Determination method and design method for Czochralski method crystal growth interface convexity

Abstract

The invention relates to the technical field of doped crystal growth, in particular to a method for determining the convexity of a Czochralski method crystal growth interface and a design method. The method comprises the following steps: recording a difference value between a part above a crystal sampling surface and a part above a solid-liquid interface where a sampling position is located as a redundant volume; the sampling surface is a crystal cross section where a sampling position is located; calculating the devitrification weight of the part, above the solid-liquid interface where the sampling position is located, of the crystal according to an equilibrium segregation formula, calculating the weight of the part, above the sampling position, of the crystal by combining a density method, and calculating the redundant volume weight by taking the difference; and calculating the redundant volume by combining the interface convexity at the sampling position, constructing a density formula of the redundant weight and the redundant volume, and solving the interface convexity. The formula for solving the convexity of the interface corresponding to different positions of the solid-liquid interface is provided, the method is simple and convenient, the calculated result can truly reflect the crystal growth state, and the breakthrough of the crystal growth key technology can be accelerated. According to the scheme, through combination of theoretical innovation and engineering modeling, the industrial pain point that the interface form is difficult to quantitatively monitor in the Czochralski method process is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of crystal preparation, and in particular to a method for determining the convexity of the crystal growth interface in the Czochralski method and a design method. Background Art

[0002] The crystallization rate of the crystal at the crystal growth interface (i.e., the solid-liquid interface) is actually the speed at which the solid-liquid interface advances into the melt. The shape of the solid-liquid interface directly affects the weight of the crystal. In particular, its convexity has an important influence on the concentration uniformity of doped ions in the radial direction. For Czochralski crystal growth, the shape of the solid-liquid interface during crystal growth is closely related to factors such as the temperature field, pulling speed, rotation rate, and crystal size, and is determined by the relative strength of natural convection and forced convection, and the flow directions of the two are opposite. When natural convection dominates, the crystal growth interface is a convex interface; when natural convection and forced convection are equivalent, the growth interface is a flat interface; when forced convection dominates, the growth interface is a concave interface. Since the flat interface and the concave interface are difficult to control and easily lead to crystal growth failure, a convex interface needs to be maintained during crystal growth.

[0003] As the crystal growth progresses, the convexity of the solid-liquid interface will gradually change. Therefore, studying the convexity of the solid-liquid interface can not only optimize the temperature field and process, but also help design appropriate crystal growth dimensions, thereby achieving maximum output.

[0004] Limited by the observation technology, it is currently impossible to directly observe the solid-liquid interface during crystal growth. Only some qualitative understandings can be obtained through numerical simulation calculations. The lack of practical understanding not only makes it difficult to break through the key technologies of crystal growth, but also slows down the process optimization progress, seriously restricting the progress of related technologies and the improvement of production capacity. Summary of the Invention

[0005] In order to overcome the defect that the solid-liquid interface during growth cannot be observed in the above-mentioned prior art, the present invention proposes a method for determining the convexity of the crystal growth interface in the Czochralski method, which is used to quickly determine the solid-liquid interface at the sampling location, provide a reference for designing the crystal growth dimensions, and assist in designing an ideal crystal.

[0006] In the method for determining the convexity of the crystal growth interface in the Czochralski method proposed by the present invention, the difference between the part above the crystal sampling surface and the part above the solid-liquid interface where the sampling location is located is denoted as the redundant volume; the sampling surface is the cross-section of the crystal where the sampling location is located.

[0007] Calculate the crystallization weight of the crystal in the part above the solid-liquid interface where the sampling location is located according to the equilibrium segregation formula, combine with the density method to calculate the weight of the part above the crystal sampling location, and take the difference to calculate the redundant volume weight.

[0008] Calculate the redundant volume in combination with the interface convexity at the sampling location, construct the density formulas for redundant weight and redundant volume, and solve for the interface convexity.

[0009] Preferably, it includes the following steps:

[0010] Determine the raw material parameters and the crystal growth process parameters. The growth process parameters include the external shape parameters of the crystal, and calculate the weight of the shoulder releasing part of the crystal;

[0011] Determine the sampling location, intercept a thin slice sample from the center of the sampling surface, and detect the doping ion concentration C at the center of the sample s , and calculate C using the equilibrium segregation formula s The corresponding crystallization weight W s ;

[0012] Determine the radius r of the crystal where the sampling surface is located and the weight W from the start of crystal growth to the sampling surface;

[0013] Determine the solid-liquid interface position, and construct a solution function of the redundant volume with respect to the convexity h; Simultaneously solve the function, the crystal density, and the weight W - W s Calculate the convexity h.

[0014] Preferably, the solid-liquid interface position is confirmed according to the following rules:

[0015] When the sampling location is in the shoulder releasing part, the solid-liquid interface is in the shoulder releasing part;

[0016] When the sampling location is in the equal diameter part: If It shows that the solid-liquid interface extends from the shoulder releasing part to the equal diameter part; conversely, it shows that the solid-liquid interface is entirely in the equal diameter part; where ρ is the crystal density, r 径 Is the radius of the equal diameter part, H 径 Is the distance from the sampling surface to the start of the equal diameter part;

[0017] When the sampling location is in the finishing part: If It shows that the solid-liquid interface extends from the equal diameter part to the finishing part; conversely, it shows that the solid-liquid interface is entirely in the finishing part; where r is the sampling surface radius, H 尾 Is the height from the sampling surface to the start of the finishing part, h 尾 Is the height of the finishing part.

[0018] Preferably, when the solid-liquid interface where the sampling location is located is in the shoulder releasing part, the calculation formula for the redundant volume V(h) is as follows:

[0019]

[0020] Among them, r is the sampling surface radius, h is the convexity of the solid-liquid interface where the sampling location is located, and h’ 肩 Is the distance from the sampling surface to the start of the shoulder releasing part.

[0021] Preferably, when the solid-liquid interface extends from the shoulder part to the equal-diameter part, the calculation formula for the redundant volume V(h) is as follows:

[0022]

[0023] where r 径 is the radius of the equal-diameter part, h is the convexity of the solid-liquid interface where the sample is taken, h′ 径 is the distance from the sample surface to the start of the equal-diameter part, and h 肩 is the height of the shoulder part.

[0024] Preferably, when the solid-liquid interface is entirely in the equal-diameter part, the calculation formula for the redundant volume V(h) is as follows:

[0025]

[0026] where r 径 is the radius of the equal-diameter part, and h is the convexity of the solid-liquid interface where the sample is taken.

[0027] Preferably, when the solid-liquid interface extends from the equal-diameter part to the finishing part, the calculation formula for the redundant volume V(h) is as follows:

[0028]

[0029] where r is the radius of the sample surface, h is the convexity of the solid-liquid interface where the sample is taken, h′ 尾 is the distance from the sample surface to the start of the finishing part, and h 尾 is the height of the finishing part.

[0030] Preferably, when the solid-liquid interface is entirely in the finishing part, the calculation formula for the redundant volume V(h) is as follows:

[0031]

[0032] where r is the radius of the sample surface, h is the convexity of the solid-liquid interface where the sample is taken, h′ 尾 is the distance from the sample surface to the start of the finishing part, and h 尾 is the height of the finishing part.

[0033] A system for determining the convexity of the crystal growth interface in the Czochralski method proposed by the present invention includes a memory and a processor. A computer program is stored in the memory, and the processor is connected to the memory. The processor is configured to execute the computer program to implement the method for determining the convexity of the crystal growth interface in the Czochralski method.

[0034] A crystal growth design method proposed by the present invention includes the following steps:

[0035] Configure raw materials, design the growth process parameters of the crystal, grow the crystal by the Czochralski method, and determine the growth convexity of each part by using the method for determining the convexity of the crystal growth interface in the Czochralski method described above;

[0036] Compare the growth convexity array of the crystal with the designed target convexity array, adjust the growth process parameters of the crystal according to the difference between the two arrays, and perform cyclic operations until the growth convexity array of the crystal is consistent with the designed target convexity array, then fix the growth process parameters and use them for growing the target crystal by the Czochralski method.

[0037] The advantages of the present invention are as follows:

[0038] (1) The method for determining the convexity of the crystal growth interface in the Czochralski method proposed by the present invention defines the difference between the crystal above the sampling surface and the part above the solid-liquid interface as the redundant volume, breaking through the limitations of traditional numerical modeling. Through the simultaneous calculation of the weight difference and the volume density, for the first time, the segregation effect is directly associated with the physical form change, providing a new idea for the quantification of the interface morphology.

[0039] (2) For different stages of crystal growth, namely shoulder formation, equal diameter growth, and ending, redundant volume calculation functions are established respectively. By judging the position of the solid-liquid interface in a segmented manner to dynamically adjust the model parameters, the adaptability of the interface convexity calculation in the complex growth process is significantly improved, and multi-stage dynamic modeling is realized.

[0040] (3) The redundant volume calculations in each stage accurately integrate parameters such as the crystal radius, height, convexity h, shoulder height h', etc., realizing the coupling optimization of geometric parameters and ensuring the accuracy of the crystal growth interface evaluation.

[0041] (4) The method for determining the convexity of the crystal growth interface in the Czochralski method proposed by the present invention can dynamically output the convexity h value. Cooperating with the crystal growth design method provided by the present invention, a closed-loop control of "detection - comparison - growth process adjustment" is realized. Through the iterative approximation of the growth convexity array and the target array, the process parameter optimization period is significantly shortened.

[0042] (5) The present invention can be applied to the determination of the convexity of the crystal growth interface of laser crystals such as YAG, GGG, MgAl 2 O 4 etc., and further realize the optimization of the growth process, and has good compatibility with crystals with core and side-core growth. Description of the Drawings

[0043] Figure 1 is the outer shape of the crystal grown by the Czochralski method;

[0044] Figure 2 is the cross-sectional view when the solid-liquid interface is entirely in the shoulder formation part;

[0045] Figure 3Cross-sectional view when the solid-liquid interface extends from the shoulder part to the equal-diameter part;

[0046] Figure 4 Cross-sectional view when the solid-liquid interface is entirely in the equal-diameter part;

[0047] Figure 5 Cross-sectional view when the solid-liquid interface extends from the equal-diameter part to the finishing part;

[0048] Figure 6 Cross-sectional view when the solid-liquid interface is entirely in the finishing part;

[0049] Figure 7 Schematic diagram of sampling in the equal-diameter part;

[0050] Figure 8 Schematic diagram of sampling in the finishing part;

[0051] Figure 9 Flowchart of a method for determining the convexity of the crystal growth interface in the Czochralski method;

[0052] Figure 10 Flowchart of a crystal growth design method. Detailed implementation mode

[0053] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0054] Based on the principle that the doping ion concentration is equal on the same solid-liquid interface, the present invention provides a method for determining the convexity of the solid-liquid interface of doped crystal growth. By measuring the doping ion concentration at the center of a certain cross-section of the crystal blank, the convexity of the solid-liquid interface where the center point is located can be determined.

[0055] For doped crystals, the equilibrium segregation formula between the doping ion concentration at a certain part of the crystal and the crystallization rate when growing to that part is:

[0056]

[0057] In the formula, C s is the doping ion concentration at the sampling point, C 0 is the doping ion concentration in the raw material, k eff is the segregation coefficient of the doping ion; W s is the crystallization rate at the sampling point, that is, the crystal weight of the part above the solid-liquid interface where the sampling point is located; W T is the total weight of the raw material. Any concentration C can be obtained using the above formulas The corresponding crystallization rate W s :

[0058]

[0059] Refer to Figure 1 , for the crystal grown by the Czochralski method, its geometric shape includes three parts: shoulder, isodiameter, and finishing. Among them, both the shoulder part and the finishing part are cones, and the isodiameter part is a cylinder. The shape parameters of the crystal include: the height h of the shoulder part 肩 , the height h of the isodiameter part 径 , the radius r of the isodiameter part 径 , the height h of the finishing part 尾 . These parameters can be obtained by measurement or can be the shape parameters designed during crystal growth.

[0060] There are 5 cases for the position of the solid-liquid interface, such as Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 shown. The solid-liquid interface can be approximated as the e 2 ce 2 ' surface, and its convexity h is the height of the e 2 ce 2 ' surface; the sampling cross-section is the e 1 e 1 ' surface, and the corresponding radius is r; the cross-section at the beginning of the isodiameter is dd'; the cross-section at the beginning of the finishing is ii'; the sampling position is at c, and the doping ion concentration is C s . The density of the crystal is denoted as ρ, and the weight from the starting point s of crystal growth to the sampling surface e 1 e 1 ' surface is W. The values of r and W can be obtained by measurement or weighing, or can be calculated from the shape parameters of the crystal.

[0061] Using the difference between W and W s , combined with geometric relationships, the interface convexity h can be obtained from known quantities. The calculation rules when the solid-liquid interface is in different positions are as follows. W s is the crystallization rate at the sampling position, that is, the weight of the crystal between the solid-liquid interface where the sampling position is located and the starting point s of crystal growth.

[0062] Refer to Figure 2 , when the solid-liquid interface is entirely in the shoulder part, the difference between W and W s is the weight of the e 1 e 2 ce 1 'e 2 ' part; h′ 肩 is from the sampling surface e 1e 1 The distance from the start of the crystal shoulder to the point is e 2 The length of c' is denoted as r', and we have:

[0063]

[0064] e 1 e 2 ce 1 'e 2 The volume of the'part is

[0065]

[0066] So:

[0067]

[0068] In the formula, the values of W and r can be obtained by weighing and measurement respectively, or calculated by the following formula

[0069]

[0070]

[0071] In this way, solving equation (5) can obtain the interface convexity h

[0072] Refer to Figure 3 , when the solid-liquid interface extends from the shoulder part to the equal-diameter part, the difference between W and W s is e 1 de 2 ce 1 'd'e 2 The weight of the'part, the distance from the sampling surface to the start of the equal-diameter part is e 1 dd'e 1 The height of the'cylinder is denoted as h′ 径 , the distance from the start of the equal-diameter part to the upper end of the solid-liquid interface is de 2 e 2 The height of the'd'frustum of a cone is denoted as h′ 肩 , the solid-liquid interface convexity h = h′ 径 +h′ 肩 e 2 The length of c' is denoted as r', and we have:

[0073]

[0074] e 1 de 2 ce 1 'de 2 The volume of the'part is

[0075]

[0076] Then:

[0077]

[0078]

[0079] In the formula, the value of W can be obtained by weighing or calculated by the following formula

[0080]

[0081] Solving equation (10) can obtain the interface convexity h.

[0082] When h′ 径 is 0, the solid-liquid interface is entirely at the shoulder part of the crystal.

[0083] When h = h′ 径 the solid-liquid interface is entirely at the equal-diameter part of the crystal.

[0084] Referring to Figure 4 , when the solid-liquid interface is entirely at the equal-diameter part, the difference between W and W s is e 1 e 2 ce 1 'e 2 The weight of the 'part, and the distance from the sampling surface to the start of the equal-diameter part is h′ 径 , e 1 e 2 ce 1 'e 2 The volume of the 'part is

[0085]

[0086] Then:

[0087]

[0088] In the formula, the value of W can be obtained by weighing or calculated by formula (11).

[0089] Solving equation (13) can obtain the interface convexity h.

[0090] Referring to Figure 5 , when the solid-liquid interface extends from the equal-diameter part to the finishing part, the difference between W and W s is e 1 ie 2 ce 1 'i'e 2 The weight of the 'part, and the distance from the sampling surface to the start of the finishing part is e 1 ii'e 1The height of the frustum of a cone is denoted as h'. 尾 , the distance from the start of the finishing to the upper end of the solid-liquid interface is ie 2 e 2 The height of the 'i' cylinder is denoted as h'. 径 , the convexity of the solid-liquid interface h = h' 尾 +h' 径 e 2 The length of c' is denoted as r', and there is

[0091]

[0092] e 1 ie 2 ce 1 'i'e 2 The volume of the 'part is

[0093]

[0094] or

[0095]

[0096] So:

[0097]

[0098] or

[0099]

[0100] In the formula, the values of W and r can be obtained by weighing and measurement respectively, or calculated by the following formula

[0101]

[0102]

[0103] Solving formula (17) or (18) can obtain the convexity h of the interface.

[0104] When h' 尾 is 0, the solid-liquid interface is entirely in the equal-diameter part of the crystal.

[0105] When h = h' 尾 , the solid-liquid interface is entirely in the finishing part of the crystal.

[0106] Referring to Figure 6 , when the solid-liquid interface is entirely in the finishing part, the difference between W and W s is e 1 e 2 ce 1 'e 2 ' part of the weight, the distance from the sampling surface to the start of the finishing is denoted as h'尾 , e 2 The length of c' is denoted as r'. There is

[0107]

[0108] e 1 e 2 ce 1 'e 2 The volume of the' part is

[0109]

[0110] So:[[]]

[0111]

[0112] In the formula, the values of W and r can be obtained by weighing and measurement respectively, or can be calculated by formula (19) and formula (20) respectively.[[]]

[0113] Solving formula (23) can obtain the interface convexity h.[[]]

[0114] It should be noted that when the sampling surface is at the equal-diameter or finishing part, it is necessary to first determine whether the solid-liquid interface is entirely at the equal-diameter or finishing part when applying, so as to select the corresponding calculation method of the convexity h.[[]]

[0115] Refer to Figure 7 , when the sampling surface is at the equal-diameter part, let the height from the sampling surface to the beginning of the equal-diameter be H 径 , and judge whether the following formula (24) holds;[[]]

[0116]

[0117] If it holds, it means that the solid-liquid interface extends from the shoulder part to the equal-diameter part. At this time, solving formula (10) can obtain the convexity of the solid-liquid interface;[[]]

[0118] If it does not hold, it means that the solid-liquid interface is entirely at the equal-diameter part. At this time, solving formula (13) can obtain the convexity of the solid-liquid interface;[[]]

[0119] If the values on both sides of formula (24) are equal, it means that the convexity of the solid-liquid interface is H 径 .

[0120] Refer to Figure 8 , when the sampling surface is at the finishing part, let the height from the sampling surface to the beginning of the finishing be H 尾 , and judge whether the following formula (25) holds;[[]]

[0121]

[0122] If it holds, it indicates that the solid-liquid interface extends from the equal-diameter part to the finishing part. At this time, the convexity of the solid-liquid interface can be obtained by solving formula (17) or (18).

[0123] If it does not hold, it indicates that the solid-liquid interface is entirely in the finishing part. At this time, the convexity of the solid-liquid interface can be obtained by solving formula (23).

[0124] If the values on both sides of formula (25) are equal, it indicates that the convexity of the solid-liquid interface is H. 尾 .

[0125] Referring to Figure 9 , the implementation steps of the method for determining the convexity of the crystal growth interface in the Czochralski method proposed by the present invention are as follows:

[0126] (1) Determine the raw material parameters and the crystal growth process parameters. The raw material parameters include the doping ion concentration C in the raw material, 0 the segregation coefficient k of the doping ion, eff the total weight W of the raw material, T , and the growth process parameters include the radius r of the equal-diameter part, 径 the total height h of the shoulder release part, 肩 the height h of the equal-diameter part, 径 and the height h of the finishing part 尾 and other shape parameters. Among them, the shape parameters can be measured by a vernier caliper or can be the shape parameters designed during crystal growth.

[0127] (2) Cut a thin slice sample from the center of the crystal cross-section, and use testing means such as laser ablation inductively coupled plasma mass spectrometry and electron probe energy spectrum to measure the doping ion concentration C at point c in the center of the sample; s Use the equilibrium segregation formula (2) to find the crystallization rate W corresponding to the doping ion concentration C at the place; s s .

[0128] (3) Determine the crystal radius r corresponding to the sampling surface and the weight W from the start of crystal growth to the sampling surface. The former can be measured by a vernier caliper or can be obtained from formula (7) or (20) according to the different positions of its sampling surface; the latter can be weighed by an electronic scale or can be calculated from formula (6) or (11) or (19) according to the different positions of its sampling surface.

[0129] (3) Determine the position of the solid-liquid interface.

[0130] When the sampling surface is in the shoulder release part, the solid-liquid interface is entirely in the shoulder release part;

[0131] When the sampling surface is in the equal-diameter part, the position of the solid-liquid interface is determined according to the comparison result of the values on both sides of formula (24);

[0132] ​When the sampling surface is at the finishing part, the solid-liquid interface position is determined according to the comparison result of the values on both sides of formula (25).

[0133] (4) According to the position of the solid-liquid interface, select different formulas to solve the convexity h of the solid-liquid interface.

[0134] When the entire solid-liquid interface is at the shoulder part, solving formula (5) can obtain the convexity h of the solid-liquid interface; when the solid-liquid interface extends from the shoulder part to the equal-diameter part, solving formula (10) can obtain the convexity h of the solid-liquid interface; when the entire solid-liquid interface is at the equal-diameter part, solving formula (13) can obtain the convexity h of the solid-liquid interface; when the solid-liquid interface extends from the equal-diameter part to the finishing part, solving formula (17) or (18) can obtain the convexity h of the solid-liquid interface; when the entire solid-liquid interface is at the finishing part, solving formula (23) can obtain the convexity h of the solid-liquid interface.

[0135] Refer to Figure 10 , the present invention can quickly calculate the convexity of each sampling point under the condition of determining the shape parameters of the crystal; it can also be used to adjust the growth process parameters to grow crystals with specific convexity to achieve crystal design. The method is as follows:

[0136] The first step: Configure raw materials, construct growth process parameters such as the temperature field, shape parameters, pulling speed, and rotation speed of crystal growth, grow crystals by the Czochralski method, and measure the shape parameters of the grown crystals; sample at a specified position, and combine the measurement parameters and weighing parameters of the sampling surface to calculate the convexity of the solid-liquid interface where the sampling is located.

[0137] The second step: Determine whether the convexity of the solid-liquid interface where the sampling is located meets the design goal; if yes, fix the growth process parameters to grow the target crystal; if not, return to the first step and re-optimize the growth process parameters.

[0138] Compared with numerical simulation calculation, the present invention only needs to measure the concentration at a single point in the center of the crystal to determine the convexity of the solid-liquid interface where it is located, which is not only simple and convenient but also can truly reflect the crystal growth state.

[0139] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below in conjunction with specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0140] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0141] The general parameters of the following embodiments are as follows:

[0142] The grown crystal is a Nd:YAG crystal with a density ρ = 4.56 g / cm 3 , the weight of the initial raw material W T = 133680 g, and the concentration of Nd in the initial raw material 3+ is C 0 = 5 at%, and the effective segregation coefficient k eff = 0.2. The crystal parameters are measured using a vernier caliper: the radius r of the equal-diameter part 径 = 100 mm, the total height h of the shoulder part 肩 = 150 mm, the height h of the equal-diameter part 径 = 200 mm, and the height h of the finishing part 尾 = 100 mm.

[0143] Example 1

[0144] A 1-mm-thick sample is cut from the center of the crystal cross-section. Using a vernier caliper, the position of the cross-section where the sample is taken is measured to be 100 mm after the start of the shoulder part of the crystal, that is, h' 肩 = 100 mm. From formula (6), the weight W from the start of crystal growth to the cross-section where the sample is taken is calculated to be 1697.17 g. From formula (7), the radius r of the cross-section where the sample is taken is calculated to be 66.67 mm. The concentration C at the sampling point is measured by laser ablation inductively coupled plasma mass spectrometry s = 1.013 at%. By successively solving the equilibrium segregation formulas (2) and (5), the convexity h of the solid-liquid interface is obtained as 20.12 mm.

[0145] Example 2

[0146] Using a vernier caliper, the position of the cross-section where the sample is taken is measured to be 50 mm after the start of the equal-diameter part of the crystal, that is, h' 径 = 50 mm. From formula (11), the weight from the start of crystal growth to the cross-section where the sample is taken is calculated to be W = 14319.2 g, and the radius r of the cross-section where the sample is taken is 100 mm. The concentration C at the sampling point is measured by laser ablation inductively coupled plasma mass spectrometry s = 1.081 at%. In this example, it is first necessary to determine whether the solid-liquid interface is entirely in the equal-diameter part or extends from the shoulder part to the equal-diameter part. First, solve the value of the equilibrium segregation formula (2) for W s , and then it can be calculated that the difference between W and W s is 2058.23 g; the value of H is calculated 径When = 50 mm, the value on the right side of formula (24) is 4772.80 g. The latter value is larger, indicating that the solid-liquid interface is entirely in the equal-diameter part, and the convexity of the solid-liquid interface is less than 50 mm. Solving formula (13) gives the interface convexity h = 21.56 mm.

[0147] Example 3

[0148] Using a vernier caliper, the position of the cross-section where the sample is taken is measured to be at 20 mm after the start of crystal tailing, i.e., h′ 尾 = 20 mm. From formula (19), the weight W from the start of crystal growth to the cross-section where the sample is taken is calculated to be 38126.33 g. From formula (20), the radius r of the cross-section where the sample is taken is calculated to be 80 mm. Using laser ablation inductively coupled plasma mass spectrometry, the concentration C at the sample-taking position is measured s = 1.285 at%. In this example, it is first necessary to determine whether the solid-liquid interface is entirely in the tailing part or extends from the equal-diameter part to the tailing part. First, solve the equilibrium segregation formula (2) for W s value, and then the difference between W and W s is calculated to be 2633.06 g; when calculating H 尾 = 20 mm, the value on the right side of formula (25) is 1374.56 g. The former value is larger, indicating that the solid-liquid interface extends from the equal-diameter part to the tailing part, and the convexity of the solid-liquid interface is greater than 20 mm. Solving formula (17) or (18) gives h′ 径 as 13.18 mm, and thus the interface convexity h = 33.18 mm is obtained.

[0149] Example 4

[0150] Using a vernier caliper, the position of the cross-section where the sample is taken is measured to be at 50 mm after the start of crystal tailing, i.e., h′ 尾 = 50 mm. From formula (19), the weight W from the start of crystal growth to the cross-section where the sample is taken is calculated to be 39973.4 g. From formula (20), the radius r of the cross-section where the sample is taken is calculated to be 50 mm. Using laser ablation inductively coupled plasma mass spectrometry, the concentration C at the sample-taking position is measured s = 1.327 at%. In this example, it is first necessary to determine whether the solid-liquid interface is entirely in the tailing part or extends from the equal-diameter part to the tailing part. First, solve the equilibrium segregation formula (2) for W s value, and then the difference between W and W s is calculated to be 775.39 g; when calculating the value of formula (25) at H 尾 = 50 mm is 1491.5 g. The latter value is larger, indicating that the solid-liquid interface is entirely in the tailing part, and the convexity of the solid-liquid interface is less than 50 mm. Solving formula (23) gives the interface convexity h = 28.68 mm.

[0151] In order to verify the use effect of the present invention, at 20.12 mm, 21.56 mm, 33.18 mm, and 28.68 mm above the cross-section where the original sampling point c ( Figures 1-5 c in Figures 1-5 e in 2 or e 2 ' in

[0152] Table 1: Comparison of doping ion concentrations at the sampling points in the examples and the top of the calculated solid-liquid interface

[0153]

[0154] It can be seen that the concentrations at the original sampling point c and the later sampling points e 2 or e 2 ' are basically the same, and the error does not exceed one-thousandth, indicating that they are on the same solid-liquid interface. Point c is the bottom of the solid-liquid interface, and e 2 and e 2 ' are the tops of the solid-liquid interface, thus proving that the present invention has good accuracy in determining the convexity of the solid-liquid interface.

[0155] Of course, for those skilled in the art, the present invention is not limited to the details of the above exemplary embodiments, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be construed as limiting the claimed rights.

[0156] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment contains only one independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0157] The technologies, shapes, and structures not described in detail in the present invention are all well-known technologies.

Claims

1. A method for determining the convexity of a crystal growth interface by a Czochralski method, characterized in that: The difference between the portion above the crystal sampling surface and the portion above the solid-liquid interface at the sampling location is recorded as the redundant volume; the sampling surface is the cross section of the crystal at the sampling location; The weight of the crystallization part above the solid-liquid interface at the sampling location is calculated according to the equilibrium segregation formula, and the weight of the part above the crystal sampling location is calculated by combining the density method, and the difference is taken to calculate the redundant volume weight; The redundant volume is calculated in combination with the interface convexity at the sampling point, and the density formulas of the redundant weight and redundant volume are constructed and the interface convexity is solved.

2. The method for determining the convexity of the CZC crystal growth interface according to claim 1, characterized in that: The following steps are involved: Determine the raw material parameters and the crystal growth process parameters, including the crystal shape parameters, and calculate the weight of the crystal shoulder; Determine the sampling point, cut a thin slice sample from the center of the sampling surface, and detect the doping ion concentration C in the center of the sample. s , using the equilibrium fractionation formula to calculate C s The corresponding crystallization weight W s ; Determine the radius r of the crystal where the sampling surface is located and the weight W from the beginning of the crystal growth to the sampling surface; Determine the position of the solid-liquid interface and construct a solution function for the redundant volume relative to the convexity h; solve the function, crystal density and weight difference WW simultaneously s Calculate the convexity h.

3. The method for determining the convexity of the CZC crystal growth interface according to claim 2, characterized in that: The position of the solid-liquid interface is determined according to the following rules: When the sampling point is located at the shoulder position, the solid-liquid interface is located at the shoulder position; When the sampling point is located at the equal diameter part: If It means that the solid-liquid interface extends from the shoulder part to the equal diameter part; conversely, it means that the solid-liquid interface is all in the equal diameter part; where ρ is the crystal density, r 径 is the radius of the equal diameter part, H 径 is the distance from the sampling surface to the beginning of the equal diameter; When the sampling point is at the end: If It means that the solid-liquid interface extends from the equal diameter part to the end part; conversely, it means that the solid-liquid interface is all at the end part; where r is the radius of the sampling surface, H 尾 h is the height from the sampling surface to the end point, 尾 The height of the end part.

4. The method for determining the convexity of the CZC crystal growth interface according to claim 2 or 3, characterized in that: When the sampling location is located at the shoulder position at the solid-liquid interface, the calculation formula of the redundant volume V(h) is as follows: Among them, r is the radius of the sampling surface, h is the convexity of the solid-liquid interface at the sampling location, and h' 肩 It is the distance from the sampling surface to the beginning of the shoulder.

5. The method for determining the convexity of the CZC crystal growth interface according to claim 2 or 3, characterized in that: When the solid-liquid interface extends from the shoulder to the equal diameter part, the calculation formula of the redundant volume V(h) is as follows: Among them, r 径 is the radius of the equal diameter part, h is the convexity of the solid-liquid interface at the sampling location, and h′ 径 h is the distance from the sampling surface to the beginning of the equal diameter, 肩 The height is the shoulder height.

6. The method for determining the convexity of the CZC crystal growth interface according to claim 2 or 3, characterized in that: When the solid-liquid interface is all at equal diameter, the calculation formula of the redundant volume V(h) is as follows: Among them, r 径 is the radius of the equal diameter part, and h is the convexity of the solid-liquid interface at the sampling location.

7. The method for determining the convexity of the crystal growth interface by the CZC method according to claim 2 or 3, characterized in that: When the solid-liquid interface extends from the equal-diameter part to the end part, the calculation formula of the redundant volume V(h) is as follows: Among them, r is the radius of the sampling surface, h is the convexity of the solid-liquid interface at the sampling location, and h′ 尾 h is the distance from the sampling surface to the beginning of the end, 尾 The height of the end part.

8. The method for determining the convexity of the crystal growth interface by the Czochralski method according to claim 2 or 3, characterized in that: When the solid-liquid interface is all at the end, the calculation formula of the redundant volume V(h) is as follows: Among them, r is the radius of the sampling surface, h is the convexity of the solid-liquid interface at the sampling location, and h′ 尾 h is the distance from the sampling surface to the beginning of the end, 尾 The height of the end part.

9. A system for determining the convexity of a Czochralski crystal growth interface, characterized in that: It comprises a memory and a processor, wherein a computer program is stored in the memory, and the processor is connected to the memory, and the processor is used to execute the computer program to implement the method for determining the convexity of the interface of the Czochralski crystal growth as described in any one of claims 1 to 8.

10. A crystal growth design method, characterized in that: The following steps are involved: Prepare raw materials, design crystal growth process parameters, grow crystals by Czochralski method, and determine the growth convexity of each part by using the method for determining the convexity of the crystal growth interface by Czochralski method as described in any one of claims 1 to 8; The growth convexity array of the crystal is compared with the designed target convexity array, and the growth process parameters are adjusted according to the difference between the two arrays. The operation is repeated until the growth convexity array of the crystal is consistent with the designed target convexity array. The growth process parameters are fixed and used to grow the target crystal by the pulling method; the growth process parameters include pulling speed, rotation speed, temperature field and crystal shape parameters.

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