- Email: [email protected]
Design and testing of a compact non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings
Accepted Manuscript Title: Design and testing of a compact non-orthogonal two-axis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings Authors: Yuki Shimizu, Ryo Aihara, Kazuki Mano, Chong Chen, Yuan-Liu Chen, Xiuguo Chen, Wei Gao PII: DOI: Reference:
S0141-6359(17)30713-4 https://doi.org/10.1016/j.precisioneng.2017.12.004 PRE 6703
To appear in:
Precision Engineering
Received date: Accepted date:
26-11-2017 4-12-2017
Please cite this article as: Shimizu Yuki, Aihara Ryo, Mano Kazuki, Chen Chong, Chen Yuan-Liu, Chen Xiuguo, Gao Wei.Design and testing of a compact non-orthogonal twoaxis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings.Precision Engineering https://doi.org/10.1016/j.precisioneng.2017.12.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Design and testing of a compact non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings Yuki Shimizu*, Ryo Aihara, Kazuki Mano, Chong Chen, Yuan-Liu Chen, Xiuguo Chen, Wei Gao Department of Finemechanics, Tohoku University
*Phone: +81-22-795-6950, Fax: +81-22-795-6953 E-mail: [email protected]
SC R
Highlights of this paper:
IP T
6-6-01 Aramaki-Aza Aoba, Aoba-ku, Sendai 980-8579, Japan
An optical setup is designed for fabrication of large-area scale gratings. The design is based on non-orthogonal 2D Lloyd’s mirror interferometer.
Grating pattern structures have been estimated by computer simulation. A 100 mm×100 mm 2D scale gratings has successfully been fabricated. 2D grating patterns with a short period of 1 m has been fabricated.
A
N
U
M
Abstract: A compact and stable two-axis Lloyd’s mirror interferometer based on a new non-orthogonal type of mirror-substrate assembly is designed for fabrication of
ED
100 mm×100 mm large-area two-dimensional (2D) diffraction scale gratings in a research laboratory or a small-scale manufacturing facility. At first, the required mirror sizes used in
PT
the new non-orthogonal type and the conventional orthogonal type are compared based on geometrical analysis. It is identified that the width of the mirror can be reduced to half in the
CC E
non-orthogonal type while the required mirror height and the expanded laser beam diameter are comparable to those in the orthogonal type. The shorter mirror width makes it possible to
A
design a compact mirror-substrate assembly so that the overall interferometer can be realized in an overall size of 1480 mm×730 mm for mounting on a commercially available general-purpose 1500 mm×1000 mm vibration isolation table for use in research laboratories. It is then verified by simulation that the selected laser source and the designed beam expansion assembly, which are the other main parts of the interferometer, are effective for fabricating the designed grating structures. Experiments are also carried out to demonstrate 1
the feasibility of the constructed interferometer for fabricating 100 mm×100 mm 2D scale gratings with a short period of 1 m. Keywords: Scale grating; Lloyd’s mirror interferometer; Polarization modulation control;
A
CC E
PT
ED
M
A
N
U
SC R
IP T
Interference; Diffraction
2
1. Introduction Diffraction gratings are important optical components [1] employed in physics and astronomy for spectroscopy. Nowadays diffraction gratings are expanding their applications to some optical measuring instruments for dimensional measurement. When one-dimensional (1D) gratings are employed in measuring instruments such as linear encoders [2], they act as
IP T
scales for measurement of the displacement or motion of a target of interest. Furthermore, in recent years, two-dimensional (2D) gratings with grating structures equally spaced along the
SC R
X- and Y-directions are also expanding their applications in planar/surface encoder systems as
scale gratings for multi-axis measurement [3-5]. In the planar/surface encoder systems, a
U
grating period of the scale grating is one of the important parameters, since a shorter grating period contributes to reduce the period of interference signals, resulting in the improvement of
N
measurement resolution in the encoder systems [5, 6]. The grating periods of scale gratings in
A
such encoder systems are therefore designed to be several m or less [2, 3] to achieve
M
nanometric resolution. Meanwhile, since the relative motion between a scale grating and an
ED
optical reading head will be detected by using interference signals, which are generated by superimposing positive and negative diffracted beams from the scale grating, the measurable
PT
range of an encoder system is theoretically restricted by the size of 2D grating to be used as a scale for multi-axis measurement. It is therefore desired to establish a method for fabrication
CC E
of 2D scale gratings having a grating period on the order of micrometers or less over a large area of 100 mm×100 mm or even larger [3-7].
A
There are several methods available for fabrication of 2D scale gratings, such as
ultra-precision machining [8, 9], mask-based optical projection lithography [10, 11] or mask-less interference lithography [12]. Although the mask-based optical projection lithography is often employed to fabricate scale gratings [13], the facility and equipment required for the processes including mask fabrication by electron-beam lithography in the projection lithography are extremely expensive [12]. Meanwhile, on the other hand, the 3
mask-less interference lithography is a good candidate for use in research laboratories in terms of fabrication costs. The mask-less interference lithography can be classified into two categories; the division of amplitude and the division of wavefront. In the division of amplitude system of Mach-Zehnder interferometer for fabrication of 1D grating on a grating substrate placed in the XY-plane, a thin collimated light from a laser source with a diameter d
IP T
is split into two beams with the same diameter d by using a beam splitter or a diffraction
grating [14-16]. Each of the split beams travels along a different path in the Mach-Zehnder
SC R
interferometer set in the YZ-plane, in which a beam expander is employed to expand its beam diameter to D, before the beam is projected onto the grating substrate. The expanded beams
U
are superimposed with each other on the substrate to form and expose a stationary interference fringe field with a set of alternating bright and dark lines for generating the 1D
N
grating line structures equally-spaced along the Y-direction. The size of the interference fringe
A
field and/or the grating area on the substrate is the same or even larger than the expanded
M
beam diameter D [14]. From this point of view, the division of amplitude system is effective
ED
for fabricating 1D large-area gratings. However, in large-area grating fabrication, the non-common optical paths of the beams are extremely long, up to several meters, resulting in
PT
an unstable interference fringe field due to the influences of external disturbances such as temperature and humidity variations, vibrations, etc. This requires a well-controlled
CC E
environment for the stable fabrication. A high power laser source is also required to shorten the exposure time for further removing the influences of residual disturbances. As a result, the
A
system becomes large and expensive, which is the major obstacle to prevent its use in research laboratories with limited space and budget. Moreover, when the division of amplitude system is expanded to fabricate 2D scale gratings with grating structures along the X- and Y-directions, it is necessary to set two Mach-Zehnder interferometers in the XZ- and YZ-planes, respectively, which will make the system to have a complicated 3D optical layout and will significantly increase the size as well as the cost of the fabrication system. For this 4
reason, large-area division of amplitude systems are basically limited in 1D grating fabrication. Although a 2D scale grating with a size of 100 mm×100 mm has been fabricated with such a system by taking a two-step exposure process, in which the grating substrate has been exposed before and after being rotated 90º, respectively [14], the structures generated in the first exposure are influenced in the second exposure. This causes the difference in the
IP T
cross-sectional profiles of the grating surface along the X- and Y-directions, which is a fatal problem for 2D scale gratings.
SC R
On the other hand, one of the biggest advantages of the Lloyd’s mirror interferometer
based on the division of wavefront [17-21] compared with the division of amplitude system is
U
its high stability although the size of the interference fringe field and/or the grating area on the substrate is quite smaller than the expanded beam diameter D. In a conventional 1D Lloyd’s
N
mirror interferometer, an expanded beam with the diameter D is projected onto a
A
mirror-substrate assembly composed of a grating substrate set in the XY-plane and a mirror set
M
in the XZ-plane (referred to as the Y-mirror), where the wavefront of the beam is divided into
ED
two sub-beams for forming the interference fringe field for generating the 1D grating line structures equally-spaced along the Y-direction. Because the non-common optical paths of the
PT
sub-beams are short, within the expanded beam diameter D, a stable interference fringe field can be generated. It is also easy to expand the Lloyd’s mirror interferometer from one-axis to
CC E
two-axis by simply adding an X-mirror (set in the YZ-plane) in the mirror-substrate assembly where the substrate, the X- and Y-mirrors are arranged orthogonally with each other [18, 19].
A
This is an important advantage in fabrication of 2D scale gratings. Since only one beam expander is necessary and a laser source with a lower power is accepted, the Lloyd’s mirror interferometer has a simpler optical configuration and is also less expensive and more compact compared with the division of amplitude system, which is attractive for use in research laboratories. However, the conventional two-axis Lloyd’s mirror interferometer with an orthogonal mirror-substrate assembly also has its inherent problems in fabrication of 5
high-precision large-area 2D gratings. A major problem is that severe optical alignments on the angles of oblique incidence of the expanded beam to the mirror-substrate assembly and the angles of mirrors with respect to the substrate are required [20]. Otherwise low-frequency error fringes with millimeter-order periods will occur in the interference fringe field due to the cross-interferences between the sub-beams after multiple reflections on both of the mirrors,
IP T
which is a significant error source in fabrication of high-precision gratings with an area of larger than 10 mm×10 mm [20]. The conventional two-axis Lloyd’s mirror interferometer has
SC R
therefore been applied only for fabrication of small-area 2D scale gratings within an area on the order of 10 mm×10 mm [19].
U
In responding to the problem in the conventional two-axis Lloyd’s mirror interferometer, the authors have proposed a new two-axis Lloyd’s mirror interferometer with a
N
non-orthogonal mirror-substrate assembly [22]. In the proposed new non-orthogonal setup,
A
the expanded beam is perpendicularly projected on the substrate surface, which makes the
M
beam alignment much easier compared with the oblique beam incidence in the conventional
ED
orthogonal setup. In addition, each of the mirror angles can be adjusted independently to set the X- and Y-directional grating periods. Since no multiple reflections occur for the sub-beams
PT
in the newly-proposed non-orthogonal substrate-mirror assembly, the low-frequency error fringes inherent in the conventional orthogonal setup can be avoided. It has been
CC E
demonstrated that the proposed non-orthogonal setup could fabricate a high-precision 2D scale grating. However, on the other hand, an area of the fabricated 2D scale grating was limited to be on the order of 10 mm×10 mm [22] due to the nature of wavefront division in
A
the Lloyd’s mirror interferometer that restrains the fabricated grating area within a small part of the expanded beam diameter D. Verification of the possibility of fabricating a large 2D scale grating over an area of 100 mm×100 mm by the proposed non-orthogonal setup in a research laboratory has still remained as an important task to be carried out, which requires an optimal design for a compact mirror-substrate assembly and an effective solution to the 6
problem of light intensity reduction due to the expansion of the beam diameter. The motivation of this research is to design and construct a compact two-axis Lloyd’s mirror interferometer that can be used in a research laboratory for fabrication of large-area 2D scale gratings with an area of 100 mm×100 mm by applying the proposed non-orthogonal setup. In this paper, it is verified by geometrical analysis that the requirement on the grating
IP T
area can be satisfied by a more compact mirror-substrate assembly, which is an important advantage of the non-orthogonal setup for fabrication of large-area scale gratings. It is also
SC R
demonstrated by simulation that the reduction of light intensity due to the expansion of the
beam diameter can be covered by extending the exposure time based on the stable optical
U
configuration of the Lloyd’s mirror interferometer, without using a higher-power of laser
A
2. Two-axis Lloyd's mirror interferometer
N
source. The design and testing of the interferometer are then presented in the paper.
M
A two-axis Lloyd’s mirror interferometer based on the orthogonal type [19, 20] or the
ED
non-orthogonal type of mirror-substrate assembly [22] can fabricate orthogonal 2D grating structures that are sufficient for use in the planar encoder systems [3, 5, 6]. Fig. 1(a) shows a
PT
schematic of the optical configuration for the two-axis Lloyd’s mirror interferometer with the orthogonal type of mirror-substrate assembly, in which two mirrors (X- and Y-mirrors) are
CC E
arranged in such a way that the normal of the X-mirror is perpendicular to that of a substrate, while that of the Y-mirror is perpendicular to both the normals of the substrate and the
A
X-mirror. There are two kinds of optical configurations for the two-axis Lloyd’s mirror interferometer based on the orthogonal-type of mirror-substrate assembly; one is a four-beam interference configuration [19], while the other is a three-beam interference configuration [20]. Although the four-beam interference configuration can be realized in a relatively simple optical setup, precise alignments of the mirrors in the mirror-substrate assembly are necessary to avoid appearances of low-frequency error fringes due to Moiré in the interference fringe 7
field [20], which severely degrade diffraction efficiency of the fabricated 2D scale grating. The three-beam interference configuration can suppress the appearance of error fringes by applying a physical optical filter and polarization modulation control unit consisting of half-wavelength plates (HWPs) [20]. However, one of the drawbacks of the two-axis Lloyd’s mirror interferometer based on the orthogonal-type of mirror-substrate assembly is its
IP T
complicated alignments of optical components in the setup since the angles of oblique incidence of laser beam and the angles of mirrors with respect to the substrate need to be
SC R
adjusted precisely and simultaneously. In addition, the adjustment tasks become more severe as the mirror-substrate assembly becomes larger.
U
On the other hand, adjustment tasks for the two-axis Lloyd’s mirror interferometer based on the non-orthogonal-type of mirror-substrate assembly [22], a schematic of which is shown
N
in Fig. 1(b), are more simple and easy compared with the orthogonal setup. The
A
non-orthogonal setup is designed by applying major modifications to the mirror-substrate
M
assembly for the traditional one-axis Lloyd’s mirror interferometer [17, 21]. As can be seen in
ED
the figure, the Y-mirror with normal parallel to the YZ-plane is added to the mirror-substrate assembly for the one-axis Lloyd’s mirror interferometer, and the angles between the substrate
PT
surface and each of the mirror surfaces are set to be larger than 90 degrees [22], while the angle of incidence of the laser beam with respect to the substrate is set to be 90 degrees. These
CC E
modifications enable the interferometer to fabricate 2D grating structures in a single exposure process, while allowing the independent adjustments of grating periods along the X- and
A
Y-directions with easy alignments of the optical components. In addition, the appearance of low-frequency error fringes, which is the major drawback of the orthogonal setup caused as a result of the superimposition of the groups of line interference fringes having different interference pattern periods and directions [20], can be suppressed. Furthermore, a polarization modulation control unit composed of two HWPs is added into the path of the incident laser light so that unnecessary interference in-between the beams reflected back from 8
the X- and Y-mirrors, which results in distorted interference fringe patterns, can be avoided [22]. Regarding the use of two-axis Lloyd’s mirror interferometer in research laboratories, the size of its optical setup is preferred to be as compact as possible. In this paper, the area sizes of two-axis Lloyd’s mirror interferometers based on the orthogonal and non-orthogonal types
IP T
of mirror-substrate assemblies for fabrication of 2D scale gratings with an area of 100
mm×100 mm are at first investigated based on geometric optics. Fig. 2 shows the case of
SC R
orthogonal type of mirror-substrate assembly. In this case, the X- and Y-directional grating periods gX and gY can be expressed as follows [19]:
2 cos cos sin
, gY
2 cos cos sin
(1)
U
gX
N
where is the light wavelength of the laser beam. and are the angles of incidence of the
A
laser beam with respect to the substrate plane and the Z-plane in Fig. 2, respectively. It
M
should be noted that the optical configuration in the case of 0º is illustrated in the figure. According to Eq. (1), the two angles and should be adjusted simultaneously for setting the
ED
grating periods, and should be adjusted to be 0º so that gX and gY become the same grating period g. In the following, is treated to be 0º. Now we assume that the collimated laser
PT
beam made incident to the mirror-substrate assembly has a radius RLaser. In the setup, the laser
CC E
beam becomes an ellipse whose semi-major axis and semi-minor axis are RLaser/cos and RLaser, respectively, on the substrate plane. As a result, from the geometric relationship, the required radius RLaser can be calculated as follows: RLaser 2Ls
A
(2)
where LS is the side length of the grating substrate. Meanwhile, regarding the light ray reflected by the X(Y)-mirror and is made incident to the point P on the substrate in the figure, the required height LM_h and width LM_w of the mirrors can be calculated from the geometric relationship as follows:
9
LM_h 2 Ls tan
(3)
LM_w 2LS
(4)
As can be seen in Eqs. (1) to (4), the required sizes of the mirrors depend on the required grating period g. In the same manner, now we consider the case of non-orthogonal type of
Y-directional grating periods gX and gY can be expressed as follows [16]:
sin 2 X
, gY
(5)
sin 2Y
SC R
gX
IP T
mirror-substrate assembly, a schematic of which is shown in Fig. 3. In this case, the X- and
where X(Y) represents the angle between the normal of substrate and the X(Y)-mirror.
U
According to Eq. (5), the grating periods along the X- and Y-directions can be adjusted independetly and easily, which is one of the advantages of the non-orthogonal type of
N
mirror-substrate assembly. Furthermore, since the laser beam is perpendicularly projected on
A
the substrate surface, optical alignments of the non-orthogonal type are easier than that of the
M
orthogonal type. Now we consider the case where X and Y are set to be the same angle so
ED
that gX and gY become the same grating period g. According to the geometric relationship, the required beam radius RLaser, the height LM_h and width LM_w of the mirrors can be calculated as
PT
follows: RLaser 2LS
CC E
(6)
(7)
LM_w LS
(8)
A
LM_h Ls 1 2 sin 2 sin
According to Eq. (6), the required beam radius is the same as the orthogonal setup. Fig. 4 shows LM_h and LM_w required for fabrication of grating structures with the period g in the orthogonal type and non-orthogonal type of mirror-substrate assemblies. As can be seen in the figure, the mirror heights required for both types are comparable. Meanwhile, the mirror width required for the non-orthogonal type is shorter than that for the orthogonal type, which 10
is a great advantage in terms of the practical optical design of the two-axis Lloyd’s mirror interferometer. Table 1 summarises the required incident beam diameter and the mirror size for fabrication of 2D scale grating with a grating period g of 1 m over an area of 100 mm×100 mm under the condition of =441.6 nm. Regarding the discussion described above,
of mirror-substrate assembly.
SC R
3. Influence of the intensity distribution of the incident laser beam
IP T
in the following of this paper, a design study is carried out based on the non-orthogonal type
3.1 Interference fringe field at each position on the grating substrate
U
Regarding the discussion described above, an optical setup for the compact non-orthogonal two-axis Lloyd’s mirror interferometer, a schematic of which is shown in Fig.
N
5, is designed for fabrication of large-area 2D scale grating. All the optical components are
A
aligned to be mounted on a commercially available general-purpose 1500 mm×1000 mm
M
vibration isolation table for use in research laboratories. For fabrication of large-area 2D
ED
grating structures over an area of 100 mm×100 mm, a diameter of the collimated laser beam D made incident to the mirror-substrate assembly should be larger than approximately
PT
283 mm, at least. In the optical setup, the collimated laser beam is designed to be generated by a beam expansion assembly composed of a large collimating lens and a spatial filter with a
CC E
pinhole and an objective lens aligned in the Keplerian configuration. The parameter D will therefore be determined by the focal lengths of the objective lens f1 and the collimating lens f2, as follows:
A
D
f2 d f1
(9)
where d is a diameter of the laser beam made incident to the objective lens. The equation is valid until the diameter of collimating lens DLens is larger than D. In the design, a large plano-convex lens with DLens and f2 of 350 mm and 677 mm, respectively, is employed as the
11
collimating lens, while f1 is set to be 2.1 mm. The resultant beam diameter becomes approximately 387 mm, which is larger than DLens (350 mm). The collimated beam diameter is therefore restricted by the lens diameter DLens, and becomes 350 mm in the designed optical setup. It should be noted that more compact optical design is expected to be achieved when an aspheric lens is employed as the collimating lens. However, on the other hand, such a
IP T
large-scale aspheric lens significantly increases the instrumentation cost. Therefore, as the first step of research, a simple plano-convex lens was employed in this paper. In most of the
SC R
cases, a laser beam emitted from a light source has a Gaussian intensity distribution. Therefore, the collimated laser beam after passing through the collimating lens also has a
U
Gaussian intensity distribution, in which the light intensity decays as the increase of the distance from the optical axis of the collimated laser beam, resulting in the decrease of the
N
light intensity of interference fringe filed at the outer position. This could result in the
A
difference of grating structures fabricated by the designed two-axis Lloyd’s mirror
M
interferometer. The interference fringe field to be generated by the designed optical setup is
ED
therefore calculated theoretically, while considering the intensity distribution in the incident laser beam.
PT
Now the intensity ID(x,y) of the light ray made directly incident to the position with the coordinates of (x,y) on the substrate as shown in Fig. 6 can be described as follows [21]:
CC E
2( x2 y 2 ) I D x, y I0 exp 2 R Laser
(10)
A
where I0 is the light intensity at the origin of the XY-coordinate in the figure that can be calculated by using the power of the laser beam P as follows [23]:
I0
2P RLaser2
(11)
Meanwhile, on the assumption that there is no loss of light intensity in the beam reflections at the mirror surfaces, the light intensities of the X-beam IX(x,y) and the Y-beam IY(x,y) at the
12
coordinates of (x,y) can be calculated as follows: (12)
2( xY beam2 yY beam2 ) I Y x, y I0 cos 2Y exp 2 RLaser
(13)
where
(14)
SC R
tan X x x xY -beam x X -beam tan , Y tan tan 2 y y X X y Y -beam X -beam y tanY tan 2Y
IP T
2( xX beam2 yX beam2 ) I X x, y I0 cos 2 X exp 2 R Laser
By using ID(x,y), IX(x,y) and IY(x,y), the intensity I(x,y) of the 2D interference fringe field to be
U
generated as a result of the superimposition of the direct beam, the X- and Y-beams can be calculated as follows:
N
I (x, y) IDC(x, y) I DX (x, y) I DY (x, y) I XY (x, y)
A
where
(15)
M
IDCx, y ID(x, y) I X (xX beam, yX beam) IY (xY beam, yY beam)
ED
I DX x, y 2 I D ( x, y) I X ( xX beam, yX beam) cos 2 x sin 2 X cos DX I DY x, y 2 I D ( x, y) IY ( xY beam, yY beam) cos 2 y sin 2Y cos DY
(16)
CC E
PT
I XY x, y 2 I X ( xX beam, yX beam) IY ( xY beam, yY beam) cos 2 y sin 2 2 x sin 2 cos Y X XY
The parameters DX, DY, XY are the angles between the polarization directions of the corresponding light rays, respectively. Now the polarization modulation control [22] is
A
introduced in the optical setup so that the interference in-between the X- and Y-beams can be eliminated; namely, DX=DY=45° andXY=90°. Therefore, I(x,y) can be rewritten as follows: I ( x, y) I D ( x, y) I X ( xX beam, yX beam) IY ( xY beam, yY beam) 2I D ( x, y) I X ( xX beam, yX beam) cos 2 x sin 2 X 2I D ( x, y) IY ( xY beam, yY beam) cos 2 y sin 2Y
13
(17)
Based on the above mentioned equations, the interference fringe fields are calculated. Fig. 7(a) shows the intensity distribution ID(x,y) of the direct beam on a substrate surface calculated by Eq. (10). The radius of the collimated laser beam RLaser is assumed to be 193.5 mm, corresponding to D=387 mm, to calculate the intensity distribution of the collimated laser beam. The angles of mirrors are set to be X=Y=13.1º, while the light
IP T
wavelength is assumed to be 441.6 nm. Interference fringes at the positions A, B and C in Fig. 7(a) are calculated based on Eq. (17), and the results are shown in Figs. 7(b), 7(c) and
SC R
7(d), respectively. The interference fringes normalized by the local maxima are also plotted as shown in Figs. 7(e), 7(f) and 7(g), respectively. As can be seen in Figs. 7(b), 7(c) and 7(d), the
U
peak intensity of the interference fringe field decays as the increase of distance from the origin of substrate. Meanwhile, on the other hand, the contrasts of normalized interference
N
fringes are comparable as shown in Figs. 7(e), 7(f) and 7(g). These results imply the
A
possibility of generating 2D grating structures over the substrate with an area of 100 mm×100
M
mm under the long period of exposure time, which is expected to be accepted by the two-axis
ED
Lloyd’s mirror interferometer based on the division of wavefront system.
PT
3.2 Computer simulation of the grating structures to be generated after the development process
CC E
In the interference lithography process, a substrate coated by a photoresist layer will be
exposed by the 2D interference fringe field generated by the interferometer at a certain period
A
of exposure time tExp. In the case of using a positive photoresist, a dissolution rate of the exposed area increases with the increase of exposure dose A that can be calculated as a product of the light intensity I(x,y) and the exposure time tExp [24]. After the lithography process, the exposed grating substrate will be developed in developing agent at a certain period of development time tDev. Since the dissolution rate of the exposed photoresist at each position is different in accordance with the light intensity distribution in the interference 14
fringe field, 2D grating structures can be acquired after the development process. In this paper, computer simulation is carried out to estimate the profile of 2D grating structures at each position on the grating substrate after the development process. It is known that the dissolution rate S of exposed positive photoresist can be expressed as follows [25]: m
IP T
A S 0 S Ae S S0 A S S 0 Ae
SC R
(18)
where S0 is the initial solubility rate, S∞ is the net development rate at a fully bleached
U
condition, and Ae is the exposure dose required to produce a net development rate equal to S0.
N
Fig. 8(a) shows the dissolution rate curve calculated based on Eq. (18), in which all the
A
parameters are determined regarding the contrast curve of the photoresist shown in Fig. 8(b)
M
provided in the specification sheet of the photoresist [26]. By using the dissolution rate curve, the 2D grating structures to be generated by the developed non-orthogonal two-axis Lloyd’s
ED
mirror interferometer are simulated. A procedure of how to estimate the 2D grating structures to be fabricated by the interferometer can be summarized as follows:
PT
Step 1: Calculate I(x,y) (shown in Fig. 7).
CC E
Step 2: Calculate the exposure dose distribution A(x,y) as the product of I(x,y) and the exposure time tExp.
Step 3: Convert A(x,y) into the dissolution rate distribution S(x,y) by using the
A
dissolution rate curve shown in Fig. 8(a).
Step 4: Calculate the height distribution h(x,y) of grating structures to be acquired through the development process with the developing period tDev.
Fig. 9 shows a schematic of the procedure described above. The height distribution h(x,y) can be calculated as follows:
15
hx, y T tDev S (x, y)
(19)
where T is the initial thickness of the photoresist. Fig. 10 shows an example of the simulated height distributions h(x,y) of grating structures at the positions A, B and C in Fig. 7(a) under the condition of tExp=1000 s and tDev=4 s. The height distributions are calculated while changing tExp and tDev, and Fig. 11 summarizes the variations of the maximum grating
IP T
structure amplitudes at the positions A, B and C in Fig. 7(a). As can be seen in Fig. 11, the amplitude of the grating structures is expected to increase with the increase of development
SC R
time tDev. The increase of exposure time tExp will also contribute to increase the amplitude of
grating structures at the beginning of exposure process, although excess exposure time tExp
U
will not contribute to further increase the amplitude of grating structures. These results also imply that the grating structures are expected to be acquired over the entire substrate when the
N
interference fringe field is exposed to the substrate with enough exposure time, and the
A
development time is sufficiently controlled. The simulation results shown in Fig. 11 can be
M
employed for the estimation of grating structures to be generated by the interferometer. It
ED
should be noted that the computer simulation is carried out in this paper to roughly estimate the shape of grating structures to be generated by the developed non-orthogonal two-axis
PT
Lloyd’s mirror interferometer. The grating structures to be acquired in a practical exposure test could be different from the simulation results due to the several reasons such as the
CC E
conditions of photoresist and developing agent used in the processes. More detailed analyses
A
should therefore be carried out for the optimization of the grating fabrication.
4. Experiments Following the computer simulation described above, experiments were carried out to verify the feasibility of the developed compact non-orthogonal two-axis Lloyd’s mirror interferometer. Fig. 12 shows a photograph of the optical setup build on a general-purpose 1500 mm×1000 mm vibration isolation table. As the light source, a He-Cd laser source with 16
the wavelength and the total power of 441.6 nm and 180 mW, respectively, was employed. It should be noted that the laser source was the same one employed for the non-orthogonal two-axis Lloyd’s mirror interferometer in the previous study [22], in which a 2D scale grating over an area on the order of 10 mm×10 mm had been fabricated. The laser beam from the light source was introduced to the beam expansion assembly composed of a spatial filter and a
IP T
collimating lens having a diameter and a focal length of 350 mm and 677 mm, respectively, to generate a collimated laser beam with a large diameter. The collimated laser beam was made
SC R
to pass through a polarization modulation control unit composed of a pair of HWPs made of polycarbonate with a size of 100 mm×100 mm, and was then made incident to the
U
non-orthogonal type of mirror-substrate assembly to generate 2D interference fringe field on a substrate, on which a photoresist layer was spin-coated in advance of the pattern exposure test.
N
The overall interferometer was realized in an overall size of 1480 mm×730 mm.
A
At first, the light intensity of the collimated laser beam after passing through the beam
M
expansion unit was evaluated. A laser power meter was placed behind the collimating lens,
ED
and the light intensity at each position on the grating substrate surface was measured. Fig. 13 shows the result. For comparison, the intensity distribution predicted by the optical design is
PT
also shown in the figure. A good agreement can be found in-between the theoretically calculated intensity distribution and the measured one.
CC E
After verifying the light intensity distribution, pattern exposure tests were carried out.
The pattern exposure tests were repeated while changing the period of pattern exposure time.
A
In each pattern exposure test, two small glass substrates with a size of 25 mm×25 mm were employed; one glass plate was placed to the position A in Fig. 13(b), while the other was placed to the position C in the figure. After the pattern exposure, the exposed grating substrates were developed by a NaOH solution with a volume concentration of 0.5%. Figs. 14(a) and 14(b) show the AFM images of the grating structures fabricated at the positions A and C, respectively, and Fig. 15 shows an example of the cross sections of fabricated grating 17
structures. As can be seen in the figures, two-dimensional grating structures can be recognized on the substrate exposed and developed at each condition. Meanwhile, each grating structure was found to have an elliptical shape. One of the main reasons of this was due to imperfect polarization modulation control with the low-cost HWPs made of polycarbonate, which were employed in the setup in terms of the instrumentation cost while sacrificing the performance
IP T
of polarization control. It should be noted that the influence of the imperfect polarization
modulation control can be suppressed by employing a high-quality HWPs in the polarization
SC R
modulation control unit, which will be carried out in future work with further precise and
careful alignments of optical components in the system. Figs. 16 and 17 summarize the
U
maximum amplitude of the grating structures subtracted from the AFM images at the positions A and C, respectively. As can be seen in the figures, the amplitude of grating
N
structures increased with the increase of the development time, as predicted in the results of
A
computer simulation. This tendency was clear especially for the grating structures fabricated
M
at the position A. It was also verified in the experiments that the grating structures with the
ED
amplitude of larger than 100 nm could be fabricated even at the position C, where the light intensity of the interference fringe field was far lower than that around the optical axis
PT
(position A). These results mean that the 2D grating structures can be fabricated over a large area of 100 mm×100 mm by the proposed compact non-orthogonal two-axis Lloyd’s mirror
CC E
interferometer. Meanwhile, on the other hand, the increase of the exposure time resulted in reducing the grating structure amplitude, especially at the position A. This phenomenon was
A
not predicted in the computer simulation. One of the possible reasons of this phenomenon was external disturbances such as thermal drifts of the optical components in the interferometer during the long-term exposure, although the developed non-orthogonal two-axis Lloyd’s mirror interferometer based on the division of wavefront system is considered to be more stable and robust against the external disturbances compared with the interference lithography based on division of amplitude system. 18
Finally, an exposure test over a large area of 100 mm×100 mm was carried out. A 100 mm×100 mm glass substrate was placed on the pattern exposure plane. The pattern exposure test was carried out with tExp of 1000 s, and the substrate was developed with tDev of 4 s. Figs. 18(a) and 18(b) show a photograph of the large substrate and optical microscopic images of the grating structures fabricated at each position on the glass substrate surface, respectively.
IP T
As can be seen in these figures, 2D grating structures were successfully fabricated over a large area of 100 mm×100 mm, which verified the feasibility of developed large-area
SC R
non-orthogonal two-axis Lloyd’s mirror interferometer.
U
5. Conclusions
A design study of the compact non-orthogonal two-axis Lloyd’s mirror interferometer for
N
fabrication of two-dimensional (2D) scale gratings over a large area of 100 mm×100 mm has
A
been carried out. To achieve a compact optical design for use in research laboratories, an
M
optical configuration of the non-orthogonal two-axis Lloyd’s mirror interferometer based on
ED
division of wavefront with the polarization modulation control has been employed, and the optical setup capable of being constructed on a commercially available general-purpose 1500
PT
mm×1000 mm vibration isolation table has successfully been designed. For fabrication of large-area 2D scale gratings, a laser beam from the laser source should be expanded by the
CC E
optical setup so that a collimated laser beam with a large diameter can be generated. In the case, the difference of the light intensity distribution on the grating surface could affect the
A
grating structures. Computer simulation has therefore been carried out to investigate the differences in the interference fringe field at the inner and outer positions on the interferometer. It has been verified that the contrast of the interference fringes will be almost uniform over the entire area of the grating surface; this fact implies the possibility of fabricating grating structures over an area of 100 mm×100 mm with the enhancement of stable and robust exposure realized by the optical setup based on the division of wavefront. It 19
should be noted that the developed non-orthogonal two-axis Lloyd’s mirror interferometer can also be employed as cost-effective manufacturing equipment in a production line for various types of large area 2D gratings. Meanwhile, the presented simulation algorithm is expected to accelerate the optimization of exposure and development processes for improving the fabrication efficiency of large area 2D gratings. Exposure tests have been carried out by using
IP T
the developed prototype compact non-orthogonal two-axis Lloyd’s mirror interferometer, and
the experimental results have demonstrated the feasibility of fabricating 2D scale gratings
SC R
over a large area of 100 mm×100 mm, which satisfies the target scale grating size of this research and is also a significant improvement compared with the 10 mm×10 mm size
U
achieved by the conventional orthogonal two-axis Lloyd’s mirror interferometer. The optimization of optical setup for fabricating uniform grating structures over the entire scale
A
M
process will be carried out in future work.
N
grating substrate surface, as well as the optimizations of exposure process and development
ED
Acknowledgements
References
Harrison GR. The Production of Diffraction Gratings I. Development of the Ruling Art.
CC E
[1]
PT
This research is supported by Japan Society for the Promotion of Science (JSPS).
J. Opt. Soc. Am. 1949;39(6):413–426. HEIDENHAIN Catalogue. Exposed Linear Encoders. 2014;AKLIP21.
[3]
Li X, Gao W, Muto H, Shimizu Y, Ito S, and Dian S. A six-degree-of-freedom surface
A
[2]
encoder for precision positioning of a planar motion stage. Precis. Eng. 2013;37(3):771–781.
[4]
HEIDENHAIN Catalogue. Two-coordinate encoders. 2016;PP281.
[5]
Gao W, Kim SW, Bosse H, Haitjema H, Chen YL, Lu XD, Knapp W, Weckenmann A, 20
Estler WT and Kunzmann H. Measurement technologies for precision engineering. CIRP Ann.-Manuf. Technol. 2015;64(2):773-796. [6]
Shimizu Y, Ito T, Li X, Kim WJ, Gao W. Design and Testing of a Four-probe Optical Sensor Head for Three-axis Surface Encoder with a Mosaic Scale Grating. Meas. Sci. Technol. 2014;25:09402. Hsieh
HL,
Pan
SW
six-degree-of-freedom
Development
displacement
of
and
a
grating-based
angle
interferometer
measurements.
Opt.
Gao
W.
Precision
Nanometrology
-Sensors
and
Nanomanufacturing. Springer 2010.
Measuring
Express.
Systems
for
Gao W, Araki T, Kiyono S, Okazaki Y, Yamanaka M. Precision nano-fabrication and
U
[9]
SC R
2015;23-3:2451-2465. [8]
for
IP T
[7]
N
evaluation of a large area sinusoidal grid surface for a surface encoder. Precis. Eng.
A
2003;27(3):289–298.
M
[10] Rogers JA, Paul KE, Jackman RJ, and Whitesides GM. Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field. Appl. Phys. Lett.
[11] Pease
RF.
ED
1997;70(20):2658–2660.
Semiconductor
technology:
imprints
offer
Moore.
Nature
PT
2002;417(6891):802–803.
CC E
[12] Lu C, Lipson RH. Interference lithography: a powerful tool for fabricating periodic structures. Laser Photonics Rev. 2010;4(4):568–580.
[13] Brueck SRJ. Optical and Interferometric Lithography-Nanotechnology Enablers. Proc.
A
of the IEEE 2005;93(10):1704–1721.
[14] Kimura A, Gao W, Kim WJ, Hosono K, Shimizu Y, Shi L, Zeng LJ. A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement. Precis. Eng. 2012;36:576-585. [15] Konkola PT, Chen CG, Heilmann RK, Joo C, Montoya JC, Chang CH, and Schattenburg ML. Nanometer-level repeatable metrology using the Nanoruler, J. Vac. 21
Sci. Technol. B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 2003;21:3097-3101. [16] Chua JK, Murkeshan VM. Patterning of Two-Dimensional Nanoscale Features Using Grating-Based
Multiple
Beams
Interference
Lithography.
Physica
Scripta
2009;80(1):015401.
IP T
[17] Li X, Shimizu Y, Ito S, Gao W. Fabrication of Scale Gratings for Surface Encoders by
Using Laser Interference Lithography with 405 nm Laser Diodes. Int. J. Precis. Eng.
SC R
Manuf. 2013;14(11):1979–1988.
[18] Boor J, Geyer N, Gösele U, Schmidt V. Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning. Opt. Lett.
U
2009;34(12):1783–1785.
N
[19] Vala M, Homola J. Flexible method based on four-beam interference lithography for
A
fabrication of large areas of perfectly periodic plasmonic arrays. Opt. Express
M
2014;22(15):18778-19789.
[20] Shimizu Y, Aihara R, Zongwei R, Chen YL, Ito S, Gao W. Influences of misalignment
ED
errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer. Opt. Express 2016;24(24):17521-27535.
PT
[21] Ikjoo B, Joonwon K. Cost-effective laser interference lithography using a 405 nm
CC E
AlInGaN semiconductor laser. J. Micromech Microeng. 2010;20(5):055024. [22] Li X, Gao W, Shimizu Y, Ito S. A two-axis Lloyd’s mirror interferometer for fabrication of
two
dimensional
diffraction
gratings.
CIRP
Ann.
-Manuf.
Technol.
A
2014;63(1):461–464.
[23] Hecht E. Optics 5th Ed. Pearson 2017. [24] Austin S, Stone FT. Fabrication of thin periodic structures in photoresist: a model. Appl. Opt. 1976;15(4):1071-1074. [25] Meyerhofer D. Photosolubility of Diazoquinone Resists. IEEE Trans. Electron Dev. 1980;ED-21(5):921-926. 22
A
CC E
PT
ED
M
A
N
U
SC R
IP T
[26] Shipley. Microposit S1800 series photo resists. 2006;ME05N12, Rev.0
23
Figure captions Figure 1
Schematics of mirror-substrate assemblies for the two-axis Lloyd’s mirror interferometer (a) Orthogonal type (b) Non-orthogonal type Schematic of the orthogonal type of mirror-substrate assembly with the incident beam (the case where 0º is illustrated)
Schematic of the non-orthogonal type of mirror-substrate assembly with the incident beam
Figure 4
Mirror height and width required for fabricating grating structures with a
U
period g over an area of 100 mm×100 mm
N
(a) Required mirror height
A
(b) Required mirror width Figure 5
SC R
Figure 3
IP T
Figure 2
Schematic of the developed optical setup of the compact non-orthogonal
M
two-axis Lloyd’s mirror interferometer for fabrication of large-area 2D scale
ED
gratings
Geometric relationship among the direct beam, the X- and Y-beams
Figure 7
Intensity distributions of the incident light with a beam diameter D=387 mm
PT
Figure 6
over the interferometer and the interference fringe field at each position on
CC E
the substrate
Figure 8
A dissolution rate and a contrast curve of the photoresist (a) A dissolution rate of the exposed photoresist as a function of exposure
A
dose
(b) A contrast curve of the photoresist as a function of log dose normalized [26]
Figure 9
A schematic of the procedure of how to calculate surface form of the grating structures to be fabricated by the interference fringe fields generated by the non-orthogonal two-axis Lloyd’s mirror interferometer 24
Figure 10
Simulated height distributions of the 2D grating structures at the positions A, B and C in Fig. 6 (tExp=1000 s, tDev=4 s)
Figure 11
Relationship among the exposure time, development time and the maximum amplitude of grating structures
Figure 12
A photograph of the developed optical configuration for the large-scale
Figure 13
IP T
non-orthogonal two-axis Lloyd’s mirror interferometer Intensity distribution of the collimated laser beam generated in the
SC R
developed setup (a) Light intensity distribution estimated based on theory (b) Measured light intensity distribution
AFM images of the developed 2D grating structures
U
Figure 14
N
(a) Position A
Figure 15
A
(b) Position C
Cross-sectional images of the fabricated 2D grating structures
Amplitude of the fabricated grating structures at the position A
ED
Figure 16
M
(Position A, tExp=500 s, tDev=5 s)
(a) Variation due to tDev
Figure 17
PT
(b) Variation due to tExp Amplitude of the fabricated grating structures at the position C
CC E
(a) Variation due to tDev (b) Variation due to tExp
Figure 18
Fabricated grating structures over an area of 100 mm×100 mm on a large
A
glass substrate
(a) A photograph of the fabricated 2D scale grating (b) Microscopic images of the 2D grating structures at each position in (a)
25
A ED
PT
CC E
IP T
SC R
U
N
A
M
Figures:
26
27
A ED
PT
CC E
IP T
SC R
U
N
A
M
28
A ED
PT
CC E
IP T
SC R
U
N
A
M
29
A ED
PT
CC E
IP T
SC R
U
N
A
M
30
A ED
PT
CC E
IP T
SC R
U
N
A
M
31
A ED
PT
CC E
IP T
SC R
U
N
A
M
32
A ED
PT
CC E
IP T
SC R
U
N
A
M
33
A ED
PT
CC E
IP T
SC R
U
N
A
M
34
A ED
PT
CC E
IP T
SC R
U
N
A
M
Table captions
Table 1:
IP T
Required incident beam diameter and mirror size in the optical setup for fabricating grating structures with a grating period g=1 m over an area of 100 mm×100 mm under the condition
SC R
of =441.6 nm Orthogonal type
Non-orthogonal type
Angle of incidence of the collimated laser beam
18.2º
0º
Mirror angle with respect to the substrate
90º
Incident beam diameter
282.8 mm
N
282.8 mm
200 mm
100 mm
430.3 mm
395.8 mm
A
CC E
PT
ED
Mirror height
103.1º (=13.1º)
A
M
Mirror width
U
Items
35
S0141-6359(17)30713-4 https://doi.org/10.1016/j.precisioneng.2017.12.004 PRE 6703
To appear in:
Precision Engineering
Received date: Accepted date:
26-11-2017 4-12-2017
Please cite this article as: Shimizu Yuki, Aihara Ryo, Mano Kazuki, Chen Chong, Chen Yuan-Liu, Chen Xiuguo, Gao Wei.Design and testing of a compact non-orthogonal twoaxis Lloyd’s mirror interferometer for fabrication of large-area two-dimensional scale gratings.Precision Engineering https://doi.org/10.1016/j.precisioneng.2017.12.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Design and testing of a compact non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings Yuki Shimizu*, Ryo Aihara, Kazuki Mano, Chong Chen, Yuan-Liu Chen, Xiuguo Chen, Wei Gao Department of Finemechanics, Tohoku University
*Phone: +81-22-795-6950, Fax: +81-22-795-6953 E-mail: [email protected]
SC R
Highlights of this paper:
IP T
6-6-01 Aramaki-Aza Aoba, Aoba-ku, Sendai 980-8579, Japan
An optical setup is designed for fabrication of large-area scale gratings. The design is based on non-orthogonal 2D Lloyd’s mirror interferometer.
Grating pattern structures have been estimated by computer simulation. A 100 mm×100 mm 2D scale gratings has successfully been fabricated. 2D grating patterns with a short period of 1 m has been fabricated.
A
N
U
M
Abstract: A compact and stable two-axis Lloyd’s mirror interferometer based on a new non-orthogonal type of mirror-substrate assembly is designed for fabrication of
ED
100 mm×100 mm large-area two-dimensional (2D) diffraction scale gratings in a research laboratory or a small-scale manufacturing facility. At first, the required mirror sizes used in
PT
the new non-orthogonal type and the conventional orthogonal type are compared based on geometrical analysis. It is identified that the width of the mirror can be reduced to half in the
CC E
non-orthogonal type while the required mirror height and the expanded laser beam diameter are comparable to those in the orthogonal type. The shorter mirror width makes it possible to
A
design a compact mirror-substrate assembly so that the overall interferometer can be realized in an overall size of 1480 mm×730 mm for mounting on a commercially available general-purpose 1500 mm×1000 mm vibration isolation table for use in research laboratories. It is then verified by simulation that the selected laser source and the designed beam expansion assembly, which are the other main parts of the interferometer, are effective for fabricating the designed grating structures. Experiments are also carried out to demonstrate 1
the feasibility of the constructed interferometer for fabricating 100 mm×100 mm 2D scale gratings with a short period of 1 m. Keywords: Scale grating; Lloyd’s mirror interferometer; Polarization modulation control;
A
CC E
PT
ED
M
A
N
U
SC R
IP T
Interference; Diffraction
2
1. Introduction Diffraction gratings are important optical components [1] employed in physics and astronomy for spectroscopy. Nowadays diffraction gratings are expanding their applications to some optical measuring instruments for dimensional measurement. When one-dimensional (1D) gratings are employed in measuring instruments such as linear encoders [2], they act as
IP T
scales for measurement of the displacement or motion of a target of interest. Furthermore, in recent years, two-dimensional (2D) gratings with grating structures equally spaced along the
SC R
X- and Y-directions are also expanding their applications in planar/surface encoder systems as
scale gratings for multi-axis measurement [3-5]. In the planar/surface encoder systems, a
U
grating period of the scale grating is one of the important parameters, since a shorter grating period contributes to reduce the period of interference signals, resulting in the improvement of
N
measurement resolution in the encoder systems [5, 6]. The grating periods of scale gratings in
A
such encoder systems are therefore designed to be several m or less [2, 3] to achieve
M
nanometric resolution. Meanwhile, since the relative motion between a scale grating and an
ED
optical reading head will be detected by using interference signals, which are generated by superimposing positive and negative diffracted beams from the scale grating, the measurable
PT
range of an encoder system is theoretically restricted by the size of 2D grating to be used as a scale for multi-axis measurement. It is therefore desired to establish a method for fabrication
CC E
of 2D scale gratings having a grating period on the order of micrometers or less over a large area of 100 mm×100 mm or even larger [3-7].
A
There are several methods available for fabrication of 2D scale gratings, such as
ultra-precision machining [8, 9], mask-based optical projection lithography [10, 11] or mask-less interference lithography [12]. Although the mask-based optical projection lithography is often employed to fabricate scale gratings [13], the facility and equipment required for the processes including mask fabrication by electron-beam lithography in the projection lithography are extremely expensive [12]. Meanwhile, on the other hand, the 3
mask-less interference lithography is a good candidate for use in research laboratories in terms of fabrication costs. The mask-less interference lithography can be classified into two categories; the division of amplitude and the division of wavefront. In the division of amplitude system of Mach-Zehnder interferometer for fabrication of 1D grating on a grating substrate placed in the XY-plane, a thin collimated light from a laser source with a diameter d
IP T
is split into two beams with the same diameter d by using a beam splitter or a diffraction
grating [14-16]. Each of the split beams travels along a different path in the Mach-Zehnder
SC R
interferometer set in the YZ-plane, in which a beam expander is employed to expand its beam diameter to D, before the beam is projected onto the grating substrate. The expanded beams
U
are superimposed with each other on the substrate to form and expose a stationary interference fringe field with a set of alternating bright and dark lines for generating the 1D
N
grating line structures equally-spaced along the Y-direction. The size of the interference fringe
A
field and/or the grating area on the substrate is the same or even larger than the expanded
M
beam diameter D [14]. From this point of view, the division of amplitude system is effective
ED
for fabricating 1D large-area gratings. However, in large-area grating fabrication, the non-common optical paths of the beams are extremely long, up to several meters, resulting in
PT
an unstable interference fringe field due to the influences of external disturbances such as temperature and humidity variations, vibrations, etc. This requires a well-controlled
CC E
environment for the stable fabrication. A high power laser source is also required to shorten the exposure time for further removing the influences of residual disturbances. As a result, the
A
system becomes large and expensive, which is the major obstacle to prevent its use in research laboratories with limited space and budget. Moreover, when the division of amplitude system is expanded to fabricate 2D scale gratings with grating structures along the X- and Y-directions, it is necessary to set two Mach-Zehnder interferometers in the XZ- and YZ-planes, respectively, which will make the system to have a complicated 3D optical layout and will significantly increase the size as well as the cost of the fabrication system. For this 4
reason, large-area division of amplitude systems are basically limited in 1D grating fabrication. Although a 2D scale grating with a size of 100 mm×100 mm has been fabricated with such a system by taking a two-step exposure process, in which the grating substrate has been exposed before and after being rotated 90º, respectively [14], the structures generated in the first exposure are influenced in the second exposure. This causes the difference in the
IP T
cross-sectional profiles of the grating surface along the X- and Y-directions, which is a fatal problem for 2D scale gratings.
SC R
On the other hand, one of the biggest advantages of the Lloyd’s mirror interferometer
based on the division of wavefront [17-21] compared with the division of amplitude system is
U
its high stability although the size of the interference fringe field and/or the grating area on the substrate is quite smaller than the expanded beam diameter D. In a conventional 1D Lloyd’s
N
mirror interferometer, an expanded beam with the diameter D is projected onto a
A
mirror-substrate assembly composed of a grating substrate set in the XY-plane and a mirror set
M
in the XZ-plane (referred to as the Y-mirror), where the wavefront of the beam is divided into
ED
two sub-beams for forming the interference fringe field for generating the 1D grating line structures equally-spaced along the Y-direction. Because the non-common optical paths of the
PT
sub-beams are short, within the expanded beam diameter D, a stable interference fringe field can be generated. It is also easy to expand the Lloyd’s mirror interferometer from one-axis to
CC E
two-axis by simply adding an X-mirror (set in the YZ-plane) in the mirror-substrate assembly where the substrate, the X- and Y-mirrors are arranged orthogonally with each other [18, 19].
A
This is an important advantage in fabrication of 2D scale gratings. Since only one beam expander is necessary and a laser source with a lower power is accepted, the Lloyd’s mirror interferometer has a simpler optical configuration and is also less expensive and more compact compared with the division of amplitude system, which is attractive for use in research laboratories. However, the conventional two-axis Lloyd’s mirror interferometer with an orthogonal mirror-substrate assembly also has its inherent problems in fabrication of 5
high-precision large-area 2D gratings. A major problem is that severe optical alignments on the angles of oblique incidence of the expanded beam to the mirror-substrate assembly and the angles of mirrors with respect to the substrate are required [20]. Otherwise low-frequency error fringes with millimeter-order periods will occur in the interference fringe field due to the cross-interferences between the sub-beams after multiple reflections on both of the mirrors,
IP T
which is a significant error source in fabrication of high-precision gratings with an area of larger than 10 mm×10 mm [20]. The conventional two-axis Lloyd’s mirror interferometer has
SC R
therefore been applied only for fabrication of small-area 2D scale gratings within an area on the order of 10 mm×10 mm [19].
U
In responding to the problem in the conventional two-axis Lloyd’s mirror interferometer, the authors have proposed a new two-axis Lloyd’s mirror interferometer with a
N
non-orthogonal mirror-substrate assembly [22]. In the proposed new non-orthogonal setup,
A
the expanded beam is perpendicularly projected on the substrate surface, which makes the
M
beam alignment much easier compared with the oblique beam incidence in the conventional
ED
orthogonal setup. In addition, each of the mirror angles can be adjusted independently to set the X- and Y-directional grating periods. Since no multiple reflections occur for the sub-beams
PT
in the newly-proposed non-orthogonal substrate-mirror assembly, the low-frequency error fringes inherent in the conventional orthogonal setup can be avoided. It has been
CC E
demonstrated that the proposed non-orthogonal setup could fabricate a high-precision 2D scale grating. However, on the other hand, an area of the fabricated 2D scale grating was limited to be on the order of 10 mm×10 mm [22] due to the nature of wavefront division in
A
the Lloyd’s mirror interferometer that restrains the fabricated grating area within a small part of the expanded beam diameter D. Verification of the possibility of fabricating a large 2D scale grating over an area of 100 mm×100 mm by the proposed non-orthogonal setup in a research laboratory has still remained as an important task to be carried out, which requires an optimal design for a compact mirror-substrate assembly and an effective solution to the 6
problem of light intensity reduction due to the expansion of the beam diameter. The motivation of this research is to design and construct a compact two-axis Lloyd’s mirror interferometer that can be used in a research laboratory for fabrication of large-area 2D scale gratings with an area of 100 mm×100 mm by applying the proposed non-orthogonal setup. In this paper, it is verified by geometrical analysis that the requirement on the grating
IP T
area can be satisfied by a more compact mirror-substrate assembly, which is an important advantage of the non-orthogonal setup for fabrication of large-area scale gratings. It is also
SC R
demonstrated by simulation that the reduction of light intensity due to the expansion of the
beam diameter can be covered by extending the exposure time based on the stable optical
U
configuration of the Lloyd’s mirror interferometer, without using a higher-power of laser
A
2. Two-axis Lloyd's mirror interferometer
N
source. The design and testing of the interferometer are then presented in the paper.
M
A two-axis Lloyd’s mirror interferometer based on the orthogonal type [19, 20] or the
ED
non-orthogonal type of mirror-substrate assembly [22] can fabricate orthogonal 2D grating structures that are sufficient for use in the planar encoder systems [3, 5, 6]. Fig. 1(a) shows a
PT
schematic of the optical configuration for the two-axis Lloyd’s mirror interferometer with the orthogonal type of mirror-substrate assembly, in which two mirrors (X- and Y-mirrors) are
CC E
arranged in such a way that the normal of the X-mirror is perpendicular to that of a substrate, while that of the Y-mirror is perpendicular to both the normals of the substrate and the
A
X-mirror. There are two kinds of optical configurations for the two-axis Lloyd’s mirror interferometer based on the orthogonal-type of mirror-substrate assembly; one is a four-beam interference configuration [19], while the other is a three-beam interference configuration [20]. Although the four-beam interference configuration can be realized in a relatively simple optical setup, precise alignments of the mirrors in the mirror-substrate assembly are necessary to avoid appearances of low-frequency error fringes due to Moiré in the interference fringe 7
field [20], which severely degrade diffraction efficiency of the fabricated 2D scale grating. The three-beam interference configuration can suppress the appearance of error fringes by applying a physical optical filter and polarization modulation control unit consisting of half-wavelength plates (HWPs) [20]. However, one of the drawbacks of the two-axis Lloyd’s mirror interferometer based on the orthogonal-type of mirror-substrate assembly is its
IP T
complicated alignments of optical components in the setup since the angles of oblique incidence of laser beam and the angles of mirrors with respect to the substrate need to be
SC R
adjusted precisely and simultaneously. In addition, the adjustment tasks become more severe as the mirror-substrate assembly becomes larger.
U
On the other hand, adjustment tasks for the two-axis Lloyd’s mirror interferometer based on the non-orthogonal-type of mirror-substrate assembly [22], a schematic of which is shown
N
in Fig. 1(b), are more simple and easy compared with the orthogonal setup. The
A
non-orthogonal setup is designed by applying major modifications to the mirror-substrate
M
assembly for the traditional one-axis Lloyd’s mirror interferometer [17, 21]. As can be seen in
ED
the figure, the Y-mirror with normal parallel to the YZ-plane is added to the mirror-substrate assembly for the one-axis Lloyd’s mirror interferometer, and the angles between the substrate
PT
surface and each of the mirror surfaces are set to be larger than 90 degrees [22], while the angle of incidence of the laser beam with respect to the substrate is set to be 90 degrees. These
CC E
modifications enable the interferometer to fabricate 2D grating structures in a single exposure process, while allowing the independent adjustments of grating periods along the X- and
A
Y-directions with easy alignments of the optical components. In addition, the appearance of low-frequency error fringes, which is the major drawback of the orthogonal setup caused as a result of the superimposition of the groups of line interference fringes having different interference pattern periods and directions [20], can be suppressed. Furthermore, a polarization modulation control unit composed of two HWPs is added into the path of the incident laser light so that unnecessary interference in-between the beams reflected back from 8
the X- and Y-mirrors, which results in distorted interference fringe patterns, can be avoided [22]. Regarding the use of two-axis Lloyd’s mirror interferometer in research laboratories, the size of its optical setup is preferred to be as compact as possible. In this paper, the area sizes of two-axis Lloyd’s mirror interferometers based on the orthogonal and non-orthogonal types
IP T
of mirror-substrate assemblies for fabrication of 2D scale gratings with an area of 100
mm×100 mm are at first investigated based on geometric optics. Fig. 2 shows the case of
SC R
orthogonal type of mirror-substrate assembly. In this case, the X- and Y-directional grating periods gX and gY can be expressed as follows [19]:
2 cos cos sin
, gY
2 cos cos sin
(1)
U
gX
N
where is the light wavelength of the laser beam. and are the angles of incidence of the
A
laser beam with respect to the substrate plane and the Z-plane in Fig. 2, respectively. It
M
should be noted that the optical configuration in the case of 0º is illustrated in the figure. According to Eq. (1), the two angles and should be adjusted simultaneously for setting the
ED
grating periods, and should be adjusted to be 0º so that gX and gY become the same grating period g. In the following, is treated to be 0º. Now we assume that the collimated laser
PT
beam made incident to the mirror-substrate assembly has a radius RLaser. In the setup, the laser
CC E
beam becomes an ellipse whose semi-major axis and semi-minor axis are RLaser/cos and RLaser, respectively, on the substrate plane. As a result, from the geometric relationship, the required radius RLaser can be calculated as follows: RLaser 2Ls
A
(2)
where LS is the side length of the grating substrate. Meanwhile, regarding the light ray reflected by the X(Y)-mirror and is made incident to the point P on the substrate in the figure, the required height LM_h and width LM_w of the mirrors can be calculated from the geometric relationship as follows:
9
LM_h 2 Ls tan
(3)
LM_w 2LS
(4)
As can be seen in Eqs. (1) to (4), the required sizes of the mirrors depend on the required grating period g. In the same manner, now we consider the case of non-orthogonal type of
Y-directional grating periods gX and gY can be expressed as follows [16]:
sin 2 X
, gY
(5)
sin 2Y
SC R
gX
IP T
mirror-substrate assembly, a schematic of which is shown in Fig. 3. In this case, the X- and
where X(Y) represents the angle between the normal of substrate and the X(Y)-mirror.
U
According to Eq. (5), the grating periods along the X- and Y-directions can be adjusted independetly and easily, which is one of the advantages of the non-orthogonal type of
N
mirror-substrate assembly. Furthermore, since the laser beam is perpendicularly projected on
A
the substrate surface, optical alignments of the non-orthogonal type are easier than that of the
M
orthogonal type. Now we consider the case where X and Y are set to be the same angle so
ED
that gX and gY become the same grating period g. According to the geometric relationship, the required beam radius RLaser, the height LM_h and width LM_w of the mirrors can be calculated as
PT
follows: RLaser 2LS
CC E
(6)
(7)
LM_w LS
(8)
A
LM_h Ls 1 2 sin 2 sin
According to Eq. (6), the required beam radius is the same as the orthogonal setup. Fig. 4 shows LM_h and LM_w required for fabrication of grating structures with the period g in the orthogonal type and non-orthogonal type of mirror-substrate assemblies. As can be seen in the figure, the mirror heights required for both types are comparable. Meanwhile, the mirror width required for the non-orthogonal type is shorter than that for the orthogonal type, which 10
is a great advantage in terms of the practical optical design of the two-axis Lloyd’s mirror interferometer. Table 1 summarises the required incident beam diameter and the mirror size for fabrication of 2D scale grating with a grating period g of 1 m over an area of 100 mm×100 mm under the condition of =441.6 nm. Regarding the discussion described above,
of mirror-substrate assembly.
SC R
3. Influence of the intensity distribution of the incident laser beam
IP T
in the following of this paper, a design study is carried out based on the non-orthogonal type
3.1 Interference fringe field at each position on the grating substrate
U
Regarding the discussion described above, an optical setup for the compact non-orthogonal two-axis Lloyd’s mirror interferometer, a schematic of which is shown in Fig.
N
5, is designed for fabrication of large-area 2D scale grating. All the optical components are
A
aligned to be mounted on a commercially available general-purpose 1500 mm×1000 mm
M
vibration isolation table for use in research laboratories. For fabrication of large-area 2D
ED
grating structures over an area of 100 mm×100 mm, a diameter of the collimated laser beam D made incident to the mirror-substrate assembly should be larger than approximately
PT
283 mm, at least. In the optical setup, the collimated laser beam is designed to be generated by a beam expansion assembly composed of a large collimating lens and a spatial filter with a
CC E
pinhole and an objective lens aligned in the Keplerian configuration. The parameter D will therefore be determined by the focal lengths of the objective lens f1 and the collimating lens f2, as follows:
A
D
f2 d f1
(9)
where d is a diameter of the laser beam made incident to the objective lens. The equation is valid until the diameter of collimating lens DLens is larger than D. In the design, a large plano-convex lens with DLens and f2 of 350 mm and 677 mm, respectively, is employed as the
11
collimating lens, while f1 is set to be 2.1 mm. The resultant beam diameter becomes approximately 387 mm, which is larger than DLens (350 mm). The collimated beam diameter is therefore restricted by the lens diameter DLens, and becomes 350 mm in the designed optical setup. It should be noted that more compact optical design is expected to be achieved when an aspheric lens is employed as the collimating lens. However, on the other hand, such a
IP T
large-scale aspheric lens significantly increases the instrumentation cost. Therefore, as the first step of research, a simple plano-convex lens was employed in this paper. In most of the
SC R
cases, a laser beam emitted from a light source has a Gaussian intensity distribution. Therefore, the collimated laser beam after passing through the collimating lens also has a
U
Gaussian intensity distribution, in which the light intensity decays as the increase of the distance from the optical axis of the collimated laser beam, resulting in the decrease of the
N
light intensity of interference fringe filed at the outer position. This could result in the
A
difference of grating structures fabricated by the designed two-axis Lloyd’s mirror
M
interferometer. The interference fringe field to be generated by the designed optical setup is
ED
therefore calculated theoretically, while considering the intensity distribution in the incident laser beam.
PT
Now the intensity ID(x,y) of the light ray made directly incident to the position with the coordinates of (x,y) on the substrate as shown in Fig. 6 can be described as follows [21]:
CC E
2( x2 y 2 ) I D x, y I0 exp 2 R Laser
(10)
A
where I0 is the light intensity at the origin of the XY-coordinate in the figure that can be calculated by using the power of the laser beam P as follows [23]:
I0
2P RLaser2
(11)
Meanwhile, on the assumption that there is no loss of light intensity in the beam reflections at the mirror surfaces, the light intensities of the X-beam IX(x,y) and the Y-beam IY(x,y) at the
12
coordinates of (x,y) can be calculated as follows: (12)
2( xY beam2 yY beam2 ) I Y x, y I0 cos 2Y exp 2 RLaser
(13)
where
(14)
SC R
tan X x x xY -beam x X -beam tan , Y tan tan 2 y y X X y Y -beam X -beam y tanY tan 2Y
IP T
2( xX beam2 yX beam2 ) I X x, y I0 cos 2 X exp 2 R Laser
By using ID(x,y), IX(x,y) and IY(x,y), the intensity I(x,y) of the 2D interference fringe field to be
U
generated as a result of the superimposition of the direct beam, the X- and Y-beams can be calculated as follows:
N
I (x, y) IDC(x, y) I DX (x, y) I DY (x, y) I XY (x, y)
A
where
(15)
M
IDCx, y ID(x, y) I X (xX beam, yX beam) IY (xY beam, yY beam)
ED
I DX x, y 2 I D ( x, y) I X ( xX beam, yX beam) cos 2 x sin 2 X cos DX I DY x, y 2 I D ( x, y) IY ( xY beam, yY beam) cos 2 y sin 2Y cos DY
(16)
CC E
PT
I XY x, y 2 I X ( xX beam, yX beam) IY ( xY beam, yY beam) cos 2 y sin 2 2 x sin 2 cos Y X XY
The parameters DX, DY, XY are the angles between the polarization directions of the corresponding light rays, respectively. Now the polarization modulation control [22] is
A
introduced in the optical setup so that the interference in-between the X- and Y-beams can be eliminated; namely, DX=DY=45° andXY=90°. Therefore, I(x,y) can be rewritten as follows: I ( x, y) I D ( x, y) I X ( xX beam, yX beam) IY ( xY beam, yY beam) 2I D ( x, y) I X ( xX beam, yX beam) cos 2 x sin 2 X 2I D ( x, y) IY ( xY beam, yY beam) cos 2 y sin 2Y
13
(17)
Based on the above mentioned equations, the interference fringe fields are calculated. Fig. 7(a) shows the intensity distribution ID(x,y) of the direct beam on a substrate surface calculated by Eq. (10). The radius of the collimated laser beam RLaser is assumed to be 193.5 mm, corresponding to D=387 mm, to calculate the intensity distribution of the collimated laser beam. The angles of mirrors are set to be X=Y=13.1º, while the light
IP T
wavelength is assumed to be 441.6 nm. Interference fringes at the positions A, B and C in Fig. 7(a) are calculated based on Eq. (17), and the results are shown in Figs. 7(b), 7(c) and
SC R
7(d), respectively. The interference fringes normalized by the local maxima are also plotted as shown in Figs. 7(e), 7(f) and 7(g), respectively. As can be seen in Figs. 7(b), 7(c) and 7(d), the
U
peak intensity of the interference fringe field decays as the increase of distance from the origin of substrate. Meanwhile, on the other hand, the contrasts of normalized interference
N
fringes are comparable as shown in Figs. 7(e), 7(f) and 7(g). These results imply the
A
possibility of generating 2D grating structures over the substrate with an area of 100 mm×100
M
mm under the long period of exposure time, which is expected to be accepted by the two-axis
ED
Lloyd’s mirror interferometer based on the division of wavefront system.
PT
3.2 Computer simulation of the grating structures to be generated after the development process
CC E
In the interference lithography process, a substrate coated by a photoresist layer will be
exposed by the 2D interference fringe field generated by the interferometer at a certain period
A
of exposure time tExp. In the case of using a positive photoresist, a dissolution rate of the exposed area increases with the increase of exposure dose A that can be calculated as a product of the light intensity I(x,y) and the exposure time tExp [24]. After the lithography process, the exposed grating substrate will be developed in developing agent at a certain period of development time tDev. Since the dissolution rate of the exposed photoresist at each position is different in accordance with the light intensity distribution in the interference 14
fringe field, 2D grating structures can be acquired after the development process. In this paper, computer simulation is carried out to estimate the profile of 2D grating structures at each position on the grating substrate after the development process. It is known that the dissolution rate S of exposed positive photoresist can be expressed as follows [25]: m
IP T
A S 0 S Ae S S0 A S S 0 Ae
SC R
(18)
where S0 is the initial solubility rate, S∞ is the net development rate at a fully bleached
U
condition, and Ae is the exposure dose required to produce a net development rate equal to S0.
N
Fig. 8(a) shows the dissolution rate curve calculated based on Eq. (18), in which all the
A
parameters are determined regarding the contrast curve of the photoresist shown in Fig. 8(b)
M
provided in the specification sheet of the photoresist [26]. By using the dissolution rate curve, the 2D grating structures to be generated by the developed non-orthogonal two-axis Lloyd’s
ED
mirror interferometer are simulated. A procedure of how to estimate the 2D grating structures to be fabricated by the interferometer can be summarized as follows:
PT
Step 1: Calculate I(x,y) (shown in Fig. 7).
CC E
Step 2: Calculate the exposure dose distribution A(x,y) as the product of I(x,y) and the exposure time tExp.
Step 3: Convert A(x,y) into the dissolution rate distribution S(x,y) by using the
A
dissolution rate curve shown in Fig. 8(a).
Step 4: Calculate the height distribution h(x,y) of grating structures to be acquired through the development process with the developing period tDev.
Fig. 9 shows a schematic of the procedure described above. The height distribution h(x,y) can be calculated as follows:
15
hx, y T tDev S (x, y)
(19)
where T is the initial thickness of the photoresist. Fig. 10 shows an example of the simulated height distributions h(x,y) of grating structures at the positions A, B and C in Fig. 7(a) under the condition of tExp=1000 s and tDev=4 s. The height distributions are calculated while changing tExp and tDev, and Fig. 11 summarizes the variations of the maximum grating
IP T
structure amplitudes at the positions A, B and C in Fig. 7(a). As can be seen in Fig. 11, the amplitude of the grating structures is expected to increase with the increase of development
SC R
time tDev. The increase of exposure time tExp will also contribute to increase the amplitude of
grating structures at the beginning of exposure process, although excess exposure time tExp
U
will not contribute to further increase the amplitude of grating structures. These results also imply that the grating structures are expected to be acquired over the entire substrate when the
N
interference fringe field is exposed to the substrate with enough exposure time, and the
A
development time is sufficiently controlled. The simulation results shown in Fig. 11 can be
M
employed for the estimation of grating structures to be generated by the interferometer. It
ED
should be noted that the computer simulation is carried out in this paper to roughly estimate the shape of grating structures to be generated by the developed non-orthogonal two-axis
PT
Lloyd’s mirror interferometer. The grating structures to be acquired in a practical exposure test could be different from the simulation results due to the several reasons such as the
CC E
conditions of photoresist and developing agent used in the processes. More detailed analyses
A
should therefore be carried out for the optimization of the grating fabrication.
4. Experiments Following the computer simulation described above, experiments were carried out to verify the feasibility of the developed compact non-orthogonal two-axis Lloyd’s mirror interferometer. Fig. 12 shows a photograph of the optical setup build on a general-purpose 1500 mm×1000 mm vibration isolation table. As the light source, a He-Cd laser source with 16
the wavelength and the total power of 441.6 nm and 180 mW, respectively, was employed. It should be noted that the laser source was the same one employed for the non-orthogonal two-axis Lloyd’s mirror interferometer in the previous study [22], in which a 2D scale grating over an area on the order of 10 mm×10 mm had been fabricated. The laser beam from the light source was introduced to the beam expansion assembly composed of a spatial filter and a
IP T
collimating lens having a diameter and a focal length of 350 mm and 677 mm, respectively, to generate a collimated laser beam with a large diameter. The collimated laser beam was made
SC R
to pass through a polarization modulation control unit composed of a pair of HWPs made of polycarbonate with a size of 100 mm×100 mm, and was then made incident to the
U
non-orthogonal type of mirror-substrate assembly to generate 2D interference fringe field on a substrate, on which a photoresist layer was spin-coated in advance of the pattern exposure test.
N
The overall interferometer was realized in an overall size of 1480 mm×730 mm.
A
At first, the light intensity of the collimated laser beam after passing through the beam
M
expansion unit was evaluated. A laser power meter was placed behind the collimating lens,
ED
and the light intensity at each position on the grating substrate surface was measured. Fig. 13 shows the result. For comparison, the intensity distribution predicted by the optical design is
PT
also shown in the figure. A good agreement can be found in-between the theoretically calculated intensity distribution and the measured one.
CC E
After verifying the light intensity distribution, pattern exposure tests were carried out.
The pattern exposure tests were repeated while changing the period of pattern exposure time.
A
In each pattern exposure test, two small glass substrates with a size of 25 mm×25 mm were employed; one glass plate was placed to the position A in Fig. 13(b), while the other was placed to the position C in the figure. After the pattern exposure, the exposed grating substrates were developed by a NaOH solution with a volume concentration of 0.5%. Figs. 14(a) and 14(b) show the AFM images of the grating structures fabricated at the positions A and C, respectively, and Fig. 15 shows an example of the cross sections of fabricated grating 17
structures. As can be seen in the figures, two-dimensional grating structures can be recognized on the substrate exposed and developed at each condition. Meanwhile, each grating structure was found to have an elliptical shape. One of the main reasons of this was due to imperfect polarization modulation control with the low-cost HWPs made of polycarbonate, which were employed in the setup in terms of the instrumentation cost while sacrificing the performance
IP T
of polarization control. It should be noted that the influence of the imperfect polarization
modulation control can be suppressed by employing a high-quality HWPs in the polarization
SC R
modulation control unit, which will be carried out in future work with further precise and
careful alignments of optical components in the system. Figs. 16 and 17 summarize the
U
maximum amplitude of the grating structures subtracted from the AFM images at the positions A and C, respectively. As can be seen in the figures, the amplitude of grating
N
structures increased with the increase of the development time, as predicted in the results of
A
computer simulation. This tendency was clear especially for the grating structures fabricated
M
at the position A. It was also verified in the experiments that the grating structures with the
ED
amplitude of larger than 100 nm could be fabricated even at the position C, where the light intensity of the interference fringe field was far lower than that around the optical axis
PT
(position A). These results mean that the 2D grating structures can be fabricated over a large area of 100 mm×100 mm by the proposed compact non-orthogonal two-axis Lloyd’s mirror
CC E
interferometer. Meanwhile, on the other hand, the increase of the exposure time resulted in reducing the grating structure amplitude, especially at the position A. This phenomenon was
A
not predicted in the computer simulation. One of the possible reasons of this phenomenon was external disturbances such as thermal drifts of the optical components in the interferometer during the long-term exposure, although the developed non-orthogonal two-axis Lloyd’s mirror interferometer based on the division of wavefront system is considered to be more stable and robust against the external disturbances compared with the interference lithography based on division of amplitude system. 18
Finally, an exposure test over a large area of 100 mm×100 mm was carried out. A 100 mm×100 mm glass substrate was placed on the pattern exposure plane. The pattern exposure test was carried out with tExp of 1000 s, and the substrate was developed with tDev of 4 s. Figs. 18(a) and 18(b) show a photograph of the large substrate and optical microscopic images of the grating structures fabricated at each position on the glass substrate surface, respectively.
IP T
As can be seen in these figures, 2D grating structures were successfully fabricated over a large area of 100 mm×100 mm, which verified the feasibility of developed large-area
SC R
non-orthogonal two-axis Lloyd’s mirror interferometer.
U
5. Conclusions
A design study of the compact non-orthogonal two-axis Lloyd’s mirror interferometer for
N
fabrication of two-dimensional (2D) scale gratings over a large area of 100 mm×100 mm has
A
been carried out. To achieve a compact optical design for use in research laboratories, an
M
optical configuration of the non-orthogonal two-axis Lloyd’s mirror interferometer based on
ED
division of wavefront with the polarization modulation control has been employed, and the optical setup capable of being constructed on a commercially available general-purpose 1500
PT
mm×1000 mm vibration isolation table has successfully been designed. For fabrication of large-area 2D scale gratings, a laser beam from the laser source should be expanded by the
CC E
optical setup so that a collimated laser beam with a large diameter can be generated. In the case, the difference of the light intensity distribution on the grating surface could affect the
A
grating structures. Computer simulation has therefore been carried out to investigate the differences in the interference fringe field at the inner and outer positions on the interferometer. It has been verified that the contrast of the interference fringes will be almost uniform over the entire area of the grating surface; this fact implies the possibility of fabricating grating structures over an area of 100 mm×100 mm with the enhancement of stable and robust exposure realized by the optical setup based on the division of wavefront. It 19
should be noted that the developed non-orthogonal two-axis Lloyd’s mirror interferometer can also be employed as cost-effective manufacturing equipment in a production line for various types of large area 2D gratings. Meanwhile, the presented simulation algorithm is expected to accelerate the optimization of exposure and development processes for improving the fabrication efficiency of large area 2D gratings. Exposure tests have been carried out by using
IP T
the developed prototype compact non-orthogonal two-axis Lloyd’s mirror interferometer, and
the experimental results have demonstrated the feasibility of fabricating 2D scale gratings
SC R
over a large area of 100 mm×100 mm, which satisfies the target scale grating size of this research and is also a significant improvement compared with the 10 mm×10 mm size
U
achieved by the conventional orthogonal two-axis Lloyd’s mirror interferometer. The optimization of optical setup for fabricating uniform grating structures over the entire scale
A
M
process will be carried out in future work.
N
grating substrate surface, as well as the optimizations of exposure process and development
ED
Acknowledgements
References
Harrison GR. The Production of Diffraction Gratings I. Development of the Ruling Art.
CC E
[1]
PT
This research is supported by Japan Society for the Promotion of Science (JSPS).
J. Opt. Soc. Am. 1949;39(6):413–426. HEIDENHAIN Catalogue. Exposed Linear Encoders. 2014;AKLIP21.
[3]
Li X, Gao W, Muto H, Shimizu Y, Ito S, and Dian S. A six-degree-of-freedom surface
A
[2]
encoder for precision positioning of a planar motion stage. Precis. Eng. 2013;37(3):771–781.
[4]
HEIDENHAIN Catalogue. Two-coordinate encoders. 2016;PP281.
[5]
Gao W, Kim SW, Bosse H, Haitjema H, Chen YL, Lu XD, Knapp W, Weckenmann A, 20
Estler WT and Kunzmann H. Measurement technologies for precision engineering. CIRP Ann.-Manuf. Technol. 2015;64(2):773-796. [6]
Shimizu Y, Ito T, Li X, Kim WJ, Gao W. Design and Testing of a Four-probe Optical Sensor Head for Three-axis Surface Encoder with a Mosaic Scale Grating. Meas. Sci. Technol. 2014;25:09402. Hsieh
HL,
Pan
SW
six-degree-of-freedom
Development
displacement
of
and
a
grating-based
angle
interferometer
measurements.
Opt.
Gao
W.
Precision
Nanometrology
-Sensors
and
Nanomanufacturing. Springer 2010.
Measuring
Express.
Systems
for
Gao W, Araki T, Kiyono S, Okazaki Y, Yamanaka M. Precision nano-fabrication and
U
[9]
SC R
2015;23-3:2451-2465. [8]
for
IP T
[7]
N
evaluation of a large area sinusoidal grid surface for a surface encoder. Precis. Eng.
A
2003;27(3):289–298.
M
[10] Rogers JA, Paul KE, Jackman RJ, and Whitesides GM. Using an elastomeric phase mask for sub-100 nm photolithography in the optical near field. Appl. Phys. Lett.
[11] Pease
RF.
ED
1997;70(20):2658–2660.
Semiconductor
technology:
imprints
offer
Moore.
Nature
PT
2002;417(6891):802–803.
CC E
[12] Lu C, Lipson RH. Interference lithography: a powerful tool for fabricating periodic structures. Laser Photonics Rev. 2010;4(4):568–580.
[13] Brueck SRJ. Optical and Interferometric Lithography-Nanotechnology Enablers. Proc.
A
of the IEEE 2005;93(10):1704–1721.
[14] Kimura A, Gao W, Kim WJ, Hosono K, Shimizu Y, Shi L, Zeng LJ. A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement. Precis. Eng. 2012;36:576-585. [15] Konkola PT, Chen CG, Heilmann RK, Joo C, Montoya JC, Chang CH, and Schattenburg ML. Nanometer-level repeatable metrology using the Nanoruler, J. Vac. 21
Sci. Technol. B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 2003;21:3097-3101. [16] Chua JK, Murkeshan VM. Patterning of Two-Dimensional Nanoscale Features Using Grating-Based
Multiple
Beams
Interference
Lithography.
Physica
Scripta
2009;80(1):015401.
IP T
[17] Li X, Shimizu Y, Ito S, Gao W. Fabrication of Scale Gratings for Surface Encoders by
Using Laser Interference Lithography with 405 nm Laser Diodes. Int. J. Precis. Eng.
SC R
Manuf. 2013;14(11):1979–1988.
[18] Boor J, Geyer N, Gösele U, Schmidt V. Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning. Opt. Lett.
U
2009;34(12):1783–1785.
N
[19] Vala M, Homola J. Flexible method based on four-beam interference lithography for
A
fabrication of large areas of perfectly periodic plasmonic arrays. Opt. Express
M
2014;22(15):18778-19789.
[20] Shimizu Y, Aihara R, Zongwei R, Chen YL, Ito S, Gao W. Influences of misalignment
ED
errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer. Opt. Express 2016;24(24):17521-27535.
PT
[21] Ikjoo B, Joonwon K. Cost-effective laser interference lithography using a 405 nm
CC E
AlInGaN semiconductor laser. J. Micromech Microeng. 2010;20(5):055024. [22] Li X, Gao W, Shimizu Y, Ito S. A two-axis Lloyd’s mirror interferometer for fabrication of
two
dimensional
diffraction
gratings.
CIRP
Ann.
-Manuf.
Technol.
A
2014;63(1):461–464.
[23] Hecht E. Optics 5th Ed. Pearson 2017. [24] Austin S, Stone FT. Fabrication of thin periodic structures in photoresist: a model. Appl. Opt. 1976;15(4):1071-1074. [25] Meyerhofer D. Photosolubility of Diazoquinone Resists. IEEE Trans. Electron Dev. 1980;ED-21(5):921-926. 22
A
CC E
PT
ED
M
A
N
U
SC R
IP T
[26] Shipley. Microposit S1800 series photo resists. 2006;ME05N12, Rev.0
23
Figure captions Figure 1
Schematics of mirror-substrate assemblies for the two-axis Lloyd’s mirror interferometer (a) Orthogonal type (b) Non-orthogonal type Schematic of the orthogonal type of mirror-substrate assembly with the incident beam (the case where 0º is illustrated)
Schematic of the non-orthogonal type of mirror-substrate assembly with the incident beam
Figure 4
Mirror height and width required for fabricating grating structures with a
U
period g over an area of 100 mm×100 mm
N
(a) Required mirror height
A
(b) Required mirror width Figure 5
SC R
Figure 3
IP T
Figure 2
Schematic of the developed optical setup of the compact non-orthogonal
M
two-axis Lloyd’s mirror interferometer for fabrication of large-area 2D scale
ED
gratings
Geometric relationship among the direct beam, the X- and Y-beams
Figure 7
Intensity distributions of the incident light with a beam diameter D=387 mm
PT
Figure 6
over the interferometer and the interference fringe field at each position on
CC E
the substrate
Figure 8
A dissolution rate and a contrast curve of the photoresist (a) A dissolution rate of the exposed photoresist as a function of exposure
A
dose
(b) A contrast curve of the photoresist as a function of log dose normalized [26]
Figure 9
A schematic of the procedure of how to calculate surface form of the grating structures to be fabricated by the interference fringe fields generated by the non-orthogonal two-axis Lloyd’s mirror interferometer 24
Figure 10
Simulated height distributions of the 2D grating structures at the positions A, B and C in Fig. 6 (tExp=1000 s, tDev=4 s)
Figure 11
Relationship among the exposure time, development time and the maximum amplitude of grating structures
Figure 12
A photograph of the developed optical configuration for the large-scale
Figure 13
IP T
non-orthogonal two-axis Lloyd’s mirror interferometer Intensity distribution of the collimated laser beam generated in the
SC R
developed setup (a) Light intensity distribution estimated based on theory (b) Measured light intensity distribution
AFM images of the developed 2D grating structures
U
Figure 14
N
(a) Position A
Figure 15
A
(b) Position C
Cross-sectional images of the fabricated 2D grating structures
Amplitude of the fabricated grating structures at the position A
ED
Figure 16
M
(Position A, tExp=500 s, tDev=5 s)
(a) Variation due to tDev
Figure 17
PT
(b) Variation due to tExp Amplitude of the fabricated grating structures at the position C
CC E
(a) Variation due to tDev (b) Variation due to tExp
Figure 18
Fabricated grating structures over an area of 100 mm×100 mm on a large
A
glass substrate
(a) A photograph of the fabricated 2D scale grating (b) Microscopic images of the 2D grating structures at each position in (a)
25
A ED
PT
CC E
IP T
SC R
U
N
A
M
Figures:
26
27
A ED
PT
CC E
IP T
SC R
U
N
A
M
28
A ED
PT
CC E
IP T
SC R
U
N
A
M
29
A ED
PT
CC E
IP T
SC R
U
N
A
M
30
A ED
PT
CC E
IP T
SC R
U
N
A
M
31
A ED
PT
CC E
IP T
SC R
U
N
A
M
32
A ED
PT
CC E
IP T
SC R
U
N
A
M
33
A ED
PT
CC E
IP T
SC R
U
N
A
M
34
A ED
PT
CC E
IP T
SC R
U
N
A
M
Table captions
Table 1:
IP T
Required incident beam diameter and mirror size in the optical setup for fabricating grating structures with a grating period g=1 m over an area of 100 mm×100 mm under the condition
SC R
of =441.6 nm Orthogonal type
Non-orthogonal type
Angle of incidence of the collimated laser beam
18.2º
0º
Mirror angle with respect to the substrate
90º
Incident beam diameter
282.8 mm
N
282.8 mm
200 mm
100 mm
430.3 mm
395.8 mm
A
CC E
PT
ED
Mirror height
103.1º (=13.1º)
A
M
Mirror width
U
Items
35