SUGISAKAMASANORI

Journal of Advances in Artificial Life Robotics
Vol. 1(1); June (2020), pp. 46–49
ON LINE ISSN 2435-8061; ISSN-L 2435-8061
https://alife-robotics.org/jallr.html

Research Article

An Effective Visual Inspection Device for Wafer Physical Defects
Xiaoyan Chen, Jianyong Chen, Chundong Zhao

College of Electronic Information and Automation, Tianjin University of Science and Technology, China

ARTICLE INFO
Article History
Received 10 November 2019
Accepted 17 July 2020
Keywords
Semiconductor manufacturing
Machine vision
Camera calibration
Programmable logic controller

ABSTRACTWafer defect detection is an indispensable part of semiconductor manufacturing. In this paper, anautomatic and efficient device is designed and constructed to detect wafer physical defects.
Programmable logic controllers (PLCs) are used as the controller of the transmission mechanismof the device, and the servo motor is used for driving. Wafer images are captured by a CMOS
camera. In addition, in order to improve the detection accuracy, the camera calibration iscompleted according to the mapping relationship between the pixel coordinate system and theworld coordinate system. A computer is adopted for wafer image processing and displaying thefinal detection results. The device proposed in this paper has low cost and high reliability. It
provides a new solution for wafer defect detection.

© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

distortion of CMOS camera and improve theidentification accuracy of the detection device. The mainstructure, motion mechanism, camera bracket andbearing platform of the device are designed andassembled. The Siemens s7-200 PLC is used as acontroller to implement the control of all parts of thedetection device.

1. Introduction
Silicon wafer processing is the basis of semiconductor
manufacturing. Wafer defect detection is one of the mostimportant steps in semiconductor wafer manufacturing.
Semiconductor wafer defect detection methods aremainly manual inspections, which are affected by humanfactors such as visual fatigue and are inefficient[1],[2],[3].
Research on the automatic wafer defect detection device
was carried out to solve the problem of manual
limitations in wafer defect detection. At present, with thedevelopment of machine vision technology, a large
number of machine vision technologies have been used
to detect chip shape, size, physical defects and otheraspects [4],[5],[6],[7],[8].
The performance of wafer defect detection device
directly affects the quality of semiconductor products andthe efficiency of semiconductor testing [9],[10]. In orderto improve the detection efficiency and positioning
accuracy of the automatic wafer defect detection device,an optical system is designed and constructed in thispaper to obtain a more complete wafer image. Camera
calibration is used to eliminate the errors caused by the2. Dual-axes motion platform
The dual-axes(x-y) motion platform is selected for wafer
defect detection. The horizontal ball screw pair of theplatform is mounted on the longitudinal ball screw pairthrough the bracket, the longitudinal ball screw pair isdirectly mounted on the base surface, and the wafer stage
is mounted on the horizontal ball screw pair through thebracket. The lead screw pair is supported by both ends,
and the drive motor and ball screw pair are directlyconnected. The assembly model is shown in Fig. 1.

Corresponding author’s E-mail: cxywxr@tust.edu.cn URL: www.tust.edu.cn

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The rated dynamic load 𝐶𝐶𝑎𝑎𝑎𝑎 can be calculated byformula (3). 𝐿𝐿𝑑𝑑 is the expected operating distance. 𝐹𝐹𝑤𝑤 is
the load coefficient, set 1.0. 𝑓𝑓𝑎𝑎 is the precision coefficient,
set 1.0. 𝑓𝑓𝑐𝑐 is the reliability coefficient.
(iv) Ball screw subbottom diameter
Ball screw subbottom diameter 𝑑𝑑2𝑚𝑚 can be calculated by
the formula (4).
10𝐹𝐹0 ×𝐿𝐿𝜋𝜋×𝜕𝜕𝑚𝑚 ×𝐸𝐸𝑑𝑑2𝑚𝑚 ≥ 10�(4)𝐹𝐹0 is the static friction of the guide rail. L is the distance
between the support shafts at both ends. 𝜕𝜕𝑚𝑚 is themaximum allowable axial deformation of the ball screw.

Fig. 1 The dual-axes motion platform. It consists of: 1. Wafer
stage 2. Bracket 3. Y-axis ball screw pair 4. Y-axis servo motor
5. X-axis servo motor 6. X-axis ball screw pair 7. Bracket

2.1. Ball screw pair2.2. Servo motor

The ball screw pair is a transmission component thatconverts rotary motion into linear motion with highprecision, high rigidity and high efficiency. The ballscrew pair is rotationally driven by balls mounted
between the spiral groove of the lead screw and the nut.
According to the corresponding function, the ball screw
pair is divided into four components, which are the screw,
the nut, the ball and the reverser. The Y-axis ball screw
pair is located in the lower layer with a larger load andhigher precision requirements. Therefore, the Y-axis ballscrew pair design parameters are used as the overall ballscrew pair design index.
(i) LeadThe lead 𝑃𝑃ℎ is generally determined according to themaximum speed of the feed 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 , the maximum speed of
the servo motor 𝑁𝑁𝑚𝑚𝑚𝑚𝑚𝑚 and the transmission ratio ibetween the motor and the screw, which can becalculated by formula (1).
𝑉𝑉

𝑚𝑚𝑚𝑚𝑚𝑚𝑃𝑃ℎ = 𝑖𝑖×𝑁𝑁

𝑚𝑚𝑚𝑚𝑚𝑚The device uses servo motor as the driving power system.
The performance of the servo motor largely determines
the positioning accuracy of the moving platform.
(i) Pulse equivalent
Pulse equivalent δ is the displacement of the actuator foreach output pulse of the servo motor. It can be calculatedfrom formula (5).
𝑃𝑃 ×𝑖𝑖𝑚𝑚
δ = 4𝑖𝑖ℎ ×𝑞𝑞

𝑖𝑖𝑚𝑚 is the electronic gear ratio of servo motor. 𝑖𝑖𝑛𝑛 is thetransmission ratio. Since the motor shaft and lead screw
are directly connected through the coupling, the value of𝑖𝑖𝑛𝑛 is 1. q is the resolution of servo motor encoder.
(ii) Capacity and torque
When the motor is running, in order to ensure the stable
operation of the system, the moment of inertia of the fullequivalent load on the motor J should match the momentof inertia of the motor rotor 𝐽𝐽𝑚𝑚 .

(1)

𝑛𝑛𝑚𝑚

J = 𝐽𝐽𝑚𝑚 + 𝐽𝐽1

𝐶𝐶×𝑓𝑓 ×𝑓𝑓𝑐𝑐

𝑚𝑚𝑊𝑊� × 𝑃𝑃ℎ𝑣𝑣

2𝑚𝑚

(6)

(7)

Capacity and torque can be calculated from formula (6),(7). 𝐽𝐽𝑖𝑖 and 𝑛𝑛𝑖𝑖 are respectively the moment of inertia andspeed of each rotating part. 𝑚𝑚1 and 𝑣𝑣1 are the mass andspeed of each linear moving part respectively. 𝐽𝐽𝑚𝑚 and 𝑛𝑛𝑚𝑚
are the moment of inertia and speed of the motor
respectively.

(2)

μ is the friction coefficient. M1 is the X-axis ball screw
counter gravity. M2 is the bearing table and the carrier
table carrier gravity.
(iii) Rated dynamic load𝑎𝑎L𝑑𝑑 = � 𝑎𝑎𝑎𝑎
𝐹𝐹 ×𝑓𝑓

21𝐽𝐽1 = ∑ 𝐽𝐽𝑖𝑖 �𝑛𝑛 𝑖𝑖 � + ∑ 𝑚𝑚1 �2𝜋𝜋×𝑛𝑛�(ii) Load and speed of ball screw pair
Equivalent load 𝐹𝐹𝑚𝑚 is the actual axial force exerted on theball screw by the transmission device. This device has nocutting operation, so equivalent load is equal to staticfriction force. 𝐹𝐹𝑚𝑚 can be calculated by formula (2).

𝐹𝐹𝑚𝑚 = 𝜇𝜇 × (𝑀𝑀1 + 𝑀𝑀2 )(5)

𝑛𝑛3. Image acquisition system
The image acquisition system designed in this paper
consists of CMOS industrial camera, lens and ring light(3)47𝑟𝑟 = 𝐴𝐴−1 ℎ1
�1
𝑟𝑟2 = 𝐴𝐴−1 ℎ2source. CMOS industrial cameras transmit data inparallel for faster speeds. The purpose of a lens is toimage an object optically onto a sensor. The diameter ofthe ring light source is 100mm-140mm, which is used tomake the image receiving light uniform and clear. Thestructure of the image acquisition system is shown in
Fig.2

�𝑥𝑥̅ = 𝑥𝑥 + 𝑥𝑥(𝑘𝑘1 (𝑥𝑥 2 + 𝑦𝑦 2 ) + 𝑘𝑘2 (𝑥𝑥 2 + 𝑦𝑦 2 )2 )�𝑦𝑦� = 𝑦𝑦 + 𝑦𝑦(𝑘𝑘1 (𝑥𝑥 2 + 𝑦𝑦 2 ) + 𝑘𝑘2 (𝑥𝑥 2 + 𝑦𝑦 2 )2 )(𝑢𝑢 − 𝑢𝑢0 )(𝑥𝑥 2 + 𝑦𝑦 2 ), (𝑢𝑢 − 𝑢𝑢0 )(𝑥𝑥 2 + 𝑦𝑦 2 )2 𝑘𝑘1
�� � =(𝑣𝑣 − 𝑣𝑣0 )(𝑥𝑥 2 + 𝑦𝑦 2 ), (𝑣𝑣 − 𝑣𝑣0 )(𝑥𝑥 2 + 𝑦𝑦 2 )2 𝑘𝑘2𝑢𝑢� − 𝑢𝑢��(15)𝑣𝑣̅ − 𝑣𝑣

�

The main role of camera calibration is to correct image
distortion and determine the positional relationshipbetween the pixel coordinate system and the world
coordinate system.
(i)
Camera internal and external parameters
As shown in formula (8), (9), The default value of Z
plane is 0. φ is the scale factor. A is the internalparameter matrix. 𝑓𝑓𝑥𝑥 ,𝑓𝑓𝑦𝑦 is the scale factor of the u-axis
and v-axis of the pixel coordinate system. γ represents
the scale deviation of pixel points in the image coordinate
system. 𝑢𝑢0 and 𝑣𝑣0 are the center of the image plane. 𝑟𝑟1 ,𝑟𝑟2 and t are rotation matrix and translation vectors
respectively.

5. Results

Fig. 3 shows a typical wafer image captured by theCMOS camera. Fig. 4 shows the defect detection resultsof Fig. 3. Normal grains are marked as purple, andphysically defective grains are marked as yellow.

(8)

(9)
Fig.3 A typical wafer image

As shown in formula (10), (11), (12), H is a homographymatrix, and the basic constraint condition of internalparameter matrix can be deduced according to theproperties of rotation matrix. The homography matrix
can be obtained by the least square method with the pixel
coordinates and world coordinates of the detected corner
points.
H = [ℎ1 , ℎ2 , ℎ3 ] = 𝐴𝐴[𝑟𝑟1 , 𝑟𝑟2 , 𝑡𝑡](13)𝑢𝑢� = 𝑢𝑢 + (𝑢𝑢 − 𝑢𝑢0 )(𝑘𝑘1 (𝑥𝑥 2 + 𝑦𝑦 2 ) + 𝑘𝑘2 (𝑥𝑥 2 + 𝑦𝑦 2 )2 )(14)
�𝑣𝑣̅ = 𝑣𝑣 + (𝑣𝑣 − 𝑣𝑣0 )(𝑘𝑘1 (𝑥𝑥 2 + 𝑦𝑦 2 ) + 𝑘𝑘2 (𝑥𝑥 2 + 𝑦𝑦 2 )2 )4. Camera Calibration

𝑓𝑓𝑥𝑥 , 𝛾𝛾, 𝑢𝑢0
A = � 0, 𝑓𝑓𝑦𝑦 , 𝑣𝑣0 �0, 0, 1

(12)

(ii)
Camera distortion factor
Ideally, the least square method can be used to calculate
the camera distortion coefficient according to formula(13) (14) (15). Ideally (no distortion), the pixel
coordinates are (u, v), and the coordinates in the image
coordinate system are (x, y). When there is distortion, thereal pixel coordinates are (𝑢𝑢�, 𝑣𝑣̅ ), and the coordinates in
the image coordinate system are (𝑥𝑥̅ , 𝑦𝑦�).

Fig.2 The image acquisition system. It consists of: 1. Camera
shaft 2. Spindle 3. Camera shaft 4. CMOS camera 5. Lightsource fixing ring 6. Flange base 7. Light source shaft 8. Fixture𝑢𝑢𝑋𝑋φ �𝑣𝑣 � = 𝐴𝐴[𝑟𝑟1 , 𝑟𝑟2 , 𝑡𝑡] �𝑌𝑌 �1
1ℎ1 𝑇𝑇 𝐴𝐴−𝑇𝑇 𝐴𝐴−1 ℎ2 = 0
𝑇𝑇 −𝑇𝑇 −1ℎ1 𝐴𝐴 𝐴𝐴 ℎ1 = ℎ2 𝑇𝑇 𝐴𝐴−𝑇𝑇 𝐴𝐴−1 ℎ2

(11)

(10)
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Authors Introduction

Fig. 4 The detection results

Dr. Xiaoyan Chen
She received the M.S. degree from theTianjin University of Science andTechnology, in 1999, and the Ph.D. degree
inmeasurement
technology
andautomation
devicesfromTianjin
University, in 2009. From 2009 to 2015,
she held a Post-doctoral position at Tianjin
University. She was invited by RPI, USA, as a Visiting
Scholar, from 2009 to 2010, and Kent, U.K., in 2012. She iscurrently a Professor and an Advisor of Postgraduate andDoctorate students with the Tianjin University of Scienceand Technology.

6. Acknowledgement
The authors would like to appreciate for the financial
support from Tianjin Municipal Science and Technology
Bureau (Grand NO.18YFZCGX00360) and from theNational Natural Science Foundation of China (GrandNO.61903274 and NO.41704131), the same appreciatefor Tianjin FLY Tech Co., Ltd for offering samples andfor Intelligent Edge Computing Joint LAB of TUST forthe testing result analyzing.

Mr. Jianyong Chen
He received the B.S. degree in automationfrom Tianjin University of Science andTechnology, China, in 2018. He iscurrently pursuing the M.S. degree incontrol science and engineering with theDepartment of Electronic Information andAutomation, Tianjin University ofScience and Technology, China, under thesupervision of Dr. Chen. His current research interests
include digital image processing, pattern recognition andmachine learning.

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Mr. Chundong Zhao
He received the B.S. degree in automationfrom Tianjin University of Science andTechnology, China, in 2018. He iscurrently pursuing the M.S. degree incontrol science and engineering with theDepartment of Electronic Information andAutomation, Tianjin University of Scienceand Technology, China, under thesupervision of Dr. Chen. His current research interests
include digital image processing, pattern recognition andmachine learning.
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