Controlling the flow of light through different media is of immense importance in photonic research. It can be in the case of solar cells [1], where the surface reflection of light drastically reduces their efficiency or the case of high-resolution CMOS image sensors that require the convergence of light to reduce crosstalk effect [2]. However, both of these aspects are not studied simultaneously or realized in one single platform. Methods to reduce surface reflection have evolved quite a lot, starting with the incorporation of antireflecting (AR) single or multilayer dielectric films. However, they have disadvantages such as limitation to specific wavelength range, material selection, and thickness control [1]. To overcome these difficulties, many light trapping techniques have been reported, including Si nanostructures to obtain a graded refractive index (RI) profile at the interface [3–7]. These nanostructures reduce reflection by trapping the incident light due to multiple scattering effects. However, these Si nanostructures absorb a major portion of the trapped light in the visible wavelength range (300–500 nm) and thus, the light could not be coupled properly to the active region of the PV cell. In addition, they also suffer from the limited spectral range and the restricted angular range of light incidence. In these regards, ZnO has emerged as a promising AR material because of its good transparency, appropriate RI ($n\sim 2$, in the visible to near-infrared [NIR] wavelength range), and the ability to form textured coatings via the anisotropic growth of nanostructures. Various kinds of ZnO nano-architectures have been reported [8–11] to provide antireflection performance. For example, Lee et al. [10] controlled the shape of a nanowire (NW) tip by varying the growth condition to achieve a continuously varying RI profile. Although they showed an average weighted reflectance of 6.6%, the reflectance is still more than 20% in the range of 400–500 nm. There are also reports on Si-ZnO hybrid nano-architectures [12–16] for AR purposes. For example, Huang et al. [14] used KOH to roughen the Si surface to make Si micro-pyramids over which ZnO NWs were grown. However, the obtained reflectance is 15% in the range of 300–400 nm and 20–25% for a wavelength longer than 1000 nm. Hence, even though the obtained weighted reflectance in all the aforementioned ZnO AR designs is reduced to 5–10%, the low reflectance value is not maintained throughout the whole wavelength spectrum. Besides, the coupling of light to the active region is not efficiently achieved, as the light is not trapped in a proper way. In addition, the directional propagation and the focusing/convergence of light are important effects in the case of selective emitter solar cells and image sensors. Light focusing or convergence in the planar optics regime needs complicated GRIN lens structures or microlenses.

In this Letter, we report new observations of light trapping and convergence in one platform by periodically patterned funnel-shaped vertical ZnO NW aggregates, here on called “ZnO funnels,” for light manipulation in solar cells and pixelated photodetectors. We have fabricated these funnel structures and analyzed their reflection spectrum. We performed finite difference time domain (FDTD) simulations to investigate the 3D RI gradient of ZnO funnels for antireflection, as well as for light convergence or “funneling.”

The ZnO funnels (as shown in Fig. 1) are grown through hexagonally arranged openings in a photoresist layer on a ZnO (seed layer) thin film deposited on a Si substrate. Here, we have fabricated three samples with periodicities of 3000, 2000, and 1500 nm, and hole diameters of 1250, 1000, and 850 nm, respectively, and labeled as samples 1, 2, and 3. The fabrication method consists of three steps. First, a ZnO seed layer is deposited on the Si surface; in the second step, a photoresist layer is patterned by a photolithography process providing openings exposing the ZnO seed layer in selected areas for ZnO NW growth. Subsequently, ZnO funnel-like structures are grown hydrothermally. Details of the hydrothermal growth procedure of ZnO NWs are described in our previous work [16,17]. The SEM images of the three fabricated structures are shown in Figs. 1(a)–1(c). The corresponding model of an optimized ZnO funnel structure obtained through FDTD simulations and its effective refractive index profile is shown in Figs. 1(d) and 1(e), respectively.

 

Fig. 1. SEM images of fabricated ZnO funnels on Si substrate. (a) Sample 1, (b) sample 2, (c) sample 3, (d) a schematic of the optimized structure obtained through FDTD simulation, and (e) a single ZnO funnel as an equivalent GRIN lens (at 480 nm wavelength).

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The growth time for the three samples is kept different such that the heights of the ZnO funnels are different for the three samples. The obtained heights in samples $-1$, 2, and 3 are about 1450, 1650, and 1000 nm, respectively. As the ZnO NWs grow with different heights, they ultimately expand to produce different cross sections at the top of the funnel. The measured average diameter (from SEM image) of the top circular cross sections are 1500, 1700, and 1050 nm for samples 1, 2, and 3, respectively. The total reflectivity of the three samples were measured using a spectrophotometer (Perkin Elmer LAMBDA 950) equipped with a 150 mm integrating sphere. The measurement wavelength range was 300–1200 nm which covers the UV to NIR regions relevant for the working of photovoltaic (PV) cells. The results obtained are presented in Fig. 2(a) and compared with the reflection spectrum of a bare Si surface.

 

Fig. 2. Total reflectance spectra of the three samples (a) experimentally measured by spectrometer and (b) obtained by FDTD simulations. The periods in samples 1, 2, and 3 are 3000, 2000, and 1500 nm, respectively.

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From Fig. 2(a), it can be seen that the reflectivity for all three samples is reduced from that of the bare Si case, and the average reflectivity (i.e., the spectrally averaged value) value reduces as the structure’s periodicity decreases. The average reflectivity for sample 1 and 2, having periods of 3000 and 2000 nm are 22% and 17%, respectively. On the other hand, when the funnels are closer to each other, as in sample 3, with a closer period (1500 nm), the average reflectivity drastically reduces to a lower value of 7.5%. To analyze the observed reflectivity of ZnO funnel structures, we simulate these structures using FDTD simulations [18]. A schematic of the ZnO funnel structure that we generated in our FDTD model is shown in Fig. 1(d). Since the structure is periodic along the transverse $XY$ directions, the 3D FDTD calculations are performed with periodic boundary conditions (BCs) along the $X$ and $Y$ directions, and PML BC along the $Z$ direction. We note here that due to practicality, in the simulations we kept the NW diameter constant at 100 nm, close to the average values found in the grown NWs. We have also arranged the NWs to be well oriented and radially divergent with height, as reported in [19], which is slightly different from the fabricated structures in this Letter. Within the limits of an FDTD model to generate such kind funnel-like structures, we matched as best as possible the simulated structures with the fabricated ZnO funnels. The simulated reflection spectra corresponding to the three samples and for the bare Si surface are shown in Fig. 2(b). By comparing the simulated and the corresponding experimental reflectance spectra, it can be inferred that the average reflectivity values and trend in which the reflectance varies with periodicity are in very good qualitative agreement.

The reduction in reflectivity can be explained by understanding the mechanisms by which the incident light is trapped in the structure. The nanorods at the base of the funnel are closely packed, and they gradually open toward the top, reducing their density. Thus, the effective RI, from the bottom to the top, of the funnel gradually decreases, as shown in Fig. 1(e) which behaves like a GRIN lens. When light is incident from the top side of the funnel, it gets trapped by the funnel and gradually converges toward the base due to the funnel shape and the lensing effect. In fact, the trapping behavior of light depends on the wavelength of light. Videos showing how light gets trapped inside the funnel structure of Fig. 1(d), for different wavelengths (see Visualization 1, Visualization 2, Visualization 3, Visualization 4 for wavelengths 450, 550, 650, and 1100 nm, respectively) are provided as supplementary materials.

In Fig. 3, we have shown the electric field (in arbitrary units) profiles in the (funnel) structure for different wavelengths of light. When the wavelength of light $<368\mathrm{nm}$ (bandedge of ZnO), the incident light gets absorbed by ZnO and only penetrates to a limited depth of the funnel [as shown in Fig. 3(a)]. When wavelength increases beyond 368 nm, ZnO becomes transparent, and light travels inside each nanorod-like optical fiber. This behavior continues up to around 700 nm of wavelength, as shown in Fig. 3(b). Beyond 700 nm each individual nanowire cannot guide the light inside it and the funnel itself behaves like a subwavelength structure. The electric field profile for wavelength $>700\mathrm{nm}$ is shown in Fig. 3(c), where light through the funnel is guided the same way as a GRIN lens and converges toward the base and to the Si substrate. Thus, we can conclude that, independent of the light wavelength, the incident light is always trapped inside the funnel and a negligible fraction comes out of the funnel. This light trapping mechanism by funneling effect is to some extent similar to that in the “Muller cells” of the vertebrate retina [20]. The end feet of the Muller cells are funnel-shaped and provide a passage of light through the retina to the photo detector cells. They cover the entire inner retinal surface and have a gradual change in refractive index.

 

Fig. 3. $E$-field profiles in ZnO funnels for different wavelengths (a) $<368\mathrm{nm}$, (b) 400–700 nm, and (c) $>700\mathrm{nm}$. (d) $XY$ cross section at 1100 nm showing the confinement of field at the base of the funnel.

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In Fig. 3(d), the transverse ($xy$) cross section of the $E$-field (for a wavelength of 1100 nm) at the bottom of the funnel is shown. As can be seen from this figure, the $E$-field is completely confined within the base area of the funnel. It looks very similar to the focal spot of a lens whose focal area is only in the range of hundreds of nanometer. This unique property, together with its broadband low reflectivity, makes the ZnO funnel structures very promising from solar cell and image sensor perspectives. In particular, for solar cells, it can serve the purpose of broadband antireflection, as well as to focus the incident light on selective small areas. Therefore, the top metal contacts can spread over large areas, thereby reducing the resistive power loss without an appreciable shadowing effect. In addition, these spread-out top contacts can use normal metals, instead of transparent conducting oxides (TCOs). This will be very useful for amorphous or low-quality solar cell materials where TCOs are otherwise essential. On the other hand, for a densely pixelated CMOS image sensor, it can serve the purpose of a microlens with a submicron confinement of light with the added advantage of suppressed top reflection.

It is worthy to note here that the average reflectivity for sample 3 is 7.5% but, for certain wavelength ranges (e.g., $>900\mathrm{nm}$), the reflectivity becomes more than 10%. Hence, we optimized our structure so that the average reflectivity is reduced below 10% and remains low throughout the whole wavelength range. As observed, the reflectivity of our structure strongly depends on the periodicity or, in other words, to the packing fraction of the unit cell. When the period of the unit cell is large, the packing fraction of funnels in a unit cell decreases. The funnel structures in this case could not shield the Si-air interface properly (samples 1 and 2), and a major portion of the incident light is directly reflected by the Si-air interface. On the other hand, if the funnels become very close to each other or they grow longer, then they overlap with each other at the top portion. According to the effective medium theory, the effective refractive index (i.e., the area ratio of funnel to the total substrate surface) increases with the filling factor. Thus, the effective RI at the top of the funnel is more compared to the region below it. This leads to a reverse gradient RI at the funnel-air interface, and the reflectivity increases. Thus, keeping this effect in mind, we optimized the filling fraction of the unit cell by tuning the period, base diameter, and height of the funnel in the FDTD simulations.

We found that a structure having a 1000 nm period, a 750 nm base diameter, and a 600 nm funnel height gives the minimum average reflectivity. The schematic of this optimized structure obtained through FDTD simulation is shown in Fig. 1(d). Although not attempted here, it is worthy to mention here that such patterns can be easily generated using advanced photolithography techniques (e.g., DUV), thus accessible for large-area manufacturing. In addition to reflectivity optimization, the angle and polarization dependency of reflectivity was analyzed by FDTD simulations. In Fig. 4(a), the total reflectivity spectrum is shown for the normal incidence (0°), as well as for other oblique angles of incidence (30°, 60°). It can be observed that the reflectivity has been reduced below 7% throughout the wavelength range of 300–1200 nm, and the average reflectivity comes out to be around 3%. It also shows that the reflection spectrum maintains its lower value, even up to a 60° angle of incidence which is advantageous for the working of a PV cell. The reflectance spectra for three different polarizations of the incident $E$-field, 0°, 45°, and 90° [Fig. 4(b)] show that the structures are nearly polarization independent.

We further analyzed the graded refractive index profile along a vertical cross section of one ZnO funnel unit of the optimized structure by calculating the effective RI. The obtained results for the optimized unit cell at four different wavelengths (352, 428, 545, and 750 nm) are shown in Fig. 5(a). It can be seen that the effective RI gradually increases from the funnel-air interface to the funnel/silicon interface. At the funnel-air interface, the effective RI is around 1.4-1.6 and, at the base of the funnel, it is around 1.8–2.2, depending on the wavelength of the light. We then compared the optimum result with a structure for which the funnels overlap at the top portion, and its result is shown in Fig. 5(b). From this figure, it can be observed that from the funnel-air interface to a region below it, the refractive index first decreases (indicated by red circle), then increases toward the bottom of the funnel. Thus, its reflectivity will be more (due to the reverse gradient RI, as discussed previously) than that of the optimized one.

 

Fig. 4. Simulated reflection spectrum of the optimized structure, compared with that of a bare Si surface: (a) at 0°, 30° and 60° incidence angles, and (b) for three different polarizations (0°, 45°, and 90°).

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Fig. 5. Calculated effective RI at cross sections of an individual ZnO funnel unit along the vertical direction ($Z$) (a) for the optimized structure and (b) when the funnels overlap with each other at the top.

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In conclusion, we report a new technique to trap light by a funneling effect in ZnO funnel-like structures. Depending on the wavelength, the incident light is trapped in the ZnO funnel due to the funneling effect and/or converges toward the base of the funnel by a GRIN lens effect. These ZnO funnel-like structures are hydrothermally grown through a photo-lithographically patterned hexagonal lattice of openings. We have analyzed the behavior of the measured reflectivity spectrum with the change in periodicity and compared the result with FDTD simulation. Finally, we have optimized our structure to get minimum reflectivity of around 3% throughout the whole wavelength spectrum (300–1200 nm). The maximum reflectivity at any wavelength is less than 7% for the whole broadband (300–1200 nm) range of wavelengths. This is unlike the other techniques reported using ZnO nanostructures, where it is more than 15–20% in some wavelength ranges. The structure maintains its low reflectivity, even up to a 60° angle of incidence, making it omnidirectional. These types of nanofeatures can be efficiently used in micro-image sensing applications. For example, as described in [21], the meta-lenses or meta-surfaces allow the miniaturization of conventional refractive optics into planar structures. Our proposed ZnO funnel with its unique light trapping and converging ability will be useful for subwavelength imaging and diffraction limited focusing, high-efficiency solar cells and dense pixel image sensors. There is a further scope of investigations on the effect of the diameter, orientation, and distributions of the ZnO NWs in the funnels on the collection mechanism.