to the right for that hue; for one hue range, the absorbers are in order of increasing EP, and for another hue range, decreasing order
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give excellent results when used for this layer. As discussed above, numerical variation of both tAbs and tAAO based on experimentally measured material properties allows us to define a colour gamut for a given absorber material. It is important to note that different materials give rise to different colour gamuts (see Figure 4b–f), even though they individually have spectrally featureless indices of refraction. While the gamuts of several elements appear similar, a plot of the EP versus hue for each absorber material together (Figure 4g) reveals that marked differences, as well as a pattern, emerge. For this plot, hue is the parameter from HSL colour space. The EP versus hue curve for all absorber materials investigated here follow a similar shape, but for the hue range ( 0.5–0.8), the absorber materials in order of increasing EP are (Ge, Cu, Fe, Ni, Co), while for most of the rest of the range ( 0.0–0.4 and 0.9–1.0), the order is exactly reversed, demonstrating that the weaknesses in gamut of one absorber material can be countered by the strengths of another. The differences are non-negligible as well; comparing the two absorber material examples of Ge and Co, at a hue of 0.04, the EP of Ge is 56% larger than the EP of Co, while at a hue of 0.71, the EP of Co is 43% larger than the EP of Ge. It is also worth noting that these large gamut differences are only from five experimentally verified elemental absorber materials; combinations and use of more judiciously chosen materials would certainly lead to even larger gains. This situation demonstrates the significance of the absorber material as another colour tuning parameter. There are several important details of this analysis. First, it is worth noting that while the xy CIE charts shown in the figures are used throughout the literature to display the colouration gamut for a structure, they only represent hue and EP, thus all colours with different brightnesses but the same hue and EP will be mapped to the same point. For a full picture, it is necessary to use a three-dimensional colour space such as an xyY plot [38,39]. This situation gives another reason for taking advantage of the properties of different absorbers, because similar looking gamuts, in Figure 4 for example, may be more different than they initially appear. They may have different brightness levels for a given hue and EP, and typically maximum brightness is desirable. Another pertinent detail is the dependence of the absorber material parameters on its thickness due to effects such as surface roughness [40–42] and quantum confinement [43,44]. Indeed, our measurements and calculations with thin Ge films indicate that the indices of refraction change significantly as the thickness is decreased. Therefore, to be fully accurate, a refractive index that is both wavelength dependent and thickness dependent should be used to calculate the gamut.
Conclusion In this study, we have demonstrated the concept of a colour gamut with respect to different absorber materials used in this structure. Although CIE chart subspaces themselves are not new, we are not aware of previous reports rigorously demonstrating the boundedness of, and presenting colour gamuts for, a structural colouration structure. We have investigated the effects of individually varying the material parameters relevant to this structure and how they give rise to a full colour gamut. Additionally, we have shown that, 6
although its role in colouring this structure has often been neglected, tAbs is another parameter that can be used for colour tunability. Lastly, we have presented the concept of the CCP to enable the mapping of desired colours to fabrication parameters in a simple way as well as providing physical insight about the structure. We would like to explore ramifications and applications of this work, such as how the bounding gamut (and constituent points) transforms with various modifications (e.g., viewing angle, crystallinity, surface roughness, etc.), its implementation as chromatic filters for display colour technology [45–49] and CMOS image sensors [50], as well as a more intentional design aspect of the colour gamut. For example, if two judiciously chosen absorber materials were combined (cosputtered, used in a multilayer absorber, or evaporated as an alloy), would the resulting gamut be a combination of their individual gamuts, or something new entirely?
Funding We are thankful for the enabling support from the National Science Foundation award number 1530547, the Army Research Laboratory award number W911NF-14–20075, and the National Science Foundation award number DMR-1408743.
Acknowledgements We are grateful to Dr. D. Li and T. Shen for experimental consultation and advice.
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