李 星輝

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博士学位論文の要旨及び審査結果の要旨 (Summary of Thesis(DR))othe

李, 星輝

Tohoku University Repository (TOUR) / 東北大学機関リポジトリ

Fabrication of Scale Gratings and Applicationto Surface Encoders著者 李 星輝号 59学位授与機関 Tohoku University学位授与番号 工博第4996号URL http://hdl.handle.net/10097/62819           り せい き  氏 名          李 星 輝  授 与 学 位          博士（工学） 学位授与年月日          平成２６年９月２４日 学位授与の根拠法規 学位規則第4条第1項 研究科，専攻の名称 東北大学大学院工学研究科（博士課程）ナノメカニクス専攻 学 位 論 文 題 目          Fabrication of Scale Gratings and Application to Surface Encoders (スケール格子の製作とサーフェスエンコーダへの応用) 指 導 教 員 東北大学教授 高 偉 論 文 審 査 委 員          主査 東北大学教授 高 偉 東北大学教授 羽根 一博              東北大学教授 桑野 博喜 東北大学准教授 清水 裕樹 論 文 内 容 要 旨          This dissertation presents the fabrication of scale gratings and development of optical sensor heads for position and error motions measurement of precision stages. Inexpensive and compact 405 nm blu-ray laser diodes (LD) have been employed in a laser interference lithography (LIL) system for achievement of a cost-effective fabrication of one-axis sub-micron short pitched scale gratings. A three-beam Lloyd’s mirror interferometer has been developed for production of two-axis gratings patterns with high pattern uniformity. A unique optical sensor head allowing a simultaneous measurement of six-DOF planar motions has been developed with using two-axis scale gratings. Both the basic performances and uncertainty of the surface encoder have been systematically investigated. In Chapter 1, the background, motivations and tasks of this research are presented. Precision stages have been widely used in today’s nanofabrication and nanometrology, such as precision machining, semiconductor manufacturing, scanning probe microscopy, and so forth. Two trends of the precision stages are ultra-precision linear stage and multi-degree-of-freedom (MDOF) planar stage. The ultra-precision linear stage is typically required to offer nanometric position accuracy to move a machining tool or a scanning probe for ultra-precision machining or metrology. The MDOF planar stage is typically required to have long motion strokes in the primary XY plane larger than 10 mm × 10 mm and a small amount of Z-directional motion in the order of 100 m associated with sub-micron positioning resolutions. Position sensors are then indispensible for both the two types of precision stages to conduct a closed-loop control. In addition to measurement of the position, small amounts of translational and angular error motions are also required to be detected for position compensation or tracking. In contrast to conventional position and error motions measurement by using multiple sensor systems, the state-of-the-art two-axis linear encoder, three-axis planar surface encoder and three-axis autocollimator offer better solutions for these measurement requirements mentioned above. However, there are still some problems and challenges existing in the state-of-the-art sensors. The surface encoder developed for measurement of three-axis translational motions and the three-axis autocollimator for ? 26 ?measurement of three-axis angular error motions cannot measure the same point, resulting in Abbe error. Fabrication of the scale gratings, which are used as the measurement standard in the surface encoder, is challenged both by the cost and limitations of conventional fabrication system.  Thus, the motivation of this research is to solve the problems in these state-of-the-art position sensors for the precision stages. The motivation is specified to be three detailed tasks. Aiming for the requirement of nanometric positioning resolution, fabrication of one-axis sub-micron short pitch scale gratings for the newly developed two-axis linear encoder is set to be the first task. Cost-effectiveness of the fabrication is of the highest priority. Aiming for the simultaneous measurement of three-axis translational motions for the MDOF planar stage, fabrication of two-axis scale grating for the planar surface encoder is set to be the second task. High pattern uniformity in the two axes of the scale grating is of the first pursuit. Aiming for a six-DOF positions and error motions measurement with high accuracy and inexpensive instruments, development of a six-DOF surface encoder by combination of the three-axis planar surface encoder and the three-axis autocollimator to achieve a simultaneous six-DOF measurement with a single sensor head and a same measurement point is the third task. Efforts and achievements for these three tasks are discussed carefully in this dissertation as below. In Chapter 2, a cost-effective and compact fabrication method has been proposed for fabrication of scale grating. A maskless lithography process called laser interference lithography (LIL) system is employed as the fabrication tool. In LIL, a collimated light source is divided by a Lloyd’s mirror interferometer into two halves and recombined, forming a periodic intensity pattern that is then recorded by exposing a photosensitive substrate. The periodic interference pattern is finally transferred onto the substrate after developing the exposed substrate. The Lloyd’s mirror interferometer is composed of a mirror and a substrate with photoresist coating. The mirror and the substrate mounted on a rotary stage are placed perpendicularly with each other and with their intersection line perpendicularly passing through the centre of the rotation stage. The centre of the rotary stage is aligned on the beam axis of the laser source. Thus, the periodicity of the interference intensity is only determined by the angle between the mirror and the beam axis that can be adjusted by rotating the rotary stage. The minimum value of the grating pitch in LIL could reach half of the wavelength, i.e. approximately 203 nm when a 405 nm blu-ray laser source was used, which allows a small signal periodicity that is desired in a measurement resolution of nanometre or sub-nanometre. Due to the wavefront-splitting configuration, the constructive and destructive interference pattern is rather stable, which allows a high-resolution grating structure. Both the fabrication cost and the system space of LIL technology have been greatly reduced by using inexpensive and compact 405 nm blu-ray laser diodes (LD). The fabrication system based on Lloyd’s mirror interferometer with using blu-ray LDs has been constructed within a compact volume of 400 mm (L) × 300 mm (W) × 250 mm (H). A low-cost multimode LD used in blu-ray laser drive and a single-mode LD with an external mode selective cavity have been employed as the lasers sources one after another. The multimode LD with a temporal coherence length Lc of around 0.68 mm successfully fabricated a 570-nm pitched continuous grating pattern covering a width of 2 mm with a high pattern ? 27 ?resolution. And the single-mode LD with an Lc of more than 1 m greatly expanded the width of continuous grating pattern that could be theoretically up to meter-order. Finally, a continuous one-axis grating pattern with high-resolution 570 nm pitch was successfully fabricated over an area of larger than 300 mm2. In Chapter 3, a new mechanism called three-beam Lloyd’s mirror interferometer for fabrication of two-axis scale gratings by means of multiple-beam interference lithography has been proposed, constructed and evaluated. The interferometer is composed of a square grating substrate with photoresist coating and two rectangular mirrors. The substrate with normal in the Z-axis is placed edge to edge with the two mirrors with normals parallel to the XZ-plane (X-mirror) and the YZ-plane (Y-mirror), respectively. A linearly polarized incident laser light is divided into three sub-beams by the two-axis Lloyd’s mirror, which are then projected onto the substrate and the two mirrors, respectively. The angle between the substrate and each mirror is set to be larger than 90 degrees so that the beams reflected by the mirrors can be superimposed with the direct beam at the substrate to produce two-axis grating structures in a single exposure. 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 verified the capabilities and advantages of the proposed interferometer in fabrication of two-axis scale gratings. An experimental setup has been designed and constructed to fabricate two-axis hole grating structures over an area of 17 mm  17 mm with a grating period of 570 nm in two orthogonal axes. Evaluation with an atomic force microscope (AFM) revealed that the average pitch and standard deviation were evaluated to be 567 nm and 2 nm, respectively. The average amplitude and standard deviation were evaluated to be were and 451 nm and 14 nm, respectively. The diffraction efficiency of the fabricated grating was evaluated by detecting the intensities of the transparent first-order diffraction beams. 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%, respectively. Those for the negative first-order diffraction beams were evaluated to be 13.2% and 2.5%, respectively. The results have indicated that the performance of the fabricated grating can meet the requirements of scale gratings for a planar encoder. In Chapter 4, an optical sensor called surface encoder that allows a simultaneous measurement of six-degree-of-freedom (six-DOF) planar motions has been developed. The six-DOF surface encoder is composed of a scale grating and an optical sensor head, which would be mounted on the moving element and stage base of an XY surface motor stage, respectively. The six-DOF measurement has been realized by combining a three-axis displacement sensor and a three-axis autocollimator in a simple manner through sharing the same laser source. The three-axis displacement sensor is constructed in a Michelson interferometer configuration while the reference mirror and moving mirror are replaced by a two-axis reference grating and a two-axis scale grating, respectively. Thus, apart from the superimposition of the reflected beams, the first order diffraction beams from these two gratings also superimpose with each other and the other four pieces of interference signals are generated. Three-axis translational motions (x, y, z) of the scale grating can be simultaneously obtained from the four signals. The ? 28 ?three-axis autocollimator is developed based on laser autocollimation. The scale grating here is used as the reflective target. The zero-th order diffraction beam is employed to measure the pitching and yawing by the same manner as that of conventional laser autocollimator, in which one of the four first order diffraction beam was innovatively employed for detection of the rolling of the scale grating.  Efforts have been made to design and construct the sensor head with a compact size of 95 mm (X) × 90 mm (Y) × 25 mm (Z) so that it can fit into an XY surface motor stage with two primary axes of motion (x, y) for precision positioning and four secondary axes of motion (z, x, y, z) for compensation of error motions with sub-micrometer/sub-arcsecond resolutions. The grating period and grating area of the planar grating were designed and fabricated to be 0.57 m and 60 mm (X) × 60 mm (Y), which dominate the resolution and measurement range in the X- and Y-directions, respectively. Experiments have been carried out to test the basic performances of the constructed six-DOF surface encoder. It has been verified that the surface encoder could distinguish 2 nm step motions in the x-, y- and z-directions, 0.1 arcsecond step motions in the x- and y-directions, 0.3 arcsecond step motion in the z-direction. The peak-to-valley amplitudes of the interpolation errors were approximately ±6 nm, ±7 nm and ±6 nm in the X-, Y- and Z-directions, respectively. The nonlinear error components were approximately 2.2 arcseconds, 1.4 arcseconds and 2.5 arcseconds for x, y and z, respectively. It should be noted that the error components can be reduced by a compensation process.  In Chapter 5, the measurement uncertainty of the surface encoder has been systematically investigated to confirm its feasibility for precision measurement of six-DOF planar motions as well as to reveal the largest uncertainty source for the surface encoder. Sources of uncertainties regarding the interpolation errors in position derivation, system stability in terms of environmentally thermal drift, misalignment factors among the scale grating, reading head and the stage and stability of the light source were considered. An uncertainty budget was summarized and a combined standard uncertainty of the developed six-DOF surface encoder was lastly calculated. Measurement results in testing of six-DOF translational motions and angular motions of the six-DOF surface encoder have been systematically evaluated in uncertainty. An expanded uncertainty of 124.4 nm has been calculated in the measurement results of testing three-axis translational motions over a travel range of 2.5 m. An expanded uncertainty of 3.8 arcseconds has been evaluated in the measurement results of testing three-axis angular motions over a travel range of ±30 arcseconds. Periodic cross-talk error components have been observed in the angular outputs, which were caused by the polarization leakage in the optical paths of the diffraction beams. The cross-talk errors of the surface encoder outputs were identified to be the largest uncertainty source for the surface encoder. Optimization of the optical design of the surface encoder has then been proposed to eliminate the cross-talk errors. In Chapter 6, conclusions and achievements of this dissertation are discussed. ? 29 ?? 30 ?

Fabrication of Scale Gratings and Application to Surface Encoders

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スケール格子の製作とサーフェスエンコーダへの応用

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