Wafer positioning and orientation method and wafer edge detection apparatus

Abstract

The present disclosure provides a wafer positioning and orienting method and a wafer edge detection device thereof, the positioning and orienting method comprising: S1, rotating the wafer by a turntable and measuring the rotation angle, and simultaneously measuring the distance between the wafer edge and the device by a distance detection device; S2, preliminarily determining the wafer gap position according to the wafer edge positions corresponding to the maximum and minimum distance difference values; S3, calculating the coordinates of the wafer center in the turntable coordinate system according to the data excluding the wafer gap position, and calculating the coordinates of the gap center in the turntable coordinate system according to the data of the gap position; and S4, calculating the initial position of the gap in the wafer coordinate system according to the wafer center coordinates and the gap center coordinates. The positioning method directly fits the angle and distance data of the wafer, avoids converting the above data into rectangular coordinates relative to the turntable coordinate system, and improves the efficiency of wafer positioning and orientation without losing positioning accuracy.

Description

Technical Field

[0001] This disclosure relates to the field of position detection, and more particularly to wafer positioning and orientation methods and wafer edge detection apparatus. Background Technology

[0002] With the continuous improvement of semiconductor manufacturing processes, production lines are placing higher demands on the precision of manufacturing equipment, while also requiring wafers to maintain high positional accuracy within the processing equipment. However, during the storage and handling of wafers, the accumulation of errors inevitably leads to a continuous decrease in their positional accuracy. Therefore, before entering processes such as photolithography and dicing, it is necessary to detect the center and notch direction of the wafer. The accuracy of this detection affects the wafer yield, while the speed affects the production rate. Wafer edge position acquisition, positioning, and orientation are the main steps in the detection process. The commonly used edge position acquisition method is edge scanning and recognition. Subsequently, algorithms are used for positioning and orientation. The traditional positioning and orientation method is to use the least squares circle fitting method to position and orient the wafer. Although this method has high accuracy, it also has high computational complexity. When using the least squares circle fitting method to fit the wafer edge, a large amount of edge data needs to be converted into Cartesian coordinates relative to the rotation axis before fitting. The data conversion process is time-consuming, reducing computational efficiency.

[0003] This invention provides a wafer positioning and orientation method that directly fits and calculates the angle and distance data of the wafer, avoiding the need to convert this data into Cartesian coordinates relative to the rotation axis coordinate system. Compared to the least squares circle fitting method, this method improves the computational efficiency of wafer positioning without sacrificing accuracy. Summary of the Invention

[0004] This disclosure provides a wafer positioning and orientation method to at least partially solve the problem of low computational efficiency caused by the prior art's use of the least squares circle fitting method for wafer positioning, which requires calculating the rectangular coordinates of each point on the wafer edge in the rotation axis coordinate system.

[0005] Based on this, this disclosure provides a wafer positioning and orientation method, including: S1, a turntable drives the wafer to rotate and adjusts the rotation angle θ. i Measurements are performed, and simultaneously the distance detection device measures the distance d from the wafer edge to itself. i S2, based on the maximum distance difference d p -d p-1 Minimum distance difference d q -d q-1 S3, based on the corresponding wafer edge position, initially determine the wafer notch position; S4, based on removing the wafer notch position (θ) i d i ) data, calculate the coordinates (a1, b1) of the wafer center in the turntable coordinate system; based on the notch position (θ)i d i S1) Calculate the coordinates (a2, b2) of the notch center in the turntable coordinate system based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2). S2) Calculate the initial position of the notch in the wafer coordinate system based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2).

[0006] According to an embodiment of this disclosure, in S2, the maximum distance difference d is used. p -d p-1 Minimum distance difference d q -d q-1 The corresponding wafer edge position is used to initially determine the wafer notch position, including: for the distance vector [d1, d2…d… n Perform difference calculations to obtain the difference vector c = [d2-d1, d3-d2, ..., d...]. n -d n-1 Find the maximum distance difference d in the difference vector. p -d p-1 Minimum distance difference d q -d q-1 The wafer edge position P1(θ) corresponding to the bottom of the wafer notch was initially determined. (p+q-1) / 2 d (p+q-1) / 2 ), select m points at each end of position P1 as the gap position, where m is half of the number of measurement points occupied by the gap and rounded down, and the position of point P1 is (p+q-1) / 2 and its integer part is taken.

[0007] According to an embodiment of this disclosure, if |pq|>2m+1, the wafer is randomly rotated by an angle within the range of [notch angle, 360° - notch angle], and then step S1 is repeated.

[0008] According to an embodiment of this disclosure, in S3, based on the removal of the wafer notch location (θ) i d i The data is used to calculate the coordinates (a1, b1) of the wafer center in the turntable coordinate system, including:

[0009] (θ) after removing wafer notch positions i d i )for exist according to:

[0010] A = (X T X) -1 X T Y

[0011] Calculate the coordinates (a1, b1) of the wafer center in the turntable coordinate system, where X = [1 - cosθ] i -sinθ iA = lr a1 b1 T Y = [d i ] T l is the distance between the detection device and the center of the turntable, and r is the wafer radius.

[0012] According to an embodiment of this disclosure, in S3, based on the notch position (θ) i d i The data is used to calculate the coordinates (a2, b2) of the center of the notch in the turntable coordinate system, including:

[0013] (θ) after the gap position i d i )for exist according to:

[0014] A1=(X1 T X1 -1 X1 T Y1

[0015] Calculate the coordinates (a2, b2) of the center of the notch in the turntable coordinate system, where X1 = [1 2(ld i cosθ i 2(ld i sinθ i ]、 Y1=[-(ld i ) 2 ] T l is the distance between the detection device and the center of the turntable, and r is the distance between the detection device and the center of the turntable. r This is the true value of the radius of the arc portion of the wafer notch.

[0016] According to an embodiment of this disclosure, S4, the initial position of the notch in the wafer coordinate system is calculated based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2), including:

[0017] The angle of the notch relative to the center of the wafer in wafer coordinates is:

[0018]

[0019] Another aspect of this disclosure provides a wafer edge detection device, comprising: a base plate; a turntable fixed above the base plate for rotating the wafer and measuring the angle of wafer rotation; a wafer support stage fixed above the turntable for loading the wafer; and a distance detection device fixed above the base plate for measuring the distance between the wafer edge and the distance detection device; the detection device uses the wafer positioning and orientation method described above to locate the wafer notch.

[0020] According to an embodiment of this disclosure, the turntable includes a rotating body and an angle detection sensor installed inside the rotating body, and the rotating body has a through hole; preferably, the rotating body is a DD motor with a through hole in the center, and the angle detection sensor is an encoder inside the DD motor.

[0021] According to an embodiment of this disclosure, the plate support is provided with a communicating air passage and a sealing wall surrounding the air passage. A through hole is provided in the middle of the plate support. A rotating joint is fixedly connected to the bottom of the through hole. The other end of the rotating joint is connected to an air pipe. The rotating joint and the air pipe can be inserted into the through hole of the turntable. The other end of the air pipe passes out from the other end of the through hole of the turntable.

[0022] According to an embodiment of this disclosure, the distance detection device includes a rangefinder and a lifting platform, the lifting platform being fixed to a base plate, and the rangefinder being fixed to the lifting part of the lifting platform.

[0023] The wafer positioning and orientation method provided according to the embodiments of this disclosure has at least the following beneficial effects:

[0024] By directly fitting and calculating the position data of the wafer edge, this method avoids the time-consuming data conversion process and low computational efficiency caused by converting the position data into Cartesian coordinates relative to the turntable coordinate system before fitting. This wafer positioning and orientation method improves positioning efficiency while ensuring computational accuracy. Attached Figure Description

[0025] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments of this disclosure with reference to the accompanying drawings, in which:

[0026] Figure 1 The flowchart illustrating the wafer positioning and orientation method provided in the embodiments of this disclosure is shown in the illustration.

[0027] Figure 2 A schematic diagram of a wafer edge detection apparatus provided in an embodiment of the present disclosure is shown.

[0028] Figure 3 The schematic diagram illustrates a wafer edge detection device provided in an embodiment of this disclosure when no wafer is loaded.

[0029] Figure 4 The schematic diagram illustrates the structure of the plate support provided in an embodiment of this disclosure.

[0030] Figure 5 The diagram schematically shows a front view of the plate support provided in an embodiment of the present disclosure.

[0031] Figure 6 The schematic diagram illustrates the principle of the wafer positioning and orientation method provided in the embodiments of this disclosure.

[0032] Figure 7 The illustration shows the standard deviation of the error after 30 fittings for the wafer positioning method provided in Embodiment 1 of this disclosure under different combinations of Gaussian noise with different standard deviations and outlier ratios.

[0033] Figure 8 The diagram illustrates the standard deviation of the error after 30 fittings for the wafer positioning method (1730 edge points) using the least squares circle fitting method, under different combinations of Gaussian noise and outlier ratios.

[0034] Figure 9 The wafer edge data provided in Embodiment 2 of this disclosure is illustrated schematically.

[0035] Figure 10 The diagram illustrates the standard deviation of the fitting error of the wafer positioning method provided in Embodiment 2 of this disclosure under different combinations of Gaussian noise and outlier ratios.

[0036] Figure 11 The diagram illustrates the standard deviation of the fitting error after fitting the wafer positioning method (3460 edge points) using the least squares circle fitting method under different combinations of Gaussian noise and outlier ratios.

[0037] In the diagram, 1-base plate, 2-turntable, 3-wafer, 4-distance detection device, 401-rangefinder, 402-lifting platform, 5-plate holder, 6-rotary joint, 7-air pipe. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0039] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0040] In this disclosure, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this disclosure according to the specific circumstances.

[0041] In the description of this disclosure, it should be understood that the terms "longitudinal", "length", "circumferential", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this disclosure and simplifying the description, and do not indicate or imply that the subsystem 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 of this disclosure.

[0042] Throughout the accompanying drawings, identical elements are represented by the same or similar reference numerals. Conventional structures or constructions have been omitted where they may cause confusion in understanding this disclosure. Furthermore, the shapes, dimensions, and positional relationships of the components in the drawings do not reflect actual size, scale, or actual positional relationships. Additionally, any reference numerals placed between parentheses in the claims should not be construed as limiting the claims.

[0043] Similarly, to simplify this disclosure and aid in understanding one or more of the various aspects of the disclosure, in the above description of exemplary embodiments of the present disclosure, various features of the present disclosure are sometimes grouped together in a single embodiment, figure, or description thereof. The use of terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refers to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present disclosure. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0044] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this disclosure, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0045] The purpose of this disclosure is to provide a wafer positioning and orientation method. By measuring the distance and corresponding angle between the wafer edge and a distance detection device, the position of the wafer notch is initially determined. Based on the wafer notch position data and the position data after removing the wafer notch, the coordinates of the notch center and the wafer center in the turntable coordinate system are calculated respectively. Based on these two coordinates, the initial position of the notch in the wafer coordinate system is calculated, thereby achieving wafer orientation based on the wafer notch. The positioning is achieved by using the coordinates of the wafer center in the turntable coordinate system. This positioning and orientation method directly utilizes the distance and corresponding angle between the wafer edge and the distance detection device for position fitting calculation, improving positioning efficiency while ensuring positioning and orientation accuracy.

[0046] Figure 1 The flowchart illustrating the wafer positioning and orientation method provided in the embodiments of this disclosure is shown in the illustration.

[0047] like Figure 1 As shown, the wafer positioning and orientation method may include, for example, operations S1 to S4.

[0048] Operation S1 causes turntable 2 to rotate wafer 3 and adjust the rotation angle θ. i Measurements are performed, and simultaneously the distance detection device 4 measures the distance d from the edge of the wafer 3 to itself. i ;

[0049] Operation S2, based on the maximum distance difference d p -d p-1 Minimum distance difference d q -d q-1 The corresponding wafer edge position is used to initially determine the wafer notch position. For the specific meanings of p and q, please refer to the explanation section of operation S2 below.

[0050] Operation S3, based on the (θ) of the wafer notch removal location. i d i ) data, calculate the coordinates (a1, b1) of the wafer center in the turntable coordinate system; based on the notch position (θ) i d i ) data, calculate the coordinates (a2, b2) of the center of the notch in the turntable coordinate system;

[0051] Operation S4 calculates the initial position of the notch in the wafer coordinate system based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2).

[0052] Figure 2 A schematic diagram of a wafer edge detection apparatus provided in an embodiment of the present disclosure is shown. Figure 3 The schematic diagram illustrates a wafer edge detection device provided in an embodiment of this disclosure when no wafer is loaded.

[0053] like Figure 2 As shown, the wafer edge detection device includes: a base plate 1; a turntable 2, fixed above the base plate 1, used to rotate the wafer 3 and measure the angle of rotation of the wafer 3; and a wafer support stage 5 (see [reference]). Figure 3 The wafer edge detection device is fixed above the turntable 2 and is used to load the wafer 3; the distance detection device 4 is fixed above the base plate 1 and is used to measure the distance between the edge of the wafer 3 and the distance detection device 4; the wafer edge detection device uses the wafer positioning and orientation method described above to locate the wafer notch.

[0054] The turntable 2 includes a rotating body and an angle detection sensor installed inside the rotating body. The rotating body drives the wafer 3 loaded on the wafer support stage 5 to rotate, and the angle detection sensor detects the rotation angle of the rotating body, i.e., the rotation angle of the wafer 3. A through hole is provided in the center of the rotating body, through which the air supply passage of the wafer support stage 5 passes and connects to an external air pump. This through hole will be further described later in conjunction with the structure of the wafer support stage 5. The rotating body of the turntable 2 can be a DD motor or a hollow rotary table, which can be selected according to actual needs by those skilled in the art. In the embodiments of this disclosure, the rotating body is a DD motor with a through hole in the center, and the angle detection sensor is an encoder inside the DD motor. In the embodiments of this disclosure, the bottom of the turntable 2 is fixed to the base plate 1 by bolts, and the upper surface is fixed to the wafer support stage 5 by bolts. Other methods can also be used to fix these three components together, which are not limited here.

[0055] The distance detection device 4 includes a rangefinder 401 and a lifting platform 402. The lifting platform 402 is fixed to the base plate 1, and the rangefinder 401 is fixed to the lifting part of the lifting platform 402. In the embodiments of this disclosure, the base of the lifting platform 402 is fixed to the base plate 1 by bolts, and the rangefinder 401 is fixed to the lifting part of the lifting platform 402 by bolts; other methods can also be used to connect the base plate 1, the lifting platform 402, and the rangefinder 401, which are not limited here. The lifting platform 402 can drive the rangefinder 401 to move up and down, so as to adapt to the situation where the signal emitted by the rangefinder 401 can be reflected by the edge of the wafer or blocked by the upper plane when performing distance detection on wafers 3 of different thicknesses. The rangefinder 401 adopts such as Figure 2 The laser rangefinder shown or such Figure 3 The CCD laser micrometer shown is divided into a laser transmitter and a receiver. The rangefinder 401 consists of a laser transmitter and a receiver. Figure 2 When the laser rangefinder in the middle performs distance detection, the laser emitted by the laser emitting device is reflected by the wafer 3 and then received by the receiving device, thereby realizing the distance detection between the distance detection device 4 and the edge of the wafer. Figure 3The CCD laser micrometer emits a row of lasers. The upper plane of the wafer blocks part of the laser. At this time, the length of the row of lasers received by the receiving device will be reduced, thereby realizing the distance detection between the distance detection device 4 and the edge of the wafer.

[0056] In different embodiments, the turntable 2 and the rangefinder 401 can be combined to form a DD motor + laser rangefinder, a DD motor + CCD laser micrometer, a hollow turntable + laser rangefinder, or a hollow turntable + CCD laser micrometer, which will not be elaborated here.

[0057] Figure 4 The schematic diagram illustrates the structure of the plate support provided in an embodiment of this disclosure. Figure 5 The diagram schematically shows a front view of the plate support provided in an embodiment of the present disclosure.

[0058] like Figure 4 As shown, the wafer support stage 5 has a communicating air passage and a sealing wall surrounding the air passage, and a through hole in the middle of the wafer support stage 5. When the wafer support stage 5 holds the wafer 3, the sealing wall located at the edge of the wafer support stage 5 forms a sealed space between the wafer support stage 5 and the wafer 3, thereby allowing the gas between the wafer support stage 5 and the wafer 3 to be extracted through the communicating air passage on the surface of the wafer support stage 5 and the through hole in the middle of the wafer support stage 5. In the embodiments of this disclosure, multiple mounting holes are machined on the edge of the sealing wall, which are used to connect the wafer support stage 5 to the upper surface of the turntable by bolts. Figure 4 This invention illustrates one configuration of the airway, but other structural forms may also be used, and this disclosure does not impose any limitations.

[0059] like Figure 5 As shown, a rotary joint 6 is fixedly connected to the through hole in the middle of the wafer stage 5. The other end of the rotary joint 6 is connected to an air pipe 7. The rotary joint 6 and the air pipe 7 can be inserted into the through hole of the turntable 2. The other end of the air pipe 7 extends out from the other end of the through hole of the turntable 2. When the turntable 2 drives the wafer 3 to rotate, the rotary joint 6 allows the gas between the wafer stage 5 and the wafer 3 to be smoothly extracted by the air pump through the air pipe 7. The through hole in the turntable 2 provides space for the rotary joint 6 and the air pipe 7. The other end of the air pipe 7 extends out from the through hole of the rotating body of the turntable 2 and is connected to a solenoid valve. The other end of the solenoid valve is connected to the air pump. The solenoid valve is used to open and close the air extraction channel and control the air extraction speed. The air pump is used to extract the gas between the wafer stage 5 and the wafer 3 through the air channel, the rotary joint 6, and the air pipe 7. When the air pump is started and the solenoid valve is opened, if the wafer 3 is placed on the wafer stage 5, the gas in the air channel is extracted, and the wafer 3 is adsorbed onto the wafer stage 5.

[0060] The following section describes the wafer positioning and orientation method using a wafer edge detection device. This method allows for the calculation of the initial position of a wafer with a notch and an arc segment when placed on the wafer stage, based on the wafer edge position, thereby enabling wafer positioning and orientation.

[0061] In the embodiments of this disclosure, in operation S2, the maximum distance difference d is used. p -d p-1 Minimum distance difference d q -d q-1 The corresponding wafer edge position is used to initially determine the wafer notch position, including: for the distance vector [d1, d2…d… n Perform difference calculations, where the distance vector [d1, d2…d] is... n [d] refers to the n distance values ​​d measured by the distance detection device 4 during one revolution of wafer 3, from the initial position (position 1) of the wafer to the final position (position n) before returning to the initial position. i The vectors formed by these vectors. This yields the difference vector c = [d2-d1, d3-d2, ..., d...]. n -d n-1 ], representing the distance d i -d i-1 The vector consists of the differences between the distances d and d. By calculating the difference vector c, the distance d can be found. i -d i-1 The location of the abrupt change in the difference. The maximum distance difference d in the difference vector. p -d p-1 This is because the ranging signal point reflected from wafer 3 moves from the non-notch position to the notch position (p is between 1 and n and point p is located within the wafer notch); correspondingly, the minimum distance difference d in the difference vector... q -d q-1 This is because the ranging signal point reflected from wafer 3 returns from the notch position to the non-notch position (q is between 1 and n, and point q-1 is located within the wafer notch). Since the starting position p and ending position q-1 of the wafer notch have been preliminarily found, the position P1 of the bottom (middle) of the wafer notch is obtained, and its position coordinates are expressed by the rotation angle θ. i and distance d i Represented as P1(θ) (p+q-1) / 2 d (p+q-1) / 2 The position of point P1 is (p+q-1) / 2, taking the integer part of it.

[0062] M points at each end of P1 are designated as notch locations. m is half the number of measurement points occupied by the notch, rounded down. The arc of the notch on wafer 3 subtends an angle of D° on the wafer. The number of points collected on the wafer circumference is n. Therefore, the number of points g within the notch is:

[0063]

[0064] Then, the value of g / 2, which represents the number of sampling points within the gap, is rounded down to obtain the value of m.

[0065] Here, after obtaining the distance abrupt change location, the bottom position of the notch is first determined, and then m points are extended outward from each end to obtain the preliminary position of the notch, instead of directly using the wafer edge between the distance abrupt change locations as the notch. This is because the arc shape of the wafer notch varies depending on the manufacturing process. For example, some notches include a bottom arc segment and straight segments at both ends, while some wafer notches are complete arcs. When the notch is not completely arc-shaped, the distance d... i Since the mutation location is not in the arc portion of the notch, the wafer edge between the mutation location and the notch cannot be used as the notch. Then, step S3 is used to calculate the center of the arc portion of the notch.

[0066] When the wafer is mounted, if the initial detection position is exactly within the wafer notch, the first abrupt change in distance will be detected in the early stages of detection, while the other abrupt change in distance will be detected near the end of one full rotation of the wafer. At this point, the previous method for preliminary notch location is no longer applicable. In order to still use the aforementioned method for preliminary notch location, the initial detection position needs to be moved out of the wafer notch. This involves randomly rotating the wafer by any angle within the range of [notch angle, 360° - notch angle], and then repeating step S1.

[0067] Figure 6 The schematic diagram illustrates the principle of the wafer positioning and orientation method provided in the embodiments of this disclosure.

[0068] According to an embodiment of this disclosure, in S3, based on the removal of the wafer notch location (θ) i d i The data is used to calculate the coordinates (a1, b1) of the wafer center in the turntable coordinate system, including:

[0069] (θ) after removing wafer notch positions i d i )for exist according to:

[0070] A = (X T Y) -1 X T Y

[0071] Calculate the coordinates (a1, b1) of the wafer center in the turntable coordinate system, where X = [1 - cosθ] i -sinθ i A = lr a1 b1 T Y = [d i ]T l is the distance between the distance detection device 4 and the center of the turntable, and r is the wafer radius.

[0072] The following, combined with Figure 6 The coordinates (a1, b1) of the wafer center in the turntable coordinate system are explained. For example... Figure 6 As shown, ∠O'OX is the initial angle of the center of wafer 3 in the coordinate system of turntable 2, denoted by β. Let the offset distance of the center O' of wafer 3 relative to the center O of the turntable be e, and the radius of wafer 3 be r. Then, for any edge point p... i Distance to the center of the turntable (Op) i for:

[0073]

[0074] During wafer handling, the offset distance e between the wafer's center O' and the turntable center O is generally less than 2mm, while the commonly used 8-inch wafer radius is 100mm and the 12-inch wafer radius is 150mm. Generally, e << r, and sin 2 (θ i Since -β)≤1, the above equation can be approximately simplified to:

[0075] Op i =r+e cos(θ) i -β)

[0076] Since the distance between the distance detection device 4 and the turntable center O is l, the theoretical distance d from the wafer edge to the rangefinder 401 is... i ′ can be represented as:

[0077] d i ′=l-Op i

[0078] d i ′=lr-ecosβcosθ i -esinβsinθ i

[0079] In the above equation, (lr), ecosβ, and esinβ are all constants, let them be a0, a1, and b1 respectively. Then the above equation can be written in the form of a Fourier series:

[0080] d i =a0-a1cosθ i -b1sinθ i

[0081] Since ecosβ and esinβ are the coordinates of the wafer center in the turntable coordinate system, a1 and b1 are the coordinates of the wafer center in the turntable coordinate system, and l-a0 is the wafer radius.

[0082] Because of d′ i For the fitted value, to evaluate how well the fitted value matches the actual value, it needs to be similar to the actual value d. i We compare the results by subtraction. Therefore, the error formula can be written as:

[0083]

[0084] make:

[0085] V = [V1 … V] n T

[0086]

[0087] A = [a0 a1 b1] T

[0088] f = [d1 … d n ] T

[0089] The model can then be further expressed as:

[0090] V = XA - Y

[0091] By the least squares principle, the optimization model can be transformed into:

[0092] f(A) = ||V|| 2 =min

[0093] Then f(A) can be further expressed as:

[0094] f(A) = (XA - Y) T (XA-Y)=min

[0095] Differentiate A with respect to A, and let f(A) = 0, then we have:

[0096] A = (X T X) -1 X T Y

[0097] This allows us to solve for a1 and b1. After calculating the coordinates (a1, b1) of the wafer center in the rotation axis coordinate system, the wafer is positioned.

[0098] According to an embodiment of this disclosure, in S3, based on the notch position (θ) i d iThe data is used to calculate the coordinates (a2, b2) of the center of the notch in the turntable coordinate system, including:

[0099] (θ after the gap position) i d i )for exist according to:

[0100] A1=(X1 T X1) -1 X1 T Y1

[0101] Calculate the coordinates (a2, b2) of the center of the notch in the turntable coordinate system, where X1 = [1 2(ld i cosθ i 2(ld i sinθ i ]、 Y1=[-(ld i ) 2 ] T l is the distance between the detection device and the center of the turntable, and r is the distance between the detection device and the center of the turntable. r This is the true value of the radius of the arc portion of the wafer notch.

[0102] The error equation for fitting the notch to the circle can be written as:

[0103]

[0104] In the formula, V i Let r_n be the error value, and r_n be the radius of the notch fitting circle. r This is the true value of the radius of the wafer notch circle.

[0105] The equation can be further expressed as:

[0106] V i =(x i -a2) 2 +(y i -b2) 2 -r r 2

[0107]

[0108]

[0109]

[0110]

[0111] In the formula, x i Let y be the x-coordinate of the notch in the turntable coordinate system.i Let be the ordinate of the notch in the turntable coordinate system, and l be the distance between the distance detection device 4 and the center of the turntable. This can be represented in matrix form as follows:

[0112] V1 = X1A1 - Y1

[0113] In the formula:

[0114] V1 = [V1 … V n ] T

[0115] X1 = [1 2(ld)] i cosθ i 2(ld i sinθ i ]

[0116]

[0117] Y1=[-(ld i ) 2 ] T

[0118] By the least squares principle, the optimization model can be transformed into:

[0119] f(A1) = ||V1|| 2 =min

[0120] Differentiating A1 and setting f(A1) = 0, we have:

[0121] A1=(X1 T X1) -1 X1 T Y1

[0122] From this, A1 can be calculated, and the center position of the notch (a2, b2) can be obtained.

[0123] According to an embodiment of this disclosure, S4, the initial position of the notch in the wafer coordinate system is calculated based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2), including:

[0124] The angle of the notch relative to the center of the wafer in wafer coordinates is:

[0125]

[0126] After obtaining the coordinates of the center of wafer 3 and the center of the wafer notch in the turntable coordinate system (i.e., coordinates in the same coordinate system), the initial position of the notch can be calculated using these two coordinate values. Specifically, when the wafer with the arc-shaped notch is placed on the wafer stage, the angle α of the notch center in the wafer coordinate system centered on the wafer center can be used for wafer orientation. Since (a1, b1) and (a2, b2) have different values, the wafer notch is located in different quadrants of the wafer coordinate system. Based on the fundamentals of trigonometric functions, expressions for the angle α within different quadrant intervals can be obtained.

[0127] The present disclosure will be further described below through specific embodiments. The wafer positioning and orientation method described above will be specifically illustrated in the following embodiments. However, the following embodiments are merely illustrative of the present disclosure, and the scope of the present disclosure is not limited thereto.

[0128] Example 1:

[0129] The wafer positioning and orientation method disclosed herein includes performing the following steps in sequence:

[0130] Step 1: Turntable 2 drives wafer 3 to rotate one revolution. During rotation, turntable 2 detects the rotation angle (θ) of wafer 3 in real time. i Simultaneously, the distance detection device 4 detects the distance (d) between the edge of the wafer 3 and itself. i A total of 1730 points were measured, i = 1, 2... 1730.

[0131] Step 2: Record the distance between the wafer 3 and itself as a vector [d1, d2…d], as detected in real time by the distance detection device. 1730 Then, take the difference c = [d2-d1, d3-d2…d] of the vector. 1730 -d 1729 Find the maximum value (d) in the difference vector. p -d p-1 ) and minimum value (d) q -d q-1 The approximate location of the bottom of the notch on wafer 3 is determined to be P1(d). (p+q-1) / 2 ,θ (p+q-1) / 2 The position of point P1 is (p+q-1) / 2, taking the integer part. The arc of the notch in wafer 3 has an angle of 1.15°. After collecting 1730 points, at least 5 points will fall inside the notch. Select 2 points at each end of P1 as the notch positions;

[0132] Step 3, the data after removing the wafer notch positions is as follows: make The distance from the detection device 4 to the center of the turntable is l, X = [1 - cosθ] i -sinθ iA = [lr a1 b1] T Y = [d i ] T Where (a1, b1) are the coordinates of the center of wafer 3 in the turntable coordinate system, obtained by the formula A = (X T X) -1 X T Y was obtained, and the wafer was positioned in the turntable coordinate system;

[0133] Step 4, wafer notch data is make The true value of the radius of the notch is r. r The center of the circle is (a2, b2), and X1 = [1 2(ld)]. i cosθ i 2(ld i sinθ i ]、 Y1=[-(ld i ) 2 ] T Through the formula A1=(X1) T X1) -1 X1 T Y1 determines the position of the center of the notch (a2, b2);

[0134] Step 5: Let α be the angle between the wafer notch at its initial position and the wafer center coordinate system (with the wafer center as the origin).

[0135]

[0136] This allows us to determine the orientation of wafer 3.

[0137] Figure 7 The illustration shows the standard deviation of the error after 30 fittings for the wafer positioning method provided in Embodiment 1 of this disclosure under different combinations of Gaussian noise with different standard deviations and outlier ratios. Figure 8 The diagram illustrates the standard deviation of the error after 30 fittings for the wafer positioning method (1730 edge points) using the least squares circle fitting method, under different combinations of Gaussian noise and outlier ratios.

[0138] Meanwhile, to further illustrate the advantages of the offset calculation formula for the wafer 3 center relative to the turntable axis proposed in step 3, a wafer simulation model was established. After randomly offsetting the wafer simulation model from the turntable axis by a certain distance and angle, 1730 edge points (θ) were obtained. i d iSince the edge points obtained in this way are theoretical values ​​and do not contain any errors, while our actual detection often includes Gaussian noise and outliers, to make the simulated data closer to real data and obtain more realistic simulation results, Gaussian noise (standard deviation σ∈[0mm,0.1mm]) and a small number of outliers (proportion ∈[0,10%)) were added to the obtained edge point data, and the simulation was repeated 30 times to obtain the absolute value of the error of the center of the wafer fitting circle 30 times and calculate the standard deviation. The results are as follows. Figure 7 , Figure 8 As shown, the wafer positioning method provided in this embodiment and the wafer positioning method based on least squares circle fitting have similar performance in terms of fitting accuracy. On a computer with a 64-bit Windows 10 operating system, an Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz, and 16Gb of memory, the average computation time for the fitting method based on step 3 was 0.149ms, while the average computation time for the least squares circle fitting method was 0.221ms. The fitting method based on step 3 is 32.5% more efficient than the least squares circle fitting method.

[0139] Example 2:

[0140] The wafer orientation method disclosed herein includes performing the following steps in sequence:

[0141] Step 1: Turntable 2 drives wafer 3 to rotate one revolution. During rotation, turntable 2 detects the rotation angle (θ) of wafer 3 in real time. i Simultaneously, the distance detection device 4 detects the distance (d) between the edge of the wafer 3 and itself. i A total of 3460 points were measured, i = 1, 2, ..., 3460.

[0142] Figure 9 The illustration schematically shows wafer edge data provided in an embodiment of this disclosure.

[0143] Step 2: Record the distance between the wafer 3 and itself as a vector [d1, d2…d], as detected in real time by the distance detection device. 3460 The collected edge location data is as follows: Figure 9 As shown. Then, take the difference c = [d2-d1, d3-d2…d...]. 3460 -d 3459 Find the maximum value (d) in the difference vector. p -d p-1 ) and minimum value (d) q -d q-1 The approximate location of the bottom of the notch on wafer 3 is determined to be P1(d). (p+q-1) / 2 ,θ (p+q-1) / 2The position of point P1 is (p+q-1) / 2, taking the integer part. The arc angle of the notch in wafer 3 is 1.15°. After collecting 3460 points, at least 11 points fall inside the notch. Select 5 points at each end of P1 as the notch positions;

[0144] Step 3, the data after removing the wafer notch positions is as follows: make The distance from the detection device 4 to the center of the turntable is l, X = [1 - cosθ] i -sinθ i A = [lr a1 b1] T Y = [d i ] T Where (a1, b1) are the coordinates of the center of wafer 3 in the turntable coordinate system, obtained by the formula A = (X T X) -1 X T Y was obtained, and the wafer was positioned in the turntable coordinate system;

[0145] Step 4, wafer notch data is make The true value of the radius of the notch is r. r The center of the circle is (a2, b2), and X1 = [1 2(ld)]. i cosθ i 2(ld i sinθ i ]、 Y1=[-(ld i ) 2 ] T Through the formula A1=(X1) T X1) -1 X1 T Y1 determines the position of the center of the notch (a2, b2);

[0146] Step 5: Let α be the angle between the wafer notch at its initial position and the wafer center coordinate system (with the wafer center as the origin).

[0147]

[0148] This allows us to determine the orientation of wafer 3.

[0149] Figure 10 The diagram illustrates the standard deviation of the fitting error of the wafer positioning method provided in Embodiment 2 of this disclosure under different combinations of Gaussian noise and outlier ratios. Figure 11The diagram illustrates the standard deviation of the fitting error after fitting the wafer positioning method (3460 edge points) using the least squares circle fitting method under different combinations of Gaussian noise and outlier ratios.

[0150] Meanwhile, to further illustrate the advantages of the formula for calculating the offset of wafer 3's center relative to the turntable axis proposed in step 3, wafer 3 was randomly offset from the turntable axis by a certain distance and angle. Gaussian noise (standard deviation σ∈[0mm,0.1mm]) and a small number of outliers (proportion ∈[0,10%)) were added to the position data (θi, di) of 3460 edge points collected. The simulation was repeated 30 times to obtain the absolute error of the wafer-fitted circle center in 30 simulations and calculate the standard deviation. The results are as follows: Figure 10 , 11 As shown, the two methods have similar performance in terms of fitting accuracy. However, the average computation time of the fitting method based on step 3 is 0.249 ms, while the average computation time of the least squares circle fitting method is 0.347 ms. The fitting method based on step 3 is 28.2% more efficient than the least squares circle fitting method.

[0151] In summary, this disclosure directly uses the collected angle and distance information of the wafer edge for wafer positioning, avoiding the need to convert the position data into Cartesian coordinates relative to the turntable coordinate system and then fit them for wafer positioning. While ensuring calculation accuracy, it improves the efficiency of wafer positioning and orientation, thereby improving the efficiency of the entire wafer processing process.

[0152] The specific embodiments described above further illustrate the purpose, technical solutions, and beneficial effects of this disclosure. It should be understood that the above descriptions are merely specific embodiments of this disclosure and are not intended to limit this disclosure. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the protection scope of this disclosure.

Claims

1. A wafer positioning and orientation method, characterized in that, include: S1, the turntable (2) drives the wafer (3) to rotate and adjusts the rotation angle θ i The measurement is performed simultaneously, and the distance detection device (4) simultaneously measures the distance d between the edge of the wafer (3) and the distance detection device (4). i ; S2, based on the maximum distance difference d p -d p-1 Minimum distance difference d q -d q-1 The wafer notch position is initially determined based on the corresponding wafer edge position; S3, based on removing the wafer notch location (θ) i d i ) data, calculate the coordinates (a1, b1) of the wafer center in the coordinate system of the turntable (2); according to the notch position (θ) i d i ) data, calculate the coordinates (a2, b2) of the center of the notch in the coordinate system of the turntable (2), where θ i The angle of rotation of wafer (3) in the turntable coordinate system; S4. Calculate the initial position of the notch in the wafer coordinate system based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2).

2. The wafer positioning and orientation method according to claim 1, characterized in that, S2, based on the maximum distance difference d p -d p-1 Minimum distance difference d q -d q-1 The wafer notch location is initially determined based on the corresponding wafer edge position, including: For distance vector Perform difference calculations to obtain the difference vector. Find the maximum distance difference d in the difference vector. p -d p-1 Minimum distance difference d q -d q-1 The wafer edge position P1 (θ) corresponding to the bottom of the wafer notch is initially determined. （p+q-1） / 2 d （p+q-1） / 2 ), select m points at each end of position P1 as the gap positions; where m is half the number of measurement points occupied by the gap and rounded down; the position of point P1 is Take its integer part.

3. The wafer positioning and orientation method according to claim 2, characterized in that, like Then, the wafer is randomly rotated within the range of [notch angle, 360° - notch angle] by one angle, and then step S1 is repeated.

4. The wafer positioning and orientation method according to claim 1, characterized in that, In step S3, based on removing the wafer notch location (θ) i d i ) data, calculate the coordinates (a1, b1) of the wafer center in the coordinate system of the turntable (2), including: After removing the wafer notch position (θ) i d i )for ,exist ,according to The coordinates (a1, b1) of the wafer center in the coordinate system of the turntable (2) are calculated, where , , , The distance between the distance detection device (4) and the center of the turntable is r, and the wafer radius is r.

5. The wafer positioning and orientation method according to claim 1, characterized in that, In S3, based on the position of the notch (θ) i d i ) data, calculate the coordinates (a2, b2) of the center of the notch in the coordinate system of the turntable (2), including: The gap location (θ) i d i )for ,exist ,according to The coordinates (a2, b2) of the center of the notch in the coordinate system of the turntable (2) are calculated, where , , , The distance between the distance detection device (4) and the center of the turntable. This is the true value of the radius of the arc portion of the wafer notch.

6. The wafer positioning and orientation method according to claim 1, characterized in that, S4, based on the wafer center coordinates (a1, b1) and the notch center coordinates (a2, b2), calculate the initial position of the notch in the wafer coordinate system, including: The angle of the notch relative to the center of the wafer in wafer coordinates is: 。

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