Journal of Advanced Mechanical Design, Systems, and Manufacturing

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1 Bulletin of the JSME Journal of Advanced Mechanical Design, Systems, and Manufacturing Vol.1, No.5, 216 Investigation on the three-dimensional light intensity distribution of the fringe patterns generated by a modified two-axis Lloyd s mirror interferometer indi CAI*, inghui LI*, Ryo AIHARA*, Ren ONGWEI*, uki SHIMIU*, So ITO* and Wei GAO* *Department of Nanomechanics, Tohoku University Aramaki Aza-Aoba, Aoba-ku, Sendai, Miyagi , Japan yuki.shimizu@nano.mech.tohoku.ac.jp Received 26 February 216 Abstract This paper presents a design study of an optical configuration for the fabrication of a two-dimensional grating, which will be used as a scale in a planar encoder system. For the modified two-axis Lloyd s mirror interferometer, in which major modifications have been made to the conventional one-axis Lloyd s mirror interferometer, computer simulation is carried out based on wave optics. Three-dimensional light intensity distributions of the fringe patterns are calculated to investigate the effect of the polarization modulation. In addition, a relationship between the asymmetry of the cross-sectional profiles of the grating pattern structures and the designed grating pattern period is also investigated. Furthermore, pattern exposure tests have been carried out by using a prototype optical setup for the modified two-axis Lloyd s mirror interferometer. Key words : Grating, Interference lithography, Lloyd s mirror interferometer, Wave optics, Micro patterns 1. Introduction An ultra-precision position sensor is one of the key components to achieve high precision positioning required for the state-of-the-art instruments for fabrication of semiconductor devices (Erkorkmaz et al., 21). For such instruments having positioning systems with multi-degree-of-freedom (M-DOF) motion axes, several position sensors such as linear encoders or laser interferometers (Renishaw plc.) are often employed (Kunzmann et al., 1993). In recent, planar encoders have been developed for measurement of multi-degree-of-freedom motion of positioning systems. A commercially-available planar encoder has achieved two-dof in-plane translational motion measurement with accuracy of ±2 µm over the measurement range of 23 mm (Heidenhain GmbH). Furthermore, a recent research has revealed that simultaneous measurement of three-dof translational motion components (, and ) and three-dof rotational motion components (θ, θ and θ ) with the resolution of sub-nanometer and sub-arcsecond, respectively, is possible with a planar encoder system (Li et al., 213). One of the advantages of such a planar encoder is that the measurement system is complying with the Abbe principle (Bryan, 1979), which is important to achieve ultra-precision positioning for the next-generation precision instruments. In planar encoders, two-dimensional diffraction gratings, which have pattern structures with a constant period both in the - and -directions, are employed in their optical configurations for position measurement. Since the diffraction grating will be employed as a scale for measurement, uniformity of the grating period is important to assure the measurement accuracy. In addition, the measurement range of the planar encoder will be determined by the size of the scale grating. Therefore, large two-dimensional diffraction gratings having highly-uniform grating patterns are preferred to be fabricated for the planar encoders. Although ultra-precision diamond turning can fabricate complicated patterns with the help of a fast tool servo (FTS) technology for precision tool control (Dornfeld et al., 26), the two-dimensional diffraction grating, with a sub-micrometric grating period is difficult to be fabricated due to its Paper No

2 physical restriction on the tool tip size (Kimura et al., 27). The direct electron-beam (EB) drawing technique is another candidate for fabrication of two-dimensional grating pattern structures (Stepanova et al., 212). With the technique, a grating period up to several-ten nm can be fabricated. However, it costs too much time for fabrication of large-area grating required for the planar encoders. Meanwhile, on the other hand, interference lithography (IL), in which interference fringe patterns generated by superimposition of several coherent laser beams are transferred to a substrate surface, is suitable for the fabrication of two-dimensional micro-patterns (Shi et al., 29) due to its simple optical configuration. Especially, the Lloyd s mirror interferometer is one of the optical setups to be used in the interference lithography (Lu et al., 21). Based on the Lloyd s mirror interferometer, a modified optical setup for fabrication of two-dimensional micro-patterns has been proposed (Li et al., 214). With the employment of the polarization modulation technique, round-shaped grating structures have successfully been fabricated (Li et al., 214, Cai et al., 215). In this paper, further detailed investigations are carried out on the modified Lloyd s mirror interferometer. Based on the wave optics, three-dimensional intensity distribution of the fringe patterns on the exposure surface is simulated to further investigate the asymmetry of the grating pattern, which affects the diffraction efficiency of the two-dimensional diffraction gratings. Some experiments are also carried out to evaluate the diffraction efficiency of the diffraction gratings fabricated by the modified Lloyd s mirror interferometer. 2. Modified two-axis Lloyd s mirror interferometer An optical configuration of the modified Lloyd s mirror interferometer (Li et al., 214) is based on a conventional one-axis Lloyd s mirror interferometer (Lu et al., 21), a schematic of which is shown in Fig. 1(a). In the optical configuration, a flat mirror is aligned in such a way that its normal is parallel with that of a substrate, on which a thin photoresist layer is prepared for pattern exposure. As shown in the figure, collimated laser beam is made incident to the Point light source Collimating lens Flat mirror Direct beam Reflected beam Photoresist layer Photoresist layer (a) Conventional Lloyd s mirror interferometer Point light source Collimating lens -mirror Direct beam Reflected -beam -mirror Photoresist layer Photoresist layer (b) Modified multi-beam two-axis Lloyd s mirror interferometer Fig. 1 Optical configuration of the modified Lloyd s mirror interferometer for fabrication of two-dimensional micro patterns 2

3 interferometer so that a part of the laser beam directly incidents to the substrate surface (referred to as the direct beam) can interfere with that reflected from the flat mirror (referred to as the reflected beam). The period g of the interference fringes to be generated by the interferometer can be expressed as follows (Hecht, 22): g = λ sin 2θ (1) where λ is the light wavelength, and θ is the incident angle of the direct beam with respect to the normal of the substrate surface. For the fabrication of the two-dimensional micro-patterns, an innovation has been made to the optical configuration of the Lloyd s mirror interferometer. Figure 1(b) shows a schematic of the modified optical configuration referred to as the modified two-axis Lloyd s mirror interferometer (Li et al., 214). The -mirror, whose normal is aligned to be parallel with the -plane, is newly added to the conventional Lloyd s mirror interferometer. Another feature of the optical configuration is that the angles of the - and -mirrors with respect to the substrate surface (θ and θ, respectively,) are independently adjustable. This unique optical configuration allows the direct beam and the reflected beams from the - and -mirrors (referred to as the - and -beams, respectively,) to be superimposed on the substrate surface for simultaneous generation of one axis fringe patterns along both the - and -directions. Following Eq. (1), the - and -directional grating periods (g and g ) can be expressed by the following equations: g = λ sin 2θ, g = λ sin 2θ (2) The two-dimensional grating patterns can thus be fabricated with a single exposure by the modified two-axis Lloyd s mirror interferometer. In the optical configuration, the direct beam is parallel with the normal of the substrate surface, whereas the - and -beams are not. As a result, each pattern exposed by the modified two-axis Lloyd s mirror can be inclined as shown in Fig. 1(b). As can be seen in the figure, inclination angle of the exposed pattern will be affected not only by the incident angle of the - and -beams but also by the refractive index of the photoresist layer prepared on the substrate surface. In the following section, computer simulation is therefore carried out to further investigate the inclination of the exposed patterns. 3. Computer simulation on the three-dimensional intensity distribution of the fringe patterns Figure 2 shows a schematic of the optical configuration for the modified two-axis Lloyd s mirror interferometer with a pair of half wave plates (HWP1 and HWP2) for polarization modulation (Li et al., 214). In the optical configuration, the HWP1 is inserted into the optical path of the direct beam, while the HWP2 is inserted into the optical path of the -beam so that both the beam passed through the HWPs can have a different polarization direction with respect to the -beam. The direct beam and the - and -beams are made incident to the substrate surface coated with a photoresist layer, which has a certain amount of thickness. When a ray in the -beam is made incident to the photoresist layer surface with the angle of incidence θ, the angle of refraction θ can be expressed by the following equation (Hecht, 22): n θ ' = arcsin sin 2θ (3) n1 where n and n 1 are refractive indexes in air and the photoresist layer, respectively. In the same manner, the angle of refraction θ of the -beam in the photoresist layer can be expressed by using the angle of incidence θ as follows: n θ ' = arcsin sin 2θ (4) n1 Now we consider the interference among the three laser beams at the point P(x,y,. According to the geometric relationship, the optical path difference (OPD () ) between the lays in the direct beam and ()- beam intersecting with each other at point P can be expressed as follows: OPD = + 1 ( x, xsinθ z tanθ 'sinθ 1 cosθ ' OPD = + 1 ( y, ysinθ z tanθ 'sinθ 1 cosθ ' (5) (6) 23

4 Point light source -mirror Polarization direction -mirror HWP1 Collimating lens HWP2 -mirror Photoresist layer Direct beam Reflected -beam θ θ θ P(x,y, θ Reflected -beam Polarization control -mirror Interference among the three beams Fig. 2 Optical configuration of the modified Lloyd s mirror interferometer for fabrication of two-dimensional micro patterns Denoting the light intensity of the direct beam as I, on the assumption that the light intensity of the laser beam is uniform across the pupil plane of the collimating lens, the light intensity I(x,y, at the point P can be expressed as follows: I( x, y, = I ( 1+ cos 2θ + cos 2θ ) + 2I + 2I + 2I cos 2θ cos 2π OPD ( x, cosδ λ cos 2θ π cos 2 OPD ( y, cosδ d λ cos 2θ π cos 2θ 2 cos λ d ( OPD ( y, OPD ( x, ) cosδ where δ d, δ d and δ are the angles between the polarization directions of the corresponding light lays, respectively. The final term in Eq. (7) is a consequence of the interference between the - and -beams, resulting in the elliptical shape of the generated grating structure (Li et al., 214), which can be eliminated by controlling the polarization direction of each laser beam. Based on Eq. (7), the three-dimensional light intensity distribution in the two-dimensional interference pattern is simulated for the optical configuration without the polarization modulation (δ d =δ d =δ =º). Parameters used in the simulation are summarized in Table 1. Figure 3(a) shows the perspective view of the calculated light intensity distribution, and Fig. 3(b) shows its cross-section image. The intensity distributions in -coordinate at the -position of nm and 4 nm are also plotted in Fig. 3(c) and 3, respectively. As can be seen in the figures, elliptical fringe patterns due to the influence of the final term in Eq. (7) are observed. In the same manner, the three-dimensional light intensity distribution in the two-dimensional interference pattern is simulated for the optical configuration with the polarization modulation. Figure 4 shows the results. In the figure, the calculated intensity distribution in the case of δ d =δ d =45º and δ =9º is plotted. As can be seen in Fig. 4(a), 4(c) and 4, round-shaped fringe patterns are observed. These results indicate that the polarization modulation is effective in improving the symmetry property of the two-axis grating. Meanwhile, as can be seen in Fig. 4(b), the fringe patterns are found to be inclined in the - and -planes, as same as the case without polarization modulation shown in Fig. 3(b), which is due to the asymmetry of the laser beams incident to the photoresist layer surface. In the modified two-axis Lloyd s mirror interferometer, the pattern period can be controlled by changing the angle of incidence of the - and -beams. The three-dimensional light intensity distribution of the interference fringe generated by the modified Lloyd s mirror interferometer is simulated for each grating period g. Figure 5 shows the results. As can be seen in Table 1 Parameters used in the simulation Parameter Value Unit Wavelength (λ) 442 [nm] Refractive index in air (n ) 1. - Refractive index in the photoresist layer (n 1 ) (7) 24

5 A (a) (c) Intensity High A (b) A A nm nm nm Low nm nm Fig. 3 Light intensity distribution of the fringe patterns calculated based on the optical configuration for the modified Lloyd s mirror interferometer without the polarization modulation (δ D = δ D = δ =º). (a) Three-dimensional light intensity distribution; (b) Cross section (-plane) of the light intensity distribution in (a); (c) Light intensity distribution in the -plane (= nm); Light intensity distribution in the -plane (=4 nm). A (a) (c) Intensity High A (b) A A nm nm nm Low nm nm Fig. 4 Light intensity distribution of the fringe patterns calculated based on the optical configuration for the modified Lloyd s mirror interferometer with the polarization modulation (δ D = δ D =45º, δ =9º). (a) Three-dimensional light intensity distribution; (b) Cross section (-plane) of the light intensity distribution in (a); (c) Light intensity distribution in the -plane (= nm); Light intensity distribution in the -plane (=4 nm). the figure, the inclination angle of the fringe patterns in the - and -planes is found to become larger as the decrease of g. According to Eq. (2), angles of incidence θ and θ are required to be large for small g. Regarding Eqs. (3) and (4), larger incident angles lead to larger angles of refraction θ and θ, resulting in the larger inclination angle of the fringe patterns. Furthermore, it is also verified that the high contrast fringe patterns are to be generated only in the shallow depth region of the photoresist layer in the case of small g. These results imply that the optimization of the photoresist layer thickness is also important for the fabrication of two-dimensional micro patterns with the pattern period of smaller than 1 µm. 25

6 (a) (b) (c) Intensity High Low nm nm Fig. 5 Light intensity distribution of the fringe patterns calculated based on the optical configuration for the modified Lloyd s mirror interferometer with the polarization modulation (δ D = δ D =45º, δ =9º) for each designed grating period g. (a) g=.5 µm; (b) g=.57 µm; (c) g=1. µm; g=2. µm; nm nm 4. Two-dimensional grating pattern fabrication by the modified Lloyd s mirror interferometer Following the computer simulation in the previous section, some experiments were carried out by using the modified Lloyd s mirror interferometer. Figure 6 shows a schematic of the experimental setup developed for the two-dimensional grating pattern fabrication (Li et al., 214, Cai et al., 215). As a light source for the interferometer, HeCd laser generating linearly polarized laser light with a wavelength of nm was employed. In the setup, a commercial spatial filter consisting of a lens and a pinhole was used to clean up the laser beam. After collimating the laser beam from the spatial filter, the laser beam was made incident to the modified Lloyd s mirror interferometer. In the optical paths of the direct beam and the -beam, HWP1 and HWP2 were placed, respectively, so that the polarization directions of each beam could be controlled. A glass substrate coated with a photoresist layer, a thickness of which was controlled to be approximately 4 nm, was then exposed by the generated two-dimensional interference fringes. Finally, the exposed photoresist was developed by using NaOH solution with the volume concentration of.5%. -mirror HWPs From HeCd Laser (λ=441.6 nm) -Mirror Spatial filter Collimating lens Fig. 6 A schematic of the experimental setup for the modified Lloyd s mirror interferometer (Cai et al., 215) (a) (b) A A (c) Height 1 nm/div A (Inclination angle calculated by Eq. (3)) A 3 position 5 nm/div. Fig. 7 Fabricated two-dimensional micro patterns measured by the AFM. (a) Micropattern fabricated without the polarization modulation; (b) Micro-pattern fabricated with the polarization modulation; (c) Cross-section of the patter profile in (b). The pattern period was designed to be.57 µm for the use of a planar encoder system. 26

7 Figure 7(a) shows the profile of the two-dimensional micro patterns fabricated without the polarization modulation. The profile was measured by using an AFM (atomic force microscope). As predicted in the computer simulation, the grating pattern structures were found to be in the elliptical shape. On the other hand, as can be seen in Fig. 7(b), the distortion of the grating pattern structure was successfully eliminated by applying the polarization modulation. Two-dimensional micro patterns with constant period of 567 nm, which was close to the designed period of 57 nm, were successfully obtained. The pattern period deviation was calculated to be 2.4 nm in the -direction and 2.3 nm in the -direction. Figure 7(c) shows the cross-section of the grating pattern structures shown in Fig. 7(b). The grating pattern structures were found to be slightly inclined, as indicated in the results of the computer simulation. Diffraction efficiencies of the fabricated grating pattern structures were also evaluated in experiments. Figure 8 shows a photogragh of the setup prepared for the experiments. The setup consists of a laser source, optical isolator consisting of a PBS and a QWP, the fabricated two-dimensional grating mounted on a manual stage system, and a screen. As the laser source, a laser diode (LD) with a wavelength of 45 nm was employed. The collimated laser beam from the LD was made to pass the optical isolator, and was made incident to the two-dimensional grating. Since the grating pattern structures were fabricated on a thin glass plate, the grating acted as a transparent grating. As can be seen in the figure, ±1st order diffracted beams were generated in both the - and -directions. By measuring the intensity of each diffracted beam, the diffraction efficiencies of the fabricated two-dimensional gratings were evaluated. Figure 9 shows the results. In the case of the two-dimensional grating fabricated without the polarization modulation, large difference was found between the diffraction efficiencies of the negative and positive 1st-order diffracted beams. Meanwhile, on the other hand, the difference was small in the case of the two-dimensional grating fabricated with the polarization modulation. A slight difference between the positive and negative directions is considered to be due to the asymmetric cross-sectional profiles of the fabricated grating structures. Further improvement of the proposed two-axis Lloyd s mirror interferometer for fabrication of the two-dimensional grating with symmetric cross-sectional profiles will be carried out as future work. PBS+QWP Grating +1 Laser source Plate +1 Manual stage -1 Fig. 8 Experimental setup for evaluation of the diffraction efficiency of the fabricated two-dimensional micro-patterns. Diffraction efficiency % Positive 1 st -order Negative 1 st -order Without polarization control Positive 1 st -order Negative 1 st -order With polarization control Fig. 9 Diffraction efficiency of the fabricated two-dimensional micro-patterns. 27

8 5. Conclusion For the modified two-dimensional Lloyd's mirror interferometer having a pair of mirrors for simultaneous exposure of the two-dimensional grating pattern structures, computer simulation has been carried out. The three-dimensional intensity distribution of the interference fringe to be generated by the modified Lloyd s mirror interferometer has been simulated based on wave optics, and the effect of the polarization modulation employed in the modified interferometer has been verified. The computer simulation results have also revealed that the asymmetric cross-sectional profiles of the fabricated grating structures could occur especially when the grating period is designed to be smaller than 1 µm. Furthermore, the optimization of the photoresist layer thickness is also important for the fabrication of the two-dimensional micro patterns with such short pattern period. Exposure tests have also been carried out to verify the feasibility of the developed optical configuration for the two-axis Lloyd s mirror interferometer with the polarization modulation of the laser beam. Further investigations including uncertainty analysis of the fabricated grating, as well as the improvement of the cross-sectional profiles of the fabricated pattern will be carried out as future work. Acknowledgement This project was supported by Japan Society for the Promotion and Science (JSPS). References Bryan, J.B., The Abbe principle revisited: An updated interpretation, Precision Engineering, Vol.1 (1979), pp Cai,., Li,., Aihara, R., Shimizu,., Ito, S., Gao, W., Laser interference lithography with a modified two-axis Lloyd s mirror interferometer for fabrication of two-dimensional micro patterns, Proceedings of the 8th International Conference on Leading Edge Manufacturing in 21st Century (LEM21), Kyoto (215). Dornfeld, D., Min, S., Takeuchi,., Recent advances in mechanical micromachining, CIRP Annals-Manufacturing Technology, Vol.55, No.2 (26) pp Erkorkmaz, K., Gorniak, J.M., and Gordon, D.J., Precision machine tool - stage utilizing a planar air bearing arrangement, CIRP Annals-Manufacturing Technology, Vol.59, No.1 (21), pp Gao, W., Precision Nanometrology, Springer, London (21). Hecht, E., Optics, Addison-Wesley, San Francisco, CA. (22). Kimura, A., Gao, W., Kiyono, S., Design and construction of a surface encoder with dual sine-grids, International Journal of Precision Engineering and Manufacturing, Vol.8, No.2 (27), pp Kunzmann, H., Pfeifer, T., Flugge, J., Scales vs laser interferometers, performance and comparison of two measuring systems, CIRP Annals-Manufacturing Technology, Vol.42, No.2 (1993), pp KGM 181 and KGM 182 grid encoders. Heidenhain GmbH. Laser Encoder. plane mirror systems: L B data sheet. Renishaw plc. Li,., Gao, W., Muto, H., Shimizu,., Ito, S., Dian, S., A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage, Precision Engineering, Vol.37, No.3 (213), pp Li,., Gao, W., Shimizu,., Ito, S., A two-axis Lloyd s mirror interferometer for fabrication of two-dimensional diffraction gratings, CIRP Annals-Manufacturing Technology, Vol.63, No.1 (214), pp Lu, C., Lipson, R.H., Interference Lithography: A Powerful Tool for Fabricating Periodic Structures, Laser & Photonics Review, Vol.4, No.4 (21), pp Shi, L., eng L.J., and Li L.F., Fabrication of optical mosaic gratings with phase and attitude adjustments employing latent fringes and a red-wavelength dual-beam interferometer, Optics Express, Vol.17, No.24 (29), pp Stepanova, M., Dew, S., Nanofabrication, Springer, Wien (212). 28