Journal of Microelectronics, Electronic Components and Materials Vol. 50, No. 1(2020), 25 – 33 https://doi.org/10.33180/InfMIDEM2020.103 Optimisation of Front Metallisation Pattern in Silicon Solar Cells for Annual Energy Yield Miha Kikelj, Benjamin Lipovšek, Marko Topic University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia Abstract: With photovoltaic installations reaching into the 1 TWp range and the demand for green electric energy on the rise, every fraction of a percent of increased solar cell efficiency counts, and would result in a substantial increase in the annual energy yield of the installed photovoltaic capacities. An optimisation of the front metallic grid would provide a relatively simple yet cost-effective boost to the solar cell efficiency. We employed a freely available 2.5D photovoltaic simulator to model shading and resistive losses of the front metallisation grid, and for further optimisation of the grid for annual energy yield regarding the irradiation distribution. We were, therefore, able to increase the effective efficiency of the simulated solar cells up to 1% over the whole year depending on the location. Keywords: Energy yield optimisation; Metallisation grid optimisation; PVMOS Optimizacija sprednje metalizacije silicijevih soncnih celic na nivoju letnega donosa energije Izvlecek: Maksimalna skupna inštalirana vršna moc soncnih elektrarn je zacela posegati v 1 TWp obmocje, popraševanje po cisti elektricni energiji pa je vedno vecje, zato je dobrodošlo tudi najmanjše povecanje izkoristka soncnih celic, ki pa bi, zaradi masovne uporabe, izdatno pripomoglo k letnem izplenu energije soncnih elektrarn. Optimizacija prednje metalizacije predstavlja enostavno in poceni možnost povecanja izkoristka soncnih celic. Z uporabo 2.5D fotovotaicnega simulatorja smo modelirali izgube zaradi upornosti in sencenja prednje metalizacije in optimizirali prednjo metalizacijo za cimvecji letni izplen energije. Na tak nacin nam je uspelo povecati efektivni izkoristek modeliranih celic za do 1% v celem letu, odvisno od modelirane lokacije. Kljucne besede: Optimizacija energijskega izplena, Optimizacija prednje metalizacije, PVMOS * Corresponding Author’s e-mail: miha.kikelj@fe.uni-lj.si 1 Introduction A booming market for photovoltaics (PV) has exceeded 400 GWp [1] of installed PV capacity in 2017 and the prognosis shows that it is to reach as much as 1 TWp of installed PV capacity by 2022/23 [2]. Operation at terawatt-scales gives us the ability to vastly increase the global energy production with even the smallest increase in the performance of each individual solar cell. As PV technologies are spreading to every corner of the globe, an idea of optimising solar cells to their expected operating conditions instead of standard test conditions (STC), has arisen, maximising their annual energy yield instead of promoting performance at STC, since they hardly ever occur during field operation. Since Silicon wafer based PV technologies still take up the majority of the global market [1], an optimisation of screen printed front metallisation of top contacted silicon solar cells, could lead to a vast energy yield in­crease with virtually no additional production costs [3]. Optimisation of front metallic grids can be approached analytically as performed by A. R. Burgers [4], and then applied to a STC or energy yield optimisation as per­formed by A.R. Burgers et al. [3]. But in order to be able to accurately evaluate the effects of more complex front metallisation grids, to optimise them and to op­timise them with respect to arbitrary operating condi­tions and annual energy yield, more elaborate numeri­cal tools need to be employed. In our contribution we evaluate the use of PhotoVoltaic Module Simulator (PVMOS) [5] as a tool to accurately simulate the effects of front metallisation shading and resistive losses on the maximum power point of a sili­con solar cell. On that basis we will further optimise the metallisation grid at different irradiation levels, and fi­nally try to estimate the impact on the annual energy yield. With that knowledge we will undertake the chal­lenge of optimising a solar cell metallisation according to yearly irradiation distributions at different locations and assess the impact on estimated annual energy yield compared to STC cell optimisation. 2 Modelling PhotoVoltaic Module Simulator (PVMOS) developed by Bart Pieters [5] is a 2.5D quasi-SPICE simulator de­signed to efficiently simulate photovoltaic devices. It allows for creation of an accurate device model in two dimensions and the third dimension is simulated by stacking and interconnecting 2D layers. Sheet resist­ances are defined for each layer, or more accurately each segment of a layer, allowing for simulation of pat­terned structures. The connection between planar pat­terned layers could either be resistive, a p-n junction (described by a one or two-diode model) or it could implement an arbitrary J-V characteristic. A simplified part of a 4-layer (ribbon, front metallisation, emitter, and bulk with bottom metallisation) silicon solar cell model could therefore be represented as shown in Fig. 1, where vertical resistive connections are omitted for simplicity. A detailed explanation of the PVMOS simula­tor is available in [6]. Figure 1: Simplified PVMOS model of a small section of a 3D cell After the simulation nodal voltages and currents along all three axes become available along with the cumula­tive I-V characteristic, which allows for evaluation of the simulated structure on the device level as well as on a local, more detailed level. In this work PVMOS will be used as a tool to model shading and resistive losses of the front metallisation pattern. We built a set of MATLAB scripts and tools around the PVMOS simulator allowing for automatic geometry generation, geometry and solar cell parameter sweeps, and energy yield estimation, since a normal simula­tion procedure would require more than 10 individual manual steps. 3 Results and discussion 3.1 Analysis of front metallisation losses According to literature [7] losses associated with the front metallisation can be divided into two categories, namely shading and resistive losses, whose individual effects on the I-V curve are depicted in Fig. 2. One can see that shading losses mainly affect the short circuit current, while resistive losses decrease the fill-factor of the cell. In the following subchapters fractional power losses of individual origin will be evaluated through PVMOS simulations and the trends will be compared to analytical expressions from previous work. All symbols used are defined in the Appendix. Figure 2: Effects of shading and resistive losses on an I-V curve. 3.1.1 Fractional power loss Since different cell configurations are evaluated, pro­ducing a variety of power-voltage curves and therefore different maximum power points (MPP), it is necessary to employ a measure of power loss that is comparable between configurations. The measure - fractional pow­er loss p [7] is defined as the ratio between lost power Ploss and power in the MPP PMPP of an ideal, unshaded cell as shown in equation (1). (1) 3.1.2 Shading losses Cell’s self-shading losses are mainly caused by direct finger and busbar shading and are generally linearly proportional to the area of the shading elements. Busbars From definition [7] busbar shading losses psb are pro­portional to the ratio of the busbar width WB and the spacing between them B, as it is evident from equa­tion (2). Fig. 3 shows shading loss obtained by PVMOS simulations and as one would expect it exhibits a linear relation. (2) Figure 3: Busbar shading loss in correlation with the number of busbars and their width. Figure 4: Finger shading loss in correlation with the number of fingers and their width. Fingers Finger shading losses are by definition [7] quite similar to the busbar case. The losses are proportional to the ratio of the finger width and their spac­ing . The relation is show in equation (3) and PVMOS simulation results in Fig. 4. (3) 3.1.3 Resistive losses From intuition resistive losses should decrease with in­creasing busbar width and with an increasing number of busbars. Resistive losses are defined according to [7] in equation (4), where is a factor related to tapering of the busbar (4 for linear tapering and 3 for uniform busbar width). (4) As we can see from Fig. 5 resistive losses do indeed decrease with increasing busbar width in a 1/x fash­ion as it is also evident from equation (4). One can also observe that a decrease in resistive losses is gradually decreasing with an increasing busbar number, which is also in accordance with equation (4). Figure 5: Busbar resistive loss in correlation the num­ber of busbars and their width. Fingers Resistive losses due to finger metallisation are actually a combined effect of resistive losses in the top layer of the p-n junction due to lateral current flow and actual resistive losses due to current flow along the fingers. Since one depends on the other we have not separated their effect because we cannot directly influence the emitter resistance with the design of the front metal­lisation. Combined equation for resistive losses due to front contact fingers prf [7] is therefore given in equa­tion (5). Parameter m relates to the tapering of the fin­gers in the same fashion as before. (5) Given the parameters of the cell one could establish which of the two parts will prevail and determine the characteristics of the implied resistive losses. Fig. 6 gives the results of finger resistive loss obtained via PVMOS simulations. The fluctuations seen in the results are probably a consequence of an inappropriate spa­tial resolution causing a discrepancy between the real and the simulated finger widths. Those points would require a higher resolution for simulation but would re­sult in longer simulation times which were out of scope for this contribution. Figure 6: Finger resistive loss in correlation with the number of fingers and their width. 3.1.4 Combined loss effect A solar cell generally exhibits a combination of the aforementioned loss effects. Their interplay is deter­mined by the chosen metallisation geometry. It can be seen from Figs. 7 and 8 that for some chosen param­eters there exists an optimal solution or combination of other free parameters minimising the loss. Figs. 7 and 8 respectively show loss change trends with different busbar and finger configurations. Figure 7: Influence of busbars on the cumulative loss­es. Number of fingers is fixed to 60 and their width to 100 µm. Figure 8: Influence of fingers on the cumulative losses. Number of busbars is fixed to 3 and their width to 2 mm. 3.2 Optimisation of front metallisation pattern for STC conditions Given the results from the previous sections, one could pose a question whether there exists an optimal metal­lisation geometry, that reduces shading and resist­ance losses to a minimum. As mentioned before one can only change (given the H-grid metallisation) the metallisation pattern in terms of busbar width WB, bus­bar number NB, finger width WF and number of fingers NF. We could, if necessary, explore other grid patterns, finger and busbar tapering for shading loss reduction and multilevel grid design, but in the scope of this work we have limited ourselves to the most common, basic, busbar-finger H-grid. We chose to make a sweep of possible different configura­tions of number of busbars (2-6) and fingers (45-80) under STC conditions. The simulations provided us with a set of I-V curves from which we were able to calculate maximum power points for every configuration as shown in Fig. 9. Figure 9: MPP dependence on finger and busbar num­ber for 100 µm/2 mm configuration. We have chosen a configuration with the highest MPP to be the optimal front metallisation grid at STC. With the chosen busbar width WB of 2 mm and chosen finger width of 100 µm, the optimal configuration turned out to be 4/60 (busbars/fingers). Since modern technolo­gies allow for finger widths under 100 µm we also re­peated our simulations at 50 µm finger width. The re­sults are shown in Fig. 10. Figure 10: MPP dependence on finger and busbar number for 50 µm/2 mm configuration. One can see, that MPP points follow the same trends as before with broader fingers. The kink at 80 fingers is due to bad resolution of the structuring image. Be­cause of the sampling, a resolution that produced fin­gers exactly 50 µm wide, missed some of the fingers. Increasing the resolution by a small fraction seemed to lessen the error because all fingers were included. But with increasing resolution fingers became narrow­er than 50 µm, which is why we think the error is still present. An accurate result would require doubling or tripling the resolution, which we could not afford in the scope of this work. Still we could deduce that the opti­mum lies somewhere around 90 fingers and 4 busbars for the 50 µm fingers. Fig. 11 shows comparison of I-V and power-voltage curves of both optimal 100 m/2mm and 50 µm/2mm configurations. One can observe, that the MPP of the 50 µm configuration is slightly higher mostly due to de­creased shading and therefore increased short circuit current, which coincides with the fact that between the cases finger width halved while the number of fingers increased by slightly less than a factor of 2. Figure 11: Difference between I-V and P-V curves for optimal 100 µm/2 mm and 50 µm/ 2mm configura­tions. Because of the required high resolution for an accurate simulation of 50 µm wide fingers and consequentially long simulation times, we could not afford to optimise the energy yield with the 50 µm/2mm grid, since we could not trust the calculation of the MPP at low reso­lutions. We therefore chose the 100 µm/2mm grid for further calculations. 3.3 Optimisation of front metallisation for yearly energy yield Using the same method, that we have used to optimize the front metallisation for STC, we approached optimi­sation for yearly yield. To further reduce the number of possible simulation combinations and decrease simu­lation time, we have fixed the WB to 2 mm and WF to 100 µm in the following simulation cases. The same process could be applied to any given grid geometry. We have chosen three inherently different places for evaluation, since yearly irradiation profiles [8] for Sa­hara Desert, Ljubljana and Stockholm should vary sig­nificantly. Fig. 12 shows annual irradiation (flat oriented surface, direct illumination) vs. irradiation level for all three places. Figure 12: Annual irradiation distribution for Ljubljana, Stockholm and Sahara. Because annual irradiation peaks lie at different irra­diation levels and distinct metallisation patterns per­form differently under various irradiation levels, we presumed that there exists a metallisation pattern that would maximise the annual energy yield. The optimal metallisation should favour irradiation level with high­est yearly irradiation, but should also provide best all-year-round performance. With respect to that one can assume that the optimal metallisation geometry of for e.g. Sahara Desert should best match the optimal one at STC, since irradiation peak is near 1000 W/m2. We performed I-V curve sweeps for different number of busbars and different number of fingers, all at different irradiation levels up to 1000 W/m2 in 100 W/m2 steps. From a pool of simulated I-V curves we calculated maxi­mum power points for each geometry and each irradia­tion level. With the aforementioned data we were able to estimate annual energy yields for each of the select­ed locations and each metallisation geometry. At each irradiation level, we took into account the efficiency of the metallisation grid and annual irradiation at the se­lected location, which gave us expected energy yield at each irradiation level. Summation of those partial energy yields gave us an estimate of the annual energy yield. In the end we chose a geometry, that produced the highest annual energy yield. Energy generation profiles are given in Fig. 13, 14 and 15 for each of the lo­cations respectively. By optimising the front metallisa­tion, we were able to increase the annual energy yield by up to approximately 1% (in the case of Stockholm), for a flat oriented surface and direct illumination. Figure 13: Sahara – Annual energy yield at different ir­radiation levels for STC optimal grid (blue) and annual irradiation level energy yield gains (AEYG) for an opti­mal grid (orange). Figure 14: Ljubljana – Annual energy yield at different irradiation levels for STC optimal grid (blue) and annual irradiation level energy yield gains (AEYG) for an opti­mal grid (orange). As it can be seen from Fig. 13, 14 and 15 optimal metal­lisation geometries allow for a performance increase over lower irradiation levels and a slight decrease at higher irradiation levels. Nevertheless, the configura­tion allows for a greater annual energy yield. Table 1 shows differences between optimal geometries for STC and optimal geometries for annual energy yield (AEY) and effective efficiencies. If we take yearly irradiation into consideration, we can see, that places with higher annual irradiation or more precisely places with an irradiation peak at higher irra­diation levels require a denser front metallisation grid for a better effective efficiency. From a theoretical point of view higher irradiation levels allow for higher opti­cally generated currents, therefore increasing resistive losses and thus requiring front metallisation patters with lower overall resistance, resulting in a higher num­ber of fingers. On the other hand, current densities at lower irradiation levels are substantially smaller there­fore resistive losses play a less important role and front metallisation is designed in such fashion that it mini­mises shading loss, while still providing a low enough resistance for current collection, resulting in a lower overall number of fingers. Shown in Fig. 16 and 17 are shading and resistive losses of optimal metallisation grids for each of the locations at different irradiation levels. It is clearly shown, that higher overall irradiation calls for denser metallisation grids and therefore higher shading loss (e.g. Sahara Desert) and lower overall ir­radiation needs a metallisation pattern that mitigates shading loss therefore increasing resistive losses (e.g. Stockholm). Ljubljana as a place of average latitude is therefore an average between two extremes with aver­age shading and resistive losses. Figure 16: Shading losses at different irradiation levels for an optimal, location specific grid. Figure 17: Resistive losses at different irradiation levels for an optimal, location specific grid. 4 Conclusion We have evaluated the effects on losses in MPP due to front metallisation. We have established that for each irradiation level there exists an optimal busbar and finger geometry. With that in mind we have optimised metallisation patterns for either STC or annual energy yield. With the aforementioned optimisation we have achieved an annual energy yield increase of up to 1% in comparison with STC case. Although our study was limited to only three places, 10 irradiation levels on a horizontal plane and that we have only optimised for finger and busbar numbers, we have still established a workflow with PVMOS as a core com­ponent, for an estimation of annual energy yield and its optimisation according to the front metallisation. With an established workflow we could also extend our optimisation to busbar and finger width, more irradia­tion level bins or different metallisation patterns (e.g. tapered fingers and busbars, other for example “organ­ic” metallisation topologies [9]). The model could also be expanded to include thermal modelling, irradiation at different orientations and inclination angles, and dif­fuse light therefore providing an extensive tool for an­nual energy yield estimation. 5 Acknowledgements M. Kikelj acknowledges the Slovenian Research Agency for funding his research activities (program P2-0197), results of which were partially presented in this paper. 6 Conflict of Interest The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the deci­sion to publish the results. 7 References 1. ‘Fraunhofer ISE Photovoltaics Report’, Mar. 2019. 2. N. M. Haegel et al., ‘Terawatt-scale photovoltaics: Transform global energy’, Science, vol. 364, no. 6443, pp. 836-838, may 2019. https://doi.org/10.1126/science.aaw1845 3. Burgers, A. R., and J. A. Eikelboom., ‘Optimizing metallization patterns for yearly yield [solar cell fab­rication].’, Conference Record of the Twenty Sixth IEEE Photovoltaic Specialist conference-1997., IEEE, 1997. https://doi.org/10.1109/PVSC.1997.654068 4. A. R. Burgers, ‘How to design optimal metalliza­tion patterns for solar cells.’, Progress in Photovol­taics: Research and applications, 7.6, pp. 457-461, 1999 https://doi.org/10.1002/(SICI)1099-159X(199911/12)7:6<457::AID-PIP278>3.0.CO;2-U 5. B. E. Pieters, PVMOS [online] Available: https://github.com/IEK-5. 6. Pieters, Bart E. “A free and open source finite-dif­ference simulation tool for solar modules.” 2014 IEEE 40th Photovoltaic Specialist Conference (PVSC). IEEE, 2014. https://doi.org/10.1109/PVSC.2014.6925173 7. 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Topic, Marko, Kristijan Brecl, and James Sites. “Ef­fective efficiency of PV modules under field con­ditions.” Progress in Photovoltaics: Research and Applications 15.1 (2007): 19-26. https://doi.org/10.1002/pip.717 8 Appendix Symbol Explanation Rf Fingers’ sheet resistance Re Emitter’s sheet resistance D1,2 First and second diode Rb Structured sheet resistance of the bulk p Fractional power loss Ploss Absolute power loss PMPP Power in the MPP Pideal Power of an ideal unshaded cell Plossy Power of the lossy cell psb Fractional busbar shading power loss psf Fractional finger shading power loss prb Fractional busbar resistive power loss prf Fractional finger resistive power loss Wc Width of the cell Hc Height of the cell WB Width of the busbars NB Number of busbars A Same as height of the cell in this case B Half the spacing between busbars WF Width of the fingers NF Number of fingers S Spacing of fingers m Tapering factor .b Resistance of the busbars .f Resistance of the fingers JMPP Current density in MPP VMPP Voltage in MPP Figure: Definitions of cell’s physical dimensions. Arrived: 19. 11. 2019 Accepted: 31. 01. 2020 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 Figure 15: Stockholm – Annual energy yield at differ­ent irradiation levels for STC optimal grid (blue) and an­nual irradiation level energy yield gains (AEYG) for an optimal grid (orange). Table 1: STC and annual energy yield optimised geometry parameters, their expected annual energy yields and ef­fective efficiencies. Optimised for STC Optimised for AEY NB NF AEY .eff NB NF AEY .eff [kWh/m2] [%] [kWh/m2] [%] Sahara 4 60 419.02 17.17 3 60 419.62 17.20 Ljubljana 4 60 210.19 16.82 3 50 211.51 16.92 Stockholm 4 60 153.22 16.65 3 45 154.65 16.81 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 M. Kikelj et al.; Informacije Midem, Vol. 50, No. 1(2020), 25 – 33 Copyright © 2020 by the Authors. This is an open access article dis­tributed under the Creative Com­mons Attribution (CC BY) License (https://creativecom­mons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.