- Email: [email protected]
A two-axis Lloyd's mirror interferometer for fabrication of two-dimensional diffraction gratings
G Model
CIRP-1110; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings Xinghui Li, Wei Gao (1)*, Yuki Shimizu, So Ito Department of Nanomechanics, Tohoku University, Sendai, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Interferometry Laser Structure
A new two-axis Lloyd’s mirror interferometer based on multi-beam interference is proposed. A square grating substrate with normal in the Z-axis is placed edge to edge with two rectangular mirrors with normals parallel to the XZ-plane (X-mirror) and the YZ-plane (Y-mirror), respectively. The angle between the substrate and each mirror is set to be larger than 908, so that the beams reflected by the mirrors can be superimposed with the direct beam at the substrate to produce two-dimensional (2D) diffraction grating structures in a single exposure. Sub-micron pitched 2D hole grating structures were fabricated and evaluated. ß 2014 CIRP.
1. Introduction One-dimensional gratings, also called line gratings [1], have long been used in physics and astronomy for study of spectra [2]. They have also been applied to the interferential optical encoder for displacement measurement as a possible alternative to the laser interferometer [3]. In a linear encoder for single axis measurement, a line grating with a grating period on the order of 1 mm is employed as the scale. A relative displacement of the scanning reading head with respect to the scale grating generates opposite phase shifts to the positive and negative first-order diffraction beams. The two beams are superimposed with each other to produce an interference signal with a signal period equal to half of the grating period, from which the displacement can be detected with a high resolution comparable to a laser interferometer [4]. In addition to the grating period, the depth of the line structures of the scale grating is also an important factor for directing most of the intensity of the illuminating laser light to the first-order diffraction beams used in generation of the interference signal. In recent years, the interferential optical encoder has been expanded for multi-axis measurement, which is referred to as the planar encoder. Instead of a line grating, a two-dimensional (2D) diffraction grating, which has a 2D array of diffracting elements of holes or posts aligned along the X- and Y-directions, is employed as the scale grating. Mask-based optical projection lithography is traditionally employed to manufacture the line scale gratings [5]. A short period of 0.55 mm has been reached for line gratings. However, the equipment used in the projection lithography as well as in the related electron-beam lithography for mask fabrication is extremely expensive, which can only be operated in large companies.
* Corresponding author. Tel.: +81 22 795 6951; fax: +81 22 795 6951. E-mail address: [email protected] (W. Gao).
The minimum grating period of a commercial 2D planar scale grating is also limited to several mm, resulting in a relatively large signal period [6]. To reduce the fabrication cost and the period of a 2D scale grating, it is expected to employ the mask-less laser interference lithography, which is much more cost-effective in fabricating periodic microstructures with a short grating period down to half of the laser light wavelength [7]. In the laser interference lithography, a laser light is split into two beams by a one-axis Lloyd’s mirror setup based on division of wavefront in a Lloyd’s mirror interferometer or by a prism or a diffraction grating based on division of amplitude in a Mach– Zehnder interferometer [7]. The equally spaced line interference fringes of the two beams are recorded by a photoresist layer coated on the surface of the grating substrate and then exposed to generate permanent line structures. A 2D hole or post structure can be generated by a second exposure process after rotating the grating substrate 908 [8]. The authors have employed the laser interference lithography for fabricating 2D scale gratings with a period of 1 mm for a red laser source [9] and those with a period of 0.57 mm for a blue-ray laser source [10]. However, the structures generated in the first exposure are influenced in the second exposure by the background light associated with the imperfection of the visibility of the interference fringes. As a result, the cross-sectional profiles along the X- and Y-directions will be different, which causes differences in the characteristics of the diffraction beams in the two directions. This is a fatal problem for 2D scale gratings. This paper presents a new multi-beam two-axis Lloyd’s mirror interferometer to solve the problems inherent in the double exposures technique for fabrication of 2D scale gratings. The proposed multi-beam setup is based on division of wavefront, which has shorter optical path differences and thus be more robust compared with the existing multi-beam techniques based on division of amplitude [11]. The principle of the two-axis interferometer and some experimental results of fabricating scale gratings with a period of 0.57 mm are described.
http://dx.doi.org/10.1016/j.cirp.2014.02.001 0007-8506/ß 2014 CIRP.
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
G Model
CIRP-1110; No. of Pages 4 2
X. Li et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
2. Principle of the two-axis Lloyd’s mirror interferometer Fig. 1 shows the principle of the Lloyd’s mirror interferometer. In a conventional one-axis Lloyd’s mirror setup shown in Fig. 1(a), a mirror, which is referred to as the X-mirror, is placed perpendicularly to the grating substrate [7]. Assume that the normals of the mirror and the substrate are parallel to the XZ-plane. The collimated incident laser light, which is assumed to have a rectangular sectional profile for clarity, is divided into two parts by the Lloyd’s mirror setup. One part of the laser light is directly projected onto the substrate. The other part is indirectly projected onto the substrate after being reflected by the mirror. The two beams interfere with each other to generate line interference fringes on the substrate coated with a layer of photoresist for recording the interference fringes after an exposure operation. The fringes are aligned along the X-direction with an equal period, which is referred to as the grating period. The period can be adjusted by rotating the entire Lloyd’s mirror setup about the Y-axis with respect to the incident laser. Three major modifications are made in the new two-axis Lloyd’s mirror setup shown in Fig. 1(b), so that the Lloyd’s mirror
interferometer can be used to fabricate 2D scale gratings in a single exposure. The first modification is to add a Y-mirror with normal parallel to the YZ-plane. As can be seen in the figure, the square substrate with normal in the Z-axis is placed edge to edge with the rectangular X- and Y-mirrors. Assume that the angle between the substrate and the X-mirror is denoted by 908 + ux and that between the substrate and the Y-mirror is denoted by 908 + uy. The second modification is to make polarization modulation by adding two half-wavelength plates (HWP1, HWP2) into the path of the incident laser light as shown in Fig. 1(b). The incident laser light with its optical axis along the Z-axis and its polarization direction along the Y-direction is assumed to have a uniform intensity distribution for simplicity. There are three sub-beams in the incident light directly or indirectly being projected onto the substrate. The sub-beams are referred to as the direct beam, the X-beam and the Ybeam, respectively. The direct beam is perpendicularly projected on the substrate over a square area indicated by ABCD after passing through HWP1. The length of each side of the square area is denoted by wd. The other two sub-beams reach the substrate after being reflected by the X- and Y-mirrors, respectively. The X-beam passes through HWP2 before it is reflected by the X-mirror. The Xdirectional width of the X-beam and the Y-directional width of the Ybeam are denoted by wx and wy, respectively. The third modification is to set ux and uy to be larger than 08 and less than 458 so that the three beams can overlap with each other on the substrate over ABCD to generate 2D interference fringes. The point A is takenastheoriginofthecoordinatesystem.ConsidertheintensityI(x,y) ofthe2DinterferencefringesatapointPwithcoordinatesof(x,y)onthe substrate. The light rays from the three sub-beams, whose intensities are denoted by Id0, Ix0, and Iy0, respectively, superimpose at P. Based on the theory of multi-beam interference [1], I(x,y) can be written as Iðx; yÞ ¼ I0 þ Idx þ Idy þ Ixy
(1)
where I0 ¼ Id0 þ Ix0 þ Iy0
(2)
pffiffiffiffiffiffiffiffiffiffiffiffi 2p x sin 2ux cos ddx Idx ¼ 2 Id0 Ix0 cos
l
Idy ¼ 2
qffiffiffiffiffiffiffiffiffiffiffiffi 2p Id0 Iy0 cos y sin 2u y cos ddy
l
qffiffiffiffiffiffiffiffiffiffiffi 2p 2p Ixy ¼ 2 Ix0 Iy0 cos y sin 2uy x sin 2ux cos dxy
l
l
(3) (4) (5)
Here, l is the wavelength of the laser light. ddx, ddy and dxy are the angles between the polarization directions of the corresponding light rays, respectively. Fig. 2 shows a cross-section of the two-axis Lloyd’s mirror setup along the XZ-plane. Based on the assumption of the uniform intensity distribution of the incident light and the geometry in Fig. 2, the following relationships can be obtained: wx ¼ wd cos 2ux wx Ix0 ¼ Id0 ¼ Id0 cos 2ux wd
Fig. 1. Principle of Lloyd’s mirror interferometer.
(6) (7)
A similar relationship between wd and wy, and that between Id0 and Iy0 can also be obtained. On the other hand, the angles between the fast axes of HWP1 and HWP2 with respect to the Y-axis are set to be 22.58 and 458, respectively. As can be seen in Fig. 1(b), the polarization direction of the direct beam after passing through HWP1 will have an angle of 458 with respect to the X-axis and that of the X-beam after passing through HWP2 will be along the X-axis. Accordingly, ddx, ddy and dxy will become 458, 458 and 908, respectively. The intensity I(x,y) of the 2D interference fringes under this condition can thus be rewritten as " # pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ cos 2ux þ cos 2uy þ 2 cos 2u x 2p pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2p Iðx; yÞ ¼ Id0 (8) cos l x sin 2ux þ 2 cos 2uy cos l y sin 2u y
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
G Model
CIRP-1110; No. of Pages 4 X. Li et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
3
Fig. 2. A cross-section of Fig. 1(b) along the XZ-plane.
Consequently, 2D grating structures along the X- and Ydirections can be generated simultaneously by the proposed two-axis Lloyd’s mirror interferometer. The X- and Y-directional grating periods can be written as gx ¼
l sin 2u x
;
gy ¼
l sin 2uy
(9)
It can be seen that the grating periods gx and gy can be set independently by adjusting ux and uy. Taking into consideration the characteristics of planar scale gratings, ux and uy are set to be the same value in the following section so that the periods as well as the amplitudes of the grating structures can be consistent in the X- and Ydirections. In this case, wx and wy are also equal to each other. Fig. 3(a) shows the normalized intensity distribution I(x,y)/Id0 of the 2D interference fringes with a grating period of 0.57 mm. The result without using the half-wavelength plates for polarization modulation is also shown in Fig. 3(b) for comparison. When no halfwavelength plates are used, the three sub-beams have the same polarization directions. As a result, ddx, ddy and dxy are all zero. The term Ixy shown in Eq. (5) will then remain in the intensity I(x,y) of the 2D interference fringes, which causes the generated grating structure to have an elliptical shape as shown in Fig. 3(b). In contrast, the term Ixy can be removed from I(x,y) by the polarization modulation technique with the half-wavelength plates. As shown in Fig. 3(a), this makes it possible to generate a round-shaped grating structure, whose symmetry property is appropriate for the planar scale grating. 3. Experiment Experiments were carried out to demonstrate the feasibility of the proposed two-axis Lloyd’s mirror interferometer. Fig. 4 shows the setup designed and constructed for the experiment. The grating period was determined to be 0.57 mm based on the specification of a planar encoder with a blue-ray laser source [10]. A single longitudinal mode HeCd laser, which is widely used in interference lithography, was chosen as the laser source. A transverse electromagnetic mode (TEM00) linearly polarized laser light with a radius of 0.6 mm was output from the laser source. The laser light had a wavelength of 441.6 nm and an output power of 150 mW. The laser spectral linewidth was 0.00065 nm, corresponding to a 300 mm coherence length. The laser light then passed through a beam-expanding unit, which was composed of an objective lens (L1) with a focal length of 4.48 mm, a pinhole with a diameter of 10 mm and a collimating lens (L2) with a focal length of 200 mm. The beam was expanded to have a diameter D of 62.6 mm at the position where L2 was located. The diameter of L2 was set to
Fig. 3. The intensity distributions of the interference patterns.
be 50 mm, which was smaller than D to exclude the outer area of the beam with low intensities. The exposure area was approximately 17 mm 17 mm in this initial experiment. The laser light from the beam-expanding unit was projected onto the grating substrate and the X-, Y-mirrors. The aluminiumcoated mirrors had a flatness of l/20 and a reflectivity of 95%. Inexpensive microscope glass slides with a length of 25 mm, a width of 20 mm and a thickness of 1 mm were employed as the grating substrates to reduce the cost of the experiment. The angle between the mirror and the substrate was set to be 115.48 for achieving the 0.57 mm grating period. It should be noted that setting of the grating period is not a critical issue for planar scale gratings since the resultant signal period of the planar encoder can be identified by calibration with a laser interferometer. In the fabrication experiment, the substrate was spin coated with a layer of an adhesion promoting agent with a thickness of 100 nm and then a layer of positive photoresist with a thickness of 700 nm. The substrate was exposed with the 2D interference pattern generated by the two-axis interferometer. The exposed grating substrate was developed by a NaOH solution with a volume concentration of 0.5%. Fig. 5 shows the fabricated grating structures imaged by a precalibrated Bruker AFM. The results with and without the polarization modulation are shown in Fig. 5(a) and (b), respectively. The exposure time and the development time, which were determined for hole structures by trial and error, are indicated in the figures. Only a part of the fabricated area is shown in each of the figures. It can be seen that the shapes of the fabricated structures are well consistent to the intensity distributions shown in Fig. 3. Round-shaped grating structures were successfully fabricated with the polarization modulation technique. The average and standard deviation of the grating period were evaluated to be 567 nm and 2 nm in Fig. 5(a), and 567 nm and 3 nm in
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
G Model
CIRP-1110; No. of Pages 4 X. Li et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
4
Fig. 4. The experimental setup.
Fig. 5(b), respectively. The average and standard deviation of the grating amplitude were evaluated to be 451 nm and 14 nm in Fig. 5(a) and 405 nm and 25 nm in Fig. 5(b), respectively. The difference between the amplitude values in Figs. 5(a) and (b) were caused by that of the intensity distributions. The diffraction efficiencies of the fabricated gratings over the fabricated area were also evaluated by scanning a 1.5 mm collimated beam from a 15 mW laser diode with a wavelength of 405 nm. The measurement pitch was 2 mm along the Xand Y-directions. The intensities of the transparent first-order diffraction beams were detected by using a photo-detector. The average and standard deviation of the diffraction efficiency of the positive first-order diffraction beam were evaluated to be 13.6% and 2.2% for the grating in Fig. 5(a), and 12.9% and 3.1% for the grating in Fig. 5(b), respectively. Those for the negative first-order diffraction beams were evaluated to be 13.2% and 2.5% for the grating in Fig. 5(a), and 8.7% and 3.3% for the grating in Fig. 5(b), respectively. It can be seen that diffraction efficiencies of the positive and negative first-order diffraction beams were more consistent with each other for the grating in Fig. 5(a) than that in Fig. 5(b), which is important for the scale grating. 4. Conclusions A two-axis Lloyd’s mirror interferometer has been proposed to fabricate scale gratings for planar encoders. The incident laser light is divided into three sub-beams by using two mirrors. The two mirror and the grating substrate are arranged in such a way that the three sub-beams can superimpose with each other on the grating substrate to form two-dimensional interference patterns as the grating structures for the scale grating. A polarization modulation technique with half-wavelength plates has been employed for removing the interference intensity term generated by the interference between the two sub-beams reflected by the two mirrors, which causes the generated grating structure to have an elliptical shape. Experiments have been carried out to demonstrate the feasibility of the proposed interferometer. An experimental setup has been
Fig. 5. The fabricated grating structures.
designed and constructed to fabricate 2D hole grating structures with a grating period of 0.57 mm. The pitch and amplitude as well as the diffraction efficiency of the fabricated grating have been evaluated. The results have indicated that the performance of the fabricated grating is satisfactory as a scale grating for a planar encoder. Further investigation including uncertainty analysis of the fabricated grating as well as improvement of the experimental setup and the fabrication process will be carried out in future work. References [1] Hecht E (2002) Optics, Addison-Wesley, San Francisco, CA. [2] Evans C (1981) Design and Construction of a Large Grating Ruling Engine. Precision Engineering 3(4):193–200. [3] Kunzmann H, Pfeifer T, Flugge J (1993) Scales vs. Laser Interferometers Performance and Comparison of Two Measuring Systems. CIRP Annals – Manufacturing Technology 42(2):753–767. [4] Teimel A (1992) Technology and Applications of Grating Interferometers in High-precision Measurement. Precision Engineering 14(3):147–154. [5] Brueck SRJ (2005) Optical and Interferometric Lithography-Nanotechnology Enablers. Proceedings of the IEEE 93(10):1704–1721. [6] Yagu¨e-Fabra JA, Valenzuela M, Albajez JA, Aguilar JJ (2011) A Thermally-Stable Setup and Calibration Technique for 2D Sensors. CIRP Annals – Manufacturing Technology 60(1):547–550. [7] Lu C, Lipson RH (2010) Interference Lithography: A Powerful Tool for Fabricating Periodic Structures. Laser & Photonics Review 4(4):568–580. [8] Byun IJ, Kim JW (2010) Cost-Effective Laser Interference Lithography Using a 405 nm AlInGaN Semiconductor Laser. Journal of Micromechanics and Microengineering 20(5):055024. [9] Kimura A, Gao W, Kim W, Hosono K, Shimizu Y, Shi L, Zeng L (2012) A SubNanometric Three-Axis Surface Encoder with Short-period Planar Gratings for Stage Motion Measurement. Precision Engineering 36(5):576–585. [10] Li X, Gao W, Muto H, Shimizu Y, Ito S, Dian S (2013) A Six-Degree-of-Freedom Surface Encoder for Precision Positioning of a Planar Motion Stage. Precision Engineering 37(3):771–781. [11] Chua JK, Murkeshan VM (2009) Patterning of Two-Dimensional Nanoscale Features Using Grating-Based Multiple Beams Interference Lithography. Physica Scripta 80(1):015401.
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
CIRP-1110; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings Xinghui Li, Wei Gao (1)*, Yuki Shimizu, So Ito Department of Nanomechanics, Tohoku University, Sendai, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Interferometry Laser Structure
A new two-axis Lloyd’s mirror interferometer based on multi-beam interference is proposed. A square grating substrate with normal in the Z-axis is placed edge to edge with two rectangular mirrors with normals parallel to the XZ-plane (X-mirror) and the YZ-plane (Y-mirror), respectively. The angle between the substrate and each mirror is set to be larger than 908, so that the beams reflected by the mirrors can be superimposed with the direct beam at the substrate to produce two-dimensional (2D) diffraction grating structures in a single exposure. Sub-micron pitched 2D hole grating structures were fabricated and evaluated. ß 2014 CIRP.
1. Introduction One-dimensional gratings, also called line gratings [1], have long been used in physics and astronomy for study of spectra [2]. They have also been applied to the interferential optical encoder for displacement measurement as a possible alternative to the laser interferometer [3]. In a linear encoder for single axis measurement, a line grating with a grating period on the order of 1 mm is employed as the scale. A relative displacement of the scanning reading head with respect to the scale grating generates opposite phase shifts to the positive and negative first-order diffraction beams. The two beams are superimposed with each other to produce an interference signal with a signal period equal to half of the grating period, from which the displacement can be detected with a high resolution comparable to a laser interferometer [4]. In addition to the grating period, the depth of the line structures of the scale grating is also an important factor for directing most of the intensity of the illuminating laser light to the first-order diffraction beams used in generation of the interference signal. In recent years, the interferential optical encoder has been expanded for multi-axis measurement, which is referred to as the planar encoder. Instead of a line grating, a two-dimensional (2D) diffraction grating, which has a 2D array of diffracting elements of holes or posts aligned along the X- and Y-directions, is employed as the scale grating. Mask-based optical projection lithography is traditionally employed to manufacture the line scale gratings [5]. A short period of 0.55 mm has been reached for line gratings. However, the equipment used in the projection lithography as well as in the related electron-beam lithography for mask fabrication is extremely expensive, which can only be operated in large companies.
* Corresponding author. Tel.: +81 22 795 6951; fax: +81 22 795 6951. E-mail address: [email protected] (W. Gao).
The minimum grating period of a commercial 2D planar scale grating is also limited to several mm, resulting in a relatively large signal period [6]. To reduce the fabrication cost and the period of a 2D scale grating, it is expected to employ the mask-less laser interference lithography, which is much more cost-effective in fabricating periodic microstructures with a short grating period down to half of the laser light wavelength [7]. In the laser interference lithography, a laser light is split into two beams by a one-axis Lloyd’s mirror setup based on division of wavefront in a Lloyd’s mirror interferometer or by a prism or a diffraction grating based on division of amplitude in a Mach– Zehnder interferometer [7]. The equally spaced line interference fringes of the two beams are recorded by a photoresist layer coated on the surface of the grating substrate and then exposed to generate permanent line structures. A 2D hole or post structure can be generated by a second exposure process after rotating the grating substrate 908 [8]. The authors have employed the laser interference lithography for fabricating 2D scale gratings with a period of 1 mm for a red laser source [9] and those with a period of 0.57 mm for a blue-ray laser source [10]. However, the structures generated in the first exposure are influenced in the second exposure by the background light associated with the imperfection of the visibility of the interference fringes. As a result, the cross-sectional profiles along the X- and Y-directions will be different, which causes differences in the characteristics of the diffraction beams in the two directions. This is a fatal problem for 2D scale gratings. This paper presents a new multi-beam two-axis Lloyd’s mirror interferometer to solve the problems inherent in the double exposures technique for fabrication of 2D scale gratings. The proposed multi-beam setup is based on division of wavefront, which has shorter optical path differences and thus be more robust compared with the existing multi-beam techniques based on division of amplitude [11]. The principle of the two-axis interferometer and some experimental results of fabricating scale gratings with a period of 0.57 mm are described.
http://dx.doi.org/10.1016/j.cirp.2014.02.001 0007-8506/ß 2014 CIRP.
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
G Model
CIRP-1110; No. of Pages 4 2
X. Li et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
2. Principle of the two-axis Lloyd’s mirror interferometer Fig. 1 shows the principle of the Lloyd’s mirror interferometer. In a conventional one-axis Lloyd’s mirror setup shown in Fig. 1(a), a mirror, which is referred to as the X-mirror, is placed perpendicularly to the grating substrate [7]. Assume that the normals of the mirror and the substrate are parallel to the XZ-plane. The collimated incident laser light, which is assumed to have a rectangular sectional profile for clarity, is divided into two parts by the Lloyd’s mirror setup. One part of the laser light is directly projected onto the substrate. The other part is indirectly projected onto the substrate after being reflected by the mirror. The two beams interfere with each other to generate line interference fringes on the substrate coated with a layer of photoresist for recording the interference fringes after an exposure operation. The fringes are aligned along the X-direction with an equal period, which is referred to as the grating period. The period can be adjusted by rotating the entire Lloyd’s mirror setup about the Y-axis with respect to the incident laser. Three major modifications are made in the new two-axis Lloyd’s mirror setup shown in Fig. 1(b), so that the Lloyd’s mirror
interferometer can be used to fabricate 2D scale gratings in a single exposure. The first modification is to add a Y-mirror with normal parallel to the YZ-plane. As can be seen in the figure, the square substrate with normal in the Z-axis is placed edge to edge with the rectangular X- and Y-mirrors. Assume that the angle between the substrate and the X-mirror is denoted by 908 + ux and that between the substrate and the Y-mirror is denoted by 908 + uy. The second modification is to make polarization modulation by adding two half-wavelength plates (HWP1, HWP2) into the path of the incident laser light as shown in Fig. 1(b). The incident laser light with its optical axis along the Z-axis and its polarization direction along the Y-direction is assumed to have a uniform intensity distribution for simplicity. There are three sub-beams in the incident light directly or indirectly being projected onto the substrate. The sub-beams are referred to as the direct beam, the X-beam and the Ybeam, respectively. The direct beam is perpendicularly projected on the substrate over a square area indicated by ABCD after passing through HWP1. The length of each side of the square area is denoted by wd. The other two sub-beams reach the substrate after being reflected by the X- and Y-mirrors, respectively. The X-beam passes through HWP2 before it is reflected by the X-mirror. The Xdirectional width of the X-beam and the Y-directional width of the Ybeam are denoted by wx and wy, respectively. The third modification is to set ux and uy to be larger than 08 and less than 458 so that the three beams can overlap with each other on the substrate over ABCD to generate 2D interference fringes. The point A is takenastheoriginofthecoordinatesystem.ConsidertheintensityI(x,y) ofthe2DinterferencefringesatapointPwithcoordinatesof(x,y)onthe substrate. The light rays from the three sub-beams, whose intensities are denoted by Id0, Ix0, and Iy0, respectively, superimpose at P. Based on the theory of multi-beam interference [1], I(x,y) can be written as Iðx; yÞ ¼ I0 þ Idx þ Idy þ Ixy
(1)
where I0 ¼ Id0 þ Ix0 þ Iy0
(2)
pffiffiffiffiffiffiffiffiffiffiffiffi 2p x sin 2ux cos ddx Idx ¼ 2 Id0 Ix0 cos
l
Idy ¼ 2
qffiffiffiffiffiffiffiffiffiffiffiffi 2p Id0 Iy0 cos y sin 2u y cos ddy
l
qffiffiffiffiffiffiffiffiffiffiffi 2p 2p Ixy ¼ 2 Ix0 Iy0 cos y sin 2uy x sin 2ux cos dxy
l
l
(3) (4) (5)
Here, l is the wavelength of the laser light. ddx, ddy and dxy are the angles between the polarization directions of the corresponding light rays, respectively. Fig. 2 shows a cross-section of the two-axis Lloyd’s mirror setup along the XZ-plane. Based on the assumption of the uniform intensity distribution of the incident light and the geometry in Fig. 2, the following relationships can be obtained: wx ¼ wd cos 2ux wx Ix0 ¼ Id0 ¼ Id0 cos 2ux wd
Fig. 1. Principle of Lloyd’s mirror interferometer.
(6) (7)
A similar relationship between wd and wy, and that between Id0 and Iy0 can also be obtained. On the other hand, the angles between the fast axes of HWP1 and HWP2 with respect to the Y-axis are set to be 22.58 and 458, respectively. As can be seen in Fig. 1(b), the polarization direction of the direct beam after passing through HWP1 will have an angle of 458 with respect to the X-axis and that of the X-beam after passing through HWP2 will be along the X-axis. Accordingly, ddx, ddy and dxy will become 458, 458 and 908, respectively. The intensity I(x,y) of the 2D interference fringes under this condition can thus be rewritten as " # pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ cos 2ux þ cos 2uy þ 2 cos 2u x 2p pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2p Iðx; yÞ ¼ Id0 (8) cos l x sin 2ux þ 2 cos 2uy cos l y sin 2u y
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
G Model
CIRP-1110; No. of Pages 4 X. Li et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
3
Fig. 2. A cross-section of Fig. 1(b) along the XZ-plane.
Consequently, 2D grating structures along the X- and Ydirections can be generated simultaneously by the proposed two-axis Lloyd’s mirror interferometer. The X- and Y-directional grating periods can be written as gx ¼
l sin 2u x
;
gy ¼
l sin 2uy
(9)
It can be seen that the grating periods gx and gy can be set independently by adjusting ux and uy. Taking into consideration the characteristics of planar scale gratings, ux and uy are set to be the same value in the following section so that the periods as well as the amplitudes of the grating structures can be consistent in the X- and Ydirections. In this case, wx and wy are also equal to each other. Fig. 3(a) shows the normalized intensity distribution I(x,y)/Id0 of the 2D interference fringes with a grating period of 0.57 mm. The result without using the half-wavelength plates for polarization modulation is also shown in Fig. 3(b) for comparison. When no halfwavelength plates are used, the three sub-beams have the same polarization directions. As a result, ddx, ddy and dxy are all zero. The term Ixy shown in Eq. (5) will then remain in the intensity I(x,y) of the 2D interference fringes, which causes the generated grating structure to have an elliptical shape as shown in Fig. 3(b). In contrast, the term Ixy can be removed from I(x,y) by the polarization modulation technique with the half-wavelength plates. As shown in Fig. 3(a), this makes it possible to generate a round-shaped grating structure, whose symmetry property is appropriate for the planar scale grating. 3. Experiment Experiments were carried out to demonstrate the feasibility of the proposed two-axis Lloyd’s mirror interferometer. Fig. 4 shows the setup designed and constructed for the experiment. The grating period was determined to be 0.57 mm based on the specification of a planar encoder with a blue-ray laser source [10]. A single longitudinal mode HeCd laser, which is widely used in interference lithography, was chosen as the laser source. A transverse electromagnetic mode (TEM00) linearly polarized laser light with a radius of 0.6 mm was output from the laser source. The laser light had a wavelength of 441.6 nm and an output power of 150 mW. The laser spectral linewidth was 0.00065 nm, corresponding to a 300 mm coherence length. The laser light then passed through a beam-expanding unit, which was composed of an objective lens (L1) with a focal length of 4.48 mm, a pinhole with a diameter of 10 mm and a collimating lens (L2) with a focal length of 200 mm. The beam was expanded to have a diameter D of 62.6 mm at the position where L2 was located. The diameter of L2 was set to
Fig. 3. The intensity distributions of the interference patterns.
be 50 mm, which was smaller than D to exclude the outer area of the beam with low intensities. The exposure area was approximately 17 mm 17 mm in this initial experiment. The laser light from the beam-expanding unit was projected onto the grating substrate and the X-, Y-mirrors. The aluminiumcoated mirrors had a flatness of l/20 and a reflectivity of 95%. Inexpensive microscope glass slides with a length of 25 mm, a width of 20 mm and a thickness of 1 mm were employed as the grating substrates to reduce the cost of the experiment. The angle between the mirror and the substrate was set to be 115.48 for achieving the 0.57 mm grating period. It should be noted that setting of the grating period is not a critical issue for planar scale gratings since the resultant signal period of the planar encoder can be identified by calibration with a laser interferometer. In the fabrication experiment, the substrate was spin coated with a layer of an adhesion promoting agent with a thickness of 100 nm and then a layer of positive photoresist with a thickness of 700 nm. The substrate was exposed with the 2D interference pattern generated by the two-axis interferometer. The exposed grating substrate was developed by a NaOH solution with a volume concentration of 0.5%. Fig. 5 shows the fabricated grating structures imaged by a precalibrated Bruker AFM. The results with and without the polarization modulation are shown in Fig. 5(a) and (b), respectively. The exposure time and the development time, which were determined for hole structures by trial and error, are indicated in the figures. Only a part of the fabricated area is shown in each of the figures. It can be seen that the shapes of the fabricated structures are well consistent to the intensity distributions shown in Fig. 3. Round-shaped grating structures were successfully fabricated with the polarization modulation technique. The average and standard deviation of the grating period were evaluated to be 567 nm and 2 nm in Fig. 5(a), and 567 nm and 3 nm in
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001
G Model
CIRP-1110; No. of Pages 4 X. Li et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx
4
Fig. 4. The experimental setup.
Fig. 5(b), respectively. The average and standard deviation of the grating amplitude were evaluated to be 451 nm and 14 nm in Fig. 5(a) and 405 nm and 25 nm in Fig. 5(b), respectively. The difference between the amplitude values in Figs. 5(a) and (b) were caused by that of the intensity distributions. The diffraction efficiencies of the fabricated gratings over the fabricated area were also evaluated by scanning a 1.5 mm collimated beam from a 15 mW laser diode with a wavelength of 405 nm. The measurement pitch was 2 mm along the Xand Y-directions. The intensities of the transparent first-order diffraction beams were detected by using a photo-detector. The average and standard deviation of the diffraction efficiency of the positive first-order diffraction beam were evaluated to be 13.6% and 2.2% for the grating in Fig. 5(a), and 12.9% and 3.1% for the grating in Fig. 5(b), respectively. Those for the negative first-order diffraction beams were evaluated to be 13.2% and 2.5% for the grating in Fig. 5(a), and 8.7% and 3.3% for the grating in Fig. 5(b), respectively. It can be seen that diffraction efficiencies of the positive and negative first-order diffraction beams were more consistent with each other for the grating in Fig. 5(a) than that in Fig. 5(b), which is important for the scale grating. 4. Conclusions A two-axis Lloyd’s mirror interferometer has been proposed to fabricate scale gratings for planar encoders. The incident laser light is divided into three sub-beams by using two mirrors. The two mirror and the grating substrate are arranged in such a way that the three sub-beams can superimpose with each other on the grating substrate to form two-dimensional interference patterns as the grating structures for the scale grating. A polarization modulation technique with half-wavelength plates has been employed for removing the interference intensity term generated by the interference between the two sub-beams reflected by the two mirrors, which causes the generated grating structure to have an elliptical shape. Experiments have been carried out to demonstrate the feasibility of the proposed interferometer. An experimental setup has been
Fig. 5. The fabricated grating structures.
designed and constructed to fabricate 2D hole grating structures with a grating period of 0.57 mm. The pitch and amplitude as well as the diffraction efficiency of the fabricated grating have been evaluated. The results have indicated that the performance of the fabricated grating is satisfactory as a scale grating for a planar encoder. Further investigation including uncertainty analysis of the fabricated grating as well as improvement of the experimental setup and the fabrication process will be carried out in future work. References [1] Hecht E (2002) Optics, Addison-Wesley, San Francisco, CA. [2] Evans C (1981) Design and Construction of a Large Grating Ruling Engine. Precision Engineering 3(4):193–200. [3] Kunzmann H, Pfeifer T, Flugge J (1993) Scales vs. Laser Interferometers Performance and Comparison of Two Measuring Systems. CIRP Annals – Manufacturing Technology 42(2):753–767. [4] Teimel A (1992) Technology and Applications of Grating Interferometers in High-precision Measurement. Precision Engineering 14(3):147–154. [5] Brueck SRJ (2005) Optical and Interferometric Lithography-Nanotechnology Enablers. Proceedings of the IEEE 93(10):1704–1721. [6] Yagu¨e-Fabra JA, Valenzuela M, Albajez JA, Aguilar JJ (2011) A Thermally-Stable Setup and Calibration Technique for 2D Sensors. CIRP Annals – Manufacturing Technology 60(1):547–550. [7] Lu C, Lipson RH (2010) Interference Lithography: A Powerful Tool for Fabricating Periodic Structures. Laser & Photonics Review 4(4):568–580. [8] Byun IJ, Kim JW (2010) Cost-Effective Laser Interference Lithography Using a 405 nm AlInGaN Semiconductor Laser. Journal of Micromechanics and Microengineering 20(5):055024. [9] Kimura A, Gao W, Kim W, Hosono K, Shimizu Y, Shi L, Zeng L (2012) A SubNanometric Three-Axis Surface Encoder with Short-period Planar Gratings for Stage Motion Measurement. Precision Engineering 36(5):576–585. [10] Li X, Gao W, Muto H, Shimizu Y, Ito S, Dian S (2013) A Six-Degree-of-Freedom Surface Encoder for Precision Positioning of a Planar Motion Stage. Precision Engineering 37(3):771–781. [11] Chua JK, Murkeshan VM (2009) Patterning of Two-Dimensional Nanoscale Features Using Grating-Based Multiple Beams Interference Lithography. Physica Scripta 80(1):015401.
Please cite this article in press as: Li X, et al. A two-axis Lloyd’s mirror interferometer for fabrication of two-dimensional diffraction gratings. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.02.001