Photovoltaic monocrystalline silicon material resistivity uniformity evaluation method

Abstract

The invention relates to a photovoltaic monocrystalline silicon material resistivity uniformity evaluation method, and belongs to the technical field of photovoltaic material detection. The method comprises the following steps: evaluating all-form resistivity and doping uniformity of a photovoltaic single crystal silicon rod, a single crystal silicon wafer and a single crystal silicon square wafer; carrying out standardized point distribution on the monocrystalline silicon wafer by using a concentric circular ring and a small circle, and calculating in-plane uniformity by using a triple integral derivation equation; the monocrystalline silicon square pieces are distributed in the form of grid small squares, and in-plane uniformity is calculated by means of a triple integral derivation equation; and for the axial direction of the silicon rod, the uniformity is quantified by utilizing range and variance models through the resistivity of the head, middle and tail wafers. Meanwhile, a continuous grid is generated through interpolation, and a 3D color mapping curved surface diagram with plane projection is drawn to visually present distribution. According to axial and in-plane uniformity results, silicon wafers are classified and graded, the doping uniformity of monocrystalline silicon is accurately reflected, and a support is provided for quality control, process optimization and silicon wafer sorting of photovoltaic monocrystalline silicon.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon material, and belongs to the technical field of photovoltaic material detection. BACKGROUND

[0002] In the photovoltaic monocrystalline silicon production and manufacturing system, monocrystalline silicon, as the core basic material of photovoltaic cells, its resistivity uniformity is directly related to the photoelectric conversion efficiency of the cell and the power output stability of the module. The uniformity of the distribution of doping elements (such as boron B, phosphorus P, gallium Ga, indium In, etc.) in silicon material determines the resistivity distribution state, and thus becomes a key factor affecting the quality and power generation efficiency of photovoltaic products. The current evaluation technology of the resistivity uniformity of photovoltaic monocrystalline silicon cannot meet the needs of the industry for efficient and accurate quality control, and has significant limitations: (1) Lack of standardization in point distribution, and insufficient evaluation representativeness Traditional monocrystalline silicon resistivity detection mostly uses the "random point selection" (such as randomly selecting several points on the surface of the silicon wafer) or "simple zoning" (only distinguishing the center and edge regions and measuring 1-2 points in each region) mode. The number of points and the spatial position are not standardized. For example, some detection processes only rely on the average value calculated from 3-5 discrete points of resistivity data, completely ignoring the subtle resistivity differences in the radial direction (from the center to the edge) and the circumferential direction (different directions of the circumference) of the monocrystalline silicon material. This leads to the fact that the evaluation results obtained from different detection links and different equipment for the same batch of silicon material cannot be effectively compared due to the difference in point distribution; it is also impossible to accurately capture the true state of the internal resistivity distribution of the silicon material, and the evaluation results have greatly reduced the guiding value for actual production.

[0003] (2) Quantitative evaluation is disconnected from spatial distribution, and it is difficult to trace the cause Existing technologies mainly rely on statistical quantities such as standard deviation and range (such as the resistivity radial non-uniformity RRV index) to describe the resistivity uniformity of monocrystalline silicon. These indicators can only reflect the overall dispersion of resistivity, but cannot present the spatial distribution characteristics of resistivity. For example, if RRV=10%, it may be that the difference between the center and the edge of the monocrystalline silicon is uniformly gradual, or it may be that the resistivity in a small local area fluctuates abnormally. These two completely different distribution patterns correspond to the same quantitative result. This makes it difficult for technical personnel to trace the cause of the non-uniformity - it is impossible to determine whether the problem is caused by uneven diffusion of dopants in the doping process or by dislocations, defects, etc. in the crystal growth process, hindering the accurate determination of the direction of process optimization.

[0004] (3) Lack of or single visualization means, and low efficiency of problem positioning In the resistivity distribution state, some schemes only list discrete point data through tables, and show the resistivity trend of limited points through line charts, which cannot intuitively restore the continuous resistivity distribution scene of single crystal silicon material in the plane and axial direction. A small number of schemes using 2D contour maps also do not deeply integrate with quantitative evaluation indicators, making it difficult to establish a correlation analysis of "overall uniformity value (such as RRV)" and "local abnormal position (such as a sudden change in the resistivity of a certain area)". Process personnel need to spend a lot of time manually comparing data and speculating abnormal positions, which cannot quickly locate the problem area, greatly reducing the response efficiency of production optimization.

[0005] (4) Quantitative and qualitative evaluation is fragmented, and quality control has loopholes The existing technology determines "uniformity, qualified, poor" mainly according to the experience threshold (such as RRV≤10% is qualified), without comprehensive judgment combined with the spatial distribution characteristics of resistivity. In actual production, there may be a case that the overall RRV of single crystal silicon is 8% (consistent with the threshold of qualified), but there is a small range of high resistance area in the local. If such hidden dangers are not identified through effective visualization means, subsequent battery production and component packaging links are prone to cause current mismatch, local overheating failure and other problems due to local resistivity abnormalities, which threatens the quality of photovoltaic products and the reliability of power station power generation.

[0006] Therefore, the photovoltaic single crystal silicon industry urgently needs an integrated solution covering "standardized distribution, quantitative and accurate evaluation, and spatial visualization presentation" to solve the pain points of "arbitrary distribution, abstract evaluation, and blind optimization" of the existing technology, and to realize accurate, intuitive and traceable evaluation of resistivity uniformity from the axial direction of the silicon rod to the full form of the silicon wafer (round wafer, square wafer), providing core technical support for high-quality production of photovoltaic single crystal silicon, classification and grading of silicon wafers, and process iteration and upgrading. SUMMARY

[0007] In view of the problems existing in the evaluation of the resistivity uniformity of the photovoltaic single crystal silicon material, the present application provides a method for evaluating the resistivity uniformity of the photovoltaic single crystal silicon material, which constructs a resistivity and doping uniformity visualization co-evaluation system around the "rod-round wafer-square wafer" full form detection requirement of the photovoltaic single crystal silicon material; taking the round wafer as the basic unit: cutting the round wafer from the head, middle and tail of the single crystal silicon rod respectively, and adopting the concentric ring array distribution for each round wafer to measure the resistivity and evaluate the in-plane uniformity; axial uniformity derivation: based on the resistivity measurement results of the head, middle and tail round wafers, the resistivity and doping uniformity of the silicon rod in the axial direction are evaluated through the range and variance model; square wafer detection extension: extending the evaluation method of the round wafer to the square wafer (such as the cut silicon wafer), and adopting the square ring distribution method to realize the resistivity uniformity evaluation of the square wafer; visualization and quantification: intuitively displaying the resistivity distribution through the 3D color mapping curved surface graph, and quantitatively calculating the doping uniformity through the triple integral model, to realize the whole process quality control from micro to macro.

[0008] A photovoltaic monocrystalline silicon material resistivity uniformity evaluation method, including full-form resistivity and doping uniformity evaluation of photovoltaic monocrystalline silicon rods, monocrystalline silicon wafers and monocrystalline silicon square wafers, and the specific steps are as follows: S1. Resistivity and doping uniformity evaluation of monocrystalline silicon wafers or monocrystalline silicon square wafers, specifically including: S11. Standardized point arrangement is performed on the monocrystalline silicon wafers or monocrystalline silicon square wafers; S12. Quantitative evaluation of monocrystalline silicon wafer or monocrystalline silicon square wafer resistivity uniformity: measuring the resistivity of each point area, calculating the total number of measurement points, calculating the average resistivity, standard deviation and coefficient of variation, and quantitatively evaluating the resistivity uniformity grade according to the coefficient of variation; S13. Intuitive visual processing of monocrystalline silicon wafer or monocrystalline silicon square wafer resistivity distribution; S14. Building a triple integral model to calculate the doping uniformity index of monocrystalline silicon wafers or monocrystalline silicon square wafers ; S2. Axial resistivity and doping uniformity evaluation of monocrystalline silicon rods, specifically including: S21. Monocrystalline silicon wafers are cut from the head, middle and tail of the monocrystalline silicon rod, respectively denoted as monocrystalline silicon wafer S, monocrystalline silicon wafer M and monocrystalline silicon wafer T; S22. The average resistivity of monocrystalline silicon wafer S, monocrystalline silicon wafer M and monocrystalline silicon wafer T is measured by using the resistivity uniformity quantitative evaluation method of monocrystalline silicon wafers, respectively denoted as , and ; S23. Axial resistivity uniformity evaluation: calculating the range reflecting the maximum fluctuation range of axial resistivity and the variance reflecting the overall dispersion degree of axial resistivity, normalizing the range and variance, and then linearly combining the weight coefficients to form an axial uniformity index of the monocrystalline silicon rod to determine the axial resistivity uniformity grade; S24. Axial doping uniformity evaluation: considering the influence of the segregation coefficient of the doping element in silicon on the axial doping, a doping concentration correction model is established; by comparing the deviation of the measured resistivity and the theoretical model, the axial doping uniformity is evaluated.

[0009] The beneficial effects of the present application are: (1) The present application covers full forms: for the first time, a "silicon rod axial-silicon wafer (circular / square)" full-process uniformity evaluation system is constructed, filling the blank of axial evaluation and meeting the quality control needs of photovoltaic monocrystalline silicon from rod to wafer; ​(2) The application realizes standardized and accurate evaluation: through standardized distribution and unified mathematical model (range, variance, triple integral derived equation), the application realizes comparable evaluation of different forms and batches of materials, and accurately quantifies the doping uniformity; (3) The application realizes visualization and application extension: 3D visualization intuitively presents the resistivity distribution, combined with classification and grading rules, to provide data support for silicon wafer sorting and process optimization (such as doping process adjustment), and to improve production efficiency and product yield. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 The figure illustrates the concentric ring and small circle array of a single crystal silicon wafer. Figure 2 The figure illustrates the small circle label of a single crystal silicon wafer. Figure 3 The figure illustrates the small circle label of a phosphorus-doped N-type single crystal silicon wafer with a diameter of 256 mm. Figure 4 The figure illustrates the 3D color mapping surface graph of the resistivity band projection of a phosphorus-doped N-type single crystal silicon wafer with a diameter of 256 mm. Figure 5 The figure illustrates the small circle label of a phosphorus-doped N-type single crystal silicon wafer with a diameter of 300 mm. Figure 6 The figure illustrates the 3D color mapping surface graph of the resistivity band projection of a phosphorus-doped N-type single crystal silicon wafer with a diameter of 300 mm. Figure 7 The figure illustrates the sampling position of the head, middle, and tail pieces of a single crystal silicon rod with edges and tail sections. Figure 8 The figure illustrates the sampling position of the head, middle, and tail pieces of a single crystal silicon rod without edges and tail sections. Figure 9 The figure illustrates the square ring and small square array of a single crystal silicon wafer. Figure 10 The figure illustrates the small square label of a single crystal silicon wafer. Figure 11 The figure illustrates the small square label of a gallium-doped P-type single crystal silicon wafer with a side length of 182 mm. Figure 12 The figure illustrates the 3D color mapping surface graph of the resistivity band projection of a gallium-doped P-type single crystal silicon wafer with a side length of 182 mm. DETAILED DESCRIPTION

[0011] The application will be further described in detail below in conjunction with specific embodiments, but the scope of protection of the application is not limited to the content described. SUMMARY A method for evaluating the resistivity uniformity of photovoltaic single crystal silicon material, including full-form resistivity and doping uniformity evaluation of photovoltaic single crystal silicon rods, single crystal silicon wafers, and single crystal silicon square wafers, the specific steps are as follows: S1. Resistivity and doping uniformity evaluation of single crystal silicon wafer or single crystal silicon square wafer, specifically including: S11. Standardized point arrangement on single crystal silicon wafer or single crystal silicon square wafer, specifically as follows: S111. Method for standardized point arrangement on single crystal silicon wafer: assuming the diameter of the single crystal silicon wafer is D, a rectangular coordinate system is established with the center coordinate of the single crystal silicon wafer as the origin, and the origin coordinate is (0, 0); N concentric circles with the origin as the center are arranged in the large circle with diameter D, and the outer circle sequence number K is 1 to N from inside to outside; A number of small circles with diameter d are uniformly distributed on each circle as measurement areas, and the center of the small circle is the measurement point. When k = 1, the first circle is the center small circle, numbered 1-1, the center is at the origin, the number of small circles n1 = 1, and the radius of the first circle R1 = 0; when k ≥ 2, the small circles are arranged in the clockwise direction from the positive direction of the x-axis, and the number of small circles is n k = 6(k-1) (increasing by multiples of 6 to ensure uniform distribution, for example, 6 when k = 2, and 12 when k = 3), and the small circles are numbered in the counterclockwise direction as k-1 to k-n k ; The radius of the kth circle (the distance from the center of the small circle to the origin) is R k , where R1 = 0 when k = 1, and R k = (k-1)d when k ≥ 2 (for example, R2 = d when k = 2, and R3 = 2d when k = 3, to ensure uniform spacing between circles); the center coordinate O k-m ; Since the angle interval between adjacent small circles is: , the angle of the mth small circle is: (Conversion to radian system: ; According to the conversion relationship between polar coordinates and rectangular coordinates, the formula for the coordinate O k-m is: ; When k = 1: R1 = 0, n1 = 1, , so O 1-1 (0, 0); When k ≥ 2: , , , the center coordinate O k-m of the mth small circle on the kth circle is simplified as: ; Parameter symbols: k is the circular ring number (k = 1, 2, …, N), m is the small circle number on the kth circular ring (m = 1, 2, …, n k ), n k is the number of small circles on the kth circular ring, R k is the radius of the kth circular ring (the distance from the center of the small circle to the origin); O k-m is the center of the mth small circle on the kth circular ring (the coordinates are ); is the resistivity measurement value of the mth small circle area on the kth circular ring; S112. Method for standardizing the layout of points on a single crystal silicon square sheet: Let the square side length of the single crystal silicon square sheet be a, and establish a rectangular coordinate system with the center coordinates of the single crystal silicon square sheet as the origin, and the origin coordinates are (0, 0); M concentric square rings with the origin as the center are arranged in the large square with a side length of a, and the square ring sequence number p from inside to outside is 1 to M; A number of small squares with a side length of l are uniformly distributed on each square ring as a measurement area, and the center of the small square is a measurement point. When p = 1, the first square ring is a central small square, numbered 1-1, with the center at the origin, and the number of small squares n1 = 1. The diameter of the first square ring is l1 = 0; when p ≥ 2, the small squares are arranged in a counterclockwise direction starting from the positive direction of the x-axis with the center point as the center, and the number of small squares is n p = 8(p-1) (increasing by multiples of 8, and uniformly distributed along the four sides of the square ring), and 2(p-1) small squares are arranged on each side of the square ring (e.g. 8 for p = 2 and 16 for p = 3), and the small squares are numbered in a counterclockwise direction as p-1 to p-n p ; The center coordinates of the qth small square on the pth square ring are O p-q , and the coordinates of O p-q The formula is: ; Parameter symbols: p is the square ring number (p = 1, 2, …, M); q is the small square number on the pth square ring (q = 1, 2, …, n p ); n p is the number of small squares on the pth square ring; O p-q is the center of the qth small square on the pth square ring (the coordinates are ); is the resistivity measurement value of the qth small square area on the pth square ring; S12. Quantitative evaluation of resistivity uniformity of single crystal silicon wafer or single crystal silicon square wafer: measure the resistivity of each point area, calculate the total number of measurement points, calculate the average resistivity, standard deviation and coefficient of variation, and quantitatively evaluate the resistivity uniformity grade according to the coefficient of variation; the specific steps are as follows: S121. Quantitative evaluation of resistivity uniformity of single crystal silicon wafer: Let the resistivity measurement value of the mth small circle of the kth annulus be When k≥2, The summation formula is: There is an origin as a measurement point in the center, so The total number of measurement points is: ; The average resistivity μ (the arithmetic mean of the resistivity of all small circles) is: ; The standard deviation σ (reflecting the deviation of each measurement value from the average value) is: ; The coefficient of variation CV (uniformity index) is: ; S122. Quantitative evaluation of resistivity uniformity of single crystal silicon square wafer: Let the resistivity measurement value of the qth small square of the pth square annulus be When , The summation formula is: ; The center point of the single crystal silicon square wafer is a measurement point, so the total number of measurement points is: ; The average resistivity (the arithmetic mean of the resistivity of all small squares) is: ; The standard deviation : ; The coefficient of variation CV (uniformity index), the ratio of the standard deviation to the average value (dimensionless, eliminating the influence of magnitude) is: ; The method for quantitatively evaluating the resistivity uniformity grade according to the coefficient of variation is: The coefficient of variation CV is less than 5%, and the resistivity uniformity grade is excellent; The coefficient of variation CV is 5% to 15%, and the resistivity uniformity grade is qualified; The coefficient of variation CV is greater than 15%, and the resistivity uniformity grade is poor. S13. Intuitively visualize the resistivity distribution of the single crystal silicon wafer or the single crystal silicon square wafer, specifically comprising: S131. Integrate the coordinates of all small circles in the single crystal silicon wafer and the resistivity data into a three-dimensional data set: ; wherein, is the plane coordinate, is the resistivity value of the point; or integrate the coordinates of all small squares in the single crystal silicon square wafer and the resistivity data into a three-dimensional data set: ; wherein, is the plane coordinate, is the resistivity value of the point; S132. Since the measurement points are discrete small circle centers, a continuous resistivity distribution surface needs to be constructed by an interpolation algorithm, therefore, Kriging interpolation or inverse distance weighted interpolation is adopted to generate dense grid points (such as 50x50 grid, 100x100 grid, etc.) in the large circle area of the single crystal silicon wafer or the large square area of the single crystal silicon square wafer based on the discrete point data, the coordinate of each grid point is , and the corresponding interpolated resistivity value is ; S133. Construct a 3D surface graph of plane coordinate-resistivity with the resistivity value of the grid point as the Z-axis height; Encode the Z-axis height (resistivity value) with a gradual color scale (such as from blue to red), the low resistivity area is displayed as blue, the high resistivity area is displayed as red, and the intermediate values are proportionally mapped to transition colors; Make the 3D surface graph continuously visualized by smooth rendering method to highlight the gradient change of resistivity; S134. Project the 3D surface graph along the Z-axis direction to the X-Y plane to form a 2D color mapping projection graph; Project the measurement value or on the 3D surface graph along the X-axis and Y-axis directions to the Y-Z plane and X-Z plane respectively to form scatter plots; the color coding of the 2D color mapping projection graph is consistent with the 3D surface, which facilitates the positioning of the resistivity abnormal area (such as high value area, low value area) on the plane; S135. Add a color bar to the 3D graph surface graph and the 2D color mapping projection graph, label the resistivity value range corresponding to the color; label the coordinate axes (X-axis and Y-axis are spatial coordinates, unit mm; Z-axis is resistivity, unit and legend to ensure that the graph is interpretable; S14. Calculate the single crystal silicon wafer or single crystal silicon square piece doping uniformity index by constructing a triple integral model ; Specifically including: S141. In photovoltaic single crystal silicon, the electrically active doping concentration (unit: cm-3) ) and the resistivity (unit: Ωcm) ) satisfy the micro form of Ohm's law: ; Where, is the electronic charge, ; , unit: is the carrier mobility, which is related to the crystal defects, temperature, and doping type of silicon material, and can be obtained through experiments or databases. Many scholars have conducted in-depth research on carrier mobility. In engineering applications, the carrier mobility in single crystal silicon at room temperature can be considered as a constant, whose value is determined by the type of single crystal silicon. N-type silicon is a donor doping, the main carrier is electron, and the hole mobility has little effect on the conductivity, so it is generally not considered, so the electron mobility is considered as the carrier mobility, that is, ; P-type silicon is an acceptor doping, the main carrier is a hole, and the electron mobility has little effect on the conductivity, so it is generally not considered, so the hole mobility is considered as the carrier mobility, that is, ; S142. Single crystal silicon is a three-dimensional continuum, and the doping concentration is a function of the spatial coordinates , in order to describe the overall doping uniformity, the degree of deviation of the doping concentration from the average value is integrated in the whole domain of the single crystal silicon wafer or single crystal silicon square piece, and a triple integral model is constructed: The doping uniformity index reflecting the relative dispersion degree of the doping concentration , ; Where, is the three-dimensional spatial domain of the silicon wafer, and the volume of the silicon wafer is , is the average doping concentration in the whole domain, ; S143. In actual detection, the continuous function cannot be directly obtained, and the doping concentration is deduced from the resistivity of the discrete measurement points of the silicon wafer, and the triple integral is discretized into summation; S1431. Volume element division of measurement points: simplify the silicon wafer along the thickness direction Z axis to a thin sheet (thickness t is much smaller than the radial size), then the three-dimensional volume element is approximated to a two-dimensional area element multiplied by the thickness , that is ; For the pth ring on the single-crystalline silicon wafer : th small circle on the pth ring: Small circle area ; Corresponding volume element ; For the pth square ring on the single-crystalline silicon wafer th small square on the pth square ring: Small square area ; Corresponding volume element ; , ; for each measurement point on the single-crystalline silicon wafer, assume that the doping is uniform in the local region, i.e. , ; combining the resistivity-doping concentration relationship, we obtain: ; ; wherein is the carrier mobility of the measurement point on the single-crystalline silicon wafer; is the carrier mobility of the measurement point on the single-crystalline silicon wafer; S1433. Discretize triple integral Global average doping concentration of single-crystalline silicon wafer Discretize as: ; wherein is the total volume of the silicon wafer, ; Replace the triple integral with discrete summation, and the doping uniformity index is: ; Global average doping concentration of single-crystalline silicon wafer Discretize as: ; wherein is the total volume of the silicon wafer, ; Replace the triple integral with discrete summation, and the doping uniformity index is: ; In actual engineering applications: to reduce the calculation complexity, the following simplifications can be made in engineering practice: Volume element equivalence: if the size of the small circle / small square is uniform, it can be allowed that or ( is the unit volume element), then is simplified as: ; ; wherein, is the total number of measurement points, and the wafer or the square wafer ; The greater the value is, the more uneven the doping distribution is (for example, the temperature field is abnormal in the crystal pulling process, and the dopant diffusion is uneven), which can directly guide the optimization of the crystal growth process (for example, adjusting the crucible rotation speed and the dopant flow rate); S2. Evaluation of axial resistivity and doping uniformity of the single crystal silicon rod, specifically comprising: S21. A single crystal silicon wafer is cut from the head, middle and tail of the single crystal silicon rod, specifically, for the single crystal silicon rod with a ridge line and a tail section, a 2-3mm thick wafer is cut from the start position of the equal diameter, a 2-3mm thick wafer is cut from the midpoint of the equal diameter length, and a 2-3mm thick wafer is cut from the end position of the equal diameter (the start position of the tail section); for the single crystal silicon rod without a ridge line and a tail section, a 2-3mm thick wafer is cut from the start position of the equal diameter, a 2-3mm thick wafer is cut from the midpoint of the single crystal silicon rod corresponding to the head and tail sections, and a 2-3mm thick wafer is cut from the position of the length D (the diameter of the single crystal silicon rod) before the disappearance of the ridge line in the equal diameter stage; the single crystal silicon wafers cut from the head, middle and tail are respectively denoted as single crystal silicon wafer S, single crystal silicon wafer M and single crystal silicon wafer T; S22. The average resistivity of the single crystal silicon wafer S, single crystal silicon wafer M and single crystal silicon wafer T is measured by using the quantitative evaluation method of the resistivity uniformity of the single crystal silicon wafer, and is respectively denoted as , and ; S23. Evaluation of axial resistivity uniformity: the range reflecting the maximum fluctuation range of the axial resistivity and the variance reflecting the overall dispersion degree of the axial resistivity are calculated, the range and the variance are normalized, and then the axial uniformity index of the single crystal silicon rod is formed by linear combination through a weight coefficient to determine the axial resistivity uniformity grade; the range formula is: ; wherein, is the range, , , ; The smaller the value is, the more stable the axial resistivity is; The variance formula is: ; wherein, the variance; the smaller the variance, the more concentrated the data, and the better the uniformity; The axial uniformity index of the single crystal silicon rod The formula is: ; wherein, the axial uniformity index of the single crystal silicon rod, the range of qualified values, the threshold value of the qualified variance, , the weight coefficient; The determination method of the axial resistivity uniformity level is: The axial resistivity uniformity index ≤0.3, the axial resistivity uniformity level is excellent; The axial resistivity uniformity index 0.3 ≤0.7, the axial resistivity uniformity level is qualified; The axial resistivity uniformity index >0.7, the axial resistivity uniformity level is poor; S24. Axial doping uniformity evaluation: considering the segregation coefficient of the doping element in silicon The influence of axial doping, a doping concentration correction model is established; by comparing the deviation of the measured resistivity and the theoretical model, the axial doping uniformity is evaluated; The doping concentration correction model is: ; wherein, the initial doping concentration, the axial position, the length of the silicon rod, wherein The value range of is the thickness of the single crystal silicon wafer, usually ; By comparing the deviation of the measured resistivity and the theoretical model, the method for evaluating the axial doping uniformity is: ; The smaller the deviation, the more uniform the axial doping.

[0013] Embodiment 1: a method for evaluating the resistivity uniformity of a photovoltaic single crystal silicon material, as shown in Figures 1-4 , taking a phosphorus-doped N-type photovoltaic single crystal silicon wafer with a diameter of 256 mm and a thickness of 2.5 mm (taken from the head piece of the M10 single crystal silicon rod production process) as an example, the specific steps are as follows: S11. Standardized distribution on a single crystal silicon wafer; the diameter of the single crystal silicon wafer is D (256 mm), a rectangular coordinate system is established with the center coordinate of the single crystal silicon wafer as the origin, and the origin coordinate is (0, 0); N (N = 5) concentric circles with the origin as the center are arranged in the large circle with a diameter of D, and the circle ring sequence number K from the inside to the outside is 1, 2, 3, 4, and 5 in turn; A number of small circles with a diameter of d (d = 30 mm) are uniformly distributed on each circle ring as a measurement area, and the center of the small circle is a measurement point. When k = 1, the first circle ring is a center small circle, numbered 1-1, the center is at the origin, the number of small circles n1 = 1, and the first circle ring radius R1 = 0; when k ≥ 2, the small circles are arranged in turn in a counterclockwise direction from the positive direction of the x-axis with the origin as the center, and the number of small circles is n k = 6 (k-1), and the small circles are numbered in turn in a counterclockwise direction as k-1 to k-n k ; specifically, Circle ring 1 (k = 1): R1 = 0, n1 = 0, meaningless; Circle ring 2 (k = 2): R2 = 30 mm, n2 = 6, ; Circle ring 3 (k = 3): R3 = 60 m, n3 = 12, ; Circle ring 4 (k = 4): R4 = 90 mm, n4 = 18, ; Circle ring 5 (k = 5): R5 = 120 mm, n5 = 24, ; Center coordinates (partial examples): O 1-1 : (0, 0); O 2-1 (m = 1): , , that is, (30, 0); O 2-2 (m = 2): , , , that is, (15, 25.98); O 3-1 (m = 1): , , that is, (60, 0); The coordinates of all small circle centers are shown in Table 1: Table 1 Coordinates of all small circle centers

[0014] S12. Quantitative evaluation of the uniformity of the resistivity of the single crystal silicon wafer: The resistivity of each point area (unit: Ω·cm) is measured: Ring 1: p 1-1 = 0.873; Ring 2: p 2-1 ~ p 2-6 = [0.874, 0.859, 0.862, 0.878, 0.856, 0.864]; Ring 3: p 3-1 ~ p 3-12 = [0.879, 0.878, 0.886, 0.896, 0.899, 0.905, 0.886, 0.901, 0.881, 0.875, 0.87, 0.88]; Ring 4: p 4-1 ~ p 4-18 = [0.912, 0.897, 0.938, 0.941, 0.936, 0.954, 0.95, 0.961, 0.928, 0.957, 0.928, 0.902, 0.939, 0.889, 0.938, 0.921, 0.906, 0.912]; Ring 5: p 5-1 ~ p 5-24 = [1.448, 1.494, 1.502, 1.566, 1.246, 1.619, 1.589, 1.725, 1.715, 1.746, 1.455, 1.393, 1.619, 1.702, 1.645, 1.463, 1.416, 1.467, 1.541, 1.514, 1.559, 1.235, 1.139, 1.482]; The total number of measurement points is calculated: ; the average resistivity is: ; the standard deviation is: ; the coefficient of variation is: ; the resistivity uniformity level is evaluated quantitatively according to the coefficient of variation, and since the coefficient of variation CV> 15%, the resistivity uniformity level is poor; S13. Intuitive visualization of the resistivity distribution of the single crystal silicon wafer: S131. Integrate the coordinates and resistivity data of all 61 small circles in the single crystal silicon wafer into a three-dimensional data set and import it into visualization software (such as MATLAB, Python-Matplotlib); S132. Generate dense grid points (50x50 continuous data) in the large circle area of the single crystal silicon wafer based on the discrete point data using Kriging interpolation; S133. The resistivity value of the grid point is Z-axis height, the construction of the plane coordinates-resistivity 3D surface map (see Figure 4 ); Z-axis for resistivity 0.856~1.746 , the color from blue (0.856) to red (1.746), the surface as a whole presents steep ups and downs (because CV≈27.19%, poor uniformity); S134. 3D surface map along the Z-axis direction projection to X-Y plane, forming a 2D color mapping projection map; The measured value on the 3D surface map , respectively, along the X-axis, Y-axis direction projection to Y-Z plane, X-Z plane, forming a scatter plot; 2D color mapping projection map color coding and 3D surface consistent; S135. In the 3D graph surface map and 2D color mapping projection map added color bar, color corresponding to the resistivity value range (0.856~1.746 ), output visualization results; S14. By constructing a triple integral model to calculate the single crystal silicon wafer doping uniformity index ; Small circle area ; The corresponding volume element ; The total volume of single crystal silicon wafer ; For N-type single crystal silicon, the relationship between doping concentration and resistivity is: ; The doping concentration (unit: ) of each point area is calculated as follows: Ring 1: =3.897072; Ring 2: =[3.901536, 3.834576, 3.847968, 3.919392, 3.821184, 3.856896]; Ring 3: =[3.923856, 3.919392, 3.955104, 3.999744, 4.013136, 4.03992, 3.955104, 4.022064, 3.932784, 3.906, 3.88368, 3.92832]; Ring 4: =[4.071168, 4.004208, 4.187232, 4.200624, 4.178304, 4.258656, 4.2408, 4.289904, 4.142592, 4.272048, 4.142592, 4.026528, 4.191696, 3.968496, 4.187232, 4.111344, 4.044384, 4.071168]; annulus 5: =[6.463872, 6.669216, 6.704928, 6.990624, 5.562144, 7.227216, 7.093296, 7.7004, 7.65576, 7.794144, 6.49512, 6.218352, 7.227216, 7.597728, 7.34328, 6.530832, 6.321024, 6.548688, 6.879024, 6.758496, 6.959376, 5.51304, 5.084496, 6.615648]; full-area average doping concentration of a single crystal silicon wafer ; doping uniformity index of a single crystal silicon wafer , the greater the doping distribution is more uneven, so the doping uniformity of the single crystal silicon wafer of the embodiment is poor.

[0015] Embodiment 2: A method for evaluating the resistivity uniformity of a photovoltaic single crystal silicon material, such as Figures 1-2 , 5 and 6, taking a phosphorus-doped N-type photovoltaic single crystal silicon wafer with a diameter of 300 mm and a thickness of 2.5 mm (taken from the head piece of a single crystal silicon rod in the production process of a G12 single crystal silicon rod) as an example, the specific steps are as follows: S11. Standardized dotting is performed on the single crystal silicon wafer; assuming that the diameter of the single crystal silicon wafer is D (300 mm), a rectangular coordinate system is established with the center coordinate of the single crystal silicon wafer as the origin, and the origin coordinate is (0, 0); N (N = 6) concentric annuli with the origin as the center are arranged within the large circle with a diameter of D, and the outer annulus sequence number K is 1, 2, 3, 4, 5 and 6 in turn; A number of small circles with a diameter of d (d = 30 mm) are uniformly distributed on each annulus as measurement regions, and the center of the small circle is a measurement point; when k = 1, the first annulus is the center small circle, the number is 1-1, the center is at the origin, the number of small circles n1 = 1, and the radius of the first annulus R1 = 0; when k ≥ 2, the small circles are arranged in the clockwise direction in turn from the positive direction of the x-axis, and the number of small circles is n k = 6 (k-1), and the small circles are numbered in the counterclockwise direction as k-1 to k-n k ; specifically,​ Annulus 1 (k = 1): R1= 0, n1= 0, Nonsense; Annulus 2 (k = 2): R2= 30 mm, n2= 6, ; Annulus 3 (k = 3): R3= 60 m, n3= 12, ; Annulus 4 (k = 4): R4= 90 mm, n4= 18, ; Annulus 5 (k = 5): R5= 120 mm, n5= 24, ; Annulus 6 (k = 6): R6= 150 mm, n6= 30, ; Center coordinates (partial examples): O 1-1 : (0, 0); O 2-1 (m = 1): , i.e. (30, 0); O 2-2 (m = 2): , , i.e. (15, 25.98); O 3-1 (m = 1): , i.e. (60, 0); The coordinates of the centers of all small circles are shown in Table 2: Table 2 Coordinates of the centers of all small circles

[0016] S12. Quantitative evaluation of the resistivity uniformity of a single crystal silicon wafer: The resistivity (unit: Ω·cm) of each point area is measured: Annulus 1: p 1-1 = 1.153; Annulus 2: p 2-1 ~ p 2-6 = [1.209, 1.181, 1.155, 1.172, 1.193, 1.167]; Annulus 3: p 3-1 ~ p 3-12 = [1.222, 1.227, 1.249, 1.229, 1.202, 1.225, 1.222, 1.234, 1.218, 1.209, 1.217, 1.229]; Annulus 4: p4-1 4-18 = [1.23, 1.243, 1.263, 1.267, 1.268, 1.274, 1.246, 1.275, 1.257, 1.211, 1.261, 1.231, 1.256, 1.229, 1.223, 1.224, 1.234, 1.234]; Ring 5: p 5-1 5-24 = [1.239, 1.245, 1.261, 1.258, 1.256, 1.265, 1.268, 1.271, 1.251, 1.267, 1.283, 1.276, 1.262, 1.241, 1.269, 1.252, 1.269, 1.246, 1.207, 1.264, 1.239, 1.258, 1.245, 1.276]; Ring 6: p 6-1 6-30 = [1.397, 1.329, 1.417, 1.345, 1.389, 1.361, 1.349, 1.344, 1.351, 1.361, 1.321, 1.382, 1.337, 1.378, 1.335, 1.363, 1.351, 1.303, 1.302, 1.311, 1.329, 1.332, 1.337, 1.334, 1.302, 1.308, 1.329, 1.346, 1.341, 1.382]; Total number of measurement points: Average resistivity: Standard deviation: Coefficient of variation: According to the coefficient of variation, the resistivity uniformity level is excellent since the coefficient of variation CV < 5%; S13. Intuitive visualization of the resistivity distribution of the single crystal silicon wafer: S131. Integrate the coordinates and resistivity data of all 91 small circles in the single crystal silicon wafer into a three-dimensional data set and import it into visualization software (such as MATLAB, Python-Matplotlib); S132. Generate dense grid points (50x50 continuous data) in the large circle area of the single crystal silicon wafer based on discrete point data using Kriging interpolation; S133. Construct a 3D surface plot of the plane coordinates-resistivity with the resistivity value of the grid point as the Z-axis height (see Figure 6 ); Z-axis is the resistivity 1.153~1.417 ​​​, the color gradually changes from blue (1.153) to red (1.417), and the overall surface presents steep ups and downs (because CV≈4.72%, the uniformity is good); S134. Project the 3D surface graph along the Z-axis direction to the X-Y plane to form a 2D color mapping projection graph; The measured values on the 3D surface graph are projected along the X-axis and Y-axis directions to the Y-Z plane and X-Z plane respectively to form scatter graphs; the color coding of the 2D color mapping projection graph is consistent with the 3D surface; S135. Add a color bar to the 3D graph surface graph and the 2D color mapping projection graph to mark the resistivity value range corresponding to the color (1.153~1.417 ), and output the visualization result; S14. Calculate the single crystal silicon wafer doping uniformity index by constructing a triple integral model; Small circle area ; Corresponding volume element ; Total volume of single crystal silicon wafer ; For N-type single crystal silicon, the relationship between doping concentration and resistivity is: ; Calculate the doping concentration (unit: ) of each distribution point area: Ring 1: =5.146992; Ring 2: =[5.396976, 5.271984, 5.15592, 5.231808, 5.325552, 5.209488]; Ring 3: =[5.455008, 5.477328, 5.575536, 5.486256, 5.365728, 5.4684, 5.455008, 5.508576, 5.437152, 5.396976, 5.432688, 5.486256]; Ring 4: =[5.49072, 5.548752, 5.638032, 5.655888, 5.660352, 5.687136, 5.562144, 5.6916, 5.611248, 5.405904, 5.629104, 5.495184, 5.606784, 5.486256, 5.459472, 5.463936, 5.508576, 5.508576]; Circle 5: =[5.530896, 5.55768, 5.629104, 5.615712, 5.606784, 5.64696, 5.660352, 5.673744, 5.584464, 5.655888, 5.727312, 5.696064, 5.633568, 5.539824, 5.664816, 5.588928, 5.664816, 5.562144, 5.388048, 5.642496, 5.530896, 5.615712, 5.55768, 5.696064]; Circle 6: =[6.236208, 5.932656, 6.325488, 6.00408, 6.200496, 6.075504, 6.021936, 5.999616, 6.030864, 6.075504, 5.896944, 6.169248, 5.968368, 6.151392, 5.95944, 6.084432, 6.030864, 5.816592, 5.812128, 5.852304, 5.932656, 5.946048, 5.968368, 5.954976, 5.812128, 5.838912, 5.932656, 6.008544, 5.986224, 6.169248]; Global average doping concentration of single crystal silicon wafer ; Doping uniformity index of single crystal silicon wafer , the greater the doping distribution is more uneven, so the doping uniformity of the single crystal silicon wafer of the embodiment is better.

[0017] Embodiment 3: A method for evaluating the resistivity uniformity of a photovoltaic single crystal silicon material, taking a phosphorus-doped N-type single crystal rod with a diameter of 256 mm and a length of 2100 mm grown at a constant diameter as an example, the specific steps are as follows (see Figures 1-4 , 7 and 8): S21. From the head (axial position 0 mm), the middle (axial position 1005 mm), and the tail (constant diameter end position (constant diameter 2100 mm)) of the single crystal silicon rod, a single crystal silicon wafer with a thickness of 2.5 mm is cut off, respectively, and recorded as single crystal silicon wafer S, single crystal silicon wafer M, and single crystal silicon wafer T; S22. The average resistivity of single crystal silicon wafer S, single crystal silicon wafer M, and single crystal silicon wafer T is measured by using the quantitative evaluation method of the resistivity uniformity of the single crystal silicon wafer in embodiment 1, and recorded as (1.79 ), respectively.​ (1.40 ) and (1.14 ); S23. Axial resistivity uniformity evaluation: Calculate the range reflecting the maximum fluctuation range of axial resistivity: Maximum value: ; Minimum value: ; Average value: ; Range: ; Calculate the variance reflecting the overall dispersion degree of axial resistivity: ; The range and variance are normalized, and then linearly combined by a weight coefficient to form a single crystal silicon rod axial uniformity index to determine the axial resistivity uniformity grade; specifically, Range qualified domain value ; Qualified variance threshold ; Weight coefficient , (the range has a higher weight on uniformity); Single crystal silicon rod axial uniformity index: ; Since the axial resistivity uniformity index > 0.7, the axial resistivity uniformity grade is poor; S24. Axial doping uniformity evaluation: considering the segregation coefficient of doping elements in silicon The influence of axial doping, establish a doping concentration correction model; by comparing the deviation of the measured resistivity and the theoretical model, evaluate the axial doping uniformity; The average resistivity of the head, middle and tail pieces of the single crystal silicon rod , , ; For phosphorus-doped single crystal silicon, the segregation coefficient of phosphorus in silicon ; The initial doping concentration is back calculated from the head resistivity (the head is the "initial reference position" of doping), and the measured doping concentration at each position is calculated using the conversion formula between resistivity and doping concentration: ; ; ; Using the modified model Calculating the theoretical doping concentration : Head piece (S, ): ; Middle piece (M, ): ; Tail piece (T, ): ; Axial doping uniformity ; It is shown that the axial doping uniformity is still poor; the actual doping concentration in the tail part is lower than the theoretical value, reflecting the deviation between the actual growth process and the theoretical model; this result can guide process optimization: the doping supply strategy or the thermal field parameters of crystal growth need to be adjusted to reduce the deviation between the measured value and the theoretical value and improve the axial doping uniformity.

[0018] Example 4: A method for evaluating the resistivity uniformity of a photovoltaic monocrystalline silicon material, taking a gallium-doped P-type photovoltaic monocrystalline silicon square piece (specification M10) with a side length of 182 mm and a thickness of 120 μm as an example, as shown in Figures 9-12 , the specific steps are as follows: S1. Evaluation of the resistivity and doping uniformity of the monocrystalline silicon square piece, specifically including: S11. Standardized point arrangement on the monocrystalline silicon square piece; Let the square side length of the monocrystalline silicon square piece be a (a = 182 mm), and establish a rectangular coordinate system with the center coordinates of the monocrystalline silicon square piece as the origin, and the origin coordinates as (0, 0); M (M = 8) concentric square rings with the origin as the center are arranged in the large square with a side length of a (a = 182 mm), and the square ring sequence number p from inside to outside is 1, 2, 3, 4, 5, 6, 7, and 8; A plurality of small squares with a side length of l (l = 13 mm) are uniformly distributed on each square ring as measurement areas, and the center of the small square is a measurement point; when p = 1, the first square ring is a center small square, numbered 1-1, with the center at the origin, and the number of small squares n1 = 1, and the diameter of the first square ring l1 = 0; when p ≥ 2, the small squares are arranged in a counterclockwise direction from the x-axis positive direction, and the number of small squares is n p = 8 (p-1), and 2 (p-1) small squares are arranged on each side of the square ring, and the small squares are numbered in a counterclockwise direction as p-1 to p-n p ; The center coordinates of the qth small square on the pth square ring are O p-q , coordinate O p-q The formula is: ; According to the above formula, the coordinates of the center of each small square (partial examples) are: O 1-1 : (0, 0); O 2-1 (p = 2, q = 1): (13, 0); O 2-2 (p = 2, q = 2): (13, 13); O 3-1 (p = 3, q = 1): (60, 0); S12. Quantitative evaluation of the uniformity of the resistivity of a single crystal silicon square sheet: Measure the resistivity of each point area (see Table 3), Table 3 Coordinates and resistivity measurement values and doping concentration of all small squares

[0019] Calculate the total number of measurement points: ; Calculate the average resistivity: ; Standard deviation: ; Coefficient of variation: ; According to the coefficient of variation, the resistivity uniformity level is evaluated quantitatively: since the coefficient of variation CV < 5%, the resistivity uniformity level is excellent; S13. Intuitive visualization of the resistivity distribution of a single crystal silicon square sheet: S131. Integrate the coordinates and resistivity data of all 225 small squares in the single crystal silicon square sheet into a three-dimensional data set and import it into visualization software (such as MATLAB, Python-Matplotlib); S132. Based on the discrete point data, generate dense grid points (50x50 grid continuous data) in the large square area of the single crystal silicon square sheet using Kriging interpolation; S133. Take the resistivity value of the grid point as the Z-axis height, construct a 3D surface plot of the plane coordinate-resistivity (see Figure 12 ); The Z-axis is the resistivity 0.536~0.676 , the color gradually changes from blue (0.536) to red (0.676), and the overall surface presents steep ups and downs (because CV ≈ 4.84%, the uniformity is excellent); S134. Project the 3D surface plot along the Z-axis direction to the X-Y plane to form a 2D color mapping projection map; Measurements on the 3D surface plot Projecting along the X-axis and Y-axis directions onto the YZ plane and XZ plane respectively, forming a scatter plot; the color coding of the 2D color mapping projection map is consistent with that of the 3D curved surface; S135. Add color bars to the 3D surface plot and the 2D color-mapped projection plot, indicating the resistivity range (0.536~0.676) corresponding to each color. Output visualization results; S14. Calculate the doping uniformity index of single-crystal silicon wafers by constructing a triple integral model. ; Area of ​​small square ; Corresponding volume element ; Total volume of single-crystal silicon wafer ; For P-type single-crystal silicon, the relationship between doping concentration and resistivity is as follows: ; Calculate the doping concentration for each distribution area (see Table 3): Global average doping concentration of single-crystal silicon wafers ; Uniformity of doping in single-crystal silicon wafers ,because The larger the doping density, the less uniform the doping distribution. Therefore, the single-crystal silicon wafer in this embodiment exhibits excellent doping uniformity.

[0020] The specific embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials, characterized in that, The evaluation of resistivity and doping uniformity across all morphologies of photovoltaic monocrystalline silicon rods, wafers, and square wafers is carried out through the following steps: S1. Evaluation of resistivity and doping uniformity of single-crystal silicon wafers or single-crystal silicon square wafers, specifically including: S11. Standardize the layout of dots on monocrystalline silicon wafers or monocrystalline silicon square wafers; S12. Quantitative assessment of resistivity uniformity of monocrystalline silicon wafers or monocrystalline silicon squares: Measure the resistivity of each area, calculate the total number of measurement points, calculate the average resistivity, standard deviation and coefficient of variation, and quantitatively assess the resistivity uniformity level based on the coefficient of variation. S13. Visualize the resistivity distribution of monocrystalline silicon wafers or monocrystalline silicon squares. S14. Calculate the doping uniformity index of monocrystalline silicon wafers or monocrystalline silicon square wafers by constructing a triple integral model. ; S2. Evaluation of axial resistivity and doping uniformity of single-crystal silicon rods, specifically including: S21. Cut monocrystalline silicon wafers from the head, middle and tail of a monocrystalline silicon rod, and denot them as monocrystalline silicon wafer S, monocrystalline silicon wafer M and monocrystalline silicon wafer T, respectively. S22. The average resistivity of monocrystalline silicon wafers S, M, and T was determined using a quantitative evaluation method for resistivity uniformity of monocrystalline silicon wafers, and denoted as follows: , and ; S23. Axial resistivity uniformity assessment: Calculate the range, which reflects the maximum fluctuation range of axial resistivity, and the variance, which reflects the overall dispersion of axial resistivity. Normalize the range and variance, and then form the axial uniformity index of single crystal silicon rod by linear combination of weighting coefficients to determine the axial resistivity uniformity level. S24. Axial doping uniformity assessment: Considering the segregation coefficient of dopants in silicon The influence of axial doping was investigated by establishing a doping concentration correction model; the uniformity of axial doping was evaluated by comparing the deviation between the measured resistivity and the theoretical model.

2. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 1, characterized in that: S11. Standardized dot layout is performed on the monocrystalline silicon wafer or monocrystalline silicon square wafer, as follows: S111. Method for standardized layout on a single-crystal silicon wafer: Let the diameter of the single-crystal silicon wafer be D. Establish a rectangular coordinate system with the center coordinates of the single-crystal silicon wafer as the origin, and the origin coordinates are (0,0). Set N concentric rings with the origin as the center inside the large circle with diameter D. The ring numbers K from the inner to the outer ring are 1 to N respectively. Each annulus is uniformly distributed with several small circles of diameter d as the measurement area. The center of each small circle is the measurement point. When k=1, the first annulus is the central small circle, numbered 1-1, with its center at the origin. The number of small circles is n1=1, and the radius of the first annulus is R1=0. When k≥2, the small circles are arranged counterclockwise from the origin along the positive x-axis, with n circles in total. k =6(k-1), the small circles are numbered sequentially from k-1 to kn in a counterclockwise direction. k ; The radius of the k-th ring is R. k When k=1, R1=0; when k≥2, R k =(k-1)d; the coordinates of the center O of the m-th small circle on the k-th annulus. k-m Coordinate O k-m The formula is: ； When k=1: R1=0, n1=1, , so O 1-1 (0, 0); When k≥2: , , The coordinates O of the center of the m-th small circle on the k-th annulus. k-m The formula simplifies to: ； S112. Method for standardized dot placement on a single-crystal silicon wafer: Let the side length of the square of the monocrystalline silicon wafer be a. Establish a rectangular coordinate system with the center coordinates of the monocrystalline silicon wafer as the origin, and the origin coordinates are (0,0). Set M concentric square rings with the origin as the center inside the large square with side length a. The numbers p of the square rings from the inside to the outside are 1 to M respectively. Each square ring has several small squares with side length l evenly distributed as the measurement area. The center of each small square is the measurement point. When p=1, the first square ring has a central small square, numbered 1-1, centered at the origin, with n1=1 small squares and l1=0 diameter of the first square ring. When p≥2, starting from the positive x-axis and centering on the central point, the small squares are arranged counterclockwise, with n small squares in total. p =8(p-1), each side of the square ring is arranged with 2(p-1) small squares, and the small squares are numbered from p-1 to pn in a counterclockwise direction. p ; The center coordinates O of the q-th small square on the p-th square ring are... p-q Coordinate O p-q The formula is: 。 3. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 1, characterized in that: S12. Quantitative evaluation of resistivity uniformity of monocrystalline silicon wafers or monocrystalline silicon square sheets, as detailed below: S121. Quantitative assessment of resistivity uniformity of single-crystal silicon wafers: Let the measured resistivity of the m-th smaller circle of the k-th ring be... The total number of measurement points is: ； Average resistivity μ: ； Standard deviation σ: ； Coefficient of variation (CV): ； S122. Quantitative evaluation of resistivity uniformity of monocrystalline silicon wafers: Let the resistivity measurement of the p-th square ring and the q-th small square be... The total number of measurement points is: ； average resistivity : ； Standard deviation : ； Coefficient of variation (CV): 。 4. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 3, characterized in that: The method for quantitatively assessing the resistivity uniformity level based on the coefficient of variation is as follows: The coefficient of variation (CV) is less than 5%, and the resistivity uniformity is rated as excellent. The coefficient of variation is 5% < CV ≤ 15%, and the resistivity uniformity level is qualified. The coefficient of variation (CV) is greater than 15%, and the resistivity uniformity is classified as poor.

5. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 1, characterized in that: S13. Visualizing the resistivity distribution of single-crystal silicon wafers or single-crystal silicon square wafers specifically includes: S131. Integrate the coordinates and resistivity data of all small circles in the single-crystal silicon wafer into a three-dimensional dataset: ； in, For planar coordinates, This is the resistivity value at that point; Alternatively, the coordinates and resistivity data of all the small squares in a single-crystal silicon wafer could be integrated into a three-dimensional dataset: ； in, For planar coordinates, This is the resistivity value at that point; S132. Using Kriging interpolation or inverse distance weighted interpolation, generate dense grid points within the large circular region of a single-crystal silicon wafer or the large square region of a single-crystal silicon wafer based on discrete point data. The coordinates of each grid point are... The corresponding interpolated resistivity value is ; S133. Using the resistivity values ​​of grid points Construct a 3D surface plot of planar coordinates versus resistivity, with the Z-axis height as the reference. The Z-axis height is encoded using gradient color stops, with intermediate values ​​mapped to transition colors proportionally. The 3D surface plot is visualized continuously using a smooth rendering method to highlight the gradient changes in resistivity. S134. Project the 3D surface map onto the XY plane along the Z-axis to form a 2D color mapping projection map; Measurements on the 3D surface plot or Projecting along the X-axis and Y-axis directions onto the YZ plane and XZ plane respectively, forming a scatter plot; the color coding of the 2D color mapping projection map is consistent with that of the 3D curved surface; S135. Add color bars to the 3D surface plot and the 2D color mapping projection plot to indicate the range of resistivity values ​​corresponding to the colors.

6. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 1, characterized in that: S14. Calculate the doping uniformity index of monocrystalline silicon wafers or monocrystalline silicon square wafers by constructing a triple integral model. Specifically, it includes: S141. Electroactive doping concentration in photovoltaic monocrystalline silicon The unit is With resistivity The unit is The microscopic form that satisfies Ohm's law is: ； in, For electron charge, ; The unit is The carrier mobility is related to the crystal defects, temperature, and doping type of silicon material, and can be obtained through experiments or databases. S142. Single-crystal silicon is a three-dimensional continuum, with a doping concentration of... Spatial coordinates The function is integrally derived over the entire domain of a single-crystal silicon wafer or a single-crystal silicon square wafer, with respect to the degree of deviation of the doping concentration from the mean, to construct a triple integral model: Doping uniformity index, which reflects the relative dispersion of doping concentration. , ； in, Let be the three-dimensional spatial domain of the silicon wafer, and let the volume of the silicon wafer be . , The global average doping concentration, ; S143. The doping concentration is inferred from the resistivity of discrete measurement points on the silicon wafer, and the triple integral is discretized into a summation. S1431. Volume element division of measurement points: Simplify the silicon wafer along the thickness direction Z-axis into a thin sheet, then the three-dimensional volume element... Approximately a two-dimensional area element Multiply by thickness ,Right now ; For the first on a single-crystal silicon wafer The first ring on the ring A small circle: Area of ​​small circle ; Corresponding volume element ; For the p-th square ring and the q-th smaller square on a single-crystal silicon wafer: Area of ​​small square ; Corresponding volume element ; S1432. Deducing Doping Concentration from Resistivity: For each measurement point on a single-crystal silicon wafer, assume uniform doping in the local area, i.e. , For each measurement point on a single-crystal silicon wafer, it is assumed that the doping is uniform in the local area, i.e. , Combining the resistivity-doping concentration relationship, we obtain: ； ； in, This represents the carrier mobility at this measurement point on a single-crystal silicon wafer. This represents the carrier mobility at this measurement point on a single-crystal silicon wafer. S1433. Discretized Triple Integral Global average doping concentration of single-crystal silicon wafers Discretized as: ； in, This refers to the total volume of the silicon wafer. ; Replacing triple integrals with discrete summation improves the doping uniformity index. for: ； Global average doping concentration of single-crystal silicon wafers Discretized as: ； in, This refers to the total volume of the silicon wafer. ; Replacing triple integrals with discrete summation improves the doping uniformity index. for: 。 7. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 1, characterized in that: The range formula for evaluating the axial resistivity uniformity in S23 is as follows: ； in, Extremely poor , , ; The variance formula is: ； in, For variance; Axial uniformity index of single crystal silicon rod The formula is: ； in, This is an index of the axial uniformity of single-crystal silicon rods. This is the acceptable range threshold. The acceptable variance threshold, , These are the weighting coefficients.

8. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 7, characterized in that: The method for determining the axial resistivity uniformity level, as stated in S23, is as follows: Axial resistivity uniformity index ≤0.3, axial resistivity uniformity is excellent; Axial resistivity uniformity index 0.3 < ≤0.7, axial resistivity uniformity level is qualified; Axial resistivity uniformity index >0.7, the axial resistivity uniformity level is poor.

9. The method for evaluating the resistivity uniformity of photovoltaic monocrystalline silicon materials according to claim 1, characterized in that: S24. Axial doping uniformity evaluation: The doping concentration correction model is as follows: ； in, The initial doping concentration, This refers to the axial position. The length of the silicon rod; The method for evaluating axial doping uniformity by comparing the deviation between measured resistivity and theoretical model is as follows: ； The smaller the value, the more uniform the axial doping.

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