We investigate the most appropriate way to optically characterize the materials and predict the spectral responses of metal–dielectric filters in the visible range. Special attention is given to thin silver layers that have a major impact on the filter’s spectral transmittance and reflectance. Two characterization approaches are compared, based either on single layers, or on multilayer stacks, in approaching the filter design. The second approach is preferred, because it gives the best way to predict filter characteristics. Meanwhile, it provides a stack model and dispersion relations that can be used for filter design optimization.
© 2014 Optical Society of America
Thin film coatings are promising solutions for spectral filtering in photonics applications requiring image sensors or color displays. They can be used as on-chip filters, and may provide more flexibility than standard organic dye filters in terms of downsizing control, or spectral capabilities in the visible and near-infrared domains. For example, one-dimensional photonic crystals, made of periodically superimposed dielectric layers, have been proposed for on-chip integration applied to day and night vision . However, this photonic crystal approach with only dielectric materials leads to complementary bandpass filtering, which is not the prevalent approach when only RGB signals are needed. Color imaging with standard postprocessing, basically needs primary bandpass filters. In this respect, the resonant enhanced tunneling effect of metal–dielectric periodic structures , or Fabry–Perot cavities [3,4] can provide more convenient spectral properties, with possibly one single transparency region in the visible and near-infrared domain. Organic resists do not provide this feature.
We focus here on two-cavity metal–dielectric Fabry–Perot filters, potentially suitable for on-chip integration on image sensors . From an optical point of view, Ag is the best metallic material to get high performance RGB metal–dielectric filters, due to its low refractive index throughout the whole visible range. Considering a fabrication with standard microelectronic equipment, the deposition and patterning processes require sufficient capability to realize filters arranged in RGB pixels with layer thicknesses close to the target, and repeatable optical constants, within a specified tolerance range. In addition, accurate techniques for the characterization of thicknesses and optical constants are needed for all the layers to predict and optimize the filter spectral responses in the design stage and to understand the origin of deviations from targeted spectral responses in the manufacturing stage. Particularly, difficulties to precisely characterize Ag thin layers have already been pointed out , because the Ag index is dependent on the film thickness, even in the continuous film regime , the temperature of the substrate during the deposition process , and on the nature of the under layer .
This study has two major objectives. The first one is to compare the relevance of several characterization techniques for the determination of layer thicknesses and material optical constants of metal–dielectric filters. In all cases, the modeling of the stacks, the dispersion relations of the materials, and the experimental samples are as simple as possible. Previous studies, based on in situ optical monitoring during layer or stack deposition, have proved to be very effective [10,11,12], but require specific equipment with in situ characterization tools, which are usually not common in microelectronic foundries. The techniques described here are the individual characterization of single layers and the global characterization of layers within multilayer stacks, following from previous works . The second objective of the study is to identify the most appropriate stack and dispersion models for the prediction and optimization of RGB metal–dielectric filter performances for color imaging. The dispersion model includes a mathematical description of optical constants, considering or not variations of optical constants of a given material with layer thickness, with the position of the layer within the stack, or within a layer. The stack model and dispersion relations should have the minimum number of parameters to satisfy the compromise between reliability of the model and complexity of the characterization procedure. In contrast to more fundamental studies on materials, the ultimate goal is not to investigate in detail the behavior of material properties, but to identify the simplest model with necessary parameters able to describe the optical properties of the targeted device, with the tolerances required by the application.
The paper is organized as follows. Section 2 describes the RGB filter stacks, sample realization, and specifications on thicknesses and optical constants. Sections 3 and 4, respectively, present the single layer and multi-filter characterization techniques, with the results found in each case for dielectric and metallic materials with different layer thicknesses. In Section 5, the optical parameters are then used to simulate the spectral responses of the targeted RGB filters. The comparison with experimental measurements drives the conclusions on the most appropriate choice for stack and dispersion model and characterization technique.
2. Description of RGB Metal–Dielectric Filters to be Modeled
A. RGB Filter Design and Realization
The design of RGB metal–dielectric filters is based on double Fabry–Perot cavities, which superimpose three semi-transparent mirror Ag layers, spaced by AlN dielectric transparent layers. The central wavelength of the filter is fixed by the thickness of AlN spacers. These are the only two layers with different thickness from B to G and R filter. The other layers of the stack have the same thickness in the three filters. Outside the cavities, the top and bottom AlN layers are anti-reflective coatings. For the purpose of this study, the filters are designed on glass substrate to allow transmittance measurements. Indeed, transmittance spectra are of particular interest for filters to be used in transmission on image sensors.
The design of the three R, G, and B filters was obtained using an in house MATLAB code, based on Abelès formalism [14,15] and simulated annealing algorithm to meet criteria developed elsewhere  related to color image sensing. The optical constants chosen in the design were taken from the literature  for Ag, and from spectrophotometric characterization performed on a single 350 nm thick layer for AlN. Targeted thicknesses are given as an example of bandpass filters in Table 1. In this design, the thickness of the central Ag layer (34 nm) was about twice the thickness of the external Ag layers (12 and 19 nm). The thicknesses of AlN layers were in the range 60–120 nm. The designed spectral responses of RGB filters are shown in Fig. 1. The simulations took into account the finite thickness of the glass substrate  in order to compare the simulation results and the measurements.
The set of RGB filters was realized without any patterning on separate glass substrates. Ag and AlN layers were successively deposited by sputtering in a solely deposition equipment, with the advantage of preventing the formation of Ag oxide or sulfide. This deposition method was preferred to ion-assisted evaporation, because a higher material density was expected. The presence of oxygen was banished from the deposition process to avoid metal-oxide interface layers, which have a well-known attenuation effect on the transmission . The three Ag layers were deposited under identical deposition conditions, with planar magnetron sputtering, using a 254 mm diameter Ag target with 99.99% (4N) purity, and positioned in front of the substrate. Film growth was carried out in DC mode with a power of 600 W, constant argon debit of 15 sccm, constant working pressure of , and at room temperature. The thinnest Ag layer was above the critical thickness , and exhibited a continuous aspect on the TEM images. AlN was obtained by ion reactive sputtering using nitrogen. The Al target was positioned with an angle relative to the substrate and the sample was rotated. The RF mode was used for the deposition with a power of 200 W. The pressure into the chamber was maintained constant at . Figure 2 shows a TEM image of a blue filter stack. The morphological aspect of AlN layers exhibits a columnar texture.
For each material, the deposition rate was previously determined using a surface profilometer on relatively thick films. The deposition rate was for a 350 nm thick AlN film, and for a 100 nm thick Ag film.
The measured spectral responses of RGB filters are shown in Fig. 1. The discrepancy with designed spectral responses is clearly visible, with lower transmission, smaller spectral width than expected, and a large blueshift of the three filters. This justifies the characterization of materials, including optical constants and thicknesses, as the measurement of thickness from TEM or SEM images is not accurate enough.
B. Specifications on Thicknesses and Optical Constants of RGB Metal–Dielectric Filters
First, it is important to quantify the sensitivity of the filter’s design to the parameters to be characterized, the thicknesses of the layers, and their optical constants. This information provides the accuracy required for characterization and also for the fabrication process.
Concerning thickness, it is assumed here that deviations from the values given in the design are mainly due to systematic errors. This can be the case in a deposition process where all the layers of a given material are realized in the same equipment, with a systematic error on thickness related to an error on the determination of the deposition speed. Therefore, the sensitivity of the design to thicknesses is evaluated considering the same relative error on all the layers of each material.
For the evaluation of design sensitivity, it is also assumed that deviations of optical constants from design values are identical for all the layers of a given material. This assumption will not be kept in the fitting (Sections 3 and 4), where variations of optical constants with layer thickness are taken into account, but it provides an order of magnitude of the required accuracy on the characterization of optical constants.
For color imaging applications, spectral responses of RGB filters typically need to be controlled within for maximum transmission, for spectral width, and for the central wavelength. The corresponding errors on layer thicknesses and optical constants are summarized in Table 2. From our experience, it appears that the most critical parameters are the Ag refractive index, which is difficult to measure with accuracy, and the thickness of AlN layers, which are difficult to control with accuracy in the deposition stage. The other parameters are less critical, but still need to be measured within the tolerances given in Table 2.
3. Single Material Characterization Technique
This approach is simple, as it basically requires the deposition of single layers on separate substrates, measurement of transmittance and/or reflectance spectra by classical techniques such as ellipsometry or spectrophotometry, and extraction of optical constants by fitting with appropriate stack model and dispersion relations of the materials. Here, single layer characterization was performed on layers with different thicknesses, because optical constants are expected to vary with thickness, both for Ag and AlN, as indicated in previous sections. Whenever possible, the samples were realized with interfaces similar to the RGB stacks, because the material properties may change with the nature of surrounding media.
In the RGB multilayer stacks, the optical constants of both Ag and AlN layers may vary due to reasons other than thickness and surrounding materials. The temperature is not regulated in the deposition chambers, and probably rises during the deposition of the stacks, which can last several tenths of minutes. Therefore, the materials may change depending on the position of the layers within the stack. In addition, the morphology of the materials may change within a layer, along the vertical axis. The possible evolutions of optical constants due to these additional reasons are not considered here, as the corresponding samples in a single layer characterization scheme would hardly be representative of the layers in complete stacks.
A. AlN Optical Characterization by Individual Fitting of Single Layer Measurements
First, a thick AlN layer (350 nm) deposited on glass substrate was characterized by spectrophotometry at near normal incidence. The spectrophotometer was an Agilent Cary 100 model with 200–3000 nm spectral range, accuracy in transmission, and in reflection. A simple Cauchy law with refractive index described by3. They were used for the design of RGB filters. The reproducibility of the measurement, repeated on several different layers with the same 350 nm thickness, was 0.01 on the refractive index. This accuracy is sufficient for the application, considering the tolerance given in Table 2.
Thinner AlN layers, with thickness typical of the RGB filter designs, were then characterized by ellipsometry, as this technique is usually more accurate than spectrophotometry for small layer thicknesses below 100 nm. Measurements were realized on a Woollam M2000DI ellipsometer with 300–1700 nm spectral range and 55°, 60°, 65°, 70°, and 75° incidence angles. The thicknesses of AlN layers deposited for single layer characterization were 20, 50, and 80 nm. The substrate was Si to avoid any back reflection, which would have been difficult to deal with in the ellipsometric analysis. It was over-coated with 500 nm thick , so that AlN grew on a material similar to glass, as the first layer of the RGB filters on glass. The deposition rates were those determined by profilometry for RGB filters, but more accurate measurements of thickness were a posteriori provided by a Bruker D8Fabline X-ray reflectometer (XRR). The thicknesses measured by XRR are shown in Table 3. Considering XRR measurements as more reliable, it appears that the values expected from the profilometer calibration were over-estimated by about 7% with a small offset:
Ellipsometric data were fitted considering a two-layer model including a bottom sub-layer and a top thin sub-layer with different properties, accounting for roughness of the layer. Thicknesses were set at the values specified in Table 3. For each sample, both layers were described by a simple Cauchy law without absorption. For the 50 and 80 nm layers, the fits and the weighted test function  were found better ( to 9) than for a single layer model ( to 15), and the refractive index values of the bottom sub-layer were close to the single layer model (). For the 20 nm layer, the fits were not good in any case (), probably due to inappropriate choice of stack model and dispersion relation.
The index variation of AlN between 50 and 80 nm thick AlN layers is approximately 0.03–0.04 in the visible range, similar to the expected tolerance (Table 2). Considering the larger extent (60–120 nm) of AlN layer thicknesses in the RGB filters design, it seems that the dispersion model of refractive index of AlN should include variations with layer thickness for a correct prediction of RGB filter spectral responses.
B. Ag Optical Characterization by Simultaneous Fitting on AlN/Ag/AlN Tri-layer Measurements
The set of Ag layers deposited for optical characterization included 10, 15, 30, and 100 nm thicknesses derived from profilometer calibration. The Ag layers had capping layers and under-layers, both made of 5 nm thick AlN, to avoid an evolution of Ag in contact with air [21,22], and to provide similar top and bottom Ag interfaces, as in the RGB stacks, because the structure and optical properties of Ag thin films may depend on the interfaces.
We first considered spectrophotometry as a possible measurement technique of the AlN/Ag/AlN tri-layers; however, the transmittance and reflectance of the stacks were found to be poorly sensitive to the Ag refractive index. Regarding the desired accuracy on Ag refractive index measurement (, see Table 2), the corresponding simulated variation in transmission and reflection was only about 1%, a value comparable with the accuracy of our spectrophotometer. In contrast, the sensitivity of psi and delta ellipsometer angles to Ag refractive index was more significant, i.e., the psi and delta variations, induced by a change on Ag refractive index, was typically 4 to 5 times larger than the uncertainties obtained with our ellipsometer. Moreover, ellipsometry was successfully used in previous studies [23,24] for the optical characterization of dielectric/metal/dielectric coatings, with Ag for the metal and ZnO or for the dielectric material. Therefore, we chose ellipsometry for the measurement technique. Here, the substrate was Si, covered by 500 nm . The thicknesses of thin AlN and Ag layers were derived from XRR measurements, and used in the analysis of ellipsometric data. The top and bottom AlN layers were found to be 6 and 5.1 nm thick, respectively. The thickness of Ag layers measured by XRR was found to be very close to values previously determined by profilometry and used for the calculation of the deposition rate (Table 4). The density of Ag layers was close to a previous work , although layers were produced by evaporation in that study.
For Ag, a single model is not sufficient to describe optical constants in the visible range, which is at the transition between two regimes. For low photon energies, the dielectric function of the free-electron-like Drude model can be used:26]. For higher photon energies, interband contributions dominate, and can be modeled by a Lorentz oscillator  with the following contribution to the dielectric function:
Following the results of previous section, AlN optical constants were modeled by a Cauchy law without absorption. The fits were simultaneously performed on the ellipsometric spectra of the four AlN/Ag/AlN stacks, with Ag layer thicknesses of 10, 15, 30, and 100 nm, assuming identical AlN top layers and identical AlN bottom layers. Due to the presence of the thin AlN layers above and below Ag, the characterization is not, strictly speaking, a single layer characterization, although it targets the optical constants of Ag. More unknown parameters have to be determined, considering the optical constants of top and bottom AlN layers in addition to Ag. The quality of the fits was poor (), with significant variations from experimental data, especially in the visible region, probably caused by inadequate material modeling and smaller variations in the near-infrared region. The refractive index of top AlN layers, determined by the ellipsometric characterization, was around 1.75 at 500 nm for the top AlN layers, and 2 for the bottom AlN layers. A significant decrease of the refractive index was observed with increasing thickness of Ag layers, from 10 to 30 nm (Fig. 4), and to 100 nm at a lesser extent. The variation is about 0.04–0.05 at 450 nm, larger than to the tolerance (Table 2). Therefore, the material dispersion model should take into account the dependence of Ag refractive index with thickness. This evolution may be correlated to the slight increase of material density measured by XRR, from thin to thick layers (Table 4), and may be explained by a variation of void fraction . In the near-infrared region, where the optical properties are essentially described by the Drude dispersion model, this behavior is also qualitatively consistent with the increase of the electron mean free path with layer thickness as long as the layers are thinner than the mean free path in bulk metal, about 50 nm for Ag . A very weak rise of Ag extinction coefficient found with increasing thickness does not have to be considered in the modeling, because the variations are smaller than the tolerance.
The refractive index of the 30 and 100 nm thick Ag sputtered layers was found in between two widely used reference data [17,29]. The extinction coefficient was higher than for the bulk samples of , but very close to the thin evaporated films of  (Fig. 5).
It should be emphasized that, due to the poor quality of the fits, the reliability of the results on Ag single layer optical constants was low. The characterization of Ag was probably affected by the inappropriate modeling of AlN, as evidenced in Section 3.A for very small AlN thickness. We tried several stack models and dispersion relations for AlN, with a higher degree of complexity, but without any significant improvement of the merit function. An interesting alternative could be the approach developed in a previous work  for island metallic films, where the whole alumina/metal/alumina tri-layer system is treated as a single layer with effective optical constants.
4. Simultaneous Characterization of Materials within Multilayer Stacks
A. Choice of Appropriate Material Dispersion Models and Set of Stacks for Multi-Filter Characterization
In this section, the characterization approach is based on a global fitting of the spectral responses of several specific Ag/AlN multilayer stacks, to simultaneously extract thicknesses and optical constants of all the layers.
Spectrophotometry is appropriate here for the optical measurement of the multilayer stacks, because near normal incidence transmittance and reflectance spectra can be very sensitive to the stack model parameters. Meanwhile, normal incidence transmittance spectra are the data used in the optimization of the RGB filter designs. Two measurements are possible for each stack, in transmission and in reflection, over a wide spectral range (200–3000 nm).
The Ag/AlN stacks and the material dispersion relations have to be carefully chosen to provide information for an accurate characterization. The simplest possible dispersion models, with few unknown parameters, are preferred to limit the number of stacks to be realized and, thus, the number of measurements; incidentally, this avoids parameter values with weak physical sense. However, the dispersion models should be sufficiently elaborate to allow a correct fit of optical measurements. The validity of the trade-off can be tested by self-consistency, depending on the quality of the fits.
Compared with the single layer characterization approach, more complex experimental samples are required with alternating Ag and AlN layers to form multilayer stacks. But the nature and optical constants of both materials should be more similar to the RGB stacks targeted in the application, and fewer parameters required in the dispersion models.
After testing several stack configurations and dispersion models, two sets of Ag/AlN stacks were chosen, each one to be used for a global fit. The first set (Table 5) included 5 stacks and it was planned for the characterization of Ag layer with a fixed thickness (17 nm) and AlN. The second set (Table 6) included only 3 stacks and it allowed to characterize Ag layers with another fixed thickness (40 nm), using AlN characteristics provided by the characterization of the first set of stacks. All the stacks were single or double cavities, exhibiting large sensitivity to thickness and optical constants. The spectral responses had various shapes and central wavelengths covering the RGB range, as the accuracy of the approach relies on the diversity of the measurements.
The first set of stacks was described by only 10 parameters: one parameter for a proportional linear correction on thickness related to the error on deposition speed calibration for each material, two parameters for a unique Cauchy law of AlN refractive index, 6 parameters for the Drude, and one Lorentz oscillator model, describing Ag optical constants.
Spectrophotometric measurements in reflection and in transmission were performed on these 5 stacks with 17 nm thick Ag layers. The spectral range of the data taken into account in the analysis was 350–1000 nm, including the region of interest for the filters. The measurements were fitted by the model of the stack with 17 nm Ag layers using least square minimization. The initial parameter values of the fit were taken from the profilometer calibration for Ag and AlN thickness, from literature for the optical constants of Ag , and from the spectrophotometric optical characterization of 350 nm thick AlN, as in the design of RGB filters. The 10 parameters of the model could then be deduced. It was verified that more extended spectral ranges did not significantly improve the fit. The thickness and optical properties of the dielectric material were then fixed, together with the thickness of Ag. A second global fit was performed to find the optical constants of Ag at 40 nm, described by 6 parameters.
Even though the thickness of AlN layers varies to some extent (60–115 nm) in the stacks, a single Cauchy dispersion relation with no absorption was sufficient to obtain good fits. In contrast, specific parameters had to be used for each different thickness of Ag layer. This was shown by the unsuccessful global fit of the whole ensemble of stacks described in Tables 5 and 6 using Ag dispersion model independent on Ag thickness, and by a complementary experiment. Five filters, with randomly variable thickness of Ag layers in the range 13–17 nm of Ag layers, and AlN thickness given by Table 5, were deposited and measured in transmission and reflection. Using only one optical index table for all these thicknesses of Ag layers in the model did not lead to a correct fit between simulated and measured spectral responses. This observation confirmed that the dispersion relation for Ag effectively needed specific parameters for different thicknesses of Ag layers.
With this choice of multilayer stacks and dispersion relations, the quality of the global fitting was found to be good, with values of for the first fit and for the second fit.
The fitted transmittances and reflectances are within 5% of the experimental data (Fig. 6). The spectral variation of the errors may typically result from systematic errors not accounted for in the model . However, the model does not need to be refined, as the errors are still within tolerances of Table 2. Systematic errors hinder a correct determination of the confidence limits and goodness-of-fit based on the assumption of a normal distribution of errors . Therefore, the values of given above should be considered with caution. A more decisive test for the reliability of the fit, related to the basic objective of this study, is the correct prediction of spectral responses of any filter designed with the fit parameters (Section 5).
B. Optical Constants of Ag and AlN Determined by Simultaneous Fitting on Multilayer Measurements
After the first global fit on spectral responses of Table 5, it was found that no correction was necessary for Ag thickness. For AlN, the proportional correction on thickness was with respect to the initial value of the fit taken from the profilometer measurement. These results are in agreement with XRR measurements, but were found independently by the global fit technique. At first glance, AlN thickness and refractive index are expected to be somehow correlated (Table 2), but the design of filters at different wavelengths for the fit, combined with the use of a dispersion law for AlN index, reduces the correlation. The small offset from the proportional correction determined by XRR is not modeled in the global fit technique, but does not need to be taken into account because the fits are good. The results given for AlN refractive index account for all the AlN layers within and among the different stacks in Table 5. They are similar to the 350 nm thick single layer on glass characterized by spectrophotometry (Fig. 3). These values of refractive index are clearly lower than for the thin single AlN layers characterized by ellipsometry, with differences larger than the confidence intervals and larger than the targeted accuracy. Yet, the thicknesses of AlN layers in Table 5 are of the same order of magnitude (60–115 nm) as the thicknesses of single layer samples (50–80 nm). The differences are difficult to interpret because both the measurement technique and the samples, including stack and substrate change between the two characterization approaches. Several hypotheses may be formulated, among the change of material properties depending on the substrate, glass or Si, the difference in roughness between a single layer deposited on a bare substrate and a layer within a multilayer stack, or other potential explanations. At this stage, additional single layer characterization might be considered to provide a more reliable comparison between the two characterization approaches. For example, ellipsometric measurements on wedged or back-side roughened glass substrates, would help to confirm whether or not the nature of the substrate is responsible for a change of AlN refractive index. However, we decided not to go into more thorough investigation of the single layer characterization, because it would be hard to make sure that single layers on glass would be processed in conditions sufficiently similar to multilayer stacks.
The refractive indices of 17 and 40 nm thick Ag layers, found by the two global fits on filters of Tables 5 and 6, are shown in Fig. 7 together with the extrapolated and interpolated data for 10, 15, and 30 nm thicknesses for comparison with single layer characterization. The decrease of Ag refractive index with increasing layer thickness is again observed, but there are significant differences with the results of single layer characterization. With the multi-filter characterization technique, the refractive index is much higher in the shorter wavelengths, especially for the thinnest layers.
As for AlN, the representativeness of Ag single layer characterization can be questioned. The optical constants of Ag single layers may effectively be different from those of Ag layers within Ag/AlN multilayers, even if Ag layers were sandwiched between very thin AlN layers in single layer characterization. In these tri-layer AlN/Ag/AlN stacks, Ag layers were deposited on a thin AlN layer with low roughness, directly on the substrate. In the multilayer stacks of Tables 5 and 6, Ag layers were deposited on thick AlN layers, which themselves may already lay on other layers, so exhibiting a surface with larger roughness. The impact of roughness on metallic layer optical constants has already been pointed out in previous studies [25,9,31]. In addition, thermal effects may occur in the multilayer stacks, where the deposition times are several hours, much more than the few tenths of seconds needed for the tri-layer stacks. As for the nature of the substrate, it was found to have negligible impact on the optical constants of 100 nm thick Ag deposited on glass, or Si with thermal oxide.
In addition, the regions at the interface of the metallic and dielectric layers may exhibit optical anisotropy, as detailed in a previous study on metallic island films . Optical anisotropy is described as a dependence of the optical constants of the film on light polarization, and it results from the shape of the metallic clusters if they are simultaneously irregular and not randomly distributed, and also from the electrodynamical coupling between the islands arranged in a plane, dependent on the incidence angle. In the present study, optical anisotropy may arise from metallic structures at the surface of the rough closed Ag films, and affect the results obtained by ellipsometry because the interface regions were not explicated in the stack model, and their dependence with the angle of incidence was not taken into account. Moreover, even where the modeling was revised, the results could hardly be applied to the normal incidence case because the effective optical constants of the interface layers may depend on the incidence angle.
For the high wavelengths, in the Drude regime, the Ag refractive index results of both techniques are much closer to each other. The extinction coefficient is stable between 17 and 40 nm, and similar to the one found on single Ag layers in the whole spectral range. The absorption of all Ag layers is higher than the reference data  used in the RGB filter design. This may explain the over-estimation of filter spectral width in the designed versus measured spectral responses.
5. Validation of the Two Characterization Approaches with RGB Filters
The dispersion models chosen for the single layer characterization technique were used to simulate the spectral responses of the RGB filters of Table 1. The optical constants of Ag layers with thickness 12, 19, and 34 nm were interpolated from the values determined for 10, 15, and 30 nm thick single layers. For AlN, the refractive indices of layers with thickness 60 to 120 nm were also interpolated from the values measured for 50 and 80 nm thick single layers.
Simulated responses are shown in Fig. 8. Compared with Fig. 1, a first change is the correction of the redshift of simulated versus measured spectra. This is mainly due to the correction on AlN layer thickness by with respect to the design values, as indicated by XRR measurements, inducing a blueshift approximately 4 times larger than the shift corresponding to the corrections on AlN refractive index. Second, the spectral width of the filters is now closer to measurements. This results from the higher values of the Ag extinction coefficient. The simulated reflectance is in relatively good agreement with the measured reflectance. However, the filter transmissions are still much higher in simulation than in measurements, especially in the blue region, where the transmission in excess is about . Roughly, considering that the other filter characteristics (central wavelength, spectral width) are correctly simulated, the over-estimated transmission directly points to an underestimation of Ag refractive index when the optical constants of single layer characterization are used in the simulation of multilayer filters.
The same validation was performed with the parameters determined by the multi-filter characterization technique. The refractive indices of Ag layers with thicknesses of Table 1 were linearly interpolated from the values found for the 17 and 40 nm layer thicknesses. The refractive index common to all AlN layers was used, and the correction on AlN layer thickness resulting from the global fit was applied.
The differences of simulated versus experimental transmittances is eliminated (Fig. 9) due to the larger refractive index of Ag compared with single layer ellipsometric characterization. In addition, the residual wavelength shift disappears, mostly resulting from the lower AlN refractive index.
The agreement between simulated and measured spectral responses is very good, both in transmittance and in reflectance, for the three RGB filters. It should be reminded that this is not a fit of the measured spectral responses, but only a comparison between measured spectral responses and simulated spectral responses, using layer parameters previously characterized from other multilayer stacks. This result clearly indicates that the parameters determined in the multi-filter characterization are suitable for the simulation of multilayer filters. This does not imply that each of the parameters was effectively determined within the expected tolerance of Table 2, due to possible correlation between several fit parameters. Summarizing the results on the analysis of filter spectral responses, it can be concluded that thickness of deposited AlN layers was smaller than expected from profilometer calibration, and both refractive index and extinction coefficient of Ag deposited layers were higher than Palik data used in the design. In addition, it was necessary to take into account variations of Ag refractive index with thickness.
We tested two characterization methods to determine the optical parameters and thickness of layers present in Ag/AlN multilayer stacks for RGB color imaging. The first technique was the individual characterization of single layers by ellipsometry and XRR. It revealed a dependence of refractive index of both Ag and AlN layers with thickness, but led to large uncertainties, especially for Ag refractive index in the low wavelengths. Ag refractive index is one of the critical parameters impacting the spectral responses of filters. In addition, the optical parameters determined with this method were not able to correctly predict the spectral responses of RGB Ag/AlN filters. More reliable results may be obtained with more complicated or specific modeling of the materials and dispersion relations. However, we did not further investigate the single layer characterization technique because we wished to limit the study to simple modeling and simple experimental conditions.
The second technique was the characterization of several multilayer stacks by simultaneous fitting of spectrophotometric responses. The expected advantage was a reduction of the number of unknown parameters, with layers in common among the different stacks. The relevance of the technique was a priori, not obvious, because the thickness dependence of optical constants did not allow a drastic decrease of the number of parameters. In practice, the dependence of refractive index with Ag layer thickness had to be considered. This was not necessary for AlN. Simple material dispersion models (Cauchy, Drude, and Lorentz) were suitable for the characterization. It was not necessary to introduce specific modeling related to position of layers within stacks, vertical gradient within layers, or interfacial layers. The optical constants and thickness correction determined by this method were suitable to simulate the spectral responses of RGB filters with excellent agreement with the measured spectrophotometric data.
The multifilter characterization method appears as a global technique, leading to layer thickness and optical constants for a very efficient prediction of metal/dielectric filter spectra, without any need for in situ monitoring tools. The material optical characterization is not a final goal, but an intermediate step in the definition of a realistic and convenient description of multilayer stacks. Key points are the choice of a simplified stack model with few parameters, and the choice of samples similar to the filter stacks in the application and sensitive to the most critical model parameters. The characterization results can be used for the optimization of new metal/dielectric filter designs .
The framework of the study was a partnership between ST Microelectronics and Leti. It was supported by the French Oseo agency through the Minimage project. The authors would like to thank Anne-Marie Papon for TEM measurements and Agathe André for ellipsometric and XRR measurements.
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