WO2017038026A1 - Imprint apparatus, imprint method, and product manufacturing method - Google Patents

Abstract

An imprint apparatus that forms a pattern of an imprint material on a substrate by bringing the imprint material into contact with a mold, includes a moving unit to hold and move the substrate and a control unit. The control unit obtains a positional deviation amount expression formula that expresses a positional deviation amount at each position on a surface of the substrate held by the moving unit, referring to information about a warping shape of the substrate in a state where the substrate is not yet held by the moving unit, calculates positional deviation amounts at positions on the substrate surface referring to the obtained formula, obtains a distortion component relating to a shot region of the substrate based on the positional deviation amounts at the positions, and controls the shape or position of at least one of the mold and the substrate according to the obtained distortion component.

Description

IMPRINT APPARATUS, IMPRINT METHOD, AND PRODUCT MANUFACTURING METHOD

The present invention relates to an imprint apparatus, an imprint method, and a product manufacturing method.

With the increasing demand of forming refined semiconductor devices and Micro Electronic Mechanical Systems (MEMS), a micro processing technique capable of forming a resin pattern on a substrate (e.g., a wafer, a glass plate, or a film substrate) by shaping an uncured resin on the substrate with a mold, which is hereinafter referred to as “imprint technique”, has attracted a great attention in these days, in addition to a conventional photolithography technique. The imprint technique is prospective in excellent capability of forming a micro body structure of nanometer order on a substrate.

A conventional lithography apparatus using the imprint technique (i.e., imprint apparatus) discussed in PTL 1 is an apparatus employing a step and flash imprint lithography (SFIL) that is advantageous in manufacturing devices.

First, the above-mentioned imprint apparatus performs an operation for coating an ultraviolet curing resin (e.g., imprint material or light curing resin) on a shot region (i.e., an imprint region) of a substrate. Next, the imprint apparatus moves the substrate to a position adjacent to a mold and fills a mold pattern region with the resin. Then, the imprint apparatus irradiates the resin with ultraviolet rays to harden the resin and then separates the region from the mold. Through the above-mentioned processes, the imprint apparatus forms a resin pattern on the substrate.

Improving the overlay accuracy is required to realize mass production using a micro pattern formation of nanometer order by the above-mentioned imprint apparatus. To this end, accurately aligning the position of the mold pattern region relative to the shot region on the substrate is important.

Further, the above-mentioned imprint apparatus can employ a die-by-die alignment for aligning the position of the mold pattern region relative to the shot region on the substrate. The die-by-die alignment is characterized by optically detecting a mold mark provided on the mold and a substrate mark provided on the substrate and correcting a positional deviation and a shape difference between the mold pattern region and the shot region on the substrate, for each shot region on the substrate.

A method discussed in PTL 2 includes correcting pattern shapes of a mold and a substrate and accurately correcting the position of each pattern shape by combining a shape correction mechanism capable of deforming the mold by applying an external force and a heating mechanism capable of deforming the substrate by applying heat.

High integration of semiconductor devices requires refined and multilayered wirings. The process of forming multilayered wirings induces a warping phenomenon of the substrate that occurs entirely because film distortions generated during a film-forming operation tend to accumulate in post-processes of a semiconductor manufacturing process. Reshaping the warped substrate into a planer substrate is feasible by causing a substrate chuck provided on a substrate stage of the imprint apparatus to attract and hold the substrate. In this case, large distortions appear in the substrate fixed on the substrate chuck. The processing time required for an alignment operation will increase if the distortion to be corrected is large. Further, the imprint apparatus performs an alignment operation during a resin charging operation in a state where the mold is pressed against the resin. On the other hand, a predetermined charging time required to attain an appropriate residual film thickness is set beforehand. In this case, the residual film thickness indicates the thickness of the resin between a bottom surface of a recessed portion of a convex-concave pattern formed by the hardened resin and a surface of the imprinted substrate. If the generated distortion is large, the alignment operation may not complete within the charging time having been set beforehand. Accordingly, there is a possibility that the positional alignment between the mold and the substrate cannot be accomplished sufficiently and the overlay accuracy decreases.

Japanese Patent No. 4185941 Japanese Patent Application Laid-Open No. 2013-98291

The present invention is directed to an imprint apparatus, an imprint method, and a product manufacturing method, which can improve the overlay accuracy.

According to an aspect of the present invention, an imprint apparatus configured to form a pattern of an imprint material on a substrate by bringing the imprint material into contact with a mold, includes a moving unit configured to hold and move the substrate, and a control unit, wherein the control unit obtains a positional deviation amount expression formula that expresses a positional deviation amount at each position on a surface of the substrate held by the moving unit, with reference to information about a warping shape of the substrate in a state where the substrate is not yet held by the moving unit, calculates positional deviation amounts at a plurality of positions on the substrate surface with reference to the obtained positional deviation amount expression formula, and obtains a distortion component relating to a shot region of the substrate based on the positional deviation amounts obtained at the plurality of positions, and controls the shape or the position of at least one of the mold and the substrate according to the obtained distortion component.

Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.

Fig. 1 is a diagram illustrating a representative apparatus configuration of an imprint apparatus according to a first exemplary embodiment. Fig. 2 is a flowchart illustrating processing for obtaining a transformation matrix based on a warping shape of a wafer. Fig. 3A is a diagram illustrating a flat wafer that is free from warping. Fig. 3B is a diagram illustrating the wafer illustrated in Fig. 3A in a state where the wafer is fixed by a wafer chuck. Fig. 3C is a diagram illustrating a wafer having a downwardly protruding convex surface. Fig. 3D is a diagram illustrating the wafer illustrated in Fig. 3C in a state where the wafer is fixed by a wafer chuck. Fig. 3E is a diagram illustrating a wafer having an upwardly protruding convex surface. Fig. 3F is a diagram illustrating the wafer illustrated in Fig. 3E in a state where the wafer is fixed by a wafer chuck. Fig. 3G is a diagram illustrating a wafer having a saddle shaped surface. Fig. 3H is a diagram illustrating the wafer illustrated in Fig. 3G in a state where the wafer is fixed by a wafer chuck. Fig. 4 is a diagram illustrating a correspondence relationship between coefficients of a warping shape expression formula and corresponding warping shapes. Fig. 5 is a diagram illustrating a correspondence relationship between coefficients of a positional deviation amount expression formula and corresponding wafer distortion shapes. Fig. 6 is a flowchart illustrating processing for performing correction according to a distortion derived from a warping shape of a processing target wafer and imprinting a shot regions. Fig. 7A is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7B is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7C is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7D is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7E is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7F is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7G is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 7H is a diagram illustrating a positional deviation and deformation relating to the shot region. Fig. 8 is a diagram illustrating a pre-alignment unit.

Hereinafter, exemplary embodiments of the present invention will be described in detail below with reference to attached drawings.

An imprint apparatus according to a first exemplary embodiment will be described in detail below with reference to Figs. 1 to 7H.

Fig. 1 is a diagram illustrating a representative configuration of an imprint apparatus 1 according to the first exemplary embodiment. The imprint apparatus 1 is an apparatus that can be used to manufacture devices (e.g., a semiconductor device) as a product. The imprint apparatus 1 can form a resin pattern on a wafer (i.e., a substrate to be processed) by shaping an uncured resin on the wafer with a mold (die). The imprint apparatus according to the present exemplary embodiment employs a light curing method. Further, in Fig. 1, a Z-axis is parallel to the optical axis of an illumination system that irradiates a resin on a wafer with ultraviolet rays, and an X-axis and a Y-axis are perpendicular to each other and provided on a plane perpendicular to the Z-axis. The imprint apparatus 1 includes a light irradiation unit 2, a mold holding mechanism 3, a wafer stage 4, a coating unit 5, a wafer heating mechanism 6, and a control unit 7.

The light irradiation unit 2 can irradiate a mold 8 with ultraviolet rays 9, in imprint processing. The light irradiation unit 2 includes a light source (not illustrated) and an optical element (not illustrated) that can adjust the ultraviolet rays 9 emitted from the light source into suitable light for the imprint processing. The reason why the imprint apparatus 1 includes the light irradiation unit 2 is that a photo-curing method is employed in the present exemplary embodiment. However, in a case where a heat curing method is employed, the light irradiation unit 2 can be replaced by a heat source unit that can cure a thermosetting resin.

The mold 8 has a rectangular outer shape and includes a pattern region (e.g., a circuit pattern or any other concave-convex pattern to be transferred) 8a that is three-dimensionally formed on its surface that faces a wafer 11. Further, the mold 8 is made of quartz or any other comparable material that can transmit the ultraviolet rays 9. Further, the mold 8 may be configured to have a cavity (i.e., recessed portion) 8b on a surface that is irradiated with the ultraviolet rays 9, so that the mold 8 can easily deform. The cavity 8b has a circular plane shape. The thickness (i.e., depth) of the cavity 8b can be appropriately set considering the size and the material of the mold 8. Further, a light transmitting member 13 is provided in an aperture region 17 (described below) in the mold holding mechanism 3, to provide a closed space 12 surrounded by a part of the aperture region 17 and the cavity 8b. Further, a pressure adjustment device (not illustrated) may be provided to control the pressure in the space 12. For example, when the mold 8 is pressed against the resin 14 on the wafer 11, the pressure adjustment device may set the pressure in the space 12 to be higher than an outer pressure. Then, the pattern region 8a of the mold 8 warps in a convex shape toward the wafer 11. Then, a central portion of the pattern region 8a contacts the resin 14. Accordingly, a gas (air) can be prevented from remaining in a closed space between the pattern region 8a and the resin 14. A convex-concave portion of the pattern region 8a can be fully filled with the resin 14.

The mold holding mechanism 3 includes a mold chuck 15 and a mold driving mechanism (i.e., a driving unit) 16. The mold chuck 15 can attract and hold the mold 8 by a vacuum suction force or an electrostatic force. The mold driving mechanism 16 can hold the mold chuck 15 and cause the mold 8 (the mold chuck 15) to move. Each of the mold chuck 15 and the mold driving mechanism 16 has the aperture region 17 at an central portion (inner side) thereof, so that the ultraviolet rays 9 emitted from the light source of the light irradiation unit 2 can reach the wafer 11. Further, the mold holding mechanism 3 includes a magnification correction mechanism (i.e., a mold deformation unit) 18 provided on a surface of the mold chuck 15 where the mold 8 is held. The magnification correction mechanism 18 can deform the shape of the pattern region 8a by applying an external force to a side surface of the mold 8 or causing a displacement of the mold 8. The magnification correction mechanism 18 can deform the shape of the mold 8 so that the shape of the pattern region 8a conforms to a shot shape of the wafer 11.

The mold driving mechanism 16 can cause the mold 8 to move in the Z-axis direction selectively in such a way as to press the mold 8 against the resin 14 on the wafer 11 or separate the mold 8 from the resin 14. A linear motor or an air cylinder is, for example, an actuator that is employable as the mold driving mechanism 16. Further, to realize highly accurate alignment of the mold 8, the mold driving mechanism 16 may be constituted by a plurality of driving systems (e.g., a combination of a coarse driving system and a fine driving system). Further, the mold driving mechanism 16 may be configured to have a position adjustment function in an X-axis direction, a Y-axis direction, or a θ (i.e., rotation around the Z axis) direction, in addition to the Z-axis direction. The mold driving mechanism 16 may be configured to have a tilt function of correcting the gradient of the mold 8. The above-mentioned pressing and separating operation of the imprint apparatus 1 may be realized by causing the mold 8 to move in the Z-axis direction, as mentioned above. Alternatively, the above-mentioned pressing and separating operation may be realized by causing the wafer stage 4 to move in the Z-axis direction, or by causing both of the mold 8 and the wafer stage 4 to move relatively.

The wafer 11 is, for example, a single crystal silicon substrate or a Silicon on Insulator (SOI) substrate. The ultraviolet curing resin (hereinbelow, simply referred to as “resin”) 14, which can be formed by the pattern region 8a, is coated on the above-mentioned processed surface.

The wafer stage (i.e., a substrate stage or a moving unit) 4 can hold (or attract) the wafer 11 and can control the positions of the mold 8 and the resin 14, when the mold 8 is pressed against the resin 14 on the wafer 11. The wafer stage 4 includes a wafer chuck (i.e., a substrate holding unit) 19 and a stage driving mechanism 20. The wafer chuck 19 can generate a suction force to hold the wafer 11. The stage driving mechanism 20 can hold the wafer chuck 19 with a mechanical tool and move the wafer chuck 19 in an XY plane. In particular, the wafer chuck 19 according to the present exemplary embodiment includes a plurality of suction portions (not illustrated), which can attract and hold a plurality of divided regions, which can be obtained by dividing a back surface of the wafer 11. These suction portions are connected to another pressure adjustment device (not illustrated), which is different from the above-mentioned pressure adjustment device. In this case, the pressure adjustment device holds the wafer 11 on the suction surface by generating an adjusted suction force in such a way as to reduce the pressure between the wafer 11 and the suction portions. Further, the pressure adjustment device can change the pressure value (i.e. chuck force) independently for each suction portion. The number of the suction portions to be provided (i.e., division number) is not limited to a specific number and can be an arbitrarily determined number. Further, the wafer chuck 19 has a reference mark 21 used in aligning the mold 8 on the surface thereof. For example, a linear motor is an actuator that is employable as the stage driving mechanism 20. The stage driving mechanism 20 may be constituted by a plurality of driving systems (e.g., a combination of a coarse driving system and a fine driving systems) in each of the X-axis direction and the Y-axis direction. Further, the stage driving mechanism 20 may be configured to include a driving system capable of adjusting the position of the wafer 11 in the Z-axis direction, or may be configured to have a capability of adjusting the position of the wafer 11 in the θ direction and a capability of correcting a tilt angle of the wafer 11.

The coating unit 5 can coat the resin (i.e., uncured resin) 14 on the wafer 11. In the present exemplary embodiment, the resin 14 is a light curing resin (i.e., imprint material), which has the nature of being hardened when it is irradiated with the ultraviolet rays 9. The resin 14 is appropriately selected with reference to various conditions (e.g., semiconductor device manufacturing processes). Further, the amount of the resin 14 discharged from a discharge nozzle of the coating unit 5 can be appropriately determined considering a desired thickness of the resin 14 formed on the wafer 11 or the density of a formed pattern. The coating position and the coating amount of the resin 14 in a single imprint operation are determined beforehand with reference to a droplet pattern. The droplet pattern includes a plurality of rectangular regions, which can be obtained by dividing a shot region. The coating amount of the resin 14 is determined for each divided region. The coating unit 5 discharges the resin to a shot region on the substrate according to the droplet pattern.

The wafer heating mechanism (i.e., substrate deformation unit) 6 can heat the wafer 11 to change the shape of the wafer 11 placed on the wafer stage 4, more specifically, the shot shape on the wafer 11 carried into the imprint apparatus 1. The wafer heating mechanism 6 can include, for example, a heating light source that can heat the wafer 11 by emitting light that can penetrate the mold 8 and reach the wafer 11, similar to the light irradiation unit 2, as illustrated in Fig. 1. The light emitted from the heating light source is infrared ray or comparable light that can be absorbed by the wafer 11 and wavelengths of which are in a specific wavelength band in which the light curing resin is not sensitized (i.e., not hardened). Further, in this case, the wafer heating mechanism 6 can include a plurality of optical elements (not illustrated) that can convert the light emitted from the heating light source into appropriate light suitable for the imprint, in addition to the heating light source (not illustrated). Instead of using the above-mentioned heating light source, the wafer heating mechanism 6 can be configured as a heater (not illustrated) installed on the wafer chuck 19 so that the wafer heating mechanism 6 can directly heat the wafer 11.

The control unit 7 can control operations and adjustments of respective elements that constitute the imprint apparatus 1. For example, the control unit 7 can be constituted by a computer, which is connected to each constituent element of the imprint apparatus 1 via a communication line. The control unit 7 controls each constituent element according to a program. The control unit 7 may be integrated with another portion of the imprint apparatus 1 (i.e., can be housed in a common casing) or can be provided separately from the imprint apparatus 1 (i.e., can be housed in another casing). The control unit 7 can input information about a displacement of the wafer 11 in a direction perpendicular to a surface of the wafer chuck 19, i.e., information about a warping amount of the wafer 11. The warping amount information can be acquired by a measurement device (not included in the imprint apparatus 1) beforehand. An operator of the apparatus can input the acquired warping amount information to the apparatus via a console. Alternatively, in a case where the imprint apparatus 1 is connected to a network (e.g., LAN), the warping amount information can be input to the apparatus via the network. The control unit 7 can calculate an estimated displacement amount (i.e., distortion) of the shot region on the wafer 11 in a direction parallel to the wafer chuck 19 in a state where a pattern is formed on the wafer 11, i.e., in a state where the wafer 11 is fixed by the wafer chuck 19, based on the warping amount information.

Further, the imprint apparatus 1 includes an alignment measurement system 22 provided in the aperture region 17. The alignment measurement system 22 can measure a positional deviation between an alignment mark formed on the wafer 11 and an alignment mark formed the mold 8 in each of the X-axis direction and the Y-axis direction, for example, as wafer alignment.

Further, the imprint apparatus 1 includes a base surface plate 24 that mounts the wafer stage 4, a bridge surface plate 25 that fixes the mold holding mechanism 3, and support shafts 26 that are extended vertically from the base surface plate 24 to support the bridge surface plate 25. Further, the imprint apparatus 1 includes a mold conveyance mechanism (not illustrated) and a substrate conveyance mechanism (not illustrated). The mold conveyance mechanism can convey the mold 8 to the mold holding mechanism 3 from the outside of the apparatus. The substrate conveyance mechanism can convey the wafer 11 to the wafer stage 4 from the outside of the apparatus.

The wafer 11 is set at a predetermined position in the imprint apparatus 1 in a state where the wafer 11 is accommodated in a wafer cassette (not illustrated). At least one wafer, normally a plurality of wafers, is stored in the wafer cassette. The substrate conveyance mechanism can pick up one wafer from the wafer cassette and place the extracted wafer in a pre-alignment unit (measurement unit) 30, which is described in detail below. The pre-alignment unit 30 corrects the azimuth and the position of the wafer 11. After the azimuth and position correction completes, the substrate conveyance mechanism sets the wafer 11 on the wafer chuck 19 to perform imprint processing. After the imprint processing completes, the wafer 11 is removed from the wafer chuck 19 by the substrate conveyance mechanism and then collected in the wafer cassette. Meanwhile, the next wafer that stands by in the pre-alignment unit 30 is conveyed and set on the wafer chuck 19. In this way, wafers can be successively subjected the imprint processing.

Next, the imprint processing that can be performed by the imprint apparatus 1 will be described in detail below. First, the control unit 7 causes the substrate conveyance mechanism to convey the wafer 11 to place and fix the wafer 11 on the wafer chuck 19 provided on the wafer stage 4. Next, the control unit 7 drives the stage driving mechanism 20 to cause a shot region on the wafer 11 to move toward the coating position of the coating unit 5. Next, the control unit 7 causes the coating unit 5 to coat the resin 14 on the shot region, as a coating process. Next, the control unit 7 drives the stage driving mechanism 20 again to move the wafer 11 so that the shot region on the wafer 11 can be positioned beneath the pattern region 8a. Next, the control unit 7 drives the mold driving mechanism 16 in such a way as to press the resin 14 on the wafer 11 to the mold 8, as a mold process. A convex-concave portion of the pattern region 8a is filled with the resin 14 as a result of the above-mentioned pressing operation. Further, the control unit 7 causes the alignment measurement system 22 to measure a positional deviation amount between the alignment mark formed on the wafer 11 and the alignment mark formed on the mold 8. Then, based on the measured positional deviation amount, the control unit 7 causes the mold driving mechanism 16, the wafer stage 4, the magnification correction mechanism 18, and the wafer heating mechanism 6 to perform an alignment operation for aligning the position of the pattern region 8a relative to the shot region on the wafer 11. In this state, the control unit 7 causes the light irradiation unit 2 to irradiate an upper surface of the mold 8 with the ultraviolet rays 9 and cure the resin 14 with the ultraviolet rays 9 having transmitted the mold 8, as a curing process. Then, after the curing of the resin 14 completes, the control unit 7 drives the mold driving mechanism 16 again in such a way as to separate the mold 8 from the resin 14, as a mold release process. Through the above-mentioned sequential processes, a resin pattern (layer) having a three-dimensional shape that conforms to the convex-concave portion of the pattern region 8a can be formed on the surface of the shot region on the wafer 11. The apparatus repeats the above-mentioned sequential imprint operation while a target shot region is sequentially changed according to the driving of the wafer stage 4. Thus, a plurality of resin patterns can be formed on one wafer 11.

Next, an example method for performing a correcting operation according to the distortion acquired based on warping shape information will be described. Fig. 2 is a flowchart illustrating processing for obtaining a transformation matrix based on a warping shape of the wafer.

In step S01, the imprint apparatus acquires warping shape information about the wafer (i.e., substrate) and stores the acquired warping shape information in a storage device of the control unit 7. More specifically, the imprint apparatus 1 acquires a plurality of pieces of warping shape information, for at least one wafer, by causing an external or internal measurement device to measure the warping shape information in a state where the wafer is not yet fixed by the wafer chuck 19. In the present exemplary embodiment, the warping shape information is a warping amount relative to a flat surface that passes through the center of the wafer surface and is parallel to the wafer surface (i.e., a distance from the flat surface) at least one point on the wafer surface. Alternatively, as for various warping shapes, a computer simulation using a finite element method may be employed in acquiring the warping shape information. Further, the imprint apparatus 1 may acquire external warping shape information. For example, an operator may input warping shape information via the console of the imprint apparatus 1. Further, in a case where the imprint apparatus 1 is connected to an appropriate network (e.g., LAN), an external measurement device, a server, or any other apparatus connected to the network may input warping shape information to the imprint apparatus 1 via the network.

In step S02, the control unit 7 obtains a warping shape expression formula based on the acquired warping shape information beforehand. Now, the warping shape information and the warping shape expression formula will be described in detail below. Each of Figs. 3A to 3H illustrates a correspondence relationship between the warping shape and the distortion generated in a state where the wafer is fixed by the wafer chuck. Fig. 3A illustrates a flat wafer that is free from warping, which is seen from an obliquely upper position. Fig. 3B is a plan view illustrating the wafer illustrated in Fig. 3A in a state where the wafer is fixed by the wafer chuck. In Fig. 3B, a circumferential circular line represents a wafer edge and internal latticed lines represent a wafer grid. The state illustrated in Fig. 3B includes no distortion because the wafer is free from warping. Similarly, Fig. 3C illustrates a wafer having a downwardly protruding convex surface, which is seen from an obliquely upper position. Fig. 3D is a plan view illustrating the wafer illustrated in Fig. 3C. In Fig. 3D, dotted lines indicate a referential wafer grid, which is free from distortion, and solid lines indicate a wafer grid distorted by the wafer chuck. In comparison with the distortion-free grid, it is understood that the grid deforms when a distortion occurs in a contraction direction. Figs. 3A to 3H are exaggeratingly illustrated so that the warping state and the distortion can be understood easily. In many cases, the actual warping amount is in the order of several hundreds μm to several mm. The actual positional deviation amount is in the order of several hundreds nm to several μm. In the present exemplary embodiment, the positional deviation amount is a two-directional displacement amount of at least one point on a wafer (i.e., substrate) in the x and y directions relative to a rectangular lattice shaped wafer grid that is free from positional deviation. Fig. 3E illustrates a wafer having an upwardly protruding convex surface, which is seen from an obliquely upper position. Fig. 3F is a plan view illustrating the wafer illustrated in Fig. 3E. Further, Fig. 3G illustrates a wafer having a saddle shaped surface, which is seen from an obliquely upper position. Fig. 3H is a plan view illustrating the wafer illustrated in Fig. 3G. When the wafer is deformed into a saddle shape, the distortion has a rotationally asymmetrical shape. As mentioned above, the correlation between the warping shape and the distortion can be known beforehand as illustrated in Figs. 3A to 3H. Therefore, it is feasible to constitute a conversion formula that is usable to convert a warping shape into a distortion with reference to the preliminarily known correlation.

First, the following formula (1) is employed as a general formula of a first formula that represents the warping shape. The warping shape expression formula employed in the present exemplary embodiment is a high dimensional polynomial of x and y that represent coordinates on the wafer surface (i.e., substrate surface).
z = C00 + C10x + C01y + C20x² + C11xy + C02y² + C30x³ + C21x²y + C12xy² + C03y³ ... (1)

It is further defined that (x, y) coordinate plane extends along the wafer surface from the origin positioned at the wafer center and z-axis extends in a direction perpendicular to the x and y axes. In the formula (1), “z” represents the height of the wafer at a point (x, y). More specifically, “z” represents the warping amount. The formula (1) includes a plurality of coefficients C00, C10, C01, ..., and C03. The term of C00 represents an up-and-down movement of the entire wafer. The terms of C10 and C01 are terms representing the gradient of the entire wafer. Therefore these terms not related to the warping shape. These terms can be corrected by controlling the position and the rotation of the wafer stage 4. Accordingly, the terms expressing the warping shape are the term of C20 and subsequent terms.

Fig. 4 illustrates a correspondence relationship between respective coefficients of the warping shape expression formula and corresponding warping shapes. Fig. 4 illustrates warping shapes that correspond to the coefficients of respective terms in the formula (1), more specifically, C20 to C03 (i.e., warping shape coefficient set C). Typically observed smooth warping shapes can be expressed by linearly connecting these terms. In practice, the warping shapes illustrated in Figs. 3A to 3H (i.e., the downwardly protruding convex shape, the upwardly protruding convex shape, and the saddle shape) can be expressed by combining these terms. If a target warping shape to be expressed includes higher-order undulation components that cannot be sufficiently expressed by using the above-mentioned formula (1), it is useful to increase the order and/or the number of terms of the formula (1) appropriately. On the other hand, in a case where the target warping shape does not include any higher-order undulation component and reducing the calculation time is desired, it is useful to reduce the order and/or the number of terms of the formula (1). It is useful to use a high dimensional polynomial of at least 2nd order.

When the formula (1) is employed to express a warping shape, it is feasible to acquire the warping shape coefficient set C by acquiring the warping amount (z) at each of a plurality of points (x, y) on the wafer surface and fitting the acquired information to the formula (1) according to the least squares method. Then, the warping shape expression formula can be obtained by applying the acquired warping shape coefficient set C to the formula (1).

In step S03, after the acquisition of the warping shape information about the wafer in step S01 has been completed, the control unit 7 conveys the wafer to the wafer chuck 19 on the wafer stage 4. Then, in step S04, the control unit 7 acquires information about the positional deviation amount of the wafer.

In a state where the wafer is attached to the wafer chuck 19, the alignment measurement system 22 (i.e., measurement unit) measures a plurality of alignment marks on the wafer surface and the control unit 7 acquires positional deviation amount information at each alignment mark. Alternatively, without measuring the alignment marks, the control unit 7 can acquire the positional deviation amount information by performing a computer simulation using the finite element method. Further, the imprint apparatus 1 may acquire positional deviation amount information from outside thereof. For example, an operator may input positional deviation amount information via the console of the imprint apparatus 1. Alternatively, in a case where the imprint apparatus 1 is connected to a network (e.g., LAN), an external measurement device, a server, or any other apparatus connected to the network may input positional deviation amount information to the imprint apparatus 1 via the network.

In step S05, the control unit 7 obtains a positional deviation amount expression formula beforehand based on the acquired positional deviation amount. The following formula (2) is employed as a general formula of a second formula that represents the positional deviation amount in a state where the wafer is fixed by the wafer chuck 19. The positional deviation amount expression formula employed in the present exemplary embodiment is high dimensional polynomials of x and y that represent coordinates on the wafer surface.
Δx = A00 + A10x + A01y + A20x² + A11xy + A02y² + A30x³ + A21x²y + A12xy² + A03y³
Δy = B00 + B10x + B01y + B20x² + B11xy + B02y² + B30x³ + B21x²y + B12xy² + B03y³ ... (2)

Similar to the formula (1), x and y represent the coordinates of an arbitrary point on the wafer surface. Further, Δx represents an x-component of the positional deviation amount at the point (x, y). Δy represents a y-component of the positional deviation amount, similarly. A00, A10, ..., A03, B00, B10, ..., and B03 are coefficients of the formula (2).

Fig. 5 illustrates a correspondence relationship between the coefficients of the positional deviation amount expression formula and corresponding wafer distortion shapes. The wafer distortion shapes illustrated in Fig. 5 correspond to respective coefficient terms of the formula (2). General distortion shapes can be expressed by linearly connecting these terms. Each distortion shape illustrated in Fig. 3 can be expressed by using a combination of these terms. However, the terms of A00 and B00 represent the shifting of the entire wafer and can be corrected by controlling the position of the wafer stage 4. Accordingly, the terms expressing the distortion shape are the terms of A10 and B10 and subsequent terms. Coefficients of these terms are referred to as positional deviation amount coefficient set A. If a target distortion shape to be expressed includes higher-order undulation components that cannot be sufficiently expressed by using the formula (2), it is desired to increase the order and/or the number of terms of the formula (2) appropriately. On the other hand, in a case where the target distortion shape does not include any higher-order undulation component and reducing the calculation time is desired, it is useful to reduce the order and/or the number of terms of the formula (2). It is useful to use a high dimensional polynomial of at least 1st order.

When the formula (2) is employed to express a positional deviation amount, it is feasible to acquire the positional deviation amount coefficient set A by acquiring the positional deviation amount at each of a plurality of points (x, y) on the wafer surface and fitting the acquired information to the formula (2) according to the least squares method. Then, the positional deviation amount expression formula can be obtained by applying the acquired positional deviation amount coefficient set A to the formula (2).

In step S06, the control unit 7 obtains a transformation matrix M based on the warping shape coefficient set C and the positional deviation amount coefficient set A acquired or obtained beforehand. Then, in step S07, the control unit 7 stores the obtained transformation matrix M in the storage device (not illustrated) of the control unit 7.

The following formula (3) is employed as a third formula that is usable in conversion between the warping shape expression formula and the positional deviation amount expression formula, more specifically, as a formula capable of obtaining the transformation matrix M based on the warping shape coefficient set C and the positional deviation amount coefficient set A.

Formula 3

In the formula (3), the transformation matrix M includes various elements M11, M12, ..., and M187. In the present exemplary embodiment, the total number of warping shape coefficients is 7 and the total number of positional deviation amount coefficients is 18. Therefore, the transformation matrix M is constituted by 18 lines and 7 columns. In other words, the transformation matrix M includes 126 elements. To obtains 126 elements of the transformation matrix M, the control unit 7 acquires a plurality of pieces of data with respect to the warping shape and the positional deviation amount by measuring the warping shape and positional deviation amounts at a plurality of spots (i.e., positions) on a surface of at least one wafer in a state where the wafer is fixed by the wafer chuck. Alternatively, the control unit 7 may acquire the information about the warping shape and the positional deviation amount from a plurality of wafers having various shapes by performing a computer simulation using the finite element method. The control unit 7 obtains the warping shape coefficient set C and the positional deviation amount coefficient set A based on the acquired warping shape and the positional deviation amount. The control unit 7 can obtain the elements of the transformation matrix M by applying and fitting the obtained information (i.e., the warping shape coefficient set C and the positional deviation amount coefficient set A) to the formula (3) according to the least squares method. In obtaining the transformation matrix M, each of the warping shape coefficient set C and the positional deviation amount coefficient set A is not limited to only one set and can be constituted by a plurality of sets. The control unit 7 stores the elements of the obtained transformation matrix M in the storage device of the control unit 7.

Fig. 6 is a flowchart illustrating processing for performing correction according to a distortion derived from a warping shape of a processing target wafer (i.e., processing target substrate) and imprinting shot regions. In step S08, the control unit 7 acquires information about the warping shape of the processing target wafer by using a method similar to that described in step S01 of Fig. 2. In the present exemplary embodiment, the processing target wafer is a target wafer to be subjected to the imprint processing (i.e., imprint material pattern forming processing) of the imprint apparatus 1.

In step S09, the control unit 7 obtains a warping shape expression formula based on the acquired warping shape information, by using a method similar to that described in step S02 of Fig. 2.

In step S10, the control unit 7 conveys the processing target wafer to the wafer chuck 19 on the wafer stage 4.

In step S11, the control unit 7 acquires the positional deviation amount coefficient set A by calculating a product of the warping shape coefficient set C of the warping shape expression formula obtained in step S09 and the transformation matrix M stored in the storage device of the control unit 7 in step S07 illustrated in Fig. 2. Then, the control unit 7 obtains a positional deviation amount expression formula by applying the acquired coefficient set to the formula (2).

In step S12, the control unit 7 obtains positional deviation amounts and distortion components of respective shot regions before imprinting these shot regions of the processing target wafer. The control unit 7 obtains positional deviation amounts at a plurality of positions on the processing target wafer (i.e., processing target substrate) by substituting coordinate information about at least two points of a shot region (e.g., four corner points of the shot region) on the wafer surface into the positional deviation amount expression formula. In the present exemplary embodiment, the coordinate information is information about the coordinates in a state where no distortion is generated and can be obtained from the design values. The control unit 7 performs distortion detection by obtaining distortion components with respect to the wafer grid and the shot shape based on the obtained positional deviation amounts. In the present exemplary embodiment, the wafer grid is a lattice that defines a plurality of shot regions arranged on the wafer. The shot shape indicates the shape of each shot region on the wafer. The distortion components to be obtained in this case are a plurality of types of distortion components (e.g., positional deviation, shot rotation, and shot magnification change) relating to the shot region. The distortion components can be obtained by using the least squares method.

Figs. 7A to 7H illustrate positional deviations and deformations relating to the shot regions. In Figs. 7A to 7H, dotted lines indicate a state where there is not any positional deviation and deformation, in which the external frame is the boundary of each shot region and the internal lattice is an in-shot grid. Further, solid lines indicate a state where there is a positional deviation or a deformation, in which the external frame is the boundary of each shot region and the internal lattice is an in-shot grid. Fig. 7A illustrates an x-directional positional deviation of the shot region. Fig. 7B illustrates a y-directional positional deviation of the shot region. Further, Fig. 7C illustrates a shot magnification change. Fig. 7D illustrates a shot rotation. The least squares method can be employed to obtain these distortion components based on positional deviation amounts at a plurality of positions (at least two points of the shot region).

In step S13, the control unit 7 performs corrections (e.g., positional deviation, shot rotation, and shot magnification change) for the shot region according to the obtained distortion component and imprints the shot region. The distortions that occur in wafer warping correction generate deformation of the wafer grid and deformation of the shot shape. Therefore, in the present exemplary embodiment, the control unit 7 performs position and shape corrections for both of the wafer grid and the shot shape. The positional deviation of the shot region (in the x-direction or the y-direction) is a component corresponding to the deformation of the wafer grid. The control unit 7 can correct the positional deviation of the shot region by controlling the position of the wafer stage 4. Further, the control unit 7 can correct the shot rotation by controlling the rotation of the wafer stage 4. Further, the shot magnification change corresponds to the deformation of the shot shape. The control unit 7 can correct the shot magnification change by causing the magnification correction mechanism 18 to change the shape of the pattern region 8a of the mold 8.

Further, the positional deviation of the shot region may be corrected by controlling the position of the mold driving mechanism 16. The shot rotation may be corrected by controlling the rotation of the mold driving mechanism 16.

As mentioned above, the control unit 7 can perform corrections by controlling the shape or the position of at least one of the mold and the processing target wafer according to the distortion component.

Further, when the coating unit 5 coats the resin 14 on the wafer 11 in the coating process, the coating unit 5 can adjust at least one of the coating position and the coating amount of the resin 14 according to the distortion component. As mentioned above, the coating position and the coating amount of the resin 14 are determined beforehand with the droplet pattern. However, according to the conventional technique, the coating position and the coating amount are not determined considering the distortion derived from a warping of the wafer. Therefore, appropriately determining the coating position and the coating amount according to the distortion is unfeasible. The mold pattern cannot be sufficiently charged with the resin. Abnormalities may occur in pattern and residual film thickness. This is the reason why it is necessary to adjust at least one of the coating position and the coating amount of the resin 14 according to the distortion.

An example of a method for adjusting at least one of the coating position and the coating amount of the resin 14 will be described in detail below. It is feasible to correct at least one of the coating position and the coating amount of the resin 14 by increasing or decreasing the coating amount of each divided region based on a positional deviation of the center position of a divided region of the droplet pattern. For example, it is now assumed that the center position of a first divided region shifts in the +X direction and coincides with the center position of a second divided region that is positioned on the +X side of the first divided region. In this case, the method includes correcting the coating position of the resin by entirely adding the coating amount of the first divided region to the coating amount of the second divided region while reducing the coating amount of the first divided region to 0. Further, as another example, it is now assumed that the center position of the first divided region shifts in the +X direction and coincides with a midpoint between the center position of the first divided region and the center position of the second divided region. In this case, the method includes correcting the coating amount of the resin by adding a half of the coating amount of the first divided region to the coating amount of the second divided region while reducing the coating amount of the first divided region to a half. The method includes increasing and decreasing the coating amount of each divided region by using a similar method even in a case where the center position of the first divided region shifts in the -X direction or ±Y directions. As mentioned above, at least one of the coating position and the coating amount of the resin 14 can be corrected for all divided regions by increasing and decreasing the coating amount considering the positional deviation of the center position of each divided region and the ratio of the distance relative to the center position of a peripheral divided region. The coating position and the coating amount of the resin 14 may be corrected independently from or concurrently with the above-mentioned shape/position correction of the mold and the processing target wafer.

Further, the distortion component to be corrected is not limited to the above-mentioned shot magnification change and can be vertical/horizontal magnification difference component, parallelogram component (skew component), or trapezoidal component. Fig. 7E illustrates an example of the vertical/horizontal magnification difference component. Fig. 7F illustrates an example of the parallelogram component. Figs. 7G and 7H illustrate examples of the trapezoidal component. Effectively correcting the distortion is feasible by correcting the above-mentioned examples. In this case, it is feasible to obtain the distortion component (e.g., vertical/horizontal magnification difference component, parallelogram component, or trapezoidal component) according to the least squares method with reference to positional deviation amounts acquired at a plurality of positions (at least two points) of the shot region. Hereinbelow, a method for obtaining the distortion component according to the least squares method based on the positional deviation amounts acquired in the shot region will be described in detail below. For example, it is assumed that S_x represents the positional deviation in the x-direction and S_y represents the positional deviation in the y-direction. Similarly, R_x and R_y represent shot rotation amounts in the x-direction and y-direction. M_x and M_y represent shot magnification change amounts in the x-direction and y-direction. A_x and A_y represent vertical/horizontal magnification difference change amounts in the x-direction and y-direction. B_x and B_y represent parallelogram change amounts in the x-direction and y-direction. The following formulae are xy functions that can express the positional deviation amounts δ_x and δ_y at the point (x, y) of the shot region.
δ_x(x, y) = S_x - R_y + M_x + A_x + B_y
δ_y(x, y) = S_y + R_x + M_y - A_y + B_x

It is assumed that (x₁, y₁), (x₂, y₂), ..., and (x_n, y_n) represent coordinates of a plurality of points included in a shot region. (Δx₁, Δy₁), (Δx₂, Δy₂), ..., and (Δx_n, Δy_n) represent positional deviation amounts in the x-direction and y-direction at these points. The following formula defines Ω in the present exemplary embodiment.
Ω = Σ_{i=1 to n}(Δx_i - δ_x(x_i, y_i))² + Σ_{i=1 to n}(Δy_i - δ_y(x_i, y_i))²

The distortion component can be obtained from the positional deviation amounts in the shot region by obtaining S_x, S_y, M, R, A, and B that minimizes the value Ω. The distortion component to be obtained can be a single component or can be a plurality of types of components.

The distortion components of respective shot shapes are not limited to the above-mentioned examples (e.g., shot magnification change, vertical/horizontal magnification difference component, parallelogram component, and trapezoidal component). For example, increasing the positional deviation amount calculation points of the shot region is useful to calculate and correct a barrel-shaped deformation component or a bobbin-shaped deformation component. Further, if there is any correctable distortion component, it can be added to the distortion components to be corrected. Further, the barrel-shaped or bobbin-shaped higher-order deformation component can be corrected by causing the wafer heating mechanism 6 to change the shot shape on the wafer 11.

Completing the above-mentioned correction before pressing the mold 8 against the resin 14 on the wafer 11 is useful to reduce the time required for an alignment operation subsequently performed. As a result, the throughput can be improved. Further, in the alignment operation, the pattern region 8a may deform when a force is applied to the resin 14. In this case, performing the above-mentioned correction is effective to reduce the correction amount in the alignment operation to be performed after the mold 8 is pressed against the resin 14 on the wafer 11. The force applied from the resin 14 to the pattern region 8a can be reduced. As a result, the deformation of the pattern region 8a can be suppressed.

Further, the above-mentioned correction using the wafer stage 4, the magnification correction mechanism 18, the mold driving mechanism 16, or the wafer heating mechanism 6 may be performed at an appropriate timing not later than the emission of the ultraviolet rays 9 by the light irradiation unit 2 in a state where the mold 8 is pressed against the resin 14 on the wafer 11.

Further, the order of step S10 in Fig. 6 can be changed appropriately unless step S13 precedes step S10. Further, the processing of step S10 and the processing of another step can be performed concurrently.

Further, in step S12 of Fig. 6, the control unit 7 obtains the distortion component of each shot region immediately before imprinting each shot region. In this case, if obtaining the distortion component takes time, the throughput will decrease. Therefore, to prevent the throughput from decreasing, it is useful to obtain distortion components of all shot regions after the warping shape information has been acquired.

Further, in steps S08 to S12 of Fig. 6, the control unit 7 obtains the positional deviation amounts and the distortion components of respective shot regions without measuring any alignment mark on the processing target wafer. Further, to improve the overlay accuracy, it is useful to obtain positional deviation amounts by measuring a part of the alignment marks and combining the obtained data with positional deviation amounts obtained by using the positional deviation amount expression formula to obtain a distortion component. For example, it is useful to designate a half of the alignment marks as measuring targets beforehand and use the positional deviation amount expression formula to obtain positional deviation amounts of non-measuring alignment marks. Alternatively, in a case where the alignment marks cannot be successfully measured, it is useful to obtain positional deviation amounts by using the positional deviation amount expression formula.

In step S14, the control unit 7 determines whether the imprint of all shot regions of the processing target wafer has been completed. If the imprint of all shot regions has been completed (YES in step S14), the control unit 7 terminates the imprint processing for the processing target wafer. If the imprint of all shot regions is not yet completed (NO in step S14), the operation returns to step S12 to obtain distortion components with respect to the wafer grid and the shot shape of the next shot region.

The warping shape coefficient set C to be obtained in step S02 of Fig. 2 or in step S09 of Fig. 6 or the positional deviation amount coefficient set A to be obtained in step S05 of Fig. 2 or in step S11 of Fig. 6 may be obtained by an external device, and the control unit 7 may acquire these coefficient sets A and C from the external device beforehand. For example, an external measurement device can acquire measurement data with respect to the warping shape and the positional deviation amount. Alternatively, an external information processing apparatus can acquire comparable calculation data. The external information processing apparatus can obtain coefficient sets. An operator can input the obtained coefficient set information to the imprint apparatus 1 via the console. Alternatively, in a case where the imprint apparatus 1 is connected to a network (e.g., LAN), an external measurement device, a server, or any other apparatus connected to the network may input the coefficient set information to the imprint apparatus 1 via the network.

Further, the warping shape expression formula and the positional deviation amount expression formula are not limited to the high dimensional polynomials and may be any other function formulae.

Accordingly, the imprint apparatus according to the first exemplary embodiment can correct the wafer grid and the shot shape and thus can improve the overlay accuracy.

An imprint apparatus according to a second exemplary embodiment will be described in detail below. Features not mentioned specifically in the following description are similar to those already described in the first exemplary embodiment.

In the present exemplary embodiment, the general formula used to express the warping shape and the positional deviation amount is a Zernike polynomial having a property to be orthogonal in the unit circle.

First, the warping shape expression formula to be obtained in step S02 of Fig. 2 will be described in detail below.

The following formula (4) can be employed to express a warping shape.
z = C₁Z₁(r, θ) + C₂Z₂(r, θ) + ... + C₉Z₉(r, θ) ... (4)

In the present exemplary embodiment, the (r, θ) coordinate plane is set on the wafer surface from the origin positioned at the wafer center and the z-axis extends in a direction perpendicular to the wafer surface. In the formula (4), “z” represents the height of the wafer at a point (r, θ). More specifically, “z” represents the warping amount. It is useful to normalize the (r, θ) coordinate plane on the wafer with the wafer radius. The formula (4) includes a plurality of coefficients C₁, C₂, …, and C₉, which is the warping shape coefficient set C. Further, functions Z₁, Z₂, ..., and Z₉ constitute Zernike polynomials, which can be expressed in the following manner.
Z₁(r, θ) = 1
Z₂(r, θ) = rcosθ
Z₃(r, θ) = rsinθ
Z₄(r, θ) = 2r² - 1
Z₅(r, θ) = r²cos2θ
Z₆(r, θ) = r²sin2θ
Z₇(r, θ) = (3r³ - 2r)cosθ
Z₈(r, θ) = (3r³ - 2r)sinθ
Z₉(r, θ) = 6r⁴ - 6r² + 1

If a target warping shape to be expressed includes higher-order undulation components that cannot be sufficiently expressed by using the above-mentioned formula, it is useful to increase the order and/or the number of terms of the formula (4) appropriately. For example, using a Zernike polynomial composed of 36 terms is often used. On the other hand, in a case where the target warping shape does not include any higher-order undulation component and reducing the calculation time is desired, it is useful to reduce the order and/or the number of terms of the formula (4).

Further, the warping shape coefficient set C defined by the formula (4) can be obtained by using a method similar to that described in the first exemplary embodiment. The warping shape expression formula can be obtained by applying the obtained warping shape coefficient set C to the formula (4).

Next, the positional deviation amount expression formula to be obtained in step S05 of Fig. 2 will be described in detail below.

The following formulae (5) can be employed to express a positional deviation amount.
Δr = A₁Z₁(r, θ) + A₂Z₂(r, θ) + ... + A₉Z₉(r, θ)
Δθ = B₁Z₁(r, θ) + B₂Z₂(r, θ) + ... + B₉Z₉(r, θ) ... (5)

In the present exemplary embodiment, coordinate data (r, θ) represents an arbitrary point on the wafer surface, similar to the formula (4). Further, Δr represents r component of the positional deviation amount at the point (r, θ). Similarly, Δθ represents θ component of the positional deviation amount at the point (r, θ). It is useful to normalize the (r, θ) coordinate plane on the wafer with the wafer radius. The formulae include a plurality of coefficients A₁, A₂, ..., A_9, B₁, B₂, …, and B₉, which is the positional deviation amount coefficient set A. Further, functions Z₁, Z₂, …, and Z₉ constitute Zernike polynomials, which can be expressed in the same manner as the formula (4).

If a target distortion shape to be expressed includes higher-order undulation components that cannot be sufficiently expressed by using the above-mentioned formula, it is useful to increase the order and/or the number of terms of the formula (5) appropriately. For example, using the Zernike polynomial composed of 36 terms is often used. On the other hand, in a case where the target warping shape does not include any higher-order undulation component and reducing the calculation time is desired, it is useful to reduce the order and/or the number of terms of the formula (5).

Further, the positional deviation amount coefficient set A defined by the formula (5) can be obtained by using a method similar to that described in the first exemplary embodiment. The positional deviation amount expression formula can be obtained by applying the obtained positional deviation amount coefficient set A to the formula (5).

Next, the transformation matrix M to be obtained in step S06 of Fig. 2 will be described in detail below.

The following formula (6) is used to obtain the transformation matrix M based on the warping shape expression formula, the positional deviation amount expression formula (third formula), the warping shape coefficient set C, and the positional deviation amount coefficient set A.

Formula 6

In the formula (6), the transformation matrix M includes various elements M11, M12, ..., and M189 . In the present exemplary embodiment, the total number of warping shape coefficients is 9 and the total number of positional deviation amount coefficients is 18. Therefore, the transformation matrix M is constituted by 18 lines and 9 columns. In other words, the transformation matrix M includes 162 elements.

Further, the elements of the transformation matrix M defined by the formula (6) can be obtained by using a method similar to that described in the first exemplary embodiment.

The warping shape expression formula and the positional deviation amount expression formula may be, for example, obtained by freely combining the high dimensional polynomials (e.g., formula (1) and formula (2)) and the Zernike polynomials (e.g., formula (4) and formula (5)) employed in the first exemplary embodiment. Further, the warping shape expression formula and the positional deviation amount expression formula are not limited to the high dimensional polynomials and the Zernike polynomials and may be any other function formulae.

Accordingly, the imprint apparatus according to the second exemplary embodiment can correct the wafer grid and the shot shape and can improve the overlay accuracy.

An imprint apparatus according to a third exemplary embodiment will be described in detail below. Features not mentioned specifically in the following description are similar to those already described in the first and second exemplary embodiments.

In the present exemplary embodiment, the pre-alignment unit 30 of the imprint apparatus 1 measures and acquires the warping shape information to be acquired in step S01 of Fig. 2. Fig. 8 illustrates the pre-alignment unit 30. The wafer 11 is taken out of the wafer cassette by a robot hand and is subsequently conveyed into the pre-alignment unit 30. The pre-alignment unit 30 is configured to be rotatable to rotate the conveyed wafer 11. An observation camera 31, which is provided above the pre-alignment unit 30, can observe a peripheral portion (e.g., edge area) of the rotating wafer 11. In this case, if the rotation center deviates from the center of the wafer 11, the edge of the wafer 11 fluctuates while the wafer 11 is rotating. Therefore, the correction of the rotation center is performed so that the rotation center coincides with the center of the wafer 11. Further, an azimuth reference mark (e.g., a notch or an orientation flat) is provided on the wafer 11. The observation camera 31 can detect the azimuth reference mark to perform azimuth alignment for the wafer 11.

If the rotation center alignment and the azimuth alignment for the wafer 11 terminate, then, a z-directional displacement measurement unit 32 provided above the pre-alignment unit 30 measures a z-directional displacement in the vicinity of the edge of the wafer 11. The z-directional displacement measurement unit 32 measures the z-directional displacement by projecting light to a measurement point and reading the position of reflection light. A laser displacement measurement device or another appropriate measurement device may be employed to measure the z-directional displacement. By performing the z-directional displacement measurement while rotating the wafer 11, z-directional displacement information about the wafer 11 can be obtained along the entire circumferential periphery thereof. The warping shape information (i.e., the z-directional displacement and the azimuth) about the wafer 11 is transmitted to the control unit 7. The control unit 7 performs processing for fitting the acquired warping shape information to the following trigonometric polynomial (7) according to the least squares method.
z = C0 + C1cosθ + S1sinθ + C2cos2θ + S2sin2θ + C3cos3θ + S3sin3θ ... (7)

In the present exemplary embodiment, the θ-coordinate plane is set on the wafer surface from the origin positioned at the wafer center and the z-axis extends in a direction perpendicular to the wafer surface. In the formula (7), “z” represents the height of the wafer at a coordinate point θ in the vicinity of the edge of the wafer 11. More specifically, “z” represents the warping amount. The formula (7) includes a plurality of coefficients C₀, C₁, ..., S₃, which is the warping shape coefficient set C. If a target warping shape to be expressed includes higher-order undulation components that cannot be sufficiently expressed by using the above-mentioned formula (7), it is useful to increase the order and/or the number of terms of the formula (7) appropriately. On the other hand, in a case where the target warping shape does not include any higher-order undulation component and reducing the calculation time is desired, it is useful to reduce the order and/or the number of terms of the formula (7).

Further, the warping shape expression formula defined by the formula (7) can be obtained by using a method similar to that described in the first exemplary embodiment. Further, the positional deviation amount expression formula can be similar to the formula (2) described in the first exemplary embodiment or the formula (5) described in the second exemplary embodiment. Therefore, the positional deviation amount expression formula can be obtained similarly.

The following formula (8) can be employed to calculate the positional deviation amount based on the warping shape expression formula by using the transformation matrix M, similarly to the first exemplary embodiment. The positional deviation amount coefficient set A is similar to that described in the first exemplary embodiment.

Formula 8

Further, the elements of the transformation matrix M defined by the formula (8) can be obtained by using a method similar to that described in the first exemplary embodiment.

Further, the warping shape information to be acquired in step S08 of Fig. 6 can be measured and acquired by the pre-alignment unit 30 of the imprint apparatus 1.

In the present exemplary embodiment, the apparatus is configured to measure the z-directional displacement at the peripheral potion of each wafer. However, if the z-directional displacement measurement unit can be configured to move in the radius direction, it is feasible to measure the warping shape effectively because the z-directional displacement of the wafer can be measured at a plurality of points on the wafer in the radius direction. In this case, the warping shape expression formula can be obtained by using the methods described in the first and second exemplary embodiments.

Accordingly, the imprint apparatus according to the third exemplary embodiment can correct the wafer grid and the shot shape and therefore can improve the overlay accuracy. Further, the pre-alignment unit 30 can acquire information about the warping shape of the processing target wafer. Therefore, it is feasible to prevent the throughput from decreasing.
<Product Manufacturing Method>

A method for manufacturing a product, such as a device (e.g., a semiconductor device, a magnetic storage device, or a liquid crystal display element), a color filter, or a hard disk, will be described in detail below. The manufacturing method includes a process for causing the imprint apparatus to form a pattern on a substrate (e.g., a wafer, a glass plate, or a film substrate). The manufacturing method further includes a process for processing the substrate on which the pattern has been formed. The processing step can include a process of removing a residual film that is not used as the pattern. Further, the manufacturing method can include conventionally known processes, such as a process for etching the substrate by using the pattern as a mask. The product manufacturing method according to the present exemplary embodiment is advantageous in at least one of product performance, quality, productivity, and production cost, compared to the conventional method.

The present invention is not limited to the above-mentioned exemplary embodiments and can be modified or changed in various ways within the spirit and scope thereof. Further, not only the imprint apparatuses according to the first to third exemplary embodiments are operable independently but also these imprint apparatuses can be combined appropriately.

As mentioned above, the present invention can provide an imprint apparatus, an imprint method, and a product manufacturing method that can improve the overlay accuracy.

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. 2015-173272, filed September 2, 2015, which is hereby incorporated by reference herein in its entirety.

Claims (26)

1. An imprint apparatus configured to form a pattern of an imprint material on a substrate by bringing the imprint material into contact with a mold, the imprint apparatus comprising:
   a moving unit configured to hold and move the substrate; and
   a control unit,
   wherein the control unit obtains a positional deviation amount expression formula that expresses a positional deviation amount at each position on a surface of the substrate held by the moving unit, with reference to information about a warping shape of the substrate in a state where the substrate is not yet held by the moving unit,
   calculates positional deviation amounts at a plurality of positions on the substrate surface with reference to the obtained positional deviation amount expression formula, and obtains a distortion component relating to a shot region of the substrate based on the positional deviation amounts obtained at the plurality of positions, and
   controls the shape or the position of at least one of the mold and the substrate according to the obtained distortion component.
   
2. The imprint apparatus according to claim 1, wherein the positional deviation amount expression formula relates to two directions on the substrate surface, and the positional deviation amounts at the plurality of positions relate to two directions on the substrate surface.
3. The imprint apparatus according to claim 1, wherein the distortion component is a plurality of types of distortion components.
4. The imprint apparatus according to claim 1, wherein the control unit obtains a first formula as a formula expressing the shape of the substrate based on the information about the warping shape,
   causes a conversion unit to convert the first formula into a second formula that expresses the positional deviation amounts at a plurality of positions on the substrate surface, and
   calculates the positional deviation amounts at the plurality of positions according to the second formula.
5. The imprint apparatus according to claim 4, wherein the conversion unit uses a transformation matrix to obtain a plurality of coefficient values of the second formula from a plurality of coefficient values of the first formula.
6. The imprint apparatus according to claim 5, wherein the transformation matrix is obtained from a formula expressing a shape of a referential substrate that is different from the substrate, which is obtainable from a general formula of the first formula and warping shape information about the referential substrate in a state where the referential substrate is not yet held by the moving unit, and a formula expressing positional deviation amounts in two directions at each position on a surface of the referential substrate, which is obtained from a general formula of the second formula and positional deviation amounts in two directions at a plurality of positions on the surface of the referential substrate in a state where the referential substrate is held by the moving unit.
7. The imprint apparatus according to claim 1, wherein the control unit controls the moving unit to move the substrate so as to overlay a pattern region of the mold on the shot region.
8. The imprint apparatus according to claim 1, further comprising a mold deformation unit configured to change a shape of a pattern region of the mold,
   wherein the control unit controls the mold deformation unit to change the shape of the mold so as to overlay the pattern region of the mold on the shot region.
9. The imprint apparatus according to claim 1, further comprising a substrate deformation unit configured to change a shape of the shot region on the substrate,
   wherein the control unit controls the substrate deformation unit to change the shape of the substrate so as to overlay a pattern region of the mold on the shot region.
10. The imprint apparatus according to claim 1, further comprising a driving unit configured to move the mold,
    wherein the control unit controls the driving unit to move the position of the mold so as to overlay a pattern region of the mold on the shot region.
11. The imprint apparatus according to claim 4, wherein the first formula can be expressed by a high dimensional polynomial of at least 2nd order.
12. The imprint apparatus according to claim 4, wherein the first formula can be expressed by a Zernike polynomial or a trigonometric polynomial.
13. The imprint apparatus according to claim 4, wherein the second formula can be expressed by a high dimensional polynomial of at least 2nd order.
14. The imprint apparatus according to claim 4, wherein the second formula can be expressed by a Zernike polynomial.
15. The imprint apparatus according to claim 1, wherein the control unit holds information relating to the warping shape that has been input from the outside.
16. The imprint apparatus according to claim 1, further comprising a measurement unit configured to measure the warping shape,
    wherein the measurement unit is used to acquire information about the warping shape.
17. The imprint apparatus according to claim 4, further comprising a measurement unit configured to measure a positional deviation amount on the substrate surface,
    wherein the control unit obtains the second formula with reference to information about the positional deviation amount on the substrate surface measured by the measurement unit.
18. An imprint apparatus configured to form a pattern of an imprint material on a substrate by bringing the imprint material into contact with a mold, the imprint apparatus comprising:
    a coating unit configured to coat an imprint material on the substrate; and
    a control unit,
    wherein the control unit controls the coating unit to change at least one of coating position and coating amount of the imprint material according to a distortion component relating to a shot region of the substrate.
19. The imprint apparatus according to claim 18, further comprising a moving unit configured to hold and move the substrate,
    wherein the control unit obtains a positional deviation amount expression formula that expresses a positional deviation amount at each position on a surface of the substrate held by the moving unit, with reference to information about a warping shape of the substrate in a state where the substrate is not yet held by the moving unit,
    calculates positional deviation amounts at a plurality of positions of the substrate surface with reference to the obtained positional deviation amount expression formula, and
    obtains a distortion component relating to a shot region of the substrate based on the positional deviation amounts at the plurality of positions.
20. An imprint method for forming a pattern of an imprint material on a substrate by bringing the imprint material into contact with a mold, the method comprising:
    obtaining a positional deviation amount expression formula that expresses a positional deviation amount at each position on a surface of the substrate held by a moving unit, with reference to information about a warping shape of the substrate in a state where the substrate is not yet held by the moving unit;
    calculating positional deviation amounts at a plurality of positions on the substrate surface with reference to the obtained positional deviation amount expression formula, and obtaining a distortion component relating to a shot region of the substrate based on the positional deviation amounts obtained at the plurality of positions; and
    controlling a shape or a position of at least one of the mold and the substrate according to the obtained distortion component.
21. The imprint method according to claim 20, wherein the positional deviation amount expression formula relates to two directions on the substrate surface, and the positional deviation amounts at the plurality of positions relate to two directions on the substrate surface.
22. The imprint method according to claim 20, wherein the distortion component is a plurality of types of distortion components.
23. The imprint method according to claim 20, further comprising:
    obtaining a first formula as a formula expressing the shape of the substrate based on the information about the warping shape;
    converting the first formula into a second formula serving as the positional deviation amount expression formula at a plurality of positions on the substrate surface; and
    calculating the positional deviation amounts at the plurality of positions according to the second formula.
24. The imprint method according to claim 23, wherein the converting is performed by using a transformation matrix for obtaining a plurality of coefficient values of the second formula from a plurality of coefficient values of the first formula.
25. The imprint method according to claim 24, wherein the transformation matrix is obtained from a formula expressing a shape of a referential substrate that is different from the substrate, which is obtainable from a general formula of the first formula and warping shape information about the referential substrate in a state where the referential substrate is not yet held by the moving unit, and a formula expressing positional deviation amounts in two directions at each position on a surface of the referential substrate, which is obtained from a general formula of the second formula and positional deviation amounts in two directions at a plurality of positions on the surface of the referential substrate in a state where the referential substrate is held by the moving unit.
26. A product manufacturing method, comprising:
    forming a pattern on a substrate using an imprint apparatus; and
    processing the substrate on which the pattern has been formed,
    wherein the imprint apparatus is configured to form a pattern of an imprint material on a substrate by bringing the imprint material into contact with a mold, and including a moving unit configured to hold and move the substrate, and a control unit,
    wherein the control unit obtains a positional deviation amount expression formula that expresses a positional deviation amount at each position on a surface of the substrate held by the moving unit, with reference to information about a warping shape of the substrate in a state where the substrate is not yet held by the moving unit,
    calculates positional deviation amounts at a plurality of positions on the substrate surface with reference to the obtained positional deviation amount expression formula, and obtains a distortion component relating to a shot region of the substrate based on the positional deviation amounts at the plurality of positions, and
    controls the shape or the position of at least one of the mold and the substrate according to the obtained distortion component.

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