JP2015050398A - Device and method for laminating substrate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform feedback control of a moving stage designed to shift a driving point and a rocker shaft from the center of gravity with high accuracy.SOLUTION: A method for laminating a substrate comprises the steps of: measuring a position (a first control amount) X and an inclination (a second control amount) θy in a translation direction of a moving stage 31 using an interferometer 42; drive-controlling the moving stage 31 in the translation direction by a thrust distributor 60d using a first operation amount Ux (a driving force Fx in the translation direction) calculated from the measurement results of the first control amount X; compensating a second operation amount Ucalculated from the measurement results of the second control amount θy using the first operation amount Ux; and drive-controlling the moving stage 31 in a θy direction using the compensated second control amount U'. Thereby, when the driving force Fx in the translation direction is generated by shifting the driving point and rocker shaft of the moving stage 31 from the center of gravity, a locking torque canceling a torque generated in a θy direction is compensated to cancel a thrust interference from the driving force Fx to the inclination θy.

Description

  The present invention relates to a substrate bonding apparatus and a substrate bonding method for bonding two substrates.

  In recent years, semiconductor device mounting technology has progressed from two-dimensional array mounting in which a plurality of semiconductor chips are arranged in a plane to three-dimensional stacked mounting in which three-dimensional stacking is performed. As a result, the wiring between the semiconductor chips is shortened, the operation speed of the semiconductor device is improved, and the mounting area efficiency of the circuit element mounted on one semiconductor device is dramatically improved.

  In addition, as a semiconductor device assembly (packaging) technique, not a chip level assembly technique but a wafer level assembly technique, that is, a semiconductor substrate (wafer) on which a plurality of circuit elements are formed is not separated into chips, A technology has been developed in which the assembly process from rewiring, resin sealing, and terminal processing is performed in the state of a wafer, and finally a device is assembled by dividing into individual pieces. Thereby, the manufacturing cost performance is improved.

  Due to these technical backgrounds, research and development of a substrate bonding apparatus for bonding two substrates such as a semiconductor wafer is underway. In the substrate bonding apparatus, a substrate stage (second stage) that moves while holding the other substrate opposite to the substrate held by the first stage with respect to the substrate stage (first stage) holding one of the two substrates. The stage) is precisely driven and aligned, and a plurality of electrodes formed on the surfaces of the two substrates are joined to each other, pressed together, and bonded together. Accordingly, in order to accurately align the substrate, precise and stable drive control of the substrate stage (particularly the second stage) is required (for example, see Patent Document 1).

  In order to precisely drive the substrate stage, it is desirable that the position of the driving point that generates the driving force and the position of the swing shaft (rotation center in the tilt direction) of the table that holds the substrate be equal to the position of the center of gravity. It is known empirically. However, in the substrate bonding apparatus, the two substrate stages are brought into contact with each other in order to bond the two substrates, so that the substrate is driven independently from the first stage to align the substrates and the substrates are bonded together. The center of gravity of the second stage is displaced when it contacts the first stage. Therefore, it is not always appropriate to adopt a substrate stage design that is empirically desirable in a substrate bonding apparatus.

  Therefore, if the substrate stage (second stage) is designed by shifting the driving point and the swing axis (rotation center in the tilt direction) from the center of gravity, the driving force in the translation direction is generated at the driving point. In addition to applying thrust in the translation direction, swing torque is applied in the rotation direction, and disturbance equivalent to the weight of the table holding the substrate is applied to the substrate stage via the center of rotation as thrust swing torque in the rotation direction. Will occur. Further, resonance occurs when the second stage is brought into contact with the first stage in order to bond the two substrates. These thrust interference and resonance can be obstacles to precise driving of the substrate stage.

US Patent Application Publication No. 2006/0273440

  From the first viewpoint, the present invention is a substrate bonding apparatus for bonding two substrates, the first stage holding one of the two substrates, and the other of the two substrates as the one substrate. And a second stage that contacts the first stage via the two substrates, and a first stage associated with a translational position and an inclination position of the second stage, respectively. And the second control amount is measured, and the second stage is driven and controlled in the translational direction using the first operation amount obtained from the measurement result of the first control amount, and obtained from the measurement result of the second control amount. A substrate bonding apparatus comprising: a control unit that compensates for the second operation amount to be performed using the first operation amount, and that drives and controls the second stage in the tilt direction using the compensated second control amount. is there.

  Here, the substrate includes not only a substrate such as a semiconductor wafer but also a semiconductor chip, and is not limited to a single-layer semiconductor wafer (or a single-layer semiconductor chip), but includes a plurality of semiconductor wafers (a plurality of semiconductor chips). Also includes stacked semiconductor members. In this specification, the term “substrate” is used as such a concept.

  According to this, it is possible to bond the two substrates in a state where the two substrates are accurately aligned.

  From a second viewpoint, the present invention is a substrate bonding method for bonding two substrates, and holds one of the two substrates facing one of the two substrates held by a first stage. Measuring the first and second control amounts respectively related to the translational position and the tilting position of the second stage that contacts the first stage via the two substrates, The first operation amount obtained from the measurement result of the first control amount is used to drive and control the second stage in the translation direction, and the second operation amount obtained from the measurement result of the second control amount is controlled by the first control. Compensation using the measurement result of the quantity, and driving control of the second stage in the tilt direction using the compensated second control quantity.

  According to this, it is possible to bond the two substrates in a state where the two substrates are accurately aligned.

It is a figure which shows roughly the structure of the board | substrate bonding apparatus which concerns on one Embodiment. It is a block diagram which shows the main structures of the control system of a board | substrate bonding apparatus. It is a figure for demonstrating the bonding process of a board | substrate. It is a figure for demonstrating the bonding process of a board | substrate. It is a figure for demonstrating the bonding process of a board | substrate. It is a figure which shows the mathematical model expressing the dynamic motion of a fixed stage and a movement stage. It is the table | surface which put together the various parameters in the mathematical model of FIG. It is the table | surface which put together the representative value of the parameter relevant to a movement stage. The driving force Fx is a Bode diagram showing the frequency response characteristic of the transfer shows the response of the position X and tilt θy translational direction of movement stage when given to moving the stage function P _11, P _21. It is a block diagram showing the structure of the feedback control system corresponding to the movement stage drive part which drives a movement stage. 11A and 11B show the control of the inclination θy when the target position Rx is given to the moving stage driving unit and when the disturbance is applied to the moving stage with respect to the design conditions of the moving stage, respectively. It is a figure which shows the time transition of an error (following error). It is a block diagram showing the structure which further incorporated the disturbance observer in the feedback control system of FIG. FIGS. 13A and 13B show the inclination θy when the target position Rx is given to the moving stage drive unit and when the disturbance is applied to the moving stage, respectively, for thrust distribution and disturbance observer application. It is a figure which shows the time transition of control error (follow-up error). FIGS. 14A and 14B are Bode diagrams illustrating frequency response characteristics of the complementary sensitivity function (amplitude and phase) of the feedback control system. FIGS. 15A to 15C are Bode diagrams showing frequency response characteristics of transfer functions (amplitude and phase) representing the input / output response of the moving stage. 16A to 16C show changes in mode influence constants D and F in the input / output response of the moving stage at the time of bonding with respect to the positions of the drive point and the swing axis (deviations Ld and Lx2 from the center of gravity). FIG. FIG. 17A to FIG. 17C are Bode diagrams showing frequency response characteristics of transfer functions (amplitude and phase) representing input / output responses of the moving stage with respect to each of the three optimal solutions. FIGS. 18A to 18C are Nyquist diagrams when feedback control is applied to a conventional design. FIG. 19A to FIG. 19C are Nyquist diagrams when feedback control is applied to the first optimal solution. FIGS. 20A to 20C are Nyquist diagrams in the case where feedback control is applied to the second optimal solution. FIG. 21A to FIG. 21C are Nyquist diagrams when feedback control is applied to the third optimal solution. 22A and 22B are Bode diagrams showing frequency response characteristics of the complementary sensitivity function (amplitude and phase) when feedback control is applied to the first optimal solution. FIGS. 23A and 23B are Bode diagrams showing frequency response characteristics of the complementary sensitivity function (amplitude and phase) when feedback control is applied to the second optimal solution. FIGS. 24A and 24B are Bode diagrams showing frequency response characteristics of the complementary sensitivity function (amplitude and phase) when feedback control is applied to the third optimal solution.

  Hereinafter, an embodiment of the present invention will be described with reference to FIGS.

  FIG. 1 schematically shows a configuration of a substrate bonding apparatus 100 according to an embodiment. As will be described later, in this embodiment, microscopes 51 and 52 are provided, and their optical axes (passing through the respective detection centers) are set in the Z axis and in the plane perpendicular to the optical axis in FIG. Are the X-axis direction, the direction perpendicular to the paper surface is the Y-axis direction, and the rotation (tilt) directions around the X-axis, Y-axis, and Z-axis are the θx, θy, and θz directions, respectively.

  The board | substrate bonding apparatus 100 has the frame 10, the fixed stage apparatus 20, the moving stage apparatus 30, the interferometers 41 and 42, and a control system (refer FIG. 2).

  The frame body 10 includes a top plate portion disposed horizontally (parallel to the floor surface) above a floor surface (not shown) parallel to the XY plane, and side wall portions that support ± X end portions of the top plate portion from below. And a bottom plate portion having a surface parallel to the floor surface. A stage surface plate 11 is provided on the bottom plate portion. A guide surface for driving a moving stage 31 described later is formed on the upper surface of the stage surface plate 11. The frame 10 accommodates other components of the substrate bonding apparatus 100.

  The fixed stage device 20 includes a fixed stage 21 that is horizontally disposed below (−Z side) the top plate portion of the frame body 10 and two support members 22 that suspend and support the fixed stage 21 on the top plate portion. Prepare.

  The fixed stage 21 has a suction device (not shown) such as an electrostatic chuck or a vacuum chuck. In FIG. 1 and the like, the fixed stage 21 holds the substrate 1 in the −Z direction by sucking the substrate holder 3 holding the substrate 1 using a suction device.

  The substrate holder 3 (and a substrate holder 4 to be described later) has a holding surface in which an electrostatic chuck or the like for attracting the substrate is embedded, and a magnet piece 5a (magnetic piece 5b) arranged outside the holding surface. . As will be described later, the substrate holders 3 and 4 are bonded using the magnet piece 5a and the magnetic piece 5b in a state where the substrates 1 and 2 held by the magnet holder 5a and the magnetic material piece 5b are bonded together.

  A microscope 51 is fixed downward (toward the −Z direction) on the side of the fixed stage 21. The microscope 51 detects an alignment mark of the substrate 2 held on the moving stage 31 described later.

  On the −X side surface of the fixed stage 21 (the microscope 51 in this embodiment), the reflecting mirror 23 is fixed with its reflecting surface facing the −X direction. Further, on the −Y side surface of the fixed stage 21, a reflecting mirror (not shown) whose longitudinal direction is the X-axis direction is fixed with its reflecting surface facing the −Y direction. These reflecting mirrors are used when measuring the position of the fixed stage 21 using the interferometer 41. Instead of the reflecting mirror, the end surface of the fixed stage 21 may be mirror-finished to form a reflecting surface.

  The two support members 22 include a load cell (not shown) that detects a load applied to the substrate 1 held by the fixed stage 21. The detection result of the load cell is transmitted to the control unit 60.

  The moving stage device 30 includes, for example, an X drive unit 32a that is levitated and supported on the stage surface plate 11 via an air bearing, a Y drive unit 32b disposed thereon, an elevating unit 32c disposed thereon, and a swinging motion. A part 32d and a moving stage 31 supported substantially horizontally by these parts are provided.

  The X drive unit 32a and the Y drive unit 32b include, for example, a linear motor or the like, and move the moving stage 31 (the lifting unit 32c and the swinging unit 32d that support this) along the guide surface of the stage surface plate 11 in the X-axis direction. And it drives with a predetermined stroke in the Y-axis direction. Note that the position of the drive point at which the drive force for driving the moving stage 31 is generated can be freely changed, particularly in the Z-axis direction, by changing the arrangement of the X drive unit 32a and the Y drive unit 32b.

  The elevating unit 32c includes an actuator (not shown) such as a voice coil motor, for example, and drives the moving stage 31 (oscillating unit 32d) in the Z-axis direction using this. A concave spherical surface is formed on the upper surface of the elevating part 32c.

  The swinging part 32 d supports the moving stage 31. The oscillating portion 32d has a spherical seat formed with a convex spherical surface that abuts the concave spherical surface of the elevating portion 32c. The movable stage 31 is displaced in the θx and θy directions by displacing the spherical seat using the concave spherical surface as a guide. And tilt in the θz direction. The position of the swing axis (rotation center in the tilt direction) of the moving stage 31 can be freely changed, particularly in the Z-axis direction, by changing the curvature of the concave spherical surface of the elevating unit 32c and the convex spherical surface of the swing unit 32d. can do.

  The above-mentioned X drive unit 32a, Y drive unit 32b, lifting unit 32c, and swing unit 32d constitute a moving stage drive unit 32 (see FIG. 2). By controlling the moving stage driving unit 32, the moving stage 31, that is, the substrate 2 supported on the moving stage 31, is driven in the direction of six degrees of freedom (X, Y, Z, θx, θy, θz) toward the target position. .

  The moving stage 31 has a suction device (not shown) such as an electrostatic chuck or a vacuum chuck. In FIG. 1 and the like, the moving stage 31 holds the substrate 2 in the + Z direction by sucking the substrate holder 4 holding the substrate 2 using a suction device.

  A microscope 52 is fixed upward (toward the + Z direction) on the side of the moving stage 31. The microscope 52 detects the alignment mark of the substrate 1 held on the fixed stage 21.

  A reflecting mirror 33 is fixed to the −X side surface of the moving stage 31 with the reflecting surface facing the −X direction. Further, on the −Y side surface of the movable stage 31, a reflecting mirror (not shown) having the X axis direction as a longitudinal direction is fixed with the reflecting surface facing the −Y direction. These reflecting mirrors are used when measuring the position of the moving stage 31 using the interferometer 42. Instead of the reflecting mirror, the end surface of the fixed stage 21 may be mirror-finished to form a reflecting surface.

  The interferometer 41 emits the measurement beam toward the reflecting mirror 23 in parallel with the X axis, and receives the reflected light from the reflecting mirror 23. The interferometer 41 emits two length measuring beams separated in the X-axis direction toward a reflecting mirror (not shown) fixed to the −Y side surface of the fixed stage 21 in parallel with the Y-axis, and the reflecting mirror. The reflected light from is received. Thereby, the interferometer 41 measures the position (X, Y, θz) of the fixed stage 21 in the XY plane. Further, by adopting a biaxial interferometer as the interferometer 41, the inclination (θx, θy) of the fixed stage 21 is measured.

  The interferometer 42 emits a length measurement beam toward the reflecting mirror 33 parallel to the X axis, and receives the reflected light from the reflecting mirror 33. The interferometer 42 emits two length measuring beams separated in the X-axis direction toward a reflecting mirror (not shown) fixed to the −Y side surface of the moving stage 31 in parallel to the Y-axis. The reflected light from is received. Thereby, the interferometer 42 measures the position (X, Y, θz) of the moving stage 31 in the XY plane. Further, by adopting a two-axis interferometer as the interferometer 42, the inclination (θx, θy) of the moving stage 31 is measured.

  The measurement results of the interferometers 41 and 42 are transmitted to the control unit 60. The control unit 60 drives the moving stage 31 by controlling the moving stage driving unit 32 (X driving unit 32a, Y driving unit 32b, elevating unit 32c, and swinging unit 32d) according to these measurement results.

  FIG. 2 shows the main configuration of the control system of the substrate bonding apparatus 100. This control system is configured around a control unit 60 including a microcomputer (or a workstation) that controls each component in a centralized manner.

  The board | substrate bonding process in the board | substrate bonding apparatus 100 of the above-mentioned structure is demonstrated.

  Prior to the start of the bonding process, as shown in FIG. 1, the moving stage 31 is retracted to the −X side retreat area on the stage surface plate 11. The substrate holder 3 holding the substrate 1 is held on the fixed stage 21, and the substrate holder 4 holding the substrate 2 is held on the moving stage 31. In addition, search alignment is performed for each of the substrates 1 and 2. In addition, baseline measurement is performed to detect a reference mark (not shown) formed on the substrate holder 3 or the fixed stage 21 (substrate holder 4 or the moving stage 31) using the microscope 52 (or the microscope 51). . These details are omitted.

  As shown in FIG. 3, the controller 60 drives the moving stage 31 in the direction of the black arrow (+ X direction), and the microscope 52 fixed thereto faces the substrate 1 held on the fixed stage 21. Move to position. Thereby, at the same time, the microscope 51 fixed to the fixed stage 21 faces the substrate 2 held by the moving stage 31.

  The controller 60 uses the microscope 52 to measure the alignment of the substrate 1 held on the fixed stage 21. Here, a large number of shot regions (circuit pattern regions) are arranged in a matrix on the surface of the substrate 1, and a circuit pattern is formed by exposure in each region, and alignment marks are attached.

  Specifically, the control unit 60 drives the moving stage 31 in the X-axis and Y-axis directions according to the measurement results of the interferometers 41 and 42 (the position of the moving stage 31 with respect to the fixed stage 21), and on the surface of the substrate 1. The alignment mark is positioned in the field of view of the microscope 52. The control unit 60 measures the positioning position of the moving stage 31 and detects the alignment mark using the microscope 52. From the measurement result of the positioning position and the detection result of the alignment mark, the XY position of the detected alignment mark is obtained. The control unit 60 performs the same measurement for two or more alignment marks.

  The controller 60 uses the microscope 51 to measure the alignment of the substrate 2 held on the moving stage 31. Here, like the substrate 1, a large number of shot regions (circuit pattern regions) are arranged in a matrix on the surface of the substrate 2, and a circuit pattern is formed by exposure in each region, and an alignment mark is attached. Has been.

  The controller 60 drives the moving stage 31 in the X-axis and Y-axis directions according to the measurement results of the interferometers 41 and 42 (position of the moving stage 31 with respect to the fixed stage 21) in the same manner as the alignment measurement of the substrate 1, and the substrate 2 An alignment mark on the surface of the microscope is positioned in the field of view of the microscope 51. The control unit 60 measures the positioning position of the moving stage 31 and detects the alignment mark using the microscope 51. From the measurement result of the positioning position and the detection result of the alignment mark, the XY position of the detected alignment mark is obtained. The control unit 60 performs the same measurement for two or more alignment marks.

  The control unit 60 uses the measurement result of the alignment measurement of the substrates 1 and 2 and the measurement result of the baseline measurement (and search alignment) to determine the target position of the moving stage 31 corresponding to the bonding position of the substrates 1 and 2. Ask. As the target position, for example, a position where the square sum of the relative distances in the XY plane between the paired alignment marks is minimized between the alignment marks of the two substrates 1 and 2 is adopted.

  When the target position is determined, as shown in FIG. 4, the control unit 60 controls the moving stage driving unit 32 (X driving unit 32a and Y driving unit 32b) to move the moving stage 31 in the direction of the black arrow (+ X The substrate 2 held on the movable stage 31 is moved to the substrate 1 held on the fixed stage 21 by tilting the moving stage 31 by controlling the swinging part 32d. Align.

  As shown in FIG. 5, the control unit 60 controls the elevating unit 32 c to drive the moving stage 31 in the direction of the black arrow (+ Z direction), thereby bringing the moving stage 31 close to the fixed stage 21, The substrates 1 and 2 held on both stages are overlapped. At this time, the magnet piece 5a on the substrate holder 3 and the magnetic piece 5b on the substrate holder 4 are fixed in a state where the substrates 1 and 2 on which the substrate holders 3 and 4 are superimposed are sandwiched therebetween.

  The controller 60 releases the suction of the substrate holder 3 by the fixed stage 21 and lowers the moving stage 31. As a result, the fixed substrate holders 3 and 4 are separated from the fixed stage 21. Further, the control unit 60 moves the moving stage 31 to the retreat area, releases the adsorption of the substrate holder 4 by the moving stage 31, and attaches the fixed substrate holders 3 and 4 to the substrate pasting using a transfer device (not shown). It is carried out of the combined device 100.

  The board | substrate holders 3 and 4 carried out from the board | substrate bonding apparatus 100 are conveyed by a heating apparatus (not shown), the board | substrates 1 and 2 are bonded together by processes, such as a heating process, and a three-dimensional lamination type is carried out. A semiconductor device is manufactured.

  Decoupling control of the moving stage 31 (independent of the fixed stage 21) in the substrate bonding apparatus 100 of the present embodiment will be described.

  In the above-described bonding step, the control unit 60 measures the interferometers 41 and 42 (measurement results of relative positions with respect to the translational direction (X, Y) and tilt (θx, θy) of the moving stage 31 with respect to the fixed stage 21). Accordingly, the moving stage drive unit 32 is controlled to generate a translational driving force (Fx, Fy) and swinging torque (Tx, Ty), thereby driving the moving stage 31 holding the substrate 2. Here, the control amounts (X, Y) and (θx, θy) in the drive control of the moving stage 31 in which the drive point and the swing axis (rotation center in the tilt direction) are deviated from the center of gravity, that is, the non-center of gravity drive stage. ) And the manipulated variables (Fx, Fy) and (Tx, Ty) are considered using a mathematical model that simulates the substrate bonding apparatus 100 of the present embodiment.

  For simplicity, only the translational motion in the X-axis direction and the inclination in the θy direction are considered as the degree of freedom of drive control of the moving stage 31. The translation stage (X-axis direction) position X and tilt (rotation position with respect to the Y-axis) θy of the moving stage 31 are measured as control amounts, and according to the results, the translation forces (X-axis direction) driving forces Fx and Y The moving stage 31 is driven and controlled by generating a swing torque Ty related to the shaft.

  FIG. 6 shows a mathematical model that expresses the dynamic motion of the fixed stage 21 and the moving stage 31 in the substrate bonding apparatus 100 of the present embodiment. FIG. 7 summarizes various parameters in the mathematical model of FIG.

  The fixed stage 21 is expressed as a rigid body having a mass m0 and an inertia moment J0 that are suspended and supported on the top plate portion of the frame 10 by two springs that simulate the two support members 22. Here, X0 is the position of the center of gravity of the fixed stage 21 in the X-axis direction, 2w0 is the distance between the two support members 22 (springs), LXU is the distance between the center of gravity of the fixed stage 21 and the reflecting mirror 23, and L0U is the fixed stage 21. L0L is the distance from the center of gravity of the fixed stage 21 to the overlapping surface (the surface of the substrate 1 supported by the fixed stage 21).

  Each of the two springs is supported at one point on the top plate portion of the frame 10 and vibrates in the Z-axis direction, and swings in a pendulum shape around the fulcrum. Therefore, the rigid body representing the fixed stage 21 moves not only in the Z-axis direction but also in the X-axis direction by being supported by being suspended by two springs. Correspondingly, the two springs are expressed by using the frictional rigidity k0z and the frictional viscosity C0z relating to the movement in the Z-axis direction and the frictional rigidity k0x and the frictional viscosity C0x relating to the movement in the X-axis direction.

  The moving stage 31 is a rigid body having a mass m2 and an inertia moment J2 supported by a movable stage having a mass m1 simulating the moving stage device 30 via a link having a stiffness kθ and a viscosity Cθ corresponding to the oscillating portion 32d so as to be tiltable. Is expressed as Here, X1 is the position of the center of gravity of the movable stage (oscillating part 32d) in the X-axis direction, θ2 is the inclination of the moving stage 31 (tilting angle of the oscillating part 32d), and Lx2 is the oscillation axis (link) of the moving stage 31 L2 is the distance from the center of gravity of the moving stage 31 to the measurement position (the surface of the substrate 2 held by the moving stage 31), and Lx is the swinging distance. This is the distance between the axis (link center) and the measurement position. The movable stage (swinging part 32d) moves in the X-axis direction, and viscosity Cx acts on the movement.

  The moving stage device 30 (lifting part 32 c) drives the moving stage 31 (swing part 32 d) in the Z-axis direction so that the substrate 2 held on the moving stage 31 is pressed against the substrate 1 held on the fixed stage 21. Then, the moving stage 31 contacts the fixed stage 21 through the substrates 1 and 2. This state is expressed as a rigid body simulating the fixed stage 21 and a rigid body simulating the moving stage 31 coupled via a spring and a damper (both not shown). The friction stiffness kwx and friction viscosity Cwx in the X-axis direction acting between the substrates 1 and 2 (between the lower surface of the rigid body simulating the fixed stage 21 and the upper surface of the rigid body simulating the moving stage 31) at this time are expressed. Note that the center of gravity L of the combined body of the fixed stage 21 and the movable stage 31 is used.

  In the mathematical model described above, the moving stage 31 that holds the substrate 2 is driven in the X-axis direction by a driving force (thrust force) Fx. Further, it is swung around the swing shaft (link center) by the swing torque Ty. Ld is a difference in height (deviation from the center of gravity of the driving point) between the driving point of the movable stage 31 and its center of gravity (position where the driving force Fx acts), and XU and X2d are X of the reflecting mirrors 23 and 33, respectively. Axial position. Further, XU = X0−LXU · θ2, X2d = X1 + Lx · θ2.

  The input / output response of the moving stage 31, that is, the response of the position X and the inclination θy in the translational direction of the moving stage 31 that are observed as control amounts when the driving force Fx and the swing torque Ty are given to the moving stage 31 as operation amounts. Can be expressed in the following matrix form:

The transfer functions P ₁₁ , P ₁₂ , P ₂₁ , and P ₂₂ are obtained in the Laplace transform form as follows by applying the mathematical model described above and deriving the Lagrangian equation of motion.

FIG. 8 summarizes representative values of parameters related to the moving stage 31. Here, the driving point where the driving force Fx is generated is designed at a distance Ld = 0.005 m downward from the center of gravity of the moving stage 31. The swing axis (rotation center in the tilt direction) of the moving stage 31 is designed on the wafer surface held by the moving stage 31. Note that the positional relationship between the reference point (measurement position by the interferometer 42) of the position measurement of the moving stage 31 and its center of gravity is fixed because of the apparatus configuration, so the relationship Lx + Lx2 = 0.039m is always established as a constraint condition. .

FIG. 9 shows frequency response characteristics of the transfer functions P ₁₁ and P ₂₁ (amplitude and phase) obtained above. The response of the transfer function P ₁₁ , that is, the position X in the translational direction of the moving stage 31 when the driving force Fx is applied to the moving stage 31, decreases its gain monotonically with respect to the frequency and keeps its phase almost constant. Exhibits rigid behavior. On the other hand, the transfer function P ₂₁ , that is, the response of the inclination θy of the moving stage 31 when the driving force Fx is applied to the moving stage 31 shows a unique behavior. The gain remains constant with respect to the frequency in the low frequency band, forms a peak in the vicinity of 3 Hz, and decreases with a constant slope with respect to the frequency in a frequency band higher than that. The phase remains constant with respect to the frequency in the low frequency band, jumps −180 degrees in the vicinity of 3 Hz, and remains constant with respect to the frequency in the frequency band higher than that.

Since the drive point and the swing axis (rotation center in the tilt direction) are deviated from the center of gravity (Ld ≠ 0, Lx2 ≠ 0), the propagation function P ₂₁ ≠ 0, that is, the coupling between the drive force Fx and the tilt θy. When a driving force Fx in the translational direction is generated at the driving point, thrust interference such as oscillation torque Ty is generated in the rotational direction (θy direction). In particular, from the specific behavior of the transfer function P ₂₁ described above, the control error of the tilt θy is expected. Therefore, thrust interference from the driving force Fx to tilt [theta] y, i.e. is required controller is designed to offset the coupling between the driving force Fx and the inclined [theta] y due to the propagation function P _21.

  Considering the thrust interference in the drive control of the moving stage 31 (non-centroid drive stage), particularly the control error of the inclination θy when the drive force Fx is given, using the mathematical model described above.

FIG. 10 shows a configuration of a feedback control system corresponding to the moving stage driving unit 32 that drives the moving stage 31. In this control system, the interferometer 42 that measures the position (first control amount) X and the tilt (second control amount) θy in the translation direction (X-axis direction) of the moving stage 31, the target values Rx, R _θy, and the first Using the measurement results of the first and second control amounts (X, θy), the operation amounts Ux, U _θy (here, the driving force Fx and the swinging torque Ty) are calculated, and the results are transmitted to the moving stage driving unit 32. And a control unit 60 that drives and controls the moving stage 31. The operation amount movable stage driving unit 32 receives Ux, by adding a driving force Fx and the swinging torque Ty is equal to accordingly U _{[theta] y} in the moving stage 31, the moving stage 31 is driven.

Here, the target value (target trajectory), the controlled variable, the manipulated variable, etc. are defined as a function of time. In FIG. 10 and other figures and the explanation using them, the Laplace transform (Laplace transform type) is used. We will use it. Further, the arithmetic expressions Ux (Rx−X) and U _θy (R _θy −θy), which will be described later, are also defined in the Laplace transform form. In other cases, unless otherwise specified, explanation will be made using Laplace transform.

The control unit 60 includes a target generation unit 60a, subtracters 60b ₁ and 60b ₂ , controllers 60c ₁ and 60c ₂ , a stabilization filter 60f, and a thrust distributor 60d. Each of these units may be configured by a microcomputer configuring the control unit 60 and software, or may be configured by hardware.

Target generator 60a is the target Rx translational direction position X and the inclination [theta] y of the moving stage 31, and generates an R _{[theta] y,} respectively, and supplies the subtractor _60b 1, 60b _2.

The subtractor 60b ₁ calculates a deviation (Rx−X) between the target value Rx and the measurement result of the translation stage position (first control amount) X of the moving stage 31 from the interferometer 42, and the controller 60c ₁ ( To the transfer function Cx). Further, the subtractor 60b ₂ calculates the target value the slope of the moving stage 31 from R _{[theta] y} and the interferometer 42 (second control amount) [theta] y of the measurement results and the deviation of the _(R θy -θy), the controller 60c ₂ (Transfer function C _θy ).

Controller 60c ₁ is the deviation (Rx-X) is such that the zero, to calculate the arithmetic operation amount Ux = Cx by (control operation) (Rx-X). Here, Cx is the transfer function of the controller 60c _1. Further, the controller 60c ₂ is the deviation _(R θy -θy) is such that the zero, to calculate the arithmetic operation amount U _{[theta] y} = C _{[theta] y} by (control _operation) (R θy -θy). Here, C _{[theta] y} is the transfer function of the controller 60c _2. The calculated operation amounts Ux, U _θy are supplied to the thrust distributor 60d via the stabilization filter 60f.

  The stabilization filter 60f stabilizes high-order mechanical resonance of the moving stage 31.

The thrust distributor 60d includes three controllers 60d ₁ , 60d ₂ , 60d ₃ and an adder (not shown). The controller 60d ₁ multiplies the manipulated variable Ux received from the controller 60c ₁ (via the stabilization filter 60f) by a gain A of ₁₁ and transmits it to the moving stage drive unit 32. The controllers 60d ₂ and 60d ₃ respectively multiply the manipulated variables Ux and U _θy received from the controllers 60c ₁ and 60c ₂ (through the stabilization filter 60f) by gains A ₂₁ and A ₂₂ and adders (non-adders). (Shown). The adder (not shown) adds the output from the controller 60d ₂ to the output from the controller 60d ₃ and transmits the result to the moving stage drive unit 32. In this embodiment, the gain A ₁₁ = A ₂₂ = 1. Therefore, the thrust distributor 60d is configured to transmit the operation amount Ux received from the controller 60c ₁ to the movable stage driving unit 32, the operation amount of receiving manipulated variable U _{[theta] y} received from the controller 60c ₂ from the controller 60c ₁ Ux is compensated as U _θy + A ₂₁ Ux, and the compensated operation amount U _θy ′ (= U _θy + A ₂₁ Ux) is transmitted to the moving stage drive unit 32.

Movable stage driving unit 32, the received operation amount Ux, _'according equal translation direction of the driving force Fx and the manipulated variable U _{[theta] y} to the operation amount _Ux' U _{[theta] y} emit equal oscillating torque Ty to. Thereby, the moving stage 31 is driven toward the driving target. The compensation A ₂₁ Ux of the operation amount U _θy gives a swinging torque that cancels the torque generated in the θy direction when the translational driving force Fx (including disturbance) is generated. Thereby, thrust interference from the driving force Fx to the inclination θy (coupling between the driving force Fx and the inclination θy) is canceled out.

In FIG. 11A, the inclination θy when the target position Rx (amplitude 100 μm, where R _θy = 0) is given to the moving stage drive unit 32 in a step shape with respect to the design conditions of the moving stage 31 is shown. The time transition (simulation result) of the control error (following error) is shown. Here, the design conditions of the moving stage 31 are as follows: (a) The height difference Ld between the driving point and its center of gravity and the distance Lx2 between the swing axis of the moving stage and its center of gravity are non-zero. (Ld ≠ 0, Lx2 ≠ 0), (b) Ideal design only for Ld, that is, center-of-gravity drive (Ld = 0, Lx2 ≠ 0), (c) Ideal design only for Lx2 (Ld ≠ 0, Lx2 = 0) and (d) Consider the four conditions of ideal design (Ld = 0, Lx2 = 0).

Note that the representative values summarized in FIG. 8 are used as the values of Ld and Lx2 and the values of other parameters. Further, the gain A _{21 of} the thrust distributor 60d (controller 60d ₃ ) is set to Ld. Thereby, in feedback control, the moment (the thrust interference to the tilt θy) generated in the θy direction when the translational driving force Fx is generated due to the driving point of the moving stage 31 being deviated from the center of gravity (Ld ≠ 0). ) Is applied by the thrust distributor 60d, and thrust interference with the inclination θy is canceled (compensated).

(D) In the case of an ideal design, there is almost no tracking error because there is no mechanical interference. Further, (c) In the case of ideal design only for Lx2 (Ld ≠ 0, Lx2 = 0), the mechanical interference due to Ld ≠ 0 is almost canceled by the gain A ₂₁ = Ld, so that a tracking error hardly occurs. The reason why the tracking error cannot be made zero is that the modeling error due to the stabilization filter is not taken into consideration. In contrast, (a) in the case of the conventional design, an overshoot with an amplitude of about 0.8 μrad occurs with respect to the stepped rise of the target position Rx at time t = 0.1 sec, followed by about 0. . Rigging appears for 3 sec, and the tracking error is substantially attenuated at time t ≧ 0.4 sec. (B) In the case of center-of-gravity driving (Ld = 0, Lx2 ≠ 0), a tracking error similarly occurs.

In this feedback control, because the gain A ₂₁ = Ld of the thrust distributor 60d (controller 60d ₃ ) is set as described above, the driving point of the moving stage 31 is deviated from the center of gravity (Ld ≠ 0). The resulting thrust interference is compensated. Therefore, it can be seen from the difference between the results of the conditions (c) and (d) that the cause of the follow-up error is the deviation of the swing axis of the moving stage 31 from the center of gravity (Lx2 ≠ 0).

Therefore, the thrust distributor 60d is designed in consideration of not only the drive point shift (Ld ≠ 0) of the moving stage 31 but also the swing axis shift (Lx2 ≠ 0). So as to cancel the thrust interference by the transfer function _{P 21,} giving the gain _{A 21} of the controller 60d ₃ as follows.

Note that A ₂₁ = Ld is derived for Lx2 = 0. As the values of the parameters, the representative values summarized in FIG. 8 are used. Thus, the control amount θy (= P ₂₁ Ux + P ₂₂ U _θy ′) = P ₂₂ U _θy is derived from the configuration of the feedback control system shown in FIG. In other words, displacement of the driving point (Ld ≠ 0) shift of the pivot axis as well (Lx2 ≠ 0) thrust interference caused by the (coupling with the driving force Fx according to the transfer function P ₂₁ and the inclined [theta] y) is canceled, the mobile Decoupling control of the stage 31 is possible.

  FIG. 11B shows a case where a rectangular pulse-like disturbance (amplitude 0.05 N, pulse width 30 msec) is applied to the moving stage 31 in the translation direction independently of the driving force Fx with respect to the design conditions of the moving stage 31. The time transition (simulation result) of the control error (following error) of the inclination θy at is shown. Here, the above four conditions are considered as design conditions for the moving stage 31.

(D) In the case of an ideal design, there is almost no tracking error because there is no mechanical interference. In the case of (b) centroid driving (Ld = 0, Lx2 ≠ 0), the tracking error hardly occurs. Therefore, it can be seen that the follow-up error of the inclination θy caused by the disturbance is insensitive to the swing axis deviation (Lx2 ≠ 0). In contrast, (a) in the case of the conventional design, an overshoot with an amplitude of about 0.8 μrad occurs with respect to the rise of the rectangular pulse of disturbance at time t = 0.1 sec, followed by about 0.3 sec. Rigging appears during this period, and the tracking error substantially attenuates at time t ≧ 0.4 sec. (C) In the case of ideal design only for Lx2 (Ld ≠ 0, Lx2 = 0), a follow-up error similarly occurs. From the difference in the results of the conditions (c) and (d), it can be seen that the inclination tracking error due to the disturbance is sensitive to the drive point deviation (Ld ≠ 0). This is because the disturbance is applied after the thrust distribution calculation, and the cancellation of the thrust interference due to the gain A ₂₁ = Ld is not reflected.

  In order to cancel the tracking error of the gradient θy resulting from the disturbance, a disturbance observer is introduced. FIG. 12 shows the configuration of the feedback control system in which the disturbance observer 60e is incorporated. The configuration is the same as that of the feedback control system shown in FIG. 10 except for the disturbance observer 60e and the controller related thereto.

In the feedback control system of FIG. 12, the measurement result of the translational position (first control amount) X from the interferometer 42 is supplied to the subtractor 60e ₂ and the output of the thrust distributor 60d (compensated operation amount). U _θy ′) is supplied to the differentiator 60e ₂ via the controller 60e ₁ (transfer function P ₁₂ ). Here, the transfer function _{P 12} of the controller 60e ₁ is given by the formula (2a) and Formula (2b). As the values of the parameters, the representative values summarized in FIG. 8 are used. Differentiator 60e ₂ generates a difference between the measurement results of the position X translational direction and the output U _{[theta] y 'P 12} of the controller 60e _1. Thus, the contribution of the coupling between the position X of the first control amount contribution thrust interference to X (swing torque Ty by the transfer function P ₁₂ and the translational direction of the oscillating torque Ty from the measurement result of the position X translational direction ) Is offset. The measurement result of the position X in the translation direction in which the thrust interference (coupling) is canceled and the output of the thrust distributor 60d (operation amount Ux ′ = Ux) are supplied to the disturbance observer 60e.

The disturbance observer 60e estimates a disturbance applied to the moving stage 31 independently of the driving force Fx from two inputs. The disturbance observer 60e supplies the estimated disturbance to an adder (not shown) constituting the thrust distributor 60d. Adder (not shown) generates a sum of the output of the disturbance observer 60e output (estimated disturbance) a controller 60c ₁ (operation amount Ux), and supplies to the controller 60d _3. Thereby, the thrust interference to the inclination θy resulting from the disturbance is also canceled, and the non-interference control of the moving stage 31 becomes possible.

In FIG. 13A, the inclination θy when the target position Rx (amplitude 100 μm, where R _θy = 0) is given to the moving stage drive unit 32 in a step shape with respect to the design conditions of the feedback control system. The time transition (simulation result) of the control error (following error) is shown. Here, as design conditions of the feedback control system, (a) conventional design, that is, the gain A ₂₁ = Ld of the controller 60d ₃ and no application of the disturbance observer, (b) design considering only the disturbance, that is, the controller 60d ₃ Gain A ₂₁ = Ld and application of disturbance observer, (c) Optimum design in this embodiment, that is, application of gain A ₂₁ = −N ₂ / N _{4 of} controller 60d ₃ and disturbance observer, and similar to the above (D) In the case of an ideal design (Ld = 0, Lx2 = 0), the following four conditions are considered: gain A ₂₁ = Ld and no application of a disturbance observer. Similar to the above, the representative values summarized in FIG. 8 are used as the parameter values.

  In the case of (a) the conventional design and (b) the design considering only the disturbance, an overshoot with an amplitude of about 0.8 μrad occurs with respect to the stepped rise of the target position Rx at time t = 0.1 sec. Subsequently, rigging appears for about 0.3 sec, and the tracking error is substantially attenuated at time t ≧ 0.4 sec. On the other hand, in the case of (c) optimal design, almost no tracking error occurs as in the case of (d) ideal design. Therefore, the thrust interference to the inclination θy derived from the driving force Fx is cancelled.

  FIG. 13B shows a case where a rectangular pulse disturbance (amplitude 0.05 N, pulse width 30 msec) is applied to the moving stage 31 in the translation direction independently of the driving force Fx, in accordance with the design conditions of the feedback control system. The time transition (simulation result) of the control error (following error) of the inclination θy at is shown. Here, the above four conditions are considered as design conditions for the feedback control system.

  (A) In the case of the conventional design, an overshoot with an amplitude of about 0.8 μrad occurs with respect to the rising edge of the disturbance rectangular pulse at time t = 0.1 sec, followed by rigging for about 0.3 sec. Thus, the tracking error substantially attenuates at time t ≧ 0.4 sec. On the other hand, in the case of (b) the design considering only the disturbance and (c) the optimum design, the tracking error hardly occurs as in the case of (d) the ideal design. Therefore, thrust interference to the inclination θy resulting from disturbance is also canceled out.

  By applying the feedback control system configured as described above, particularly the thrust distributor 60d (see FIG. 12), even when the design conditions of the moving stage 31 are different from the ideal design (Ld = 0, Lx2 = 0), the driving force It has been proved that thrust interference from Fx (including disturbance) to the tilt θy is canceled, and that the moving stage 31 can be controlled to be non-interfering.

  The optimum design of the moving stage 31 (optimization of the driving point and the position of the swing shaft) will be described. It should be noted that the stage used for the non-interacting control analysis and the stage used for the optimal design analysis to be described below are remarkably different in the size of the mechanism, and the numerical values cannot be directly associated with each other.

  In the substrate bonding apparatus 100 of the present embodiment, the moving stage 31 is driven to contact the fixed stage 21 in order to bond the substrate 1 held by the fixed stage 21 and the substrate 2 held by the moving stage 31. Therefore, when the movable stage 31 is driven independently of the fixed stage 21 to align the substrates 1 and 2, and when the movable stage 31 contacts the fixed stage 21 to bond the substrates 1 and 2, The center of gravity of the moving stage 31 is displaced. Accordingly, it is considered that the conventional empirical optimum design that matches the driving point and the swing axis (rotation center in the tilt direction) of the moving stage 31 with the center of gravity is not appropriate for the substrate bonding apparatus 100. Therefore, in the substrate bonding apparatus 100 of the present embodiment, rather, the resonance (resonance behavior) that occurs at the time of substrate bonding is reduced, and the drive point and the swing shaft are set so that a higher bandwidth of feedback control is possible. Optimize position.

  In the conventional feedback control system, the control unit 60 measures the interferometers 41 and 42 (measurement results of the relative positions of the movable stage 31 with respect to the translation stage (X, Y) and tilt (θx, θy) with respect to the fixed stage 21). The substrate 2 held by the moving stage 31 is controlled by driving the moving stage 31 by controlling the moving stage driving unit 32 and generating the driving force (Fx, Fy) and the swinging torque (Tx, Ty) in the translation direction. Is pressed against the substrate 1 held on the fixed stage 21.

  14 (A) and 14 (B) show complementary sensitivity functions T (s) (amplitude (in the case where two substrates (manufactured by company I) are pressed into contact with each other with a pressure of 5 N and 20 N, respectively) in a conventional feedback control system. The frequency response characteristics of gain) | T (s) | and phase arg (T (s))) are shown. Here, s = jω = j2πf, j = √ (−1), and f is a frequency. The solid line represents the actual measurement result, and the broken line represents the result reproduced using the mathematical model described above (FIG. 6). In the reproduction using the mathematical model, the complementary sensitivity function (or transfer function) derived using the mathematical model is reproduced by determining the values of various parameters using the least square method so that the actual measurement result is reproduced. The

  The complementary sensitivity function T (s) exhibits a complicated behavior. At any applied pressure, resonance appears in the vicinity of 20 Hz, 120 Hz, and 130 to 150 Hz. (An anti-resonance appears in the vicinity of 60 Hz.) Of these, the resonance that appears in the vicinity of 20 Hz shows almost the same behavior regardless of the pressure applied to the two substrates. Therefore, it is considered that this resonance is derived from the spring characteristics of the two support members 22 that support the fixed stage 21. The resonance appearing in the vicinity of 120 Hz is not particularly considered in the feedback control in the present embodiment, and is not considered here. It can be confirmed that the position of resonance (referred to as primary resonance) appearing in the vicinity of 130 to 150 Hz is shifted with respect to the applied pressure of the two substrates. Therefore, this resonance is considered to originate from the joining of two substrates. More specifically, the spring characteristic (vibration k0z of the spring element and the viscosity C0z of the spring element) relating to the vibration in the Z-axis direction of the two support members 22 that support the fixed stage 21 acts between the joint surfaces of the substrates 1 and 2. This is due to the coupled vibration due to the spring characteristics (friction rigidity kwx and friction viscosity Cwx).

  It should be noted that spring characteristics (spring element stiffness k0x and spring element viscosity C0x) related to vibration in the X-axis direction of the two support members 22 and spring characteristics (friction stiffness kwx and friction viscosity) acting between the joining surfaces of the substrates 1 and 2. Resonance (referred to as secondary resonance) derived from coupled vibration with Cwx) appears in the high frequency band (near 2000 Hz). However, since the stiffness k0x of the spring element is larger than the stiffness k0z of the spring element, the frequency band in which the secondary resonance appears is sufficiently high, and the degree of behavior is the gain line in FIGS. 14 (A) and 14 (B). It is so small that it cannot be confirmed in the figure. Therefore, here, primary resonance derived mainly from the above-described coupled vibration is considered.

By using the mathematical model, the complementary sensitivity function when the two substrates are pressed against each other with the applied pressures 5N and 20N shown in FIGS. 14 (A) and 14 (B) is reproduced. The friction stiffness kwx and the friction viscosity Cwx acting in between are obtained as kwx = 4 × 10 ⁷ , Cwx = 4500, kwx = 5 × 10 ⁷ , and Cwx = 5500, respectively. It can be seen that the mathematical model parameters (friction stiffness kwx and friction viscosity Cwx) vary depending on the pressure applied to the two substrates.

  15A to 15C, the moving stage 31 reproduced using the mathematical model (FIG. 6) described above for the bonding of different substrates (part 1 to part 3) is shown. A frequency response characteristic of a transfer function (amplitude and phase) expressing the output response is shown. The solid line indicates the characteristics when the two substrates are pressed against each other with the applied pressure of 5N and the broken line with the applied pressure of 20N.

  By using the mathematical model, in the frequency response characteristics of the transfer function, the resonance derived from the spring characteristic of the support member 22 that appears in the vicinity of 20 Hz, the anti-resonance that appears in the range of 60 to 90 Hz, and the two substrates that appear in the vicinity of 130 to 150 Hz. The resonance derived from the junction is reproduced. The transfer function keeps the amplitude and phase constant in a frequency band of 20 Hz or less, rapidly increases and decreases the amplitude due to resonance in the vicinity of 20 Hz and decreases the phase to 180 degrees, and rapidly increases the amplitude due to anti-resonance at 60 to 90 Hz. As the frequency decreases and increases, the phase is increased to 180 degrees, and further, the amplitude is rapidly increased and decreased by resonance near 130 to 150 Hz, and the phase is decreased to 180 degrees. These indicate continuous peaks, valleys, and mountain shapes and valleys and peaks in the gain diagram and the phase diagram, respectively. That is, the transfer function exhibits a resonance mode in phase with the rigid body mode.

  The resonance that appears in the vicinity of 20 Hz shows almost the same behavior with respect to the type of substrate to be bonded and the applied pressure. On the other hand, the resonance that appears in the vicinity of 130 to 150 Hz is in response to the bonding state such as the type of substrate to be bonded (the material of the substrate, the presence or absence of a pattern, the state of the bonding surface depending on the type) and the pressure contact force (pressing force). Various behaviors. In particular, the position is shifted. Therefore, since resonance in the vicinity of 130 to 150 Hz shows different behavior depending on the bonding state of the two substrates, it can be expected that it can be a particularly serious obstacle to precise and stable control of the moving stage 31.

  The input / output response of the moving stage 31 (strictly speaking, the moving stage 31, the fixed stage 21, and the composite of the substrates 1 and 2 held by them) at the time of bonding, which is a control target, is the following mode decomposition type It can be expressed using a transfer function.

The first and second terms on the right side represent rigid body characteristics, and the third and fourth terms represent primary and secondary resonances, respectively. However, in the third and fourth terms, since the coefficients C and E are almost zero, only the coefficients (referred to as mode influence constants) D and F are considered. When the mode influence constants D and F are positive (that is, the resonance is in phase with respect to the rigid body characteristics) and the absolute value is small, the resonance behavior becomes negligibly small, and the bandwidth of the feedback control can be increased.

  Therefore, the input / output response of the moving stage 31 is calculated using the mathematical model described above, and the mode influence constants D and F are obtained with respect to the positions of the drive point and the swing axis (deviations Ld and Lx2 from the center of gravity). Ld and Lx2 are optimized so that they become sufficiently small positive values. However, on the apparatus structure of the board | substrate bonding apparatus 100, they are optimized under restrictions Ld> = 0.04 and Lx2> = 0.

  In FIG. 16A, the deviation Ld from the center of gravity of the driving point is a conventional design (Ld = 0.0462 m (see the numerical value shown in FIG. 8)), and the bonding to the deviation Lx2 from the center of gravity of the swing shaft is performed. The change of the mode influence constants D and F in the input / output response of the moving stage at the time is shown. The mode influence constant D is about 0.006 with respect to the conventional design (Ld = 0.0462, Lx2 = 0.103), which is a positive but large value. For this reason, the primary resonance exhibits a unique behavior in the frequency characteristics of the complementary sensitivity function T (s) shown in FIGS. 14 (A) and 14 (B). Therefore, it is necessary to optimize the oscillation axis deviation Lx2 so that the constant D shows a value sufficiently smaller than this value.

  The mode influence constant D shows a peak structure with respect to the oscillation axis deviation Lx2. That is, the maximum value is taken in the vicinity of Lx2 = 0, and the value is decreased as Lx2 decreases and increases. Here, the constant D takes a substantially zero value at Lx2 = −0.246 and 0.6. On the other hand, the mode influence constant F is sufficiently small in the range of Lx2 = −0.2 to 0.6. Therefore, Lx2 = 0.6 (Ld = 0.0462) is obtained as the optimum solution (first optimum solution) of the swing axis deviation Lx2 from the constraint condition (Lx2 ≧ 0).

  In FIG. 16B, the deviation Lx2 from the center of gravity of the swing axis is a conventional design (Lx2 = 0.103 m (see the numerical value shown in FIG. 8)), and the mode influence on the deviation Ld from the center of gravity of the drive point. Changes in the constants D and F are shown. It is necessary to optimize the drive point deviation Ld so that the mode influence constant D shows a value sufficiently smaller than the value (about 0.006) with respect to the conventional design (Ld = 0.0462 m, Lx2 = 0.103). is there. The mode influence constant D decreases monotonously with respect to the drive point shift Ld. Here, the constant D takes a substantially zero value at Ld = 0.257. On the other hand, the mode influence constant F is sufficiently small in the range of Ld = −0.1 to 0.4. Therefore, Ld = 0.257 (Lx2 = 0.103) is obtained as the optimum solution (second optimum solution) of the drive point deviation Ld from the constraint condition (Ld ≧ 0.04).

  In this way, the resonance behavior can be suppressed by optimizing the drive point deviation Ld and increasing it relative to the value of the conventional design, that is, by moving the position of the drive point away from the center of gravity. However, it is not preferable to increase the drive point deviation Ld in the non-interference control of the moving stage 31. Rather, it is desirable to optimize the drive point deviation Ld so that a smaller optimum value is obtained for the oscillation axis deviation Lx2. Therefore, both the drive point and the swing axis deviations Ld and Lx2 are optimized as follows.

  FIG. 16C shows changes in the mode influence constants D and F with respect to the deviations Ld and Lx2 from the center of gravity of the drive point and the swing axis. First, there is no optimal solution for the driving point deviation Ld where the mode influence constant D takes a zero value for the oscillation axis deviation Lx2 = −0.3 and −0.1. Next, with respect to Lx2 = 0.1, the constant D takes a zero value at Ld≈0.26. However, since this condition is almost equal to the above-mentioned second solution, another solution is searched for. Next, for Lx2 = 0.3, the constant D takes a zero value at Ld = 0.105. This condition gives an optimum value smaller than the first solution (Lx2 = 0.6) for the oscillation axis deviation Lx2. Finally, for Lx2 = 0.5 and 0.6, the constant D takes a zero value when Ld≈0.05. However, this condition is almost equal to the above-mentioned first solution, and cannot be adopted as a new optimum solution. On the other hand, the mode influence constant F is sufficiently small in the range of Ld = −0.1 to 0.4. Therefore, Ld = 0.105 and Lx2 = 0.3 are obtained as the third optimum solution.

  FIGS. 17A to 17C show the case where the substrate 3 is pressed against the first to third optimum solutions with a pressure of 20 N (5 N only for the third optimum solution), respectively. A frequency response characteristic (broken line) of a transfer function (amplitude and phase) representing the input / output response of the moving stage 31 reproduced using a mathematical model (FIG. 6) is shown. For comparison, the propagation function (solid line) for the conventional design (Ld = 0.462, Lx2 = 0.103) is also shown.

  For the first optimum solution Lx2 = 0.6 (Ld = 0.0462) (see FIG. 17A), the primary resonance appearing in the vicinity of 130-150 Hz together with the anti-resonance appearing at 60-90 Hz is shown in the Bode diagram. To the extent that it cannot be confirmed, the secondary resonance that appears in the vicinity of 2000 Hz is also suppressed to a negligible level. Further, the gain increases by about 40 dB in the low frequency band. In the conventional design, the resonance derived from the spring characteristics of the support member 22 that appears in the vicinity of 20 Hz shifts its position in the vicinity of 6 Hz.

  In contrast to the second optimum solution Ld = 0.257 (Lx2 = 0.103) (see FIG. 17B), the primary and secondary resonances are suppressed to such an extent that they can be ignored. Anti-resonance is suppressed to such an extent that it cannot be confirmed.

  For the third optimum solution Ld = 0.105 and Lx2 = 0.3 (see FIG. 17C), as in the case of the first optimum solution, 2 to the extent that primary resonance and anti-resonance cannot be confirmed. The secondary resonance is also suppressed to a negligible level. Further, the gain is increased by about 20 dB in the low frequency band. Note that the resonance derived from the spring characteristics of the support member 22 has shifted its position to around 10 Hz.

  The primary resonance is sufficiently suppressed for any optimum solution.

  18A to 18C, for comparison, three substrates (No. 1 to No. 3 (see FIG. 15)) in the conventional design (Ld = 0.462, Lx2 = 0.103) are shown. A Nyquist diagram for the bonding is shown. The solid line indicates the characteristics when the two substrates are pressed against each other with the applied pressure of 5N and the broken line with the applied pressure of 20N. For any condition (substrate and applied pressure), the Nyquist locus includes two loops derived from resonance. One of them shows only a part of it in the figure, and it passes through the vicinity of the point (1, 1), the point (0, 0), and the point (0, -1) for each condition. Since the trajectory is traced, it is determined that the resonance is caused by the spring characteristic of the support member 22 that appears in the vicinity of 20 Hz. The other appears at the lower right in the figure, and since the size of the loop is particularly different depending on the applied pressure, it is determined that the resonance is due to the resonance (primary resonance) derived from the joining of the two substrates.

  For any of the conditions, the Nyquist trajectory does not surround the point (−1, 0) and passes through the right side thereof, and therefore satisfies the Nyquist stability condition. However, in the Nyquist trajectory, the size of a loop due to resonance originating from the joining of two substrates varies significantly depending on conditions (pressure contact force and substrate type), and the point (-1, 0) particularly for substrate 1 or 3 thereof. To a distance of 0.5. In FIG. 18A and other figures, a circle with a radius of 0.5 centered on the point (−1, 0) is drawn as an index of stability. Therefore, although the conventional control system is stable, it is evaluated that its degree is low.

  FIGS. 19A to 19C show Nyquist diagrams for bonding of three substrates (part 1 to part 3 (see FIG. 15)) in the first optimum solution. 19A to 19C, the Nyquist trajectories for the pressurizing forces 5N and 20N almost overlap each other. For any condition (substrate and pressure), the Nyquist locus does not surround the point (−1, 0) and passes through the right side thereof, and thus satisfies the Nyquist stability condition. In any condition, a loop due to the primary resonance does not appear, and the Nyquist locus is sufficiently away from the point (−1, 0) and passes on the right side. In addition, since the moment of inertia is increased and the resonance frequency is decreased due to a large shift of the swing axis from the center of gravity, the display range of FIGS. 19A to 19C is derived from the spring characteristics of the support member 22. Large loops due to resonance do not appear (appear outside the display range).

  20A to 20C show Nyquist diagrams for the bonding of three substrates (part 1 to part 3 (see FIG. 15)) in the second optimum solution. 20A to 20C, the Nyquist trajectories for the pressurizing forces 5N and 20N almost overlap each other. For any condition (substrate and pressure), the Nyquist locus does not surround the point (−1, 0) and passes through the right side thereof, and thus satisfies the Nyquist stability condition. In any condition, a loop due to the primary resonance does not appear, and the Nyquist locus is sufficiently away from the point (−1, 0) and passes on the right side.

  FIGS. 21A to 21C show Nyquist diagrams for bonding of three substrates (No. 1 to No. 3 (see FIG. 15)) in the third optimum solution. In FIGS. 21A to 21C, the Nyquist trajectories for the pressurizing forces 5N and 20N almost overlap each other. Similar to the Nyquist diagram for the first optimal solution (see FIGS. 19A to 19C), the Nyquist trajectory is a point (−1, 0) for any condition (substrate and applied pressure). ) And it passes the right side of it, so it satisfies the Nyquist stability conditions. In any condition, a loop due to the primary resonance does not appear, and the Nyquist locus is sufficiently away from the point (−1, 0) and passes on the right side. In addition, since the moment of inertia is increased and the resonance frequency is decreased due to a large shift of the swing axis from the center of gravity, the display range of FIGS. 19A to 19C is derived from the spring characteristics of the support member 22. Large loops due to resonance do not appear (appear outside the display range).

  For any optimal solution, primary resonance was sufficiently suppressed, and a large margin was obtained. Therefore, the gain of feedback control is increased until the Nyquist trajectory approaches a range of distance 0.5 from the point (-1, 0).

  FIGS. 22A and 22B show complementary sensitivities when feedback control is applied to the first optimal solution for bonding substrates (part 3) with pressures of 5 N and 20 N, respectively. The frequency response characteristic (dashed line) of the function (amplitude and phase) is shown. Similarly, feedback control is performed for the second optimal solution in FIGS. 23A and 23B, and for the third optimal solution in FIGS. 24A and 24B. The frequency response characteristic (broken line) of the complementary sensitivity function (amplitude and phase) when applied is shown. In any case, for comparison, the frequency response characteristic (solid line) of the complementary sensitivity function (amplitude and phase) with respect to the conventional design (Ld = 0.0462, Lx2 = 0.103) is also shown.

  The optimal design of the moving stage 31 (optimization of the drive point and the position of the swing axis) suppresses the unique behavior due to the primary resonance in any optimal solution, and the feedback control gain is improved by about 20 times. The bandwidth is increased from 25 Hz to 50 to 65 Hz.

When considering the non-interference control of the moving stage 31 when the substrates are bonded together, the moving stage 31 is not driven in the translational direction but is positioned at a certain position (that is, the target position Rx = 0). It is not necessary to consider the thrust interference to the inclination θy derived from the driving force Fx considered in FIG. 13, and the thrust interference to the inclination θy derived from the disturbance considered in FIG. 13B (conditions (b) and (c)) Only need to be considered. Therefore, in the feedback control system to which the disturbance observer of FIG. 12 is applied, either the gain A ₂₁ = −N ₂ / N ₄ or A ₂₁ = Ld of the controller 60d ₃ in the thrust distributor 60d may be selected. Since the gain A ₂₁ of the controller 60d ₃ need not incorporate shift Lx2 of the pivot axis, can be employed first or third optimal solution of the optimal solution of the above.

In the decoupling control of the moving stage 31 independent of the fixed stage 21 described above, in the feedback control system to which the disturbance observer of FIG. 12 is applied, the gain A ₂₁ = −N ₂ / N of the controller 60d ₃ in the thrust distributor 60d. ₄ was selected. Therefore, when the movable stage 31 is driven independently of the fixed stage 21 in order to align the substrates 1 and 2, the gain A ₂₁ = −N ₂ / N ₄ of the controller 60d ₃ is bonded to the substrates 1 and 2. Therefore, when the moving stage 31 is brought into contact with the fixed stage 21, the gain A ₂₁ is switched to Ld. Thereby, it is possible to perform highly accurate feedback control both when the movable stage 31 is driven independently of the fixed stage 21 and when the movable stage 31 contacting the fixed stage 21 is driven.

As described above, according to the feedback control of the moving stage 31 in the substrate bonding apparatus 100 according to the present embodiment, the position (first control amount) X and the tilt ( (Second control amount) θy is measured, and the moving stage 31 is moved in the translation direction by using the first operation amount Ux (the driving force Fx in the translation direction) obtained from the measurement result of the first control amount X by the thrust distributor 60d. While controlling the drive, the second operation amount U _θy obtained from the measurement result of the second control amount θy is compensated using the first operation amount Ux, and the moving stage 31 is used using the compensated second control amount U _θy ′. Is controlled in the θy direction. Thus, the torque generated in the θy direction when the driving force Fx in the translational direction is generated due to the drive point and the swing axis of the moving stage 31 being deviated from the center of gravity (Ld ≠ 0, Lx2 ≠ 0) is canceled. The swing torque is compensated, and thrust interference from the driving force Fx to the inclination θy (coupling between the driving force Fx and the inclination θy) is canceled out. Therefore, it is possible to feedback control the moving stage 31 designed with the drive point and the swing axis shifted from the center of gravity with high accuracy.

Further, according to the feedback control of the moving stage 31 in the substrate bonding apparatus 100 according to the present embodiment, the measurement result of the position (first control amount) X of the moving stage 31 in the translation direction, the first operation amount Ux, and the second operation. The disturbance in the translational direction applied to the moving stage 31 is estimated using the amount U _θy (or U _θy ′), and offset by compensating the second operation amount U _θy using the first operation amount Ux. Thereby, thrust interference to the inclination θy resulting from disturbance is also canceled, and the moving stage 31 can be feedback-controlled with high accuracy.

  Moreover, according to the board | substrate bonding apparatus 100 which concerns on this embodiment, the movement stage 31 is the fixed stage 21 by optimizing the drive point of the movement stage 31, and the position (shift | offset Ld, Lx2 from a gravity center) of a rocking | fluctuation shaft. The resonance behavior shown when touching is made unobservable. As a result, the moving stage 31 can be accurately and stably feedback controlled, and the two substrates can be aligned and bonded with high accuracy. For example, large-diameter wafers can be superposed with high accuracy, for example, on the order of 100 nm, and as a result, a three-dimensional stacked semiconductor device with high mounting area efficiency can be efficiently manufactured.

  In this embodiment, the position is selected as the control amount of the fixed stage 21 and the movable stage 31 that are the control targets. Instead, the measurement amount related to the position, such as speed and acceleration, is selected as the control amount. Also good. In such a case, the speed and acceleration may be calculated and used from the first floor difference or second floor difference calculation of the measurement results of the interferometers 41 and 42. Alternatively, a speed measuring device, an acceleration measuring device, and the like independent from the interferometers 41 and 42 are installed, and speed, acceleration, and the like are measured using them.

  1, 2 ... Substrate, 3, 4 ... Substrate holder, 10 ... Frame, 20 (21, 22, 23) ... Fixed stage device (fixed stage, support member, reflector), 30 (31, 32, 33) ... Moving stage device (moving stage, moving stage drive unit, reflecting mirror), 41, 42 ... interferometer, 51,52 ... microscope, 60 (60d, 60e) ... control unit (thrust distributor, disturbance observer), 100 ... substrate Bonding device.

Claims (14)

A substrate bonding apparatus for bonding two substrates,
A first stage for holding one of the two substrates;
A second stage that moves while holding the other of the two substrates opposite to the one substrate, and that contacts the first stage via the two substrates;
First and second control amounts related to the translational position and the tilting position of the second stage are measured, respectively, and the second operation amount is obtained using a first operation amount obtained from the measurement result of the first control amount. The stage is driven and controlled in the translation direction, and the second operation amount obtained from the measurement result of the second control amount is compensated by using the first operation amount, and the second operation amount is compensated by using the compensated second control amount. A control unit that drives and controls the two stages in the tilt direction;
A substrate bonding apparatus comprising:   The control unit compensates the second operation amount using the first operation amount, so that the inclination of the translational direction thrust applied to the second stage by the drive control using the first operation amount is performed. The board | substrate bonding apparatus of Claim 1 which cancels the thrust distributed to the drive to a direction.   The control unit estimates a translational disturbance applied to the second stage using the measurement result of the first control amount and the first and second operation amounts, and uses the first operation amount for the disturbance. The substrate bonding apparatus according to claim 1, wherein the second operation amount is compensated by canceling.   The control unit compensates for the second operation amount when driving and controlling the second stage in contact with the first stage and when driving and controlling the second stage independently of the first stage. The board | substrate bonding apparatus as described in any one of Claims 1-3 which switches.   The control unit compensates the second operation amount in consideration of a shift from the center of gravity of the drive point in the translation direction of the second stage when driving the second stage that contacts the first stage. The substrate bonding apparatus according to claim 4.   When the second stage is driven and controlled independently of the first stage, the control unit shifts the driving point from the center of gravity in the translation direction of the second stage and the center of rotation in the tilt direction of the second stage. The substrate bonding apparatus according to claim 4, wherein the second operation amount is compensated in consideration of a deviation from the center of gravity.   The second stage is optimized when at least one of a deviation from the center of gravity of the drive point in the translation direction of the second stage and a deviation from the center of gravity of the rotation center in the tilt direction is optimized and comes into contact with the first stage. The board | substrate bonding apparatus as described in any one of Claims 1-6 which makes non-observable the resonance behavior which shows. A substrate laminating method for laminating two substrates,
A translation direction of the second stage that moves while holding the other of the two substrates while facing the one of the two substrates held by the first stage and contacting the first stage via the two substrates Measuring the first and second control amounts respectively related to the position and the position in the inclination direction;
The second stage is driven and controlled in the translation direction using the first operation amount obtained from the measurement result of the first control amount, and the second operation amount obtained from the measurement result of the second control amount is set to the first operation amount. Compensating using the measurement result of the controlled variable, and driving the second stage in the tilt direction using the compensated second controlled variable;
A substrate bonding method including:   In the drive control, the second operation amount is compensated using the measurement result of the first control amount, so that the translational direction applied to the second stage by the drive control using the first operation amount is performed. The substrate bonding method according to claim 8, wherein the thrust distributed to the drive in the tilt direction is canceled out of the thrust.   In the drive control, a disturbance to the drive in the translational direction of the second stage is estimated using the measurement result of the first control amount and the first and second manipulated variables, and the disturbance is converted into the first disturbance. The substrate bonding method according to claim 8 or 9, wherein the second operation amount is compensated by using a measurement result of a control amount to cancel.   In the drive control, when the second stage that contacts the first stage is driven and controlled, and when the second stage is driven and controlled independently of the first stage, the second operation amount is reduced. The board | substrate bonding method as described in any one of Claims 8-10 which switches compensation.   In the drive control, when the second stage that contacts the first stage is driven and controlled, the second operation amount is set in consideration of the deviation of the drive point from the center of gravity in the translational direction of the second stage. The substrate bonding method according to claim 11, wherein compensation is performed.   In the drive control, when the second stage is driven and controlled independently of the first stage, the shift of the drive point from the center of gravity in the translation direction of the second stage and the tilt direction of the second stage. The substrate bonding method according to claim 11, wherein the second operation amount is compensated in consideration of a deviation of the center of rotation from the center of gravity.   At least one of the deviation from the center of gravity of the drive point in the translation direction of the second stage and the deviation from the center of gravity of the rotation center in the tilt direction is a resonance exhibited by the second stage when contacting the first stage. The substrate bonding method according to claim 8, wherein the substrate bonding method is optimized so as to make the behavior unobservable.