nanomaterials Article

Numerical Study of Complementary Nanostructures for Light Trapping in Colloidal Quantum Dot Solar Cells Jue Wei 1,2 , Qiuyang Xiong 1 , Seyed Milad Mahpeykar 1 and Xihua Wang 1, * 1 2

*

Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada; [email protected] (J.W.); [email protected] (Q.X.); [email protected] (S.M.M.) Key Laboratory of Coherent Light and Atomic and Molecular Spectroscopy of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China Correspondence: [email protected]; Tel.: +1-780-492-3523

Academic Editor: Guanying Chen Received: 15 February 2016; Accepted: 21 March 2016; Published: 25 March 2016

Abstract: We have investigated two complementary nanostructures, nanocavity and nanopillar arrays, for light absorption enhancement in depleted heterojunction colloidal quantum dot (CQD) solar cells. A facile complementary fabrication process is demonstrated for patterning these nanostructures over the large area required for light trapping in photovoltaic devices. The simulation results show that both proposed periodic nanostructures can effectively increase the light absorption in CQD layer of the solar cell throughout the near-infrared region where CQD solar cells typically exhibit weak light absorption. The complementary fabrication process for implementation of these nanostructures can pave the way for large-area, inexpensive light trapping implementation in nanostructured solar cells. Keywords: solar cells; nanostructures; light trapping

1. Introduction In the last few years, colloidal quantum dot (CQD) solar cells have received a great deal of attention due to their potential for large-area, high-throughput, and low-cost manufacturing [1]. Despite all the achievements in CQD synthesis, surface treatment and film deposition technologies [2], the power conversion efficiency of this type of solar cell continues to lag behind traditional silicon solar cells. Because of the lack of long diffusion lengths for photo-generated carriers in CQD films, a CQD film capable of taking advantage of all the incident solar power would be too thick to extract all the generated carriers, leading to an absorption-extraction trade-off [3–5]. Light trapping, or effectively increasing optical path lengths in the absorbing material through structuring without any change in light absorbing material’s thickness, is one option to overcome the aforementioned trade-off [6]. Periodic nanostructured gratings have been extensively explored for light trapping in various types of thin-film solar cells and various silicon or metamaterial-based structures have been proposed, such as nanopillar, nanowire, nanohole, and pyramid arrays [7–14]. The downside, however, is that these structures are difficult to fabricate due to their complicated structures or material compositions. Metallic gratings have also been considered for light harvesting enhancement by taking advantage of surface plasmons [15–17]. However, parasitic light absorption intrinsic to metallic structures which can compete against useful absorption in light absorbing layer has severely limited the application of metallic nanostructures in photovoltaic devices [18].

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Recently, we reported on periodic nano-branch indium-doped tin oxide (ITO) electrodes as diffraction gratings for light absorption enhancement in CQD solar cells [19]. Using numerical simulations, a significant polarization-independent broadband light absorption enhancement was observed for two-dimensional ITO nano-branch gratings and the absorption enhancement was demonstrated to be almost independent of common fabrication flaws in nano-branch structure. On the other hand, current fabrication technologies are unable to implement the fabrication of such nanostructures due to the difficulty of keeping the periodicity of the structure over a large area and also incorporation of CQDs into such porous structure. In order to be able to apply a periodic nanostructure for practical and tangible light trapping in solar cells, maintaining the periodicity of the structure over a large area is the key requirement. Therefore, the fabrication process used to impose the periodic pattern must be able to produce periodic patterns over large areas and also inexpensive at the same time. Recent advances in large-scale nanofabrication techniques have allowed sophisticated nanostructures to be employed in solar cells and photodetectors with impressive results [20,21]. In this work, in order to fully satisfy the large-area requirement of light trapping structures, we consider two experimentally available nanostructures (nanocavity and nanopillar) for light absorption enhancement in CQD solar cells due to their potential for easy large-area fabrication and CQD incorporation. A facile fabrication process is performed to achieve large-area periodic pattern of the nanocavity and nanopillar structures. The simulation results show that compared to the reference flat structure, our proposed structures can achieve relatively high absorption enhancement in CQD solar cells. 2. Results and Discussion 2.1. Structure Design The main reason that nanocavity and nanopillar arrays are proposed as nanostructured electrodes to improve absorption enhancement in PbS CQD solar cells is that such nanostructures can be easily fabricated over large areas by a low-cost pattern transfer method known as nanosphere lithography (NSL). As a proof of concept, PDMS nanopillar and silver nanocavity arrays were fabricated utilizing nanosphere lithography. The proposed process steps for fabrication of nanocavity and nanopillar arrays is presented schematically in Figure 1a. Firstly, colloidal nanosphere mask is deposited on a Si substrate. After nanosphere mask formation, oxygen plasma is employed to shrink the nanospheres to ideal diameter needed for the intended structure through reactive ion etching (RIE). The next step is to deposit the desired material, in this case silver (Ag), on the sample covered by colloidal mask. The final step is to lift off the nanosphere mask, which is usually done in ultrasonic bath with organic solvents such as acetone, after which the nanocavity array is formed on the substrate. In addition to being a standalone light trapping structure, the fabricated nanocavity array can be utilized for fabrication of nanopillar array through PDMS casting and peel off. This is possible because the nanocavity array can act as a mold for formation of nanopillar array. The Scanning Electron Microscope (SEM) images of the cavity and pillar arrays fabricated using the described fabrication process are shown in Figure 1b. We believe a similar procedure with minimal modification can be used to fabricate well-defined ITO nanocavity and nanopillar electrodes. Substituting the silver with ITO in material deposition step will easily lead to ITO nanocavity structure and depositing ITO on top of fabricated PDMS nanopillars can form the desired ITO nanopillars suitable for light absorption enhancement in CQD solar cells.

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Figure 1. (a) The proposed process flow for fabrication of nanocavity and nanopillar arrays. (b) Top

Figure 1. (a) (a) The proposed proposed process flow flow for fabrication fabrication of nanocavity schematic and nanopillar nanopillar arrays. (b) (b) Top Top Figure 1. The process for nanocavity and view scanning electron microscope (SEM) images and of cross-sectional of the arrays. nanocavity view scanning electron microscope (SEM) images and cross-sectional schematic of the nanocavity (left) and nanopillar arrays fabricated using the process. schematic of the nanocavity view (left) scanning electron (right) microscope (SEM) images andproposed cross-sectional and nanopillar (right) arraysarrays fabricated usingusing the proposed process. (left) and nanopillar (right) fabricated the proposed process. The periodic ITO electrodes proposed in this work are designed for a typical depleted heterojunction cell structure. The in depleted heterojunction architecture 2 The periodic ITO electrodes proposed this are designed for a utilizes typicala TiO depleted The periodic CQD ITO solar electrodes proposed in this work work designed depleted layer as the n-side of the junction and p-type PbS quantum dots as the p-side. The bottom contact to heterojunction heterojunction CQD CQD solar cell structure. The The depleted depleted heterojunction heterojunction architecture architecture utilizes utilizes a TiO22 the junction is formed on a glass substrate and consists of a thin transparent conductive ITO layer. layer as the n-side of the junction and p-type PbS quantum dots as the p-side. The bottom contact to The top contact employs a deep work function metal such as gold to collect photo-excited holes and the is aa glass consists of conductive the junction junction is formed formed on glass substrate substrate and the consists of aa thin thin transparent transparent conductive ITO layer. also reflect back anyon unabsorbed photons and into light absorbing layer. A conformal layer ofITO TiOlayer. 2 The top contact employs a deep function as gold collect and photo-excited with thickness of 50 nm was work considered as ametal layer such between ITO to electrode active layer.holes The and also reflect reflect back anyunabsorbed unabsorbed photons into light layer. A of2 TiO back any photons into thethe light layer. A conformal layerlayer of TiO with2 designed periodic nanostructures are implemented at absorbing theabsorbing interface between theconformal ITO bottom contact with thickness of Figure 50 nmconsidered considered as of a the layer between ITO and active and PbS QDs. 2awas shows theas schematic structure of PbS QDelectrode solaractive cell with patterned ITO The thickness of 50 nm was a layer between ITO electrode and layer. Thelayer. designed electrode used nanostructures for simulation. Asare depicted theinterface figure, when the light normally incident on ITO designed periodic implemented at the interface between the ITO bottom contact periodic nanostructures are implemented atinthe between theisITO bottom contact and PbS diffraction gratings through the schematic transparent forward diffraction of light and QDs.2aFigure shows the ofsubstrate, the structure ofsolar PbS QD cell can withinduce patterned ITO QDs.PbS Figure shows2a the schematic of the structure of PbS QD cell solar with patterned ITO light electrode effectively increasing optical path lengths the absorbing materialon especially for electrode usedbyfor simulation. As in depicted in the figure, whenis the light isincident normally incident on ITO used trapping for simulation. As depicted the figure, when theinside light normally ITO diffraction higher diffracted orders supported by the grating structure. Optical constants of the materials used diffraction gratings the transparent substrate, forward of diffraction light light can induce light gratings through thethrough transparent substrate, forward diffraction light can of induce trapping by in the simulation model are shown in Figure 2b.

trapping effectively increasing opticalinside path the lengths insidematerial the absorbing material especially for effectivelyby increasing optical path lengths absorbing especially for higher diffracted higher by the grating constantsused of the used orders diffracted supportedorders by the supported grating structure. Opticalstructure. constantsOptical of the materials in materials the simulation in the simulation are2b. shown in Figure 2b. model are shown model in Figure

(a)

(b)

Figure 2. (a) Schematic of light diffraction in PbS quantum dot (QD) solar cell with patterned indium-doped tin oxide (ITO) electrode. (b) Optical constants of the materials used in the simulation model.

(a)

(b)

Figure Figure 2. 2. (a) (a) Schematic Schematic of of light light diffraction diffraction in in PbS PbS quantum quantum dot dot (QD) (QD) solar solar cell cell with with patterned patterned indium-doped (ITO) electrode. (b) Optical constants of the materials used in theused simulation indium-doped tin tinoxide oxide (ITO) electrode. (b) Optical constants of the materials in the model. simulation model.

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2.2. 2.2. Light Trapping Trapping Analysis Analysis Grating was firstly used to analyze thethe diffraction behavior of the Grating far-field far-fieldprojection projectionanalysis analysis[22] [22] was firstly used to analyze diffraction behavior of proposed periodic grating structures in PbS CQD solar cells. The resulting transmission efficiencies the proposed periodic grating structures in PbS CQD solar cells. The resulting transmission of the simulated illustrated Figure 3. in AsFigure is clear3.from figure, efficiencies of thepatterned simulatedstructures patternedare structures areinillustrated As isthe clear fromboth the cavity pillar structures demonstrate transmission efficiency in wavelength of 700 nm figure,and both cavity and pillar structureshigh demonstrate high transmission efficiencyrange in wavelength to 900 of nm. the hand, of transmitted power is not significant 900 nm. range 700On nm toother 900 nm. Onthe theamount other hand, the amount of transmitted power isbeyond not significant This trend, broken for bothisnanocavity and nanopillar at aroundarrays the wavelength beyond 900however, nm. This is trend, however, broken for both nanocavityarrays and nanopillar at around of nm with aofstrong increase the amount ofin transmitted power. The samepower. behavior also the950 wavelength 950 nm with ainstrong increase the amount of transmitted Theissame observed in the case of the cavity array at wavelength of 1080 nm, the intensity of which, however, behavior is also observed in the case of the cavity array at wavelength of 1080 nm, the intensity of is not ashowever, strong asisthe at 950 as nm. sudden transmitted power can be attributed which, notpeak as strong theThis peak at 950 increase nm. Thisinsudden increase in transmitted power to the resonant coupling of the incident light into wave guiding modes supported by the PbS CQD can be attributed to the resonant coupling of the incident light into wave guiding modes supported layer adjacent the ITOadjacent grating to structures to the periodicdue nature of their structure [19]. by thelocated PbS CQD layertolocated the ITO due grating structures to the periodic nature of Although throughout the spectrum, a portion incidentalight is not (shown as diffracted the order their structure [19]. Although throughout the of spectrum, portion of diffracted incident light is not (0,0)), by as paying close attention the total transmission values differencevalues with order (shown the order (0,0)), by to paying close attention to the and totaltheir transmission and (0,0), their itdifference is obviouswith thatorder a significant of energy diffractedamount into higher orders,isespecially resonance (0,0), itamount is obvious that a is significant of energy diffractedatinto higher wavelengths. This can contribute to light absorption in CQDtolayer by absorption increasing orders, especially at greatly resonance wavelengths. This can enhancement greatly contribute light the optical path length of the light inside the layer or light trapping through resonant coupling enhancement in CQD layer by increasing the optical path length of the light inside the layer or with light the incident light [19]. The transmission efficiencies of two the The strongest diffracted orders (1,1) trapping through resonant coupling with the incident lightof[19]. transmission efficiencies of and two (2,0) are plotted in Figure 3. of the strongest diffracted orders (1,1) and (2,0) are plotted in Figure 3.

Figure 3. 3. The The normalized normalized transmission transmission spectra spectra of of simulated Figure simulated patterned patterned ITO ITO structures: structures: (a) (a) nanocavity, nanocavity, (b) nanopillar. The plot shows the relative power transmitted into different diffracted orders and and the the (b) nanopillar. The plot shows the relative power transmitted into different diffracted orders net total transmitted power normalized to the simulation source power. Two of the strongest net total transmitted power normalized to the simulation source power. Two of the strongest diffracted diffracted (1,1)are and (2,0) are (0,0)the represents the partpower of incident power not being orders (1,1)orders and (2,0) plotted. (0,0)plotted. represents part of incident not being diffracted by diffracted by the structures. the structures.

Figure 4 depicts the simulated light absorption spectra for PbS CQD layer of the modelled Figure 4 depicts the simulated light absorption spectra for PbS CQD layer of the modelled depleted heterojunction solar cell normalized to the AM1.5G solar spectrum (Figure 4a) and depleted heterojunction solar cell normalized to the AM1.5G solar spectrum (Figure 4a) and simulation simulation light source (Figure 4b). In order to be able to compare the effect of proposed structures light source (Figure 4b). In order to be able to compare the effect of proposed structures on absorption on absorption enhancement in PbS CQD layer, a flat ITO layer was considered as the reference. The enhancement in PbS CQD layer, a flat ITO layer was considered as the reference. The available power available power from AM1.5G spectrum is also included in the figure for comparison. As is obvious from AM1.5G spectrum is also included in the figure for comparison. As is obvious from the figure, from the figure, both nanocavity and nanopillar arrays can induce more light absorption in CQD both nanocavity and nanopillar arrays can induce more light absorption in CQD layer than the flat layer than the flat ITO layer within most parts of the near-infrared region. It is also noticeable that ITO layer within most parts of the near-infrared region. It is also noticeable that both proposed both proposed structures have achieved almost perfect absorption in the range of 720 nm to 850 nm structures have achieved almost perfect absorption in the range of 720 nm to 850 nm by absorbing by absorbing all the power available from the sun in this range. As for beyond this range, especially all the power available from the sun in this range. As for beyond this range, especially in the case of in the case of cavity structure, the resonant coupling of the incident light into guided modes cavity structure, the resonant coupling of the incident light into guided modes supported by CQD supported by CQD layer is the major responsible for strong but narrowband absorption layer is the major responsible for strong but narrowband absorption enhancements at resonant peaks, enhancements at resonant peaks, previously predicted by grating projection analysis. This is possible because of the major difference in refractive indices of the CQD layer and the ITO layer which can form an efficient waveguide in the middle of the cell’s structure.

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previously predicted by grating projection analysis. This is possible because of the major difference in refractive indices of the CQD layer and the ITO layer which can form an efficient waveguide in the Nanomaterials 2016, 6, 55structure. 5 of 9 middle of the cell’s In order to have an overall evaluation for the light absorption enhancement performance of the In order to havethe an average overall evaluation the light absorption enhancement performance of the proposed structures, absorptionfor enhancement of the structures over the entire simulated proposed structures, the average absorption enhancement of the structures over the entire simulated spectrum was measured against the flat reference structure using the following equation: spectrum was measured against the flat reference structure using the following equation: Absorption Enhancement p%q “ pPg ´ Pr q{Pr ˆ100 (1) Absorption Enhancement (%) = (Pg − Pr)/Pr ×100 (1) where where PPgg depicts the total power power absorbed absorbed by the the cell cell with with grating grating structure structure and and PPrr denotes denotes the the power power absorbed absorbed by by the the reference reference flat flat structure. structure. According According to to the the equation, equation, the the calculated calculated absorption absorption enhancement grating structures compared to the flatflat structure are enhancementfactors factorsfor fornanocavity nanocavityand andnanopillar nanopillar grating structures compared to the structure 15.0% and 13.6%, respectively. This amount of absorption enhancement can significantly boost charge are 15.0% and 13.6%, respectively. This amount of absorption enhancement can significantly boost carrier and thus short-circuit current density of a density CQD solar which can cell ultimately charge generation carrier generation and thus short-circuit current of cell a CQD solar which lead can to remarkable inimprovement power conversion efficiency of the efficiency cell. ultimately leadimprovement to remarkable in power conversion of the cell.

Figure 4. 4. The forfor PbS colloidal quantum dotdot (CQD) layer incorporated into Figure Thelight lightabsorption absorptionspectra spectra PbS colloidal quantum (CQD) layer incorporated different ITO ITO structures normalized to (a)toAM1.5G spectra and and (b) simulation light light source. The into different structures normalized (a) AM1.5G spectra (b) simulation source. absorption enhancement for both cavity andand pillar structures over thethe reference flatflat structure is The absorption enhancement for both cavity pillar structures over reference structure obvious especially at resonance wavelengths of 950 nm for both structures and 1080 nm for cavity is obvious especially at resonance wavelengths of 950 nm for both structures and 1080 arrays. A slight absorption loss by by ITO ITO layer layer was was also also observed, observed, as as shown shown in in Figure Figure 4b. 4b. arrays.

To clearly demonstrate the influence of nanocavity and nanopillar resonance effect on To clearly demonstrate the influence of nanocavity and nanopillar resonance effect on absorption absorption enhancement in CQD layer, the electric field distributions inside the PbS CQD layer with enhancement in CQD layer, the electric field distributions inside the PbS CQD layer with patterned patterned structures were investigated and are shown in Figure 5. The on resonance profiles for structures were investigated and are shown in Figure 5. The on resonance profiles for nanocavity and nanocavity and nanopillar structures are plotted at wavelength of 950 nm and the off resonant nanopillar structures are plotted at wavelength of 950 nm and the off resonant profile wavelength is profile wavelength is chosen at 1000 nm for both structures. The on resonance profiles for both chosen at 1000 nm for both structures. The on resonance profiles for both structures reveal various structures reveal various absorption hot spots for on-resonance wavelengths where as in the case of absorption hot spots for on-resonance wavelengths where as in the case of off resonance profiles, no hot off resonance profiles, no hot spot is visible at off-resonance wavelengths. It is obvious that the spot is visible at off-resonance wavelengths. It is obvious that the presence of high intensity E-field presence of high intensity E-field spots (hot spots) indicates the occurrence of strong absorption spots (hot spots) indicates the occurrence of strong absorption inside PbS CQD layer. In addition, the inside PbS CQD layer. In addition, the periodic pattern of the hot spots observed in the obtained periodic pattern of the hot spots observed in the obtained profiles discloses the type of resonance to profiles discloses the type of resonance to be the guided mode kind usually excited by periodic be the guided mode kind usually excited by periodic dielectric nanostructures [6]. The difference in dielectric nanostructures [6]. The difference in field distribution observed between on and off field distribution observed between on and off resonance profiles implies the impressive light trapping resonance profiles implies the impressive light trapping performance of the proposed structures at performance of the proposed structures at resonance wavelengths. This confirms the superiority of the resonance wavelengths. This confirms the superiority of the proposed structures for absorption proposed structures for absorption enhancement in CQD solar cells through resonant coupling of the enhancement in CQD solar cells through resonant coupling of the incident light with supported incident light with supported waveguide modes inside the CQD layer. waveguide modes inside the CQD layer.

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Figure 5. Simulated electric field distributions inside the PbS QDs layer with patterned structures. Figure 5. Simulated electric field distributions inside the PbS QDs layer with patterned structures. The hot hot spots spots present present at at resonance resonance wavelengths wavelengths (950 (950 nm nm for for both both structures) structures) with with high high field field intensity intensity The indicate strong strong absorption absorption inside inside PbS PbS CQD. CQD. No No hot hot spots spots are are observed observed at at off off resonance resonance wavelengths wavelengths indicate (1000 nm for both structures) suggesting the importance of resonant coupling of the incident into (1000 nm for both structures) suggesting the importance of resonant coupling of the incident into CQD CQD layer for significant absorption enhancement. layer for significant absorption enhancement.

3. Materials and Methods 3. Materials and Methods 3.1. Complementary Complementary Structure Structure Fabrication Fabrication 3.1. Self-assembly of of nanospheres nanospheres in in Si Si substrate substrate was was accomplished accomplished by by the the air/water air/water interface interface Self-assembly self-assembly process [23]. The etching of deposited nanospheres was done by using a 20 W O2 self-assembly process [23]. The etching of deposited nanospheres was done by using a 20 W O2 plasma plasma at oxygen 5 sccsmflow oxygen 1 min. E-beam evaporation was useddeposition. for Silver The deposition. The at 5 sccsm for 1flow min.for E-beam evaporation was used for Silver nanosphere nanosphere mask was removed through sonication in acetone for 10 min. PDMS nanopillars were mask was removed through sonication in acetone for 10 min. PDMS nanopillars were fabricated by fabricated by mixing silicone elastomer with curing agent184 from a Sylgard 184 Midland, kit (Dow MI, Corning, mixing silicone elastomer with curing agent from a Sylgard kit (Dow Corning, USA) Midland, USA) 10 wt was % ratio. mixture then degassed in aand desiccator for 30 min in 10 wt %MI, ratio. Thein mixture thenThe degassed in awas desiccator for 30 min was spin-coated onand the ˝ was spin-coated on the nanocavity structures at 200 rpm for 30 s. The resulting film was then cured nanocavity structures at 200 rpm for 30 s. The resulting film was then cured on a hot plate at 80 C for hotwhich plate at 80 °C for 2 off h after it was peeled off using a doctor blade. The images 2onh aafter it was peeled usingwhich a doctor blade. The SEM images were obtained by SEM a Ziess EVO were obtained by a Ziess EVO Scanning Electron Microscope (Carl Zeiss, Oberkochen, Germany). Scanning Electron Microscope (Carl Zeiss, Oberkochen, Germany). 3.2. Simulation Methods 3.2. The Lumerical LumericalFDTD FDTDSolutions Solutions software (Lumerical Solutions Vancouver, Canada) was The software (Lumerical Solutions Inc, Inc, Vancouver, Canada) was used used for simulations in this work. A period of 500 nm was chosen for both cavity and pillar for simulations in this work. A period of 500 nm was chosen for both cavity and pillar structures which structures which is same the diameter of for nanospheres used for pattern cavity depth is same as the diameter of as nanospheres used pattern generation. A cavitygeneration. depth and A pillar height of and pillar of 80 of nm and of 360 nmwas for both structures was foundvalue. to be The an optimum 80 nm andheight a diameter 360 nma diameter for both structures found to be an optimum PbS QD value.was Theconsidered PbS QD layer considered to be a quasi-bulk film (QDs were not layer to be awas quasi-bulk homogeneous film (QDshomogeneous were not considered as individual considered as individual particles) any(excluding voids andthe its thickness (excluding the nanostructure) particles) without any voids and itswithout thickness nanostructure) is chosen to be 300 nm, is chosen to be 300 nm, which is usually considered the maximum thickness forcollection. efficient which is usually considered the maximum thickness for efficient photo-generated carrier photo-generated carrier collection. The TiO2 layer was assumed to be 50 nm thick. Both gold and SiO2 glass layers are considered with infinite thickness for ease of modeling. The optimum thickness

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The TiO2 layer was assumed to be 50 nm thick. Both gold and SiO2 glass layers are considered with infinite thickness for ease of modeling. The optimum thickness of ITO layer (excluding the nanostructure) was found to be 500 nm. It should be noted here that the periodic grating structure layer consists of both ITO and PbS materials. The multi-coefficient fitting tool inside the simulation software was utilized to model optical constants of materials from available experimental data [24–27]. In the case of PbS QDs, the optical constants of commonly used QDs with a bandgap of 1.3 eV were used for simulations. The light source was considered a planewave source placed inside the substrate (SiO2 layer) to simplify the simulations. The wavelength range of 700–1200 nm was chosen as the simulation wavelength span because PbS CQD solar cells are currently in need of absorption enhancement mostly in this region of sunlight [27]. For directions perpendicular to the incident light propagation direction, Bloch boundary conditions and for directions parallel to the light propagation direction, perfectly matched layer (PML) boundary conditions were defined. The amount of absorption inside the CQD layer was measured by placing two power monitors at the either sides of the layer. This configuration can calculate the power flow entering and exiting the layer and thus the power absorbed inside the layer can be obtained by calculating the difference between the measurements from the two monitors. In the case of transmission measurements, all the shown powers are normalized with respect to the power from the light source. For absorption spectra, however, the absorbed powers are normalized to AM1.5G solar spectrum data available from NREL [28]. 4. Conclusions In this work, ITO nanocavity and nanopillar diffraction gratings are proposed as light trapping structures in CQD solar cells to realize absorption enhancement and power conversion efficiency improvement. A facile fabrication process is demonstratedfor patterning these periodic nanostructures over a large area which is a critical requirement of practical light trapping structures designed for photovoltaic devices. The simulation results show that both proposed periodic structures can effectively increase the light absorption in CQD layer of the solar cell throughout the near-infrared region where CQD solar cells typically exhibit weak light absorption. The overall absorption enhancement of 15.0% and 13.6% was achieved for nanocavity and nanopillar structures, respectively. It is verified that the two nanostructures are useful for enhancing the efficiency of photovoltaics as large-area, inexpensive light trapping structures. Abbreviations The following abbreviations are used in this manuscript: CQD ITO NSL RIE SEM PDMS FDTD

Colloidal Quantum Dot Indium-doped Tin Oxide Nano Sphere Lithography Reactive Ion Etching Scanning Electron Microscope Polydimethylsiloxane Finite Difference Time Domain

Acknowledgments: This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant, the University of Alberta Start-Up Fund, and the IC-IMPACTS Centres of Excellence. J.W. also gratelfully acknowledges financial support from China Scholarship Council. Author Contributions: J.W. and X.W. conceived and designed the study; J.W. and Q.X. performed the experiments; J.W. and S.M.M. performed and analyzed the simulations; All the authors contributed to the preparation of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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Numerical Study of Complementary Nanostructures for Light Trapping in Colloidal Quantum Dot Solar Cells.

We have investigated two complementary nanostructures, nanocavity and nanopillar arrays, for light absorption enhancement in depleted heterojunction c...
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