JP2009065058A - Method of designing driver, method of designing stage device, method of manufacturing stage device, method of manufacturing exposure apparatus and stage device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of designing a stage device that achieves highly precise position control, a method of manufacturing same, a method of manufacturing exposure apparatus and the stage device. <P>SOLUTION: Y stage mass or moment of inertia around the center of gravity of the Y stage is determined so that the real part of a zero point has a minus value by obtaining a transfer function of a dynamic system including X stage and the Y stage moving on the X stage. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a drive device design method, a stage device design method, a stage device manufacturing method, an exposure apparatus manufacturing method, and a stage device.

Conventionally, in the design of a drive device such as a stage device (see, for example, Patent Document 1), a first phase for designing a structure as a structure of the stage device itself and the position control of the structure are performed. There is a second phase in which the control system is designed. Usually, after the stage apparatus structure is designed in the first phase, the first position is controlled so that optimum position control is performed on the designed structure. The procedure of designing the control system in two phases is taken.
JP 2004-14915 A

By the way, the characteristic of the position control in the stage apparatus which is a control target is characterized by a transfer function determined based on the structure of the stage apparatus. This transfer function can be described by a denominator P = N _P (s) / D _P (s) having a denominator D _P (s) and a numerator N _P (s) each represented by a predetermined polynomial. Here, s is a differential operator with respect to time. Here, a solution with denominator = 0 is called a pole, and a solution with numerator = 0 is called a zero. The poles and zeros are factors that affect the stability and dynamic characteristics of the control, and the design of the control system of the stage apparatus needs to be taken into consideration.

However, in the conventional stage apparatus, even if the influence of the pole can be eliminated by the optimum design of the control system (controller), the influence of the zero point cannot be eliminated, and high-precision position control of the stage apparatus is realized. There was a problem that it was difficult. That is, if the transfer function of the control system is the denominator D _C (s) and the denominator C = N _C (s) / D _C (s) of the numerator N _C (s), the transfer function of the entire stage apparatus including the control system Is represented as PC / (1 + PC). Therefore, the pole of the synthesized transfer function (the denominator 1 + PC = 0 solution) is different from the single pole of the stage apparatus main body (the solution of D _P (s) = 0), whereas the synthesized transfer. A part of the zero of the function (the solution of the numerator PC = 0) is also the zero of the stage apparatus main body (the solution of N _P (s) = 0). Therefore, no matter how the control system of the stage apparatus is designed, the zero point existing in the stage apparatus main body alone will remain, and depending on the characteristics of the zero point, it becomes difficult to perform highly accurate position control. is there.

  The present invention has been made in view of the above points, and an object of the present invention is to provide a stage apparatus design method, a stage apparatus manufacturing method, an exposure apparatus manufacturing method, and a stage capable of performing highly accurate position control. To provide an apparatus.

  The present invention has been made to solve the above-described problem, and includes a first part and a second part that are movable in the first direction with respect to the base. In the dynamic system model, the first part and the second part are provided. A moving member that can be regarded as equivalent to being connected to the second part via a spring component; an actuator that moves the moving member along the first direction; and the second part. And a measurement target unit used as a measurement target when obtaining information on the position of the two parts. The drive device design method includes the first part, the second part, and the measurement target part. A transfer function representing a relationship between the force applied to the actuator and information related to the position of the second part is obtained with respect to the dynamic system, and the real part of the zero point of the obtained transfer function is a negative value. 2 parts Determining the mass or moment of inertia about the center of gravity of the second portion, and sets the second portion produced on the specifications of to meet the determined mass or moment of inertia.

  According to the present invention, by making the real part of the zero point of the transfer function have a negative value, the position control of the drive device can be performed with high accuracy. This is based on the knowledge that when the real part of the zero of the transfer function has a positive value (especially its absolute value is small), the drive device exhibits an undesired behavior called an inverse response. The value of the zero point of the transfer function can be adjusted to a desired value by appropriately setting the mass or moment of inertia of the second part. The mass and moment of inertia of the second part can be adjusted by appropriately setting the shape and material (density) of the second part.

The present invention also includes a first part and a second part that are both movable in the first direction with respect to the base. In the dynamic system model, the first part and the second part are connected via a spring component. A movable member that can be regarded as equivalent to being connected, an actuator that moves the movable member along the first direction, and a second member that is provided in the second part and measured when obtaining information about the position of the second part. In a method for designing a drive device including a measurement target unit used as a target, the following formula Iy ≧ mL (l−L) + μ2 / {4 (k−mgL)}
(Where Iy is the moment of inertia around the center of gravity of the second part, m is the mass of the second part, L is the distance from the rotational center of the rotational movement of the second part to the center of gravity of the second part, and l is The distance from the rotation center to the measurement target part, μ is an attenuation coefficient between the first part and the second part, k is a torsional rigidity between the first part and the second part, and g is a gravitational acceleration). The mass of the second part or the moment of inertia around the center of gravity of the second part is determined as described above, and the production specifications of the second part are set so as to satisfy the determined mass or moment of inertia. And

  According to the present invention, since the real part of the zero point of the transfer function has a negative value when the above equation is satisfied, the position control of the drive device can be performed with high accuracy.

  The present invention also includes a first part and a second part that are both movable in the first direction with respect to the base. In the dynamic system model, the first part and the second part are connected via a spring component. A movable member that can be regarded as equivalent to being connected, an actuator that moves the movable member along the first direction, and a second member that is provided in the second part and measured when obtaining information about the position of the second part. And a measurement target unit used as a target, wherein the dynamic unit including the first part, the second part, and the measurement target part is given to the evil estimator. A transfer function representing a relationship between force and information on the position of the second part is obtained, and the measurement target part is provided in the second part so that the real part of the zero point of the obtained transfer function becomes a negative value. Determining the position And features.

  The present invention also provides a first stage that is movable in a first direction with respect to a base, a second stage that is coupled to the first stage so as to be movable in a second direction with respect to the first stage, and the first stage. A driving unit configured to move the stage along the first direction; and a measurement target unit provided on the second stage and used as a measurement target when obtaining information regarding the position of the second stage. In the design method of the stage apparatus, the relationship between the force applied to the driving means and the information on the position of the second stage is represented for the dynamic system including the first stage, the second stage, and the measurement target unit. Determining a transfer function, determining the mass of the second stage or the moment of inertia around the center of gravity of the second stage so that the real part of the zero point of the determined transfer function is a negative value; And setting the specifications produced on the second stage so as to satisfy the serial determined mass or moment of inertia.

  According to the present invention, by making the real part of the zero point of the transfer function have a negative value, the position control of the stage device can be performed with high accuracy. This is based on the knowledge that when the real part of the zero point of the transfer function has a positive value (especially its absolute value is small), the stage device exhibits an undesired behavior called an inverse response. The zero value of the transfer function can be adjusted to a desired value by appropriately setting the mass or moment of inertia of the second stage. The mass and moment of inertia of the second stage can be adjusted by appropriately setting the shape and material (density) of the second stage.

The present invention also provides a first stage that is movable in a first direction with respect to a base, a second stage that is coupled to the first stage so as to be movable in a second direction with respect to the first stage, and the first stage. A driving unit configured to move the stage along the first direction; and a measurement target unit provided on the second stage and used as a measurement target when obtaining information regarding the position of the second stage. In the stage device design method, the following formula Iy ≧ mL (l−L) + μ2 / {4 (k−mgL)}
(Where Iy is the moment of inertia around the center of gravity of the second stage, m is the mass of the second stage, L is the distance from the rotational center of the rotational movement of the second stage to the center of gravity of the second stage, and l is The distance from the rotation center to the measurement target part, μ is an attenuation coefficient between the first stage and the second stage, k is a torsional rigidity between the first stage and the second stage, and g is a gravitational acceleration). Determining the mass of the second stage or the moment of inertia around the center of gravity of the second stage so as to satisfy, and setting the specifications for manufacturing the second stage so as to satisfy the determined mass or moment of inertia. Features.

  According to the present invention, since the real part of the zero point of the transfer function has a negative value when the above equation is satisfied, the position control of the stage device can be performed with high accuracy.

  The present invention also provides a first stage that is movable in a first direction with respect to a base, a second stage that is coupled to the first stage so as to be movable in a second direction with respect to the first stage, and the first stage. A driving unit configured to move the stage along the first direction; and a measurement target unit provided on the second stage and used as a measurement target when obtaining information regarding the position of the second stage. In the design method of the stage apparatus, the relationship between the force applied to the driving means and the information on the position of the second stage is represented for the dynamic system including the first stage, the second stage, and the measurement target unit. A transfer function is obtained, and a position where the measurement target part is provided on the second stage is determined so that the real part of the zero point of the obtained transfer function becomes a negative value.

The present invention also provides a first stage that is movable in a first direction with respect to a base, a second stage that is coupled to the first stage so as to be movable in a second direction with respect to the first stage, and the first stage. A drive unit that moves the stage along the first direction; a measurement target unit that is provided on the second stage and is used as a measurement target when obtaining information on the position of the second stage; and the measurement target unit. And a position detection sensor that measures information related to the position of the second stage using the following equation: Iy ≧ mL (l−L) + μ2 / {4 (k−mgL)}
(Where Iy is the moment of inertia around the center of gravity of the second stage, m is the mass of the second stage, L is the distance from the rotational center of the rotational movement of the second stage to the center of gravity of the second stage, and l is The distance from the rotation center to the measurement target part, μ is an attenuation coefficient between the first stage and the second stage, k is a torsional rigidity between the first stage and the second stage, and g is a gravitational acceleration). In this stage device, the mass of the second stage and the moment of inertia around the center of gravity of the second stage are set so as to satisfy the above condition.

  According to the present invention, since the real part of the zero point of the transfer function has a negative value, the position control of the stage device can be performed with high accuracy.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 is a configuration diagram of a stage apparatus according to an embodiment of the present invention.
Two X-axis guides 2 extending in the X direction are laid in parallel on the upper surface of the base 1 at intervals in the Y direction (one of them is shown in the figure). An X carriage 3 is movably provided so as to straddle both side portions and the upper portion of the shaft guide 2. A Y beam guide 4 is suspended and fastened to the upper portion of the X carriage 3 in a bridge shape that extends in the Y direction (direction perpendicular to the paper surface) and connects the two X carriages 3. A plurality of air bearings 5 are arranged between the X carriage 3 and the X guide 2. The air bearing 5 is fixed to the X carriage 3, and the X carriage 3 and the Y beam guide 4 supported floating (non-contact) with respect to the X guide 2 are guided by the X guide 2 and are movable in the X direction. It has a configuration.

  A Y carriage 7 is placed on the Y beam guide 4. A plurality of air bearings 8 (base bearings) are arranged between the Y carriage 7 and the upper surface of the Y beam guide 4, and between the Y carriage 7 and both side surfaces of the Y beam guide 4, the air bearing 9. A plurality of (side bearings) are arranged. The air bearings 8 and 9 are fixed to the Y carriage 7, and the Y carriage 7 that is floating (non-contact) supported by the Y beam guide 4 is guided by the Y beam guide 4 and is movable in the Y direction. It has become.

  On the Y carriage 7, the plate table 10 is supported by a plurality of support mechanisms (not shown). On the plate table 10, a plate holder 11 for sucking and holding a glass substrate and the like, and a position sensor 12 for measuring the position are provided. The position sensor 12 (measurement target unit) is, for example, a movable mirror that constitutes a part of an interference measuring instrument (laser interferometer). Laser light from an external light source is used as measurement light on the movable mirror. The position of the plate holder 11 is precisely measured by irradiating and reflecting and causing interference with the reference light in the interference measuring instrument.

  An actuator (driving means, for example, an X linear motor) (not shown) is provided at both ends (the front side and the back side of the paper surface) of the Y beam guide 4 and is mounted on the X carriage 3 by driving the X linear motor. The object moves along the X guide 2 in the X direction. A Y linear motor 6 is provided on the side surface of the Y carriage 7, and the structure mounted on the Y carriage 7 moves in the Y direction along the Y beam guide 4 by driving the Y linear motor 6. In other words, the X stage 100 is formed by the X carriage 3, the Y beam guide 4, and the X linear motor, the X stage 100 moves in the X direction, and the Y carriage 7, the plate table 10, the plate holder 11, and the position sensor. 12 and the Y linear motor 6 form a Y stage 200, and the stage apparatus is configured such that the Y stage 200 moves in the Y direction.

FIG. 2 is a diagram showing a dynamic system model of the stage apparatus.
X-stage 100 has a mass M, attached at the base 1 and the attenuation coefficient (coefficient of viscosity) _{C x.} For example, if the X stage 100 is supported by the air bearing 5 so as to be relatively movable with respect to the base 1, the damping coefficient resulting from the air bearing 5 is the damping coefficient C _x . The Y stage 200 has a mass m, and is coupled to the X stage 100 with a damping coefficient μ and a torsional rigidity k with respect to the rotational motion around the rotational center C. When a force f is applied to the X stage 100 by the X linear motor, the X stage 100 and the Y stage 200 on the X stage 100 move along the X direction. At this time, the Y stage 200 further rotates by a small amount around the rotation center C as shown in FIG. 2 due to the presence of the damping coefficient μ and the torsional rigidity k. In the present embodiment, it is assumed that the air bearings 8 and 9 act as spring components having a finite rigidity value, thereby generating a rotational motion component between the Y stage 200 and the X stage 100. The center of this rotational motion is set as the rotational center C. When the X stage 100 is supported on the base 1 via the air bearing 5 as described above, a spring component having a finite rigidity value also acts here. Therefore, the effect of the rigidity of the air bearing of the X stage 100 is eliminated by matching the height of the center of gravity of the stage with the height of the actuator mounting, and modeling is performed as shown in FIG.

  In the description of the present embodiment, the fact that a plurality of members (for example, the X stage 100 and the Y stage 200) are related with each other under a predetermined condition is appropriately expressed by the expression “join”. It may be in a mechanically direct contact state or a non-contact state with a gas or the like interposed. For example, the Y stage 200 is mounted on the X stage 100 via the air bearings 8 and 9, and when the X stage 100 moves in the X direction, the Y stage 200 similarly moves in the X direction. Further, the Y stage 200 can be moved relative to the X stage 100 in the Y direction by air bearings 8 and 9. Further, as described above, a rotational motion is generated between the X stage 100 and the Y stage 200, and the rotation center C as shown in the dynamic system model of FIG. 2 exists.

  In such a dynamic system model, the X coordinate position X1 of the X stage 100 and the X coordinate position X2 of the Y stage 200 are given by the equations (1) and (2) shown in FIG. The position X2 is, for example, the position of the exposure area on the surface of the substrate, and is a final control target position in the position control of the stage apparatus. Where Iy is the moment of inertia around the center of gravity G of the Y stage 200, L is the distance from the center of rotation C to the center of gravity G of the Y stage 200, l is the distance from the center of rotation C to the position sensor 12, and g is the acceleration of gravity. is there. The right side of the equations (1) and (2) is a transfer function representing the response of this dynamic system, and s is a differential operator (s≡d / dt) with respect to time.

  Here, the equation of transfer function denominator = 0 is called a characteristic equation, and the solution is called a pole. The solution of the equation of transfer function numerator = 0 is called zero point. Both the pole and the zero are important factors that determine the response characteristics of the above dynamic system, that is, the positions X1 and X2 of each stage. As described below, each parameter of the dynamic system is set by paying attention to the zero. As a result, the stage device can be positioned with high accuracy.

  An equation for deriving a zero point regarding the position X2 of the Y stage 200 from the equation (2) is expressed by the following equation (3) as a quadratic equation of s.

  The zeros are obtained by solving the equation (3), and the values can be classified into the following four cases 1 to 4.

(Case 1) When the following equation (4) holds, the above equation (3) becomes a linear equation, and there is only one zero.

(Case 2) When the following equation (5) holds, the above quadratic equation (3) has multiple solutions.

(Case 3) When the following equation (6) holds, the above quadratic equation (3) has two real solutions.

(Case 4) When the following equation (7) holds, the above quadratic equation (3) has two complex solutions.

  FIG. 4 is a diagram showing the zeros and poles on the complex plane for Case 2 to Case 4 described above. In FIG. 4, in case 3, zeros exist at positive and negative positions on the real axis. Of these, the positive zero is called the unstable zero. In contrast, in case 2 and case 4, the real part of the zero is a negative value and no unstable zero exists, and the position X2 can be precisely controlled by adopting an appropriate control algorithm. is there. The specific control algorithm is not related to the essence of the present invention, and the description thereof is omitted.

  Therefore, in this stage apparatus, the moment of inertia Iy and the mass m of the Y stage 200 are such that the transfer function (formula (2)) does not have an unstable zero, that is, formula (5) or formula (6) is established. The value is determined so that the real part of the zero point becomes a negative value. Thereby, the position X2 of the Y stage 200 can be positioned with high accuracy.

As a specific example, it will be described below that the response characteristic of the position X2 can be changed by changing the inertia moment Iy (shape of the Y stage 200) while the mass m of the Y stage 200 is constant.
Here, as shown in FIG. 2, it is assumed that the Y stage 200 is a rectangular parallelepiped having a width b and a height h. The inertia moment Iy of the Y stage 200 having this shape is given by the following equation (8).

  FIG. 5 is a diagram showing values of width b, height h, and moment of inertia Iy when the value of width b is shaken while the mass m of Y stage 200 is kept constant. The inertia moment Iy is changed from “condition 1” to “condition 16” in FIG. 5 to determine the behavior of the zero point and the response of the position X2 to the step input f. At this time, the distance from the rotation center C to the position sensor 12 remains the same at the position where the case 3 is in the state. The obtained result is shown in FIG. FIG. 6 is a diagram illustrating a zero point locus in which the zero point is indicated on the complex plane for each of “condition 1” to “condition 16”.

In FIG. 6, the zero point in the case of “condition 1” is indicated by A. “Condition 1” corresponds to the case 3 described above, and the arrangement of the points A is the same as the case 3 in FIG. As the structure of the Y stage 200 changes to “condition 2”, “condition 3”,..., “Condition 13”, the zero point gradually moves to the position B. The region (trajectory) from “Condition 1” to “Condition 13” indicates the movement of the zero in the case 3, and the zero exists at the positive and negative positions on the real axis. That is, an unstable zero exists. Under “condition 14”, the position of the zero point is C, and the zero point gradually moves to the position D as the structure of the Y stage 200 changes to “condition 15” and “condition 16”. The region (trajectory) from “condition 14” to “condition 16” indicates the movement of the zero point in the case 4, and the zero point exists on the left side of the imaginary axis and its real part has a negative value. That is, there are no unstable zeros. Note that the movement (trajectory) from point A to point B changes to the movement (trajectory) from point C to point D in the vicinity where width b = 0.355, and width b is slightly smaller than 0.355. However, if it is small, it will be in the state of case 3, and if the width b is slightly larger than 0.355, it will be in the state of case 4.
Strictly speaking, there is a state corresponding to Case 1 and Case 2 between “Condition 13” and “Condition 14”, but it is omitted in FIG. 6 and the above description.

  In this way, the zero point can be changed from the case 3 state to the case 4 state by changing the value of the moment of inertia Iy (or width b or height h) of the Y stage 200 (structural change). In other words, design specifications such as the width b and height h of the Y stage 200 (specifications in manufacturing the Y stage 200) are set to the state of the case 4 or the case 2 (the real part of the zero point is negative). It is possible to position the position X2 of the Y stage 200 with high accuracy. Therefore, even if the condition of case 3 is satisfied in the structure of the normal stage apparatus, if the structure of the stage apparatus is set with the design specifications as described above, the condition of case 4 is satisfied and the Y stage 200 is satisfied. High-precision positioning can be realized.

The stage apparatus according to the present embodiment described above can be used as a stage apparatus for an exposure apparatus that prints a fine circuit pattern on a glass substrate or a semiconductor substrate, for example.
FIG. 7 is a block diagram of an exposure apparatus to which the above-described stage apparatus is applied. The exposure apparatus 31 includes an illumination optical system 32, a mask stage apparatus 33 that moves while holding the mask M, a projection optical system PL, and a substrate stage apparatus 35 that holds and moves the glass substrate P. Is done.

The illumination optical system 32 includes a light source unit, a shutter, a secondary light source forming optical system, a beam splitter, a condenser lens system, a reticle blind, and an imaging lens system, all of which are not shown, and is held by a mask stage device 33. A predetermined illumination area (including a circuit pattern) on the mask M is illuminated with a uniform illuminance by the illumination light IL.
The projection optical system PL is an optical system (for example, a refractive optical system) having a plurality of lens elements arranged at predetermined intervals along the direction of the optical axis AX, and the mask M is illuminated by illumination light IL from the illumination optical system 32. When the illumination area is illuminated, the illumination light that has passed through the mask M projects an upright image of a predetermined magnification of the circuit pattern of the illumination area on the mask M onto the glass substrate P via the projection optical system PL. Thus, the photoresist applied to the surface of the glass substrate P is exposed.

  The above-described stage apparatus of FIG. 1 is used for at least one of the mask stage apparatus 33 and the substrate stage apparatus 35. Here, when used as the mask stage device 33, the mask M is held by the plate holder 11, and when used as the substrate stage device 35, the glass substrate P is held by the plate holder 11.

  As described above, the embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to the above, and various design changes and the like can be made without departing from the scope of the present invention. It is possible to

  For example, in the case 2 to case 4 described above, it is assumed that the distance l from the rotation center C to the position sensor 12 is fixed, that is, the position sensor 12 is installed on the upper surface of the plate table 10. The state of the zero point is changed between the case 2 and the case 4 by changing the moment Iy. However, the present invention is not limited to this. The structure of the Y stage 200 such as the moment of inertia Iy and the mass m is fixed, and the distance l from the rotation center C to the position sensor 12 is changed as a parameter, so that the zero point state is obtained. Can be changed between case 2 and case 4. In the case of this modification, equations (5) to (7) are solved for distance l, and the value of distance l may be set so as to satisfy the condition of case 4 (equation (7)), for example.

  FIG. 8 is a diagram showing the locus of the zero point at this time on a complex plane. The zero point gradually moves from point A to point B and from point C to point D as the distance l increases. The region (trajectory) from point A to point B shows the movement of the zero in the case 4, and both zeros exist on the left side of the imaginary axis and the real part thereof has a negative value. That is, there is no unstable zero. At this time, the zero point position moves away from the origin as the position of the position sensor 12 is moved away from the rotation center (rotation axis) C. When the position of the position sensor 12 is moved further upward and away from the origin, the region (trajectory) from the point C to the point D is shifted through the case 2. The region (trajectory) from this point C to point D shows the movement of the zero point in the case 3, and one zero point exists at each of a positive position and a negative position on the real axis. That is, an unstable zero exists. Although not shown, the boundary between the case 4 and the case 3 is the case 2, and the case 1 exists in the vicinity thereof. In this way, it is also possible to change the zero point position of the plant (for example, the stage device) by changing the position (distance l) of the position sensor (structure change).

  Therefore, in the case of this modification, the distance between the position of the position sensor 12 (measurement target part) of the stage device and the rotation center C (position related to the coupled state of the Y stage 200 and the X stage 100) is considered. Thus, the design specifications for producing the stage device are determined based on these. Further, attention may be paid to other points to obtain conditions that satisfy the equation (7), and the design specifications may be set based on the conditions.

Here, the influence which the zero of the plant (for example, stage apparatus) demonstrated by this embodiment has on the performance of feedback control is shown. It should be noted that the above equation (2) can be expressed by a general form of a second-order / fourth-order plant composed of a rigid model and a resonance model. As the feedback controller, a feedback controller composed of a PID (proportional / integral / differential) controller and a notch filter is used. FIG. 9 shows the step response when the feedback controller is applied to each case of the plant. When an unstable zero exists, as shown in case 3 of FIG. 9, the displacement of the plant once occurs in the direction opposite to f with respect to the step input f, and the deviation from the instructed input becomes large. Such a response is called a reverse response. In a dynamic system in which this reverse response appears, it is impossible to eliminate the reverse response by using any control algorithm for controlling the position of the controlled object (plant). This becomes a big problem when trying to precisely control the position of the stage. That is, when the plant is in the state of the case 3 due to its structure, it is difficult to precisely control the position of the plant. Also, the absolute value of the overshoot is larger than in other cases. On the other hand, in the case 3b in which the unstable zero is set to the stable zero by the structural change, the reverse response disappears and the absolute value of the overshoot is the same as the other cases.
From the above results, it can be seen that the unstable zero of the plant causes an inverse response in the feedback control system, but the inverse response can be suppressed by changing the unstable zero to a stable zero by changing the structure.

Further, the influence of the zero point on the performance of the feedforward control will be described. A PTC design designed for a controlled object model consisting of a rigid body mode and a main resonance mode is a damping PTC method (Paper “Complete tracking method using multi-rate feedforward control”; Hiroshi Fujimoto et al., Transactions of the Society of Instrument and Control Engineers 36 Vol. 9, No. 9, pp. 766-772, 2000), but here, multi-rate damping PTC method (Paper “High-speed and high-precision positioning control of large ultra-precision step stage using damping PTC”; Fujimoto) Hiroshi et al., 7th Control Division Conference of the Society of Instrument and Control Engineers, 065-3-1, 2007) was applied to enable the plant to perform complete follow-up control by tracking control with respect to the actual position. FIG. 10 shows a simulation result when the feedforward controller set by the multi-rate damping PTC is applied to each case of the plant (comparison between cases 3 and 3b). However, the result is a simulation of only the feedforward controller. As shown in FIG. 10, the case 3b in which the unstable zero point is eliminated by the structural change can be completely followed during acceleration / deceleration and constant speed. However, in Case 3 having an unstable zero, a tracking error occurs during acceleration / deceleration and constant speed.
From the above results, it can be seen that the unstable zero of the plant causes a tracking error in the feedforward control, but the tracking error can be suppressed by changing the unstable zero to a stable zero by changing the structure.

  A program for realizing the design method or manufacturing method of the stage apparatus as described above may be recorded on a computer-readable recording medium, and the program may be read into a computer system and executed. Here, the “computer system” includes an OS and hardware such as peripheral devices. The “computer-readable recording medium” refers to a storage device such as a flexible medium, a magneto-optical disk, a portable medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. Further, the “computer-readable recording medium” refers to a volatile memory (RAM) in a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. In addition, those holding programs for a certain period of time are also included. The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, what is called a difference file (difference program) may be sufficient.

  The stage apparatus according to the present invention is not limited to the stage apparatus used in the exposure apparatus, and its application range is arbitrary, and can be applied to, for example, a robot arm. In the stage apparatus described in the embodiment, the second stage and the first stage where the measurement target portion is provided are separate members, and the first and second stages move in the first direction (in the X direction) Although the two stages are configured to move in the second direction (Y direction) with respect to the first stage, the present invention is not limited to such a configuration. A member that can move in the translational direction (for example, movement in the X direction) and a member that can move in the rotational direction can also be applied to a configuration in which the members are connected by a link mechanism. Even if the degree of freedom is limited to one (for example, translational movement in one axial direction), the structure is composed of a plurality of mass bodies (inertial bodies), and the rigidity of the portion sandwiched between these mass bodies If is weak, it may behave as if rotational motion is combined with translational motion. Furthermore, even if the mass bodies are integrated, if the rigidity of a certain part is relatively weak, it can be said that it is composed of a plurality of mass bodies on the boundary when viewed equivalently. It is also possible that it will occur. In such a case, it can be regarded as equivalent to the fact that a plurality of mass bodies (parts) are connected via a spring (torsion spring) component with a position where the rotational motion is performed as a boundary. Therefore, the present invention can be applied by setting the center of the rotational motion as the rotational center C.

It is a block diagram of the stage apparatus by one Embodiment of this invention. It is a figure which shows the dynamical system model of a stage apparatus. It is a formula showing the transfer function of a stage device. It is the figure which showed the zero and the pole on the complex plane. It is the figure which showed each value of the width | variety b of the Y stage used for calculating | requiring the characteristic of FIG. 6, height h, and the moment of inertia Iy. It is the figure which showed the locus | trajectory of the zero point on the complex plane with respect to each condition of FIG. It is a block diagram of the exposure apparatus to which the stage apparatus of FIG. 1 is applied. It is the figure which showed the locus | trajectory of the zero point on the complex plane when the distance l is a parameter. FIG. 6 is a step response diagram showing a result of simulating a response indicated by a position X2 of the Y stage by numerical calculation with respect to the conditions 1 and 14 in FIG. It is a figure showing the simulation result with respect to case 3 and case 3b.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Base 2 ... X-axis guide 3 ... X carriage 4 ... Y beam guide 5, 8, 9 ... Air bearing 6 ... Y linear motor 7 ... Y carriage 10 ... Plate table 11 ... Plate holder 12 ... Position sensor 100 ... X stage 200 ... Y stage

Claims (13)

A first part and a second part which are both movable in the first direction with respect to the base; and in the dynamic system model, the first part and the second part are connected via a spring component; A moving member that can be regarded as equivalent, an actuator that moves the moving member along the first direction, and a measuring object that is provided in the second part and is used as a measuring object when obtaining information about the position of the second part. And a drive device design method comprising
For a dynamic system including the first part, the second part, and the measurement target part, a transfer function representing a relationship between the force applied to the actuator and information on the position of the second part is obtained.
Determining the mass of the second part or the moment of inertia around the center of gravity of the second part such that the real part of the zero point of the obtained transfer function is a negative value;
A method for designing a driving device, wherein the specifications for producing the second portion are set so as to satisfy the determined mass or moment of inertia. A first part and a second part which are both movable in the first direction with respect to the base; and in the dynamic system model, the first part and the second part are connected via a spring component; A moving member that can be regarded as equivalent, an actuator that moves the moving member along the first direction, and a measuring object that is provided in the second part and is used as a measuring object when obtaining information about the position of the second part. And a drive device design method comprising
The following formula Iy ≧ mL (l−L) + μ2 / {4 (k−mgL)}
(Where Iy is the moment of inertia around the center of gravity of the second part, m is the mass of the second part, L is the distance from the rotational center of the rotational movement of the second part to the center of gravity of the second part, and l is The distance from the rotation center to the measurement target part, μ is an attenuation coefficient between the first part and the second part, k is a torsional rigidity between the first part and the second part, and g is a gravitational acceleration)
Determining the mass of the second part or the moment of inertia around the center of gravity of the second part to satisfy
A method for designing a driving device, wherein the specifications for producing the second portion are set so as to satisfy the determined mass or moment of inertia. A first part and a second part which are both movable in the first direction with respect to the base; and in the dynamic system model, the first part and the second part are connected via a spring component; A moving member that can be regarded as equivalent, an actuator that moves the moving member along the first direction, and a measuring object that is provided in the second part and is used as a measuring object when obtaining information about the position of the second part. And a drive device design method comprising
For a dynamic system including the first part, the second part, and the measurement target part, a transfer function representing a relationship between the force applied to the turbulent eater and information on the position of the second part is obtained.
A method for designing a driving device, wherein a position at which the measurement target portion is provided in the second part is determined so that a real part of a zero point of the obtained transfer function has a negative value. A first stage movable in a first direction relative to a base; a second stage coupled to the first stage movable in a second direction relative to the first stage; and the first stage in the first direction A stage apparatus design method comprising: a driving unit that moves along a line; and a measurement target unit that is provided on the second stage and is used as a measurement target when obtaining information on the position of the second stage. In
For a dynamic system including the first stage, the second stage, and the measurement target unit, a transfer function representing a relationship between a force applied to the driving unit and information on the position of the second stage is obtained,
Determining the mass of the second stage or the moment of inertia around the center of gravity of the second stage so that the real part of the zero point of the obtained transfer function is a negative value;
Specifications for producing the second stage so as to satisfy the determined mass or moment of inertia are set. A first stage movable in a first direction relative to a base; a second stage coupled to the first stage movable in a second direction relative to the first stage; and the first stage in the first direction A stage apparatus design method comprising: a driving unit that moves along a line; and a measurement target unit that is provided on the second stage and is used as a measurement target when obtaining information on the position of the second stage. In
The following formula Iy ≧ mL (l−L) + μ ² / {4 (k−mgL)}
(Where Iy is the moment of inertia around the center of gravity of the second stage, m is the mass of the second stage, L is the distance from the rotational center of the rotational movement of the second stage to the center of gravity of the second stage, and l is The distance from the center of rotation to the measurement target part, μ is an attenuation coefficient between the first stage and the second stage, k is a torsional rigidity between the first stage and the second stage, and g is a gravitational acceleration)
Determining the mass of the second stage or the moment of inertia around the center of gravity of the second stage to satisfy
Specifications for producing the second stage so as to satisfy the determined mass or moment of inertia are set. A first stage movable in a first direction relative to a base; a second stage coupled to the first stage movable in a second direction relative to the first stage; and the first stage in the first direction A stage apparatus design method comprising: a driving unit that moves along a line; and a measurement target unit that is provided on the second stage and is used as a measurement target when obtaining information on the position of the second stage. In
For a dynamic system including the first stage, the second stage, and the measurement target unit, a transfer function representing a relationship between a force applied to the driving unit and information on the position of the second stage is obtained,
A design method of a stage apparatus, wherein a position where the measurement target part is provided on the second stage is determined so that a real part of a zero point of the obtained transfer function becomes a negative value.   The said 2nd direction is a direction which crosses the said 1st direction, The said 1st stage and the said 2nd stage are couple | bonded through the elastic component, The any one of Claim 4-6 characterized by the above-mentioned. 2. A design method for a stage apparatus according to item 1.   The method for manufacturing a stage apparatus according to claim 4, wherein the second stage is manufactured using the design method according to claim 4.   The method for manufacturing a stage apparatus according to claim 5, wherein the second stage is manufactured using the design method according to claim 5.   The method for manufacturing a stage apparatus according to claim 6, wherein the measurement target part is set at a position determined using the design method according to claim 6.   The stage apparatus design method according to any one of claims 4 to 6, wherein the information related to the position of the second stage is measured by irradiating the measurement target portion with measurement light. In an exposure apparatus manufacturing method for exposing a mask pattern held on a mask stage onto a photosensitive substrate held on a substrate stage,
An exposure apparatus manufacturing method, wherein at least one of the mask stage and the substrate stage is manufactured using the stage apparatus manufacturing method according to claim 8 or 9. A first stage movable in a first direction relative to a base; a second stage coupled to the first stage movable in a second direction relative to the first stage; and the first stage in the first direction Driving means that moves along the second stage, a measurement target unit that is provided in the second stage and is used as a measurement target when obtaining information on the position of the second stage, and the second stage using the measurement target unit A position detection sensor for measuring information related to the position of the stage device,
The following formula Iy ≧ mL (l−L) + μ ² / {4 (k−mgL)}
(Where Iy is the moment of inertia around the center of gravity of the second stage, m is the mass of the second stage, L is the distance from the rotational center of the rotational movement of the second stage to the center of gravity of the second stage, and l is The distance from the center of rotation to the measurement target part, μ is an attenuation coefficient between the first stage and the second stage, k is a torsional rigidity between the first stage and the second stage, and g is a gravitational acceleration)
A stage apparatus in which the mass of the second stage and the moment of inertia around the center of gravity of the second stage are set so as to satisfy

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