Control method for resistance of monocrystalline silicon ingot, and monocrystalline silicon ingot, silicon wafer and solar cell

Abstract

Provided in the present application are a control method for the resistance of a monocrystalline silicon ingot, and a monocrystalline silicon ingot, a silicon wafer and a solar cell. The control method comprises: acquiring the concentration of phosphorus and the concentration of stibium in a recharged material; acquiring the concentration of phosphorus and the concentration of stibium in a residual material in a crucible; on the basis of the concentration of phosphorus in the recharged material and the concentration of phosphorus in the residual material in the crucible, calculating the concentration of phosphorus in the recharged material and the residual material in the crucible with respect to the total full charge weight in the current charging section, and on the basis of the concentration of stibium in the recharged material and the concentration of stibium in the residual material in the crucible, calculating the concentration of stibium in the recharged material and the residual material in the crucible with respect to the total full charge weight in the current charging section; on the basis of the concentration proportion of phosphorus, calculating a required concentration of phosphorus, and on the basis of the concentration proportion of stibium, calculating a required concentration of stibium; and on the basis of the required concentration of phosphorus, the total full charge weight in the current charging section and the concentration of a phosphorus master alloy, calculating the doping amount of the phosphorus master alloy, and on the basis of the required concentration of stibium and the total full charge weight in the current charging section, calculating the doping amount of stibium. The control method of the present application can accurately calculate the doping amounts of a phosphorus master alloy and stibium, thereby accurately controlling the resistance of a monocrystalline silicon ingot; and the monocrystalline silicon ingot and a silicon wafer have excellent resistance uniformity.

Description

Methods for controlling the resistance of monocrystalline silicon rods, monocrystalline silicon rods, silicon wafers, and solar cells. Technical Field

[0001] This application mainly relates to the field of photovoltaic technology, and in particular to a method for controlling the resistance of a monocrystalline silicon rod, a monocrystalline silicon rod, a silicon wafer, and a solar cell. Background Technology

[0002] The electrical performance parameters of silicon wafers are among the key factors determining the conversion efficiency of solar cells. Currently, the photovoltaic industry mainly improves these parameters by controlling resistivity and impurity content. Among these, resistivity concentration is a crucial electrical performance parameter. Compared to conventional phosphorus-doped monocrystalline silicon rods, monocrystalline silicon rods can significantly improve the resistivity concentration of silicon wafers; however, the high volatility of antimony increases the difficulty of controlling resistance. Therefore, how to precisely control the resistance of monocrystalline silicon rods is a hot topic in this field. Summary of the Invention

[0003] The technical problem to be solved by this application is to provide a method for controlling the resistance of a monocrystalline silicon rod, a monocrystalline silicon rod, a silicon wafer, and a solar cell. The method for controlling the resistance of the monocrystalline silicon rod can accurately calculate the doping amount of phosphorus masterbatch and antimony, thereby achieving precise control of the resistance of the monocrystalline silicon rod. The monocrystalline silicon rod and silicon wafer have excellent resistance uniformity.

[0004] To address the aforementioned technical problems, this application provides a method for controlling the resistance of a single-crystal silicon rod, comprising: obtaining the phosphorus and antimony concentrations in the re-feed material; obtaining the phosphorus and antimony concentrations in the remaining material in the crucible; and calculating the concentration ratio (C0) of phosphorus in the re-feed material and the remaining material in the crucible within the total weight of the full pot in the current feeding section based on the phosphorus concentrations in the re-feed material and the remaining material in the crucible. r磷 Based on the antimony concentration in the re-added material and the remaining material in the crucible, calculate the concentration ratio (C) of antimony in the re-added material and the remaining material in the crucible in the total weight of the full pot in the current feeding section. r锑 The required phosphorus concentration is calculated based on the phosphorus concentration ratio, and the required antimony concentration is calculated based on the antimony concentration ratio. The doping amount of the phosphorus master alloy is calculated based on the required phosphorus concentration, the total weight of the current feeding section, and the phosphorus master alloy concentration. The doping amount of antimony is calculated based on the required antimony concentration and the total weight of the current feeding section.

[0005] In one embodiment of this application, the phosphorus concentration in the re-feeding is an average concentration, and the method for calculating the average phosphorus concentration includes: converting the target resistance into the phosphorus concentration at the head of the single-crystal silicon rod (C). s磷 According to the formula Calculate the phosphorus concentration (C) at the tail of the single-crystal silicon rod. e磷 ), the k 磷 The effective segregation coefficient of phosphorus, C0磷 Indicates the initial phosphorus concentration, f s The concentration is 0% to 95%; based on the head phosphorus concentration (C) s磷 ) and the tail phosphorus concentration (C e磷 Calculate the average phosphorus concentration.

[0006] In one embodiment of this application, the antimony concentration in the re-feeding material is an average concentration. The method for calculating the average antimony concentration includes: converting the target resistance into the antimony concentration at the head of the single-crystal silicon rod (C). s锑 According to the formula Calculate the antimony concentration (C) at the tail of the single-crystal silicon rod. e锑 ), the k 锑 The C represents the effective segregation coefficient of antimony. 0锑 Indicates the initial antimony concentration, f s The concentration is 0% to 95%, where H represents the overall mass transfer coefficient of antimony in the thermal field; based on the head antimony concentration (C) s锑 ) and the tail antimony concentration (C e锑 Calculate the average concentration of antimony.

[0007] In one embodiment of this application, the phosphorus concentration ratio (C) is calculated according to the following formula. r磷 ):

[0008] In one embodiment of this application, the antimony concentration ratio (C) is calculated according to the following formula. r锑 ):

[0009] In one embodiment of this application, the phosphorus requirement concentration is calculated according to the following formula: Wherein, the k 磷 This represents the effective segregation coefficient of phosphorus.

[0010] In one embodiment of this application, the required antimony concentration is calculated according to the following formula: Wherein, the k 锑 This represents the effective segregation coefficient of antimony.

[0011] In another aspect, this application also proposes a single-crystal silicon rod in which the resistance of the single-crystal silicon rod is controlled using the method described in any of the preceding claims during the drawing process, wherein the axial resistance change rate of the single-crystal silicon rod is not greater than 13.6%, and / or the radial resistance change rate at the head of the single-crystal silicon rod is not greater than 8%, the radial resistivity at the middle of the single-crystal silicon rod is not greater than 15%, the radial resistance change rate at the tail of the single-crystal silicon rod is not greater than 10%, and / or the resistance hit rate of the single-crystal silicon rod is not less than 80%.

[0012] This application also proposes a silicon wafer cut from a single-crystal silicon rod as described above.

[0013] This application also proposes a solar cell whose substrate is made of silicon wafers as described above.

[0014] Compared with the prior art, the present application has the following advantages: the control method of the present application can accurately calculate the doping amount of phosphorus master alloy and antimony, thereby realizing the precise control of the resistance of multiple rods in a single furnace. Compared with empirical methods, the control method of the present application can significantly improve the uniformity of the resistance of single crystal silicon rods.

[0015] Overview of the attached figures

[0016] The features and performance of the present invention are further described by the following embodiments and accompanying drawings.

[0017] Figure 1 is a flowchart illustrating a method for controlling a single-crystal silicon rod resistor according to an embodiment of this application.

[0018] Preferred embodiments of the present invention

[0019] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this application. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.

[0020] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include plural forms. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0021] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0022] In the description of this application, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is usually based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this application and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this application; the directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0023] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0024] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, these terms have no special meaning and therefore should not be construed as limiting the scope of protection of this application. In addition, although the terminology used in this application is selected from commonly known and used terms, some terms mentioned in this application's specification may have been chosen by the applicant according to his or her judgment, and their detailed meanings are explained in the relevant sections of this description. Moreover, this application should be understood not only through the actual terms used, but also through the meaning implied by each term.

[0025] Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, various steps can be processed in reverse order or simultaneously. Furthermore, other operations may be added to these processes, or one or more steps may be removed from these processes.

[0026] The following examples illustrate the method for controlling the resistance of a monocrystalline silicon rod (hereinafter referred to as the "control method"), the monocrystalline silicon rod, the silicon wafer, and the solar cell of this application.

[0027] Referring to the flowchart of a control method in one embodiment shown in Figure 1, the control method of this embodiment includes the following steps S110 to S150.

[0028] S110: Obtain the phosphorus and antimony concentrations in the re-feeding material;

[0029] S120: Obtain the phosphorus and antimony concentrations in the remaining material in the crucible;

[0030] S130: Calculate the phosphorus concentration ratio (C) of the re-feeding material and the remaining material in the crucible to the total weight of the full pot in the current feeding section, based on the phosphorus concentration in the re-feeding material and the remaining material in the crucible. r磷 Based on the antimony concentration in the re-feeded material and the remaining material in the crucible, calculate the concentration ratio (C) of antimony in the re-feeded material and the remaining material in the crucible in the total weight of the full pot in the current feeding section. r锑 );

[0031] S140: Calculate the required phosphorus concentration based on the phosphorus concentration ratio, and calculate the required antimony concentration based on the antimony concentration ratio;

[0032] S150: Calculate the doping amount of phosphorus master alloy based on the phosphorus demand concentration, the total weight of the full pot in the current feeding section, and the phosphorus master alloy concentration; calculate the antimony doping amount based on the antimony demand concentration and the total weight of the full pot in the current feeding section.

[0033] The following describes steps S110 to S150 in detail.

[0034] The single-crystal silicon rod of this application is a phosphorus-antimony co-doped single-crystal silicon rod. In step S110, the phosphorus concentration and antimony concentration in the re-doped material are obtained. Re-doped material is generated during the processing of the single-crystal silicon rod and is added to the crucible for reuse.

[0035] In one embodiment, the phosphorus concentration in the re-feeding refers to the average phosphorus concentration, and the method for calculating the average phosphorus concentration includes the following steps S111 to S113.

[0036] S111: Convert the target resistance to the phosphorus concentration at the head of the single-crystal silicon rod (C). s磷 To elaborate, the target resistance (ρ) of the single-crystal silicon rod is set, and the target resistance (ρ) is converted into the head phosphorus concentration (C) according to the following formula. s磷 ):

[0037] Among them, C s The concentration of phosphorus and antimony in the head is calculated using the following formula:

[0038] Where x = log 10 ρ, A0=-3.1083, A1=-3.2626, A2=-1.2196, A3=-0.13923, B1=1.0265, B2=0.38755, B3=0.041833. C s磷 =C s ×y

[0039] Where y represents the concentration ratio of phosphorus in antimony phosphorus.

[0040] S112: According to the formula Calculate the phosphorus concentration (C) at the tail of the single-crystal silicon rod. e 磷 ), k 磷 C represents the effective segregation coefficient of phosphorus. 0磷 f represents the initial phosphorus concentration. s It ranges from 0% to 95%, for example, f s Take 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 95%, f s = 1 - weight of remaining material in the crucible / weight of the upper section of the full crucible, f s k 磷 C 0磷 The C obtained by substituting into the above formula L磷 The phosphorus concentration in the tail (C) e 磷 ).

[0041] S113: Based on head phosphorus concentration (C) s磷 ) and tail phosphorus concentration (C e磷Calculate the average phosphorus concentration. For example, the average phosphorus concentration can be equal to the head phosphorus concentration (C). s磷 ) and tail phosphorus concentration (C e磷 Divide the sum of () by 2.

[0042] In another embodiment, the antimony concentration in the re-feeding refers to the average concentration of antimony, and the method for calculating the average concentration of antimony includes the following steps S114 to S116.

[0043] S114: Convert the target resistance to the antimony concentration at the head of the single-crystal silicon rod (C). s锑 To elaborate, the target resistance (ρ) of the single-crystal silicon rod is set, and the target resistance (ρ) is converted into the head antimony concentration (C) according to the following formula. s锑 ):

[0044] Z is calculated using the following formula: C s Antimony = C s ×(1-y)

[0045] Please refer to the previous text for an explanation of the parameters in the formula; they will not be elaborated upon here.

[0046] S115: According to the formula Calculate the antimony concentration (C) at the tail of the single-crystal silicon rod. e锑 ), k 锑 C represents the effective segregation coefficient of antimony. 0锑 The initial antimony concentration is represented by H, and the overall mass transfer coefficient of antimony in the thermal field is represented by f. s The range is 0% to 95%. For example, f s Take 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 95%, f s = 1 - weight of remaining material in the crucible / weight of the upper section of the crucible. H can be determined based on the number of induction cycles, constant diameter growth time, power, etc. This application does not limit the specific method for determining H. f s k 锑 C 0锑 Substituting H into the above formula to calculate C L锑 The concentration of antimony at the tail (C) e锑 ).

[0047] S116: Based on head antimony concentration (C) s锑 ) and tail antimony concentration (C e锑 Calculate the average antimony concentration. For example, the average antimony concentration can be equal to the head antimony concentration (C). s锑 ) and tail antimony concentration (C e锑 Divide the sum of () by 2.

[0048] In step S120, the phosphorus concentration and antimony concentration in the remaining material in the crucible are obtained. More specifically, the phosphorus concentration at the tail end (C) calculated earlier can be used as a reference. e磷 ) and tail antimony concentration (C e锑 These are respectively considered as the phosphorus concentration and antimony concentration in the remaining material in the crucible, because during the straightening process of the single crystal silicon rod, the phosphorus concentration at the tail of the single crystal silicon rod is basically equal to the phosphorus concentration in the remaining material in the crucible, and the antimony concentration at the tail is basically equal to the antimony concentration in the remaining material in the crucible.

[0049] In step S130, the concentration ratio (C) of phosphorus in the re-feed and the remaining material in the crucible is calculated based on the phosphorus concentration in the re-feed and the remaining material in the crucible to the total weight of the full pot in the current feeding section. r磷 The phosphorus concentration ratio (C) can be calculated using the following formula. r磷 ):

[0050] Calculate the concentration percentage of antimony in the re-feeded material and the remaining material in the crucible, based on the antimony concentration in these two materials within the total weight of the full pot in the current feeding section (C). r锑 The antimony concentration percentage (C) can be calculated using the following formula. r 锑 ):

[0051] In this context, the phosphorus content in the re-feed material is equal to the sum of the phosphorus contents in the re-feed material at different resistance levels. The phosphorus content in the re-feed material at a specific resistance level is equal to the weight of the re-feed material at that resistance level multiplied by its phosphorus concentration. Similarly, the antimony content in the re-feed material is equal to the sum of the antimony contents in the re-feed material at different resistance levels. The antimony content in the re-feed material at a specific resistance level is equal to the weight of the re-feed material at that resistance level multiplied by its antimony concentration.

[0052] This section explains the meaning of "total weight of the current feeding section in the crucible" in the context of the single-crystal silicon rod pulling process. First, during the production of the previous single-crystal silicon rod, "refilling" occurs. "Residual material in the crucible" refers to the raw material remaining in the crucible after the previous single-crystal silicon rod is pulled. Next, after the previous single-crystal silicon rod is pulled, the current single-crystal silicon rod is pulled. During this process, refilling is added to the crucible, and the remaining material in the crucible is also used as the raw material for the current section. Finally, "total weight of the current feeding section in the crucible" refers to the weight of the raw material in the crucible during the pulling of the current single-crystal silicon rod.

[0053] In step S140, the phosphorus demand concentration is calculated based on the phosphorus concentration ratio, and the antimony demand concentration is calculated based on the antimony concentration ratio. The phosphorus demand concentration can be calculated using the following formula:

[0054] Where, k 磷 This represents the effective segregation coefficient of phosphorus.

[0055] The required concentration of antimony can be calculated using the following formula:

[0056] Where, k 锑 This represents the effective segregation coefficient of antimony.

[0057] In step S150, the doping amount (W1) of the phosphorus masterbatch is calculated based on the required phosphorus concentration, the total weight of the full pot in the current feeding section, and the concentration of the phosphorus masterbatch. Specifically, the formula for calculating the doping amount (W1) of the phosphorus masterbatch is as follows:

[0058] The doping amount (W1) of the phosphorus masterbatch alloy calculated by the above formula is in kilograms.

[0059] The antimony doping amount (W2) is calculated based on the required antimony concentration and the total weight of the full pot in the current feeding section. Specifically, the formula for calculating the antimony doping amount (W2) is as follows:

[0060] The antimony doping amount (W2) calculated by the above formula is in kilograms.

[0061] The control method described in this application can accurately calculate the doping amount of phosphorus masterbatch and antimony, thereby achieving precise control of the resistance of multiple rods in a single furnace. Compared with empirical methods, the control method of this application can significantly improve the uniformity of the resistance of single-crystal silicon rods. Using the control method described above to control the resistance of single-crystal silicon rods, the resistance uniformity of the obtained single-crystal silicon rods is as follows: the axial resistance variation rate of the single-crystal silicon rod is not greater than 13.6%, for example, the axial resistance variation rate is 6%, 8%, 10%, or 12%. The axial resistance variation rate can refer to the ratio of the difference between the head resistance and the tail resistance to the head resistance, i.e., (head resistance - tail resistance) / head resistance. And / or, at the head of the monocrystalline silicon rod, the radial resistivity change rate is no greater than 8%, for example, 4% or 6%; at the middle of the monocrystalline silicon rod, the radial resistivity is no greater than 15%, for example, 4%, 6%, 8%, 10%, 12%, or 14%; at the tail of the monocrystalline silicon rod, the radial resistivity change rate is no greater than 10%, for example, 4%, 6%, or 8%. The aforementioned radial resistivity change rate can refer to the ratio of the difference between the edge resistance and the center resistance along the radial direction of the same cross-section of the monocrystalline silicon rod to the center resistance, i.e., (edge ​​resistance - center resistance) / center resistance. And / or, the resistance hit rate of the monocrystalline silicon rod is no less than 80%, for example, 85%, 90%, or 95%. "Resistance hit rate" refers to the proportion (m / n) of a batch of single-crystal silicon rods (assuming there are n rods) that fall within a predetermined resistance range (assuming there are m rods). Here, the resistance can refer to the head resistance, and a and b can be set according to actual needs. In one embodiment, a hit is considered when the resistance is within ±0.1Ω of the target resistance.

[0062] In another aspect, this application also proposes a monocrystalline silicon rod, a silicon wafer, and a solar cell. During the pulling process of the monocrystalline silicon rod, the resistance of the monocrystalline silicon rod is controlled using the method described above. The silicon wafer is cut from the monocrystalline silicon rod as described above, and the substrate of the solar cell is processed from the silicon wafer as described above.

[0063] The basic concepts have been described above. Obviously, for those skilled in the art, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore remain within the spirit and scope of the exemplary embodiments of this application.

[0064] Furthermore, this application uses specific terms to describe embodiments of the application. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of the application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different locations in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of the application can be appropriately combined.

[0065] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this disclosure method does not imply that the subject matter of the present application requires more features than those mentioned in the claims. In fact, the embodiments contain fewer features than all the features of the single embodiments disclosed above.

[0066] In some embodiments, numbers describing the quantity of components and attributes are used. It should be understood that such numbers used in the description of embodiments are modified in some examples with the terms "approximately," "approximately," or "generally." Unless otherwise stated, "approximately," "approximately," or "generally" indicates that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may be changed depending on the characteristics required by individual embodiments. In some embodiments, numerical parameters should take into account specified significant digits and employ a general method of digit reservation. Although the numerical ranges and parameters used to confirm their breadth of scope in some embodiments of this application are approximate values, in specific embodiments, such values ​​are set as precisely as feasible.

[0067] Although this application has been described with reference to specific embodiments, those skilled in the art should recognize that the above embodiments are only used to illustrate this application, and various equivalent changes or substitutions can be made without departing from the spirit of this application. Therefore, any changes or modifications to the above embodiments within the essential spirit of this application will fall within the scope of the claims of this application.

Claims

1. A method for controlling the resistance of a single-crystal silicon rod, characterized in that, include: Obtain the phosphorus and antimony concentrations in the re-feeding material; Obtain the phosphorus and antimony concentrations in the remaining material in the crucible; Calculate the phosphorus concentration ratio (C) of the re-feeding material and the remaining material in the crucible in the total weight of the full pot in the current feeding section based on the phosphorus concentration in the re-feeding material and the remaining material in the crucible. r磷 Based on the antimony concentration in the re-added material and the remaining material in the crucible, calculate the concentration ratio (C) of antimony in the re-added material and the remaining material in the crucible in the total weight of the full pot in the current feeding section. r锑 ); The required phosphorus concentration is calculated based on the phosphorus concentration ratio, and the required antimony concentration is calculated based on the antimony concentration ratio. The amount of phosphorus doping is calculated based on the phosphorus required concentration, the total weight of the current feeding section, and the phosphorus master alloy concentration. The amount of antimony doping is calculated based on the antimony required concentration and the total weight of the current feeding section.

2. The control method as described in claim 1, characterized in that, The phosphorus concentration in the re-feeding material is an average concentration, and the method for calculating the average phosphorus concentration includes: Convert the target resistance to the phosphorus concentration at the head of the single-crystal silicon rod (C). s磷 ); According to the formula Calculate the phosphorus concentration (C) at the tail of the single-crystal silicon rod. e磷 ), the k 磷 The effective segregation coefficient of phosphorus, C 0磷 Indicates the initial phosphorus concentration, f s The percentage ranges from 0% to 95%. According to the head phosphorus concentration (C) s磷 ) and the tail phosphorus concentration (C e磷 Calculate the average phosphorus concentration.

3. The control method as described in claim 1, characterized in that, The antimony concentrations in the re-feeding materials are all average concentrations. The method for calculating the average antimony concentration includes: Convert the target resistance to the antimony concentration at the head of the single-crystal silicon rod (C). s锑 ); According to the formula Calculate the antimony concentration (C) at the tail of the single-crystal silicon rod. e 锑 ), the k 锑 The C represents the effective segregation coefficient of antimony. 0锑 Indicates the initial antimony concentration, f s The value ranges from 0% to 95%, where H represents the overall mass transfer coefficient of antimony in a thermal field; According to the head antimony concentration (C) s锑 ) and the tail antimony concentration (C e锑 Calculate the average concentration of antimony.

4. The control method as described in claim 1, characterized in that, The phosphorus concentration percentage (C) is calculated according to the following formula. r磷 ):

5. The control method as described in claim 1, characterized in that, The antimony concentration percentage (C) is calculated using the following formula. r锑 ):

6. The control method as described in claim 1, characterized in that, The required phosphorus concentration is calculated using the following formula: Wherein, the k 磷 This represents the effective segregation coefficient of phosphorus.

7. The control method as described in claim 1, characterized in that, The required antimony concentration is calculated using the following formula: Wherein, the k 锑 This represents the effective segregation coefficient of antimony.

8. A single-crystal silicon rod, characterized in that, During the pulling process of the single-crystal silicon rod, the resistance of the single-crystal silicon rod is controlled using the method described in any one of claims 1 to 7, wherein the axial resistance change rate of the single-crystal silicon rod is not greater than 13.6%, and / or the radial resistance change rate at the head of the single-crystal silicon rod is not greater than 8%, the radial resistivity at the middle of the single-crystal silicon rod is not greater than 15%, the radial resistance change rate at the tail of the single-crystal silicon rod is not greater than 10%, and / or the resistance hit rate of the single-crystal silicon rod is not less than 80%.

9. A silicon wafer, characterized in that, The silicon wafer is cut from a single-crystal silicon rod as described in claim 8.

10. A solar cell, characterized in that, The substrate of the solar cell is fabricated from the silicon wafer as described in claim 9.

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