Available via license: CC BY 4.0
Content may be subject to copyright.
Citation: Fan, J.; Lu, S.; Zou, J.; Yang,
K.; Zhu, Y.; Liao, K. High-Precision
Wafer Bonding Alignment Mark
Using MoiréFringes and Digital
Grating. Micromachines 2022,13, 2159.
https://doi.org/10.3390/mi13122159
Academic Editors: Ching-Liang Dai
and Yao-Chuan Tsai
Received: 17 November 2022
Accepted: 5 December 2022
Published: 7 December 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
micromachines
Article
High-Precision Wafer Bonding Alignment Mark Using Moiré
Fringes and Digital Grating
Jianhan Fan 1, Sen Lu 2, Jianxiao Zou 1,3, Kaiming Yang 2,* , Yu Zhu 2and Kaiji Liao 4
1School of Automation Engineering, University of Electronic Science and Technology of China,
Chengdu 611731, China
2State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University,
Beijing 100084, China
3Shenzhen Institute for Advance Study, University of Electronic Science and Technology of China,
Shenzhen 518110, China
4State Grid Sichuan Electric Power Corporation Metering Center, Wanjing Road I, Chengdu 610000, China
*Correspondence: yangkm@tsinghua.edu.cn; Tel.: +86-134-6658-1887
Abstract:
This paper investigates a moiré-based mark for high-precision wafer bonding alignment.
During alignment, the mark is combined with digital grating, which has the benefits of high precision
and small size. A digital grating is superimposed on the mark to generate moiréfringes. By
performing a phase calculation on the moiréfringe images corresponding to the upper and lower
wafers, the relative offset of the upper and lower wafers can be accurately calculated. These moiré
fringes are exceptionally stable, thereby enhancing the alignment stability. In this study, through
practical experiments, we tested the rationality and practicability of the mark.
Keywords: wafer bonding; moiréfringe; wafer bonding alignment
1. Introduction
Moore’s law predicts that the scale of integrated circuits in chips will become larger and
more prominent in the future, but reducing the size of transistors to improve performance
is quite challenging. Accordingly, three-dimensional (3D) integration in integrated circuit
technology has emerged as a promising new direction [
1
,
2
]. Wafer bonding technology is
an essential technology for achieving precise 3D integration. Wafer bonding is the process
of bonding two silicon-based wafers with circuits etched together as shown in Figure 1. In
the bonding phase, ensuring the two wafers are aligned is necessary.
Micromachines 2022, 13, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/micromachines
Article
High-Precision Wafer Bonding Alignment Mark Using Moiré
Fringes and Digital Grating
Jianhan Fan 1, Sen Lu 2, Jianxiao Zou 1,3, Kaiming Yang 2,*, Yu Zhu 2 and Kaiji Liao 4
1 School of Automation Engineering, University of Electronic Science and Technology of China,
Chengdu 611731, China; 202211060913@std.uestc.edu.cn (J.F.); jxzou@uestc.edu.cn (J.Z.)
2 State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University,
Beijing 100084, China; lusenxyz@tsinghua.edu.cn (S.L.); zhuyu@tsinghua.edu.cn (Y.Z.)
3 Shenzhen Institute for Advance Study, University of Electronic Science and Technology of China,
Shenzhen 518110, China
4 State Grid Sichuan Electric Power Corporation Metering Center, Wanjing Road I, Chengdu 610000, China;
lkj970816@gmail.com
* Correspondence: yangkm@tsinghua.edu.cn; Tel.: +86-134-6658-1887
Abstract: This paper investigates a moiré-based mark for high-precision wafer bonding alignment.
During alignment, the mark is combined with digital grating, which has the benefits of high preci-
sion and small size. A digital grating is superimposed on the mark to generate moiré fringes. By
performing a phase calculation on the moiré fringe images corresponding to the upper and lower
wafers, the relative offset of the upper and lower wafers can be accurately calculated. These moiré
fringes are exceptionally stable, thereby enhancing the alignment stability. In this study, through
practical experiments, we tested the rationality and practicability of the mark.
Keywords: wafer bonding; moiré fringe; wafer bonding alignment
1. Introduction
Moore’s law predicts that the scale of integrated circuits in chips will become larger
and more prominent in the future, but reducing the size of transistors to improve per-
formance is quite challenging. Accordingly, three-dimensional (3D) integration in inte-
grated circuit technology has emerged as a promising new direction [1,2]. Wafer bonding
technology is an essential technology for achieving precise 3D integration. Wafer bond-
ing is the process of bonding two silicon-based wafers with circuits etched together as
shown in Figure 1. In the bonding phase, ensuring the two wafers are aligned is neces-
sary.
Figure 1. Wafer bonding schematic: (a) silicon-based wafer; (b) wafer with circuits; (c) wafer pair
bonding.
The alignment process in wafer bonding is one of the most critical steps in the wafer
bonding process, and the alignment accuracy directly determines the quality of the
bonding. To achieve high alignment accuracy, the relative displacement of the upper and
lower wafers in the XY plane after bonding should be less than ±50 nm, and the relative
deflection of the upper and lower wafers should be less than ±1 μrad. For such precision,
a high-precision alignment technique is necessary.
(a) (b) (c)
Citation: Fan, J.; Lu, S.; Zou, J.; Yang,
K.; Zhu, Y.; Liao, K. High-Precision
Wafer Bonding Alignment Mark
Using Moiré Fringes and Digital
Grating. Micromachines 2022, 13, x.
https://doi.org/10.3390/xxxxx
Academic Editors: Ching-Liang Dai
and Yao-Chuan Tsai
Received: 17 November 2022
Accepted: 5 December 2022
Published: 7 December 2022
Publisher’s Note: MDPI stays neu-
tral with regard to jurisdictional
claims in published maps and insti-
tutional affiliations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/license
s/by/4.0/).
Figure 1.
Wafer bonding schematic: (
a
) silicon-based wafer; (
b
) wafer with circuits; (
c
) wafer pair bonding.
The alignment process in wafer bonding is one of the most critical steps in the wafer
bonding process, and the alignment accuracy directly determines the quality of the bonding.
To achieve high alignment accuracy, the relative displacement of the upper and lower wafers
in the XY plane after bonding should be less than
±
50 nm, and the relative deflection of the
upper and lower wafers should be less than
±
1
µ
rad. For such precision, a high-precision
alignment technique is necessary.
Wafer bonding alignment methods are generally divided into designing mechanical
structures and methods based on alignment mark recognition. Sang Hwui Lee et al.
designed a keyed alignment structure to facilitate alignment [
3
]. Alignment was performed
by adding a PECVD oxide layer to the etched wafer to obtain a trapezoidal structure.
Micromachines 2022,13, 2159. https://doi.org/10.3390/mi13122159 https://www.mdpi.com/journal/micromachines
Micromachines 2022,13, 2159 2 of 13
Isao Sugaya et al
. proposed using a multi-axis interferometer and a weight sensor to make
a special clipper for alignment [
4
]. Chenxi Wang et al. designed a centrosymmetric grating
mark combined with image processing for alignment [
5
]. Using the designed mechanical
structure yielded low alignment accuracy and was difficult to achieve and expensive.
Designing alignment marks with digital image processing methods for alignment is well
recognized and widely used for causing less damage to the wafer, lower production costs,
and facilitating implementation.
Today, the cross mark is the most commonly used alignment mark in the wafer
bonding alignment process. Typically, a direct image algorithm is used to obtain the
center point position coordinates of the child and mother marks. Then, using two position
coordinates can calculate the deviation of the upper and lower wafers in the alignment
process. Calculating the mark’s center position employs direct digital image processing,
and the calculated center position coordinate error is too large. Therefore, meeting the
precision requirements of the front-end wafer bonding alignment process is challenging.
Chenxi Wan and Boyang Huang proposed a moiré-fringe-based centrosymmetric square
mark. The mark can accurately calculate the deviation of the upper and lower wafers in the
alignment process. Nonetheless, this mark has several deficiencies: controlling the distance
between the upper and lower wafers is required; otherwise, diffraction effects will occur,
resulting in poor image quality; additionally, it is too large and will occupy a portion of the
lithography space [6–8].
Nevertheless, the detection method based on moiréfringes still has excellent devel-
opment potential. Moiréfringes generated by two similar linear gratings or concentric
circular gratings are frequently used to measure displacement because they can more easily
reveal minute relative displacements. For moiréfringes to be utilized in the design of wafer
bonding alignment marks, the measurement of the alignment deviation of the upper and
lower wafers should be equivalent to the measurement of the relative displacement of the
upper and lower wafers.
Based on the aforementioned concepts and requirements, a novel two-dimensional
centrosymmetric mark for non-destructive measurement of the alignment deviation of
the upper and lower wafers during the wafer bonding process was designed, and the
alignment process was also optimized. It has the following advantages: (1) high measure-
ment accuracy; (2) small mark; (3) capability of measuring multiple degrees of freedom
concurrently; (4) capability of measuring significant displacement differences, etc.
2. Alignment Process
The design of the alignment method must be compatible with the bonding process,
so the alignment mark must be based on the actual situation of the existing bonding
equipment. The alignment process and the structure of the bonding equipment in the wafer
bonding process are extremely complex, and many of the steps involve improving motion
precision, which is not the focus of this article. For the purpose of this study’s subject
matter, the alignment procedure can be simplified as follows:
2.1. Coaxial Alignment
Align the four cameras, aligning the upper and lower cameras on both sides (with
the same field of view) and the left and right sides (the range of the field of view in the Y
direction is the same). When alignment is complete, each camera moves from its coaxial
position to its alignment position. The bonding equipment is as shown in Figure 2.
Micromachines 2022,13, 2159 3 of 13
Micromachines 2022, 13, x FOR PEER REVIEW 3 of 13
(a) (b) (c)
Figure 2. Bonding equipment: (a) simple structure of bonding equipment (coaxial alignment pro-
cess) (top view); (b) bonding equipment schematic diagram (front view); (c) wafer bonding align-
ment machine.
2.2. Lower Wafer Position Record
The lower carrier stage (which carries the lower wafer, with the bonding surface
facing up) moves from the pick-up position to the alignment position. The upper camera
captures the mark of the lower wafer and calculates and records the center coordinates of
the mark. On the carrier stage (adsorb the upper wafer; the bonding side is facing down),
stay in the pick-up position, as shown in Figure 3a.
(a) (b)
Figure 3. Alignment process: (a) lower wafer position record; (b) upper wafer position record.
2.3. Upper Wafer Position Record
The lower carrier stage moves to the pick-up position, the upper carrier stage moves
to the alignment position, the lower camera captures the upper wafer, and the mark
center coordinates are calculated and recorded, as shown in Figure 3b.
Figure 2.
Bonding equipment: (
a
) simple structure of bonding equipment (coaxial alignment process) (top
view); (b) bonding equipment schematic diagram (front view); (c) wafer bonding alignment machine.
2.2. Lower Wafer Position Record
The lower carrier stage (which carries the lower wafer, with the bonding surface facing
up) moves from the pick-up position to the alignment position. The upper camera captures
the mark of the lower wafer and calculates and records the center coordinates of the mark.
On the carrier stage (adsorb the upper wafer; the bonding side is facing down), stay in the
pick-up position, as shown in Figure 3a.
Micromachines 2022, 13, x FOR PEER REVIEW 3 of 13
(a) (b) (c)
Figure 2. Bonding equipment: (a) simple structure of bonding equipment (coaxial alignment pro-
cess) (top view); (b) bonding equipment schematic diagram (front view); (c) wafer bonding align-
ment machine.
2.2. Lower Wafer Position Record
The lower carrier stage (which carries the lower wafer, with the bonding surface
facing up) moves from the pick-up position to the alignment position. The upper camera
captures the mark of the lower wafer and calculates and records the center coordinates of
the mark. On the carrier stage (adsorb the upper wafer; the bonding side is facing down),
stay in the pick-up position, as shown in Figure 3a.
(a) (b)
Figure 3. Alignment process: (a) lower wafer position record; (b) upper wafer position record.
2.3. Upper Wafer Position Record
The lower carrier stage moves to the pick-up position, the upper carrier stage moves
to the alignment position, the lower camera captures the upper wafer, and the mark
center coordinates are calculated and recorded, as shown in Figure 3b.
Figure 3. Alignment process: (a) lower wafer position record; (b) upper wafer position record.
2.3. Upper Wafer Position Record
The lower carrier stage moves to the pick-up position, the upper carrier stage moves
to the alignment position, the lower camera captures the upper wafer, and the mark center
coordinates are calculated and recorded, as shown in Figure 3b.
2.4. Position Deviation Correction
The lower wafer travels to the coordinate position recorded by the lower wafer in the
alignment position. The motion system calculates the deviation between the two wafers in
the alignment position and corrects the deviation.
Micromachines 2022,13, 2159 4 of 13
The structure of the bonding equipment is complex, and it has strict requirements for
size, vibration, precision, cost, etc. It is difficult to alter the motion process significantly, and
only a portion of it can be optimized. Therefore, the design of the alignment method must
account for the movement process, and it is necessary to ensure the alignment’s precision
without modifying or optimizing the movement process.
3. Mark Design
3.1. MoiréFringe Formation Principle
Moiréfringes were initially identified as a phenomenon observed when two similar
but not identical grating systems are overlapped and reflected or passed through one
another. In addition to the original grating, a periodic structure can be observed at this
point. The phenomenon of grating and shadow overlapping to form moiréfringes emerges
with industrial growth, but its essence is consistent with the formation principle of moiré
fringes. Consequently, the general moiréfringes are described as follows: moiréis the
result of the interaction between two or more co-located periodic structures; it is a spatially
modulated intensity pattern created by alternating dark and bright stripes; these dark
stripes constitute the moirépattern and are referred to as moiré[9–12].
In recent years, moiréfringes have been widely used to measure displacement, defor-
mation, and other fields [
12
–
15
]. In this paper, calculating the deviation of the upper and
lower wafers corresponds to calculating the relative displacement of the upper and lower
wafers. Hence, the moiréfringes are ideally suited to this situation.
3.2. Calculation of MoiréFringes
Using the overlapping of two gratings as an example (Figure 4), the periods and angles
of the two gratings are
P1
and
P2
, respectively, and the angle between the two gratings
is
θ
. Typically, the difference between
P1
and
P2
is minimal, and the wavelength of the
incident light is considerably shorter than the grating period. The effect of diffraction is
also negligible. Currently, the period W of the formed moiréfringes is as follows:
W=P1P2
qP2
1+P2
2−2P1P2cosθ
(1)
Micromachines 2022, 13, x FOR PEER REVIEW 4 of 13
2.4. Position Deviation Correction
The lower wafer travels to the coordinate position recorded by the lower wafer in
the alignment position. The motion system calculates the deviation between the two
wafers in the alignment position and corrects the deviation.
The structure of the bonding equipment is complex, and it has strict requirements
for size, vibration, precision, cost, etc. It is difficult to alter the motion process signifi-
cantly, and only a portion of it can be optimized. Therefore, the design of the alignment
method must account for the movement process, and it is necessary to ensure the align-
ment’s precision without modifying or optimizing the movement process.
3. Mark Design
3.1. Moiré Fringe Formation Principle
Moiré fringes were initially identified as a phenomenon observed when two similar
but not identical grating systems are overlapped and reflected or passed through one
another. In addition to the original grating, a periodic structure can be observed at this
point. The phenomenon of grating and shadow overlapping to form moiré fringes
emerges with industrial growth, but its essence is consistent with the formation principle
of moiré fringes. Consequently, the general moiré fringes are described as follows: moiré
is the result of the interaction between two or more co-located periodic structures; it is a
spatially modulated intensity pattern created by alternating dark and bright stripes; these
dark stripes constitute the moiré pattern and are referred to as moiré [9–12].
In recent years, moiré fringes have been widely used to measure displacement, de-
formation, and other fields [12–15]. In this paper, calculating the deviation of the upper
and lower wafers corresponds to calculating the relative displacement of the upper and
lower wafers. Hence, the moiré fringes are ideally suited to this situation.
3.2. Calculation of Moiré Fringes
Using the overlapping of two gratings as an example (Figure 4), the periods and
angles of the two gratings are and , respectively, and the angle between the two
gratings is . Typically, the difference between and is minimal, and the wave-
length of the incident light is considerably shorter than the grating period. The effect of
diffraction is also negligible. Currently, the period W of the formed moiré fringes is as
follows:
(1)
Figure 4. Formation of moiré fringes.
Figure 4. Formation of moiréfringes.
When moiréfringes are used for measuring displacement,
θ
is typically set close
to zero, and
W=P1P2/|P1−P2|
, where
P1
is the grating to be measured and
P2
is the
detection grating. The newly formed moiréfringes have a magnification effect in relation to
the grating being measured, with the magnification formula being
K=W/P1=P2/|P1−P2|
.
Clearly, as the magnification increases, the periods of the two gratings become closer together.
Micromachines 2022,13, 2159 5 of 13
3.3. Synthesis of MoiréFringes
Digital grating is an artificially produced digital image of grating type, and its
parameters—including shape, period, and duty cycle—can be artificially defined. The
digital grating operates similarly to a digital filter, and a matrix of
B=m×n
represents
its mathematical model; m and n represent the number of rows and columns of the image
resolution obtained by the imaging system, respectively, and the matrix contains only 0
and 1 elements. When the element in
B
is 0, the digital grating is “opaque”, whereas when
it is 1, the digital grating is “transmitting”. Then, the digital raster superimposes the actual
raster to create a new image:
C1=A×B(2)
C2=A×B(3)
A=m×n
is the actual grating image, while
B=
1
−B
is the reverse. The superim-
posed image is as shown in Figure 5.
Micromachines 2022, 13, x FOR PEER REVIEW 5 of 13
When moiré fringes are used for measuring displacement, is typically set close to
zero, and , where is the grating to be measured and is the de-
tection grating. The newly formed moiré fringes have a magnification effect in relation to
the grating being measured, with the magnification formula being
. Clearly, as the magnification increases, the periods of the two gratings be-
come closer together.
3.3. Synthesis of Moiré Fringes
Digital grating is an artificially produced digital image of grating type, and its pa-
rameters—including shape, period, and duty cycle—can be artificially defined. The dig-
ital grating operates similarly to a digital filter, and a matrix of represents its
mathematical model; m and n represent the number of rows and columns of the image
resolution obtained by the imaging system, respectively, and the matrix contains only 0
and 1 elements. When the element in is 0, the digital grating is “opaque”, whereas
when it is 1, the digital grating is “transmitting”. Then, the digital raster superimposes
the actual raster to create a new image:
(2)
(3)
is the actual grating image, while is the reverse. The super-
imposed image is as shown in Figure 5.
Figure 5. (a) Actual grating; (b) digital grating; (c) ; (d) .
The line width of the digital grating is , and the duty cycle is 50%. The two over-
lapping grating images are then integrated to produce two light intensity curves and
:
(4)
(5)
Figure 5. (a) Actual grating; (b) digital grating; (c)C1; (d)C2.
The line width of the digital grating is
i
, and the duty cycle is 50%. The two overlapping
grating images are then integrated to produce two light intensity curves I1and I2:
I1j=Zn
x=1Zi+2i(j−1)
y=1+2i(j−1)I(x,y)dxdy (4)
I1=[I11,I12, . . . , I1m](5)
I2j=Zn
x=1Z2i+2i(j−1)
y=1+2i(j−1)I(x,y)dxdy (6)
I2=[I21,I22, . . . , I2m](7)
The moirésignal curve I can then be calculated as follows:
Micromachines 2022,13, 2159 6 of 13
I=I1−I2
I1+I2
(8)
The extracted light intensity curve and moirésignal curve are shown in Figure 6.
Micromachines 2022, 13, x FOR PEER REVIEW 6 of 13
(6)
(7)
The moiré signal curve I can then be calculated as follows:
(8)
The extracted light intensity curve and moiré signal curve are shown in Figure 6.
Figure 6. (a) Light intensity curve ; (b) light intensity curve ; (c) moiré signal .
3.4. Solution of Grating Displacement
The ideal state of the moiré signal is a triangular wave. However, in practice, due to
the limitations of camera imaging function, environmental interference, the precision of
grating fabrication, etc., the moiré signal (I) is typically a sine wave. Therefore, the ex-
tracted moiré signal (I) can be considered a sinusoidal signal with interference. Using the
variational mode decomposition (VMD) algorithm [16], the interference signal in the
moiré signal (I) can be removed, and the fundamental signal can be obtained, as
depicted in Figure 7.
Figure 6. (a) Light intensity curve I1; (b) light intensity curve I2; (c) moirésignal I.
3.4. Solution of Grating Displacement
The ideal state of the moirésignal is a triangular wave. However, in practice, due
to the limitations of camera imaging function, environmental interference, the precision
of grating fabrication, etc., the moirésignal (I) is typically a sine wave. Therefore, the
extracted moirésignal (I) can be considered a sinusoidal signal with interference. Using the
variational mode decomposition (VMD) algorithm [
16
], the interference signal in the moiré
signal (I) can be removed, and the fundamental signal
v(n)
can be obtained, as depicted in
Figure 7.
Micromachines 2022, 13, x FOR PEER REVIEW 7 of 13
Figure 7. VMD filter effect.
Then, we obtain the phase difference between the two moiré signals. The discrete
Fourier transform (DFT) algorithm transforms two discrete signals with signal length N
into the following form [17]:
(9)
According to Euler’s formula
(10)
there are
(11)
The phases of the two discrete signals are as follows:
(12)
The final phase difference between the two signals is as follows:
(13)
The displacement difference between the two grating images can be obtained by
using the phase difference:
(14)
where L is the grating’s period. The deviation between the upper and lower wafers in the
XY plane is equivalent to the relative displacement between the upper and lower wafers
in the XY plane. Thus, the relative displacement between the gratings can be precisely
determined, as well as the precise deviation between the upper and lower wafers.
Figure 7. VMD filter effect.
Micromachines 2022,13, 2159 7 of 13
Then, we obtain the phase difference between the two moirésignals. The discrete
Fourier transform (DFT) algorithm transforms two discrete signals with signal length N
into the following form [17]:
Vi(k) =
∞
∑
n=−∞
vi(n)e−j2πkn
N=
N−1
∑
n=0
vi(n)e−j2πkn
N,i=1, 2 (9)
According to Euler’s formula
e−j2πkn
N=cos2πkn
N−jsin2πkn
N(10)
there are
Vi(k) =
N−1
∑
n=0
vi(n)cos2πkn
N−jsin2πkn
N,i=1, 2 (11)
The phases of the two discrete signals are as follows:
ϕi=arctg Im(Vi(k))
Re(Vi(k))=∑N−1
n=0vi(n)sin2π
Nnk
∑N−1
n=0vi(n)cos2π
Nnk,i=1, 2 (12)
The final phase difference between the two signals is as follows:
∆ϕ=ϕ1−ϕ2(13)
The displacement difference between the two grating images can be obtained by using
the phase difference:
∆D=∆ϕ
2πL(14)
where Lis the grating’s period. The deviation between the upper and lower wafers in the
XY plane is equivalent to the relative displacement between the upper and lower wafers
in the XY plane. Thus, the relative displacement between the gratings can be precisely
determined, as well as the precise deviation between the upper and lower wafers.
3.5. Design Results
Our bonding device’s imaging system parameters are as follows: the camera’s resolu-
tion is 3856
×
2764, the pixel size is 1.67
µ
m
×
1.67
µ
m, and the objective lens’s theoretical
magnification is 5. Consequently, one pixel in the image captured by the imaging sys-
tem should be calibrated as a rectangular block measuring 0.334
µ
m
×
0.334
µ
m in the
actual space. However, lens processing, camera damage, environmental interference,
and other factors will result in a theoretical calibration result that differs from the actual
one. To improve the accuracy of subsequent calculations, we calibrated the imaging sys-
tem using Zhang’s calibration method [
18
]: in actual space, one pixel corresponds to a
0.360 µm×0.360 µm rectangular square.
The following mark was designed by combining the above theory with the actual
working conditions of the bonding equipment and the imaging system (Figure 8):
The intended marking period is 6
µ
m, and the duty cycle is 50%; consequently, the line
width is 3
µ
m, the number of cycles is 11, and the total mark size is 63
µm×
63
µm
. Create a
cross mark in the mark’s center, which has two advantages: (1) the NCC algorithm [
19
] can
be used to quickly locate the approximate position of the mark through this cross mark, and
the mark can be intercepted, which significantly reduces the amount of calculation; (2) the
relative displacement of the two intercepted marks can be calculated, replacing a large-scale
displacement difference with a small-scale displacement difference, and the solution result
must be within one pixel (the NCC positioning accuracy is pixel-level). There is no need to
consider the relative displacement as being excessively large, causing inaccurate results.
The solution accuracy is enhanced, and the calculation difficulty is diminished.
Micromachines 2022,13, 2159 8 of 13
Micromachines 2022, 13, x FOR PEER REVIEW 8 of 13
3.5. Design Results
Our bonding device’s imaging system parameters are as follows: the camera’s res-
olution is 3856 × 2764, the pixel size is 1.67 μm × 1.67 μm, and the objective lens’s theo-
retical magnification is 5. Consequently, one pixel in the image captured by the imaging
system should be calibrated as a rectangular block measuring 0.334 μm × 0.334 μm in the
actual space. However, lens processing, camera damage, environmental interference, and
other factors will result in a theoretical calibration result that differs from the actual one.
To improve the accuracy of subsequent calculations, we calibrated the imaging system
using Zhang’s calibration method [18]: in actual space, one pixel corresponds to a 0.360
μm × 0.360 μm rectangular square.
The following mark was designed by combining the above theory with the actual
working conditions of the bonding equipment and the imaging system (Figure 8):
Figure 8. Design mark.
The intended marking period is 6 μm, and the duty cycle is 50%; consequently, the
line width is 3 μm, the number of cycles is 11, and the total mark size is 63 μm × 63 μm.
Create a cross mark in the mark’s center, which has two advantages: (1) the NCC algo-
rithm [19] can be used to quickly locate the approximate position of the mark through
this cross mark, and the mark can be intercepted, which significantly reduces the amount
of calculation; (2) the relative displacement of the two intercepted marks can be calcu-
lated, replacing a large-scale displacement difference with a small-scale displacement
difference, and the solution result must be within one pixel (the NCC positioning accu-
racy is pixel-level). There is no need to consider the relative displacement as being ex-
cessively large, causing inaccurate results. The solution accuracy is enhanced, and the
calculation difficulty is diminished.
Except for the cross marks, the remaining components are plane gratings, allowing
the X direction, Y direction, and relative deflection of the upper and lower wafers to be
measured by superimposing different digital gratings in a single image.
Extract the calculation area of two gratings, as shown in Figure 9a, and the relative
displacement of the two gratings in the X direction can be determined. As depicted in
Figure 9b, by extracting the calculation area of the two gratings, the relative displacement
of the two gratings along the Y-axis can be determined. By extracting the two calculation
regions of a grating, as depicted in Figure 9c, the trigonometric function can be used to
calculate the grating’s horizontal deflection. The relative deflection of the two gratings
can be calculated by combining them in the horizontal direction.
Figure 8. Design mark.
Except for the cross marks, the remaining components are plane gratings, allowing
the X direction, Y direction, and relative deflection of the upper and lower wafers to be
measured by superimposing different digital gratings in a single image.
Extract the calculation area of two gratings, as shown in Figure 9a, and the relative
displacement of the two gratings in the X direction can be determined. As depicted in
Figure 9b, by extracting the calculation area of the two gratings, the relative displacement
of the two gratings along the Y-axis can be determined. By extracting the two calculation
regions of a grating, as depicted in Figure 9c, the trigonometric function can be used to
calculate the grating’s horizontal deflection. The relative deflection of the two gratings can
be calculated by combining them in the horizontal direction.
Micromachines 2022, 13, x FOR PEER REVIEW 9 of 13
Figure 9. (a) Relative displacement calculation along the X-axis; (b) the relative displacement cal-
culation in the Y direction; (c) the relative deflection calculation of the two gratings.
According to the above design, the bonding device’s upper two cameras or lower
two cameras can be removed, and the infrared light path can be increased (Figure 10).
Figure 10. Improved structure.
As shown in Figure 11, the alignment process can be enhanced based on the im-
proved structure.
Figure 9.
(
a
) Relative displacement calculation along the X-axis; (
b
) the relative displacement
calculation in the Y direction; (c) the relative deflection calculation of the two gratings.
Micromachines 2022,13, 2159 9 of 13
According to the above design, the bonding device’s upper two cameras or lower
two cameras can be removed, and the infrared light path can be increased (Figure 10).
As shown in Figure 11, the alignment process can be enhanced based on the im-
proved structure.
Through this enhancement, the coaxial alignment process in the initial alignment
process can be eliminated, the coaxial alignment error can be directly eliminated, and the
number of cameras and associated costs can be decreased. After implementing the moiré
fringe solution, the designed mark is smaller than the original mark, and the deviation
calculation accuracy of the upper and lower wafers is improved. Compared to the original
direct digital image processing, the moiré-fringe-based solution method requires less
computation, operates more quickly, and provides greater precision.
Micromachines 2022, 13, x FOR PEER REVIEW 9 of 13
Figure 9. (a) Relative displacement calculation along the X-axis; (b) the relative displacement cal-
culation in the Y direction; (c) the relative deflection calculation of the two gratings.
According to the above design, the bonding device’s upper two cameras or lower
two cameras can be removed, and the infrared light path can be increased (Figure 10).
Figure 10. Improved structure.
As shown in Figure 11, the alignment process can be enhanced based on the im-
proved structure.
Figure 10. Improved structure.
Micromachines 2022, 13, x FOR PEER REVIEW 10 of 13
Figure 11. Improved alignment process.
Through this enhancement, the coaxial alignment process in the initial alignment
process can be eliminated, the coaxial alignment error can be directly eliminated, and the
number of cameras and associated costs can be decreased. After implementing the moiré
fringe solution, the designed mark is smaller than the original mark, and the deviation
calculation accuracy of the upper and lower wafers is improved. Compared to the orig-
inal direct digital image processing, the moiré-fringe-based solution method requires less
computation, operates more quickly, and provides greater precision.
4. Experimental Verification
In order to test the practicality of the markers mentioned above, we designed and
constructed the following experimental equipment (Figure 12):
Figure 12. Experimental equipment.
The experimental design of this paper is as follows: whenever the micro-movement
stage moves, the capacitive sensor records the displacement of the micro-movement
stage while, simultaneously, the camera captures the position of the grating, and this is
repeated multiple times. The capacitive sensor’s measurements are used as the actual
Figure 11. Improved alignment process.
Micromachines 2022,13, 2159 10 of 13
4. Experimental Verification
In order to test the practicality of the markers mentioned above, we designed and
constructed the following experimental equipment (Figure 12):
The experimental design of this paper is as follows: whenever the micro-movement
stage moves, the capacitive sensor records the displacement of the micro-movement stage
while, simultaneously, the camera captures the position of the grating, and this is repeated
multiple times. The capacitive sensor ’s measurements are used as the actual displacement.
The results of the displacement calculation method utilized in this paper were compared
to the displacement results calculated by widely recognized image calculation software
available on the market. The outcomes are shown in Figures 13 and 14.
Micromachines 2022, 13, x FOR PEER REVIEW 10 of 13
Figure 11. Improved alignment process.
Through this enhancement, the coaxial alignment process in the initial alignment
process can be eliminated, the coaxial alignment error can be directly eliminated, and the
number of cameras and associated costs can be decreased. After implementing the moiré
fringe solution, the designed mark is smaller than the original mark, and the deviation
calculation accuracy of the upper and lower wafers is improved. Compared to the orig-
inal direct digital image processing, the moiré-fringe-based solution method requires less
computation, operates more quickly, and provides greater precision.
4. Experimental Verification
In order to test the practicality of the markers mentioned above, we designed and
constructed the following experimental equipment (Figure 12):
Figure 12. Experimental equipment.
The experimental design of this paper is as follows: whenever the micro-movement
stage moves, the capacitive sensor records the displacement of the micro-movement
stage while, simultaneously, the camera captures the position of the grating, and this is
repeated multiple times. The capacitive sensor’s measurements are used as the actual
Figure 12. Experimental equipment.
Since the capacitive sensor’s precision is exceptionally high, the measured parameters
are used as the actual displacement. As calculated in this paper, the average error between
the X direction and the capacitive sensor was 5.22 nm. In contrast, the average error
between the X direction and capacitive sensor calculated using commercial software was
48.54 nm. The presented methodology calculated an average error of 8.26 nm between the
Y direction and the capacitive sensor, whereas commercial software calculated an average
error of 37.13 nm. The presented methodology had a repeat calculation error of ±3.23 nm
in the X direction and a repeat calculation error of
±
2.87 nm in the Y direction. Clearly, the
calculation accuracy was greatly improved after using the grating designed in this paper
and the digital grating. The errors in the X and Y directions were within 10 nm, significantly
improving the alignment process’s accuracy.
Micromachines 2022,13, 2159 11 of 13
Micromachines 2022, 13, x FOR PEER REVIEW 11 of 13
displacement. The results of the displacement calculation method utilized in this paper
were compared to the displacement results calculated by widely recognized image cal-
culation software available on the market. The outcomes are shown in Figures 13 and 14.
(a)
(b)
(c)
Figure 13. Experimental results: (a) the comparative results of X-direction displacement data; (b)
the comparative results of Y-direction displacement data; (c) the comparative results of on-plane
displacement data.
Figure 13.
Experimental results: (
a
) the comparative results of X-direction displacement data; (
b
) the
comparative results of Y-direction displacement data; (
c
) the comparative results of on-plane displace-
ment data.
Micromachines 2022,13, 2159 12 of 13
Micromachines 2022, 13, x FOR PEER REVIEW 12 of 13
Figure 14. The comparative data on the differences with respect to the sensor data.
Since the capacitive sensor’s precision is exceptionally high, the measured parame-
ters are used as the actual displacement. As calculated in this paper, the average error
between the X direction and the capacitive sensor was 5.22 nm. In contrast, the average
error between the X direction and capacitive sensor calculated using commercial soft-
ware was 48.54 nm. The presented methodology calculated an average error of 8.26 nm
between the Y direction and the capacitive sensor, whereas commercial software calcu-
lated an average error of 37.13 nm. The presented methodology had a repeat calculation
error of ±3.23 nm in the X direction and a repeat calculation error of ±2.87 nm in the Y
direction. Clearly, the calculation accuracy was greatly improved after using the grating
designed in this paper and the digital grating. The errors in the X and Y directions were
within 10 nm, significantly improving the alignment process’s accuracy.
5. Conclusions
Using grating marks and digital gratings based on moiré fringes can significantly
improve the accuracy of calculating the deviation of the upper and lower wafers in the
alignment process, and it can control the estimated error to within 10 nm. These technical
achievements satisfy all requirements for high-precision bonding. Moreover, the calcula-
tion effect and speed are superior to those of commercially available image processing
software. In addition, the designed grating marks are small enough to increase the space
on the wafer for etched circuits. This marker can also continuously optimize the moiré
signal by adjusting the superimposed digital grating to achieve the best solution results
and can simultaneously calculate the results for all three degrees of freedom. It is also
possible to cut down on the number of keys and processes, which not only lowers the
cost but also cuts out a part of the bonding process, which lowers the overall error rate.
Author Contributions: Conceptualization, J.F. and K.Y.; methodology, J.F.; software, J.F.; valida-
tion, J.F., S.L., and K.Y.; formal analysis, J.Z.; investigation, J.F.; resources, Y.Z.; data curation, J.F.;
writing—original draft preparation, J.F.; writing—review and editing, S.L. and K.Y.; visualization,
J.F. and K.L.; supervision, S.L. and K.Y.; project administration, S.L.; funding acquisition, S.L. and
Y.Z. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China
(No.52105578) and the State Key Laboratory of Tribology Tsinghua University (No.SKLT2020D23).
Data Availability Statement: The data presented in this study are available upon request from the
corresponding author.
Conflicts of Interest: The authors declare no conflicts of interest.
Figure 14. The comparative data on the differences with respect to the sensor data.
5. Conclusions
Using grating marks and digital gratings based on moiréfringes can significantly
improve the accuracy of calculating the deviation of the upper and lower wafers in the
alignment process, and it can control the estimated error to within 10 nm. These technical
achievements satisfy all requirements for high-precision bonding. Moreover, the calculation
effect and speed are superior to those of commercially available image processing software.
In addition, the designed grating marks are small enough to increase the space on the
wafer for etched circuits. This marker can also continuously optimize the moirésignal by
adjusting the superimposed digital grating to achieve the best solution results and can
simultaneously calculate the results for all three degrees of freedom. It is also possible to
cut down on the number of keys and processes, which not only lowers the cost but also
cuts out a part of the bonding process, which lowers the overall error rate.
Author Contributions:
Conceptualization, J.F. and K.Y.; methodology, J.F.; software, J.F.; valida-
tion, J.F., S.L. and K.Y.; formal analysis, J.Z.; investigation, J.F.; resources, Y.Z.; data curation, J.F.;
writing—original
draft preparation, J.F.; writing—review and editing, S.L. and K.Y.; visualization, J.F.
and K.L.; supervision, S.L. and K.Y.; project administration, S.L.; funding acquisition, S.L. and Y.Z.
All authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the National Natural Science Foundation of China (No.52105578)
and the State Key Laboratory of Tribology Tsinghua University (No.SKLT2020D23).
Data Availability Statement:
The data presented in this study are available upon request from the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Na, D.J.; Aung, K.O.; Choi, W.K.; Kida, T.; Ochiai, T.; Hashimoto, T.; Kimura, M.; Kata, K.; Yoon, S.W.; Yong, A.C.B. TSV
MEOL (Mid End of Line) and Packaging Technology of Mobile 3D-IC Stacking. In Proceedings of the 2014 IEEE 64th Electronic
Components and Technology Conference (ECTC), Orlando, FL, USA, 27–30 May 2014; pp. 596–600.
2.
Panigrahi, A.K.; Bonam, S.; Ghosh, T.; Vanjari, S.R.K.; Singh, S.G. Low Temperature, Low Pressure CMOS Compatible Cu—Cu
Thermo-Compression Bonding with Ti Passivation for 3D IC Integration. In Proceedings of the 2015 IEEE 65th Electronic
Components and Technology Conference (ECTC), San Diego, CA, USA, 26–39 May 2015; pp. 2205–2210.
3.
Lee, S.H.; Niklaus, F.; McMahon, J.J.; Yu, J.; Kumar, R.J.; Li, H.F.; Gutmann, R.J.; Cale, T.S.; Lu, J.Q. Fine keyed alignment and
bonding for wafer-level 3D ICs. MRS Online Proc. Libr. 2006,914. [CrossRef]
4.
Sugaya, I.; Mitsuishi, H.; Maeda, H.; Okada, M.; Okamoto, K. New Precision Alignment Methodology for CMOS Wafer Bonding.
In Proceedings of the 2014 SOI-3D-Subthreshold Microelectronics Technology Unified Conference (S3S), IEEE, Milbrae, CA, USA,
6–9 October 2014; pp. 1–3.
5.
Wang, C.; Taniyama, S.; Wang, Y.H.; Suga, T. High-precision alignment for low-temperature wafer bonding. J. Electrochem. Soc.
2009,156, H197–H201. [CrossRef]
Micromachines 2022,13, 2159 13 of 13
6.
Wang, C.; Suga, T. A Novel MoiréFringe Assisted Method for Nanoprecision Alignment in Wafer Bonding. In Proceedings of the
2009 59th Electronic Components and Technology Conference, IEEE, San Diego, CA, USA, 26–29 May 2009; pp. 872–878.
7.
Huang, B.; Wang, C.; Fang, H.; Zhou, S.; Suga, T. Moiré-based alignment using centrosymmetric grating marks for high-precision
wafer bonding. Micromachines 2019,10, 339. [CrossRef] [PubMed]
8.
Wang, C.; Suga, T. MoiréMethod for Nanoprecision Wafer-to-Wafer Alignment: Theory, Simulation and Application. In
Proceedings of the 2009 International Conference on Electronic Packaging Technology & High Density Packaging, Beijing, China,
10–13 August 2009; pp. 219–224.
9.
Castagna, R.; Lucchetta, D.E.; Rippa, M.; Xu, J.H.; Di Donato, A. Near-frequency photons Y-splitter. Appl. Mater. Today
2020
,
19, 100636. [CrossRef]
10. Bryngdahl, O. Polarization-grating moire. JOSA 1972,62, 839–848. [CrossRef]
11.
Shalit, A.; Lucchetta, D.E.; Piazza, V.; Simoni, F.; Bizzarri, R.; Castagna, R. Polarization-dependent laser-light structured
directionality with polymer composite materials. Mater. Lett. 2012,81, 232–234. [CrossRef]
12.
King, M.C.; Berry, D.H. Photolithographic Mask Alignment Using MoiréTechniques. Appl. Opt.
1972
,11, 2455–2459. [CrossRef]
[PubMed]
13.
Zhong, Z.; Li, C.; Li, S.; Li, P.; Ma, Q.; Zhao, H.; Zhang, J.; Wei, Y. High Speed, High Accuracy Displacement Extraction
from Sinusoidal like MoiréFringes in a Novel Optical Encoding Technology. In Metrology, Inspection, and Process Control for
Microlithography XXXIV; SPIE: Bellingham, WA, USA, 2020; Volume 11325, pp. 549–558.
14.
Ri, S.; Tsuda, H.; Chang, K.; Hsu, S.; Lo, F.; Lee, T. Dynamic deformation measurement by the sampling Moirémethod from video
re-cording and its application to bridge engineering. Exp. Tech. 2020,44, 313–327. [CrossRef]
15. Morimoto, Y.; Fujigaki, M. MoiréMethods For Shape, Displacement And Strain Analysis. Opt. Eng. 2011,50, 101506.
16. Dragomiretskiy, K.; Zosso, D. Variational mode decomposition. IEEE Trans. Signal Process. 2013,62, 531–544. [CrossRef]
17.
Pfister, H. Discrete-Time Signal Processing. Lect. Note. Available online: http://pfister.ee.duke.edu/courses/ece485/dtsp.pdf
(accessed on 16 November 2022).
18.
Zhang, Z. A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell.
2000
,22, 1330–1334. [CrossRef]
19. Yoo, J.C.; Han, T.H. Fast normalized cross-correlation. Circuits Syst. Signal Process. 2009,28, 819–843. [CrossRef]
