Patent Publication Number: US-2023145758-A1

Title: Imprint apparatus and article manufacturing method

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention is related to an imprint apparatus. 
     Description of the Related Art 
     Conventionally, there has been a demand for improving an overlay accuracy by reducing a distortion caused by a relative tilt between a mold and a substrate when a pattern of an imprint material is formed in an imprint apparatus. 
     Japanese Patent Application Laid-Open No. 2017-157639 discloses an imprint apparatus which changes a tilt of a mold based on a contact position of the mold in a surface direction of a substrate in order to reduce a relative tilt between the mold and the substrate due to a tilt of a substrate holding unit which holds the substrate when the mold and an imprint material on the substrate are brought into contact with each other. 
     As described above, the method disclosed in Japanese Patent Application Laid-Open No. 2017-157639 is effective in reducing the relative tilt between the mold and the substrate caused by the tilt of the substrate holding unit. 
     However, in the imprint apparatus, it is known that the relative tilt between the mold and the substrate changes not only by the above but also by a thickness of the imprint material on the substrate or a pressing force of the mold when the mold is brought into contact with the imprint material on the substrate, for example. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide an imprint apparatus capable of effectively reducing a relative tilt between a mold and a substrate when a pattern of an imprint material is formed. 
     The imprint apparatus according to the present invention is an imprint apparatus for forming a pattern of an imprint material on a substrate surface of a substrate by using a mold, in which the imprint apparatus includes a mold holding unit configured to hold the mold, a mold driving unit configured to move the mold holding unit, a substrate holding unit configured to hold the substrate, a substrate driving unit configured to move the substrate holding unit, and a controller configured to control the mold driving unit and the substrate driving unit. The controller is configured to perform a contacting step of moving at least one of the mold holding unit and the substrate holding unit by at least one of the mold driving unit and the substrate driving unit such that the mold and the imprint material on the substrate surface are brought into contact with each other, an obtaining step of obtaining a driving force in a first direction parallel to the substrate surface for the substrate holding unit by the substrate driving unit after performing the contacting step, and a tilt correcting step of rotating the mold holding unit about a second direction perpendicular to the first direction in the substrate surface by the mold driving unit based on a magnitude of the driving force obtained in the obtaining step. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic cross-sectional view of an imprint apparatus according to a first embodiment of the present invention. 
         FIG.  2 A  is a partially enlarged cross-sectional view of the imprint apparatus according to the first embodiment when a mold and a substrate are brought into contact with each other. 
         FIG.  2 B  is a partially enlarged cross-sectional view of the imprint apparatus according to the first embodiment when a mold and a substrate are brought into contact with each other. 
         FIG.  3    is a flowchart showing an imprint process in the imprint apparatus according to the first embodiment. 
         FIG.  4    is a graph illustrating an example of time dependence of each of a driving force of an actuator and a tilt variation amount of a mold holding unit in some steps in an imprint process performed by the imprint apparatus according to the first embodiment. 
         FIG.  5    is a flowchart showing an imprint process in an imprint apparatus according to a second embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Hereinafter, an imprint apparatus according to the present invention is described in detail with reference to the accompanying drawings. The drawings described below may be drawn on a scale different from the actual scale in order to facilitate understanding of the present invention. 
     First Embodiment 
     In response to a recent demand for further miniaturization in semiconductor devices, micro electro mechanical systems (MEMS) or the like, an imprint technique capable of forming a fine pattern (structure) on the order of several nanometers on a substrate has attracted attention in addition to a conventional photolithography technique. 
     Specifically, the imprint technique is a microfabrication technique to form a pattern of an imprint material corresponding to a fine concave-convex pattern formed on a mold, on a substrate by supplying (coating) an uncured imprint material onto the substrate, bringing the imprint material into contact with the mold, and curing the imprint material. 
     There is a photocuring method as one method for curing an imprint material in the imprint technique. 
     The photocuring method is a method of forming a pattern of an imprint material on a substrate by curing the imprint material supplied to a shot region on the substrate by irradiating the imprint material with light such as ultraviolet light in a state in which the imprint material and a pattern region of a mold are brought into contact with each other. 
     In addition, there is known a method to suppress remaining of bubbles in a pattern region of a mold by deforming the pattern region of the mold into a convex shape so as to protrude toward a substrate, and bringing the mold and an imprint material on the substrate into contact with each other. 
     In general, when the mold and the imprint material on the substrate are brought into contact with each other, at least one of the mold and the substrate is controlled such that a relative tilt between the mold and the substrate becomes zero, namely a surface of the mold on which a pattern is formed and a substrate surface become parallel to each other. 
     However, when the mold and the substrate are brought into contact with each other in a state in which the pattern region of the mold is deformed into a convex shape as described above, it is difficult to make the relative tilt between the mold and the substrate zero due to a warpage of the substrate, a deformation according to a rigidity of the substrate holding unit, and an imprint condition including a position of a shot region. 
     Accordingly, a technique has been proposed for reducing a moment which changes the relative tilt between the mold and the substrate generated when the mold and the imprint material on the substrate are brought into contact with each other. 
     Specifically, in the above-described technique, an imprint process is performed on a test substrate in advance, and a moment is obtained in each period such as an imprint period in which a mold is brought into contact with an imprint material on the substrate or a filling period in which a pattern region of the mold is filled with the imprint material. Further, a target value of the relative tilt at which the moment falls within an allowable range is determined. 
     In the imprint process on the subsequent substrate, the moment can be reduced by bringing the mold and the imprint material on the substrate into contact with each other after setting the relative tilt between the mold and the substrate so as to be the determined target value. 
     Although a method of performing a correction using a result acquired by performing the imprint process in advance as in the above-described technique is useful, a robustness is low since a factor causing the moment is not accurately found in the first place. 
     That is, when the imprint process is performed under an imprint condition which is slightly different from that in the imprint process performed in advance, the difference affects the relative tilt between the mold and the substrate, and thus it becomes difficult to reduce the moment. 
     As a result of intensive studies, the inventors of the present application have focused on the fact that a movement of the substrate holding unit after the mold and the substrate are brought into contact with each other is one of factors which generate the moment. 
     Accordingly, an object of the present invention is to provide the imprint apparatus capable of effectively reducing the relative tilt between the mold and the substrate based on a driving force applied to a substrate stage in the movement of the substrate holding unit. 
       FIG.  1    shows a schematic cross-sectional view of an imprint apparatus  1  according to a first embodiment of the present invention. 
     The imprint apparatus  1  according to the present embodiment is used to manufacture a device such as a semiconductor device as an article. Specifically, the imprint apparatus  1  is a lithography apparatus which performs an imprint process of forming a pattern of an imprint material  30  on a substrate  29  by using a mold  19 . 
     Specifically, in the imprint apparatus  1  according to the present embodiment, an energy for curing is applied to the imprint material  30  after the imprint material  30  supplied onto the substrate  29  and the mold  19  are brought into contact with each other. Thereby, a pattern of a cured product to which a concave-convex pattern of the mold  19  is transferred can be formed. 
     As shown in  FIG.  1   , the imprint apparatus  1  according to the present embodiment includes an illuminating unit  2 , a mold holding mechanism  3 , a substrate stage  4 , a supplying unit  5 , a mold controller  7  (a controller), an alignment measuring unit  8  (a position measuring unit), and a substrate controller  10  (a controller). 
     A curable composition (also referred to as an uncured resin) which is cured by an application of the energy for curing is used as the imprint material  30  used in the imprint apparatus  1  according to the present embodiment. 
     As the energy for curing, an electromagnetic wave, a heat or the like is used. As the electromagnetic wave, light such as infrared rays, visible rays or ultraviolet rays having a wavelength selected from a range between 10 nm and 1 mm is used, for example. 
     That is, the curable composition is a composition which is cured by a light irradiation or heating. 
     In particular, a photocurable composition which is cured by the light irradiation contains at least a polymerizable compound and a photopolymerization initiator, and may contain a non-polymerizable compound or a solvent as necessary. 
     The term “non-polymerizable compound” herein refers to at least one compound selected from a group consisting of a sensitizer, a hydrogen donor, an internal release agent, a surfactant, an antioxidant and a polymer component. 
     In the imprint apparatus  1  according to the present embodiment, the imprint material  30  may be coated in a film form onto the substrate  29  by a spin coater or a slit coater forming the supplying unit  5 . 
     Alternatively, the imprint material  30  may be coated onto the substrate  29  in the form of a droplet, an island formed by connecting a plurality of droplets, or a film by a liquid injecting head forming the supplying unit  5 . 
     The viscosity (at 25° C.) of the imprint material  30  used in the imprint apparatus  1  according to the present embodiment is 1 mPa·s or more and 100 mPa·s or less, for example. 
     In the imprint apparatus  1  according to the present embodiment, a glass, a ceramic, a metal, a semiconductor, a resin or the like may be used as a material of the substrate  29 , and a member made of a material different from that of the substrate  29  may be formed on a surface of the substrate  29  as necessary. 
     Specifically, the substrate  29  used in the imprint apparatus  1  according to the present embodiment includes a silicon wafer, a compound semiconductor wafer and quartz glass. 
     The imprint apparatus  1  according to the present embodiment employs a photocuring method as a method for curing the imprint material  30 . 
     A direction parallel to an optical axis of the illuminating unit  2  which irradiates the imprint material  30  on the substrate  29  with curing light  12  (a direction perpendicular to a substrate surface) is defined as a Z axis, and two directions orthogonal to each other in a plane perpendicular to the Z axis (in the substrate surface) are defined as an X axis and a Y axis (a first direction and a second direction). 
     As shown in  FIG.  1   , the mold holding mechanism  3  includes a mold holding unit  20  which holds the mold  19 , a mold base which holds the mold holding unit  20 , and a mold driving unit  31  which moves the mold holding unit  20  with respect to the mold base. 
     The mold holding unit  20  sucks to hold the mold  19  by attracting an outer peripheral region of a surface of the mold  19  on which the curing light  12  is incident by a vacuum suction or an electrostatic force. 
     For example, when the mold holding unit  20  holds the mold  19  by a vacuum suction force, the mold holding unit  20  is connected to a vacuum pump (not illustrated) provided outside, and an attachment and a detachment (holding and releasing) of the mold  19  can be switched by turning on and off the vacuum pump. 
     The mold driving unit  31  moves the mold holding unit  20  which holds the mold  19  in the Z direction so as to selectively press the mold  19  against the imprint material  30  on the substrate  29  (an imprint process) and separate the mold  19  from the imprint material  30  on the substrate  29  (a mold releasing process). 
     Actuators applicable to the mold driving unit  31  include a linear motor and an air cylinder, for example. 
     The mold driving unit  31  may be formed by a plurality of driving systems including a coarse movement driving system, a fine movement driving system and the like in order to position the mold  19  with a high accuracy. 
     The mold driving unit  31  is configured to be capable of moving the mold  19  in the X direction and the Y direction in addition to the Z direction. 
     Further, the mold driving unit  31  is configured to have a tilt function for adjusting a position of the mold  19  in a θ Z  direction (a rotation direction around the Z axis) and positions of the mold  19  in a θ X  direction and a θ Y  direction (a rotation direction around the X axis and a rotation direction around the Y axis) corresponding to tilts of the mold  19 . 
     Note that although the imprint process and the mold releasing process in the imprint apparatus  1  according to the present embodiment are performed by moving the mold  19  in the Z axis direction, the present invention is not limited thereto, and they may be performed by moving the substrate  29  (namely, the substrate stage  4 ) in the Z axis direction. 
     Alternatively, they may be performed by relatively moving both of the mold  19  and the substrate  29  in the Z axis direction. 
     In each of the mold holding unit  20 , the mold base, and the mold driving unit  31  forming the mold holding mechanism  3 , an opening is formed on the inside including a central portion such that the imprint material  30  on the substrate  29  is irradiated with the curing light  12  from the illuminating unit  2 . 
     A light transmitting member for sealing a space surrounded by a part of the opening and the mold  19  is arranged in the opening, and a pressure in the sealed space is adjusted by a pressure adjusting device (not illustrated) including a vacuum pump or the like. 
     For example, when the imprint material  30  on the substrate  29  and the mold  19  are brought into contact with each other, the pressure adjusting device can deflect (deform) a pattern region  19   a  of the mold  19  into a convex shape toward the substrate  29  by increasing the pressure in the sealed space higher than an external pressure. 
     Accordingly, the mold  19  can be brought into contact with the imprint material  30  on the substrate  29  from a central portion of the pattern region  19   a  of the mold  19 . 
     Thereby, it is possible to suppress air from remaining between the pattern region  19   a  of the mold  19  and the imprint material  30  during the contact, and to fill the imprint material  30  into every corner of the pattern region  19   a  of the mold  19 . 
     The imprint apparatus  1  according to the present embodiment can form the pattern of the mold  19  on the imprint material  30  on the substrate  29  as described above. 
     The substrate stage  4  can perform an alignment of the substrate  29  with respect to the mold  19  when the pattern of the imprint material  30  is formed on the substrate  29  by moving with holding the substrate  29 . 
     As shown in  FIG.  1   , the substrate stage  4  includes a Y stage  23  (a substrate holding unit) which sucks to hold the substrate  29  and is movable at least in the Y direction, and an X stage  24  (a substrate holding unit) which mechanically holds the Y stage  23  and is movable at least in the X direction. 
     Further, the substrate stage  4  includes an encoder system  25 , a Y actuator  41  (a substrate driving unit) and an X actuator  42  (a substrate driving unit). 
     The Y stage  23  can be moved by driving a Y actuator  41  including a Y movable unit  41   a  and a Y fixed unit  41   b,  and the X stage  24  can be moved by driving an X actuator  42  including an X movable unit  42   a  and an X fixed unit  42   b.    
     For example, a linear motor or a planar motor can be used as the Y actuator  41  and the X actuator  42 . 
     Note that each of the Y stage  23  and the X stage  24  may be formed by a plurality of stages including a coarse moving stage, a fine moving stage and the like in order to position the substrate  29  with a high accuracy. 
     The X stage  24  may be configured to be capable of moving the substrate  29  in the Z direction. 
     In addition, the X stage  24  may be configured to have a tilt function for adjusting a position of the substrate  29  in the θ Z  direction and positions of the substrate  29  in the θ X  direction and the θ Y  direction corresponding to tilts of the substrate  29 . 
     The encoder system  25  corresponding to the X direction, the Y direction and the Z direction are arranged on side surfaces of the Y stage  23  and the X stage  24 . 
     The encoder system  25  measures respective positions of the Y stage  23  and the X stage  24  in real time by irradiating an encoder scale  26  with a beam from an encoder head  27 . 
     Then, the substrate controller  10  performs positioning of each of the Y stage  23  and the X stage  24  based on a measured value of the encoder system  25 . 
     The alignment measuring unit  8  irradiates the mold  19  and the substrate  29  with alignment light  32  and detects it reflected by the mold  19  and the substrate  29  when positioning of the substrate  29  with respect to the mold  19  is performed. 
     Thereby, a relative position deviation amount between the mold  19  and the substrate  29  can be measured by measuring a position in the substrate surface of an alignment mark (a first mark) formed on the mold  19  and a position in the substrate surface of an alignment mark (a second mark) formed on the substrate  29 . 
     The relative position deviation amount measured here is used when the mold driving unit  31  moves the mold holding unit  20 , or the Y actuator  41  and the X actuator  42  move the Y stage  23  and the X stage  24  to reduce the relative position deviation between the mold  19  and the substrate  29 . 
     It is also possible to reduce the relative position deviation between the mold  19  and the substrate  29  by deforming a shape of the pattern region  19   a  of the mold  19  or a shape of a shot region on the substrate  29  by a shape correcting unit (not illustrated). 
     The supplying unit  5  supplies (applies) the imprint material  30  onto the substrate surface of the substrate  29  which has moved immediately below. The supplying unit  5  may supply the imprint material  30  to the entire substrate surface of the substrate  29  all at once, or may supply the imprint material  30  to each shot region arranged in a line or to each shot region on which the imprint process is performed. 
     When the imprint material  30  is supplied to the entire substrate surface of the substrate  29  in advance before the substrate  29  is carried into the imprint apparatus  1  according to the present embodiment, the supplying unit  5  may not be provided. 
     The controller including the mold controller  7  and the substrate controller  10  is formed by a computer including a CPU, a memory and the like, and controls each unit of the imprint apparatus  1  in accordance with a program stored in the memory. 
     Specifically, the mold controller  7  controls the imprint process of forming the pattern of the imprint material  30  on the substrate  29  by controlling an operation, an adjustment or the like of each unit of the imprint apparatus  1 . 
     The substrate controller  10  controls the substrate stage  4  to move the substrate stage  4  to a supplying area of the supplying unit  5  for supplying the imprint material  30  to the substrate  29  or a position for bringing the substrate  29  into contact with the mold  19 . 
     Further, the substrate controller  10  issues a command to the Y actuator  41  and the X actuator  42  in order to perform positioning by moving the substrate  29  relative to the mold  19  in the X direction and the Y direction after bringing the mold  19  and the substrate  29  into contact with each other. 
     As shown in  FIG.  1   , the imprint apparatus  1  according to the present embodiment includes a stage base plate on which the substrate stage  4  is placed, a bridge base plate which fixes the mold holding mechanism  3 , and support columns which are supported by the stage base plate and supports the bridge base plate. 
     In addition, vibration isolating units are arranged on a base plate supported by a floor in the imprint apparatus  1  according to the present embodiment, and the vibration isolating units support the stage base plate to reduce a vibration propagating from a floor surface to the stage base plate. 
     Further, the imprint apparatus  1  according to the present embodiment includes a mold conveying unit (not illustrated) which conveys the mold  19  to the mold holding mechanism  3  from the outside, a substrate conveying unit (not illustrated) which conveys the substrate  29  to the substrate stage  4  from the outside, and the like. 
     Next, an operation performed after bringing the mold  19  and the imprint material  30  on the substrate  29  into contact with each other in the imprint process performed by the imprint apparatus  1  according to the present embodiment is described. 
       FIGS.  2 A and  2 B  show partially enlarged cross-sectional views of the imprint apparatus  1  according to the present embodiment when the mold  19  and the imprint material  30  on the substrate  29  are brought into contact with each other. 
     Specifically, for example, as shown in  FIG.  2 A , the X stage  24  moves in the −X direction after the pattern region  19   a  of the mold  19  and the imprint material  30  on the substrate  29  are brought into contact with each other, in order to reduce the relative position deviation between the mold  19  and the substrate  29  measured by the alignment measuring unit  8 . 
     When the alignment between the mold  19  and the substrate  29  is performed by moving the X stage  24  in the −X direction, a force along a shearing direction (here, the X direction) is applied to the pattern region  19   a  of the mold  19 . 
     As a result, the pattern region  19   a  of the mold  19  rotates around the Y axis, namely it has a predetermined tilt in the θ Y  direction, as shown in  FIG.  2 A . 
     At this time, the mold driving unit  31  performs tilt driving of the mold holding unit  20 , namely it rotates the mold holding unit  20  about the Y-axis to correct this tilt in the pattern region  19   a  of the mold  19  in the imprint apparatus  1  according to the present embodiment, as shown in  FIG.  2 B . 
     Thereby, it is possible to reduce the relative tilt between the pattern region  19   a  of the mold  19  and the substrate  29 . 
     Here, a position variation amount of the substrate stage  4  when the relative position deviation between the mold  19  and the substrate  29  is reduced as described above also includes an influence of deformations of the Y stage  23  and the X stage  24  provided between the substrate  29  and a position where the position measurement is performed in the substrate stage  4 . 
     In addition, the shearing force applied to the pattern region  19   a  of the mold  19  by the movement of the substrate stage  4 , the relative tilt between the pattern region  19   a  of the mold  19  and the substrate  29 , and the tilt driving amount required for the mold holding unit  20  also depend on a moving distance and a moving speed in the movement of the substrate stage  4 . 
     Accordingly, the imprint apparatus  1  according to the present embodiment performs the tilt driving of the mold holding unit  20  by the mold driving unit  31  by feeding back driving forces by the Y actuator  41  and the X actuator  42  which are applied to the Y stage  23  and the X stage  24  of the substrate stage  4  to the mold driving unit  31 . 
       FIG.  3    shows a flowchart illustrating the imprint process in the imprint apparatus  1  according to the present embodiment. 
     First, when the imprint process is started in the imprint apparatus  1  according to the present embodiment, an imprint condition is set (step S 110 ). 
     Note that the imprint condition (a parameter) herein includes a material of the imprint material  30 , a thickness of the imprint material  30  on the substrate surface, a size of a shot region, a layout of the shot regions, an order of the shot regions to be subjected to the imprint process and the like, for example. 
     In the step S 110 , a tilt correction coefficient described in detail below is determined from the set imprint condition. 
     Specifically, in the step S 110 , the tilt correction coefficient can be determined by using a result of the imprint process previously performed under the same imprint condition in the imprint apparatus  1  according to the present embodiment. 
     Accordingly, when the imprint process is performed for the first time under a different imprint condition, it is preferred to confirm a result by performing the imprint process on a test substrate or the like under the different imprint condition in advance. 
     In the step S 110 , the tilt correction coefficient may be determined by performing a simulation based on the set imprint condition. 
     Next, the substrate  29  is moved by driving the substrate stage  4  to a position (a supplying area) where the supplying unit  5  supplies the imprint material  30  to a shot region on the substrate  29  where a pattern is to be formed by the imprint process (step S 111 ). 
     After the substrate stage  4  is moved to the position in the step S 111 , the imprint material  30  is supplied onto the shot region by the supplying unit  5  with moving the substrate  29  (step S 112 ). 
     Next, the substrate  29  is moved by driving the substrate stage  4  such that a predetermined shot region among the shot regions to which the imprint material  30  has been supplied in the step S 112  is arranged at a position facing the pattern region  19   a  of the mold  19  (step S 113 ). 
     Then, the mold driving unit  31  is driven to lower the mold  19  such that the imprint material  30  on the predetermined shot region and the pattern region  19   a  of the mold  19  are brought into contact with each other (step S 114 , a contacting step). 
     Next, a relative position deviation amount between the mold  19  and the substrate  29  is measured by the alignment measuring unit  8 , and the Y stage  23  and the X stage  24  are moved so as to reduce the measured relative position deviation amount to start an alignment between the mold  19  and the substrate  29  (step S 115 , start of a position correction process). That is, in the step S 115 , the alignment between the mold  19  and the substrate  29  is started based on measurement results of positions of alignment marks formed on the mold  19  and the substrate  29  by the alignment measuring unit  8 . 
     Then, values of driving forces of the Y actuator  41  and the X actuator  42  when the Y stage  23  and the X stage  24  are moved in the step S 115 , namely command values of the driving forces from the substrate controller  10  are obtained (step S 116 , an obtaining step). 
     Then, the mold holding unit  20  is rotated by the mold driving unit  31  in order to correct a tilt in the pattern region  19   a  of the mold  19  generated by movements of the Y stage  23  and the X stage  24  in the step S 115  (step S 117 , a tilt correcting step). 
     A calculation of a rotation amount of the mold holding unit  20 , namely a tilt variation amount of the mold  19  in the step S 117  will be described in detail later. 
     Thereafter, the alignment between the mold  19  and the substrate  29  by the movements of the Y stage  23  and the X stage  24  is ended (step S 118 , end of the position correction process). 
     Next, an exposure is performed by irradiating the imprint material  30  on the predetermined shot region of the substrate  29  with curing light  12  using the illuminating unit  2  (step S 119 ). 
     After the exposure is performed in the step S 119 , the mold driving unit  31  is driven to lift the mold  19  such that the mold  19  is separated from the imprint material  30  on the predetermined shot region of the substrate  29  (step S 120 ). Thereby, a pattern of the cured imprint material  30  is formed on the predetermined shot region of the substrate  29 . 
     Next, it is determined whether or not the exposure process in the steps S 113  to S 120  has been performed on all shot regions of the substrate  29  on which the pattern is to be formed (step S 121 ). 
     If there is a shot region on which the exposure process has not been performed (No in the step S 121 ), the process returns to step S 113 , and the exposure process is performed on the shot region. 
     On the other hand, when the exposure process has been performed on all the shot regions of the substrate  29  (Yes in the step S 121 ), the process proceeds to step S 122 . 
     In the step S 122 , it is determined whether or not the imprint condition set in the step S 110 , namely the material of the imprint material  30 , the thickness of the imprint material  30 , the size of the shot region, the layout of the shot regions, the order of the shot regions in which the imprint process is performed and the like is a new condition. 
     If the imprint condition is not the new condition (No in the step S 122 ), the imprint process on the substrate  29  is ended. 
     On the other hand, when the imprint condition is the new condition (Yes in the step S 122 ), the process proceeds to step S 123 . 
     In the step S 123 , an overlay position deviation amount on the substrate  29  on which the pattern of the imprint material  30  is formed is confirmed in order to calculate the tilt correction coefficient under the new imprint condition. 
     Specifically, a high magnification scope (not illustrated) provided in the imprint apparatus  1  is used to measure the position deviation amount of each mark formed in the shot region of the substrate  29  on which the pattern of the imprint material  30  is formed. 
     In the step S 123 , the position deviation amount of each mark formed in the shot region of the substrate  29  may be measured by using a measuring device provided outside the imprint apparatus  1  after the substrate  29  on which the pattern of the imprint material  30  is formed is carried-out from the imprint apparatus  1 . 
     The overlay position deviation amount measured in the step S 123  includes several components such as a shift component, a magnitude component, a torsion component, a rotation component and a tilt component. 
     Here, a tilt component in the substrate surface which affects a distortion in the shot region is extracted among such components. 
     The reason for this is that a distortion amount in the shot region changes by 0.5 nanometers when the tilt variation amount of the mold  19  is 1 microradian, for example, under a predetermined imprint condition, namely it is found that a distortion variation amount in the shot region depends on the tilt variation amount of the mold  19 . 
     Accordingly, the tilt variation amount of the mold  19  is calculated from a magnitude of the distortion in the shot region in the imprint apparatus  1  according to the present embodiment. 
     When the material of the imprint material  30  is new in the imprint condition, it is better to confirm a relation between the distortion and the tilt variation amount by performing the exposure process on each of the plurality of substrates  29  with making the tilt variation amounts of the mold  19  different from each other, for example. 
     As described above, in the step S 123 , the distortion in the shot region is extracted from the measured overlay position deviation amount on the substrate  29 , and the tilt variation amount of the mold  19  is calculated from the extracted distortion in the shot region. 
     Then, the driving forces of the Y actuator  41  and the X actuator  42  obtained in the step S 116  and the calculated tilt variation amount of the mold  19  are compared with each other. 
     Specifically, the driving force in the X direction by the X actuator  42 , and the tilt variation amount of the mold  19  corresponding to the driving force, namely an angle of the mold  19  formed with respect to the X direction (the angle in the rotation direction around the Y axis) are represented by F X  and T X , respectively. 
     Similarly, the driving force in the Y direction by the Y actuator  41 , and the tilt variation amount of the mold  19  corresponding to the driving force, namely an angle of the mold  19  formed with respect to the Y direction (the angle in the rotation direction about the X axis) are represented by F Y  and T Y , respectively. 
     At this time, by substituting these values into the following expressions (1) and (2), proportional coefficients, namely tilt correction coefficients C X  and C Y  are calculated (step S 124 , a determining step). 
         T   X   =C   X   ×F   X   (1)
 
         T   Y   =C   Y   ×F   Y   (2)
 
     Here, the tilt variation amounts T X  and T Y  of the mold  19  can be calculated as driving forces applied to a plurality of actuators provided in the mold driving unit  31 . 
     In addition, the driving forces F X  and F Y  of the X actuator  42  and the Y actuator  41  can be calculated as a command value from the substrate controller  10 . 
     Here, the tilt correction coefficients C X  and C Y  are constants which are not affected from other axes. 
     Although the tilt correction coefficients C X  and C Y  are calculated for each shot region in the above description, the present invention is not limited to this. 
     For example, the tilt correction coefficients C X  and C Y  may be determined so as to reduce an error by collectively performing a least squares method on all shot regions on which the imprint process of the substrate  29  has been performed. 
     Further, the tilt correction coefficients C X  and C Y  may be determined in accordance with a region where the imprint process has been performed in the shot region. 
     That is, the tilt correction coefficients C X  and C Y  may be determined so as to minimize the error between the shot regions for which the imprint process has been performed on an entire region, for example. 
     Further, the tilt correction coefficients C X  and C Y  may be determined so as to minimize the error between the shot regions for which the imprint process has been performed on a predetermined partial region. 
     As an example, when the driving force F X  in the X direction is 3 N and the tilt variation amount T X  at that time is 1.5 microradian under a predetermined imprint condition, C X  is calculated as 0.5 microradian/N by substituting them into the expression (1). 
     Then, the tilt correction coefficients C X  and C Y  for the tilt correction in the mold  19  calculated in the step S 124  are reflected in the imprint condition set in the step S 110 . 
       FIG.  4    shows an example of time dependence of each of the driving force F of the X actuator  42  and the tilt T of the mold holding unit  20  when the X stage  24  is moved in the steps S 115  to S 118  of the imprint process by the imprint apparatus  1  according to the present embodiment. 
     The time dependence shown herein is the same for the driving force of the Y actuator  41  when the Y stage  23  is moved. 
     As shown in  FIG.  4   , when the mold  19  is lowered in the step S 114 , a predetermined driving force F 1  is generated by the X actuator  42  in order to stop the substrate stage  4  immediately below the mold  19 . 
     In the step S 114 , the tilt T of the mold holding unit  20  is assumed to be T 1 . 
     Next, in the step S 115  in which the movement of the X stage  24  is started after the mold  19  and the substrate  29  are brought into contact with each other, a shearing force is generated in a shearing direction (the X direction) in the X stage  24 , and thus the driving force F of the X actuator  42  starts to change with time. 
     Then, a predetermined driving force F 2  is generated by the X actuator  42  at the time t a  immediately before the step S 118  at which the movement of the X stage  24  is finished. 
     Information of the driving force F 2  obtained in the step S 116  is transmitted from the substrate controller  10  to the mold controller  7 , and the mold controller  7  rotates the mold holding unit  20  by the tilt variation amount T X  calculated from the above-described expression (1) using the mold driving unit  31  based on the received information. 
     Thereby, the tilt T of the mold holding unit  20  changes from T 1  to T 2 . Note that a timing at which the mold holding unit  20  is rotated by the mold driving unit  31  may be any timing between the measurement of the driving force F by the X actuator  42  at the time t a  and the start of the exposure in the step S 119 . 
     In this way, by changing the tilt of the mold holding unit  20  to correct a relative tilt between the mold  19  and the substrate  29  before starting the exposure, it is possible to reduce an influence of the relative tilt, namely a distortion in a pattern of the imprint material  30  formed on the substrate  29 . 
     As described above, in the imprint process in the imprint apparatus  1  according to the present embodiment, the tilt variation amounts T X  and T Y  of the mold  19  are determined from the driving forces F X  and F Y  by the Y actuator  41  and the X actuator  42  in the steps S 115  and S 116 , and the tilt correction coefficients C X  and C Y  determined from the imprint condition. 
     Then, the distortion caused by the relative tilt between the mold  19  and the substrate  29  can be reduced to improve an overlay accuracy by performing the exposure process after the mold  19  is rotated by the tilt variation amounts T X  and T Y  determined in the step S 117 . 
     The calculation of the tilt correction coefficient in the step S 124  is not limited to the above-described method using actually measured values, and may be performed based on a simulation result. 
     The tilt correction coefficient is calculated in the step S 124  when the imprint condition is new in the imprint apparatus  1  according to the present embodiment, but the present invention is not limited to this. 
     That is, the step S 124  may be performed in order to increase an accuracy of the tilt correction coefficient under the same imprint condition in the imprint apparatus  1  according to the present embodiment. 
     Further, the tilt variation amounts T X  and T Y  of the mold  19  are determined from the driving forces F X  and F Y  by the Y actuator  41  and the X actuator  42  as shown in the expressions (1) and (2) in the above description, but the present invention is not limited thereto. 
     That is, an amount affected by deformations of the Y stage  23  and the X stage  24  is sufficiently reduced by appropriately changing a material of the imprint material  30  or by measuring positions of the Y stage  23  and the X stage  24  at positions close to the substrate  29 . 
     In this case, the tilt variation amounts T X  and T Y  of the mold  19  can be determined from position variation amounts of the Y stage  23  and the X stage  24 , namely driving amounts of the Y stage  23  and the X stage  24  instead of the driving forces F X  and F Y  by the Y actuator  41  and the X actuator  42  to be fed back to the mold driving unit  31 . 
     The control for reducing the tilt variation of the mold  19  generated when the substrate stage  4  is driven so as to reduce the relative position deviation amount between the mold  19  and the substrate  29  in the step S 115  has been described above. 
     However, the present invention is not limited thereto, and the imprint apparatus  1  according to the present embodiment can also be applied to a case of calculating to correct the tilt variation amount of the mold  19  from a shearing force in a shearing directions (X direction and Y direction) applied to the substrate  29  by bringing the mold  19  and the imprint material  30  on the substrate  29  into contact with each other, for example. 
     That is, when the pattern region  19   a  of the mold  19  is brought into contact with the imprint material  30  on the substrate  29  in a state in which the mold  19  has a relative tilt with respect to the substrate  29 , the shearing force in the shearing direction (X direction and Y direction) due to the contact may be applied to the substrate  29  in addition to a driving force for stopping the substrate stage  4 . 
     In this case, the relative tilt of the mold  19  with respect to the substrate  29 , namely the tilt variation amount of the mold  19  can be calculated from the applied shearing force based on the above-described discussion. 
     By rotating the mold  19  so as to correct the calculated tilt variation amount, the relative tilt between the mold  19  and the substrate  29  can be reduced. 
     In other words, in the imprint apparatus  1  according to the present embodiment, the driving forces by the Y actuator  41  and the X actuator  42  are obtained after the pattern region  19   a  of the mold  19  and the imprint material  30  on the substrate  29  are brought into contact with each other. 
     Then, the relative tilt between the mold  19  and the substrate  29  can be reduced by calculating the tilt variation amount of the mold  19  from magnitudes of the obtained driving forces to rotate the mold  19  so as to correct the calculated tilt variation amount. 
     In the above description, the driving forces F X  and F Y  by the Y actuator  41  and the X actuator  42  are calculated as a command value from the substrate controller  10 , but the present invention is not limited thereto. For example, they may be measured by providing a strain gauge or the like on the substrate  29  or the Y stage  23  which holds the substrate  29 . 
     Second Embodiment 
       FIG.  5    shows a flowchart illustrating an imprint process in an imprint apparatus according to a second embodiment of the present invention. 
     Since the imprint apparatus according to the present embodiment has the same structure as the imprint apparatus  1  according to the first embodiment, the same members are denoted by the same reference numerals, and a description thereof is omitted. 
     As shown in  FIG.  5   , the imprint process in the imprint apparatus according to the present embodiment is identical to the imprint process in the imprint apparatus  1  according to the first embodiment except that a step S 215  is performed instead of the steps S 115  to S 117 . 
     Thus, descriptions of the steps S 110  to S 114  and the steps S 118  to S 124  are omitted, and only the step S 215  is described below. 
     In the step S 215 , movements of the Y stage  23  and the X stage  24  for reducing a relative position deviation between the mold  19  and the substrate  29  and a rotation of the mold holding unit  20  for correcting a tilt in the pattern region  19   a  of the mold  19  are performed in synchronization with each other. 
     That is, in the step S 215 , the rotation of the mold holding unit  20  is performed after the movements of the Y stage  23  and the X stage  24  are performed. 
     Then, after the movements of the Y stage  23  and the X stage  24  are performed in order to reduce the relative position deviation between the mold  19  and the substrate  29  caused again by the rotation of the mold holding unit  20 , the rotation of the mold holding unit  20  is performed in order to correct the tilt in the pattern region  19   a  of the mold  19  caused again by the movements of the Y stage  23  and the X stage  24 . 
     Such a repeated operation is performed until the relative position deviation between the mold  19  and the substrate  29  becomes equal to or less than a predetermined threshold value and the relative tilt between the mold  19  and the substrate  29  becomes equal to or less than a predetermined threshold value. 
     Note that the present invention is not limited thereto, the repeated operation may be performed until a temporal variation amount of the relative position deviation between the mold  19  and the substrate  29  becomes equal to or less than a predetermined threshold value and a temporal variation amount of the relative tilt between the mold  19  and the substrate  29  becomes equal to or less than a predetermined threshold value. 
     Here, in the step S 215 , the rotation operation of the mold holding unit  20  may be performed over an entire period from a start to an end of the movements of the Y stage  23  and the X stage  24 . 
     Further, in the step S 215 , the rotation operation of the mold holding unit  20  may be performed intermittently, for example, every 0.1 seconds between the start and the end of the movements of the Y stage  23  and the X stage  24 . 
     Note that the case where the movements and the rotation are synchronized with each other such that the rotation operation of the mold holding unit  20  is performed only once immediately before the end of the movements of the Y stage  23  and the X stage  24  in the step S 215  corresponds to the position correction process in the imprint process in the imprint apparatus  1  according to the first embodiment. 
     As described above, in the imprint process performed by the imprint apparatus according to the present embodiment, the tilt variation amounts T X  and T Y  of the mold  19  are determined with synchronizing the movements of the Y stage  23  and the X stage  24  with the rotation of the mold holding unit  20  in the step S 215 . 
     By performing an exposure process after the relative position deviation between the mold  19  and the substrate  29  becomes equal to or less than a predetermined threshold value and the relative tilt between the mold  19  and the substrate  29  becomes equal to or less than a predetermined threshold value, it is possible to reduce a distortion caused by the relative tilt between the mold  19  and the substrate  29  to improve an overlay accuracy. 
     According to the present invention, it is possible to provide an imprint apparatus capable of effectively reducing the relative tilt between the mold and the substrate when a pattern of the imprint material is formed. 
     Article Manufacturing Method 
     A pattern of a cured product formed by using the imprint apparatus according to the present invention is used permanently in at least a part of various articles or temporarily when manufacturing the various articles. 
     Examples of the article include an electric circuit element, an optical element, a MEMS, a recording element, a sensor and a mold. 
     Further, examples of the electric circuit element include volatile or non-volatile semiconductor memories such as a dynamic random access memory (DRAM), a static random access memory (SRAM), a flash memory and a magnetoresistive random access memory (MRAM), and semiconductor elements such as a large scale integration (LSI), a charge coupled device (CCD), an image sensor and a field programmable gate array (FPGA). 
     Furthermore, an example of the mold includes a mold for imprinting. 
     The pattern of the cured product formed by using the imprint apparatus according to the present invention is used as it is as a constituent member of at least a part of the above-described article. 
     Alternatively, the pattern of the cured product is temporarily used as a resist mask, and the resist mask is removed after etching, ion implantation or the like is performed in a step for processing a substrate. 
     Although preferred embodiments have been described above, the present invention is not limited to these embodiments, and various modifications and changes can be made within the gist of the present invention. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2021-183520, filed Nov. 10, 2021, which is hereby incorporated by reference herein in its entirety.