Main-grid-free back contact battery

By designing a back contact battery without a main gate and using a segmented thin gate and an edge collection gate structure, the problem of difficult to achieve both warping and photoelectric conversion efficiency of the back contact battery in the prior art is solved, and more efficient battery performance and lower warping risks are achieved.

CN223007837UActive Publication Date: 2025-06-20CHINT NEW ENERGY TECH CO LTD
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Patent Information

Application Number
CN202422155403.5
Authority / Receiving Office
CN · China
Patent Type
Utility models(China)
Current Assignee / Owner
Filing Date
2024-09-02
Publication Date
2025-06-20
Estimated Expiration
2034-09-02

AI Technical Summary

Technical Problem

The existing back contact batteries have thin grids of both polarities on the back, resulting in huge welding materials and concentrated stress, causing serious warping of the battery cells, making it difficult to solve the warping problem while ensuring high photoelectric conversion efficiency.

Method used

A back contact battery without a main gate is designed, and its back includes a positive electrode fine gate, a negative electrode fine gate, a positive electrode bus fine gate, a negative electrode bus fine gate, a positive electrode edge collection gate and a negative electrode edge collection gate. Through the design of segmented fine gate and edge collection gate, the welding material and contact area are reduced and the risk of warping is reduced.

Benefits of technology

The amount of solder and insulating adhesive on the back of the battery cell is reduced, the probability of warping is reduced, and the photoelectric conversion efficiency and external output power are improved.

✦ Generated by Eureka AI based on patent content.

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Abstract

The utility model relates to the field of photovoltaic manufacturing, in particular to a main-grid-free back contact battery, and the back surface of the main-grid-free back contact battery comprises an anode fine grid, a cathode fine grid, an anode confluence fine grid, a cathode confluence fine grid, an anode edge collection grid and a cathode edge collection grid, the positive pole fine grids and the negative pole fine grids are sectional fine grids; the positive electrode edge collecting grid is electrically connected with the edge positive electrode confluence fine grid through the positive electrode fine grid, and the negative electrode edge collecting grid is electrically connected with the edge negative electrode confluence fine grid through the negative electrode fine grid; the positive pole confluence fine grid and / or the negative pole confluence fine grid are segmented confluence fine grids; the segmented confluence fine grid comprises two edge segments; and the two edge sections are respectively positioned at the two ends of the back surface of the main-grid-free back contact battery in the second direction. Waste of a power generation area is avoided, and the photoelectric conversion efficiency is improved.
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Description

Technical Field

[0001] The utility model relates to the field of photovoltaic manufacturing, in particular to a main-gridless back-contact battery. Background Art

[0002] A photovoltaic solar cell is a device that converts solar light energy into electrical energy. As the harm of fossil energy to the environment continues to emerge and its stockpile continues to decrease, photovoltaic solar cells, as renewable energy sources, have received increasing attention from all sectors of society.

[0003] When both the positive and negative electrodes of a solar cell are located on the back of the solar cell, the solar cell is called a back-contact battery. Since there are no metal electrodes on the front of the back-contact battery to block the incident sunlight, it has a higher photoelectric conversion efficiency and is one of the current technical directions for realizing high-efficiency crystalline silicon cells. However, in the existing back-contact batteries, since the fine grids of both polarities are arranged on the back, the welding materials used on the back are huge, and the stress concentration caused on the back is much higher than that of other types of photovoltaic cell wafers, resulting in serious warping of the cell wafers.

[0004] Therefore, how to solve the warping problem of the cell wafers on the premise of ensuring a high photoelectric conversion efficiency is an urgent problem to be solved by those skilled in the art. Summary of the Utility Model

[0005] The purpose of the utility model is to provide a main-gridless back-contact battery to solve the problem in the prior art that it is impossible to have both a high photoelectric conversion efficiency and a low warpage rate of the bottom cell wafers.

[0006] To solve the above technical problems, the utility model provides a main-gridless back-contact battery. The back of the main-gridless back-contact battery includes a positive fine grid, a negative fine grid, a positive busbar fine grid, a negative busbar fine grid, a positive edge collection grid, and a negative edge collection grid;

[0007] The positive fine grid and the negative fine grid extend along a first direction and are alternately arranged in a second direction perpendicular to the first direction;

[0008] Both the positive fine grid and the negative fine grid are segmented fine grids; the positive busbar fine grid and the negative busbar fine grid are arranged at the interval between segments of the segmented fine grids and are connected to the corresponding fine grids;

[0009] The positive edge collection grid and the negative edge collection grid are respectively arranged on two sides of the main-gridless back-contact battery perpendicular to the first direction and are connected to the segments of the adjacent same-polarity fine grids;

[0010] The positive edge collection grid is electrically connected to the edge positive busbar fine grid through the positive fine grid, and the negative edge collection grid is electrically connected to the edge negative busbar fine grid through the negative fine grid;

[0011] The positive current collecting fine grid and / or the negative current collecting fine grid is / are segmented current collecting fine grids;

[0012] The segmented current collecting fine grid includes two edge segments;

[0013] The two edge segments are respectively located at both ends of the back surface of the main-gridless back-contact battery in the second direction.

[0014] Optionally, in the main-gridless back-contact battery, the length range of the edge segment is from 2 mm to 20 mm, including the end values.

[0015] Optionally, in the main-gridless back-contact battery, the positive fine grid and / or the negative fine grid are provided with widened welding points in the solder tape connection area;

[0016] The width of the widened welding point in the second direction is greater than the width of the corresponding fine grid in the second direction.

[0017] Optionally, in the main-gridless back-contact battery, each positive fine grid and / or each negative fine grid is provided with the widened welding point.

[0018] Optionally, in the main-gridless back-contact battery, the positive fine grid and the negative fine grid on the waist area of the back surface of the main-gridless back-contact battery are provided with the widened welding points; the waist area does not coincide with the edge segment.

[0019] Optionally, in the main-gridless back-contact battery, the size of the widened welding point gradually increases from both ends of the waist area to the center.

[0020] Optionally, in the main-gridless back-contact battery, the distance between the positive edge collecting grid and the closest negative current collecting fine grid, and the distance between the negative edge collecting grid and the closest positive current collecting fine grid range from 1 mm to 6 mm, including the end values.

[0021] Optionally, in the main-gridless back-contact battery, the distance between adjacent positive current collecting fine grids and negative current collecting fine grids in the first direction ranges from 4 mm to 20 mm, including the end values.

[0022] Optionally, in the main-gridless back-contact battery, the distance between adjacent segments of the positive fine grid and / or the negative fine grid ranges from 0.3 mm to 2.0 mm, including the end values.

[0023] The back-contact battery without main grid provided by the present utility model, the back surface of the back-contact battery without main grid includes a positive fine grid, a negative fine grid, a positive busbar fine grid, a negative busbar fine grid, a positive edge collection grid and a negative edge collection grid; the positive fine grid and the negative fine grid extend along a first direction and are alternately arranged in a second direction perpendicular to the first direction; the positive fine grid and the negative fine grid are both segmented fine grids; the positive busbar fine grid and the negative busbar fine grid are arranged at the interval between segments of the segmented fine grid and are connected to the corresponding fine grid; the positive edge collection grid and the negative edge collection grid are respectively arranged on two sides of the back-contact battery without main grid perpendicular to the first direction and are connected to the segments of the adjacent fine grids of the same polarity; the positive edge collection grid is electrically connected to the edge positive busbar fine grid through the positive fine grid, and the negative edge collection grid is electrically connected to the edge negative busbar fine grid through the negative fine grid; the positive busbar fine grid and / or the negative busbar fine grid is a segmented busbar fine grid; the segmented busbar fine grid includes two edge segments; the two edge segments are respectively located at both ends of the back surface of the back-contact battery without main grid in the second direction.

[0024] In the present invention, the back-contact battery without main grid is adopted, which not only reduces the amount of paste used for setting the grid lines, but also greatly reduces the amount of solder used in the welding process between the back surface of the battery chip and the solder strip. At the same time, since there is no main grid, the width of the contact area between the solder strip and the battery chip is further reduced, and the proportion in the interval between segments of the segmented fine grid is also reduced accordingly, making it less likely to accidentally touch the endpoints of the segments of the opposite-sex fine grid and cause leakage. Therefore, the amount of insulating glue used on the back surface of the back-contact battery without main grid can be further reduced, that is, the amount of solder and insulating glue used on the back surface of the battery chip of the present utility model is less than that in the related technology, greatly reducing the probability of warping of the battery chip. At the same time, by connecting the edge collection grid located at the edge of the battery chip to the corresponding busbar fine grid through the fine grid, the current in the position that cannot be collected under the conventional back-contact structure without main grid is collected, avoiding the waste of part of the power generation area of the battery chip, and also greatly improving the overall photoelectric conversion efficiency and external output power of the back-contact battery without main grid. Description of the Drawings

[0025] In order to more clearly illustrate the technical solutions of the embodiments of the present utility model or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present utility model. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0026] Figure 1 It is a schematic structural diagram of a specific embodiment of the back-contact battery without main grid provided by the present utility model;

[0027] Figure 2 This is a partial structural schematic diagram of a specific embodiment of the main-gridless back-contact battery provided by the present utility model.

[0028] In the figure, it includes 01 - widened welding point, 11 - positive fine grid, 12 - negative fine grid, 21 - positive busbar fine grid, 21' - edge positive busbar fine grid, 22 - negative busbar fine grid, 22' - edge negative busbar fine grid, 31 - positive edge collection grid, 32 - negative edge collection grid, 40 - insulating glue, A1 - the distance between the negative edge collection grid and the closest positive busbar fine grid, A2 - the distance between adjacent positive busbar fine grids and negative busbar fine grids in the first direction, A3 - the length of the edge segmentation, A4 - the distance between adjacent segments of the positive fine grid, A5 - the distance between adjacent segments of the negative fine grid. Specific embodiment

[0029] In order to enable those skilled in the art to better understand the solution of the present utility model, the present utility model will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present utility model, rather than all of the embodiments. Based on the embodiments of the present utility model, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present utility model.

[0030] The core of the present utility model is to provide a main-gridless back-contact battery, and a structural schematic diagram of a specific embodiment thereof is as Figures 1 to 2 shown, which is called specific embodiment one. The back surface of the main-gridless back-contact battery includes a positive fine grid 11, a negative fine grid 12, a positive busbar fine grid 21, a negative busbar fine grid 22, a positive edge collection grid 31 and a negative edge collection grid 32;

[0031] The positive fine grid 11 and the negative fine grid 12 extend along the first direction and are alternately arranged in the second direction perpendicular to the first direction;

[0032] Both the positive fine grid 11 and the negative fine grid 12 are segmented fine grids; the positive busbar fine grid 21 and the negative busbar fine grid 22 are arranged at the inter-segment intervals of the segmented fine grids and are connected to the corresponding fine grids;

[0033] The positive edge collection grid 31 and the negative edge collection grid 32 are respectively arranged on two sides of the main-gridless back-contact battery perpendicular to the first direction and are connected to the segments of the adjacent same-polarity fine grids;

[0034] The positive edge collection grid 31 is electrically connected to the edge positive busbar fine grid 21' through the positive fine grid 11, and the negative edge collection grid 32 is electrically connected to the edge negative busbar fine grid 22' through the negative fine grid 12;

[0035] The positive current collecting fine grid 21 and / or the negative current collecting fine grid 22 are segmented current collecting fine grids;

[0036] The segmented current collecting fine grid includes two edge segments;

[0037] The two edge segments are respectively located at both ends of the back surface of the main-gridless back-contact cell in the second direction.

[0038] Generally, the first direction and the second direction represent the directions of two pairs of opposite sides of the cell of the main-gridless back-contact cell. In some cases, the current collecting fine grid closest to the positive edge collecting grid 31 is the negative current collecting fine grid 22, and the current collecting fine grid closest to the negative edge collecting grid 32 is the positive current collecting fine grid 21. At this time, it is necessary to cross the closest current collecting fine grid and be electrically connected to the current collecting fine grid of the same polarity. When crossing the closest current collecting fine grid with different polarities, materials such as insulating glue 40 are required for electrical insulation treatment. And the edge negative current collecting fine grid 22' mentioned above refers to the negative current collecting fine grid 22 closest to the negative edge collecting grid 32, and the edge positive current collecting fine grid 21' refers to the positive current collecting fine grid 21 closest to the positive edge collecting grid 31.

[0039] Segmenting the current collecting fine grid can provide positioning for the welding of the solder strip while further reducing raw material consumption.

[0040] Please refer to Figure 1 , the segmented current collecting fine grid only includes two edge segments arranged at both ends of the cell in the second direction. The two edge segments are arranged at both ends of the cell, which can better provide a positioning function for the subsequent welding of the solder strip.

[0041] Furthermore, the length of the edge segment (denoted by A3 in the figure) ranges from 2 millimeters to 20 millimeters, including the endpoint values, such as any one of 2.0 millimeters, 10.8 millimeters, or 20.0 millimeters. The above range is the best range after a large number of theoretical calculations and actual tests. Of course, it can also be adjusted according to the actual situation, and the present utility model does not make a limitation here.

[0042] As a preferred embodiment, the positive fine grid 11 and / or the negative fine grid 12 are provided with widened welding points 01 in the solder strip connection area;

[0043] The width of the widened welding point 01 in the second direction is greater than the width of the corresponding fine grid in the second direction.

[0044] Since the second direction is also the extending direction of the solder ribbon, the welding point where the fine grid contacts the solder ribbon is modified into a widened welding point 01, that is, the width of the fine grid is increased in the second direction to form the widened welding point, which can greatly increase the contact area between the fine grid and the solder ribbon and reduce the welding difficulty. The widened welding point 01 can be a circular welding point, a rectangular welding point, a square welding point, an irregular polygon welding point, etc. The corresponding major axis ranges from 0.05 mm to 0.50 mm, such as any one of 0.050 mm, 0.115 mm or 0.500 mm, and the corresponding minor axis ranges from 3 μm to 15 μm, including any one of 3.0 μm, 9.5 μm or 15.0 μm. In the above ranges, the size of the widened welding point 01 will not be too small to cause an insignificant gain in welding, nor will it be too large to cause accidental electrical connection between fine grids with different polarities, resulting in leakage. Of course, different parameter ranges can also be selected according to actual situations, and the present utility model does not make limitations here. Reference can be made to Figure 2 , Figure 2 is Figure 1 a partial enlarged schematic view of the position within the dashed box in

[0045] As a preferred embodiment, the widened welding point 01 is provided on each of the positive fine grids 11 and / or the negative fine grids 12. By providing the widened welding point 01 on each of the positive fine grids 11 and / or the negative fine grids 12, the welding stability of the solder ribbon is further improved, and the welding difficulty of the solder ribbon is reduced. Of course, other solutions can also be adopted, such as providing the widened welding point 01 on the corresponding fine grids at intervals of a certain number of fine grids, etc. The present utility model does not make limitations here.

[0046] As a preferred embodiment, the widened welding point 01 is provided on the positive fine grid 11 and the negative fine grid 12 in the waist area on the back surface of the main-gridless back-contact battery; the waist area does not coincide with the edge segments.

[0047] In this preferred embodiment, the two edge segments of the segmented busbar fine grid are located at both ends in the second direction on the back surface of the cell, and when the solder ribbon is welded along the second direction, it is in contact with the corresponding edge segments at both ends of the cell to ensure effective connection. In the preferred embodiment, the widened welding point 01 is further provided on the fine grids in the middle section on the back surface of the cell, that is, the waist area. When the solder ribbon passes through the cell along the second direction, there are corresponding structures at both ends and in the middle section of the cell to strengthen the welding, further improving the firmness of the welding and the working stability of the cell.

[0048] Further, the size of the widened welding point 01 gradually increases from both ends of the waist region towards the center. In other words, the size of the widened welding point 01 at the center of the waist region is the largest, and the closer it is to the edge of the waist region, the smaller the size of the widened welding point 01. Here, the "size" can be the major axis size and / or the minor axis size of the widened welding point 01. Additionally, it should be noted that during the process of approaching the center from the edge of the waist region, it is not necessary to ensure that the sizes of each widened welding point 01 are different. As long as it is ensured that the one with a smaller size is closer to the edge than the one with a larger size.

[0049] The distance between the positive electrode edge collecting grid 31 and the closest negative electrode current collecting fine grid, and the distance between the negative electrode edge collecting grid 32 and the closest positive electrode current collecting fine grid (denoted as A1 in the figure) ranges from 1 millimeter to 6 millimeters, including the end point values, such as any one of 1.0 millimeter, 2.5 millimeters, or 6.0 millimeters. Usually, the polarity of the current collecting fine grid closest to the edge collecting grid is opposite to the polarity of the corresponding edge collecting grid. Please refer to Figure 1 As shown in, the negative electrode current collecting fine grid 22 is the closest to the positive electrode edge collecting grid 31, and the positive electrode current collecting fine grid 21 is the closest to the negative electrode edge collecting grid 32. The distance between the adjacent positive electrode current collecting fine grid and the negative electrode current collecting fine grid in the first direction (denoted as A2 in the figure) ranges from 4 millimeters to 20 millimeters, including the end point values, such as any one of 4.0 millimeters, 12.1 millimeters, or 20.0 millimeters. Of course, usually, the current collecting fine grids are arranged alternately, that is, one of the adjacent two current collecting fine grids is the positive electrode current collecting fine grid 21 and the other is the negative electrode current collecting fine grid 22. The distance between adjacent segments of the positive electrode fine grid 11 and / or the negative electrode fine grid 12 (denoted as A4 and A5 in the figure, A4 represents the distance between adjacent segments of the positive electrode fine grid 11, and A5 represents the distance between adjacent segments of the negative electrode fine grid 12) ranges from 0.3 millimeter to 2.0 millimeters, including the end point values, such as any one of 0.30 millimeter, 1.11 millimeter, or 2.00 millimeters. Both the positive electrode fine grid 11 and the negative electrode fine grid 12 are segmented fine grids. The adjacent fine grid segments conform to the above range, which can leave sufficient space for the solder tape welded between adjacent segments, and at the same time, it does not affect the current collection on the battery cell. Of course, other parameter ranges can also be adopted, and the present invention does not make any limitations here.

[0050] The back-contact battery without main grid provided by the present utility model, the back of the back-contact battery without main grid includes a positive fine grid 11, a negative fine grid 12, a positive bus fine grid 21, a negative bus fine grid 22, a positive edge collection grid 31 and a negative edge collection grid 32; the positive fine grid 11 and the negative fine grid 12 extend along a first direction and are alternately arranged in a second direction perpendicular to the first direction; the positive fine grid 11 and the negative fine grid 12 are both segmented fine grids; the positive bus fine grid 21 and the negative bus fine grid 22 are arranged at the interval between segments of the segmented fine grid and are connected to the corresponding fine grids; the positive edge collection grid 31 and the negative edge collection grid 32 are respectively arranged at two sides of the back-contact battery without main grid perpendicular to the first direction and are connected to the segments of the adjacent fine grids of the same polarity; the positive edge collection grid 31 is electrically connected to the edge positive bus fine grid 21' through the positive fine grid 11, and the negative edge collection grid 32 is electrically connected to the edge negative bus fine grid 22' through the negative fine grid 12; the positive bus fine grid and / or the negative bus fine grid is a segmented bus fine grid; the segmented bus fine grid includes two edge segments; the two edge segments are respectively located at both ends of the back of the back-contact battery without main grid in the second direction. In the present invention, the back-contact battery without main grid is adopted, which greatly reduces the solder consumption during the welding process between the back of the battery cell and the solder strip. At the same time, since there is no main grid, the width of the contact area between the solder strip and the battery cell is further reduced, and the proportion in the interval between segments of the segmented fine grid is also reduced accordingly, making it less likely to accidentally touch the endpoints of the segments of the fine grid and cause leakage. Therefore, the amount of the insulating glue 40 on the back of the back-contact battery without main grid can be further reduced, that is, the solder and the insulating glue 40 used on the back of the battery cell of the present utility model are both less than those in the related art, greatly reducing the probability of warping of the battery cell. At the same time, the edge collection grid located at the edge of the battery cell is connected to the corresponding bus fine grid through the fine grid, so that the current in the position that cannot be collected under the conventional back-contact battery without main grid structure can be collected, avoiding the waste of part of the power generation area of the battery cell, and also greatly improving the overall photoelectric conversion efficiency and external output power of the back-contact battery without main grid.

[0051] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and reference can be made to the description of the method part for the relevant parts.

[0052] It should be noted that in this specification, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the said element.

[0053] The above has introduced in detail the passivated emitter and rear contact (PERC) cell provided by the present utility model. Specific examples are used herein to illustrate the principle and implementation manner of the present utility model. The description of the above embodiments is only for helping to understand the method and its core idea of the present utility model. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present utility model, several improvements and modifications can be made to the present utility model, and these improvements and modifications also fall within the protection scope of the claims of the present utility model.

Claims

1. A busbar-free back contact battery, characterized in that: The back side of the main grid-free back contact battery includes a positive electrode fine grid, a negative electrode fine grid, a positive electrode bus fine grid, a negative electrode bus fine grid, a positive electrode edge collecting grid and a negative electrode edge collecting grid; The positive electrode fine grids and the negative electrode fine grids extend along a first direction and are alternately arranged in a second direction perpendicular to the first direction; The positive electrode fine grid and the negative electrode fine grid are both segmented fine grids; the positive electrode busbar fine grid and the negative electrode busbar fine grid are arranged at the intervals between the segments of the segmented fine grids and are connected to the corresponding fine grids; The positive edge collecting grid and the negative edge collecting grid are respectively arranged on two sides of the main grid-free back contact battery perpendicular to the first direction, and are connected to adjacent segments of fine grids of the same polarity; The positive electrode edge collecting grid is electrically connected to the edge positive electrode bus fine grid through the positive electrode fine grid, and the negative electrode edge collecting grid is electrically connected to the edge negative electrode bus fine grid through the negative electrode fine grid; The positive electrode bus bar and / or the negative electrode bus bar are segmented bus bars; The segmented busbar includes two edge segments; The two edge segments are respectively located at two ends of the back side of the busbar-free back contact cell in the second direction.

2. The busbar-free back contact cell according to claim 1, characterized in that: The length of the edge segment ranges from 2 mm to 20 mm, inclusive.

3. The busbar-free back contact cell according to claim 1, characterized in that: The positive electrode fine grid and / or the negative electrode fine grid are provided with a widened welding point in the welding strip connection area; The width of the widened welding point in the second direction is greater than the width of the corresponding fine grid in the second direction.

4. The busbar-free back contact cell according to claim 3, characterized in that: The widened welding point is arranged on each of the positive electrode fine grid and / or the negative electrode fine grid.

5. The busbar-free back contact cell according to claim 3, characterized in that: The widened welding point is provided on the positive electrode fine grid and the negative electrode fine grid in the waist area of ​​the back side of the main grid-free back contact battery; the waist area does not overlap with the edge segment.

6. The busbar-free back contact cell according to claim 5, characterized in that: The size of the widened welding point gradually increases from both ends of the waist area to the center.

7. The busbar-free back contact cell according to claim 1, characterized in that: The spacing between the positive electrode edge collecting grid and the closest negative electrode bus bar, and the spacing between the negative electrode edge collecting grid and the closest positive electrode bus bar range from 1 mm to 6 mm, including the end values.

8. The busbar-free back contact cell according to claim 1, characterized in that: The distance between adjacent positive electrode bus bars and negative electrode bus bars in the first direction ranges from 4 mm to 20 mm, including the end values.

9. The busbar-free back contact cell according to claim 1, characterized in that: The distance between adjacent segments of the positive electrode fine grid and / or the negative electrode fine grid ranges from 0.3 mm to 2.0 mm, including the end values.

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