JP2001230303A - Centering method for semiconductor wafer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To align the center of a semiconductor wafer and the positional angle (orientation flat) of a flat part accurately at the time of carrying the wafer. SOLUTION: Edge position of a wafer is detected and stored in correspondence with each rotational angle of a wafer rotating means under rotation. Assuming the edge position signals when the wafer rotating means is rotated by 90 deg., 180 deg. and 270 deg. from a rotation angle of detecting an edge position signal Lx1 are Lx2, Lx3 and Lx4, only four output signals Lx1-Lx4 of edge position signal are detected and stored from a time point when output of the edge position signals is stopped before the wafer rotating means rotates by one revolution. Since a CPU can be occupied in the operation before the wafer rotating means rotates by one revolution and the CPU begins operation of the eccentricity Le and eccentric angle θe at the central position of the wafer, the eccentricity Le and eccentric angle θe of the wafer can be matched with high accuracy in a short time.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for accurately adjusting the position angle (orientation flat) of a center and a flat portion of a semiconductor wafer when a semiconductor wafer is carried in a semiconductor manufacturing apparatus.

[0002]

2. Description of the Related Art In a semiconductor wafer manufacturing apparatus, when a semiconductor wafer is stacked and stored from a cassette to another cassette, or to each stage for inspection or processing, or when transferring between stages, an accurate operation is required. Alignment of the wafer to the center (align the center position of the wafer to the reference position)
Need to do. Further, it is necessary to adjust the angle of the flat portion (or notch) of the wafer (to adjust the center line of the flat portion (or notch) of the wafer to a specific angle). Usually, a cassette or each stage does not have this centering function. Therefore, a method of adding a device for centering a wafer and aligning an angle of a flat portion (or a notch) of a wafer during transfer between the cassettes and the stages. Is being done.

[0003] An apparatus for this purpose focuses on the fact that a wafer is previously processed into an almost perfect circle state by an NC apparatus or the like, and rotates the wafer to detect an edge position corresponding to the rotation angle. The eccentricity and the eccentric angle of the center position of the wafer are calculated based on the maximum value and the minimum value of the detection signal, and the center of the wafer is adjusted based on the eccentricity data. A flat portion (or a notch) called an orientation flat is provided in the peripheral portion to indicate that the edge position changes more sharply at the start and end points of these orientation flat portions than at other portions. The angle at which the orientation flat (or notch) exists is determined by calculating where the rate of change of the edge position signal has exceeded a certain value, and the orientation flat (or notch) is determined. Is notched, the angle of the center line (a straight line connecting the center position of the wafer 1 and the center position of the orientation flat (or notch)) is corrected, and the orientation flat or the like is moved to another stage such as a transfer device. There has been proposed an apparatus in which the same apparatus is used so as to be located at a specific position.

FIG. 1 is a configuration diagram showing an example of such a conventional apparatus. In FIG. 1, reference numeral 1 denotes a semiconductor wafer to be centered, which is mounted on a turntable 2. Reference numeral 3 denotes a turntable rotating mechanism for rotating the turntable 2, which is driven by an electric motor 4.
Reference numeral 5 denotes a detector for detecting an edge position of the wafer 1, and includes a light projector 5a and an optical sensor 5b.
The output of the optical sensor 5b continuously changes while maintaining a specific relationship in accordance with the amount of received light, and includes a CCD (charge-coupled device) and a product name PSD (position sensor).
A device whose output changes linearly with respect to the amount of incident light, which is referred to as a “savedetector”, is used. Reference numeral 6 denotes an encoder for detecting the rotation amount of the electric motor 4 corresponding to the rotation angle of the turntable 2. Reference numeral 7 stores the output of the optical sensor 5b and the output of the encoder 6 as a pair of data for each fixed rotation angle of the turntable 2. Memory circuit. If the output of the optical sensor 5b is an analog signal, an A / D converter is provided between the storage circuit 7 and the optical sensor 5b to convert the signal into a digital signal. Numeral 8 writes the output signal of the A / D converter into the storage circuit 7, reads it out when necessary, calculates the amount of eccentricity and the eccentricity angle of the center position of the wafer 1, and corrects the signals (each signal of the rotation angle and the horizontal position). And a central processing circuit (hereinafter referred to as a CPU) for outputting the data. The CPU 8 uses a microcomputer to rotate the table when an edge position is detected by a program, and once receives a signal corresponding to each rotation angle of the wafer and transfers the signal to the storage circuit 7. Reference numeral 9 denotes a servo control circuit for controlling the rotation of the motor 4 for driving the turntable. The servo control circuit 9 drives the motor 4 in response to a command signal from the CPU 8 and stops the motor 4 when the rotation amount matches the command amount from the CPU 8. Is a servo control circuit. Reference numeral 10 denotes an XY table type moving mechanism for moving the turntable 2 together with its rotary drive mechanism in the XY horizontal plane in the figure, and for correcting the position of the wafer 1 by moving the table 2 according to the output of the CPU 8. And the position is controlled by the XY table driving control circuit 11. Here, before describing FIGS. 1 to 3, the positional relationship between the wafer 1 and the turntable 2 will be described with reference to FIG. 4 of the related art. FIG. 2B is a diagram in which the wafer 1 is mounted on the turntable 2 so that the center position Wc of the wafer 1 and the rotation center position Tc of the turntable 2 coincide with each other. A straight line connecting the rotation center position Tc of the table 2 is defined as an X axis.
An axis orthogonal to the axis is defined as a Y axis. Next, FIG. 4D is a view in which the wafer 1 is mounted on the turntable 2 at an arbitrary position angle, and first, the center position Wc of the wafer 1 is eccentric with respect to the rotation center position Tc of the turntable 2. In addition to the above, the X-axis (a straight line connecting the optical sensor 5b and the rotation center position Tc of the turntable 2), the center position Wc of the wafer 1 and the rotation center position Tc of the turntable 2 are added. Eccentric angle θv with a straight line connecting
(The eccentric angle of the prior art).

The operation of the apparatus shown in FIG. 1 will be described with reference to the flowchart shown in FIG. In FIG. 1, when a wafer 1 is placed on a turntable 2 by a transfer device (not shown), an electric motor 4 rotates, and the turntable rotating mechanism 3 driven by this rotates the wafer by a predetermined angle (for example, 1 degree). . At this time, the optical sensor 5b of the edge position detector 5 generates an output corresponding to the amount of light that reaches and is reduced by the wafer immediately below the sensor, and this output is output as a pair of data (θx, Lx) together with the wafer rotation amount signal. It is stored in the storage circuit 7. Further, the turntable 2 is rotated by a predetermined angle, the detection and storage of the edge position are repeated, and the process is continued until the wafer is rotated 360 degrees from the original position (θx = 0). When the detection of the edge positions on the entire circumference of the wafer is completed, the CPU 8 sequentially reads out the data stored in the storage circuit 7 and obtains the maximum value Lmax and the minimum value Lmin of the edge position signal.
And the rotation angles θmax, θ of the corresponding wafers
Calculate min. From the difference between the edge position signals Lmax and Lmin, the CPU 8 calculates the eccentricity amount signal ΔL in the radial direction with respect to the rotation center position Tc of the turntable 2 of the wafer.
(Lmax−Lmin) / 2, and θmax (or θmin)
, The eccentricity angle signal is obtained from the rotation center position Tc of the turntable 2 and the eccentricity signal (x, y) of the center position Wc of the wafer 1 on the x, y plane = (ΔLcos θmin, Δ
L sin θ min) or (x, y) = (− ΔL cos θ)
max, -ΔL sin θ max), and supplies a correction signal determined by these to the XY table control circuit 11 to perform centering.

Here, the wafer edge position detector 5 and signals obtained therefrom will be described. FIG. 3 is an enlarged explanatory view showing a part of the detector 5, and those having the same functions as those in FIG. 1 are denoted by the same reference numerals. The light from the light projector 5a is blocked by the wafer 1 as schematically shown by an arrow in the figure, a part thereof is reduced, and the rest reaches the optical sensor 5b. Therefore, if a sensor whose output changes in direct proportion to the input light quantity is used as the optical sensor 5b, the output becomes a signal proportional to the length of L which changes according to the position of the edge portion of the wafer 1. Therefore, if the center position Wc of the wafer is displaced toward the edge position detector 5 with respect to the rotation center position Tc of the turntable, the output signal is small, and if the center position Wc is displaced on the opposite side, the output signal is large. Becomes

FIG. 4 is a diagram showing how the output of the optical sensor 5b changes at this time. 12A and 12C, the horizontal axis represents the rotation angle θ of the wafer, and the vertical axis represents the output L of the optical sensor 5b.
There is. FIG. 3A shows an output when the wafer 1 is aligned with the center of the turntable 2 as shown in FIG. 3B. In this case, as described above, the wafer 1 is The output of the optical sensor 5b becomes a straight line because it is processed into a perfect circle by the above method. FIG. 3C shows that the center of the wafer 1 is displaced from the rotation center position Tc of the turntable 2 by the distance .DELTA.L at the eccentric angle .theta.v in the direction of the first quadrant of the XY table 10 as shown in FIG. The output at the time is shown. At this time, the output of the optical sensor 5b changes in a substantially sinusoidal manner as the turntable 2 rotates in the direction of the arrow in the drawing (when the turntable 2 rotates, the wafer 1 also rotates). If the maximum value of the output is Lmax and the minimum value is Lmin, the amplitude of the change is (Lmax-Lmin), which is equivalent to twice the amount of eccentricity ΔL. The angle θmin when L = Lmin corresponds to the eccentric angle θv of the wafer 1 before the rotation of the wafer 1 starts. Therefore, from these signals, the current center position of the wafer is represented by coordinates (x, y) = (ΔLcos θmin, ΔLs
inθmin). (When adopting θmax, (x, y) = (− ΔLcosθmax, −ΔLsin
θmax). Therefore, the wafer can be centered by moving the XY table by -ΔLcos θmin in the x direction and by -ΔLsinθmin in the y direction.

In the conventional apparatus shown in FIG. 1, the operation for simultaneously performing the center alignment and the alignment of the orientation flat portion (or notch portion) when the orientation flat portion (or notch portion) is provided in the peripheral portion of the wafer is as follows. Will be described.

FIG. 5A is a plan view of a wafer provided with an orientation flat (a) at a part of the peripheral edge, and FIGS. 5B to 5E show wafers having such a shape. FIG. 6 shows examples of output waveforms of the edge position detector 5 when the eccentricity is placed on a turntable in various directions. When a wafer having a shape as shown in FIG. 5A is rotated, as shown in FIGS. 5B to 5E, another circumferential portion is formed in the orientation flat portion (or cutout portion) (a). Shows a significantly different output change. In particular, since both ends show an extremely large change rate, the position of the orientation flat can be detected by monitoring the change rate of the output of the edge position detector 5. For this reason, the program of the CPU 8 is configured so that a point where the change rate of the edge position detection signal becomes equal to or more than a predetermined value is determined as the end of the orientation flat portion.

In this case, the limit of the change rate is the difference between the maximum value and the minimum value of the output signal, that is, the approximate wafer eccentricity, because the maximum change rate when the circumferential portion is detected varies depending on the eccentricity of the wafer. What is necessary is just to determine according to quantity. In addition, since the method of calculating the amount of eccentricity differs depending on the position of the orientation flat (or notch) and the eccentric angle of the wafer 1, it is necessary to determine the eccentricity.

FIGS. 6 and 7 show flowcharts for performing this operation. Steps 1 to 7 are the same as those in FIG. 4 without the orientation flat. The maximum value and the minimum value of the output signal of the optical sensor 5b may not have a true value because of the presence of the flat portion. In step 8, the maximum value Lmax and the minimum value obtained in step 7 are obtained. (Lmax-Lmin) is obtained from Lmin and the upper limit α of the rate of change is determined. Next, at step 9, the angle θ = 0 to 3
The change rate ΔLx / Δθx of the output signal L during 60 degrees is calculated, and the angle θ1 of the first position and the angle θn of the last position that satisfy {the absolute value of ΔLx / Δθx ≧ α} are searched. This θ
When the intermediate angle Δθ = {(θn−θ1) / 2} + θ1 between 1 and θn is obtained, the center of the flat portion exists at a position rotated by Δθ from the original rotation position.

Next, it is determined whether or not the angle θmax at which the output reaches the maximum (L = Lmax) is in the relationship of θ1 ≦ θmax ≦ θn. If θ1 ≦ θmax ≦ θn is satisfied, the wafer is first removed. Since the position corresponding to the maximum value Lmax of the step 7 obtained by the rotation is in the state shown in FIG. 5C included in the orientation flat portion, the true maximum value Lmax has not been obtained. . Therefore, the minimum value L
The angle θmin corresponding to Lmin is defined as the eccentric angle (the angle of the center deviation), and a point 90 degrees away from this (θmin + 90 degrees when θmin ≦ 270 degrees, θmin>
The output of [theta] min-90 [deg.] At 270 [deg.] Is adopted as the intermediate value Lc, and the eccentric amount [Delta] L of the center position Wc of the wafer 1 is equal to Lc.
-Lmin is obtained. From this result, the center position Wc of the wafer 1 is obtained.
Current position coordinates (x, y) = (ΔLcosθmin, ΔL
sin θmin). (However, the direction of the optical sensor 5b is + x.)

On the other hand, the angle θ at which the output L reaches the maximum value Lmax
When max is not between .theta.1 and .theta.n, the orientation flat portion is located at another position, so Lmax obtained in step 7 is adopted as the maximum eccentric amount, and .theta. is set as the angle corresponding to the eccentric angle .theta.v.
Use max. In this case, the actual center position Wc of the wafer 1 is in the direction of θmax + 180 degrees. (FIG. 5
Cases such as (b), (d), and (e). )

Next, an angle θf adjacent to +90 degrees or an angle θf adjacent to −90 degrees with respect to θmax (hereinafter referred to as a flat portion determination angle θf) is an angle (θ1) indicating the orientation flat portion (or notch portion).
To θn), and if it is within the angle indicating the orientation flat (or notch), the angle 270 degrees ahead (or 90 degrees or 270 degrees before) of θmax is set to the intermediate angle. θc, and the output value of the edge position detector 5 at that time is adopted as the intermediate value Lc. If the flat portion determination angle θf is not within the angle indicating the orientation flat portion (or notch portion), the flat portion determination angle θf is set to the intermediate angle θc, and the output value of the edge position detector 5 at that time is set to the intermediate value L.
c, the amount of eccentricity of the wafer 1 ΔL = Lmax−L
Get c. At this time, the intermediate angle θc is as shown in Table 1. That is, when the flat portion determination angle θf is not within the angle indicating the orientation flat portion (or notch portion) of the wafer 1, θ
Let c = θf. Note that the output value of the edge position detector 5 corresponding to the intermediate angle θc becomes the intermediate value Lc. However, when the flat portion determination angle θf is within the angle indicating the orientation flat portion (or notch portion) of the wafer 1, the flat portion determination angle θ
An angle that differs from f by 180 degrees is defined as an intermediate angle θc.
The edge position detector 5 corresponding to the intermediate angle θc
Becomes the intermediate value Lc. However, since the range of the angle data stored in the storage means is 0 degrees to 360 degrees, the flat portion determination angle θf and the intermediate angle θc need to be within the range of the angle data. In order to satisfy this condition, it is necessary to divide the cases as shown in Table 1.

[0015]

[Table 1]

FIG. 8 shows an example of the output waveform of the detector at this time. FIG. 3A corresponds to 1 in Table 1 (b), (c) corresponds to 2 in Table 1, and (d) corresponds to 3 in Table 1 (provided that θ1
<Θf <θn). From the above result, the current position coordinates (x, y) of the center position Wc of the wafer 1 = (− ΔLcos θ)
max, -ΔL sin θ max).

[0017]

The accuracy of the center alignment of the wafer is becoming increasingly strict at present, for example, ± 0.25 mm at the center position, and the accuracy of the angular alignment of the orientation flat portion is ± 0. Approximately 25 degrees is required. In order to satisfy such a requirement, at least 360 degrees / 0.25 degrees = 1,44 in one rotation of the wafer.
Data relating to an edge position signal of 0 or more is required.
In addition, there is a slight error in accuracy in the drive mechanism of the turntable for rotating the wafer, and the shift of the center position of the wafer and the shift of the orientation flat position angle exist simultaneously (FIG. 5A). , Or (e)), since an edge position signal is obtained as a result of integrating them, the detection accuracy is further deteriorated. Is required. Therefore, usually, about 7,500 pieces of data are taken per rotation.

However, in the above-mentioned conventional apparatus, the output of the edge position detector 5 is once taken into the CPU 8 and
In accordance with the program set to 8, the data relating to the edge position signal is sequentially written and stored in the storage circuit. Here, the edge position of the wafer is detected by an edge position detector 5, the detected value is converted into a digital signal by an A / D converter, and stored in a storage circuit 7 via a CPU 8.
Consider when storing in In this case, the operation time of the A / D converter is 30 μm per data relating to the edge position signal.
and a CPU for extracting data from the A / D converter and writing the data to a predetermined address of the storage circuit 7.
Approximately 50 μs is required for processing time of 8 and a total of 80 μs
Is required as the processing time per data. Here, assuming that the wafer is rotated once (360 degrees) per second,
The speed of data detection and storage is 1 / (80 × 10 −6) = 1
The upper limit is 25,000. Normally, considering the safety of operation, the limit is about 60% of the limit, that is, about 7,500 times. With this selection, the CPU is completely occupied during the detection and storage of the required number of data, and there is no room for other operations. Therefore, the calculation of the shift amount of the center position of the wafer, the shift angle of the orientation flat position, and the correction amount thereof is performed by rotating the wafer once, storing all the data relating to the edge position signal, and reading out these data. become.

Therefore, conventionally, in order to improve the detection accuracy, the center shift is first calculated by the first edge position detecting operation, the center position shift is corrected based on the result, and then the wafer is rotated again to obtain a substantially straight line. The position data of the shape and the data of the shape in which only the orientation flat is convex upward are obtained, the orientation of the orientation flat is detected by calculating from this data, and the operation of matching the position of the orientation flat to a predetermined angle is performed based on the result. Like that. For this reason, in the conventional apparatus, 1 second.times.2 times = 2 times for detecting and storing data relating to the wafer rotation and the edge position signal.
Seconds, 1.5 seconds × 2 times = 3 seconds for reading stored data, 3 to 5 seconds are required for calculating and correcting the center position shift and the shift angle of the orientation flat portion depending on the read data, for a total of 8 to 10 seconds. Seconds were needed.

[0020]

According to a first aspect of the present invention, an edge position of the wafer is detected and stored in correspondence with each rotation angle during rotation of the wafer rotation means, and an edge position signal is detected. One is Lx1, and 90 °, 180 ° and 270 ° from the rotation angle at which the edge position signal Lx1 is detected (when the rotation angle of the wafer rotation means from the state where the wafer is first placed on the wafer rotation means is 360 ° or more, When is 3
The angle position signal when the wafer rotating means is rotated is defined as Lx2, Lx3, and Lx4, respectively, and the edge from when the output of the edge position signal is stopped before the wafer rotating means makes one rotation is edged. Position signal L
Only the four output signals x1, Lx2, Lx3, and Lx4 are detected and stored, and the central processing unit (CPU) is occupied for the operation before the time when the wafer rotating means makes one rotation. Since the calculation of the eccentricity Le and the eccentric angle θe of the center position of the wafer is started, the central processing circuit can be occupied for the calculation before the time when the wafer rotating means makes one rotation, and the eccentricity Le of the wafer Le This is a method for centering a semiconductor wafer, which can adjust the eccentric angle θe with high accuracy in a short time.

Further, the invention of claim 2 at the time of filing of the present invention is directed to a wafer having a flat portion or a notch in a part of a peripheral edge thereof in accordance with each rotation angle during rotation of the wafer rotating means. The edge position is detected and stored, and the edge position signal of the position of the end of the flat portion or the notch is defined as Lx1, and the edge position signal Lx1 is 90 degrees, 180 degrees from the detected rotation angle.
And 270 degrees (when the rotation angle of the wafer rotation means from the state where the wafer is first placed on the wafer rotation means becomes 360 degrees or more, the angle is reduced by 360 degrees) Edge position when the wafer rotation means is rotated Signals are Lx2 and Lx3 respectively
And Lx4, a flat portion or a notch portion where the edge position signal is detected as four output signals Lx1, Lx2, Lx3, and Lx4 from the time when the output of the edge position signal is stopped before the time when the wafer rotating means makes one rotation. An edge position signal of the edge position is detected and stored, and the central processing circuit is occupied for calculation before the time when the wafer rotating means makes one rotation, and the central processing circuit eccentrically shifts the center position of the wafer. Le
Since the calculation of the eccentric angle θe and the angle of the center line of the flat portion or the notch portion of the wafer is started, the central processing circuit can be occupied for the calculation before the time when the wafer rotating means makes one rotation. A method of centering a semiconductor wafer, wherein the eccentricity Le and the eccentric angle θe of the wafer and the angle of the center line of the flat portion or the notch portion of the wafer can be adjusted with high accuracy in a short time.

In addition, the invention of claim 3 at the time of filing of the present invention is directed to a wafer having a flat portion or a notch in a part of a peripheral edge thereof in accordance with each rotation angle during rotation of the wafer rotating means. The edge position is detected and stored, and the edge position signal of the edge position of the wafer excluding the flat portion or the notch portion and the edge portion is defined as Lx1, and the rotation angle at which the edge position signal Lx1 is detected is 90 degrees and 180 degrees. And 270 degrees (an angle reduced by 360 degrees when the rotation angle of the wafer rotation means from the state where the wafer is first placed on the wafer rotation means is 360 degrees or more) Edge position signal when the wafer rotation means is rotated Lx2, Lx3 and Lx4, respectively, from the time when the output of the edge position signal is stopped before the time when the wafer rotating means makes one rotation, the edge position signal is converted into four output signals Lx1, Lx2, Lx3 and Lx4. The detected edge position signal of the edge position of the flat portion or the notch is detected and stored, and the central processing circuit is occupied for calculation before the time when the wafer rotating means makes one rotation, so that the central processing circuit The calculation of the eccentric amount Le and the eccentric angle θe of the center position of the wafer and the angle of the center line of the flat portion or the notch portion of the wafer is started, and the central processing circuit is operated before the time when the wafer rotating means makes one rotation. And a center line angle of a flat portion or a notch portion of the wafer can be adjusted with high precision in a short time with high accuracy. It is.

Further, the invention of claim 4 at the time of filing shows a specific method of calculating the eccentric amount Le and the eccentric angle calculation angle θ0 described in claims 1 to 3.

[0024]

FIG. 9 shows an embodiment of the present invention. In FIG. 1, a wafer 1 is placed on a turntable 2, and the turntable 2 is driven to rotate around a θ-axis by an electric motor 4, and the amount of rotation is detected by a θ-axis encoder 6. A signal relating to the edge position of the wafer 1 is supplied to a wafer edge position detector 5.
Is detected as an analog signal by the optical sensor 5b. These are the same as the conventional device shown in FIG. Also, a turntable 2 and an electric motor 4 for rotationally driving the turntable 2
And the encoder 6 are mounted on an X-axis table 21. The X-axis table 21 is driven by an electric motor 22a for driving the X-axis table and a feed screw 22b.
Moved in the direction. The amount of movement in the X-axis direction is
This is detected by the X-axis encoder 22c connected to a. A lifter 23a lifts and separates the wafer 1 from the turntable, and is connected to an air cylinder 23c driven by a solenoid valve 23b and driven in the Z direction in the figure. An A / D converter 24 converts an analog signal output of the optical sensor 5b into a digital signal. 25 is a storage circuit, 26 is a DMA data transfer circuit, 27 is a central processing circuit (CPU), 28a and 28b are motor control circuits, 29a and 29b are comparators, and receives a motor rotation amount command signal from the CPU 27. The outputs of the motor control circuits 28a and 28b, which convert the signals into rotation amount signals of the respective motors 4 and 22a, are compared with the outputs of the encoders 6 and 22c, and each motor is driven by the difference signal.

When a pulse motor is used as an electric motor for driving the turntable 2 and the X-axis table 21, the encoders 6 and 22c are not necessary, and C
What is necessary is just to drive according to the number of drive command pulses from PU27.

Next, the DMA data transfer circuit 26 will be described. The DMA data transfer circuit 26 is an abbreviation of a direct memory access circuit, and a circuit corresponding to a CPU to be combined is commercially available in the form of an LSI. For example, when using Intel's 8085 MPU as the CPU, the DMA 8237A type, the Z80 DMA type for Zilog's Z80 MPU, and the 6844 type DM for Motorola's 6809 MPU.
A (both are model names of US manufacturers).

This DMA data transfer circuit is a circuit for directly transferring data between an input / output device, between an input / output device and a memory, and between a memory and a memory without passing through a CPU. Since the CPU only needs to exchange signals for releasing and returning the data bus, the time occupying the CPU is limited
Only a short time of less than a few percent is required when transferring via.
As a result, the wafer edge position detection / storage operation and data processing can be performed while the wafer is rotating.

The embodiment shown in FIG. 9 will be described below with reference to FIGS. First, before describing the flowcharts of FIGS. 10 and 11, a method of geometrically calculating the eccentric amount Le and the eccentric angle θe will be described with reference to FIG.

In FIG. 12, the rotation angle of the turntable 2 corresponding to the end portion of the flat portion or the notch portion of the wafer is defined as θx1, and the rotation angles of the turntable 2 different from the rotation angle θx1 by 90 degrees are respectively θx2 and θx3. And θx4
And Further, a straight line connecting the position of the edge position detector 5 and the rotation center position of the turntable 2 is defined as the X axis, and the edge position Px1 of the wafer at the end of the flat portion or the notch portion corresponding to the rotation angle θx1. A straight line connecting the rotation center position of the turntable 2 is defined as a base line. If the edge position signals for the rotation angles θx1 to θx4 are Lx1 to Lx4, the CPU 27 controls the CPU 27 to shift the center position Wc of the wafer 1 with respect to the rotation center position Tc of the turntable 2 (eccentricity) Le and the wafer with respect to the X axis. Can be calculated by (Equation 1) to (Equation 3). However, the eccentric angle calculation angle θ0 is a straight line (hereinafter, referred to as an eccentric angle axis) connecting the rotation center position Tc of the turntable 2 and the center position Wc of the wafer 1 when rotated 360 degrees (same as before the start of rotation). Angle between base line and θ
ST is the angle between the X axis and the base line at this time. In the case of FIG. 12, for example, the magnitude of θST is (360
(° −θx1), and becomes known when θx1 is determined. Further, the correlation among the rotation center position Tc of the turntable 2, the center position Wc of the wafer, the X axis, θx1 to θx4, etc. is as shown in FIG. 12, and it can be easily understood that the formulas are established from this.

[0030]

(Equation 1)

(Equation 2)

(Equation 3)

Next, using Le, θe, and θ0, centering (aligning the center position of the wafer to the reference position), angle alignment of the flat portion (or notch portion) (alignment of the flat portion (or notch portion) of the wafer). A method for adjusting the center line to a specific angle will be described. First, the turntable 2 is rotated by θe to move the center position Wc of the wafer 1 on the X axis. Next, the lifter 23a is raised, and the wafer 1 is lifted from the turntable 2. After this, the X-axis table 21
Is moved by Le (in the case of FIG. 12). Further, when the lifter 23a is lowered and the wafer is returned on the turntable, the centering (centering) is completed.

Thereafter, the turntable 2 is rotated to rotate the center line of the flat portion (a straight line connecting the center position Wc of the wafer 1 and the center position of the orientation flat portion (a position corresponding to the angle θxc)).
Are rotated until they match the predetermined angle, and the angle adjustment is completed.

When the centering is completed, the center line of the orientation flat is inclined with respect to the X axis. When the center line of the orientation flat is aligned with the X axis, the amount of eccentricity Le is usually small. Can be obtained by correcting the angle of the turntable 2 by (θ0 + ／ · α). However, the amount of eccentricity L
When e is large or when it is desired to exactly match the center line of the orientation flat to a predetermined angle, the eccentric angle calculation angle θ0 and the eccentricity Le and the angles θx1 and θ to the end point of the orientation flat section are set.
From the edge position signal Lx1 or the like corresponding to x1, the eccentricity corrected angle θk is mathematically calculated, and the eccentric angle calculation angle θ0 is calculated.
Instead, the angle θk after the correction of the eccentricity may be used. That is, the turntable 2 may be rotated by (θk + ／ · α). For example, in the case of FIG. 12, the angle θk after the correction of the eccentricity can be mathematically calculated as follows. The eccentricity-corrected angle θk is, as shown in FIG. 12, an eccentric angle axis connecting the rotation center position Tc of the turntable 2 and the center position Wc of the wafer 1, a center position Wc of the wafer 1 and an angle θx1. Is an angle made with a straight line connecting the position Px1 corresponding to. First, a distance TcPx1 (a distance Tc) from the rotation center position Tc of the turntable 2 to the position Px1.
Px1 corresponds to Lx1. That is, since the distance between the edge position detector and the turntable 2 is determined by the specification, if Lx1 is known, the distance TcPx1 can be calculated.) The amount of eccentricity Le and the angle θ0 for calculating the eccentric angle, The distance WcPx1 from the center position Wc to the position Px1 can be calculated by the following equation. The wafer is
Since the specifications such as the diameter and the size of the flat portion are determined, the value of WcPx1, which is the radius of the wafer 1, can be a value determined by the specifications. ^{WcPx1 = √ (TcPx1 2 + Le} 2 -2 * TcPx1 * Le * co
s (θ0)) Further, assuming that the intersection point when a straight line perpendicular to the eccentric angle axis is drawn from the position Px1 is the position Pk, ∠PkPx1Tc can be calculated by the following equation. ∠PkPx1Tc = 180−90−θ0 [°] Further, the distance PkPx1 from the position Pk to the position Px1 can be calculated by the following equation. PkPx1 = TcPx1 * cos θ (θ = ∠PkPx1Tc) Therefore, θk can be calculated by the following equation. θk = sin-1 (PkPx1 / WcPx1) [°] Furthermore, in order to set the center line of the orientation flat to a position inclined by γ degrees with respect to the X axis, the center line of the orientation flat is positioned with respect to the X axis when the centering is completed. Since it is tilted by (θ0 + ／ · α), it may be rotated by γ- (θ0 + ／ · α). Also in this case, when the eccentricity Le is large or when it is desired to exactly match the center line of the orientation flat with the predetermined angle, the corrected eccentricity angle θk is used instead of the eccentric angle calculation angle θ0 as in the case described above. Then, the turntable 2 may be rotated by γ− (θk + ／ · α).

Next, the embodiment of FIG. 9 will be described with reference to the flowcharts of FIGS. 9 to 11, when the wafer 1 is placed on the turntable 2 by the transfer means (not shown), the centering operation of the wafer 1 and the angle adjusting operation of the orientation flat portion of the wafer 1 are started. First, .theta.x and the counter x stored in the storage circuit are set to 0, and after waiting for the output of the optical sensor 5b, it is stored in the storage circuit 25 together with the rotation angle .theta.x (= 0) at that time. Also,
Since the output of the optical sensor 5b is at least about 1 V, in step 5, the output signal Lx
Is read and input to the CPU to determine whether Lx ≠ 0. If Lx ≠ 0, it is determined that measurement has started, and the process proceeds to step 6. If Lx = 0, the output signal Lx of the optical sensor is read from the storage circuit 25 again and input to the CPU. Determine if there is. In step 6, the optical sensor 5b read from the storage circuit 25 and input to the CPU
ΔLx = Lx−Lx−1 is calculated from the output signal Lx. In step 7, ΔLx / Δθx> ΔLmax (where Δθx is the unit rotation angle, and ΔLmax is the output change rate ΔLx until then).
/ Maximum value of Δθx). When starting, of course, Lx
= Lx-1 and ΔLx = ΔLmax = 0, so ΔLx / Δθx = Δ
Lmax = 0, and the routine proceeds to step 9. If ΔLx / Δθx> ΔLmax is satisfied in step 7, this ΔLx / Δθx is set as a new ΔLmax in step 8. Thereafter, the process proceeds to step S13. In step 9, θ
It is determined whether x ≧ 360 degrees. When θx ≧ 360 degrees, since the turntable 2 is rotated by 360 degrees, the edge position signals Lx1 to Lx4 corresponding to the angles θx1 to θx4 are calculated in step 12, and thereafter, in step 2,
Move to 1. If θx ≧ 360 degrees is not satisfied in step 9,
Move to step 10. In step 10, it is determined whether or not the angles θx1 to θx4 have been selected. If the angles θx1 to θx4 have been selected, the process proceeds to step 11, and if the angles θx1 to θx4 have not been selected, the process proceeds to step 18.
In step 11, it is determined whether all the edge position signals Lx1 to Lx4 corresponding to the angles θx1 to θx4 can be calculated, that is, it is determined whether all the edge positions at the angles θx1 to θx4 have been detected. If so, in step 12, the edge position signals Lx1 to Lx4 corresponding to the angles θx1 to θx4 are calculated, and then the process proceeds to step 21. If θx ≧ 360 degrees is not satisfied at this time, the process proceeds to step 21 after rotating the turntable 2 to 360 degrees. If it is determined in step 11 that all the edge position signals Lx1 to Lx4 cannot be calculated, the process proceeds to step 18.

Next, at step 13, the sign of (x-1) is determined (whether the rotation of Δθx has been performed twice or more). At the start, x = 0, ie, x-1 = -1
Therefore, x-1> 0 is not established. for that reason,
Skipping to step 18, the turntable 2 is further rotated by Δθx, and x = x + 1 and θx = θx +
Execute Δθx. After step 18, the process returns to step 4 to store (θx, Lx) in the storage circuit. Thereafter, steps 5 to 13 are executed. At this time, since x = 1, x-1> 0 is not established in step 13. Therefore, skip to step 18 again and turntable 2
Are rotated by Δθx, and x = x + 1 and θx = θ
Execute x + Δθx. Thereafter, steps 4 to 13 are executed in the same manner as described above. At this time, since x = 2, x-1> 0 is satisfied in step 13. for that reason,
Move to step 14.

In step 14, ΔLx at this time and 1
A comparison is made with the previous ΔLx−1 to check ΔLx / ΔLx−1> k (where k is a predetermined constant).
After moving to 8, the steps after step 4 are executed.
When ΔLx / ΔLx−1> k, the change amount of the edge position is large, so it is determined that the orientation flat is the start end, and the process proceeds to step S15. In step 15, the rotation angle θx = X · Δθx and the center angle α of the orientation flat portion which is known in advance are not within the orientation flat (including the end portion), and are mutually separated by a rotation angle of 90 degrees. Angle (θx1, θx2, θx3, θx
Select 4). Thereafter, the process proceeds to step S16. In step 16, edge position signals Lx1, Lx2, Lx3, Lx4 corresponding to the above-mentioned θx1, θx2, θx3, θx4 are calculated.
At this time, the angle to be adopted as θx1 is, for example, an angle θx1 = θx + obtained by adding the central angle α of the orientation flat portion to the current θx.
α may be adopted, but the other three points are determined as shown in Table 2 depending on the value of (θx + α).

[0037]

[Table 2]

It is determined in step 17 whether or not all the data at these points has been obtained by the previous wafer rotation. If not, the process proceeds to step 18 and the turntable 2 is further rotated by Δθx. Steps 4 to 16 are repeated. If θx1 to θx4 and the corresponding edge position signals of Lx1 to Lx4 have been obtained, the process proceeds to step 19, where the remaining angles are rotated to 360
It stops when it has been rotated degrees.

When Le, θe, and θ0 are calculated in step 21, the CPU 27 issues a command to the turntable driving motor control circuit 28a to rotate the turntable 2 by θe in step 22, and outputs a deviation angle. Is corrected, and the center position Wc of the wafer 1 is moved on the X axis.
Next, in step 23, the CPU 27 issues a command to the solenoid valve 23b to operate the air cylinder 23c, and the lifter 23a
And lift the wafer 1 from the turntable 2. Thereafter, the CPU 27 sets the X-axis driving motor control circuit 2
A command to move 8b to Le (in the case of FIG. 12) is output, and the electric motor 22a rotates to rotate the feed screw 22b to move the X-axis table 21 by Le. Further, in step 25, the lifter 23a is lowered to return the wafer onto the turntable (centering is completed).

Thereafter, in step 26, the turntable 2 is rotated so that the center line of the orientation flat portion (a straight line connecting the center position Wc of the wafer 1 and the center position of the orientation flat portion (position corresponding to the angle θxc)) has a predetermined angle. Rotate until it matches and finish.

In steps 19 and 20, 3
Although it was rotated to 60 degrees, by changing the calculation formula at the time of position correction, the rotation for detecting the edge position was stopped at the position where the data of Lx1 to Lx4 corresponding to θx1 to θx4 was obtained in step 17. , Step 21 may be performed. In this case, since the wafer has not returned to the initial position, the rotation angle θx up to this point may be added to the calculation and correction of the shift angle and shift amount.

It should be noted that the present invention is not limited to the center alignment of wafers having the above-mentioned orientation flats and the angle adjustment of the orientation flats. It can also be applied to the alignment of plate-like objects.

[0043]

As described above, according to the present invention, even when the DMA data transfer means is not used, the edge position signal of the edge position detected first is set to Lx1, and the edge position signal Lx1 is detected. The edge position signals when the wafer rotating means are rotated by 90 degrees, 180 degrees, and 270 degrees from the rotation angles set as Lx2, Lx3, and Lx4, respectively, and the output of the edge position signal before the time when the wafer rotating means makes one rotation. From the time of stopping, the edge position signals are changed to Lx1, Lx2, L
detecting and storing the four output signals x3 and Lx4 and the detected edge position signal of the edge position of the flat part or the notch part,
The CPU is occupied for calculation before the time when the wafer rotation means makes one rotation, and the CPU causes the eccentricity L of the center position of the wafer to be calculated.
Since the calculation of e and the eccentric angle θe is started, the CPU can be occupied for the calculation before the time when the wafer rotating means makes one rotation, and the eccentric amount Le and the eccentric angle θe of the wafer can be set shorter than in the prior art. Can be adjusted with high precision.

Further, according to the present invention, the DM
When the edge position is detected by rotating the wafer by using the A data transfer means, the data is directly stored in the storage circuit from the A / D converter by the DMA data transfer means without passing through the CPU. The CPU occupies almost no time for detecting and storing the wafer edge position, and in parallel with the detection and storage, the calculation for detecting the orientation flat position becomes possible, thereby reducing the time required for centering. be able to. Also, since the CPU is hardly occupied for edge position detection and storage, the unit rotation angle for obtaining data at the same rotation speed can be reduced to a fraction of that of the conventional device even at the same rotation speed. it can. As a result, in the related art, the required accuracy cannot be obtained unless the wafer is rotated again after the detection and correction of the center position deviation of the wafer 1 and the change in the edge position is detected only by the change in the orientation flat portion to detect the orientation flat position. On the other hand, sufficient accuracy can be obtained even if the displacement of the center position and the detection of the orientation flat position are simultaneously performed by only one rotation.

In the apparatus of the present invention, as in the conventional apparatus described with reference to FIG. 1, the result when the wafer is rotated at one rotation per second was examined. In this case, the rotation of the wafer for detecting the edge position is set to one time, and instead, the number of data to be collected per rotation is set to three to four of the conventional value.
As a result, the wafer rotation / detection storage and the orientation flat portion were found as a result of performing center alignment and orientation flat alignment in the procedure shown in the flowcharts of FIGS.
It took one second to select x1 to θx4, and then two to three seconds to calculate and correct θe and Le. The total was completed in three to four seconds, and the accuracy was sufficient. This required time is as short as 30 to 40% of the time required by the conventional apparatus, and a great effect of the present invention was confirmed. The difference in the required time fluctuates by a maximum of about 1 second as illustrated, for example, due to the difference in the amount of displacement between the orientation flat position and the center position from the rotation start position.

[Brief description of the drawings]

FIG. 1 is a connection diagram showing an example of a conventional device.

FIG. 2 is a flowchart for explaining the operation of the apparatus of FIG. 1;

FIG. 3 is an explanatory diagram of a detector for detecting a wafer edge position.

FIG. 4 is a diagram showing a state of an output change of an optical sensor 5b of an edge position detector 5;

FIG. 5 is a plan view of a wafer provided with a flat portion (orientation flat) and a diagram showing a change in output of an optical sensor 5b when an edge position of the wafer is detected.

FIG. 6 is a flowchart (1) of calculating a wafer eccentricity as shown in FIG. 5 in the conventional apparatus of FIG. 1;

FIG. 7 is a flowchart (2) of calculating the eccentricity of the wafer as shown in FIG. 5 in the conventional apparatus of FIG. 1;

8 is a diagram for explaining another method of adopting an edge position signal of a wafer provided with a flat portion in the conventional apparatus of FIG. 1;

FIG. 9 is a connection diagram showing an embodiment of the present invention.

FIG. 10 is a flowchart (1) for explaining the operation of the embodiment in FIG. 9;

FIG. 11 is a flowchart (2) for explaining the operation of the embodiment in FIG. 9;

FIG. 12 is an explanatory view when centering and orienting the wafer having an orientation flat portion by the procedure of the embodiment of FIG. 9 and the flowcharts of FIGS. 10 and 11;

[Explanation of symbols]

 Reference Signs List 1 wafer 2 turntable 4 turntable rotating motor 5 edge position detector 5a projector 5b optical sensor 6 encoder 21 X-axis table 22a X-axis table driving motor 22b feed screw 22c X-axis encoder 23a lifter 23b solenoid valve 23c air cylinder 24A / D converter 25 Storage circuit 26 DMA data transfer circuit 27 Central processing unit (CPU) 28a Motor control circuit for turntable drive 28b Motor control circuit for X-axis drive 29a Comparator 29b Comparator

Claims (4)

[Claims] 1. A process of mounting a circularly shaped wafer on a wafer rotating means, and detecting an edge position of the wafer by an edge position detector corresponding to each rotation angle during rotation of the wafer rotating means. Outputting a signal relating to the edge position, outputting an edge position signal obtained by converting the signal relating to the edge position into a digital signal, and setting one of the edge position signals to Lx1 and the edge position signal Lx1 to Lx1. 90 °, 180 °, and 270 ° are rotated from the detected rotation angle so that the rotation angle of the wafer rotation unit from the state where the wafer is first placed on the wafer rotation unit is 3 degrees.
Outputting the edge position signals at the time of the angle rotation reduced by 360 degrees as Lx2, Lx3 and Lx4 when the angle position is equal to or more than 60 degrees, and the edge position when the edge position signals Lx2, Lx3 and Lx4 are output A process of stopping the output of the signal, a straight line connecting the position of the edge position detector and the rotation center position of the wafer rotating means is set as the X axis, and the edge position of the wafer corresponding to the edge position signal Lx1 and the wafer rotation Using the straight line connecting the rotation center position of the means as a base line and calculating the eccentricity Le and the eccentric angle calculation angle θ0 using the edge position signals Lx1, Lx2, Lx3, and Lx4 from the time when the output of the edge position signal is stopped. And the angle θS between the eccentric angle calculation angle θ0 and the X axis and the base line.
A step of calculating an eccentric angle θe of a difference from T, and a step of centering the wafer in accordance with the eccentricity Le of the center position of the wafer and the eccentric angle θe. The central processing circuit detects and stores the edge position of the wafer and stops the output of the edge position signal before the time when the wafer rotating means makes one rotation. Eccentric angle θe
Is calculated, and the eccentricity Le and the eccentric angle θe of the wafer are adjusted to each other. 2. A process of mounting a wafer having a flat portion or a notch on a part of a peripheral edge thereof in a circular shape and mounting the wafer on a wafer rotating means, and adjusting the wafer in accordance with each rotation angle during rotation of the wafer rotating means. A step of detecting the position of the flat portion or the notch while detecting the edge position with the edge position detector and outputting a signal relating to the edge position, and an edge position signal obtained by converting the signal relating to the edge position into a digital signal. A step of outputting the edge position signal corresponding to each of the rotation angles from the storage circuit, and a central processing circuit from the state where the wafer is first placed on the wafer rotation means, and a rotation center position of the wafer rotation means. Calculating the rate of change of the edge position of the wafer from the rotation angle signal and the edge position signal when rotating about the center of rotation, and using the calculated rate of change. Determining the rotation angle of the wafer rotation means corresponding to the end of the flat portion or the notch portion of the wafer, and converting the edge position signal at the determined rotation angle to L.
x1, and 90 °, 180 °, and 270 ° from the rotation angle at which the edge position signal Lx1 was detected, and the rotation angle of the wafer rotation means from the state where the wafer was first placed on the wafer rotation means was changed by rotating the wafer rotation means. Outputting 360 ° or more edge position signals at the time of the angle rotation reduced by 360 degrees as Lx2, Lx3 and Lx4, respectively,
A step of stopping the output of the edge position signal when the edge position signals Lx1, Lx2, Lx3, and Lx4 are output, and a straight line connecting the position of the edge position detector and the rotation center position of the wafer rotation unit with X Axis, a straight line connecting the edge position of the wafer corresponding to the edge position signal Lx1 and the rotation center position of the wafer rotating means is used as a base line, and the edge position signals Lx1, Lx
2, the process of calculating the eccentricity Le and the eccentric angle calculation angle θ0 using Lx3 and Lx4, and the eccentric angle of the difference between the eccentric angle calculation angle θ0 and the angle θST between the X axis and the base line. calculating the angle θe and calculating the angle of the center line of the flat portion or the notch portion connecting the center position of the flat portion or the notch portion and the center position of the wafer using the eccentric angle calculation angle θ0. And the step of adjusting the center of the wafer and the angle of the center line of the flat portion or notch of the wafer to a specific angle according to the eccentricity Le and the eccentric angle θe of the center position of the wafer, While detecting the edge position of the wafer during the rotation of the wafer rotating means, the position of the flat portion or the notch portion is also detected and stored in a non-contact manner,
The central processing circuit calculates the eccentricity Le and the eccentric angle θe of the center position of the wafer from the time when the output of the edge position signal is stopped before the time when the wafer rotating means makes one rotation, and the flat portion of the wafer or A method of centering a semiconductor wafer in which the angle of the center line of the notch is also calculated, and the eccentricity Le and the eccentric angle θe of the wafer and the angle of the center line of the flat portion or the notch of the wafer are matched. 3. A process in which a wafer having a circular shape and having a flat portion or a notch in a part of a peripheral edge is mounted on a wafer rotating means, and the wafer is rotated in accordance with each rotation angle during rotation of the wafer rotating means. A step of detecting the position of the flat portion or the notch while detecting the edge position with the edge position detector and outputting a signal relating to the edge position, and an edge position signal obtained by converting the signal relating to the edge position into a digital signal. A step of outputting the edge position signal corresponding to each of the rotation angles from the storage circuit, and a central processing circuit from the state where the wafer is first placed on the wafer rotation means, and a rotation center position of the wafer rotation means. Calculating the rate of change of the edge position of the wafer from the rotation angle signal and the edge position signal when rotating about the center of rotation, and using the calculated rate of change. Determining the rotation angle of the wafer rotating means corresponding to the edge of the flat portion or the notch portion of the wafer, and rotating the wafer rotating device corresponding to the edge position of the wafer excluding the flat portion or the notch portion and the edge thereof. The edge position signal at the angle is Lx1, and the wafer rotation unit is rotated by 90 degrees, 180 degrees, and 270 degrees from the rotation angle at which the edge position signal Lx1 is detected, from the state where the wafer is first placed on the wafer rotation unit. The rotation angle of the wafer rotation means is 360
When the angle position is equal to or more than 360 degrees, the process of outputting the edge position signals at the time of the angle rotation reduced by 360 degrees as Lx2, Lx3 and Lx4, respectively, and when the edge position signals Lx1, Lx2, Lx3 and Lx4 are output, The process of stopping the output of the position signal, the straight line connecting the position of the edge position detector and the rotation center position of the wafer rotating means is defined as the X axis, and the edge position of the wafer corresponding to the edge position signal Lx1 and the wafer The eccentricity Le and the eccentric angle calculation angle θ0 are determined by using the edge position signals Lx1, Lx2, Lx3, and Lx4 from the point in time when the output of the edge position signal is stopped, with the straight line connecting the rotation center position of the rotating means as the base line. Calculating, an eccentric angle θe of a difference between the eccentric angle calculating angle θ0 and an angle θST between the X axis and the base line, and a wafer rotating unit corresponding to the edge position signal Lx1. Calculating the angle of difference between the rotation angle of the wafer and the rotation angle of the wafer rotating means corresponding to the end of the flat portion or the notch portion of the wafer, and using the calculated difference angle and the eccentric angle calculation angle θ0. Calculating the angle of the center line of the flat portion or the notch portion connecting the center position of the flat portion or the notch portion of the wafer to the center position of the wafer, and the eccentricity Le and the eccentric angle θe of the center position of the wafer. Detecting the edge position of the wafer during rotation of the wafer rotating means. While the position of the flat portion or the notch portion is also detected and stored in a non-contact manner, the central processing circuit determines the center of the wafer from the time when the output of the edge position signal is stopped before the time when the wafer rotating means makes one rotation. Rank The eccentricity Le and the eccentric angle θe of the wafer are calculated, and the angle of the center line of the flat portion or the notch of the wafer is also calculated. Of aligning the center of the semiconductor wafer. 4. An eccentricity Le calculated by a central processing circuit.
Is 1/2 ｛(Lx3-Lx1) ² + (Lx4-Lx2) ^{2 2 1/2}
And the eccentric angle calculation angle θ0 is tan ⁻¹ ｛(Lx2
The semiconductor wafer centering apparatus according to claim 1, 2 or 3, wherein -Lx4) / (Lx1-Lx3)}.