Silicon Thin-Film Solar Cells Approaching the Geometric Light

Article Cite This: ACS Photonics XXXX, XXX, XXX−XXX

Silicon Thin-Film Solar Cells Approaching the Geometric LightTrapping Limit: Surface Texture Inspired by Self-Assembly Processes Asman Tamang,† Hitoshi Sai,‡ Vladislav Jovanov,† Koji Matsubara,‡ and Dietmar Knipp*,†,§ †

Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany Research Center for Photovoltaic Technologies, National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan

‡

S Supporting Information *

ABSTRACT: A new device design of microcrystalline silicon thin-film solar cell allows for approaching the geometric light-trapping limit. The solar cell is based on triangular textured surfaces in combination with optimized front and back contacts with very low optical losses. In comparison to crystalline silicon solar cells with record energy conversion efficiency the material usage of the thin-film solar cells is reduced to 1−2%, while exhibiting the potential to achieve short circuit current densities of more than 80% of their counterparts. The short circuit current density of the thin-film solar cells is approaching the geometric light-trapping limit commonly known as the Yablonovitch limit under perpendicular incidence. The design of the solar cell is described considering the electrical and optical properties of the textured solar cell. KEYWORDS: light trapping, thin-film solar cells, electronic defects, indium tin oxide, hydrogen-doped indium oxide, Yablonovitch limit

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strates the concentration of electronic defects is increased, which limits the energy conversion efficiency of microcrystalline silicon solar cells.7,10,12,14,17−21 Hence, a proper optimization of the solar cell geometries, materials, and thicknesses is required to enhance the light trapping of the solar cells, while avoiding the formation of voids or cracks. The optimization process is based on maximizing the absorption of light in the solar cells, while minimizing the absorption of light in regions of the solar cells that do not contribute to the short circuit current density.

hin-film silicon solar cells are potential candidates to achieve high short circuit current density and energy conversion efficiency while minimizing the material usage.1−4 Surface texturing of the solar cells is extensively used to enhance the scattering and diffraction of light, which increases both the quantum efficiency and short circuit current density of the solar cells.1−9 Microcrystalline silicon solar cells fabricated on hexagonal textured substrates exhibit record short circuit current density and energy conversion efficiency of 32.9 mA cm−2 and 11.9%, respectively.1−4 The record short circuit current density of 32.9 mA cm−2 is achieved for a 4 μm thick hexagonal textured solar cell, while the record energy conversion efficiency is achieved for an approximately 2 μm thick hexagonal textured solar cell.1−4 The short circuit current density of the microcrystalline silicon solar cell exhibiting the record energy conversion efficiency is 28.7 mA cm−2.1−3 Crystalline silicon solar cells exhibit a record short circuit current density of 42.6 mA cm−2 using silicon wafers with a thickness of >200 μm.2 The proposed hexagonal textured solar cell based on microcrystalline silicon reaches >75% of the short circuit current density of the crystalline silicon solar cell while using only 1−2% of the material.1,2,4 In the current study, we investigate the potential of microcrystalline silicon thin-film solar cells. Previous simulation studies have mainly focused on idealized solar cell structures, while experimental studies are limited by parasitic losses.6,7,10 However, the optimization of solar cell structure is complex because changes of the surface texture affect not only the short circuit current density but also the open circuit voltage and fill factor.5,7,10−22 The textured substrates cause microstructure-induced defects, commonly called cracks or voids, in the microcrystalline silicon films.1,7,10,12,14,17−21 With increasing roughness of the sub© XXXX American Chemical Society

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SOLAR CELL DEVICE STRUCTURE 3D morphological algorithms are used to determine the interface morphology of each layer of the solar cells. These algorithms allow for modeling of the three fundamental semiconductor processes: lithography, etching, and deposition.6,7,10,17,23,24 The substrate of the solar cell consists of a patterned silicon oxide (SiO2) substrate. The etching of the SiO2 film takes place in the direction of the local surface normal with a nominal etch radius (d). The etching process is visualized in the Supporting Information (Figure S1(a)). In next step, the actual solar cell is prepared on the textured substrate. The deposition of a silicon film on the substrate is again described by the morphological algorithm and is illustrated in the Supporting Information (Figure S1(b)). More information on the modeling of the etching and deposition processes can be found in the Supporting Information and literature.6,10,23,24 After depositing the solar cell layers on the substrate the resulting solar cell surface Received: November 20, 2017

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DOI: 10.1021/acsphotonics.7b01397 ACS Photonics XXXX, XXX, XXX−XXX

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ACS Photonics resembles a surface covered with spheres.7,25,26 The packing of the spheres on the surface represents the densest possible packing of spheres on a planar surface. Side views of calculated solar cell surfaces on hexagonal, square, and triangular textured substrates are illustrated in Figure S2 (Supporting Information) and the literature.7

efficiency of the i-layer is 100%. Hence, all calculated quantum effiiencies and short circuit current densities presented in this study represent an upper limit. Further details on the calculation of the quantum efficiency and short circuit current density are given in the Supporting Information and the literature.9

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RESULTS Optimizing the Textured Solar Cell. Microcrystalline silicon solar cells fabricated on hexagonal textured substrates demonstrate a short circuit current density of 32.9 mA cm−2 and energy conversion efficiency of 11.9%, representing the highest values for the silicon thin-film solar cells.1−4 However, it remains unclear if hexagonal textured substrates represent the best possible substrate. In a previous simulation study, our research group showed that microcrystalline silicon solar cells on hexagonal, square, and triangular textured substrates exhibit comparable light trapping if the solar cell thickness and period of the textured substrates are equal.7 However, the solar cells on a triangular textured substrate are less susceptible to the formation of cracks.7 Furthermore, the tools to describe the crack formation process and to calculate the critical thickness are developed in a previous study.17 The calculated interface morphologies of the solar cells are used as input parameters to determine the critical thickness. The critical thickness defines a thickness at which the crack formation starts.7,17 The calculated critical thicknesses in hexagonal textured solar cells are compared to transmission electron microscope (TEM) images, and a good agreement between the measurred and calculated critical thickness is observed.17 Hence, it is assumed that the morphological model can be used for predicting the crack formations and defining realistic surface morphologies of solar cells based on other tiled surfaces such as square and triangular textured substrates.7 A comparison of three substrates reveals that the triangular textured substrate is superior to the square and hexagonal textured substrates. Further details on the comparison of the solar cells prepared on different substrates are provided in the literature.7 Hence, this study entirely focuses on crack formation calculation, interface morphology calculation, and optical simulation of solar cells on triangular textured substrates. Figure 1(a) and (b) show respective top and 3D side views of a textured SiO2 substrate prior to the deposition of the microcrystalline silicon films. The SiO2 substrate is etched through an etch mask consisting of a triangular array of holes. The period (P) and height to period ratio (H/P) of the textured substrate is 3 μm and 0.45, respectively. Next, the Ag/ZnO:B layers are placed on top of the SiO2 film. The calculated top and 3D side views of the silicon film surfaces are shown in Figure 1(c) and (d), respectively. Corresponding cross sections of the solar cells along directions A and B as indicated in Figure 1(a) are shown in the Supporting Information (Figure S4(a) and (b)). The microcrystalline silicon solar cell exhibits an i-layer thickness of 2.2 μm. Previous experimental and simulation studies of hexagonal textured solar cells have shown that the short circuit current density is the highest if the period is approximately equal to the solar cell thickness.1,6,14 Furthermore, this observation is valid for simulated solar cells on square and triangular textured substrates.7 The influence of the substrate morphology on the propagation and formation of cracks on the silicon films is visualized in Figure 2(a−c). Furthermore, the evolutions of the interface morphologies for different substrates with identical

MATERIAL PROPERTIES The optical properties of all materials of the solar cell sequence except for the front transparent conductive oxide (TCO) layer are taken from the literature.27−32 The optical properties of sputtered indium tin oxide (In2O3:Sn, ITO) and hydrogendoped indium oxide (In2O3:H, IOH) are modeled using an extended Drude−Lorentz model.32−35 Further details on the optical properties of the ITO and IOH films are provided in the subsequent section. The investigated n−i−p solar cells consist of a silver (Ag) back reflector, which is placed on a textured SiO2 substrate, followed by a boron-doped zinc oxide (ZnO:B) layer. The ZnO:B layer is usually prepared by a low-pressure chemical vapor deposition (LPCVD) process.8,32 The ZnO:B is used as back TCO layer to minimize plasmonic losses of the textured metal back reflector.36,37 Next, the μc-Si:H n−i−p diode is placed on the back TCO layer. Wide band gap silicon oxide (Si1−xOx) is used for the p-layer and n-layer of the n−i−p diode to minimize optical losses.14,19,38−40 Both the p-layer and n-layer of the n−i−p diode have a thickness of 10 nm, while the i-layer thickness is varied. Several datasets have been published on the material properties of microcrystalline silicon.28,29,41 Distinct variations of the extinction coefficient and absorption coefficient are observed. Early measurements of the absorption coefficient exhibit values distinctly larger than crystalline silicon throughout the complete spectral range.29,41 More recently, several studies have shown that the absorption coefficient can be described by the combination of amorphous silicon and crystalline silicon phases depending on the crystalline volume fraction of the material.28 However, the published optical data are inconsistent with data extracted from measured microcrystalline silicon cells.4 In the current study, we used three different datasets ranging from material with a high absorption coefficient (Remes dataset29) to a dataset that exhibits a rather low absorption coefficient for longer wavelengths (Ding dataset28). Furthermore, we used monocrystalline silicon (Green dataset30) as a reference dataset. The complex refractive indexes of all three datasets are provided in the Supporting Information (Figure S3). Finally, the front TCO layer of the microcrystalline silicon solar cell consists of a 70 nm thick ITO or IOH layer. Cross sections of the solar cell are shown in the Supporting Information (Figure S4). The aforementioned solar cell layer sequences and film thicknesses are consistent with fabricated mirocrystalline silicon thin-film solar cells.1,3,4,6,7,14,17

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OPTICAL SIMULATION METHOD The finite difference time domain (FDTD) method is used to model the optical wave propagation in the solar cells.6,7,9,10,17,42 The calculated interface morphologies, the film thicknesses, and optical properties of each material are used as inputs to simulate the 3D electric field distribution for the solar cells. Based on the calculated electric fields, the power loss profiles are calculated. Next, the absorption for each layer of the solar cell is calculated. It is assumed that the quantum efficiecy of the solar cell can be approximated by the absorption in the i-layer of the n−i−p solar cell. This implies that the collection B


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ACS Photonics

representing the reference angle. Regions where the opening angle is smaller than 180° are observed in the transition region from the arches to the flat surface regions. The smallest opening angles are observed if the two arches directly meet. These are the regions where the cracks are potentially formed, as indicated by white solid lines in Figure 1(c) and red dotted lines in Figure 2(b) and (c). In this study, the opening angle maps are presented along direction B because direction B is most sensitive to the formation of cracks compared to direction A.7 Cracks are not formed in the 3 μm thick silicon film for the substrate with an H/P ratio of 0.25, but are potentially formed at a film thickness of 3.54 μm (Figure 2(d)). On the other hand, the crack formations are observed at a film thickness of 3 μm for an H/P ratio of 0.3 as shown in Figure 2(b) and (d). The calculated critical thickness is equal to the nominal thickness of the solar cell. If the H/P ratio is increased to 0.45, the critical thickness drops to 2.2 μm (Figure 2(c)). The critical thicknesses are denoted by red dotted lines as presented in Figure 2(b) and (c). Hence, it can be concluded that for the given period of 3 μm and thickness of 3 μm the H/P ratio of 0.3 represents an upper limit of the potential roughness of the substrate. The critical thickness increases as the period of the textured substrate increases, and in contrast, it decreases as the H/P ratio decreases. The calculated critical thicknesses for the triangular textured substrates with different period and H/P ratio are shown in Figure 2(d). Hence, it can be concluded that the thickness of the solar cell should be equal to or smaller than the critical thickness to avoid the formation of cracks. In the following, light trapping of solar cells on triangular textured substrates is studied. All simulated device structures are crack free. Based on this condition three different optimization strategies are implemented and compared assuming the period of the textured substrate to be 3 μm. Constant Thickness Approach. In a first step, the nominal thickness of the solar cell is selected to be 3 μm. In the next step, the H/P ratio is increased until the critical thickness is equal to the nominal thickness of the silicon film. That means the calculated H/P ratio is 0.3 (Figure 2(b)). Constant H/P Ratio Approach. In a first step, the H/P ratio of the textured substrate is selected to be 0.25. In the next step, the silicon film thickness on the solar cell can be increased up to the critical thickness. In this case, the calculated critical thickness is 3.54 μm (Figure 2(d)). Maximal H/P Ratio Approach. The H/P ratio of the textured substrate is increased to its maximal achievable value. The maximal H/P ratio is determined by the semiconductor process used to pattern the substrate. In our case, the wet etching process limits the maximal H/P ratio to approximately 0.5. Hence, the critical thickness is calculated to be 2.2 μm (Figure 2(c)). We have studied the light trapping of the solar cells following all three optimization approaches. All three solar cell structures exhibit comparable short circuit current densities. However, the maximal H/P ratio approach allows for achieving such high short circuit current density for the thinnest solar cells. Hence, we have selected this structure as being the optimized device desgin. In next section, the solar cells are further optimized by reducing parasitic optical losses in the back reflector and front contact of the solar cells. Plasmonic Losses and Alternative Back Reflector Designs. Cross sections of the solar cell optimized according to the maximal H/P approach are presented in Figure 4(a) and

Figure 1. (a) Top and (b) side views of calculated interface morphologies of a triangular textured substrate with a period of 3 μm and height to period ratio of 0.45. (c) Top and (d) side views of calculated interface morphologies of final solar cell. The direction lines A and B are shown in (a). Potential crack formation regions are marked in (c) by white lines.

Figure 2. (a−c) Calculated line profiles for silicon films prepared on triangular textured substrates with a period of 3 μm along direction B. The H/P ratio of the substrates is (a) 0.25, (b) 0.3, and (c) 0.45. The opening angle is overlaid in (a)−(c). The critical thickness is marked by the red dotted line. (d) Calculated critical thicknesses as a function of period for different H/P ratios.

period governed by different H/P ratios are presented in Figure 2(a−c). The black lines show the evolution of the interface morphologies as a function of the film thicknesses. The period for all substrates is 3 μm, while the H/P ratio is 0.25 (Figure 2(a)), 0.3 (Figure 2(b)), and 0.45 (Figure 2(c)). The calculated interface morphologies are overlaid on the opening angles maps. The opening angle is calculated as the angle between two neighboring tangent spaces. Prior to calculating the opening angles the tangent space and surface normal for each point of the cross sections of the solar cells are calculated.7,17 If the surface is flat (smooth), the opening angle is equal to 180°, C


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Figure 3. Simulated absorptions of light in 2.2 μm thick microcrystalline silicon solar cells prepared on a (a) standard reflector and (b) “selective back reflector”. ITO is used as front contact, period of 3 μm and H/P ratio of 0.45.

metal back contact in combination with a textured dielectric interlayer.6 In this study, a triangular textured SiO2 layer is placed between the ZnO:B layer and the flat metal reflector, as shown in Figure 4(d). The metal back contact in this configuration is referred to as a “selective back reflector”.6 The electrical contact between the solar cell on the Ag back reflector is formed in regions where the ZnO:B layer is in contact with the Ag back reflector. We are currently working on the experimental realization of the solar cell with the “selective back reflector”. However, a precise control of the patterning process of the SiO2 film is required, so that a sufficiently large opening can be etched in the SiO2 layer. An electrical interconnect between the ZnO:B and the Ag back reflector is required to form an electrical contact to the solar cell. The opening has to be sufficiently large to ensure that the short circuit current density and fill factor are not limited by the series resistance. Preliminary results reveal that the series resistance of the solar cell is still dominated by the front contact grid. The selective back reflector of the solar cell can be realized by using standard semiconductor fabrication methods. Due to the modified design of the back reflector, the optical back contact loss decreases significantly from 4.4 mA cm−2 (Figure 3(a)) to 1.5 mA cm−2 (Figure 3(b)). As a result, the short circuit current density is increased from 30.8 mA cm−2 (Figure 3(a)) to 32.8 mA cm−2 (Figure 3(b)). The corresponding power loss profiles are shown in Figure 4 for solar cells with textured and planar back reflectors. The power loss profiles are shown for incident wavelengths of 700 and 1100 nm along direction B (Figure 1(a)). Most of the shorter wavelength light (300−500 nm) is absorbed by the first few tens of nanometers of the solar cells, and the light does not reach the back contact. Hence, the corresponding power loss maps are not included in Figure 4. On the other hand, longer wavelengths light is scattered and diffracted by the textured front and back contacts, causing distinct losses of the back contact as presented in Figure 4(b), (c), (e), and (f). The optical loss of the back reflector increases for long wavelength (>650 nm). The optical losses in two different back reflectors are shown in Figure 4(c) and (f). In the case of the textured metal back reflector the main optical loss is observed near the silver tips at the interface between the ZnO:B interlayer and silver back reflector. On the other hand, by replacing the textured silver back reflector with a “selective back reflector” the optical back reflector loss is reduced as shown in Figure 3. Hence, the optical path length of the light is increased and the number of reflections by the front and back metal oxide layer is increased. Hence, the front contact losses of the solar cells increase slightly from 3.5 mA

Figure 4. Cross sections of 2.2 μm thick solar cells using a (a) standard and a (d) “selective back reflector”. The cross sections are shown along direction B with a period of 3 μm and H/P ratio of 0.45. Corresponding power loss profiles are shown for the incident wavelengths of (b, e) 700 nm and (c, f) 1100 nm. The solar cell is optimized according to the maximal H/P ratio approach.

the Supporting Information (Figure S4). Simulated quantum efficiency and the absorptions in each layer of the solar cells as a function of wavelengths are shown in Figure 3(a). The simulated solar cell exhibits a short circuit current density of 30.8 mA cm−2, while the back contact loss is 4.4 mA cm−2, front contact loss is 3.5 mA cm−2, and reflectance loss is 4.4 mA cm−2 (Figure 3(a)). The front contact loss is the sum of loss in the front TCO layer and p-layer, while back contact loss is the sum of loss in the n-layer, back TCO layer, and metal back contact. For the microcrystalline silicon the Remes dataset is used with a high absorption coefficient.29 In order to minimize the optical losses of the textured metal back contact and increase the quantum efficiency of the solar cells, the textured metal (Ag) back contact is replaced by a flat D


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Figure 5. Simulated quantum efficiencies and absorptions and Yablonovitch limits (geometric light-trapping limits) for (a) microcrystalline (Remes dataset), (c) monocrystalline (Green dataset), and (e) microcrystalline (Ding dataset) silicon films. (b, d, and f) Corresponding calculated round trips of light in the solar cells for the Remes, Green, and Ding datasets. Furthermore, the Yablonovitch limit is added. The Yablonovitch limit is only valid for weak absorption, which is the case for tp > 2d.

cm−2 (Figure 3(a)) to 4.3 mA cm−2 (Figure 3(b)) with a negligible change in reflectance loss. Furthermore, this result is visually supported by Figure 4(c) and (f). Front Contact Materials with Low Free Carrier Absorption. In the next step, the optical loss of the front contact is reduced by replacing the standard front contact consisting of an ITO layer with an alternative material that is characterized by a higher charge carrier mobility. In this study, IOH is used as an alternative material. Hence, the doping concentration of the front contact can be varied, while using front contacts with identical sheet resistance and identical thickness. By using low doping concentrations, the free carrier absorption of the transparent front contact can be reduced. Different studies have been published on ITO and IOH transparent conductive oxides and comparison of solar cells with these materials as front contacts. In this study, we refer to the work published by Koida and co-workers, who presented a comparison of ITO and IOH films with almost equal resistivity and sheet resistance.43,44 Instead of using the published complex refractive indices we used an extended Drude− Lorentz model to describe these two materials.32−35 By using the Drude−Lorentz model we are able to study the influence of

the doping concentration and the charge carrier mobility of the metal oxide front contact on the quantum efficiency and short circuit current density of the solar cells. A brief description of the Drude−Lorentz model is provided in the Supporting Information. The parameters of the extended Drude−Lorentz model are determined by fitting measured transmittance, absorption, and reflectance of ITO or IOH films on glass substrates. The ITO and IOH films are prepared, and the absorption, transmittance, and reflectance of the films are measured by Koida and co-workers.43 The measurement and simulation results are included in the Supporting Information (Figure S5). A good agreement between the measured and simulated absorption, transmittance, and reflectance is observed. A summary of the parameters used to calculate the complex refractive index of ITO and IOH is provided in Table S1 (Supporting Information). The sheet resistance (Rsh) of the transparent conductive oxide films is given by R sh ≈ E

q × Nopt

1 × μopt × d

(1) DOI: 10.1021/acsphotonics.7b01397 ACS Photonics XXXX, XXX, XXX−XXX

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ACS Photonics where d is the thickness of the transparent conductive oxide layer, q is the elementary charge, and Nopt and μopt are the respective doping concentration and charge carrier mobility extracted from optical measurements. The IOH film exhibits an approximately 3−5 times higher carrier mobility compared to an ITO film. Hence, the doping concentration of the IOH film is decreased accordingly. As a consequence, the plasma wavelength (λN) for the IOH film is shifted to longer wavelengths as described by the following equation: λN =

2π × c q

ε0ε∞ × m* Nopt

generation of the short circuit current density. The Yablonovitch limit is given by A(λ) =

α (λ ) α (λ ) +

1 4n 2 d

(3)

where α(λ) and n(λ) are the respective absorption coefficient and refractive index (real part of complex refractive index) of microcrystalline and crystalline silicon, which are taken from the literature.28−30 d is the silicon film thickness of 2.2 μm. The simulated quantum efficiencies and Yablonovitch limits are compared in Figure 5(a), (c), and (e) for microcrystalline (Remes dataset), monocrystalline (Green dataset), and microcrystalline (Ding dataset) silicon films, respectively. The aim of the comparison is to benchmark the quantum efficiency of the solar cells to a well-studied reference. We will focus here only on the case of perpendicular incidence of the light. It has to be stated that a detailed and complete comparison of the solar cell structure with the Yablonovitch limit requires the angledependent analysis of the solar cell.45,46 It is observed that the simulated quantum efficiencies approach the geometric lighttrapping limits under perpendicular incidence even by considering optical losses. The quantum efficiency of the solar cells is determined by light trapping for longer wavelengths. In this case, the penetration depth (tp) is larger than 2 times the film thickness (d). The penetration depth, tp, is given by 1/α(λ). The number of round trips of light in the solar cells is calculated and presented in Figure 5(b), (d), and (f). The number of round trips in the case of the Yablonovitch limit is given by 2n2. The Yablonovitch limit under perpendicular incidence is compared to the number of round trips calculated for the optical simulations. The number of round trips, rt(λ), is given by

(2)

where c is the speed of light in space, m* is the effective mass of the electron, and ε0 and ε∞ are the vacuum and relative permittivity of the metal oxide film, respectively. Hence, the extinction coefficient of the IOH film is distinctly reduced compared to the ITO film. A comparison of the calculated and measured complex refractive index of ITO and IOH is provided in Figure S6 (Supporting Information). A relatively good agreement between the two sets of data is observed. The calculated and measured electrical parameters of the ITO and IOH layers are provided in Table S2 (Supporting Information). The electrical input parameters (mobility and charge carrier concentration) used for the calculations of the complex refractive index of the ITO and IOH film agree with the electrically measured electrical parameters. Hence, it can be concluded that the films used in this study exhibit equal sheet resistance and thickness, allowing for a fair comparison of the two materials, and are consistent with experimentally measured materials. The simulated quantum efficiencies of the solar cells with the ITO and IOH front contacts are shown in Figure S7 (Supporting Information). The absorption of light in the front IOH layer is lower for wavelengths longer than 400 nm compared to front ITO layer, which leads to an enhanced quantum efficiency for wavelengths longer than 550 nm. The front contact losses decrease significantly from 4.3 mA cm−2 to 1 mA cm−2 (Figure 3(b) and the Supporting Information Figure S7). Consequently, the short circuit current density is increased from 32.8 mA cm−2 to 35.3 mA cm−2. Up to this point it can be concluded that three factors are crucial in optimizing the short circuit current density of microcrystalline silicon n−i−p solar cells: • Triangular textured substrates allow for using higher H/P ratios in comparison to hexagonal and square textured substrates. • “Selective back reflectors” in comparison to conventional textured back reflectors allow for minimizing optical losses of the back reflector and maximizing the quantum efficiency. • The charge carrier mobility of the transparent conductive front contact should be as high as possible to minimize optical losses. Using an IOH front contact as a replacement for an ITO front contact allows for reducing optical losses of the front contact. Operating at the Light-Trapping Limit. In the following, the simulated quantum efficiency of the solar cell optimized according to the maximal H/P ratio approach is compared to the geometric light-trapping limit, or Yablonovitch limit. The Yablonovitch limit represents a statistical geometric/ray optics limit assuming that all absorbed photons contribute to the

rt(λ) =

1 × 2 × α (λ ) × d

1 1 QE(λ)

−1

(4)

A comparison of the number of round trips with the Yablonovitch limits under perpendicular incidence shows that the limits are reached for all three datasets, which underlines the excellent light trapping of the proposed solar cell design. A direct comparison of the simulated quantum efficiencies and Yablonovitch limits under perpendicular incidence for all three datasets is provided in Figure 5 and the Supporting Information (Figure S8). Furthermore, the short circuit current densities for the different spectral ranges are provided in Table S3 (Supporting Information). The low absorption coefficient determined for the Ding dataset leads to a drop of the quantum efficiencies and Yablonovitch limits for wavelengths of >700 nm compared to quantum efficiencies and Yablonovitch limits for Remes and Green datasets (Supporting Information Figure S8). As a result, the lowest red (700−1100 nm) and total (300− 1100 nm) short circuit current densities are obtained for the Ding dataset compared to the Remes and Green datasets which are shown in Table S3 (Supporting Information). On the other hand, the highest total short circuit current densities of 35.5 and 38.5 mA cm−2 are obtained for the Remes dataset for the simulated quantum efficiency and Yablonovitch limit, respectively.

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DISCUSSION In a previous simulation study, we showed that short circuit current densities in excess of 30 mA cm−2 can be reached for F


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ACS Photonics crack-free solar cells with a thickness of 3 μm.7 In this study, a distinctly higher short circuit current density is reached for a thinner solar cell using a triangular textured solar cell. The triangular textured substrate is superior to hexagonal or square textured substrates.7 The final surface morphology of the solar cell resembles the densest possible packing of nanospheres on a planar surface. Surfaces covered with a triangular arrangement of spheres can be realized by the self-assembly process of nanospheres. Detailed descriptions of the fabrication of such surfaces are provided in the literature.25,26 Such processes might be used in the fabrication of the triangular textured solar cells. The self-assembly process might allow for replacing the photolithography process.1,3,4,6,14,17 Furthermore, a significant gain of the short circuit current density is achieved by minimizing the optical losses of the back reflector and front contacts. The use of the maximal H/P ratio approach allows for reaching short circuit current densities up to 35.5 mA cm−2 for a solar cell thickness of only 2.2 μm. The thickness of the solar cell is comparable with the thickness used for the current world record solar cell prepared on a hexagonal textured substrate.1−3 The current world record solar cell exhibits an open circuit voltage of 550 mV and a fill factor of 0.75.1−3 By combining the record values of the open circuit voltage and the fill factor with the simulated short circuit current density in this study the energy conversion efficiency could be increased from 11.8% to 13.2% or even potentially 14.6% depending on the optical constants of the microcrystalline silicon material.

Vladislav Jovanov: 0000-0002-2220-1394 Dietmar Knipp: 0000-0002-7514-3407 Present Address §

Geballe Laboratory for Advanced Materials, Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States. Notes

The authors declare no competing financial interest.

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SUMMARY Triangular textured microcrystalline silicon solar cells on triangular textured substrates allow for approaching the geometric light-trapping limit. The optics of the solar cells is investigated by 3D FDTD optical simulations, while the interface morphologies of the solar cell layers are calculated by 3D morphological algorithms. All investigated solar cells are crack free. The triangular textured solar cells are less sensitive to the formation of cracks as compared to both the hexagonal and square textured solar cells. The use of the maximal H/P ratio approach allows for reaching a short circuit current density up to 35.5 mA cm−2 for a solar cell thickness of only 2.2 μm. The optical losses of the front and back contacts of the solar cells are decreased by using a “selective back reflector” and front transparent conductive oxide with high charge carrier mobility. The short circuit current density of the solar cells is approaching the geometric light-trapping limit, taking realistic device structures into account, which provides a route for experimentally realizing silicon thin-film solar cells with very high short circuit current densities.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b01397. Additional information (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Asman Tamang: 0000-0001-7215-9748 G


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Silicon Thin-Film Solar Cells Approaching the Geometric Light

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