Enhancing energy absorption in quantum dot solar cells via periodic light-trapping microstructures

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1 Journal of Optics PAPER Enhancing energy absorption in quantum dot solar cells via periodic light-trapping microstructures To cite this article: Christopher Wayne Miller et al J. Opt. 00 Manuscript version: Accepted Manuscript Accepted Manuscript is the version of the article accepted for publication including all changes made as a result of the peer review process, and which may also include the addition to the article by IOP Publishing of a header, an article ID, a cover sheet and/or an Accepted Manuscript watermark, but excluding any other editing, typesetting or other changes made by IOP Publishing and/or its licensors This Accepted Manuscript is IOP Publishing Ltd. During the embargo period (the month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND.0 licence after the month embargo period. After the embargo period, everyone is permitted to use copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permissions will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. View the article online for updates and enhancements. This content was downloaded from IP address... on /0/ at :0

2 Page of 0 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R 0 Enhancing Energy Absorption in Quantum Dot Solar Cells via Periodic Light-trapping Microstructures Christopher Wayne Miller, Yulan Fu, Rene Lopez Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC, Abstract: Colloidal quantum dot (CQD) solar cells prove to be promising devices for optoelectronic applications due to their tunable absorption range, deep infrared absorption capabilities, and straightforward processability. However, there remains a need to further enhance their device performance -particularly when one has to adhere to strict physical limitations on their physical structure. Here we present a three-dimensional numerical model of CQD solar cells in COMSOL Multiphysics based on the finite element method. With this model we have simulated the optical characteristics of several CQD solar cells across varying photonic structures and physical parameters to investigate how distinct photonic structures may enhance the light absorption and current output of CQD solar cells using identical physical parameters. Of the many cells simulated, one notable model increased the predicted current in the active layer PbS by. % as compared to a flat solar cell with identical physical parameters, and produced a current of. ma/cm by implementing a cross-shaped photonic structure built on top of a flat substrate of glass and ITO. This cross-shaped model serves as a key example of how unique photonic structures can be implemented to further enhance light absorption. Introduction: PbS colloidal quantum dot (CQD) solar cells have attracted great attention as next generation solar cells in recent years due to their tunable energy band gap, their simple solutionprocessability (potentially leading to low cost construction), size-dependent optical and electrical properties, and their deep infrared spectral response which extends up to 0 nm light wavelenght depending on the nanocrystal size[-]. The ability of CQD solar cells to further enhance the energy conversion efficiency beyond that of traditional Shockley and Queisser limits for Si based solar cells has also generated interest in their potential applications in past years []. Their wide-spread absorption range is especially important since % of the sun s energy is radiated in IR wavelengths beyond 00 nm; However, given that their charge harvesting physics is hampered by abundant traps, typical CQD cells exhibit limited operational thicknesses to less than 0 nm [0,]. As a consequence, one cannot simply continue to thicken the cell to thicknesses needed (~ µm) to absorb all those IR photons. There is indeed an important need to find feasible ways of improving cell efficiencies by enhancing light absorption while simultaneously observing limited carrier transport lengths. Furthermore, while increasing CQD efficiency is entirely possible within simulations, being able to manufacture a solar cell within the confines of physical constraints is also a priority, thus a simple geometrical pattern ought to be evaluated for this goal. In previous work Fu et al. showed that by employing a grating type two-dimensional (D) photonic structure, one can overcome the limited carrier transport in CQDs and enhance the light absorption of the CQD solar cell. The numerical model predicted a power conversion efficiency (PCE) as high as.% with a short circuit current density of. ma/cm, a value that is nearly. times larger than that of conventional flat solar cell models with identical physical parameters (PbS thickness was 0 nm). For that work the electronic parameters were taken from a recent champion experimental cell as reported. The full optoelectronic model showed that as long as at no point the thickness of the PbS QD layer exceed the effective transport length, the pure optical absorption would translate almost totally to short circuit current. Experimentally, sub-wavelength sized structured substrates for bottom-illuminated solar cells have been demonstrated and shown broadband absorption enhancement while maintaining short collection distances for photogenerated carriers []. Patterned devices with larger length scale have

3 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R Page of 0 0 also been presented and have shown a high PCE []. In this paper, we analyze a diverse family of periodic CQD solar cells built with distinct D and D photonic structures to determine whether this light trapping strategy could further enhance light absorption within the active layers with more stringent transport limitations, i.e. not those of champion devices, but of more common transport length parameters of today s laboratory cells (< 0 nm) and likely what one would expect in a large scale cell manufacturing realization in the future. The models were constructed utilizing a three-dimensional numerical model in COMSOL Multiphysics. They incorporate all complete realistic optical physics via finite element time domain calculations. This work focused on highlighting how unique photonic structures may improve solar cell light absorption while maintaining identical physical parameters and transport length limitations. Specifically, we explored and compared the optical characteristics of models using a cross-shaped D photonic structure, grating shaped D photonic structure, and conventional flat structure. For each photonic structure we initially varied the PbS layer thickness using distinct values of nm, 00 nm, 0 nm, and 0 nm, thus setting a maximum allowed transport length. Then, for each structure s PbS values, we set the in-plane period of the structure to 0 nm and then varied the value of the structure height from 00 nm to 00 nm in discrete steps. Subsequently, for each set of models we calculated the PbS layer current output and absorption spectra in the ITO, PbS, and Au layers. For the thinnest PbS layer, our models predict a.% increase in PbS current output as compared to a flat type structure utilizing identical physical parameters at a value of. ma/cm. Although our current model structure has yet to be optimized they all employ simple square shapes it serves as a key example to illustrate how different and distinct photonic structures can further enhance light absorption within CQD solar cells adhering to physical limitations unrelated to the optics. In addition to this, our results provide insight as to how device performance changes in accordance with these photonic structures across different layer thicknesses; where diminishing returns start to make clear higher structure aspect ratios become unnecessary. This in turn helps establish the minimum and maximum physical parameters that enhance or limit improved device performance. In contrast to our earlier reports[,] which have been restricted to a particular D solar device structure, employed full optoelectronic calculations, and optimized for all the employed layers; this work includes a large number of D and D device geometries that are modeled only at the optical level. We chose to do not explore the electronic transport physical issues in these patterned structures due to the inherit complexity and computational costs associated with implementing them at the needed detail in D simulations. Thus, we want to stress that given this restriction, the results reported here are only valid assuming there are not charge transport losses for the PbS layer, a good assumption for the thin thicknesses explored here. However, by focusing in the optical absorption and limiting the number of parameters subject to variation to the most salient ones, this work is able to explore a wider range of device geometrical shapes and aspect ratios. It is also important to point out that by opting out of exhaustive optimization, the highest performing device identified in this work was slightly lower in projected photocurrent to the one described in reference [], but nevertheless the trends found here are more insightful regarding the sensitivity of the devices performance to their most prominent geometrical features. Theoretical Background: To simulate our solar cell models we applied a D numerical model based on the finite element method using the commercial simulation software COMSOL Multiphysics. To obtain accurate calculations of the optical behavior of our device, we applied the photonic characteristics of CQD quantum junction solar cells to our numerical model [,]. As noted above, given that we were primarily concerned with the optical characteristics of our model, we chose not to calculate the electrical and carrier transport mechanisms. To find the optical field distribution within the periodic solar cells we

4 Page of 0 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R 0 applied Maxwell s equations to a unit cell surrounded by Floquet-Bloch boundaries []. As for the light illumination source, we used a normal incident monochromatic plane wave and performed a wavelength sweep across the sun s input energy from 0 nm to 00 nm wavelengths. The input power distribution was in accordance with the AM.G solar reference spectrum and the cell response to both s and p polarizations of light were averaged for each wavelength. With these conditions in place, we were able to obtain the local wavelength dependent carrier generation profiles for our models by using the equation below: g ( x, y, ) P( x, y, ) / hc with P(x, y, λ) representing the light intensity within the active layer volume in terms of position (x, y) and λ the light wavelength. h represents the Planck s constant, c stands for the speed of light in vacuum, α = πκ/λ is the absorption coefficient at that given wavelength, and κ represents the imaginary component of the frequency dependent complex refractive index. With this equation we can easily calculate the total generation rate distribution G(x, y) by integrating g(x, y, λ) over λ for our absorption spectral band. With the total generation and the AM.G solar reference spectrum, we can then calculate the charge current densities the device would generate assuming each photon would produce an electron-hole pair that is collected with 00% efficiency. All optical constants for the materials involved were taken from reference []. In order to gain a better understanding of the CQD solar cells behavior with different photonic structures, we built several different cell models with varying geometric parameter values. These parameters allowed us to freely alter namely the thickness of the PbS layers, and the height and width of our modelled device structures. It was through this process that we were able to develop the models presented here. a)

5 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R Page of 0 0 b) c) Fig.. (a) Schematic diagram of flat unit solar cell. (b) Schematic diagram of grating unit cell. (c) Schematic diagram of cross-shaped unit cell. Results & Discussion: We modeled each solar cell structure via a simple architecture with layers of ITO, TiO, PbS, MoO, and Au on a glass substrate. In the case of our flat unit cell models, the materials were stacked on top of each other in the order seen in Figure (a). The grating type cell structure is constructed in the same manner as described in reference [] and it is shown in Figure (b). Lastly, we constructed our cross-shaped model by conformally placing TiO, PbS, MoO, and Au on top of a symmetric crossshaped structure of air placed on top of a flat substrate (Figure (c)). The height of the inner air core of the cell controls the overall structure height.

6 Page of 0 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R 0 The ITO, TiO, MoO, and Au parameters were set to constant values that worked particularly well with the flat model (flat ITO layer of nm, a shaped TiO layer of nm, a shaped MoO layer of nm, and a shaped Au layer of nm). This meant that only the PbS layer thicknesses and structure height varied across our models when examining the effect of distinct photonic structures. In all instances the substrate is composed of ITO on glass of nm and semi-infinite thickness respectively. Naturally, in all cases light is incident from the glass side. From our simulations we verified that unique values for PbS thickness and structure height exist that maximize the total useful light absorption. In Figure (a), the current extracted from a PbS layer of 00 nm is plotted against the structure height for both the grating and cross type models. The figure shows that across varying structure heights, the cross models current from the PbS layer is continuously higher than grating models using the identical physical parameters. Figure (b) plots the overall percent increase in PbS current as compared to an equivalent flat model for the cross and grating structures as a function of the structure height for the devices from Figure (a) using a PbS layer thickness of 00 nm. This increase is to be expected as the cross structure is effectively packing more PbS volume per unit area vs. the grating, and both relative to the flat reference cell. However, it is remarkable that the effectiveness of an approach such as this peaks relatively quickly with structure height. At a structure height value of 0 nm, the cross-structure device shows its highest percent increase in PbS current for the data set at a value of. %. This percent increase corresponds to a current of. ma/cm for the cross model. Figure (c) shows the absorption spectrum for this particular model structure. We can observe that the cross type model has noticeably higher IR absorption than its grating equivalent, and both show a vast improvement over a flat model with identical physical parameters. The trend is reversed in the blue side of the spectrum, as the extra ITO needed to coat the patterned structures decreases the useful blue light that is captured by the PbS. These trends, albeit less dramatic in magnitude, were found to be repeated for thinner PbS layers. Figure (d) shows the absorption spectrum for a model with a nm thickness PbS layer with a structure height of 00 nm. Similar to the PbS 00 nm thickness and 0 nm structure height model, the D cross model generally performed better than all of its grating equivalents with its highest recorded percent increase of. %. The absorption spectrum of this model illustrates an increase in light absorption in its PbS layer compared to its grating and flat equivalents.

7 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R Page of 0 0 Fig.. (a) Current extracted from 00 nm PbS layer for flat, grating, and cross models and (b) percent increase in 00 nm PbS current in cross model compared to flat model as a function of cell structure height. (c) Absorption spectrum in 00 nm PbS layer with 0 nm structure height and (d) absorption spectrum in nm PbS layer with 00 nm structure height as a function of wavelength for flat, grating, and cross models. Figure (a) shows the current extracted from a 0 nm PbS layer plotted against the structure height for flat, grating, and cross models. In contrast to the trend observed in Figure (a), there is a decline in the improvement of extracted current when using a thicker PbS. At structure height values of 00 nm and 00 nm, the cross model actually performed worse than its equivalent grating models. For example, for the cross model with a structure height of 00 nm, the percent difference in PbS current compared to a flat model was actually.0 % less than its grating equivalent. Furthermore, when the cross model was able to perform slightly better than its grating equivalent, its percent increase over the grating model was only about.0 %; the actual percent increase compared to its flat equivalent was.0 % as shown in Figure (b). In contrast to this behavior, the best performing model from the 00 nm PbS models showed significantly higher performance than both its flat and grating equivalents. To further illustrate this point, simulations were performed with grating and cross structures with 0 nm PbS as shown in Figures (c) and (d). For these models, all of the cross models failed to generate a current that was at least equal to that of the current from their grating equivalents. Instead, they consistently generated a percent increase less than that of their grating equivalents. Overall the models with a thinner PbS layer were consistent improvements over their grating equivalents unlike the inconsistent and rather detrimental behavior shown by our thicker PbS models.

8 Page of 0 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R 0 Fig.. (a) Current extracted from 0 nm PbS layer for flat, grating, and cross models and (b) percent increase in 0 nm PbS current in cross model compared to flat model as a function of cell structure height. (c) Current extracted from 0 nm PbS layer for flat, grating, and cross models and (d) percent increase in 0 nm PbS current in cross model compared to flat model as a function of cell structure height. For further insight into why the grating model is able to overall outperform its cross model equivalent for thicker PbS values, the absorption spectra for each model were also shown in Figure. Figure (a) shows the total power density absorbed in the PbS 0 nm layer for the grating and cross models. At the structure height values of 00 nm and 00 nm, where the grating models outperformed their cross equivalents, it can be seen that the grating models had significantly higher absorption in their PbS layers. However, the question still remains: why is the absorption in the PbS layers enhanced for these particular models? The answer seems to be in the ITO losses. Figures (b) and (c) show the absorption spectra within the ITO layer for two models of PbS 0 nm thickness with structure heights of 00 nm and 0 nm, respectively. For the 00 nm structure height model, the cross-structure absorbs slightly more light in its ITO layer than its grating equivalent. In this case, the cross-structure s ITO total power density was. W/m, while the grating model s was calculated to be. W/m. On the other hand, with a 0 nm structure height, the cross-structure absorbs less light in its ITO layer than its grating equivalent with values of. W/m and. W/m respectively. The D device cross structure with

9 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R Page of nm PbS thickness and 00 nm structure height performed worse than its grating equivalent as evidenced by its decrease in extracted PbS current; while on the other hand, the 0 nm PbS thickness and 0 nm structure height cross model performed slightly better than its grating equivalent by enhancing both light absorption and the extracted current. As for the 0 nm PbS thickness models, we observed the same issue: decreased performance in the cross-structure could be attributed to increased light absorption solely in the ITO layer for that model. Light absorption by the ITO layer happens at the expense of light absorption by the PbS layer, and only light absorption by the latter results in useful current being extracted. These simulated results could be a guide for the solar cell device fabrication, especially for the patterned devices with nanoscale optical structures which is relatively easier to fabricate in experiment. If one was interested in the ideal type of cell structure within predetermined size constraints, this work aims to elucidate the ideal type of cells to consider for this specific purpose. For a thin PbS layer of roughly 00 nm, our work suggests that the cross-shaped models are able to noticeably outperform their grating counterparts that are implementing the same physical parameters. However, for larger PbS values, our work also illustrates that the grating shaped devices show slightly better performance than their crossshaped counterparts.

10 Page of 0 AUTHOR SUBMITTED MANUSCRIPT - JOPT-0.R 0 Fig.. (a) Total power density absorbed in 0 nm PbS layer for grating and cross models as a function of cell structure height. (b) Absorption spectrum in nm ITO layer for 0 nm PbS with 00 nm structure height and (c) Absorption spectrum in nm ITO layer for 0 nm PbS layer with 0 nm structure height as a function of wavelength. Conclusion: A series of D models based on the finite element method have been developed and tested across several CQD solar cells with varying photonic structures and physical parameters. The optical characteristics of the solar cells were calculated across the various CQD solar cells simulated. Of the many cells simulated, one notable model increased the light absorption in the active layer PbS by.% as compared to a flat solar cell with identical physical parameters by implementing a cross-shaped photonic structure built on top of a flat substrate of glass and ITO. This cross-shaped model is capable of further enhancing the light absorption within the PbS layer of CQD solar cells as compared to grating models and flat models with identical physical parameters and serves as a key example of how unique photonic structures can be implemented to further enhance light absorption. It this clear though that the enhancement via this strategy limits itself quickly and peak performances are reached at relatively low aspect ratio device structures. Demonstration of devices with lengths scales similar to those evaluated here were recently shown in reference []. Nanofabrication with the controlled length scales and optically negligible roughness can be achieved to match the dimensions and optical response depicted here; however, achieving true layer conformal deposition quality in terms of maintaining adequate charge transport characteristics to realize these predictions remains significantly more challenging [-]. Acknowledgement: This material is based upon work funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award Number DE-SC000. We also acknowledge support by Research Corporation for the Science Advancement #. References:. Kim J K, Voznyy O, Zhitomirsky D and Sargent E H th anniversary article: Colloidal quantum dot materials and devices: A quarter-century of advances Adv. Mater. () 0. Bawendi M G, Steigerwald M L and Brus L E 0 The quantum mechanics of larger semiconductorclusters ( quantum dots ) Annu. Rev. Phys. Chem ()

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