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Article Cite This: ACS Omega 2018, 3, 4123−4128
Optimizing Photovoltaic Charge Generation of Hybrid Heterojunction Core−Shell Silicon Nanowire Arrays: An FDTD Analysis Vivek Kumar,*,†,§ Deepak Gupta,† and Rajesh Kumar‡ †
Department of Physics, National Institute of Technology, Bijni Complex, Shillong, Meghalaya 793003, India Material Research Laboratory, Discipline of Physics & MEMS, Indian Institute of Technology Indore, Simrol 453552, India
‡
S Supporting Information *
ABSTRACT: Development of highly efficient nanowire-based photovoltaic devices requires an accurate modeling of light scattering from interfaces and optical carrier generation inside the cell. A comprehensive study of optical absorption and carrier generation enables us to tap the full potential of nanowire arrays (NWAs). In this study, we have done a systematic study to optimize the core−shell structure of vertically aligned silicon nanowire (Si NW) arrays coated with PTB7:PC71BM by means of finite difference time domain optical simulations to maximize the photon absorption. Initially, the core thickness of hybrid Si NWs has been optimized for the most efficient light absorption. The further improvement of light absorption has been studied by varying the coating thickness of low-band gap organic polymer PTB7:PC71BM on Si NWAs. A delineative analysis shows that NWs with a 150 nm thick silicon core and 60 nm thick coating of PTB7:PC71BM exhibit broad band absorption and the optimum ideal current density of about 34.95 mA/cm2, which are larger than those of their planar counterpart with the same amount of absorbing material and also better than those previously reported for NWs. The basic principle and the physical process taking place during absorption and current generation have been also discussed. The optimization of the hybrid heterojunction Si NW arrays and understanding of their optical characteristics may contribute to the development of economical and highly efficient hybrid solar cells.
1. INTRODUCTION The recent advances in the semiconductor nanowire array (NWA) technology provide new opportunities to realize economical and highly efficient photovoltaic (PV) devices because of their distinctive unidimensional geometry with striking electrical and optical features.1−5 It has been observed that Si NWA-based solar cells have a higher efficiency limit than planar cells because the restricted aperture of Si NWAs suppresses the optical and entropy losses.6,7 The vertically grown nanowires (NWs) provide an elongated optical path which enhances the photon absorption.3 Because the diameter of the NWs is of the order of the wavelength of the incident wave, it subdues optical reflection over the wide spectral range.8 This reduces the time and cost of anti-reflection coating imperative in planar PV structures.9,10 Moreover, the Si NWA structures provide high collection probability because charge separation occurs in the radial orientation. Such optically favorable design principles of Si NWAs substantially surpass the conventional Shockley−Queisser efficiency limit.11 Different types of the Si NWA-based heterojunction have been studied by varying the doping concentration and embedding carbon quantum dots and the Schottky junction based on graphene nanoribbons for improved efficiency of Si NWA-based PV devices.12,13 These studies show that the morphological and © 2018 American Chemical Society
geometrical improvements of Si NWAs enhance their inherent properties of the elongated optical path, radial carrier transportation, reduced optical reflection, and exaggerated surface area which give them an upper hand over planar geometry-based solar cells.14,15 Recently, hybrid polymer-/NW-based solar cells have attracted a lot of interest because they are significant in the endeavor to develop inexpensive, mass-producible, and lightweight solar cells.15−18 Many groups have studied hybrid NW/ P3HT (binary blend)17,19 structures, but the maximum efficiency of a binary blend single-junction device is limited to 12% because of the limited optical absorption and low charge transfer of the photoactive layer.18 To overcome this limitation, researchers are attempting to develop ternary blend organic PVs.18,20−22 Here, polymers of contrasting electron affinities and ionization potentials are blended together.23 These ternary blend hybrid structures form dispersed heterojunctions that can significantly generate excitons within diffusion lengths.24,25 For the better light harvesting, dissociation of excitons is an essential step in the production of free Received: February 20, 2018 Accepted: March 20, 2018 Published: April 12, 2018 4123
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over the absorbing region of NWAs to calculate the exciton generation rate. Finally, two monitors were placed, one above the light source and the other below the substrate to measure optical reflectance and optical transmittance, respectively. Figure 2i represents optical reflectance (R) of hybrid Si NWA/PTB7:PC71BM structures without and with varying
carriers; however, photoinduced excitons should be produced in the diffusion length range of the heterojunction interface. Extensive studies of the dispersed heterojunction-based solar cells reveal that their efficiencies are determined by their nanoscale morphologies.24,26−28 Despite numerous geometrical advantages and administering all morphological issues of dispersed heterojunction-based silicon nanowire (Si NW) solar cells,29,30 they have been less efficient and have relatively found less commercial relevance compared to the conventional bulk silicon solar cells.31−34 The absence of properly optimized structures may be the main reason behind that. Further development of hybrid Si NW/polymer-based solar cells requires sheathing of an organic polymer which can efficiently harvest the major part of the solar spectrum.35,36 The analysis of NW-based PV devices requires an accurate modeling of light scattering from interfaces and optical carrier generation inside the cell for efficient light harvesting. The processes that contribute to their absorption are interrelated and highly dispersive, so the only current method of optimizing the absorption is by intensive numerical calculations.37 In view of this, here, we have done geometrical optimizations and a systematic study of optical characteristics of low-band gap organic polymer PTB7:PC71BM-coated Si NWAs to capitalize optical absorption. The finite difference time domain (FDTD) simulated generation rates, and ideal short-circuit current densities have been studied for different core−shell combinations to optimize the proposed hybrid structures. The detailed analysis shows that the optical absorptance is maximum only for a singular combination of the core and the shell. The basic principle and the physical process taking place during absorption and current generation have also been discussed.
2. RESULTS AND DISCUSSION Figure 1a shows the three-dimensional schematic of 5 μm long, 3 × 3 Si NWAs/PTB7:PC71BM, which is equivalent to the Figure 2. (i) Optical reflectance and (ii) transmittance curves of (a) uncoated 150 nm Si NW core and with PTB7:PC71BM coating of thickness (b) 20, (c) 60, and (d) 80 nm.
organic coating across the predominant part of the solar spectrum. A conspicuous amount of reflectance is observed over the complete region for bare Si NWAs. For wavelengths up to 560 nm and beyond 950 nm, the optical reflectance decreases continuously as the organic coating thickness is increased. In the wavelength zone of 700−950 nm, the optical reflectance undulates and behaves in contrast to lower and higher wavelength regions. In this wavelength zone, optical reflection increases as the coating thickness increases. The optical reflectance peak surpasses the bare Si NWA peak at the optimum coating thickness of 60 nm. Overall, the hybrid Si NWAs/PTB7:PC71BM assembly has exceptionally low optical reflectance for coating thicknesses of 60 nm, with the peak not exceeding 15%, in contrast to bare Si NWAs and other extensively studied hybrid NWAs structures. Figure 2ii represents optical transmittance (T) for uncoated Si NWAs with and without PTB7:PC71BM coating as a function of wavelength. Coating initially increases and subsequently reduces the optical transmission, hitting the lowest of 5% transmittance for 60 nm thick PTB7:PC71BM coating in the higher frequency region. In the low frequency region, sharp rises and falls are observed in the optical transmittance. Overall, optical transmission for the proposed
Figure 1. (a) Schematic representation of three-dimensional periodic PTB7:PC71BM-coated 3 × 3 silicon NWAs under FDTD simulation and (b) two-dimensional transverse cross section of simulated nanowires with polymer coating.
density of 6.25 × 108 NWs/cm2. The variation of average optical absorptance for different lengths of NWs has been simulated and shown in the Supporting Information in Figure S4. The optimized length of NWs obtained is 5 μm. Figure 1b represents the actual two-dimensional lengthwise cross section of the nanowire in which the FDTD simulation was executed. While applying an FDTD simulation region, perfectly matching layer (PML) boundaries were also implemented to diminish the interior reflections completely. A solar analysis group was set 4124
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absorptance. So, we have also considered all these structures for further optimization of PV charge generation. A rapid exciton generation rate and prompt carrier separation are the prerequisites for a superior PV material.39 Mathematically, the exciton generation rate (G) is given by G = ∫ over simulated region(Pabs/ℏω). Figure 4a,b shows the simulated
structure offers 20% lower optical transmission than bare Si NWAs. The optical absorptance (A) is estimated using the energy balance relation A(λ) = 1 − R(λ) − T(λ). Figure 3 shows the
Figure 3. Optical absorptance curves of (a) uncoated 150 nm Si NW core and with PTB7:PC71BM coating of thickness (b) 20, (c) 60, and (d) 80 nm.
optical absorptance of uncoated and PTB7:PC71BM-coated Si NWAs with respect to the wavelength. For all wavelengths under 700 nm and beyond 950 nm, as the thickness of the photoactive shell increases, optical absorptance reaches the maximum for an optimum coating of 60 nm. For the wavelength band of 700−950 nm, optical absorptance fluctuates because of unsteady optical reflection in this wavelength region. Overall, Si NWAs/PTB7:PC71BM have wide and enhanced optical absorption ranging from the low to high wavelength region which is foremost to take complete advantage of any NWA-based PV structure. This can be explained by using the following electrostatic approximation: the enhanced optical absorption as a function of the wavelength for bare Si NWAs is given by35,38 |Ecore/Einc|2 = |2εext/(εext + εcore)|2, where εext = 1 (permittivity of air), Einc is the electric field intensity of the incident light, and Ecore is the electric field intensity of the Si NW core. At the incident light of 600 nm wavelength, εcore = (15.590 + 0.216j), which gives |Ecore/Einc|2 = 0.014. When the optimized layer of PTB7:PC71BM is coated on silicon NWAs, the expression of enhanced absorption modifies to |Ecore/Einc|2 = |2εext/(εext + εcoat)|2|2εcoat/(εcore + εcoat)|2, where εcoat = (3.605 + 1.283j) for the incident light of 600 nm wavelength,31 which gives |Ecore/Einc|2 = 0.026. By these calculations, we can see that about 1.9 times enhancement in optical absorption can be obtained with a 60 nm organic shell than the uncoated Si NWs. This explains the observed enhancement in optical absorption for Si NWs/PTB7:PC71BM, as shown in Figure 3. The average optical absorptance (%) values of hybrid Si NWAs for different Si NW core thicknesses such as 110, 130, 150, 160, and 170 nm and for different PTB7:PC71BM shell thicknesses are summarized in Table S1 given in the Supporting Information. It is observed that the shell with 60 nm thickness offers the highest average optical absorptance of nearly 96% for all cores. If the thickness of the shell is further increased, optical absorptance falls gradually. Surprisingly, it is observed that for constant shell thickness of 60 nm and with decreasing core thickness, there is a minor increase in the average optical
Figure 4. (a) Calculated optical power absorption per unit volume (Pabs), (b) calculated optical generation rate (G) of electron−hole pairs in the y−z cross section for the 150 nm silicon core coated with 60 nm thick PTB7:PC71BM organic shells, and (c) schematic of light propagation and carrier generation in the proposed core−shell structure.
optical power absorption per unit volume (Pabs) and simulated exciton generation rate (G), respectively, in the logarithmic scale for an optimized Si NW with a core thickness of 150 nm and a coating thickness of 60 nm. Here, a choropleth approach is used to demonstrate the strength and distribution of guided modes along the NW length. These plots illustrate the opulent optical confinement along the entire height of NWs. The simulations performed for the 5 μm long and 150 nm thick Si NW core and for varying coating thickness of PTB7:PC71BM under broad solar irradiance of 300−1100 nm have been shown in the Supporting Information in Figure S5a,b. A delineative analysis of Figure S5a,b shows that NWs with a 150 nm thick silicon core and 60 nm thick coating of PTB7:PC71BM exhibit the optimum generation rate, which is in contrast to other core−shell structures. Figure 4c shows the schematic of light propagation and carrier generation in the proposed core−shell structure; yellow 4125
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ACS Omega arrows show the elongated optical path in the axial direction. White arrows represent the radial carrier transportation and the blue-colored structure represents the formation of the standing wave at optimum thickness of the core and the shell. The main aim of optimizing the core−shell geometry is to synchronize optical field’s standing wave nodes with the heterojunction interface, which is schematically shown in Figure 4c. This process boosts the carrier separation process and utilizes the maximum length of the NWAs.40,41 The pragmatic application of an organic coating of thickness nearly half of the coat thickness provides optimum light absorption, exciton generation, and free carrier transportation. These hybrid Si NWAs/PTB7:PC71BM allow a high amount of photons to scatter in the structure and give them further chances to generate electron−hole pairs to make use of the entire incident light on the cell without the need for an additional light-trapping mechanism such as surface texturing. The ideal short-circuit current density (Isc) for NWAs with varying Si core thicknesses and a 60 nm thick shell of PTB7:PC71BM at zero external voltage is shown in Figure 5.
Figure 6. Schematic of PTB7:PC71BM-coated silicon NWs demonstrating exciton dissociation at the heterojunction interface. The schematic of the dispersed heterojunction solar cell design is shown in the inset.
other core−shell combinations, it was observed that the bare Si NWs core of 150 nm thickness exhibits the optimum optical absorption. However, with PTB7:PC71BM organic low-band gap polymer coating on the 150 nm Si NW core, a phenomenal optical absorption was observed. A detailed analysis shows that NWAs with a 150 nm thick silicon core and 60 nm thick coating of PTB7:PC71BM exhibit broad band absorption. A delineative analysis of optical generation rates of these optimized structures shows higher light-harvesting properties. The optimized hybrid structures of the 150 nm thick Si NW core with a 60 nm thick PTB7:PC71BM shell exhibit the optimum ideal photogenerated current of about 34.95 mA/cm2, which is larger than the planar counterpart42 with the same amount of absorbing material and also better than that previously reported for NWs.37,42 This study indicates that hybrid Si NWA-based solar cells are likely to have greater efficiency than planar solar cells, thereby raising the position of hybrid Si NWAs for the practical experiment of the promising hybrid solar cells.
Figure 5. Ideal short-circuit current density (Isc) for different Si NW core thickness coated with 60 nm thick PTB7:PC71BM organic shells.
The Isc initially undulates and then increases steadily with a peak at 34.95 mA/cm2 for a 150 nm thick core coated with a 60 nm thick PTB7:PC71BM shell and then drops continuously for thicker configurations of cores. This shows the optimized structure that shows maximum Isc. The current generation process in these hybrid Si NW heterojunctions is shown in Figure 6. When an electron donor polymer (PTB7) and an electron acceptor polymer (PC71BM) are brought in contact, a regional field develops at their interface. This regional field accelerates all the excitons produced within the diffusion length to the interface, where they dissociate. As a result, charge separation is far more efficient at the heterojunction interface. The hybrid Si NWAs have the efficient ability of charge carrier transfer to the electrodes without losses due to recombination at boundaries. Also, in the PTB7:PC71BM interface, the interface dipole and the band bending are absent because of their identical charge neutrality levels. Because of the abovestated reasons, these hybrid Si NWs/PTB7:PC71BMs show better ideal Isc. The principle and the processes followed here to achieve an optimum core−shell combination are also valid for all hybrid NWA-based PV devices.
4. COMPUTATIONAL METHODS In this article, the optical simulations for Si NWAs/ PTB7:PC71BM have been performed by means of the FDTD method. The FDTD is a state-of-art grid-based numerical analysis technique that works out Maxwell’s differential equations for intricate geometries by employing temporal and spacial discretization using central difference approximations to perform optical simulations. Maxwell curl equations associate the changes in electric/magnetic field in time with the changes in the magnetic/electric field over space, respectively. This resembles the basic FDTD forward development-in-time relationship. Now, anywhere in space, a forward time-stepped value of the electric field can be determined by the localized spatially distributed magnetic field and by the previously evaluated value of the electric field. In a similar manner, the magnetic field can also be developed in time to compose a continuous electromagnetic wave. These nibbles of the electric field and magnetic field are time-developed numerically in every Yee-cell under various conformal boundary conditions to
3. CONCLUSIONS In conclusion, the optical attributes of the PTB7:PC71BMcoated Si NWAs were studied using the FDTD method with an aim to optimize the PV charge generation. In comparison to 4126
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evaluate different optical attributes. We adopt the PML boundary condition and normal irradiance of the standard AM 1.5 G profile as a plane wave source. The n-type Si NWs of the doping concentration 2.3 × 1014 cm−3 are simulated here. The chemical structure and the composition of polymer PTB7:PC71BM have been shown in the Supporting Information in Figure S1a,b. The refractive indices31,38 of Si and PTB7:PC71BM are shown in Figures S2 and S3 in the Supporting Information, respectively, for a wavelength span of 300−1100 nm. Optical absorptance, power absorbed per unit volume, exciton generation rate, and ideal short-circuit current density have been simulated for a broad spectral range of 300− 1100 nm wavelength.
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ASSOCIATED CONTENT
* Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b00303. Composition of the polymer and chemical structure, refractive index of silicon and PTB7:PC71BM, average optical absorptance of different heights of NWs, optical power absorption and optical generation rate, and average optical absorptance for various thicknesses of core and shell combinations (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected],
[email protected] (V.K.). ORCID
Vivek Kumar: 0000-0003-3386-0755 Rajesh Kumar: 0000-0001-7977-986X Present Address §
V.K.: Department of Physics, Indian Institute of Information Technology Design and Manufacturing Kancheepuram, off Vandalur-Kelambakkam Road, Chennai 600127, India Notes
The authors declare no competing financial interest.
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AM stands for air mass, G stands for global and its value 1.5 units describes the amount of incident radiation absorbed by earth’s atmosphere or dust particles at an incident solar angle of 48.2°.
ACKNOWLEDGMENTS
Authors acknowledge financial support from Science and Engineering Research Board, Department of Science and Technology (SERB-DST), Govt. of India (file no. ECR/ 2016/001715). Authors also acknowledge Dr. V. A. Volodin, Institute of Semiconductor Physics, Novosibirsk, Russia for his valuable suggestions.
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ABBREVIATIONS HOMO LUMO PTB7
highest occupied molecular orbital least unoccupied molecular orbital poly[(4,8-bis-(2-ethylhexyloxy)benzo(1,2-b:4,5-b′)dithiophene)2,6-diyl-alt-(4-(2-ethylhexyl)-3fluorothieno[3,4-b]thiophene-)-2carboxylate-2-6-diyl)] PC71BM [6,6]-phenyl-C71-butyric acid methyl ester PTB7:PC71BM/Si NWAs PTB7:PC 71 BM coated silicon NWAs 4127
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