1. Introduction

Guided-mode resonance filters (GMRFs) are diffraction gratings with spectrally narrow reflectance peaks due to resonance anomalies, i.e., coupling of incident light into a semi-guided mode in a corrugated waveguide [1–5]. In its simplest form the GMRF consists of a single high-index dielectic layer on a periodically corrugated transparent substrate. The spectral position and width of the resonance reflection peak then depend critically on the grating period, profile height, coating layer thickness and the refractive indices of the dielectric materials, as well as the angle of incidence and the state of polarization of the incident light beam [3]. Regarding applications, sensitive and inexpensive GMRFs fabricated by sub-micron microreplication on thin plastic sheets have been demonstrated as bio-chemical sensors [6].

Atomic layer deposition (ALD) [7, 8] of TiO₂ on SiO₂ substrates provides the means for producing high-quality GMRFs with a uniform coating on all facets of a binary substrate profile [9]. While ALD is a low-cost method, the use of an inorganic substrate requires individual etching of each sample. Aiming at an economic overall production process of GMRFs in large quantities, we demonstrate here the use of organic substrate materials (polymers), in which the corrugation can be created by replication techniques such as hot embossing [10] before ALD coating. Polymers are more flexible and less brittle than inorganic substrate materials, but their thermal expansion and thermo-optic coefficients are substantially larger [11–13]. This could potentially lead to a large spectral thermal shifts of the resonance peak position in analogy with waveguide Bragg gratings [14,15]. This would be unacceptable in most applications (excluding temperature sensing, strain measurements, etc.).

In Sect. 2 we present the basic structure of the devices to be demonstrated, as well as their typical spectral characteristics. We then proceed, in Sect. 3, to model the thermal properties of these devices with calculations by the Fourier Modal Method (FMM) [16]. We find that, despite of the large values of the thermal expansion coefficient (TEC) and the thermo-optic coefficient (TOC), the spectral position of the resonance peak should remain nearly stable over a large temperature range above the room temperature. This is enabled, in part, by choosing an ALD-deposited TiO₂ with a negative TOC as the high index cover layer. After discussing the details related to fabrication and characterization of the GMRFs in Sect. 4, we verify the main theoretical findings experimentally in Sect. 5. Finally, some conclusions are drawn in Sect. 6.

2. Device structure and design

Figure 1 illustrates the ideal GMRF structure we are aiming at. We first have a polymer (polycarbonate) substrate with a binary grating profile characterized by height h, period d and ridge width c so that we can define the fill factor as f = c/d. This grating is coated by a thin dielectric (TiO₂) layer grown by ALD. Owing to the conformal nature of the ALD process, the thickness t of the high-index layer is assumed to be the same on all sides of the profile (top and bottom of the grooves as well as the vertical sidewalls). The superstrate is assumed to be air; the depth of the final air-filled groove is then h and its width w = d – c – 2t is assumed to be greater than zero. The polymer substrate (with the binary grating profile) has a uniform refractive index n_s, and the TiO₂ cover layer has a refractive index n_c. The GMRF is illuminated from air by a linearly polarized plane wave incident at an angle θ, and we are primarily interested in the spectral efficiency curve of the specularly reflected plane wave.

 

Fig. 1 Basic device structure: a binary polymer grating is coated by a TiO₂ layer. The fill factor is defined as f = c/d.

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By appropriate choices of the parameters d, f, h, t, n_c, n_s, and θ, we can obtain a guided-mode resonance with 100% reflectance for either TE or TM polarized light at a desired wavelength λ_r. In our examples we use FMM to design the GMRFs particularly for TE polarized illumination at center resonance wavelength λ_r = 853 nm and angle of incidence θ = 20°. Our material choices fix the refractive indices: we use the room-temperature values n_s = 1.57 from Refs. [12, 17, 18] and n_c = 2.3224 obtained by in-house measurement at λ = 853 nm. In the design, d, f, h, and t are therefore treated as variable parameters.

One possible set of experimentally realizable parameters is d = 425 nm, f = 0.63, h = 120 nm, and t = 61 nm. Figure 2 shows the effect of varying different parameters around the design values, and the spectral shape of the resonance peak with the parameters listed above is illustrated explicitly in Fig. 3a. Figure 2a shows the specular reflectance R of the GMRF (index 1 means 100% reflectance) when the grating ridge height h and the TiO₂ film thickness t are varied, and implies that an error in one parameter can be compensated by changing the other. Hence, if one finds that the ridge height of the polymer grating is incorrect, one can still obtain the resonance at the correct spectral position by adjusting t appropriately in the ALD process, which is the final fabrication step (see Sect. 4). Figure 2b demonstrates the possibility of fine tuning the resonance wavelength by adjusting the angle of incidence, and Fig. 2c shows the reflectance when the ridge height h and the fill factor f are varied. Thus, for example, an increase in pattern height can be compensated by reducing the fill factor. Finally, Fig. 2d illustrates the (rather tight) tolerances for variations in the refractive indices of the two materials.

 

Fig. 2 Fourier modal analysis of the effects of parameter variations in specular reflectance R. (a) Variations of ridge height h and TiO₂ film thickness t. (b) Variations of wavelength λ and angle of incidence θ. (c) Variations of ridge height h and fill factor f. (d) Variations of refractive indices n_s and n_c of the polycarbonate substrate and TiO₂ cover layer.

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Fig. 3 (a) Spectral variation of the specular reflectance R(λ) with room-temperature values of all design parameters. (b) Calculated spectral reflectance curves at T = 100 °C due to thermal expansion alone (curve 1-TEC), due to thermo-optic effect alone (curve 2-TOC), and due to combination of both effects (curve 3-TEC-TOC).

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Theoretical results for the effect of TiO₂ layer thickness on resonance peak position for TE mode are shown in Fig. 4. An increase in t from 61 nm to 71 nm leads to a shift of λ_r from 853 to 871.6 nm when θ = 20°.

 

Fig. 4 (a) Simulated room-temperature spectral variation of the reflectance as a function of TiO₂ layer thickness. (b) Spectral lineshapes of GMRFs with TiO₂ layer thicknesses t = 61 nm (blue curve 1) and t = 71 nm (red curve 2).

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3. Modeling of thermal behavior

In view of the results shown in Fig. 2, the resonance wavelength λ_r depends critically on the refractive indices n_s and n_c of the two materials, which in turn depend on operating temperature T because of the thermo-optic effect. Furthermore, λ_r is affected by modifications of the dimensional parameters of the structure, caused by thermal expansion. The latter is a potentially serious issue since the thermal expansion coefficients of polymers are known to be nearly ten times larger than those of optical glasses [11]. Complete modeling of the thermal behavior of GMRFs therefore requires consideration of both thermo-optic properties of the materials and thermal expansion of the entire structure.

For polycarbonate, we use the thermal refractive-index data from Refs. [12,13]. We measured the thermal dependence of the refractive index of the TiO₂ films by home made heating assembly directly attached with ellipsometry (Sect. 4). In modeling, thermal expansion was taken into account by assuming that the period and height of the polycarbonate grating expand linearly with T while the fill factor f remains constant. Also the TiO₂ layer thickness t was assumed to increase with T, making the air gap narrower with increasing temperature. The thermal expansion coefficient of polycarbonate is taken to be 6.55 × 10⁻⁵ °C⁻¹ [11, 12, 14], and we used the value 8 × 10⁻⁶ °C⁻¹ [11] of crystalline TiO₂ to approximate the thermal expansion coefficient of amorphous TiO₂. Then direct FMM calculations were applied to the resulting dimensional parameters and refractive indices at each temperature, ranging from 25 °C to 100 °C in 5 °C steps.

The results of the FMM calculations for TE mode are presented in Fig. 5, where we consider thermal expansion effects (TEC) and thermo-optic effects (TOC) separately, as well as the combined effect. All calculated results can be well approximated by straight lines, also shown in Fig. 5. As shown in Fig. 5b, since the TEC fit slope is positive and that of TOC is negative, the combined effects lead to partial athermalization of the device, i.e.,

 

Fig. 5 Effect of temperature change T in the spectral shift Δλ_r of the resonance peak. (a) Individual TEC and TOC effects of TiO₂ and PC. (b) Combined TEC and TOC effects of TiO₂ and PC.

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It is interesting to note from Fig. 5 that the negative TOC of TiO₂ has a significant role in athermalization, although its magnitude is an order of magnitude smaller than that of PC. This is explained by a large overlap of the guided mode with the TiO₂ film. There are ways to further reduce ∂λ_r/∂T, for example, a plastic material with a smaller thermal expansion coefficient would do this. On the other hand, one could change the TiO₂ layer thickness t, which would have an effect in the thermal expansion contribution but also on the thermo-optic contribution since thinner TiO₂ films tend to have more negative values of the TOC. Changing t would of course require adjustments of the other structural parameters to retain λ_r at the original value.

4. Fabrication and characterization techniques

Our fabrication process of GRMF structures of the type illustrated in Fig. 1 consists of three main steps:

The process starts from a 2” diameter Si wafer with 〈100〉 crystal orientation. The wafer is first spin coated by a high-resolution negative resist HSQ XR-1541 from Dow Corning, with constituents isobutyl methyl ketone, hydrogen silsesquioxane, and toluene. The rotation speed and spin coating time are adjusted so as to get film thickness of 120 nm, which was the desired height of grating structure. The HSQ film thickness was measured by Dektak 150 stylus surface profilometer manufactured by Veeco Metrology. The grating patterns are then written on the HSQ resist over an area of 25 mm² by Vistec EBPG5000+ES HR electron beam pattering tool at a scaled dose of 4800 μC/cm². After exposure, the resist is developed with MP 351 developer, which contains disodium tetraborate decahydrate and sodium hydroxide and water solution with the ratio 1:3, followed by rinsing with isopropanol and water for 90 and 30 seconds, respectively. After development, the sample is heat treated for 3 hours at a temperature of 300 °C in an oven. The heat treatment makes HSQ more fragile, depicting properties analogous to silica as a hard stamping material. The heat treated sample is then subjected to surface treatment to deposit a silane layer with silanization solution composed of a mixture of HFE 7100 engineering solvent with 0.2% of trimethylhydroxysilane (TMS) in presence of nitrogen atmosphere to act as a de-adhesive layer for stamping into polycarbonate substrate.

The replication was performed in polycarbonate sheets with thickness of a few hundred microns (from Makrofol DE) by using Obducat Eitre imprinter. In the replication process the stamp is heated at a temperature of 165 °C, slightly above the glass transition temperature of polycarbonate. Then a pressure of 50 bar was applied for 2 minutes and finally air cooling was applied. Replication was followed by thin films deposition (61 and 71 nm) of amorphous TiO₂ by using Beneq TFS 500 ALD reactor at a deposition temperature of 120 °C with commonly known precursor TiCl₄ and H₂O materials. Si wafers were also deposited by TiO₂ films in the same experiment to find out exact film thickness in relation to the number of ALD cycles and to determine the refractive index of deposited amorphous TiO₂ films with ellipsometer.

Structural characterization was performed by scanning electron microscope (SEM LEO 1550 Gemini). Thermal optical properties were characterized by a variable angle spectroscopic ellipsometer VASE manufactured by J. A. Woollam Co. The ellipsometer was employed to measure the spectral reflectance resonance peak for TE-Mode at θ = 20° in the wavelength range 750–880 nm with beam spot size of 3 mm by scanning the wavelength with steps of 0.2 nm. The polycarbonate grating was placed firmly against a home-built aluminum hot plate whose temperature was controlled and monitored carefully. The heating rate was 0.5 ± 0.1 °C/min during each measurement interval. The surface temperature of the sample was measured using Convir ST8811 Handheld Infrared Thermometer by Calex Electronics Limited Company with an accuracy of ±2 °C. The calibration of both the Aluminum hotplate thermocouple and Convir was checked by measuring simultaneously the temperature of heated water with a good quality liquid thermometer. The Infrared thermometer is based on the principle of detection of emitted thermal radiation from heated samples which depends on emissivity of source materials. The emissivity of water is found exactly equal to Convir as well as our polycarbonate substrate material (0.95). The surface of the aluminum hot plate was rubbed with a fine sand paper to eliminate any back reflections and it was tested by an initial transmittance and corresponding reflectance measurement at room temperature without the presence of hot aluminum plate. The comparison of both measurements at room temperature (with and without aluminum hot plate) was made and matched prior to the start of thermal measurements with hot plate. Since each thermal spectral measurement was performed by a temperature interval of 5 °C, the material may be considered at thermal equilibrium at each temperature interval. The refractive indices of ALD coated TiO₂ films at various temperatures were measured by ellipsometer and then employed directly in calculations (Sect. 3) on the behavior of central resonance wavelength shift.

5. Experimental results and discussion

Figure 6 illustrates grating profiles after different fabrication steps. The dimensions of the structure are close to the values assumed in the design and simulations of Sect. 3. However, the profile is not quite of the type assumed in Fig. 1, mainly because of some rounding of edges of the polycarbonate grating that takes place primarily in the hot embossing step. As seen in Fig. 6c, the TiO₂ layer follows the profile of the polycarbonate grating in a highly conformal manner. The TiO₂ films coated by ALD exhibit high optical quality due to atomic scale growth and corresponding dense microstructure. Deposition process by any technique leads to adsorption of water molecules in the microstructure voids on surface of TiO₂ films [19]. On raising the temperature water molecules deadsorb and leave empty voids which causes reduction of refractive index. The TiO₂ films deposited by other techniques such as evaporation, sputtering etc. exhibit more volume fraction of voids and consequently have larger decrease of refractive index with temperature [20].

 

Fig. 6 Scanning electron micrographs of cut GMRF samples. (a) Si-master stamp. (b) Polycarbonate grating. (c) Final structure after TiO₂ coating (t = 61 nm) by atomic layer deposition.

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We first measured the TE-mode reflectance spectra at room temperature, and experimental results for a few different angles of incidence are shown in Fig. 7 together with theoretical simulations where the ideal profile of the type depicted in Fig. 1 is assumed. The measured resonance wavelength at θ = 20° is λ_r = 827.6 nm, i.e., it is shifted ∼ 3 % from the theoretically predicted value of λ_r = 853 nm. Furthermore, the measured resonance lines are somewhat wider than the theoretical ones and the experimental lineshapes do not feature the off-resonance zero crossing that is present in the theoretical curves. All of these features result from the non-ideal profile shape of the polycarbonate grating.

 

Fig. 7 TE-mode reflectance spectra of GMRFs with TiO₂ film thickness t = 61 nm for three different angles of incidence θ = 18°, θ = 19°, and θ = 20°. (a) Simulated results for an ideal profile. (b) Measured results.

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The thermal behavior of the GMRF samples were measured by ellipsometry as already described. The measured values of n_c as a function of temperature, at the wavelength 853 nm are shown in Fig. 9a. Figure 8a shows the spectral measurements at temperatures 30 °C, 35 °C and 55 °C. The difference in the peak reflectance is only about 0.4 nm between the spectra at 35 °C and 55 °C. Figure 9b shows the measured shift in resonance wavelength as a function of temperature, from 25 °C to 85 °C. The shift in the resonance wavelength is about 1.4 nm for this large temperature range. The experimental results are in relatively good agreement with the theoretical simulations predicting a shift of about 0.7 nm for the temperature range from 25 °C to 100 °C (see Fig. 5b).

 

Fig. 8 Spectral measurements of GMRF with TiO₂ thickness t=61 nm. (a) Spectral reflectance curves at temperatures T = 30 °C, 35 °C and 55 °C. (b) Room-temperature spectral lineshape subjected to thermal measurements up to T = 85 °C.

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Fig. 9 (a) Measured temperature dependence of refractive index of TiO₂ film of thickness t=61 nm at wavelength 853 nm. Thermal measurements of GMRF with TiO₂ layer thickness t = 61 nm. (b) Peak thermal spectral shift. (c) Peak resonance reflectance.

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The most noticeable feature in the thermal behavior of the organic-inorganic GMRFs considered here is the reduction of the peak reflectance at high temperatures shown in Figures. 9c and 10c. This can not be attributed to changes of the structural parameters in a perfectly periodic profile since such changes would only shift the resonance wavelength, even if the profile is not of the ideal shape assumed in Fig. 1. The most plausible explanation for the reduced reflectance is uneven swelling of the grating in the sense that the grating profile becomes increasingly space-variant at high temperatures. As a result, the resonance conditions would depend on position, which would widen the resonance peak and simultaneously decrease the peak reflectance. The useful temperature range depends on the reflectance value required by the particular application and can be judged from Fig. 9. Importantly, the thermal reduction of the peak efficiency is reversible: after cooling back down to room temperature, the resonance peak efficiency returns to the original value and the spectral line resumes its original shape within the measurement accuracy (see Fig. 8b).

 

Fig. 10 Spectral measurements of GMRF with TiO₂ layer thickness t = 71 nm. (a) Room-temperature peak resonance lineshape. (b) Peak thermal spectral shift. (c) Peak resonance reflectance.

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To further elucidate the good correspondence between theoretical and experimental results, we fabricated another set of samples with the same polymer grating profile but a TiO₂ layer thickness t = 71 nm. Figure 10a shows the measured lineshape of such a grating, with room-temperature peak at 843.8 nm (at angle of incidence θ = 20°). In view of Fig. 10b, a shift of 0.4 nm in peak spectral position takes place at 30°C. Thereafter the peak position remains constant (within our measurement accuracy of 0.2 nm), until a final shift of 0.8 nm occurs at 85°C. The corresponding peak reflectance values, shown in Fig. 10c, exhibit the same trend as for the grating with 61 nm TiO₂ layer thickness. The experimental peak position λ_r = 843.8 nm is again some 3 % smaller than the theoretical value λ_r = 871.6 nm.

6. Conclusions

We have demonstrated organic-inorganic guided-mode resonance filters fabricated by a atomic-layer deposition of TiO₂ on replicated polycarbonate gratings. This is a low-cost fabrication method, which is suitable for large-scale production. Both theoretical simulations and experiments show that nearly athermal operation can be achieved with such filters despite of the large values of thermo-optic and thermal expansion coefficients of the polymer substrate. This is a result of opposite signs of spectral resonance-peak shifts caused by the two effects. Moreover, the results given in Fig. 5 indicate that even more exact athermalization could be achieved using, e.g., polymers with slightly lower thermal expansion coefficients. This would be of interest for filter designs with substantially narrower resonance reflection band (in the 1 nm range or less). The main thermal limitation of organic substrates is the reduction of resonance-peak reflectance at high temperatures, but this effect was found to be reversible in the sense that temporary presence at temperatures up to 85 °C does not destroy the device permanently.

The proposed approach for athermal organic-inorganic GMRFs has applications in various fields. For each application there are specific issues that need to be taken into account when designing the device. For example, in medical diagnostics the analyte is often a liquid, which means that the TOC of the liquid, acting as the superstrate of the GMRF, has to be included in the design. On the other hand, these types of diagnostic devices are typically used in a laboratory environment, which means that athermal operation within less than ±5 °C would be more than enough.