Wafer shape modeling method and wafer manufacturing method

Abstract

Provided is a method for modeling a wafer shape by means of a function which is a function for calculating a displacement (z) of a wafer in the thickness direction and which is the sum of a plurality of functions including: a first function g (r) which is a polynomial of more than one order with the distance (r) from the center of the wafer as a variable; and a second function g (r) which is a polynomial of more than one order with the distance (r) from the center of the wafer as a variable. A second function Ar * h (N [theta]) obtained by multiplying a sine function or a cosine function h (N [theta]) by the coefficient A and the distance r, the sine function or the cosine function h (N [theta]) having a first angle [theta] as a variable and an integer N as a constant, the first angle [theta] being a reference to a predetermined position in the circumferential direction of the wafer; and a third function Br * i (M (theta-phi)), wherein a sine function or a cosine function i (M (theta-phi)) is multiplied by the coefficient B and the distance r, wherein the sine function or the cosine function takes the first angle (theta) as a variable and takes a second angle (phi) with the specified position as a reference and an integer M as constants.

Description

Technical Field

[0001] The invention relates to a wafer shape modeling method and a wafer manufacturing method. Background Art

[0002] Conventionally, semiconductor wafers are required to have high flatness. The flatness of wafers is usually measured using a capacitive or optical interferometer shape measuring device and evaluated using parameters such as deformation or nano-topography.

[0003] As a technique for evaluating wafer flatness, Patent Document 1 discloses a method for evaluating nanotopology with high accuracy by eliminating processing strain at the outer periphery as interference when measuring the wafer shape using an electrostatic capacitance type shape measuring device.

[0004] Patent Document 2 discloses a method of expressing the shape along the radial direction of the wafer by a polynomial having the position r of the wafer in the radial direction as a variable, and repeating the polynomial at every predetermined angle θ to digitize the surface shape of the entire wafer surface.

[0005] Prior art literature

[0006] Patent Literature

[0007] Patent Document 1: Japanese Patent No. 5862492

[0008] Patent Document 2: Japanese Patent No. 6899080 Summary of the invention

[0009] Technical problem to be solved by the invention

[0010] However, in the method described in Patent Document 1, the processing strain in the outer peripheral portion of the wafer is excluded in order to perform the evaluation based on the nanotopography, and therefore the waviness in the outer peripheral portion cannot be evaluated.

[0011] Furthermore, the method described in Patent Document 2 can grasp the radial shape of the wafer, but cannot grasp the circumferential waviness.

[0012] An object of the present invention is to provide a wafer shape modeling method and a wafer manufacturing method that can reproduce the circumferential waviness of the wafer over the entire wafer and can accurately evaluate the waviness of the wafer.

[0013] Solutions for solving technical problems

[0014] The wafer shape modeling method of the present invention is a method for modeling the wafer shape by a function, characterized in that the function is a function for calculating the displacement z in the thickness direction of the wafer, and is the sum of multiple functions including the following functions: a first function g(r), a polynomial of first degree or higher with the distance r from the center of the wafer as a variable; a second function Ar×h(Nθ), a sine function or cosine function h(Nθ) with a first angle θ based on a specified circumferential position of the wafer as a variable and an integer N as a constant multiplied by a coefficient A and the distance r; and a third function Br×i(M(θ-φ)), a sine function or cosine function i(M(θ-φ)) with the first angle θ as a variable and a second angle φ based on the specified position and an integer M as constants multiplied by a coefficient B and the distance r.

[0015] In the above wafer shape modeling method, the second function may be A1r×h1(N1θ)+A2r×h2(N2θ)+…+A n r×h n (N n θ) (n is an integer greater than 1), the third function is a function represented by B1r×i1(M1(θ-φ))+B2r×i2(M2(θ-φ))+…+B m r×i m (M m (θ-φ)) (m is an integer greater than or equal to 1).

[0016] In the above-mentioned wafer shape modeling method, the specified position may be a reference position for indicating the crystal orientation, and the second angle φ may be an angle formed by a cutting feed direction when the wafer is cut from an ingot and a straight line connecting the reference position and the center of the wafer.

[0017] In the above-mentioned wafer shape modeling method, the first function may be a cubic polynomial, the second function may be Ar×sin4θ, and the third function may be B1r×cos2(θ-φ)+B2r×cos3(θ-φ).

[0018] The wafer manufacturing method of the present invention is characterized in that it has the following steps: a slicing step, in which the wafer is obtained by cutting a crystal ingot; a grinding step, in which both sides of the wafer are polished; a modeling step, in which the wafer shape is modeled using any of the above-mentioned wafer shape modeling methods; and an evaluation step, in which the wafer is evaluated based on the obtained model.

[0019] In the wafer manufacturing method described above, the evaluation may be performed based on the magnitude of the coefficient of the function obtained by the wafer shape modeling method. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a schematic diagram illustrating the positional relationship between a wafer and a wire saw according to one embodiment of the present invention.

[0021] Figure 2 3 is a diagram illustrating the distribution of wafer ripples modeled by the first function.

[0022] Figure 3A 3 is a diagram illustrating the distribution of wafer ripples modeled by the second function.

[0023] Figure 3B 3 is a diagram illustrating the distribution of wafer ripples modeled by the second function.

[0024] Figure 4 This is a graph used in the method of calculating the coefficient of the first function.

[0025] Figure 5 This is a diagram for explaining the measurement points of the displacement z when calculating the coefficients of the second function and the third function.

[0026] Figure 6 This is a graph used in the method of calculating the coefficients of the second function and the third function.

[0027] Figure 7 This is a flowchart illustrating a method for manufacturing a wafer according to one embodiment of the present invention.

[0028] Fig. 8A This is the distribution diagram created in Example 1.

[0029] Figure 8B This is the distribution diagram created in Example 1.

[0030] Fig.9A This is a distribution diagram created in Example 2.

[0031] Fig. 9B This is a distribution diagram created in Example 2. DETAILED DESCRIPTION

[0032] Hereinafter, one embodiment of the present invention will be described with reference to the drawings.

[0033] The wafer shape modeling method according to the embodiment of the present invention is a method of reproducing the shape of a wafer sliced ​​from a single crystal ingot manufactured by the CZ method (Czochralski method) or the like as a model using a function (expression).

[0034] The model is created by a function that calculates the displacement in the thickness direction of the wafer using the distance from the center of the wafer, the angle with respect to a predetermined position in the circumferential direction of the wafer, and the like as variables.

[0035] The wafer manufacturing method is characterized in that the shape of the wafer after the grinding step is modeled and the wafer is evaluated using the model thus produced.

[0036] First, a method of modeling a wafer shape will be described. In the following description, the diameter of the wafer is set to 300 mm, but the invention is not limited to this.

[0037] The wafer shape modeling method of the present embodiment is a method of modeling the wafer shape by the following function (1). Function (1) calculates the displacement z in the thickness direction of the modeled wafer. The displacement z in the thickness direction of the wafer can be represented by the following function (1) with the distance r from the center of the wafer and the first angle θ based on the notch position as variables.

[0038] z=f(r,θ)

[0039] =ar 3 +br 2 +cr+d

[0040] +Ar×sin4θ

[0041] +B 1r ×cos2(θ-φ)+B2r×cos3(θ-φ)…(1)

[0042] That is, function (1) is a function that contains the first function (ar 3 +br 2 +cr+d), the second function (Ar×sin4θ) and the third function (B1r×cos2(θ-φ)+B2r×cos3(θ-φ)).

[0043] Here, the displacement in the thickness direction of the wafer represents the minimum distance from any point on the thickness center plane of the wafer to the best fit plane of the thickness center plane. The thickness center plane of the wafer refers to a plane formed by a set of points that are the center of the thickness of any point on the wafer, with the vertical width of the wafer when the wafer is placed on a horizontal plane in a natural state as the thickness. The natural state refers to a state where no external force is applied to cause the wafer to be adsorbed on the horizontal plane. The best fit plane of the thickness center plane refers to the least squares plane relative to the thickness center plane.

[0044] like Figure 1 As shown, in this embodiment, the reference of the angle θ is set to the position where the notch Nt for indicating the crystal orientation is formed (notch position, reference position). Here, the angle θ is taken as the positive direction in the counterclockwise direction from the notch position. The reference of the angle θ is not limited to the notch position, and can be set to a predetermined position commonly set on the wafer and indicating the reference in the circumferential direction, for example, it can also be set to the position where the orientation plane is formed.

[0045] Furthermore, the reference of the angle θ is not limited to the position of the notch Nt or the orientation plane, and can be appropriately changed according to the mechanism of wafer waviness formation and the like.

[0046] φ (second angle) is the angle between the cutting feed direction FD when slicing a single crystal ingot into wafers using a wire saw and the straight line L connecting the notch position and the center of the wafer W. Here, the angle φ is taken as the positive direction in the counterclockwise direction from the notch position. The cutting feed direction FD of the wire saw is a direction orthogonal to the extension direction of the wire Wi of the wire saw.

[0047] In function (1), “ar 3 +br 2 +cr+d" (referred to as the first function) is a polynomial that approximates the warpage shape of the wafer. The first function is a cubic polynomial of a single variable with the variable set to the distance r from the center of the wafer. a, b, c, d are coefficients calculated by the calculation method described later, and are mainly used to determine the parameters of the warpage shape of the model obtained by function (1).

[0048] In this embodiment, the first function is a cubic polynomial, but is not limited thereto and can be changed according to the accuracy required by the model, etc. For example, if the wafer warping is considered simple, it can be a linear polynomial, and if the wafer warping is considered complex, it can be a quartic or higher polynomial.

[0049] In function (1), “Ar×sin4θ” (called the second function) is approximately Figure 2 The sine function of the shape shown fluctuates four times in the circumferential direction of the wafer W (the shape of a sine wave that vibrates four times in one cycle, a cross-shaped ripple that appears on the wafer). The "A" of the second function is a coefficient calculated by the calculation method described later, and is mainly a parameter that determines the size of the circumferential ripple of the model obtained by the function.

[0050] The inventors found that grinding the wafer would produce Figure 2 The second function is introduced to reflect the waviness in the model. Examples of grinding methods that generate such waviness include resin bonding grinding (see Japanese Patent Application Laid-Open No. 2011-249652, etc.) and single-side buffing grinding.

[0051] The second function of this embodiment is "Ar×sin4θ", but as a trigonometric function, not only the sine function (sin) can be used, but also the cosine function (cos) can be used to approximate the shape of the ripples because they are the same in periodic change. In addition, in this embodiment, the number of ripples is set to 4, but the number of ripples can be changed according to the shape of the ripples to be generated.

[0052] That is, the second function may be a function Ar×h(Nθ) obtained by multiplying a sine function or a cosine function h(Nθ) having the first angle θ as a variable and the integer N as a constant by the coefficient A and the distance r.

[0053] Furthermore, in order to model the wafer shape based on further insights, the number of trigonometric functions may be increased. That is, the second function may be a function represented by the following equation:

[0054] A1r×h1(N1θ)+A2r×h2(N2θ)+……+A n r×h n (N n θ)

[0055] (n is an integer greater than or equal to 1)

[0056] In function (1), "B1r×cos2(θ-φ)+B2r×cos3(θ-φ)" (called the third function) is approximately Figure 3A , Figure 3B The cosine functions of a shape that fluctuates twice in the circumferential direction of the wafer (a shape of a sine wave that vibrates twice in one circle) and a shape that fluctuates three times (a shape of a sine wave that vibrates three times in one circle) are shown.

[0057] “B1, B2” of the third function are coefficients calculated by a calculation method described later, and are mainly parameters for determining the size of the waviness of the wafer model obtained by the function, similarly to “A” of the second function.

[0058] The inventors discovered that when a single crystal ingot is sliced ​​using a wire saw to obtain wafers, ripples such as those described above are generated in accordance with the cutting feed direction FD of the wire saw, and introduced a third function to reflect the ripples in the wafer model.

[0059] The third function of this embodiment is "B1r×cos2(θ-φ)+B2r×cos3(θ-φ)", but as a trigonometric function, not only the cosine function (cos) but also the sine function (sin) can be used to approximate the shape of the ripples. In addition, in this embodiment, the number of ripples is set to 2 or 3, but the number of ripples can also be changed according to the shape of the generated ripples. In addition, the number of trigonometric functions of the third function can be one.

[0060] That is, the third function may be a function Br×i(M(θ-φ)) obtained by multiplying a sine function or a cosine function i(M(θ-φ)) with the first angle θ as a variable and the second angle φ and the integer M as constants by a coefficient B and a distance r.

[0061] Furthermore, similarly to the second function, in order to model the wafer shape based on further insights, the number of trigonometric functions may be increased. That is, the third function may be a function represented by the following equation:

[0062] B1r×i1(M1(θ-φ))+B2r×i2(M2(θ-φ))+……+B m r×i m (M m (θ-φ))

[0063] (m is an integer greater than or equal to 1)

[0064] [Calculation method of coefficients of the first function (cubic polynomial)]

[0065] Next, a method for calculating the coefficients (a, b, c, d) of the polynomial will be described.

[0066] (1) The displacement z is measured at multiple points at each distance r from the center of the wafer. r , and averaged in the circumferential direction.

[0067] Regarding the wafer to be modeled, the displacement z is measured at a plurality of points on the circumference of the wafer at a distance r from the center of the wafer. r . Wafer displacement z r is the value of the displacement measured by a measuring device, for example, it can be measured by an electrostatic capacitance type shape measuring device. The multiple points on the circumference are preferably set at equal intervals, for example, the measurement can be performed at 360 points every 1°. The displacement z measured at the multiple points is r The average value of is set to the displacement z at a distance r from the center avg . And, displacement z at a distance r from the center is performed at multiple distances r avg The distance r is preferably set finer, and in this embodiment, it is set in 1 mm increments from r=0 (center of the wafer) to r=146 (near the periphery of the wafer).

[0068] (2) Find the displacement z relative to the distance r from the center avg The approximate formula of .

[0069] like Figure 4 As shown, the distance r and displacement z are plotted on the graph avg , find the approximate expression of the cubic polynomial. The approximate expression can be found using the least squares method. The coefficients (a, b, c, d) of the obtained approximate expression become the coefficients of the first function.

[0070] In addition, as described above, the approximation formula is not limited to a cubic polynomial.

[0071] [Calculation method of coefficients of the second and third functions]

[0072] Next, a method for calculating the coefficients (A, B1, B2) of the second function and the third function will be described.

[0073] (1) An arbitrary value of the distance r from the center of the wafer is determined.

[0074] Determine the displacement z in the thickness direction of the measured wafer r The distance r from the center of the wafer can be any value. In the present embodiment, the distance r is set to 146 mm. The distance r from the center of the wafer can be any value, but since the waviness of the wafer increases on the outer peripheral side, the distance r is preferably set to a larger value.

[0075] (2) Measure the displacement z in the thickness direction of the wafer r .

[0076] At a distance r, the displacement z in the thickness direction of the wafer is measured for each arbitrary angle in the circumferential direction. r .like Figure 5 As shown in FIG. 1 , the arbitrary angle can be set to 22.5°, for example. In this case, the number of measurement points is 16 points at equal intervals in the circumferential direction. r The measurement is carried out counterclockwise, starting from the position of θ=0°.

[0077] (3) Find the displacement z relative to the value obtained by multiplying the trigonometric function by the distance r r The approximate formula of .

[0078] like Figure 6 As shown, the value obtained by multiplying the trigonometric function (sin4θ, cos2(θ-φ), or cos3(θ-φ)) by the distance r and the displacement z are plotted on the graph. r , and find a first-order approximation.

[0079] As described above, φ is an angle determined by the cutting feed direction FD, and can be set to -45°, for example.

[0080] For example, when the coefficient A of the second function (Ar×sin4θ) is obtained, the horizontal axis is r×sin4θ and the vertical axis is the displacement z. r Then, for example, when the coefficient A of the second function (Ar×sin4θ) is obtained, the displacement z in the thickness direction of the wafer is measured every 22.5°. r In the case of r×sin4θ, the value (value on the horizontal axis) becomes three kinds (0( Figure 5 △(triangle) mark), r( Figure 5 ○(circle) mark), -r( Figure 5□(square) mark)), but depending on the trigonometric function obtained and the above arbitrary angle, the number of values ​​of r×trigonometric function and the number of displacements drawn in the values ​​of each horizontal axis will change.

[0081] Alternatively, the approximate formula may be obtained using the least square method. The coefficients of the obtained approximate formula become the coefficients (A, B1, B2) of the second function and the third function.

[0082] Through the above steps, coefficients a, b, c, d, A, B1, and B2 are calculated to obtain function (1). The operator can draw a model of the wafer by inputting function (1) into a computer or the like, thereby understanding the shape (warp, waviness) of the wafer.

[0083] Furthermore, even without drawing a model, the shape of the wafer can be understood from the coefficients obtained. For example, the larger the coefficients A, B1, and B2 are, the larger the waviness of the wafer periphery can be determined to be.

[0084] [Wafer manufacturing method]

[0085] Next, a method for manufacturing a wafer to which the above-described wafer shape modeling method is applied will be described.

[0086] like Figure 7 As shown, the wafer manufacturing method includes a slicing step S1 , a grinding step S2 , a modeling step S3 , an evaluation step S4 , an etching step S5 , and a mirror polishing step S6 .

[0087] The slicing step S1 is a step of cutting a single crystal ingot (or a block obtained by cutting a single crystal ingot) using a cutting mechanism such as a wire saw to cut a plurality of wafers. Thus, for example, a plurality of wafers with a thickness of about 1 mm can be obtained. The cutting feed direction FD of the wire saw can be determined, for example, according to the notch position.

[0088] In addition, a rough polishing (grinding) process is sometimes performed between the slicing process S1 and the grinding process S2. Also, although the process of chamfering the outer edge of the wafer is not particularly shown, the chamfering process may be performed by performing a primary chamfering after the slicing process S1 and performing a secondary chamfering with a chamfering amount greater than the primary chamfering after the grinding process S2.

[0089] The grinding step S2 is a step of grinding both surfaces of the wafer using a grinding device. Examples of the grinding method include resin bonding grinding, single-side polishing grinding, and double-side simultaneous grinding.

[0090] In the modeling step S3, the wafer that has been through the grinding step S2 is modeled using a wafer shape modeling method. Specifically, a displacement z in the thickness direction of the wafer is measured for each distance r using a capacitance type shape measuring device or the like. rThe coefficients a, b, c, d, A, B1, and B2 of function (1) are obtained, and the model of the wafer is drawn by a computer or the like using the obtained function (1).

[0091] In the evaluation step S4, the operator evaluates the wafer with reference to the wafer model obtained in the modeling step S3. The operator can understand the warpage or waviness of the wafer by referring to the model. The operator can grind again or determine whether the wafer is good or bad according to the warpage or waviness of the wafer.

[0092] The etching step S5 is a step of performing chemical etching to remove damage caused by machining that has adhered to the wafer surface in the previous step.

[0093] The mirror polishing step S6 is a step of polishing both surfaces of the wafer using a polishing device.

[0094] In the etching step S5 and the mirror polishing step S6 , the etching method and the polishing method can be adjusted based on the result of the evaluation step S4 .

[0095] According to the wafer shape modeling method described above, function (1) includes a trigonometric function, and the circumferential waviness can be reproduced on the entire wafer by the trigonometric function, so the wafer waviness can be evaluated with high accuracy.

[0096] In particular, circumferential ripples estimated to have occurred in the wire saw or ripples estimated to have occurred in the grinding process can be independently reproduced.

[0097] Furthermore, by increasing the degree of the first function or the number of trigonometric functions, the accuracy of the model can be improved.

[0098] According to the above-described wafer manufacturing method, at a stage before the etching step S5 or the mirror polishing step S6 is performed, the warpage or waviness of the wafer can be grasped and the wafer can be evaluated.

[0099] [Example 1]

[0100] Next, the present invention will be described in more detail with reference to examples. In Example 1, a distribution map of a wafer was prepared using only measured values, while a distribution map was prepared using a model obtained by the wafer shape modeling method of the present invention, and the two were compared.

[0101] First, the shape of the wafer was measured using an electrostatic capacitance shape measuring device, and the following Fig. 8A The distribution diagram shown.

[0102] Then, the wafer shape modeling method of the present invention is used to obtain a function, and the following is produced based on the model modeled by the function: Figure 8BThe distribution diagram is shown in Table 1. The coefficients of the function are shown in Table 1.

[0103] [Table 1]

[0104] <![CDATA[a(μm / mm 3 )]]> <![CDATA[b(μm / mm 2 )]]> c(μm / mm) d(μm) A(μm / mm) <![CDATA[B1(μm / mm)]]> <![CDATA[B2(μm / mm)]]> φ(deg) <![CDATA[-1.02×10 -7 ]]> <![CDATA[-5.27×10 -4 ]]> <![CDATA[-1.35×10 -2 ]]> 7.01 <![CDATA[1.55×10 -2 ]]> <![CDATA[5.91×10 -3 ]]> <![CDATA[5.99×10 -3 ]]> -44.3

[0105] As compared Fig. 8A and Figure 8B It can be seen that the distribution map created using only the measured values ​​and the distribution map created using the model are very consistent, especially with respect to the ripples on the outer peripheral side.

[0106] [Example 2]

[0107] Next, Example 2 of the present invention will be described. In Example 2, two wafers that have undergone a grinding process were modeled using a wafer shape modeling method.

[0108] Fig.9A , Fig. 9B This is a distribution diagram based on the measured values ​​of the two prepared wafers W1 and W2, and it can be seen that the shapes are greatly different. Both wafers have been through the grinding process (resin paste grinding).

[0109] Table 2 shows various coefficients calculated using the wafer shape modeling method for two wafers.

[0110] [Table 2]

[0111] <![CDATA[a(μm / mm 3 )]]> <![CDATA[b(μm / mm 2 )]]> c(μm / mm) d(μm) A(μm / mm) <![CDATA[B1(μm / mm)]]> <![CDATA[B2(μm / mm)]]> φ(deg) Wafer 1 <![CDATA[-9.71×10 -7 ]]> <![CDATA[-1.60×10 -5 ]]> <![CDATA[-3.15×10 -2 ]]> 4.42 <![CDATA[1.67×10 -2 ]]> <![CDATA[3.76×10 -3 ]]> <![CDATA[4.84×10 -3 ]]> -45 Wafer 2 <![CDATA[7.03×10 -7 ]]> <![CDATA[2.04×10 -5 ]]> <![CDATA[-1.91×10 -2 ]]> 1.54 <![CDATA[1.68×10 -2 ]]> <![CDATA[6.84×10 -3 ]]> <![CDATA[4.36×10 -3 ]]> -45

[0112] Since the coefficient A of wafer W1 and wafer W2 is substantially the same, it is estimated that the strength of the waviness caused by the grinding process is similar. In addition, since the coefficients a, b, c, and d of the polynomial are greatly different, it can be seen that the greatly different distribution diagrams are affected by the warpage shape of the wafer.

[0113] Description of Reference Numerals

[0114] L-straight line connecting the notch position and the center of the wafer, Nt-notch, r-distance from the center of the wafer, W-wafer, z-displacement of the wafer in the thickness direction, θ-a first angle based on the notch position, φ-a second angle based on the cutting feed direction, S1-slicing process, S2-grinding process, S3-modeling process, S4-evaluation process, S5-etching process, S6-mirror polishing process.

Claims

1. A method for modeling a wafer shape, which is a method for modeling a wafer shape by a function, wherein: The function is a function for calculating the displacement z of the wafer in the thickness direction, and is the sum of multiple functions including the following functions: A first function g(r) is a polynomial of degree or higher with the distance r from the center of the wafer as a variable; A second function Ar×h(Nθ) is a function that multiplies a coefficient A and the distance r by a sine function or a cosine function h(Nθ) having a first angle θ as a variable and an integer N as a constant based on a predetermined position in the circumferential direction of the wafer; and The third function Br×i(M(θ-φ)) is a sine function or cosine function i(M(θ-φ)) which takes the first angle θ as a variable and the second angle φ based on the specified position and the integer M as constants, multiplied by the coefficient B and the distance r.

2. The wafer shape modeling method according to claim 1, wherein: The second function is A1r×h1(N1θ)+A2r×h2(N2θ)+…+A n r×h n (N n θ), where n is an integer greater than 1, The third function is B1r×i1(M1(θ-φ))+B2r×i2(M2(θ-φ))+…+B m r×i m (M m (θ-φ)), where m is an integer greater than 1.

3. The wafer shape modeling method according to claim 1 or 2, wherein: The specified position is a reference position for indicating the crystal orientation. The second angle φ is an angle formed between a cutting feed direction when the wafer is cut from an ingot and a straight line connecting the reference position and the center of the wafer.

4. The wafer shape modeling method according to claim 3, wherein: The first function is ar 3 +br 2 +cr+d, The second function is Ar×sin4θ, The third function is B1r×cos2(θ-φ)+B2r×cos3(θ-φ).

5. A method for manufacturing a wafer, comprising the following steps: A slicing step of obtaining the wafer by cutting the ingot; A grinding process for polishing both sides of the wafer; A modeling step of modeling the wafer shape using the wafer shape modeling method according to claim 1; and The evaluation step evaluates the wafer based on the obtained model.

6. The method for manufacturing a wafer according to claim 5, wherein: The evaluation is performed based on the magnitude of the coefficient of the function obtained by the wafer shape modeling method.

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