1. Introduction

Bioinspired and biomimetic photonics have been areas of intense research over recent years owing to the prospect of designing novel devices and systems based on the exotic photonic structures prevalent in numerous animals, plants and microorganisms [1–12]. Among a plethora of living organisms relevant to this field of study, diatoms belonging to the genus Coscinodiscus have been the subject of detailed investigation owing to their unique, yet conveniently experimentally realizable morphological structures [13–16]. Numerous photonic and optoelectronic devices, such as energy harvesters [14,17–19], lasers [20], biosensors [21,22], sub-diffractive light focusing and imaging systems [23–25], have been designed and fabricated by replicating the porous silica-based exoskeleton of Coscinodiscus diatom, which is also known as the frustule. In our previous work it has been shown that multi-layered stacks comprising of nanopores- having the hierarchical porous structure of Coscinodiscus sp. diatoms- offer a simple yet effective means of photon-management in thin-film photonic devices [26]. Near-unity, broadband light absorption characteristics were attained with GaAs-based bi-layered photonic structures, where $SiO_{2}$ filled nano-holes were periodically arranged in two layers, with square-lattice orientation.

Though Coscinodiscus sp. is observed to have a hexagonal, quasi-periodic arrangement of micropores in its frustule [14,17–25], it has been shown that absorptance over the visible spectral region is comparatively lower for the hexagonal-lattice than for the square one when a single layer of nanopores is considered [26]. Compared to the peak absorptance of 95% obtained for the square-lattice, the maximum absorptance obtained for an equivalent hexagonal-lattice is about 80%. The observed difference has been attributed to the higher out-of-plane reflection of TE polarized light incident onto the hexagonal array. Notwithstanding such advantages of the square-lattice variant of the single-layered structure, it remains to be seen whether such differences prevail between multi-layered structures. Such a study is important not only for a better understanding of the role of hexagonal arrangement of pores in the photon management technique of Coscinodiscus sp., but also for gaining further insight into the design of multi-layered photonic structures so that enhanced tunability of absorption characteristics can be attained in terms of angle-of incidence, spectral wavelength, polarization, and direction of the incident light.

In the present study, which is a continuation of our previous work reported in [26], we report a detailed comparison between light absorption characteristics of Coscinodiscus diatom inspired bi-layered photonic structures comprising of hexagonal and square lattice arrangements of nanopores. Besides studying the impact of relative orientation of nanopores, this work investigates polarization and incidence angle dependence of absorption, reflection and transmission characteristics of the structures. The finite-difference time domain based numerical analysis of this work shows that irrespective of the direction of incident light, the hexagonal lattice-based bi-layered structure exhibits significantly higher light absorption compared to its equivalent square lattice-based structure. Furthermore, for both TM- and TE- polarization of the incident light, the hexagonal lattice-based system outperforms its square-lattice based counterpart at high angles of incidence. The prospect of tuning the peak absorption wavelength of the proposed bi-layered structures has also been discussed in this work based on effective medium theory based theoretical modeling. The results of this work provide guidelines for designing thin-film devices comprising of multi-layered photonic structures, which hold significant promise for future photo-detection and energy harvesting related applications.

2. Analyzed bi-layered structures

The theoretical insight behind the design of the bi-layered absorber stack is obtained from the experimental characterization of marine diatom Coscinodiscus sp. harvested from northern Norwegian Sea. The experimental characterization of the diatom is discussed in detail in [26]. Scanning electron microscopy (SEM) image of the processed sample exhibits hexagonal orientation of nanopores arranged in multiple layers (Fig. 1(a)). In contrast with our previous study, where the nanopores of both the bottom and top layers were arranged in square-lattice [26], we consider here hexagonal orientation of the arrays. Two different cases of the bi-layered photonic structures have been considered herein. In the first case, the structure is designed such that centers of the nanopores of the top layer are aligned with centers of nanopores of the bottom layer. In this arrangement, referred to as the centric structure in this work (shown in Fig. 1(b)), lattice constants of the two layers are identical. As the diameters of the nanopores of the two layers are different, the centric structure has different areal densities of nanopores in the two layers. The second type of structure, shown in Fig. 1(c), contains nanopores of equal areal density in the two layers. In this arrangement, lattice constant of the top and bottom arrays are different owing to the different diameters of nanopores in the arrays. Similar to the case of Coscinodiscus sp., the pore-centers of the bottom and top layers are not aligned with each other in this structure and hence it is referred to as the off-centric structure. Considering feasibility of practical implementation, nanoporese of both the centric and off-centric structures are considered to be filled with SiO$_{2}$. As the extinction coefficient of SiO$_{2}$ (shown in Fig. 1(d)) is essentially negligible over a wide range of the electromagnetic (EM) spectra, incorporation of SiO$_{2}$ ensures that the incident solar radiation is solely absorbed by the GaAs active region.

 

Fig. 1. (a) FE-SEM image of Coscinodiscus sp. frustule. Schematic illustration of the GaAs-based bi-layered (b) off-centric and (c) centric structures having hexagonal arrangements of pores (top-view of the structures are shown as insets). (d) The utilized extinction coefficient and refractive index of GaAs used in this study, fitted against experimental results reported in [27].

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Absorption characteristics of the proposed structures have been analyzed by solving Maxwell’s electromagnetic equations using finite difference time domain analysis techniques (FDTD). The obtained results are compared with absorption characteristics of bi-layered structures having square lattice of nanopores, arranged in centric or off-centric manners in the two layers. This comparison provides insight into the impact of hexagonal-lattice arrangement of the arrays on absorption characteristics. In what follows, absorption characteristics of hexagonal and square lattice cases of the bi-layered centric and off-centric structures are discussed for different dimensions and areal densities of the nanopores and also for different angular incidences of light. In addition to this, absorption profiles for the case of larger pores in the top-layer and smaller pores in the bottom layer are compared with the case of having smaller pores on the top. The second case is referred to as the inverted structure in this study. The regular and inverted cases are compared for both centric and off-centric arrays of hexagonal and square lattice orientations of the pores. Based on these results, the prospect of these structures for bi-facial light absorption related applications is discussed.

3. Comparison between hexagonal- and square-latticed centric structures

In our previous study it has been observed that in a GaAs-based material system, peak absorption is attained for pore radius ranging from 100-120 nm [26]. In the present study, absorption profiles obtained for hexagonal and square lattice arrangements are compared by varying pore radius of one of the layers, while keeping the radius of the other layer constant at 120 nm. Absorption spectra obtained for structures having larger pore radius on the top layer are shown in Fig. 2(a), whereas the case of structures having smaller pore radius on the top layer are shown in Fig. 2(b). Though similar absorptance values are obtained for square and hexagonal lattices at ultra-violet and visible wavelengths, in the near-infrared regime the absorptance values are higher for the square lattice because of photonic crystal effects. According to the photonic band-structures of the hexagonal and square lattices (Figs. 2(c),(d)), the photonic bandgap (PBG) of the square lattice exists at a much longer wavelength (beyond 980 nm) compared to the PBG obtained for the hexagonal lattice. Consequently over the wavelength range of interest, a greater fraction of light is reflected from the hexagonal lattice. This ultimately results in the slightly smaller absorptance values of hexagonal bi-layered structures compared to their square-lattice counterparts.

 

Fig. 2. (a) Absorption spectra of bi-layered centric structures having square and hexagonal unit cell for 120 nm hole-radius of the top-layer while bottom layer radius is varied; (b) absorption spectra of bi-layered centric structures for hexagonal and square unit cell having different hole-radii at the top layer and a constant hole radius of 120 nm at the bottom layer; Photonic band structures of (c) square and (d) hexagonal lattice of nanoporous arrays having $r/a$ ratio of 0.48, where $a$ is the lattice constant; corresponding periodic arrays and Brillouin zones for square and hexagonal lattices are shown as insets.

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To gain further insight into the absorption characteristics, mode profiles of the photonic structures have been analyzed. Mode profiles of single layered arrays having 120 nm and 50 nm pore radii are shown in Figs. 3(a) and 3(b), respectively. It is evident that x-y symmetry is present in the field distribution of square unit cells. The mode profile at the x-y interface of the bi-layered centric structure formed with these two layers is shown in Fig. 3(c). By comparing these mode profiles, it can be inferred that field-distribution of the top layer has a greater impact on the overall field distribution of the structure. Similar characteristics are observed in the mode profile of the bi-layered structure comprising hexagonal lattice. In Figs. 3(d),(e), mode profiles of hexagonal single layers having 120 nm and 50 nm radii are shown. In this case circular symmetry of the field distribution is observed in both layers. This symmetry is retained in the centric bi-layered structure (shown in Fig. 3(f)), where the field distribution is governed by modal characteristics of the top layer. The dominance of the top layer becomes evident from the absorption spectra of Figs. 2(a),(b) also. It can be observed that absorption spectra changes more significantly when the top layer’s pore radius is varied (Fig. 2(b)) compared to the case of Fig. 2(a), where the bottom layer’s pore radius has been varied.

 

Fig. 3. Mode profiles (electric field) of the single layer structures having (a) 120 nm and (b) 50 nm pore radius, and (c) mode profile (electric field) at the interface of the bi-layered structure formed with these two layers. Mode profiles (electric field) of hexagonal single layered structures having (d) 120 nm and (e) 50 nm pore radius and the profile obtained at the interface of the hexagonal bi-layered structure formed with these two layers.

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To compare the tunability of absorption characteristics, fill-factor of the hexagonal and square arrays are varied while keeping the pore radii of bottom and top layers constant. Here fill factor is defined as volume fraction of $SiO_{2}$ in the photonic structure. For the centric structure, the bottom layer’s fill factor ($f_{2}$) is related to the top layer’s fill factor ($f_{1}$) by the relation $f_{2}=f_{1}{(r_{2}/r_{1})}^2$. The overall fill factor of the structure is given by $f=(f_{1}t_{1}+f_{2}t_{2})/(t_{1}+t_{2})$, where $t_{1}$ and $t_{2}$ are thicknesses of the top and bottom layers respectively. As shown in Fig. 4(a), resonant peaks (residing above 500 nm) systematically blue-shifts as the fill-factor is increased. This is further illustrated in Fig. 4(b), which plots peak absorption value and wavelength as a function of fill-factor of the top layer. As absorber material in the system decreases with increasing fill-factor, the peak absorption value decreases for both types of lattices. It is noteworthy that in all cases the peak absorptance (residing withing 400-450 nm range) is about 5% higher for the hexagonal case compared to the square one. The broad peak appearing at the peak absorption wavelength (denoted as $\lambda _{abs}$ in Fig. 4(b)) indicates the presence of multiple higher order modes. Distinct resonant peaks corresponding to higher order modes are also observed, which gradually shift with fill factor. These resonant modes (denoted as $\lambda _r$ in Fig. 4(b)) can be theoretically modelled within the framework of Maxwell Garnett approximation of the effective medium theory [28]. As shown in Fig. 4(b), for both hexagonal and square unit cells, the theoretical calculations are qualitatively in accordance with FDTD simulation results. It is important to note that the effective medium approximation based theoretical model does not take into account the geometrical arrangement of the holes, thereby resulting in identical values of $\lambda _r$ for the hexagonal and square unit cells.

 

Fig. 4. (a) Absorption spectra obtained for varying fill factors of the top layer of centric-structure having hole radius of $r_1=120 nm$ and $r_2=50 nm$ respectively; (b) dependence of peak-absorption, peak-absorption wavelength ($\lambda _{abs}$) and resonant wavelength ($\lambda _{r}$) of centric bi-layered structure on fill factor (solid and dashed lines are guide to the eye while dotted lines represent theoretical calculations). Polarization and incidence angle dependence of the (c) peak-absorption and (d) reflectance values of centric bi-layered structure with $r_1 = 120 nm$ and $r_2 = 50 nm$.

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To understand polarization and angle dependence of the centric structures comprising hexagonal and square unit cells, peak absorptance is calculated for both TE and TM polarization of light incident at different angles. As can be observed from Fig. 4(c), irrespective of the polarization of light, peak absorptance remains higher than 95% at up to $\sim 30^{o}$ angle of incidence for both types of unit cells. At higher angles of incidence, light absorption appear to be strongly polarization sensitive for square unit cells, with TM polarized light being more strongly absorbed by the structure. Such characteristics are related to the polarization dependent reflectance of the structures (shown in Fig. 4(d)). At peak absorption wavelength, Brewster angle ($\theta _{B}$) for both square and hexagonal arrays is calculated to be about $60^{\circ }$. Around this angle of incidence, TE polarized light is strongly reflected by both bi-layered structures. In particular for incidence angles of $40^{\circ }$ or higher, absorptance is about 1.5 to 2 times higher for TE-polarized light incident onto the square lattice-based structure, compared to the case of hexagonal array. Consequently, at high angles of incidence, absorptance in the hexagonal arrangement of pores appears to be higher.

To further investigate absorption characteristics of the centric bi-layered structures, angle dependent absorption and reflection characteristics of the constituent single layers have been analyzed in Fig. 5. The absorptance and reflectance spectra for square unit cells having pore radius of 120 nm and 50 nm are shown in Figs. 5(a),(b). It is noteworthy that absorption and reflection characteristics obtained for the r=120 nm square array are qualitatively similar to the trends obtained for the bi-layered structure having $r_{1}=120 nm, r_{2}=50 nm$. Such similarity holds for hexagonal arrangement of the pores as well, i.e., reflectance and absorption characteristics of r=120 nm single-layer hexagonal array (shown in Fig. 5(c)) are qualitatively similar to the characteristics obtained for the bi-layered hexagonal array having $r_{1}=120 nm, r_{2}=50 nm$ (Fig. 4(c)). These results confirm that angle dependent absorption of the centric bi-layered structure is also governed by the top layer of the structure. Nonetheless, the bottom layer appears to have an important impact on the absorptance values of the arrays. As can be observed from Figs. 5(b) and 5(d), in both square and hexagonal arrays, absorptance increases with increasing angle of incidence when the light is TM polarized. This increase is accompanied by a corresponding decrease of reflectance at high angles. At all angles of incidence- for both TM and TE polarization- reflectance of the r=50 nm hexagonal array remains about 8-10% lower compared to the reflectance obtained for the r=50 nm square array. This ultimately results in about 8-10% higher absorption of light in the bi-layered hexagonal array compared to the bi-layered square-lattice array.

 

Fig. 5. Polarization and incidence angle dependence of peak-absorption and reflectance values of constituent single layers of the (a),(b) square and (c),(d) hexagonal unit cell based centric bi-layered structures.

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4. Comparison between hexagonal and square lattice-based off-centric structures

Having analyzed absorption characteristics of centric structures, we next study absorption properties of structures formed with square and hexagonal arrays of pores- which are oriented in an off-centric manner in the bottom and top layers. Absorption spectra of the regular off-centric structures (having larger pore radius on the top and smaller pore radius in the bottom layer respectively) are shown in Fig. 6(a). Here pore-radius of the top layer is kept constant at 120 nm while the pore-radius of the bottom layer is varied from 50 nm to 100 nm. Absorption spectra of inverted structures having smaller pore radius on the top and larger pore radius in the bottom have also been analyzed (Fig. 6(b)). A constant fill factor of 50% is maintained in these structures so that the change of absorption properties can be attributed to the relative size of the pores, i.e., whether the top layer has smaller or larger pores compared to the bottom layer. As can be observed, an absorption peak at around 420nm exists in the spectra of all the structures. This is correlated to the high absorption coefficient of GaAs around this wavelength. The absorption peaks at higher wavelengths correspond to the resonant modes arising from multiple-scattering mediated trapping of light- a phenomenon that has been observed in the modal characteristics of centric structures as well. However, it is interesting to note that contrary to the case of the centric structure, light absorption for hexagonal lattice-based off-centric structures is significantly higher than its square lattice-based counterpart when the inverted geometry is utilized. To investigate the underlying reason, reflectance and transmission spectra of both regular and inverted orientations are compared in Figs. 6(c),(d). As can be observed, compared to the hexagonal lattice-based inverted structure, a significantly greater fraction of light is reflected from, as well as transmitted through, the square lattice-based inverted bi-layered system. Consequently, the overall absorption of light in the square lattice-based array is significantly diminished.

 

Fig. 6. Absorption spectra of bi-layered structures having larger hole radius at the (a) top and (b) bottom. Comparison of (c) reflectance and (d) transmittance spectra of the off-centric structures for regular and inverted geometries.

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To have a quantitative estimate of light absorption characteristics of the regular and inverted structures, light absorption efficiency ($LAE$) and enhancement factor ($EF$) are calculated based on the theoretical definitions described in [26]. In Table 1, the calculated $LAE$ and $EF$ values, along with the peak absorptance values, are shown for the off-centric bi-layered structures. Here $LAE$ and $EF$ have been computed over the wavelength range of 300-700nm. The results of Table 1 suggest that light absorption in hexagonal off-centric structures remain high both in regular and inverted structures, though the absorption efficiency is about 10% higher for the regular structure. Such characteristics make the hexagonal off-centric structure promising for applications related to bi-facial cells [29,30]. On the other hand, square lattice-based off-centric structures having $r_{1}=120 nm, r_{2}=50 nm$, though exhibit similar characteristics as the hexagonal system, under inverted condition it has a rather small absorption efficiency of 15%. Because of the high transmittance and reflectance of the square lattice based inverted array, its peak absorptance is limited to 19% only - which is more than 4 times smaller than the value obtained with hexagonal lattice-based inverted systems. To better understand this significant difference, field profiles of the top and bottom layers of inverted structures (having $r_{1}$ = 50 nm, $r_{2}$ =120 nm) of hexagonal and square lattices are compared at 426 nm wavelength. From the field profiles, it is obvious that in both hexagonal and square lattice based arrays, field intensity in the top layer is about 5 to 10 times higher than the field intensity obtained for the bottom array. This is in accordance with our previous observation that absorption characteristics are dominated by top-layer of the bi-layered structures. Comparison of field profiles of top layers of the two structures indicate the interesting attribute that E-field is more uniformly distributed in the GaAs absorber layer of the hexagonal lattice-based array (Fig. 7(a)). This is in contrast with the field profile obtained for top layer of the square lattice-based array, where the field intensity periodically varies in the GaAs absorber layer (Fig. 7(b)). The uniform distribution in the hexagonal lattice arises from its closed-packed structure, which facilitates coupling of adjacent modes. Such characteristics have been observed in nanowire based absorber media, where coupling of near field evanescent modes between closely spaced nanowires enhances light absorption of the absorber medium [31]. In spite of the identical fill factor of 50%, the pores of the square array are more sparsely positioned compared to the pores of the hexagonal array. Consequently, the resonant modes formed in between adjacent pairs of pores of the square array are rather weakly coupled, thereby resulting in the reduced absorptance compared to its hexagonal lattice based counterpart.

 

Fig. 7. Electric field profiles of the (a) top and (b) bottom layers of the inverted off-centric bi-layered structure having hexagonal lattice. Electric field profiles of the (c) top and (d) bottom layers of inverted off-centric bi-layered structure having square lattice. All the field profiles are obtained at 426 nm.

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Table 1. Comparison of calculated LAE, EF, and peak absorptance values of off-centric bi-layered structures with hexagonal and square unit cell

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A summary of the results obtained for the optimized centric structures are also shown in Table 2. A comparison between the $LAE$ and $EF$ values of Table 1 and 2 shows that hexagonal off-centric structures have superior absorption characteristics compared to their equivalent centric structures. With square lattice, the centric inverted structure significantly outperforms the off-centric one in terms of absorption characteristics. With $r_{1}=120 nm, r_{2}=50 nm$, the centric square lattice-based structure has slightly better $LAE$ and $EF$ values compared to its hexagonal lattice based counterpart. Nonetheless, considering high absorption characteristics both under regular and inverted conditions, it can be concluded that off-centric hexagonal lattice-based bi-layered structures similar to those of Coscinodiscus have the most promising absorption characteristics, particularly in regards to bi-facial light detection and energy harvesting applications.

Table 2. Comparison of calculated LAE, EF, and peak absorptance values of centric bi-layered structures with hexagonal and square unit cell

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5. Fabrication scheme

For practical realization of centric/off-centric bi-layered structure based photonic devices, careful consideration of processing and fabrication is essential. An schematic illustration of the possible fabrication steps of the proposed structures is shown in Fig. 8. As shown in Fig. 8(a), fabrication of the off-centric array based device can be initiated by patterning and etching of the epitaxially grown device structure, and subsequent deposition of the bottom oxide layer. This will be followed by metal grid or transparent conductive layer deposition to form the back contact of the device. Next the device structure containing the bottom oxide layer and back contact has to be transferred to a host substrate employing bonding and substrate removal techniques. It is noteworthy that over the recent years there have been a number of reports on the fabrication of high-efficiency GaAs-based solar cells based on substrate removal technique [32–34]. The layer transfer process will be followed by etching and oxide deposition to form the top oxide layer. While doing so, instead of extending the top oxide layer till the bottom oxide layer, a thin epilayer can be maintained in between the two layers. In our previous study in [26], it has been shown that such an epilayer does not significantly alter the absorption characteristics of the device. The last step of the fabrication would involve metal deposition to form the top contact.

 

Fig. 8. Schematic illustration of the proposed fabrication scheme of (a) off-centric and (b) centric bi-layered photonic structure based bi-facial devices.

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Possible fabrication steps of the centric bi-layered structure based device are schematically shown in Fig. 8(b). As centers of holes of the two layers of this structure are aligned, the bi-layered pattern in this case can be formed by back-to-back lithography and etching steps. Then a single oxide deposition would be sufficient to form the top- and bottom-oxide layers of the bi-layered structure. Depending on design, top and bottom contacts can be realized in the form of metal-grids or as transparent conducting layers. Similar to the case of off-centric structures, layer transfer and substrate removal techniques can be applied in the fabrication of centric structures. However it is obvious that fabrication of the centric structure is more convenient compared to the off-centric structure because of the alignment of the holes of the two layers. Either way, the proposed fabrication schemes of off-centric or centric bi-layered structures offer a novel pathway for experimentally realizing bi-facial photonic devices, which are usually fabricated with anti-reflection coatings or textured surfaces on both sides [35,36]. A detailed comparison between the proposed bi-layered structure based devices, and devices fabricated with anti-reflection coating/texturing would require analysis of electrical transport characteristics, coupled with electromagnetic simulations of light absorption characteristics. Such an analysis was beyond the scope of the present work.

6. Conclusion

Inspired by the morphology of Coscinodiscus diatom frustule having hexagonal oriented nanopores, a comprehensive study on the absorption characteristics of bi-layered photonic structures comprising of hexagonal and square lattice oriented nanopores have been presented in this work. Two-types of bi-layered structures- namely the centric and off-centric have been considered herein for hexagonal and square lattice arrangement of the pores. The same lattice constant is maintained in the two layers of the centric structure, whereas in the off-centric structure the areal density of the layers is kept constant. With optimized areal density and dimensions of the nanopores, both square and hexagonal lattices show near-perfect, tunable light absorption characteristics over a wide range of the optical spectrum. However, as far as angular incidence is concerned, hexagonal lattice-based systems offer superior performances for both TM and TE polarization of the incident light. In particular for TM polarization of light, peak absorptance is observed to remain above 95% till up to 60$^{\circ }$ angle of incidence. The hexagonal arrangement of pores is also found to be better suited for systems which are to be used for light absorption from both sides of the structure. Only 19% peak absorptance is obtained with a square lattice-based system when light is incident onto the layer containing smaller pore radius, whereas with hexagonal lattice the peak absorptance is obtained to be around 83%. Such attributes make hexagonal lattice based systems more suitable for bi-facial light absorption related applications. Therefore, this work presents the interesting new finding that by controlling lattice structure (square/hexagonal) and relative orientation of the pores (centric/off-centric), it is possible to preferentially control light absorption in the bi-layered absorber medium depending on whether light is being incident from the bottom or top of the device. This concept offers the prospect of designing a plethora of photonic and optoelectronic devices and systems using multi-layered, composite photonic crystal structures.