1. Introduction

The detection of biological species using microarrays and lab-on-a-chip systems is a powerful diagnostic tool enabling the acquisition of genetic, proteomic, and cellular information [1–3]. These systems are used for massively parallel, highly sensitive and rapid analysis of biomolecules for disease diagnostics, drug discovery, or food and environmental analysis. Besides chemiluminescence [4] and colorimetry [5], fluorescence is one of the commonly used methods for the detection of DNA, proteins and cells in microarrays [6]. If the targeted biological species do not exhibit fluorescent properties, they are functionalized with fluorescent probe molecules, which are selectively bonded to the targeting species [7]. The fluorescence is excited by illuminating a solution containing either the species or the species bonded with the fluorescent probe molecules, by an external excitation laser light. The intensity of the emission light is proportional to the concentration of the targeting/probe molecules, allowing accurate quantification. In microarrays, hydrogenated amorphous silicon (a-Si:H) pin photodiodes with low dark current and high quantum efficiency in the visible range (300 nm – 750 nm) are used as single photodetectors [8]. Low processing temperatures (< 250 °C) in plasma enhanced chemical vapor deposition (PECVD) allows substrates such as glass or flexible polymers to be used and facilitates the integration of this technology in microarrays and lab-on-a-chip applications [8–13]. Since a-Si:H photodiodes are broadband detectors for visible light, optical filtering is necessary to detect weak fluorescent emission light and to reject the strong excitation light.

Absorption filters made of amorphous silicon carbide (a-SiC:H) have been used as optical filters [12]. The content of carbon in the films, which is controlled by the flow rates of SiH₄ and C₂H₄ during deposition, defines the optical bandgap (E_opt) of the material_, which in turn determines the edge of the optical absorption of the short-wavelength light. The E_opt is set so that it efficiently absorbs the wavelengths of the excitation light while transmitting the emission wavelengths to reach the detector [14]. Despite several advantages of this filtering solution (single layer, low cost, simple integration into a-Si:H photodetectors) they are inefficient when excitation and emission wavelengths are in close proximity as in the case of small Stokes’ shift fluorophores (Δλ < 50 nm). Other solutions based on interference filters exhibit higher filtering efficiencies but require a large number of layer pairs (up to 20) to be deposited and for each layer its thickness to be tuned accurately [15, 16].

In this paper we introduce a filtering concept based on diffraction gratings that can be fabricated by modern nano-lithographic processes [17] and requires fewer fabrication steps than interference filters. Diffraction gratings as wavelength-selective optical structures have been applied in various fields including telecommunications and integrated optics [18, 19]. The filters are modelled and optimized based on three-dimensional optical simulations. We show that a properly designed dielectric diffraction grating significantly improves selectivity when compared to an absorbing filter for detecting fluorophores with small Stokes shifts. In particular, we focus on detecting the green fluorescence protein (GFP) [20, 21] using an amorphous silicon p-i-n photodiode as the photodetector, although it is applicable to detecting other fluorophores if optimized properly. Also other detector configurations are possible. The non-toxic protein GFP is one of the most widely studied and exploited proteins in biochemistry and cell biology [22]. It can be used either directly as a targeting biomolecule or as a marker selectively bonded to other targeting biomolecules [22–25]. The peak GFP excitation and emission wavelength are at λ_exc = 480 nm and λ_em = 510 nm, respectively. At Δλ = 30 nm the Stokes shift is very small [26] and requires extremely sharp optical filtering to selectively extract weak emission light.

In this paper, three types of filtering configurations based on diffraction gratings are introduced and optimized by means of optical simulations: (i) a diffraction grating fabricated on the surface of a-SiC:H absorbing filter, (ii) a diffraction grating inside a host material with low refractive index, and (iii) a diffraction grating inside a host material with an absorbing filter beneath. For analysis and structure optimization, we performed 3-D rigorous optical modelling using COMSOL Multiphysics simulation software [27]. The grating and its dependence on the period, height and duty-cycle is studied and optimized with respect to the rejection of the excitation light and the high transmission of emission light. To approach “real” conditions, we investigated the role that oblique incident angles have on excitation and emission light and the role that fabrication errors have on RR. The high rejection ratio obtained in an ideal case is expected to be lower than in reality. For this reason, real conditions will be simulated and the results discussed.

2. Biodetector structure and simulation tool

2.1 Detector structure

Figure 1(a) is a schematic representation of a fluorescence based biodetector.

 

Fig. 1 a) Schematic representation of a fluorescence based biodetector with a thin-film hydrogenated amorphous silicon (a-Si:H) p-i-n photodiode. b) GFP excitation and emission spectra showing the maximum fluorescence excitation wavelength (λ_exc) sensitivity at 480 nm and the maximum emission wavelength (λ_em) intensity at 510 nm [26].

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Glass is used as the substrate for the detector. The p-i-n photodiode deposited in a n-i-p sequence consists of a 20 nm n-a-SiC:H layer, followed by a 500 nm i-a-Si:H layer (absorber) and a 10 nm p-a-Si:H layer. A 300 nm thick layer of aluminum is used as the back contact while a transparent conductive oxide (TCO), typically an indium tin oxide (ITO) with a thickness of 75 nm, is used as the front electrode. This is followed by the integrated optical filter (Fig. 2). On top of the filter, a SiO₂ immobilization layer is deposited (d > 100 nm) as described in [10]. This layer provides a well-defined surface for the immobilization of biomolecules. The solution containing the GFP labelled biomolecules is in direct contact with the SiO₂ layer.

 

Fig. 2 Schematic presentation of different filter configurations: a) a flat absorbing filter (AF) consisting of a single layer of a-SiC:H (reference), b) a filter with a diffraction grating on top (GAF), c) a diffraction grating in a low refractive index layer (EG), and d) a combination of diffraction grating in a low refractive index host layer on top of flat absorbing filter (EG + AF). The grating materials can be either TiO₂ or p-a-SiC:H, the hosting material is SiO₂ in all cases, h and P are the height and period of the diffraction grating, respectively, and is the thickness of the low-index spacer layer.

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During the simulations, the detector’s structure was simplified by assuming that SiO₂ acts as the incident medium for light, and by neglecting that any reflections occurring at the interface between the liquid (n ≈1.33) and the SiO₂ layer (n ≈1.5). Under this assumption, simulations were bound to the device only. For other configurations, where the liquid solution is not in direct contact with the detector, for example when enclosed in a PDMS cuvette, the refractive index of PDMS (n ≈1.4) has to be considered in simulations.

During simulations, the detector structure was considered to be a plan-parallel multi-layer stack with flat interfaces, which is close to the real case. Three-dimensional (3-D) simulations were carried out since in the actual filters we propose the gratings to be two dimensional. In the model, we apply a single excitation (λ_exc = 480 nm) and emission light beam (λ_em = 510 nm) corresponding to the excitation and emission maxima of the GFP (Fig. 1(b)). In the final calculations, we considered the entire spectrum of the emission light. For the external excitation light we assume a monochromatic light (laser) source. The thickness of the flat absorbing filter (d_AF) was set to 2000 nm and the optical gap (E_opt) to 2.22 eV, resulting in a high bandpass filtering characteristic suitable for detecting GFP [12].

2.2 Filtering structures

A critical component in a fluorescence detector is the optical filter. The filter must block strong excitation light from reaching the photodetector, while allowing weak emission light to be transmitted to the detector where the optical signal is converted into an electrical current (photocurrent). Filter concepts, based on a diffraction grating are shown in Fig. 2(b)-2(d). A flat a-SiC:H filter was used as a reference (Fig. 2(a)).

Figure 2(b) shows the grating absorbing filter (GAF), which has the diffraction grating on top of the absorbing a-SiC:H layer. In the simulations, SiO₂ was considered as the material filling the vacancies in the grating structure. The grating is described by the period (P) and the height (h) of the corrugations. In our case we apply the same P in both lateral directions. By optimizing P and h it should be possible to improve the wavelength dependent reflection and scattering characteristics of the periodic diffraction grating [28]. In the case of scattering, diffraction modes are wavelength dependent. By scattering the excitation light only, absorption is increased by prolonging the optical path, while the emisson light does not scatter. Theoretically, this is true since λ_exc < λ_em and because the scattering process at the grating occurs if λ ≥ P [28], where λ is the wavelength of light in the incident layer.

In the embedded grating - EG, (Fig. 2(c)) a grating with a material with a high refractive index, such as a-Si:H (n ≈3.8 at λ = 480 nm), is embedded in a low refractive index layer in this case SiO₂ (n = 1.5 at λ = 480 nm). Low refractive index materials are assumed to be above and below the grating, i.e. above the SiO₂ acts as an immobilization layer while below it acts as a spacer. The concept of using a grating with a high refractive index [29, 30] has been investigated in other optoelectronic devices, such as vertical cavity surface emitting lasers and high-Q optical resonators [19, 31]. We used two materials with a high refractive index: TiO₂ (n = 2.56 at λ_exc = 480 nm) and p-doped amorphous silicon carbide (n = 3.77 at λ_exc = 480 nm) same as for the p-layer in the p-i-n photodiode (Fig. 2(c)). Besides there being differences in the actual refractive index of TiO₂ and p-a-SiC:H, the latter exhibits much higher absorption for both the excitation and emission light. Table 1 summarizes actual refractive indices, n, and extinction coefficients, k, of the materials used in the simulations. The data for the layers were obtained experimentally.

Table 1. Complex refractive indices of used materials at excitation (480 nm) and emission (510 nm) wavelengths.

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In the third concept (EG + AF, Fig. 2(d)) we combined an embedded grating (p-a-SiC:H grating in a hosting SiO₂ material) with the flat absorbing filter.

In the case of an actual working device, the device would be manufactured using state-of-the-art nano-lithographic processes. First, the two-dimensional grating texture, covering the entire surface of the photo-detector (approximately 200 x 200 μm), could be fabricated on top of either the a-SiC:H (GAF) or SiO₂ layer (EG) using electron beam lithography. Electron beam lithography enables extremely high resolution well within the range of grating dimensions proposed [17]. The filling material, SiO₂ in the case of GAF and TiO₂ or p-a-SiC:H in the case of EG filtering concepts, could then be deposited on top of the grating followed by chemical mechanical planarization (CMP) to flatten the surface [32]. Alternatively, the original (master) e-beam fabricated grating could also be patterned in quartz and then repeatedly transferred onto either the a-SiC:H (GAF) or SiO₂ layer (EG) using step-and-flash nano-imprint lithography (NIL), which would reduce manufacturing costs while retaining good uniformity of the transferred grating texture [33–36].

2.3 Simulation

Each filter design was simulated using the COMSOL Mulitphysics software package [27]. Light is represented as planar electromagnetic waves propagating in either a perpendicular or oblique direction. Both polarizations, transversal electric (TE) and transversal magnetic (TM) are in equal proportion. Rigorous solving of Maxwell's equations is based on the finite element method (FEM) [37]. Special attention was given to the discretization of the structure, especially for the highly absorbing material and at the wavelength of excitation where sharp transitions in the electro-magnetic field occur. For structures with lateral periodicity and symmetrical properties, integrated symmetry boundary conditions enabled a simulation to be made over one quarter of a structure period only, reducing the time of simulation significantly. COMSOL enables the dynamic adjustment of the meshing depending on the wavelength of the light. Since meshing in FEM is not restricted to rectangular elements, these structures can be modelled with great geometrical precision. This is important, since the gratings are sensitive to the geometry of the device. The FEM method requires separate simulations for each wavelength of light. As input parameters we used typical complex refractive indexes for λ_exc and λ_em (Table 1) combined with the actual thicknesses of the layers [15]. Here we analyzed a specific detector structure, but such filtering concepts are also applicable to other configurations. Simulations must be repeated if materials/layers are exchanged inside the filter, to find new optima with respect to geometry.

Initially, we simulated an optical system consisting of a SiO₂-incident medium/filter substructure without the photodetector at the bottom, where on the back side of the filter we applied absorbing boundary conditions [38]. Thus, no back reflection at the a-SiC:H/ITO, ITO/p-a-SiC:H, and other interfaces were considered. Finally, the complete device in a SiO₂-incident medium / filter / ITO / p-i-n / Al configuration was analyzed. Special attention was given to selecting the mesh-grid in order to avoid numerical errors, especially when the filtering characteristics rise steeply (around λ_exc). Here discrete elements were as small as 1 nm in size.

The spectral response of the p-i-n photodiode was calculated by assuming ideal extraction of generated charge carriers in the i-layer and neglecting the contributions from the p- and n-doped layers [39]. Rejection ratios for the transmitted light (T) through the filter’s substructure (RR_T), and for the spectral response (SR) of the entire detector (RR_SR), were calculated using Eq. (1) and Eq. (2), respectively, considering T and SR values at λ_exc and λ_em. In the final calculation, the SR of the entire emission spectrum of GFP and not only of the central wavelength λ_em was taken into account.

3. Results and discussion

3.1 Spectral properties of filters

For all three types of filters with gratings (Fig. 2(b)-2(d)) we simulated the rejection ratio of the transmitted light (RR_T) as a function of the period (P) and height (h) of the grating. Results are presented in Fig. 3(a)-3(d). This figure shows how P and h play a crucial role in affecting the transmission characteristics of the filter and thus on RR_T in all filtering concepts. In the case of EG (Fig. 3(b)-3(d)), RR_T is especially sensitive to P and h but extremely high RR_Ts are obtained in these cases. Table 2 gives the optimal P and h values for the highest RR_Ts. For GAF (Fig. 3(a)) we observe that for large values of P and h a region exists with high RR_T values, with a maximum RR_T = 12.98 (reference RR_T = 10.21 for flat absorbing filter). Some improvements by introducing a diffraction grating are already apparent in the case of GAF.

 

Fig. 3 Contour plots showing the rejection ratio (RR_T) dependence on P and h for different filters: a) GAF, b) TiO₂ EG, c) p-a-SiC:H EG, and d) p-a-SiC:H EG with flat AF . The reference RR_T corresponding to the flat absorbing filter is RR_T = 10.21 (not denoted in plots). Note: the RR_T color scale in the plot (a) is linear, while plots b, c, and d have logarithmic RR_T scales.

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Table 2. RR_T and RR_SR values for different filter concepts. The optimal periods and heights for different gratings are presented with the best results in terms of RR. RRs considering manufacturing errors as well as different incident angles of the excitation (0.5°) and emission (45°) light are also presented. Finally, RR_SRs with the entire GFP emission spectrum, under ideal and real conditions, are given in the final column.

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Figure 3(b) and Fig. 3(c) corresponding to an EG (Fig. 2(c)) are shown for two types of grating materials: TiO₂ and p-a-SiC:H, respectively. As a low refractive index material, SiO₂ was chosen in both cases. Extremely high RR_Ts are observed in both cases: RR_T = 44000 and 16000, respectively. The small islands visible in Fig. 3(b)-3(d) are the result of the highly sensitive behavior of RR_T to P and h (discussed later). Additional simulations indicated that the spacer layer (d_LIM) must be sufficiently thick to obtain high RR_Ts, originating from the extremely low transmittance of the excitation light (Fig. 4). Simulations suggest that the near field, established around the grating, must not be disrupted by an abrupt change in refractive index and the next layer must be spaced apart from the grating. According to our simulations (Fig. 4), the d_LIM should be at least 650 nm thick for a TiO₂ grating (P = 380 nm, h = 129 nm) and at least 350 nm for a p-a-SiC:H grating (P = 295 nm, h = 94 nm).

 

Fig. 4 The dependence of excitation light transmittance on the SiO₂ spacer layer thickness for a TiO₂ (P = 380 nm, h = 129 nm) and p-a-SiC:H (P = 295 nm, h = 94 nm) grating.

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We also performed simulations for the other filter configurations and determined the d_LIM for their optimal performance. Table 2 gives d_LIM values the for optimized configurations (P and h). The simulations also show that the thickness of the SiO₂ spacer layer has a negligible effect on transmittance of the emission light.

Figure 3(d) shows the simulation results obtained for the filter configuration EG + AF (Fig. 2(d)). The highest RR_Ts are observed here (RR_T = 190,000 at P = 295, h = 94 nm, d_LIM = 350 nm) as a consequence of the interaction of both effects (AF + EG).

Next we studied the optical effects of the filter in the EG (Fig. 2(c)) in more detail. Simulations revealed that two different effects result in high RR_Ts when using either TiO₂ (Fig. 3(b)) or p-a-SiC:H (Fig. 3(c)). For the TiO₂ grating, which is a weakly absorbing material at λ_exc and λ_em, the main cause of low transmittance of the excitation light is an increase in the reflectance, where R > 90% at λ_exc (Fig. 5(a)), i.e. reflective EG – R-EG. This behaviour follows that of high contrast gratings [29]. For the p-a-SiC:H grating i.e. a highly absorbing grating material, the low transmittance is a result of absorption, where A > 90% at λ_exc, as observed in Fig. 5(b), i.e. absorbing EG – A-EG.

 

Fig. 5 Transmittance (T), reflectance (R), and absorbance (A) spectra for an embedded grating in a SiO₂ host. The grating is made of a) TiO₂ - weakly absorbing material (P = 380 nm, h = 129 nm, d_LIM = 650 nm) and b) p-a-SiC:H - absorbing material (P = 295 nm, h = 94 nm, d_LIM = 350 nm). Note: a linear scale is used here. Absolute values of the electric field |E| (a.u.) at the excitation and emission wavelengths along with the corresponding transmittances are specified.

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For a weakly absorbing grating material (TiO₂) with optimized dimensions, reflection affects only a narrow region around the central excitation wavelength (Fig. 5(a)), and transmittance at the emission wavelength remains almost unaffected. For TiO₂ (T_em = 0.98) this is close to 100%. For a highly absorbing grating material, absorption affects a broader range of wavelengths, also affecting λ_em where a substantial absorption is observed (Fig. 5(b)). For p-a-SiC:H, transmittance falls to 54% (T_em = 0.54). The best overall properties are achieved for the A-EG (Fig. 5(b)) filtering concept.

Figure 6 shows transmittance spectra of the different filtering configurations at optimum P and h combinations (Fig. 3). The curve for the flat absorbing filter (solid line) is added as a reference. In this case, different transmittance values (T_exc = 0.014, T_em = 0.14), resulting in a RR_T = 10.21, are a consequence of the absorption characteristics of the absorbing filter (dictated by E_opt). The transmittance characteristic is not sharp in the small wavelength range of interest. The GAF (Fig. 2(b)) shows a slight improvement in the inclination of the transmittance curve, resulting in an improved RR = 12.98 (long dashed line in Fig. 6). Other characteristics all correspond to the optimized embedded diffraction gratings in the SiO₂ host material and exhibit a sharp dip around λ_exc, which acts as a notch-like filter, and results in extremely high RR_T values, specified as the best RR_Ts in Fig. 6 and Table 2, column 5. For absorbing materials (A-EG), transmittance decreases also at λ_em. This limits the use of a highly absorbing material, since the transmittance of the emission light must be sufficient to generate a measureable photocurrent [12]. Assuring a high transmittance at λ_em is important if different filtering solutions are to be combined e.g. an embedded grating (p-a-SiC:H grating) with better overall properties (smaller dependence on both the incident angle and manufacturing errors compared to TiO₂ grating) with a flat absorbing filter (AF + EG). Figure 6 shows the effect both filters have on transmittance. The inclination of the T(λ) characteristics comes from the absorbing filter, while the notch effect is from the embedded grating.

 

Fig. 6 Comparison of transmittance dependence on the wavelength for optimized filtering structures.

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It is important to mention that this concept is also valid for other materials, with the only limitations being that the refractive index of the grating material must be sufficiently larger than the refractive index of the surrounding material, and that it allows good transmission of emisson light (low absorption at λ_em). Furthermore, additional simulations (not presented here) revealed that we are not constrained by ideal rectangular-like checker-board gratings. Since the grating shape can be chosen independently with respect to the FEM method, arbitrary grating shapes can be included and optimized for achieving the highest RR. It is even possible to take into account predicted fabrication errors during optimization making optical simulation a powerful design tool. In this paper we focused only on ideal rectangular gratings to demonstrate the concept.

3.2 The role of the grating duty-cycle

To optimize further the filtering characteristics of the structures based on diffraction gratings, we investigated the role of the duty-cycle η i.e. the ratio between the length of the grating segment and the entire period length. All gratings analyzed in the previous section exhibited a fixed duty-cycle of 0.5 (equal lengths of the grating and spacing materials). Here, we present the results for the embedded grating concept using a p-a-SiC:H grating (A-EG) only (Fig. 2(c)). Results of three selected η values are presented in Fig. 7. Simulations showed that as η changes so do the optimal P and h values for a certain grating filter. Thus, for each of the analyzed η values we searched for the optimal combination of P and h (Fig. 7).

 

Fig. 7 Comparison of different duty-cycles for the p-a-SiC:H grating. For duty-cycle η = 0.25, an optimum of P = 359 nm, h = 262 nm, and d_LIM = 400 nm resulted in RR_T = 130000. For η = 0.5, an optimum at P = 295, h = 94 nm, and d_LIM = 350 nm resulted in RR_T = 16000. And for η = 0.75, an optimum at P = 345 nm, h = 85 nm and d_LIM = 200 nm resulted in RR_T = 2.2.

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Figure 7 shows the affect that η has on RR_T. For the p-a-SiC:H grating the optimum value was η ≈0.25. This corresponds to the following relation between the grating segment length (p₁) and host material length (p₂): p₁*n₁ = p₂*n₂; p₁ + p₂ = P, where n₁ is the refractive index of p-a-SiC:H and n₂ that of SiO₂. The optimal value is obtained when η ≈n₂/(n₁ + n₂) at λ_exc. Under such conditions, the resonant behavior of the structure is even more pronounced. We obtained a RR_T >149000 when η = 0.25, P = 359 nm, h = 262 nm, and a d_LIM = 400 nm.

3.3 The role of the incident angles of light

To study “real” conditions in the detector, we first analyzed the affect oblique incident angles have on the excitation and emission light. Whereas the angle of the excitation laser is adjustable (assuming true perpendicular direction), we need to take into account the broad angular distribution of the emission fluorescent light (spherical point sources). Figure 8 shows simulations of transmittance as a function of different incident angles of λ_exc and λ_em for embedded gratings made of TiO₂ (R-EG) and p-a-SiC:H. The plot shows how the transmittance at λ_exc is highly dependent on the incident angle, especially for TiO₂ grating, where a deviation of Δθ = 1° from perpendicular causes a more than 3 decade rise in T_exc, resulting in a 3 decade reduction in RR. Less sensitive is the p-a-SiC:H grating, here a deviation of Δθ = 1° from perpendicular results almost in no change in T_exc. For larger angles, the opposite is observed (Fig. 8). Thus, careful adjustment of the laser beam in a perpendicular direction ( ± 1°) is crucial. It is also assumed that all the excitation light reaches the filter in its initial direction and there is no scattering in the liquid solution.

 

Fig. 8 Transmittance dependence on the incident angle for the excitation (bottom scale) and emission (top scale) light for a TiO₂ grating (P = 380 nm, h = 129 nm) and p-a-SiC:H grating (η = 0.5, P = 295 nm, h = 94 nm and η = 0.25, P = 359 nm, h = 262 nm). For comparison the angle dependence for the flat absorbing filter (d_AF = 2000 nm) is added.

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In contrast to the excitation light, the emission light is much less dependent on the incident angle (remains within one decade - Fig. 8 – top scale). Here T_em values even for large incident angles do not fall below 10%. For the emission light, high transmittance for all incident angles may be assumed, which is appropriate since fluorophores are optical point sources.

3.4 The role of fabrication errors in diffraction gratings

As mentioned in section 3.1, filtering characteristics of the embedded grating is highly dependent and sensitive to the period and the height of the grating. Simulations show how small deviations in P and h shift the narrow dip observed in the wavelength characteristics, which leads to noticeable loses in RR. Because of this, it is important that the diffraction grating is made as precise as possible, preferably with nanometer accuracy. To determine the effect manufacturing errors have on RRs, we simulated different filter configurations with known degrees of tolerance in the grating dimensions. Although state-of-the-art photolithographic technologies such as electron beam lithography and nano-imprint lithography already allow nanometric accuracy [36] we took the following two inaccuracy ranges into account: (i) a large range of Δ_i = ± 0-5 nm and (ii) a more optimistic range of Δ_ii = ± 0-3 nm inaccuracies in half period segments (p₁ and p₂) and in height (h). The results for the embedded TiO₂ and p-a-SiC:H gratings are presented in Fig. 9(a) and 9(b), respectively. They are shown with and without the flat absorbing filter beneath in the case of a perpendicular incident angle of both the excitation and emission light. In the analysis, we randomly selected deviations in both half-periods and heights for P/2 = P_optimal/2 + Δ_i ( ± 5 nm) and h = h_optimal + Δ_i ( ± 5 nm). We also took into consideration 7 half-periods in lateral directions, creating a net of 49 alternating blocks of SiO₂ and grating material, with random tolerance distribution in both P/2 and h. Simulations reveal that the extreme transmittance decay observed at the excitation wavelength in the ideal case disappears (Fig. 9). However, a noticeable decay still remains and RR_T in the case of Δ_i ( ± 5 nm) inaccuracies (P/2 and h) is around 40 for TiO₂ and 60 for p-a-SiC:H grating.

 

Fig. 9 Effect of manufacturing uncertainties (on period (Popt/2 + Δ) and height (hopt + Δ) in range Δi = ± 0-5 nm and Δii = ± 0-3 nm) on T(λ) characteristics for: a) TiO2 grating (Popt = 380 nm, hopt = 129 nm) with and without the absorbing filter and b) p-a-SiCH grating (Popt = 295 nm, hopt = 94 nm) with and without the absorbing filter. Added are the ideal Texc values for both embedded gratings, without the absorbing filter.

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If we accept smaller deviations from the optimal P/2 and h, i.e. Δ_ii ( ± 3 nm), we achieve even better results. The RR_T is around 90 and 210 for the TiO₂ and p-a-SiC:H grating, respectively. We repeated the simulation for the p-a-SiC:H grating with a duty-cycle of η = 0.25. Similarly, there was no observable extreme decay at the excitation wavelength. With errors of Δ_i ( ± 5 nm) we get a RR_T of around 35 and around 100 for a Δ_ii of ± 3 nm. It is clear that the embedded grating with a smaller duty-cycle (η = 0.25) is more sensitive to manufacturing errors. This is because the grating half period is much smaller than when η ≈ 0.5, thus a tolerance of ± 5 nm causes a greater relative change in half-period. The p-a-SiC:H grating with a duty-cycle of 0.5 was the least sensitive to manufacturing errors. Manufacturing errors have little or no effect on the transmittance of the emission light making a combination of the embedded grating with absorbing filters meaningful. Simulations reveal that when a p-a-SiC:H grating with inaccuracies of Δ_i ( ± 5 nm) is combined with an absorbing filter RR_T values of 800 are obtained, while for Δ_ii ( ± 3 nm) RR_Ts of > 4000 are achievable (Table 2, column 7).

3.5 Spectral response of the detector including different filtering solutions

Finally, we simulated the spectral response (SR) of a complete biodetector, including the pin photodiode with a filter on top. In Fig. 10 we compare SRs of the detector (a) without a filter, (b) the reference, (c) with the flat absorbing filter and diffraction grating on the top surface, (d) a TiO₂ grating embedded in SiO₂, (e) a p-a-SiC:H grating embedded in SiO₂ (f) a p-a-SiC:H grating embedded in SiO₂ with a η = 0.25, and (g) a p-a-SiC:H embedded grating in SiO₂ combined with a flat absorbing filter (for cases c, d, e and g η = 0.5).

 

Fig. 10 Spectral response (SR) of the detector with different filtering solutions.

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Figure 10 shows the SR results obtained in an ideal case: perpendicular light and no errors in the gratings. The corresponding RR_SR are given in Table 2. Generally, the observation is that the trends in the SR characteristics follow those observed for T. The difference in behavior of RR_SR towards RR_T (Table 2) is a consequence of additional interference effects occurring within the multilayer structure of the entire detector. In a real case, these effects are diminished due to the omni-directional properties of the emission light. Figure 10 shows how AF and GAF express broad high pass filter characteristics in the range of wavelengths investigated. All other structures with an EG express a notch-like filter characteristic with the main narrow stop occurring at the excitation wavelength. The best result was achieved using a p-a-SiC:H grating with a η = 0.25.

To approach real conditions, we included the effects of a) non-perpendicular incident angles – 0.5 degree of deviation from perpendicular direction for λ < 495 nm (including λ_exc) and an average angle of 45 degrees for λ > 495 nm (including λ_em), and b) manufacturing errors in grating fabrication (random Δ_i = ± 5 nm) in the half-periods and height of the grating. Figure 11 shows the results of our simulations, while Table 2 gives the corresponding RR_SRs.

 

Fig. 11 SR for different filter configurations for realistic conditions. Here less wavelengths were simulated (due to the large simulation model), thus lines are more rugged than in previous graphs.

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Comparing the ideal case (Fig. 10) with real conditions (Fig. 11) we observe a steep decline in the RR_SR as a consequence of manufacturing errors; the dominant effect causes a higher SR of the excitation light, thus decreasing RR_SR. An incident angle of 0.5° at the excitation wavelength has little effect, and for small incident angles of < 1° the excitation light, SR_exc remains low. A mean incident angle of 45 degrees is assumed for the emission light. By taking into account real conditions (entire structure including photodetector, incident angle, manufacturing inaccuracies), there remains an increase in RR_SR compared to AF. The p-a-SiC:H grating in combination with AF gave the best RR_SR value (310). Also, with other embedded gratings we still obtain higher RR_SRs compared to AF (Table 2, column 8).

So far in our simulations we have presented the emission spectrum using a monochromatic component, where λ_em = 510 nm. As a last point in our investigation we consider the entire spectrum of the GFP emission light (Fig. 1b) and scale it so that the integral of the total emission power is equal to unity. A new SR_em is then calculated as the integral of the product of the scaled emission spectrum and SR_em between λ = 500 – 600 nm. Finally, the RR_SRs were calculated using Eq. (2). As there are no sudden changes in the emission spectra or in SR_em, an integration step of 10 nm was applied. The RR_s for the detectors with AFs are considerably improved, by exploiting the higher transmittance at higher wavelengths, while for an embedded grating only a small reduction in the RR_SRs is observed. The RR_SRs under ideal conditions are presented in Table 2, column 9. The best RR_SR obtained under real conditions are for a p-a-SiC:H grating combined with an absorbing filter (A-EG + AF), which has a RR_SR value >1100. This represents a >60 times improvement over an AF. Results for all the filter types are presented in Table 2, column 10.

4. Conclusions

Diffraction gratings have been proposed for the purpose of improved optical filtering in fluorescence detection using GFP as an example of a small Stokes’ shift biomolecule. Three filter concepts were investigated using numerical simulations. First, the placement of a diffraction grating on the surface of an absorbing filter was analyzed, showing minimal improvements. The other two concepts, both based on diffraction gratings embedded in a low refractive index material, either as a single filter or combined with a flat absorbing filter, gave high RRs (over 10⁵). When P and h are optimized, efficient notch like filters can be created, implying large possibilities for selective optical filtering in biodetectors, especially in the case of small Stokes’ shift fluorophores, such as the green fluorescent protein. Comparison of absorbing and nonabsorbing grating materials revealed absorbance and reflectance to be the cause of low transmittance of excitation light, respectively. Also, a higher dependence of the angle of incidence for nonabsorbing grating material was observed. The disadvantage of such filters is their high sensitivity to grating fabrication errors and to the incident angle of the excitation light. Fabrication errors could be reduced by using modern manufacturing techniques capable of nanometer accuracy while close to perpendicular incident angles can be obtained using a laser. Even allowing for some inaccuracy in manufacturing (Δ_i = ± 5 nm), high RR are still achievable. Embedded grating in combination with a flat absorbing filter (A-EG + AF), showed that RR_SRs of >1100 are feasible, which is a 60 times improvement over a flat absorbing filter.