Screen pattern simulation for an improved front‐side Ag‐electrode metallization of Si‐solar cells

Flatbed screen printing proves to be the dominant metallization approach for mass production of silicon (Si)‐solar cells because of its robust and cost‐effective production capability. However, the ongoing demand of the PV industry to further decrease the width of printed Ag‐electrodes (contact fingers) requires new optimizations. This study presents the latest results on Si‐solar cell metallization using fine‐line screens down to screen opening widths of wn = 15 μm. The best experimental group achieved a record finger geometry with a mean finger width of wf = 19 μm and a mean finger height of hf = 18 μm. Furthermore, solar cell performance using a front‐side grid with a screen opening width of wn = 24 μm is investigated, reporting cell efficiencies up to 22.1% for Passivated Emitter and Rear Contact (PERC) solar cells. Finally, a novel screen pattern simulation is presented, revealing a correlation between the measured lateral finger resistance and the novel dimensionless parameter screen utility index (SUI). It describes the ratio between the average size of individual openings defined by the screen mesh angle and the chosen underlying mesh type. For SUI < 1, the printing result will strongly depend on the screen configuration, whereas for values of SUI > 1, the impact of the screen on the overall printability diminishes.


| INTRODUCTION
The metallization process of silicon (Si)-solar cells in today's market is dominated by flatbed screen printing because of its cost-effective production capabilities and its numerous optimizations throughout the years. Within the last decade, flatbed screen printing has made tremendous progress in reducing the printed width of the electrodes (contact fingers) from approx. 120-100 μm in 2005 to published results of 26 μm in 2019. [1][2][3] Figure 1 shows the evolution of published results for printed finger widths on a scientific level. The International Technology Roadmap for Photovoltaic (ITRPV) prediction from 2011 is in excellent agreement with this trend for achievable finger width on an industrial level. 4 The current ITRPV from 2019 is predicting that the pace at which the reduction is likely to continue will slow down in the upcoming years. 5 However, recent results on scientific scale do outperform this prediction significantly, indicating that the old reduction rate can be continued up to this date. However, when optimizing the finger geometry, one must always consider the impact on the solar cell as an optimal trade-off between the total shading of contact fingers (the product of the average finger width and the total number of contact fingers), the series resistance contribution (the lateral grid resistance and the contact resistance), and overall Ag-consumption (optimized by the uniformity of contact fingers). 6 Therefore, further optimization of screen-printed finger widths is becoming increasingly challenging as all of these aspects have to be considered. Additionally, when a sufficient printability of front-side Ag paste at high flooding and printing speeds is desired, a low viscosity in the high shear regime seems to be necessary. [7][8][9][10][11][12] The printability in terms of sufficient paste transfer usually comes at the cost of inducing high shearing forces into the paste sample, resulting in significant spreading and the loss of high aspect ratios. Xu et al. 13 and Tepner et al. 1 showed in separate studies that an improved slip behavior of the paste during flooding could help to optimize this trade-off further because slip between the paste and emulsion surface allows for relative movement without the induction of unnecessary shearing forces. The question arises if only further development of the metallization paste can push the limits of fine-line screen printing.
In recent years, screen manufacturers have started to contribute significant improvements to this problem by adjusting the screen architecture to enhance the paste transfer during flooding and screen snap-off. 14,15 Figure 2 illustrates how the underlying mesh and partially opened emulsion define the screen architecture. The mesh consists of woven metal wires with a diameter d, separated by the distance d 0 . On top of this mesh, an emulsion is applied and partially opened to create a rectangular channel with a width w n . Further, this screen opening is placed at a specific angle φ in reference to the quadratic woven mesh. State-of-the-art screens are usually made with an angle of φ = 22.5 . [16][17][18] Because of this choice, wire crossings always exist within each screen opening, limiting the printability and reducing the local finger height, respectively. In recent years, so-called "knotless screens" emerged, where the mesh is aligned at a 0 angle, avoiding any wire crossings within the screen opening, thus increasing the potential paste transfer. 3,[19][20][21] In order to establish a comprehensive understanding of the significance of the presented screen parameters, Ney et al. published a method to model the screen opening based on those parameters. 22 Later, Tepner et al. expanded this simulation model to derive specific conclusions by simulating and studying the dependency of the wire crossings on such screen parameters. 19 They were able to show that the state-of-the-art method of describing a screen channel by the established parameter open area OA % is not sufficient when fine-line screen printing below 30 μm is desired. They concluded that the rate at which the open area OA % changes across the screen opening is crucial to the screen performance. Therefore, they introduced a new parameter σ OA , describing the average deviation of OA % across the screen opening length. 22 In this study, we will elaborate on these results by running a full simulation of different screen architectures and then perform solar cell metallization experiments for five different screen architectures at four different screen opening widths w n . Afterwards, the simulation results are directly correlated to the printing performance to create a complete understanding of how changes to the screen architecture are influencing fine-line screen printing.

| Screen simulation approach
In this study, we utilize the simulation approach first published by Ney et al. 22 and then extended by Tepner et al. 19 to perform a complete F I G U R E 1 Evolution of published results for the achieved finger width for solar cell metallization since 2005. The figure has been slightly adapted from Lorenz et al. 3 and novel results since the original publication are added (see figure legend for details). The complete reference list for all data points shown can be taken from the original publication. 3 Additionally, the prediction trend line of the ITRPV 3rd and 10th edition has been added [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 2 This SEM image presents a typical screen opening channel. Its geometric architecture is defined by the dimension of the underlying mesh with the wire diameter d and the wire-to-wire distance d 0 , the screen opening width w n , the channel length l, and finally the angle between emulsion edge and mesh φ (commonly referred to as the screen angle φ) 22 screen pattern analysis on different screen openings to derive conclusions about their expected screen printing performance for solar cell metallization. The simulation approach is based on a mathematical model that calculates all intersection points between an arbitrary quadratic grid and a rectangle with the width w n and the length l, which is placed at an angle φ on that grid. A Boolean calculation was set up in MATLAB MathWorks©, which finds all existing intersection points, further calculates their exact coordinates, and connects the intersection points to polygons. Afterwards, the shape and exact size of all polygons are calculated, creating a full mathematical description of any screen opening defined by its wire diameter d, the mesh count MC (or wire-to-wire distance d 0 ), the screen opening width w n , and the screen angle φ (illustrated in Figure 2). 22 The simulation approach was experimentally verified in both previous publications. Table 1 shows the range and increment of the sweep for the screen parameters and the alignment on the screen perpendicular to the screen opening direction. This alignment κ 0 defines the position of the screen opening (see Figure 2) in reference to the underlying mesh.
In this study, all simulation results are presented as average values for a full sweep of κ 0 because any conclusion derived needs to be true for all 120 screen openings on the entire screen. The simulation approach is repeated for three types of mesh with a mesh count and wire diameter of 380 inch −1 /0.014 mm, 440 inch −1 /0.013 mm, and 480 inch −1 /0.011 mm. The simulation output data include the area of all individual openings and the average frequency of occurrence for each type of shape.

| Experimental screen evaluation
In order to evaluate the printability of different screen opening patterns, four different fine-line screens (delivered by Murakami Ltd., Japan) and one reference screen from a different supplier are investigated in two separate experimental steps. In the first run, a test layout with four solar cell grid segments with 120 contact fingers of different screen opening width w n (15, 18, 21, and 24 μm) separated by five busbars is used. The design of the test layout is presented in Figure 3.
It allows a standard measurement of the busbar-to-busbar grid resistance R BB-BB using an industrial cell tester and thus a statistical determination of the mean lateral resistance R L of the contact fingers (also commonly known as grid line resistance R L ) for each segment.
The geometry of the contact fingers is statistically analyzed by confocal microscopy and image analysis using an algorithm developed at Fraunhofer ISE. 23 To get statistically significant data on the printed finger geometry, the finger width w f , the finger height h f , and the cross-sectional area A f is measured for each screen opening width w n at three different fingers (#30, #60, #90) in the middle between corresponding busbars on five different wafers. Finally, a scanning electron microscopy (SEM) analysis of selected finger cross-sections is carried out.
In the second experimental step, solar cells are fabricated by applying a fine-line metallization and contact firing step on industrially

| Simulation results
A systematic screen pattern simulation approach was carried out to determine the shape, size, and exact location of all individual opened areas that can occur within a screen opening. The method is well described in literature. 19,22 We have found that only seven different types of opening shapes can mathematically exist within a screen opening defined by two straight parallel edges superimposed onto a quadratic mesh. If the screen opening width w n is smaller than the wire-to-wire distance d 0 , the quadratic shape can be removed from the investigation, resulting in six remaining different types of shapes presented in Figure 4.

| Correlation of screen simulation results and printing performance
In Figure  .
The index "shapes" accounts for the iteration between all possible shapes presented in (4). The question arises, how is A Ind:Opening influencing the paste transfer, that is, the printability for a given paste.
In order to address this question, we introduce an empirical nondimensional screen parameter screen utility index (SUI), which can be used to gain additional information on the expected printability of a screen with respect to a given paste. As seen in Figure 2, the introduction of an angle will tilt the pattern of individual openings and increases its number. Furthermore, the SUI will increase with a finer mesh (decreasing d and d 0 ) and decreases with a reduction of the screen opening width w n (A Ind:Opening depends on w n as seen in Figure 5). We cannot state an equation that describes the full dependency of the SUI on the screen angle φ for any angle above 0 because A Ind:Opening depends on the screen angle φ itself.
Therefore, the calculation of the SUI requires the presented simulation model. In Figure 9, the relationship between the lateral finger resistance R L for each group and the SUI value is shown. In order to get a more complete picture, published data from Tepner et al. have also been included. 1 The comparison is suitable because the same paste and very similar printing process parameters have been chosen in that study, making the screen architecture the only variable between studies. The data indicate that at SUI = 1, the relationship between the printability and the screen architecture changes. In the regime where SUI < 1 applies, there is a strong increase in lateral finger resistance R L , which indicates that screen parameter choices will significantly influence the expected printing performance. For SUI > 1 values, the average size of individual openings is wide enough to guarantee a stable and sufficient paste transfer indicating that the screen architecture is not the limiting factor. In order to make the right screen parameter choices, one has to run a full simulation on all potential combinations of screen opening widths w n and screen angles φ for all available mesh types.
Afterwards, all screen candidates can be ranked relative to each other by comparison of the SUI.
For today's mass production of Si-solar cells, a SUI < 1 should be avoided at all costs, as small deviations of screen configurations due to manufacturing tolerances might significantly influence the expected printing result. If manufacturing tolerances for screen angle alignment and the wire-to-wire distance on meshes decrease in the future, smaller SUI values might become suitable for mass production. At this point, the interaction with an arbitrary paste is completely neglected as any highly filled suspension with a certain average particle size will cause significant clogging of a portion of these individual openings.
This would cause an increase of the measured lateral finger resistance R L eventually. In future studies, the determination of the nominator of Further paste development was enough to drive this evolution as SUI values for screens during that time were far beyond SUI > 1, revealing that the screen was not the limiting factor when it comes to printability. With the ongoing reduction of screen opening widths, this will change dramatically in the upcoming years. Improvements on screen manufacturing tolerances will likely become a major driver for continuing the presented evolution to maintain a controllable and sufficient mass production environment.

| CONCLUSIONS
In this work, a screen pattern analysis by a novel simulation approach was conducted and revealed that the screen angle has a significant results for all screen configurations are correlated with printing results, revealing a relationship that can be explained by a novel dimensionless parameter, the SUI, giving a quantitative value for any screen configuration to describe its impact on printability.