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Abstract
Ordered micro-holes with controllable period, diameter and depth are fabricated in Si (001) substrates via a feasible approach based on nanosphere lithography. They dramatically reduce the reflectance in a broad wavelength range of 400-1000 nm, which can be deliberately modulated by tailoring their geometrical parameters. The simulated reflectance via finite-difference time-domain (FDTD) method agrees well with the experimental data. The FDTD simulations also demonstrate substantially enhanced light absorption of a Si thin film with ordered micro-holes. Particularly, the light-filled distributions around micro-holes disclose fundamental features of two types of modes, channel modes and guided modes, involving the wavelength-dependence, the origin, the dominant location region and the interference pattern of the light field around micro-holes. Our results not only provide insights into the antireflection and the substantially enhanced absorption of light by ordered micro-holes, but also open a door to optimizing micro-hole arrays with desired light field distributions for innovative device applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photovoltaic (PV) technology has been of great interest since it can effectively convert sunlight into clean energy and provide a virtually unlimited amount of energy. Given the rapid development of the PV industry, terawatt-scale photovoltaics are expected in the near future [1]. The key challenge remained to be overcome is the further efficiency improvement by new solar cell designs and cost reduction by minimizing materials usage. One solution may be the utilization of nanostructures. Accordingly, enormous effort has been devoted to the new generation of solar cells based on nanostructures. In particular, pillars or nanowires (NWs) have been widely investigated for their application in solar cells [2–9]. These nanostructures are ideal anti-reflectors due to light scattering or coupling into guided modes in nanostructures [2]. They also possess remarkably enhanced absorption cross-section [5]. Moreover, they can facilitate the radial p-n junction to decouple the light incidence and the charge transport, as results in a long distance in the incident (vertical) direction for optimal light absorption and a short distance in the orthogonal (horizontal) direction for effective collections of photon-generated carriers [3,4]. Therefore, pillars or NWs have a great potential in the new generation of solar cells. The PV conversion efficiency of solar cells based on NWs can be up to 17.8% [9]. Recently, the array of holes, or so-called anti-pillars, exhibits some more promising features. In comparison with the pillar counterparts, the array of holes is far superior in aspects of mechanical robustness, electrode fabrication and the carrier collection. They overcome the fragility problem of the free-standing pillars in electrode fabrication [10], which can additionally reduce the cost and enhance the stability of solar cells. Theoretical calculation indicates that solar cells based on nanohole arrays can have higher efficiency than those based on nanorod arrays for practical thicknesses [11]. The radial p-n junction solar cell based on nanohole arrays has also been realized, which shows higher energy conversion efficiency than that based on NWs [10]. For PV applications, the nanohole arrays with short periods are not suitable because the light may not be efficiently absorbed [12]. Moreover, the microstructured holes has also been employed in the high speed and high efficiency Si photodiode at 900-1000 nm wavelength [13], the photoelectrochemical water splitting [14], the biosensors [15], and etc. To fully exploit the array of holes in innovative PV devices or other optoelectronic devices, systematic studies on the light manipulations around the holes is highly in demand.
In this report, a feasible approach based on a nanosphere lithography is developed to fabricate ordered micro-holes with controllable geometrical profiles in silicon substrates. The antireflection and the inherent light manipulations around micro-holes are investigated in detail. The measured total reflectance of micro-hole arrays demonstrates remarkable antireflection in a broad wavelength range of 400-1000 nm, which is intimately associated with the geometrical profiles of micro-holes. The simulated reflectance by three-dimensional finite-difference time-domain (FDTD) method agrees well with the experimental data. Moreover, the transmittance and the absorption, as well as the wavelength- and depth-dependent light field distribution around micro-holes, are extracted from the FDTD simulations. They clearly demonstrate two types of fundamental light modes supported by ordered micro-holes in terms of the coupling wavelength, the origin, the dominant location region and the interference pattern of light filed distributions. Our results not only provide insights into the comprehensive light manipulations by ordered micro-holes, but also open a door towards realizing micro-hole arrays with desired light management for innovative PV devices and other optoelectronic devices.
2. Experimental details
The samples of two-dimensionally ordered micro-holes in Si (001) substrates are obtained by a nanosphere lithograph and an inductive coupled plasma reactive ion etching (ICP-RIE, Oxford PlasmaLAB 180). By using a modified Langmuir-Blodgett (LB) method [16], a monolayer of self-assembled polystyrene (PS) spheres are firstly compactly arranged in a hexagonal lattice on the surface of a cleaned Si (001) substrate, as schematically shown in Fig. 1(a). The PS spheres are then etched by a reactive ion etching (RIE) using oxygen as the reactive gas to shrink the diameter to a desired size, as schematically shown in Fig. 1(b). After that, a Cr film of ∼30 nm is deposited on the PS-covered substrate by a thermal evaporation at room temperature, as schematically shown in Fig. 1(c). Subsequently, the PS spheres are removed by dissolving in a tetrahydrofuran solution. A net-like Cr film is remained on the Si substrate, as schematically shown in Fig. 1(d). It serves as a hard mask for the ICP etching with a mixed gas of SF6 and C4F8 to obtain periodic holes. Finally, the net-like Cr film is completely removed by immersing in the mixed solution of perchloric acid and ceric ammonium nitrate. The holes in the Si substrate are arranged in a hexagonal lattice with the period determined by the diameter of the original PS spheres, as schematically shown in Fig. 1(e). The diameter of holes is mainly determined by the diameter of the PS spheres after RIE etching. The depth of the holes can be controlled by the conditions of ICP etching. In addition, the geometrical profiles of holes especially around the top can be further modified by dipping in KOH solution due to the anisotropic wet-etching of Si. Such ordered holes with desired period, diameter and depth can be readily obtained in the scale of centimeters except for some domain boundaries, which mainly result from the lateral shift (generally < 200 nm) between neighboring domains. The minimum hole-diameter is ∼100 nm. In our cases, ordered holes of several micrometers in depth are generally obtained on (1.4 × 2.0 cm2) Si (001) substrates of 0.45 mm in thickness. The average domain size is ∼15 µm. In comparison with the electron beam lithography or the optical lithography, the nanosphere lithography is cheaper and more feasible to obtain arrays of holes with the size in the range of 100 nm to several micrometers in a large area.
Fig. 1. The schematic diagram of fabrication processes of ordered holes, (a) a monolayer of PS spheres on a Si substrate, (b) after O2 RIE to shrink PS spheres, (c) after the deposition of 30 nm Cr film, (d) after removing PS spheres, (e) ordered holes in a Si substrate. P in (a) and (e) denotes the period of ordered holes. d in (b) and (e) denotes the diameter of holes.
The geometries of periodic micro-holes on Si substrates are characterized by scanning electron microscopy (SEM: Zeiss Sigma). The total reflectance is measured by a PerkinElmer LAMBDA 950 UV/Vis/NIR spectrophotometer (PerkinElmer, Waltham, MA, USA) with an integrating sphere. The light source is unpolarized tungsten-halogen lamp of 250 W in the wavelength range of 400-1000 nm. The measured area is 1.0 × 1.0 cm2. The numerical analyses of the reflectance and the light field distribution around the ordered micro-holes on Si substrates are carried out by three-dimensional finite-difference time-domain (FDTD) simulations. In simulations, the boundary conditions of perfectly matched layer (PML) are imposed in the z axis (out of plane). Periodic boundary conditions are employed in the x and y axes (in-plane). The size of simulation cell is 2.1 µm x 3.6 µm x 11 µm. The mesh size is 4 nm x 5 nm x 5 nm. The incident light is a plane wave with the polarization along the x axis (the polarization direction essentially has no effect on the results). The material absorption is considered by using the imaginary part of permittivity of Si. The reflection is obtained by integrating pointing vectors at the input port (x-y plane at z =−3.5 µm) with time domain.
3. Results and discussions
Figures 2(a)–2(c) show the typical top-view SEM images of arrays of micro-holes with the period of ∼0.82 µm and tuned diameters of 680, 620, and 460 nm, respectively. In these cases, the original PS sphere with the same diameter of 0.82 µm is employed. Whereas, they are reduced via RIE etching for 100, 175 and 215 seconds before the deposition of Cr film, respectively. The other fabrication processes are nearly the same. The original PS spheres with a different diameter naturally give rise to the micro-hole array with a different period. Figure 2(d) shows a top-view SEM image of ordered micro-holes with the period of 1 µm and the diameter of 680 nm, which is obtained by adopting the PS spheres with the diameter of 1 µm. The edge of micro-holes in Fig. 2(d) is slightly rough. This roughness can be efficiently reduced by a chemical cleaning via the RCA method. The geometrical profiles especially around the top of micro-holes can be further modified by the KOH wet-etching. Figure 2(e) shows the top-view SEM image of the micro-holes in Fig. 2(d) after dipping in a 0.3 mol/L KOH solution at 30°C for 30 seconds. Due to the anisotropic etching of Si in a KOH solution, {1,1,1} facets appear around the top of holes after etching [16]. Accordingly, the top of micro-hole in Fig. 2(e) becomes larger and generally appears octagon-like for a limited etching time, in comparison with that in Fig. 2(d). In general, the diameter and the period of arrays of holes should be comparable with the wavelength of visible and near-infrared light to effectively realize the anti-reflection and the trapping of them. Accordingly, micro-holes with the size of ∼1 µm are mainly considered in the following. In fact, the period and the diameter of holes can be readily modified by employing PS spheres of different diameters and different RIE conditions in the present method.
Fig. 2. Top-view SEM images of ordered micro-holes on Si(001) substrates with the period of 0.82 µm and the diameter of (a) 680 nm, (b) 620 nm, (c) 460 nm, with the period of 1µm and the diameter of 680 nm (d) before, (e) after KOH wet etching. The scale bar for all images is shown in (e).
In addition, the depth of micro-holes can be deliberately changed by adjusting the etching conditions of ICP. Figures 3(a)–3(c) show the side-view SEM images of arrays of micro-holes with the depth of 0.9, 2.5 and 4.2 µm, respectively. The period and the diameter of the micro-hoes is 1 µm and 660 nm, respectively. These micro-holes are obtained via nearly same fabrication processes except for the different ICP etching time of 7, 14 and 21 minutes. Given the high reproducibility of the ICP etching, the depth of micro-holes can be generally predetermined by the etching time. In addition, the top of micro-holes become slightly larger with the increase of micro-hole depth for the longer ICP etching time. This is attributed to the slight lateral etching of Si underlying the Cr mask during the ICP etching. Although the lateral etching can be effectively suppressed by optimizing ICP etching conditions, a slope at the sidewall of micro-hole due to the lateral etching generally favors the antireflection of light, as described below.
Fig. 3. Side-view SEM images of arrays of micro-holes with the period of 1 µm, the diameter of 660 nm, and the depth of (a) 0.9, (b) 2.5, (c) 4.2 µm. The coordinates X,Y and Z in (a) are adopted in the simulations..
The total reflectance of micro-holes arrays with different geometrical parameters, e.g. the diameter or the depth of micro-holes, are obtained experimentally to characterize the antireflection properties of arrays of micro-holes. Figure 4(a) shows the reflectance of arrays of micro-holes with the diameter of 460, 570, 640 and 680 nm. The period and the depth of these micro-holes are essentially the same of 0.82 and 1 µm, respectively. Obviously, the reflectance is decreased with the increase of micro-hole diameter for the visible and infrared light in the present range of micro-hole diameters. By broadening the top of micro-holes with {111} facets via the KOH etching, the reflectance is also dramatically decreased, particularly to be less than 3% for the light of wavelength over 600 nm, as shown in Fig. 4(b). In addition, with the increase of micro-hole depth, the reflectance is also substantially decreased, as shown in Figs. 4(c) and 4(d). Particularly, for micro-holes of over ∼4.0 µm in depth, the reflectance is smaller than 5% for all visible and infrared light. Apparently, the reflectance of a Si substrate with a micro-hole array is much smaller than that of a normal flat Si substrate, which is over 30% for light in the wavelength range of 400-1000 nm due to the large difference of the refractive indices of Si and air. Such a pronounced antireflection of the microstructured surface is frequently interpreted by an effective medium theory [8,17,18]. Analogue to the cases of periodic pillars or NWs, the ordered micro-holes in a Si substrate give rise to an innovative medium with an effective refractive index (ERI) in-between those of Si and air. The reflectance of such an effective medium mainly originates from the two interfaces of air/effective medium/Si. It is well known, from the Fresnel equations, that the large difference of refractive indices leads to a strong reflection from the interface of two media with different refractive indices [19]. With the increase of the micro-hole diameter, the difference of the refractive indices around the interface of air/effective medium becomes smaller, while that around the interface of effective medium/Si becomes larger. Thus, the reflectance around the interface of air/effective medium decreases, while that around the interface of effective medium/Si increases. In the range of the present micro-hole diameters, the former effect overwhelms the later one. As a result, the overall reflectance of micro-holes arrays decreases with the increase of micro-hole diameter, as shown in Fig. 4(a). It is noteworthy that, for micro-holes with too large diameters, the latter effect plays the dominant role in the reflectance. Accordingly, with further increasing the diameter of micro-holes, the reflectance may be increased. An optimized diameter-to-periodicity ratio of 0.875 has been proposed for a micro-hole array to realize the strongest antireflection [19].
Fig. 4. Experimental reflectance of arrays of micro-holes, (a) with the diameters of 460, 570, 640 and 680 nm (the period and the depth of holes are 0.82 and 1.0 µm, respectively), (b) with the period of 1.0 µm, the diameter of 680 nm and the depth of 2.5 µm before and after KOH etching, (c) with the depth of 0.9, 3.0 and 5.0 µm (the period and the diameter are 0.82 µm and 640 nm, respectively), (d) with the depth of 0.9, 2.5 and 4.2 µm (the period and the diameter are 1.0 µm and 660 nm, respectively).
Moreover, the total reflectance can be substantially decreased if there is a gradient of ERI of micro-holes arrays, as addressed in previous reports [8,20,21]. This scenario explains the remarkable decrease of the total reflectance of micro-holes array after the KOH etching, as shown in Fig. 4(b). The appearance of {111} facets after the KOH etching gives rise to a gradient of the ERI around the top of micro-holes, which significantly reduce the reflectance around the interface of air/effective medium. As a result, the total reflectance of the micro-hole array is substantially decreased. The gradient of ERI of micro-holes arrays also contributes to the decrease of the total reflectance with the increase of micro-hole depth. A slope at the sidewall of micro-holes always exists, which is induced by the slight lateral etching during the ICPRIE etching. It naturally arises a gradual change of ERI from air to Si. In addition, such a gradient of the ERI becomes progressively smaller with the increase of micro-hole depth. The smaller the gradient of the ERI, the less reflectance of the microstructured surface. As a result, the total reflectance of micro-holes arrays decreases with the increase of micro-hole depth, as shown in Figs. 4(c) and 4(d).
The antireflection of microstructured surface is intrinsically associated with the strong light scattering around the microstructure, which can effectively prolong the optical path length and trap light in the medium. Accordingly, the thickness of the active medium for sufficient light absorption can be substantially reduced. It is critical for the thin film solar cells in terms of the material consumption and the photon-generated carrier collection. Accordingly, the depth of micro-holes is the key parameter to optimize desired micro-hole arrays. In fact, for micro-hole structures, the depth plays the important role in the light modulation, as demonstrated in Figs. 4(c) and 4(d). In order to comprehensively characterize the effects of micro-hole depth on the light modulation, the spectra of reflectance, transmittance and absorption of Si thin films containing micro-holes with different depths are simulated by FDTD method in a broad wavelength range of 400-1000 nm. In the simulation, a plane wave is vertically incident on Si substrates with micro-holes of 0.9, 2.5 or 4.2 µm in depth, as shown in Fig. 3. The geometrical profiles of micro-holes, e.g. depth, diameter and sidewall slope of micro-holes, are essentially extracted from SEM images. Giving the size dispersion of PS spheres, a slight variation of period around 1.0 µm is considered in the simulation. The reflectance (R) and the transmittance (T) at a plane of 6 µm below the surface are obtained from the FDTD simulations. The absorption (A) is then calculated to be A = 1-R-T for the corresponding Si film of 6 µm, which contains micro-holes. A Si film of 6 µm without micro-holes is also consider for comparison in simulations. Figures 5(a)–5(c) shows the simulated and the measured spectra of reflectance from the Si films with ordered micro-holes of 0.9, 2.5 and 4.2 µm in depth, respectively. The rather good agreement between the simulated and the measured reflectance spectra further demonstrates the decrease of reflectance with the increase of micro-hole depth. It also provides a support for the reliability of the simulated transmittance and absorption spectra of Si films with micro-holes, as shown in Figs. 5(d) and 5(e), respectively. It can be seen that the transmittance of light with the wavelength smaller than ∼600 nm is rather small, and almost the same in all cases even without micro-holes. Such a small transmittance is attributed to the effective absorption of the corresponding light in Si, given that the light energy is considerably larger than the band gap of Si. Interestingly, the absorption of light in this wavelength range is dramatically enhanced for the Si films with micro-holes in comparison with the flat Si film. Moreover, the enhancement of light absorption become more pronounced for the deeper micro-holes, which can be ∼60% in this wavelength range for the micro-holes of 4.2 µm in depth. For the light in the wavelength range of ∼600 nm to ∼800 nm, the transmittance of light is not so much different in all cases even without micro-holes. The absorption of light is enhanced by ∼55% in average for the Si film with micro-holes in comparison with the flat Si film. But it is only increased slightly with the micro-hole depth. For the light of wavelength larger than ∼800 nm, the transmittance of light is slightly increased with the micro-hole depth. Whereas, the absorption of light is nearly independent on the micro-hole depth, which is enhanced by ∼60% in average for all micro-holes with respect to that of the flat Si film.
Fig. 5. Experimental (solid lines) and simulated (symbol lines) reflectance of arrays of micro-holes with the depth of (a) 0.9 µm, (b) 2.5 µm and (c) 4.2 µm, the corresponding simulated (d) transmittance, and (e) absorption of Si films of 6 µm in thickness with arrays of micro-holes of the same geometries as those in (a)-(c). The slope angles of micro-hole sidewall are 2.0 °, 3.0 °, and 3.5 ° in (a), (b) and (c), respectively, which are extracted from the SEM images. For comparison, the simulated transmittance and absorption of a flat Si film of the same thickness without micro-holes are also shown in (d) and (e).
To gain an insight of above results and the comprehensive light manipulations by ordered micro-holes in Si substrates, the light field distribution around micro-holes is extracted from the FDTD simulations, in addition to the reflectance, transmittance and absorption. Figures 6(a) and 6(b) show the cross-sectional light field distribution across micro-holes in X-Z and Y-Z plane schematically shown in Fig. 3(a), respectively. Apparently, the light field distributions around micro-holes are intimately associated with the wavelength. It can generally be categorized into three regions. For short wavelengths, e.g. 420 and 540 nm, the light is mainly localized within micro-holes. It is generally denoted by channel modes [22]. Moreover, the light filed in micro-holes is characterized by the lateral fringe pattern, which results from the constructive interference between the incident light and the reflected light from the bottom of the micro-hole. Such an interference effect efficiently suppresses the reflection of light and in turn traps light in micro-holes. The trapped light can be finally absorbed at the direct vicinity of micro-hole sidewalls [22]. As a result, the absorption of light is remarkably enhanced. The light filed in Si region around micro-holes is rather weak, particularly below micro-holes. For moderate wavelength, e.g. 630 and 730 nm, the light filed is distributed in both micro-holes and the surrounded Si region. Moreover, the light filed in the Si region around micro-holes concentrates in some spots, which result from the constructive interference of scattered light from laterally ordered micro-holes. This result demonstrates the coupling between the vertically incident light and the guided modes in the laterally ordered micro-holes. Such guided modes mainly originate from the periodic scattering in micro-hole array and propagate horizontally [23,24]. The horizontal propagation of the guided mode substantially increases the optical path length in the Si film with micro-holes. Accordingly, the absorption of light can be dramatically enhanced. In addition, the light field of guided modes essentially disappears within micro-holes, but extends into the Si region below the micro-hole arrays, as demonstrated by the spot pattern of light field distribution there. The extension of guided modes into the Si regions below micro-hole array is associated with the limited depth and the slope at sidewalls of micro-holes. For long wavelength, e.g. 860 and 970 nm, most of light distributes in Si region around micro-holes. In addition, the spot pattern of light field in Si region become more pronounced. This means that the vertically incident light is predominately coupled into the guided modes in the micro-holes array. As a result, the reflection of light is substantially reduced. The absorption of light can in turn be remarkably enhanced. This unique feature has been exploited to realize high-speed high-efficiency silicon photodiodes at 900-1000 nm [13]. To some degree, the transmittance of light can also be enhanced for a thin film due to the extension of the guided mode into the Si region below the micro-hole array, as demonstrated in Fig. 5(d). Accordingly, to reduce the transmittance of light in addition to the enhancement of the antireflection, the geometrical profiles of micro-holes should be deliberately designed.
Fig. 6. Wavelength-dependent light field distribution across micro-holes in (a) X-Z plane, (b) Y-Z plane. The coordinates X, Y and Z for micro-hole array are schematically shown in Fig. 3(a). The diameter, period and depth of micro-holes are 660 nm, 1 µm and 2.5 µm, respectively. The white dashed lines represent the boundaries of holes. The white numbers 420, 540, 630, 730, 860 and 970 nm are the corresponding wavelengths.
Figure 7 shows the light filed distribution around the micro-holes of 0.9, 2.5 and 4.2 µm in depth for wavelengths 420, 730 and 970 nm, which are typically associated with the channel modes and the guided modes in micro-holes arrays. The incident light of 420 nm in wavelength is mainly coupled into the channel mode, which is essentially localized within micro-holes. With the increase of micro-hole depth, the light field above the micro-holes arrays is apparently weakened, while more light is coupled into the channel modes in micro-holes, as shown in Fig. 7(a). The light field in the Si region around micro-holes is substantially weak and nearly independent on the micro-hole depth. These unique features of channel modes contribute to the nearly constant transmittance and the increase of the absorption of light of 400-600 nm in wavelength with the increase of micro-hole depth, as shown in Figs. 5(d) and 5(e), respectively. For the wavelength of 730 nm, more light is concentrated in the Si region around micro-holes with the increase of micro-hole depth, as demonstrated by the pattern of more strong spots there in Fig. 7(b). This means that the increase of micro-hole depth facilitates the coupling of the incident light into the guided modes distributed in Si region around micro-holes. In addition, the increase of micro-hole depth may also enable the coupling of the incident light into the channel modes, as demonstrated by the fringe pattern within micro-holes of 4.2 µm in depth in bottom component of Fig. 7(b). Figure 7(c) shows the light filed distribution around micro-holes of 0.9, 2.5 and 4.2 µm for the wavelength of 970 nm. The rather strong spot pattern appears in the Si region around micro-holes, and become more pronounced with the increase of micro-hole depth. This means that more incident light is coupled into the guided modes with the increase of micro-hole depth. Moreover, with the increase of micro-hole depth, the strong spot pattern tends to move towards the substrates. This means that the field distribution of guided modes become more extensive in Si region below micro-holes with the increase of micro-hole depth. As a result, for a thin film with the thickness comparable with the depth of micro-holes, the light transmission can be enhanced with the micro-hole depth, but the overall light absorption can essentially not be affected even though the total Si material is remarkably reduced with the increase of micro-hole depth. This scenario explains the increase of the transmittance of light of 800-1000 nm with the increase of micro-hole depth, particularly in comparison with the case of flat Si, as shown in Fig. 5(d). Whereas, the absorption of light of 800-1000 nm is nearly independent on the micro-hole depth, although it is remarkably enhanced in comparison with that of flat Si, as shown in Fig. 5(e).
Fig. 7. Depth-dependent light field distribution around micro-holes of 0.9, 2.5 4.2 µm in depth for typical wavelength (a) 420 nm, (b) 730 nm, (c) 970 nm. In each component, the left and the right panels show the cross-sectional light field distribution in X-Z plane and Y-Z plane, respectively. The coordinates X,Y and Z are schematically shown in Fig. 3(a). The diameter and period of micro-holes are 660 nm and 1 µm, respectively. The sidewall slope of micro-hole is considered in the simulation, which is extracted from the SEM image. The white dashed lines represent the boundaries of holes. The white numbers 420, 730 and 970 nm are the corresponding wavelengths. The black numbers 0.9, 2.5 and 4.2 µm at the right side denote the depth of micro-holes.
It is worth mentioning that, for the actual thin film with a reflector at its bottom, the absorption of light in the wavelength range of 600-1000 nm can even be enhanced more significantly with the increase of the micro-hole depth. In the present simulation, the light at the bottom of the thin Si film of 6 µm with micro-holes is completely not reflected back into the thin film to fit the reflectance of the top surface since the present samples with micro-holes is fabricated on Si substrate of ∼0.5 mm in thickness. Whereas, this transmitted light can be generally reflected back into the thin film with a reflector at the bottom, e.g. the bottom covered with a Silver film. Moreover, the light reflected at the bottom will also couple again into the guided modes of the ordered micro-holes near the top of the thin film. As a result, the absorption of light in the wavelength range of 600-1000 nm can be further enhanced by the second light- coupling into guided modes. The reflector at the bottom of the thin film may essentially not affect the absorption and the transmission of light in the wavelength range of 400-600 nm since the transmittance of light in that wavelength range is substantially small, as shown in Fig. 5(d). Based on the present simulation, the absorption of light in the broad wavelength range of 400-1000 nm for a thin Si film with ordered micro-holes can be enhanced by over 55% in comparison with that for a flat Si film of the same thickness. For an actual thin Si film with micro-holes on the top and a reflector at the bottom, the light absorption can be further improved. In addition, ordered micro-holes favor the realization of ultimate limit solar cells since it can help to direct the light reversibly back to the sun [24]. Accordingly, a thin Si film with a micro-hole array has a great potential in the application of innovative solar cells. In addition, the light of the wavelength less than the micro-hole diameter can be readily coupled into channel modes with the light field concentrated in the micro-holes, as shown in Figs. 6 and 7(a). Therefore, the Si film with micro-holes can also be promising templates for applications in photoelectrochemical water splitting [14] and biosensors [15].
4. Conclusions
In conclusions, a feasible method based on nanosphere lithography is explored to fabricate ordered micro-holes in a large area in Si (001) substrates. The period, diameter and depth of micro-holes can be readily modified by adjusting the size of PS nanosphere and the RIE conditions. Systematic studies of the total reflectance of various micro-hole arrays demonstrate that the micro-hole array can substantially reduce the reflectance of light in a broad wavelength range of 400-1000 nm. The simulated light reflectance of ordered micro-hole via FDTD method agrees well with the experimental data. Moreover, the absorption and the transmittance of light, as well as the light field around micro-holes, are extracted from the FDTD simulations. It is found that the absorption of light of a thin Si film with ordered micro-holes can be remarkably enhanced in comparison with that of a flat one, particularly for the deep micro-holes. The simulated distributions of light field around micro-holes reveal unique features of two types of distinguished modes, channel modes and guided modes, supported by the periodic micro-holes. Particularly, the light of wavelength less than the diameter of micro-holes is mainly coupled into the channel modes with the light field predominately concentrated in the micro-holes, which is generally characterized by fringe patterns in the micro-holes. Whereas, the light of other long wavelengths is generally coupled into the guided modes with the light field distributed in the Si regions around micro-holes and characterized by spot patterns there. These results shed light on the comprehensive light manipulations by micro-holes, involving the antireflection, the remarkably enhanced absorption and unique wavelength-dependent light filed distributions. Our results provide guidelines to design micro-hole arrays with optimized light field distributions for innovative photovoltaic or photo-detection applications.
Funding
National Natural Science Foundation of China (11774062).
Acknowledgments
Part of the characterization was performed at the Fudan Nano-Fabrication Laboratory.
Disclosures
The authors declare no conflicts of interest.
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