WO2007133011A1

WO2007133011A1 - Method and apparatus for detecting in-plane position in a planar stage by measuring air gap displacement

Info

Publication number: WO2007133011A1
Application number: PCT/KR2007/002317
Authority: WO
Inventors: Kwang Suk Jung; Eui Sang Park; Keun Soo Ban; Jun Kyu Park; Sang Heon Lee
Original assignee: Chungju National University Industry-Academic Cooperation Foundation
Priority date: 2006-05-12
Filing date: 2007-05-10
Publication date: 2007-11-22
Also published as: KR100671241B1

Abstract

Disclosed are an apparatus and a method for detecting an in-plane position in a planar stage, and more particularly to a method and an apparatus for measuring displacement along 3 axes of the planar stage capable of implementing 2-axis motion and yaw motion of a moving unit. According to the present invention, the method and the apparatus are capable of measuring planar motion along two axes and rotational motion of a moving unit as much as tens of degrees, by measuring air gaps of platens processed in respectively different slope gradients and operated associatively with the moving unit and detecting the in-plane position indirectly through conversion relations, in order to finally detect planar displacement, that is, in-plane positions (x, y, ϑ) on a planar stage performing 2-dimensional motion by linear motors arranged in a grid form on a fixed base.

Description

METHOD AND APPARATUS FOR DETECTING IN-PLANE POSITION IN A PLANAR STAGE BY MEASURING AIR GAP

DISPLACEMENT

Technical Field

[1] The present invention relates to a method and an apparatus for detecting an in-plane position in a planar stage by measuring air gap displacement. More particularly, the present invention relates to a method and an apparatus for measuring displacement along 3 axes of the planar stage capable of implementing 2-axis motion and yaw motion of a moving unit. Background Art

[2] A planar stage is one of essential equipment used in a wafer stepper for exposure of semiconductors, various measuring devices such as an electron microscope, and inspection devices such as a thin film transistor-liquid crystal display (TFT-LCD). In order to reduce the cost in manufacturing a wafer as large as 12 inches and the TFT- LCD using multi-panel technology, relevant companies are conducting researches on a stage having a larger work area. Accordingly, a sensor for measuring position of the stage and feeding back the measurement result has been demanded to operate even in more extreme conditions.

[3] FIG. 1 shows the structure of a conventional planar stage for detecting an in-plane position using laser interference, as disclosed in KR Patent Registration No. 10-0193153.

[4] Referring to FIG. 1, linear motors 2, 3, 2 and 3 on a base 1 generates y-axis motion of a platen 5 for exposure. Another linear motor 4 arranged perpendicularly to the linear motors 2 and 3 generates x-axis motion of a platen 5. The linear motor 4 is mounted with a platen 5 for exposure. Displacement of the platen 5 along the x-axis and the y-axis is measured using interference among laser beams projected to an L- shape mirror 9 disposed on the platen 5.

[5] FIG. 2 shows another related art, that is, the structure of a laser interferometer for detecting in-plane positions (x, y, θ) of a general ultra-precision planar stage, which is disclosed in KR Patent Registration No. 10-0193253 and applied to a surface motor by Holmes (refer to pp. 191-209, Vol. 24, Precision engineering, 2000).

[6] In FIG. 2, a block 12 performs y-axis motion on a base 11 whereas a block 13 performs x-axis motion on the block 12. Planar displacement of the block 13 is measured using interference among laser beams 14 projected on respective large-area mirrors 15. The respective projected laser beams 14 are reflected from the mirrors 15 and passed through interferometers 17 and 17' of each axis, a diversion mirror and a beam splitter 18, thereby entering a signal processor.

[7] In the related arts as shown in FIG. 1 and FIG. 2, however, optical parts constituting the laser interferometer occupies so much space for size of the platen of the stage. Accordingly, the whole system becomes bulky. Furthermore, since the laser beams reflected from the mirrors should be incident to a light receiving unit in the laser interferometer, deviation of an optical axis beyond a predetermined range is impermissible. Therefore, the measurement range of rotational displacement is so restricted.

[8] The conventional measuring methods using the laser interferometer as shown in

FIG. 1 and FIG. 2 generally focus on the x-axis motion and the y-axis motion. However, the above methods hardly work in a perfect magnetic levitation stage wherein a moving unit of the stage is driven in levitation, owing to the relatively significant yaw motion. Moreover, application of the laser interferometer is difficult in general industrial fields unequipped with dedicated purifying facilities since the environment should be very clean to apply the laser interferometer.

[9] FIG. 3 shows a plane version of a linear encoder, that is, a surface encoder suggested by W. Gao etc. (refer to pp. 329-337, Precision Engineering).

[10] Referring to FIG. 3, permanent magnets 32 and 33 are perpendicularly arranged along an x-axis and a y-axis, respectively, under a moving unit 31. The permanent magnet generates linear thrust force to the x-axis and the y-axis in association with coils 35 and 36 disposed on the base 34. A gap between the moving unit 31 and the base 34 is maintained by a pneumatic bearing 37 seated on four corners. Here, position detection of the planar motion is performed as follows. A laser beam is projected onto a target pattern 38 processed in a trigonometric function grid pattern under the moving unit and received in a photodetector, passing through optical parts 40. The received laser beam is processed into signals, thereby obtaining the displacement to the x-axis and the y-axis. Simultaneously, minor rotational displacement can be detected as well.

[11] However, in the system of FIG. 3, manufacturing of the target pattern 38 of the surface encoder, which is a decisive factor determining repeatability and resolution of the detector, is very difficult since curves need to be drawn omnidirectionally in the trigonometric function grid pattern.

[12] FIG. 4 shows the structure of a detection system using infrared light emitting diodes

(LEDs) and light receiving units, to explain a planar displacement detection method suggested by Saffert etc. (refer to pp. 357-362, IEEE AMC2000-Nagoya, 2000).

[13] The detection system of FIG. 4 comprises grid patterns 52 arranged on a moving unit 51 in perpendicular directions, infrared LEDs 55 for ejecting light, and light receiving units 56 for receiving the light reflected from the grid patterns 52. The detection method according to the above system obtains planar positions through a combination 53 of the infrared LEDs 55 and the light receiving units 56 arranged in an x-axis direction and combinations 54 and 54' in a y-axis direction.

[14] This grid-based method is highly subject to accuracy of the grid pattern, as well as the method of FIG. 3. In addition, since the positions are determined by the average of signals from the infrared light receiving units, difference in physical properties among the respective light receiving units should be compensated. However, the compensation remains unsolved.

[15] FIG. 5 shows a stepper- type Sawyer's motor, which is a surface motor, disclosed in

US Patent No. 3,857,078.

[16] Flattened U-shaped electromagnets 73 and 75 are disposed on a driving block 71.

When power is applied through electromagnets 72 and 74, the surface motor is moved step by step using variation of reluctance with respect to stator teeth 76. Therefore, the stepper-type surface motor does not need a sensor.

[17] In this system, more specifically, the surface motor is moved step by step without a feedback sensor in the same manner as a step motor. The accuracy is subject to processing accuracy of each tooth of the stator teeth 76. Accordingly, open loop control can be achieved and therefore industrial use of this system is widespread. However, this system is not applicable to an ultra-precision system because accuracy of the grid is related to resolution of the system. Furthermore, although the feedback sensor is used, cogging force among the teeth is so strong that setting of interpolation is hindered.

Disclosure of Invention

Technical Problem

[18] The present invention has been made in view of the above-mentioned problems, that is, the bulky structure owing to the peripheral devices and inefficiency in measuring rotational displacement in a surface encoder as well as a laser interferometer. Therefore, it is an object of the present invention to provide a method and an apparatus for detecting an in-plane position indirectly by measuring a relative air gap between a sloped platen and a base disposed under the platen.

[19] It is another object of the present invention to provide a method and an apparatus for detecting planar displacement, that is, an in-plane position on a 2- axis planar stage for driving a large-scale substrate or a planar stage driven in levitation by the air or magnetism through air gap position measurement, very simply by detecting variation of the air gap of a sloped platen and converting the variation to the in-plane position.

[20] Yet another object of the present invention is to provide a method and an apparatus for measuring displacement along 3 axes of the planar stage capable of implementing 2- axis motion and yaw motion of a moving unit. [21] Still another object of the present invention is to provide a method and an apparatus for measuring planar motion along two axes and rotational motion of a moving unit as much as tens of degrees, by measuring air gaps of platens processed by respectively different slope gradients and operated associatively with the moving unit and detecting the in-plane positions indirectly through conversion relations, in order to finally detect planar displacement, that is, in-plane positions (x, y, θ) on a planar stage performing 2-dimensional motion by linear motors arranged in a grid form on a fixed base. Technical Solution

[22] In order to achieve the above object of the present invention, there are provided a method and an apparatus for measuring in-plane displacement on a planar stage driven by respective guiders or a planar stage of which a platen is driven in levitation. In other words, there are provided a method and an apparatus for indirectly detecting an in- plane position to measure displacement on a large- area plane merely by measuring variation of an air gap caused by planar motion of a sloped platen. The air gaps of three unitary platens having respectively different slope gradients are measured by 3-dimensionally expanding the detection method, thereby detecting not only planar displacement in an x-axis direction and a y-axis direction but also rotational displacement within about 45°.

Advantageous Effects

[23] As aforementioned, a method and an apparatus according to the present invention detect planar displacement, that is, an in-plane position on a 2-axis planar stage for driving a large-scale substrate or a planar stage driven in levitation by the air or magnetism through an air gap position measured. Especially, the method of the present invention performs the detection very simply by detecting variation of an air gap of a sloped platen and converting the variation to the in-plane position, in order to overcome increase of the whole size caused by measuring devices such as a laser interferometer used in a conventional stage, and difficulty in measuring yaw motion of the stage. Consequently, conventional expensive servo devices can be omitted.

[24] According to the present invention, information on the in-plane position is obtained indirectly through a relative air gap between the sloped platen and a base. Therefore, bulky size by peripheral devices and inefficiency in measuring rotational displacement in a surface encoder and a laser interferometer can be overcome with a simplified structure and low cost.

[25] The method and the apparatus according to the present invention are capable of detecting planar displacement, that is, an in-plane position on a 2-axis planar stage for large-scale substrate or a planar stage driven in levitation by the air or magnetism through an air gap position measured, very simply by detecting variation of the air gap of a sloped platen and converting the variation to the in-plane position. [26] According to the present invention, in addition, the method and the apparatus are capable of measuring displacement along 3 axes of the planar stage capable of implementing 2-axis motion and yaw motion of a moving unit. [27] The method and the apparatus according to the present invention are capable of measuring planar motion along two axes and rotational motion of a moving unit as much as tens of degrees, by measuring air gaps of platens processed in respectively different slope gradients and operated associatively with the moving unit and detecting the in-plane position indirectly through conversion relations, in order to finally detect planar displacement, that is, in-plane positions (x, y, θ) on a planar stage performing

2-dimensional motion by linear motors arranged in a grid form on a fixed base.

Brief Description of the Drawings [28] The foregoing and other objects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which: [29] FIG. 1 shows the structure of a conventional planar stage for detecting an in-plane position using laser interference, as disclosed in KR Patent Registration No.

10-0193153; [30] FIG. 2 shows the structure of a conventional laser interferometer for detecting an in-plane position of a general ultra-precision planar stage, the laser interferometer disclosed in KR Patent Registration No. 10-0193253; [31] FIG. 3 shows the structure of a conventional surface encoder for detecting in-plane positions of three axes in a planar stage; [32] FIG. 4 shows the structure of a conventional detection system using an infrared

LED and a light receiving unit for detecting an in-plane position in a planar stage; [33] FIG. 5 shows a Sawyer's motor disclosed in US Patent No. 3,857,078;

[34] FIG. 6 is a schematic view of an apparatus for detecting an in-plane position by measuring an air gap, according to an embodiment of the present invention; [35] FIG. 7 is a conceptual view illustrating a method for detecting

2-dimensionaldisplacement by measuring an air gap, according to the present invention; [36] FIG. 8 is a schematic view of a planar stage adopting an in-plane position indirect detection apparatus according to the present invention; and [37] FIG. 9 is a flowchart illustrating a method for detecting 6 degrees of freedom positions by measuring an air gap, according to the present invention.

Best Mode for Carrying Out the Invention [38] Hereinafter, an exemplary embodiment of the present invention will be described in greater detail with reference to the accompanying drawings.

[39] FIG. 6 is a schematic view of an apparatus for detecting an in-plane position by measuring an air gap, according to an embodiment of the present invention.

[40] As sloped square platens 102, 103 and 104 move in arrowed directions x, y and θ of

FIG. 6, air gaps 105, 106 and 107 between the respective platens and air-gap sensors 101 fixed to a base, vary due to the slopes. Displacement in the x, y and θ directions can be obtained indirectly, by establishing appropriate operational relations using information on the three air gaps.

[41] Here, the slopes of the platens, that is, directions of vertical vector of the respective platens can be set different from one another by controlling heights 108 and 110 at diagonally directing corners of the platens 102 and 104, and heights p and q at both diagonal sides of the platen 103. Therefore, cross-coupling between variation of the respective air gaps and the in-plane positions can be removed.

[42] FIG. 7 is a conceptual view illustrating a method for detecting 2-dimensional displacement by measuring an air gap, according to the present invention. The detection method of FIG. 6 will be further elucidated by FIG. 7.

[43] In a linear motor having a stator 122 and a mover 121, the mover 121 is sloped by a predetermined angle 125. Therefore, a linear displacement x of the mover 121 can be detected by measuring air gaps 126 and 127 by air-gap sensors 123 and 123 disposed on the stator 122. For example, assuming that αrefers to the sloping angle 125 and that g refers to the air gap 126 detected by the air-gap sensor 123 when the mover 121 is moved as much as x, relationship among those three variables can be expressed as follows:

[44] χ =g X cotα

(i)

[45] Thus, detection of the displacement x can be achieved by measuring the displacement of the air gap g.

[46] Assuming that gl and g2 respectively refer to the air gaps 126 and 127 measured by the two air-gap sensors 123 and 123 of FIG. 7, if the mover is movable in a z-axis direction, relationship between the air gaps gl and g2 and the displacements x and z can be established. Here, the slope of the moving unit may be processed in the shape of V or inverse V so that encoding of the air gap information occurring by the displacement x is symmetrically performed. For example, when the slope gradients of the both slopes forming the inverse V are all α, the information on the displacement x and z can be expressed as follows:

[47]

(2)

[48]

Z _= — g i + g:

2

(3)

[49] By 3-dimensionally expanding the above concept, the planar displacements x, y and θ can be obtained by measuring the air gap information of the three platens shown in FIG. 6.

[50] More specifically, assuming that s refers to both heights 108 and 110 of diagonally directing corners, respectively of the platen 102 sloped only in the y-axis direction and the platen 104 sloped only in the x-axis direction, that p and q respectively refer to the heights at both diagonal sides of the sloped platen 103 as shown in FIG. 6, and that gl, g2 and g3 respectively refer to the air gaps 107, 105 and 106 of when the planar displacements x, y and θ are performed, variation of the respective air gaps can be obtained through geometrical homogeneous conversion of the platen slopes and relative distances from the air-gap sensors to the slopes of the platens, as follows:

[51]

A₁₁ gi= — ^■ — [xcos θ +ys inθ -mcos θ +msinθ ]

Al2

(4)

[52]

[ycos θ -xs i n θ -mcos θ -ms i n θ ]

(5) [53] ga= — - — [ Bu (xcos θ +ys inθ )+ B 12 (ycos θ ^~xsinθ )-Bu m(cos θ -sinθ )+ Bi2in(sin θ -cos θ ) ]

D 13 (6)

[54] wherein, coefficients A and B are defined as follows:

[55]

A ^L ₁ ¹ ₁ ¹ =^~ - ΛH ^S^^"

(7)

[56]

(8)

[57] m

B₁₁ =

VmHpHq¹

(9)

[58]

(10)

[59]

(H)

[60] By solving simultaneous equations using the equations (4), (5) and (6), the displacements x, y and θ can be expressed using the information on the three air gaps gl, g2 and g3, as follows:

[61]

X= 2₍ - _{)3 3} [V4s²(p-q)Mpgi+qg₂-sg?,)²ms(p-q)(sg3-q(gi+g2))]+ms(p-q)

[2s²(p-q)²-(pgi+qg₂-sg₃)(p(gi+g2)-sg₃)] (12)

[62]

1

Y - 2_{ - _{)3 3} W4s²(ρ-q)²-(pgi+qg2-sg₃)²ms(p-q)(p⁽gi+g2)-sg₃)]+ms⁽p-q)

[2s²(p-q)²-(pgi+qg₂-sgs)(q(gi+g2-sg₃))] (13)

[63]

(14) [64] When (pg +qg -sg ) of equation (14) is minus, equation (14) is effective. However, when (pg +qg -sg ) is plus, θ becomes -θ. The planar displacements x, y and θ can be obtained indirectly by the three air gaps gl, g2 and g3 and the above equations.

[65] FIG. 8 schematically shows a planar stage applying a method indirectly detecting in-plane positions according to the present invention.

[66] Two pairs of perpendicular linear motors 202 and 203 are disposed on a base(not shown), and a stage 201 performs planar motion by the linear motors 202 and 203. Here, air gaps between the linear motors 202 and 203 and the stage 201 are maintained by pneumatic bearings 204 disposed at four corners of the base.

[67] Position of an air gap between the base and the stage 201 is measured by three first air-gap sensors 205 mounted in the hollow-shaft pneumatic bearings 204, thereby obtaining a stabilized position signal in a levitation direction. In addition, the in-plane position can be measured indirectly by measuring the air gaps of three platens 206 operated along with the stage 201 by a second air-gap sensor 207, and applying the detection method of FIG. 7.

[68] FIG. 9 is a flowchart illustrating a method for measuring 6 degrees of freedom positions by measuring an air gap, according to the present invention.

[69] When the stage is non-contactingly driven in space, 6 feedbacks including

X(horizontality), Y(verticality), Z(depth), pitch, yaw, and roll are required by a controller. The 6 position information can be all obtained by measuring the air gap. As shown in FIG. 8, more specifically, displacement of an air gap for in-plane motion is measured by detecting the air gap displacements of the sloped platen, and displacement of an air gap for out-plane motion by the air gap of the pneumatic bearing. Thus, all of those 6 information can be obtained with only 6 air gap information acquired through the 6 air-gap sensors mounted in the base.

[70] The obtained air gap information are digitalized through an analog-digital converter, converted to in-plane position information through equations (12) to (14) by an operator, and input to the controller. Therefore, a linear motor driver controls driving voltage and current applied to the linear motors using proper principles. As a result, the planar stage can be control as desired.

[71] While the invention has been shown and described with reference to certain embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Industrial Applicability

[72] The present invention is useful in detecting an in-plane position of a planar stage which is applied to a wafer stepper for exposure of semiconductors, various measuring devices such as an electron microscope, and inspection devices such as a TFT-LCD. [73]

Claims

[1] A displacement measuring apparatus for a planar stage, comprising: a base for mounting the planar stage thereon; at least one sloped platen moved over an upper part of the base in association with the planar stage; and at least one sensor for measuring an air gap between the base and the platen.

[2] The apparatus of claim 1, further comprising a controller that includes an algorithm for calculating the displacement of the planar stage using information on the air gap and geometrical structure of the platen, and generates a feedback signal corresponding to the displacement.

[3] The apparatus of claim 2, wherein the sensor is provided in number three corresponding to three platens, which are the object of measurement, to measure the respective air gaps and thereby obtain 3-axis information on the in-plane position of the planar stage.

[4] The apparatus of claim 3, wherein the respective platens have a square shape, and the information on the geometrical structure includes a slope gradient, height of each corner, and length of each side of the respective platens.

[5] The apparatus of claim 4, wherein the respective platens are processed with regular repetitive patterns, and the sensor and the controller measure gradient variation of surfaces of the platens and convert the gradient variation to the displacement information.

[6] The apparatus of claim 5, wherein the platens have respectively different slope gradients from one another.

[7] A method for calculating displacement of a planar stage using information on the air gap and the geometrical structure of the platens, by the measuring apparatus according to any of claims 1 through 6.

[8] The method of claim 7, wherein, assuming that s refers to height of the highest corners of the three platens, that p and q refer to height of the rest corners of a middle platen, that m refers to length of each side of the platens, that gl, g2 and g3 respectively refer to air gaps between the platens and the base, and that x, y and θ refer to placements in directions of three axes of the platen, the displacement of the planar stage can be calculated by the following equations:

gi= — : — [xcos θ +ysinθ -mcos θ +msinθ ]

Al2

g2 = . ⁿ [ycos θ -χs i n θ -mcos θ -ms i n θ ]

Al2 1

[B₁₁ (xcosθ+ysinθ)+B₁₂(ycosθ-χsinθ)-B,,m(cosθ-sinθ)+B,₂m(sinθ-cosθ)] a is

1

X = [\/4s²(p-q)²-(pgi+qg2-sg3)²ms(p-q)(sg3-q(gi+g2))]+ms(p-q)

2(p-q)³s³ [2s²(p-q)²-(pgi+qg₂-sg₃)(p(gi+g2)-sg₃)]

1 y = - [N/4s²(p-q)²-(pgi+qg2-sg3)²ms(p-q)(p(gi+g₂)-sg₃)]+ms(p-q)

2(p-q)³s³

[2s²(p-q)²-(pgi+qg₂-sg₃)Cq(gi+g₂-sg3) , and