Patent Publication Number: US-2009231568-A1

Title: Method of measuring wavefront error, method of correcting wavefront error, and method of fabricating semiconductor device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2008-062885, filed on Mar. 12, 2008; the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method of measuring a wavefront error, a method of correcting the wavefront error, and a method of fabricating a semiconductor device. The present invention more particularly relates to a technology for measuring a wavefront error that occurs in an optical system of an exposure apparatus. 
     2. Description of the Related Art 
     In the course of fabricating a semiconductor device by using the technique of photolithography, an exposure apparatus is used to transfer a mask pattern that is formed on a reticle onto a process object such as a wafer on which a resist is formed. The exposure apparatus is required to project the mask pattern in a high-resolution and at high-precision. Various factors such as wavefront error (i.e., wavefront aberration) affect imaging properties of a projection optical system. The wavefront error may disadvantageously shift a focus position depending on, for example, density of the mask pattern. If the focus position is shifted, it is difficult to project the mask pattern that is formed on the reticle in the high-resolution and high-precision manner. JP-A 2002-250677 (KOKAI), for example, discloses a technology that makes it is possible to accurately measure the wavefront error of the projection optical system. 
     A typical reticle includes a pellicle as a dust prevention film so that an image of dust that is attached to the mask pattern cannot be focused on the process object. The pellicle is a film made of a material transparent to an exposure light. A phase of the light that passes through the pellicle changes depending on film thickness, refractive index of the material of the pellicle, and incident angle of the light. To satisfy needs for improvement in precision and integration of the pattern that is formed on the semiconductor device, there has been a trend toward using a projection optical system having a larger numerical aperture in the exposure apparatuses that are used to fabricate the semiconductor device. As the numerical aperture of the projection optical system increases, the wavefront error occurring due to the pellicle increases. The effect of the wavefront error becomes remarkable when, for example, the numerical aperture is 1 or larger, specifically, about 1.3 or larger. Even if the wavefront error resulting from the projection optical system is corrected accurately, the presence of the pellicle can makes it difficult to project the pattern formed on the reticle in the high-resolution and the high-precision manner. 
     BRIEF SUMMARY OF THE INVENTION 
     According to an aspect of the present invention there is provided a method of measuring a wavefront error of an exposure light that occurs when the exposure light passes through an optical system that is used in an exposure apparatus. The method includes measuring the wavefront error of the exposure light by using a measurement optical element including a pellicle arranged in an optical path of the exposure light that passes through the optical system. 
     According to another aspect of the present invention there is provided a method of correcting a wavefront error of an exposure light that occurs when the exposure light passes through an optical system that is used in an exposure apparatus. The method includes acquiring a third wavefront error as a combined error of a first wavefront error and a second wavefront error, the first wavefront error being a wavefront error occurring due to a projection optical system that is used to project an image having a predetermined pattern, and the second wavefront error being a wavefront error occurring due to a pellicle that is arranged in an optical path of the exposure light; and adjusting the projection optical system based on the third wavefront error. 
     According to still another aspect of the present invention there is provided a method of fabricating a semiconductor device by projecting an image having a predetermined pattern that is formed on a reticle onto a process object via a pellicle that is arranged on the reticle and a projection optical system. The method including acquiring a third wavefront error as a combined error of a first wavefront error and a second wavefront error, the first wavefront error being a wavefront error occurring due to the projection optical system, and the second wavefront error being a wavefront error occurring due to the pellicle; and adjusting the projection optical system based on the third wavefront error. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of an exposure apparatus with which a method of fabricating a semiconductor device according to a first embodiment is performed; 
         FIG. 2  is a cross-sectional view of a reticle shown in  FIG. 1 ; 
         FIG. 3  is a schematic diagram of relevant parts of a wavefront sensor shown in  FIG. 1 ; 
         FIG. 4  is a cross-sectional view of a measurement blank; 
         FIG. 5  is a schematic diagram for explaining behavior of an exposure light passing through a pellicle that is formed on the reticle; 
         FIG. 6  is a flowchart of a process of correcting a wavefront error; 
         FIG. 7  is a schematic diagram of an arrangement of the exposure apparatus to measure the wavefront error; 
         FIG. 8  is a flowchart of a process of fabricating the semiconductor device; 
         FIG. 9  is a flowchart of a process of correcting the wavefront error according to a second embodiment; 
         FIG. 10  is a flowchart of an exposure process that is a part of a process of fabricating the semiconductor device according to a third embodiment; 
         FIG. 11  is a graph of a relation among transmittance, incident angle, and thickness of the pellicle; and 
         FIG. 12  is a schematic diagram for explaining calculation for properties of the pellicle. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Exemplary embodiments of a method of measuring a wavefront error, a method of correcting the wavefront error, and a method of fabricating a semiconductor device are described below while referring to the accompanying drawings. The present invention is not limited to the embodiments explained below. 
       FIG. 1  is a schematic diagram of an exposure apparatus  10  with which a method of fabricating a semiconductor device according to a first embodiment of the present invention is performed. The exposure apparatus  10  transfers a mask pattern that is formed on a reticle  13  onto a process object  16  by exposure via the reticle  13 . The exposure apparatus  10  is a reduction-projection exposure apparatus. That is, in the exposure apparatus  10 , an image having the pattern that is formed on the reticle  13  is reduced and the reduced image is projected by using a projection lens  15 . The exposure apparatus  10  includes a main unit and a wavefront measuring device. The main unit includes a light source  11 , an illumination optical system  12 , a reticle stage  14 , the projection lens  15 , a wafer stage  18 , and a control system (including a main control unit  26 ). Assume that an optical axis AX is the central axis of both the illumination optical system  12  and the projection lens  15 . 
     The light source  11  emits, for example, an ultraviolet pulse light as an exposure light. The light source  11  can be, for example, an excimer-laser light source that emits an ArF excimer laser, a KrF excimer laser, or the like. The illumination optical system  12  illuminates the reticle  13  with the exposure light emitted from the light source  11 . The illumination optical system  12  includes, although not shown, a homogenization optical system, a reticle blind, and a light-collection optical system. The homogenization optical system homogenizes the intensity of the light received from the light source  11 . The reticle blind determines the exposure target area on the reticle  13  that is to be exposed with the exposure light. The light-collection optical system collects the exposure light. The illumination optical system  12  can include, for example, a polarizer that polarizes the exposure light to a predetermined polarization state and a mirror to bend an optical path. 
     The reticle stage  14  supports the reticle  13  by, for example, vacuum contact. A reticle-stage driving unit  23  is operative to move the reticle stage  14  in a movable area. The current position of the reticle stage  14  within the movable area is continuously detected by a detection unit (not shown). Positional data indicating the current position of the reticle stage  14  is sent to the main control unit  26  via a stage control unit  27 . The main control unit  26  causes the stage control unit  27  and the reticle-stage driving unit  23  to move the reticle stage  14  based on the positional data. By the movement of the reticle stage  14 , replacement between the reticle  13  and a measurement blank  50  at a position on the optical axis AX is performed. 
       FIG. 2  is a cross-sectional view of the reticle  13 . The reticle  13  includes a plurality of mask patterns  32  made of, for example, a chromium oxide film or a chromium film. The mask patterns  32  are formed on an exit surface of a glass substrate  31 . An exit surface of a member, e.g., the glass substrate  31 , is a surface from where light exits the member. The glass substrate  31  is made of a material transparent to the exposure light, for example, quartz. A pellicle film  33  is formed on the glass substrate  31  to cover the mask patterns  32 . A pellicle frame  34  is formed surrounding the pellicle film  33 . The pellicle frame  34  is, for example, 5 mm in height. A pellicle includes the pellicle film  33  and the pellicle frame  34 . 
     The pellicle film  33  works as a protection film that protects the mask patterns  32  from dust. The pellicle film  33  is a film made of a material that is transparent to the exposure light. In the present embodiment, the pellicle film  33  is made of, for example, a fluorine-based polymer that is transparent to the exposure light emitted from the light source  11 . Moreover, the pellicle film  33  is formed such that transmittance of the exposure light to the pellicle film  33  that enters the pellicle film  33  at the right angle becomes close to the maximum. In other words, for example, the pellicle film  33  is formed such that its refractive index is about 1.40, and layer thickness is about 830 nanometers. When the process object  16  is exposed with the exposure light received from the illumination optical system  12 , the reticle  13  is arranged in such a manner that the plane of the exposure light and the plane of the mask patterns  32  match. Moreover, an entrance surface of the glass substrate  31  and an exit surface of the pellicle film  33  are inclined to the plane on which the exposure light received from the illumination optical system  12  is focused. An entrance surface of a member, for example, the glass substrate  31 , is a surface from where light enters the member. Due to this, even if dust is present on the entrance surface of the glass substrate  31  or the exit surface of the pellicle film  33 , an adverse effect of this dust on the imaging of the mask patterns  32  can be suppressed. 
     Referring back to  FIG. 1 , the projection lens  15  is arranged in a position where it can receive the exposure light coming out of the reticle  13 . The projection lens  15  is a projection optical system that projects the image of the mask patterns  32  that is present on the reticle  13 . Projection magnification of the projection lens  15  is, for example, ¼, ⅕, and ⅙. The projection lens  15  includes a plurality of lens elements that are arranged on the optical axis AX. Optical adjustment, such as interval adjustment among the lens elements and eccentricity adjustment, is performed by appropriately moving one or more of the lens elements. The imaging properties of the projection lens  15  can be adjusted to desired imaging properties by performing such optical adjustment. 
     The projection lens  15  includes a plurality of driving elements for moving the lens elements. The driving elements can be, for example, piezoelectric elements. The driving elements can independently move each of the lens elements. The driving elements move the lens elements, for example, in a direction parallel to the optical axis AX. The lens elements can be configured to, for example, be inclinable in a plane that is perpendicular to the optical axis AX, in addition to be movable in the direction parallel to the optical axis AX. An imaging-property correcting controller  24  controls driving of the driving elements based on a signal received from the main control unit  26 . The main control unit  26  adjusts the imaging properties of the projection lens  15 , such as distortion, curvature of field, astigmatism, comatic aberration, and spherical aberration, by causing the imaging-property correcting controller  24  to appropriately move the lens elements. 
     A wafer holder  17  is fixed on the wafer stage  18 . The wafer holder  17  firmly holds the process object  16  by, for example, the vacuum contact. A wafer-stage driving unit  25  moves the wafer stage  18  in a plane perpendicular to the optical axis AX. Moreover, the wafer-stage driving unit  25  inclines the wafer holder  17  in the plate perpendicular to the optical axis AX, or moves the wafer holder  17  in a direction parallel to the optical axis AX. A position of the wafer stage  18  within a movable area and a position of the wafer holder  17  within a movable area are always detected by a detection unit (not shown). Positional data indicative of the current position of the wafer holder  17  and the wafer stage  18  are sent to the main control unit  26  via the stage control unit  27 . The main control unit  26  causes the stage control unit  27  and the wafer-stage driving unit  25  to move the wafer stage  18  and the wafer holder  17  based on the positional data about the wafer stage  18  and the wafer holder  17 . The process object  16  is a substrate as a wafer on which a resist is formed. The wafer is made of, for example, silicon. By the movement of the wafer stage  18 , replacement between the process object  16  and a wavefront sensor  21  at a position on the optical axis AX can be performed. 
     The main control unit  26  includes a CPU, a ROM, and a RAM, and controls the exposure apparatus  10 . For example, an external storage device  28  including a hard disk is connected to the main control unit  26 . The external storage device  28  stores therein results of measurement by the wavefront measuring device and data that is calculated from the results of measurement. The waveform measuring device includes the wavefront sensor  21  and a wavefront-data processing unit  22 . The wavefront sensor  21  is arranged on the wafer stage  18 . 
       FIG. 3  is a schematic diagram of relevant parts of the wavefront sensor  21 . The wavefront sensor  21  includes a collimator lens  41 , a lens array  42 , and a CCD  44 . The CCD  44  is an imaging device including a plurality of light-receiving elements arranged in a matrix. The process object  16  is replaced with the wavefront sensor  21  by the movement of the wafer stage  18 . When the wavefront sensor  21  receives the light, the collimator lens  41  converts the light into a parallel light. The lens array  42  includes a plurality of lens elements  43  arranged in a matrix within a plane perpendicular to the optical axis AX. The lens elements  43  focus the received light onto the light-receiving elements of the CCD  44 . The wavefront sensor  21  can be configured to include one or more mirrors to bend the optical path, or one or more relay lenses. 
     Referring back to  FIG. 1 , the wavefront-data processing unit  22  calculates the wavefront error of the optical systems in the exposure apparatus  10  by using the result of imaging by the CCD  44 . The external storage device  28  stores therein data about the wavefront error that is calculated by the wavefront-data processing unit  22 . The main control unit  26  drives the imaging-property correcting controller  24  based on the data about the wavefront error stored in the external storage device  28 . Any method of exposure can be used by the exposure apparatus  10 , such as the step-and-repeat or the step-and-scan. The exposure apparatus  10  can be a liquid-immersion exposure apparatus in which a space between the projection lens  15  and the process object  16  is filled with liquid, for example, water. 
       FIG. 4  is a cross-sectional view of the measurement blank  50 . The measurement blank  50  is arranged in the optical path of the exposure light when measuring the wavefront error. The measurement blank  50  is placed in place of the reticle  13  by the movement of the reticle stage  14 . The measurement blank  50  includes an aperture plate  51  having an aperture  52 . The aperture plate  51  is formed on an exit surface of a transparent substrate  55  as a light-shielding member. Only a part of the exposure light entering the aperture  52  can pass through the aperture plate  51 . The measurement blank  50  is arranged in such a manner that both an entrance surface and an exit surface of the aperture plate  51  are perpendicular to the optical axis AX. Moreover, the measurement blank  50  is arranged in such a manner that the plane of the exposure light coming from the illumination optical system  12  matches with the exit surface of the aperture plate  51 . 
     A measurement pellicle film  53  is a pellicle that is provided to the measurement blank  50 . The pellicles used in the embodiments are made of the same material and have the same structure as a typical pellicle that is formed on a typical reticle. The function of the pellicles is not limited to protection of the mask patterns from dust. The measurement pellicle film  53  is formed on the exit surface of the aperture plate  51 . The measurement pellicle film  53  is formed in the same manner as the pellicle film  33  according to the present embodiment (see  FIG. 2 ) is formed on the reticle  13 . 
     The measurement pellicle film  53  is made of, in the same manner as the pellicle film  33  that is formed on the reticle  13 , a material that is transparent to the exposure light emitted from the light source  11 , for example, a fluorine-based polymer. Moreover, the measurement pellicle film  53  is formed, in the same manner as the pellicle film  33  is formed on the reticle  13 , so that the refractive index is, for example, about 1.40 and the layer thickness is, for example, about 830 nanometers. The measurement blank  50  includes a pellicle frame  54  surrounding the measurement pellicle film  53 , in the same manner as the reticle  13  includes. After passing through the aperture  52 , the exposure light passes through the measurement pellicle film  53  and then exits the measurement blank  50 . The measurement blank  50  can be configured to have a mask pattern for measurement of the wavefront error. 
       FIG. 5  is a schematic diagram for explaining the behavior of the exposure light when the exposure light passes through the pellicle film  33  that is formed on the reticle  13 . Assume that the pellicle film  33  is made of a material having the refractive index different from that of a surrounding air layer. Due to this, a part of the light that enters the pellicle film  33  from a first surface S 1  is reflected by a second surface S 2 , which is opposite to the first surface S 1 , toward the first surface S 1 . The other part of the light that enters from the first surface S 1  exits the pellicle film  33  from the second surface S 2 . A part of the reflected light that is reflected by the second surface S 2  is further reflected by the first surface S 1 ; and the reflected light goes toward the second surface S 2 . The other part of the reflected light that is reflected from the first surface S 1  to the second surface S 2  goes out of the pellicle film  33  from the first surface S 1 . The pellicle film  33  outputs an overlapped light as a result of the multiple reflections between the first surface S 1  and the second surface S 2 . 
     Assume that an angle between the incident light that fall on the pellicle film  33  and the optical axis AX is an incident angle. The reflectance of the first surface S 1  and the reflectance of the second surface S 2  depend on this incident angle. In the exposure apparatus  10 , the incident angle of the exposure light to the reticle  13  is up to, for example, about 20 degrees. The larger the incident angle is, the higher the reflectance of the first surface S 1  and the reflectance of the second surface S 2  become. The phase of the components of the light that goes out from the second surface S 2  varies depending on the number of reflections between the first surface S 1  and the second surface S 2 . Thus, the thickness of the pellicle film  33  affects the phase. In this manner, the phase of the light that goes out of the pellicle film  33  from the second surface S 2  varies depending on the thickness of the pellicle film  33 , the refractive index of the material making the pellicle film  33 , and the incident angle of the incident light. 
     The smaller the wavefront error, which is deviation between a real wavefront of the exposure light and a spherical ideal wavefront, on an entrance surface of the process object  16  is, the higher-resolution image can be projected through the projection lens  15 . The change in the phase of the exposure light that occurs in the pellicle film  33  depending on the incident angle acts in the same manner as the aberration that occurs in the lenses acts. In other words, the change in the phase that occurs due to the presence of the pellicle film  33  may increase the wavefront error. Because the change in the phase that occurs in the pellicle film  33  depends on the incident angle of the exposure light, the wavefront error that occurs due to the pellicle film  33  increases as the NA of the projection lens  15  increases. The larger the wavefront error is, to the larger extent the properties at which the dimension error of each pattern becomes the minimum value (hereinafter “best-focus properties”) change. This change decreases the depth at which the images of the mask patterns  32  focus. As a result, even the wavefront error due to the projection lens  15  is corrected extremely precisely, it is difficult to project the patterns formed on the reticle  13  in the high-resolution and high-precision manner. 
       FIG. 6  is a flowchart of a process of correcting the wavefront error according to the first embodiment. The measurement blank  50  is moved onto the optical axis AX within the optical path of the exposure light by the movement of the reticle stage  14  (Step S 1 ). The wavefront sensor  21  is also moved onto the optical axis AX by the movement of the wafer stage  18 . 
       FIG. 7  is a schematic diagram of an arrangement of the exposure apparatus  10  when measuring the wavefront error. Only relevant parts of the exposure apparatus  10  are illustrated in  FIG. 7 . The measurement blank  50  is arranged in such a manner that the aperture  52  of the aperture plate  51  (see  FIG. 4 ) is on the optical axis AX. The wavefront sensor  21  is arranged in such a manner that the center axis of the collimator lens  41  coincides with the optical axis AX. When the exposure light coming from the illumination optical system  12  enters the measurement blank  50 , a spherical wave almost in the shape of the ideal wavefront generates at the aperture  52  of the measurement blank  50 . The collimator lens  41  converts the spherical wave into a parallel light. If there is a wavefront error due to the measurement pellicle film  53  or a wavefront error due to the projection lens  15 , the spherical wave is deformed due to the wavefront error before entering the collimator lens  41 . The parallel light output from the collimator lens  41  enters the lens elements  43  of the lens array  42 , and is focused on the light-receiving elements of the CCD  44 . 
     Imaging by the CCD  44  is performed at Step S 2 . The CCD  44  detects a brightness distribution on the imaging surface by using the light-emitting elements. The wavefront error of the optical systems in the exposure apparatus  10  is calculated from the result of imaging by the CCD  44  (Step S 3 ). The calculated wavefront error is a third wavefront error that is a combined wavefront error of a first wavefront error due to the projection lens  15  and a second wavefront error due to the measurement pellicle film  53 . The third wavefront error is acquired at Step S 3 . Because the wavefront error is calculated where the measurement blank  50  including the measurement pellicle film  53  is arranged in the optical path of the exposure light, it is possible to extremely precisely measure the wavefront error that occurs in the optical systems of the exposure apparatus  10  including the measurement pellicle film  53 . 
     The optical adjustment of the projection lens  15  is performed based on data about the third wavefront error (Step S 4 ). The projection lens  15  is adjusted to the optimum state such that, for example, an aberration root mean square (aberration RMS), which represents an average of the gap between the ideal wavefront and the real wavefront, becomes the smallest value. Thus, the process of the correction of the wavefront error that occurs in the optical systems of the exposure apparatus  10  goes to end. In this manner, the wavefront error that occurs in the optical systems of the exposure apparatus  10  can be corrected extremely precisely. The correction of the wavefront error according to the first embodiment is performed, for example, at installation of the exposure apparatus  10 , or periodically after the installation of the exposure apparatus  10 . 
       FIG. 8  is a flowchart of a process of fabricating the semiconductor device according to the first embodiment. The resist is formed by applying a photosensitizer onto the wafer (Step S 11 ). The process object  16  is exposed by using the exposure apparatus  10  in which the wavefront error is corrected as in the manner described with reference to  FIG. 6  (Step S 12 ). More particularly, the image based on a pattern that is formed on the reticle  13  is projected onto the process object  16  via the pellicle film  33  and the projection lens  15  (Step S 12 ). Because the exposure apparatus  10  in which the wavefront error is corrected extremely precisely is used, it is possible to project the pattern that is formed on the reticle  13  in the high-resolution and high-precision manner. 
     The process object  16  that has been exposed at Step S 12  is then developed (Step S 13 ). After that, unnecessary resist is removed from the process object  16  by etching (Step S 14 ). Those steps are repeated, and thus some patterns are overlapped on the wafer. After the patterned wafer is subjected to various subsequent steps, the semiconductor-device fabricating process goes to end. It is possible to boost the yield of the semiconductor device by increasing the resolution and the precision at which the pattern formed on the reticle  13  is projected. 
     The thickness of the pellicle film  33  that is formed on the reticle  13  can be set to any appropriate value. The thickness of the measurement pellicle film  53  that is formed the measurement pellicle film  53  is set to equal to the thickness of the pellicle film  33  that is formed on the reticle  13 . It is permissible that the thickness of the pellicle film  33  is set to such a value that, for example, when the wavefront error due to the pellicle film  33  is expanded by using Zernike expansion, a ratio of components of the RMS represented by terms having the Zernike order of 10 or higher to components of the RMS represented by terms having the Zernike order of 5 or higher is lower than 10%. The Zernike expansion is an expansion by using Zernike polynomials (see, for example, JP-A 2002-250677 (KOKAI)). More particularly, if there are various components representing the spherical aberration including 4(Z 4 ), 9(Z 9 ), 16(Z 16 ), 25(Z 25 ), and 36(Z 36 ) with respect to the Zernike order, the thickness of the pellicle film  33  can be decided to such a value that the high-ordered components, such as the components of Z 16 , Z 25 , and Z 36 , are close to zero, i.e., the absolute values of the components decreases as possible. 
     In the field of projection lenses that have been widely used, it is easy to correct the low-ordered aberration components (e.g., Z 4  and Z 9 ) efficiently, while it is difficult to correct the high-ordered aberration components (e.g., Z 16 , Z 25 , and Z 36 ). If the thickness of the pellicle film  33  is adjusted to the value at which the absolute values of the difficult-to-correct components decreases as possible, it is possible to decrease the spherical aberration to a larger extent by the optical adjustment of the projection lens  15 . For example, taking it into consideration that the absolute value of the component of Z 16  is likely to be larger than the absolute values of the other high-ordered components of Z 25  and Z 36 , the thickness of the pellicle film  33  is decided to such a value that the absolute value of the component of Z 16  becomes the smallest. If the absolute value of the component of Z 16  is the smallest when the thickness of the pellicle film  33  is 822 nm, then the thickness is decided to 822 nm. It can be configured to make such a decision about the thickness of the pellicle film  33  only when the NA of the projection lens  15  is equal to or larger than 1. 
     Moreover, it is allowable to adjust the projection lens  15  in such a manner that the absolute value of the component of Z 9 , from among the components representing the wavefront error due to the pellicle film  33 , is the smallest. It can be configured to make the adjustment of the projection lens  15  for obtaining the smallest absolute value of the component of Z 9 , only when the numerical aperture of the projection lens  15  is equal to or larger than 1. Thus, the wavefront error that occurs in the optical systems of the exposure apparatus  10  decreases effectively. It is allowable to use, for the calculation for deciding the thickness of the pellicle film  33 , an average value of the wavefront error where an s-polarized light is used as the incident light to the pellicle film  33  and the wavefront error where a p-polarized light is used as the incident light. In this case, the wavefront error is decreased by an averaged value between when the s-polarized light is used and when the p-polarized light is used. 
       FIG. 9  is a flowchart of a process of correcting the wavefront error according to a second embodiment of the present invention. It is assumed that the exposure apparatus  10  is used to implement the second embodiment. The first wavefront error, which is the wavefront error due to the projection lens  15 , is measured at Step S 21 . More particularly, the measurement blank  50  used in the first embodiment from which the measurement pellicle film  53  and the pellicle frame  54  are excluded is used as the measurement blank at Step S 21 . 
     After that, the second wavefront error, which is the wavefront error due to the pellicle film  33  that is formed on the reticle  13 , is estimated at Step S 22 . More particularly, the second wavefront error is calculated at Step S 22  based on the properties of the pellicle film  33 , for example, the film thickness and the optical coefficients (e.g., the refractive index and the extinction coefficient). That is, the second wavefront error due to the pellicle film  33  that is expected to occur when the pellicle film  33  having the predetermined properties is arranged in the optical path of the exposure light within the exposure apparatus  10  is calculated at Step S 22 . In this second wavefront error calculation, the thickness of the pellicle film  33  is used as a parameter, assumed that the film thickness is, for example, an average value of a range of a manufacturing error. 
     The third wavefront error is calculated by combining the first wavefront error measured at Step S 21  and the second wavefront error calculated at Step S 22 , at Step S 23 . The optical adjustment of the projection lens  15  is performed based on data about the third wavefront error that is calculated at Step S 23 , at Step S 24 . The projection lens  15  is adjusted, in the same manner as in the first embodiment, to the optimum state such that, for example, the aberration RMS becomes the smallest value. 
     In the second embodiment, the wavefront error that occurs in the optical systems of the exposure apparatus  10  can be corrected extremely precisely. Moreover, the drop in the wavefront error for various reticles  13  is averaged by calculating the wavefront error from data representing the averaged properties of the reticle  13  and correcting the calculated wavefront error. This makes it possible to achieve a high-resolution and high-precision projection by the exposure apparatus  10 . With this configuration, the yield of the semiconductor device that is fabricated through the exposure performed by the exposure apparatus  10  improves. The correction of the wavefront error can be performed every replacement of the reticle  13  including the pellicle film  33  having different properties. This makes it possible to correct the wavefront error extremely precisely by adjusting the properties of the pellicle film  33 . 
       FIG. 10  is a flowchart of an exposure process that is a part of a process of fabricating the semiconductor device according to a third embodiment of the present invention. It is assumed that the exposure apparatus  10  is used to implement the third embodiment. The salient feature of the third embodiment is to decide the properties of the pellicle film  33  based on a lens apodization of the projection lens  15  that is the optical property of the exposure apparatus  10 . The lens apodization is mainly caused by fluctuation in the properties of the materials making the lens and processing accuracy on the surface. The lens apodization is a phenomenon that the light intensity is attenuated unevenly so that a drop in the light intensity changes depending on the optical path of the light passing through the lens. 
     As described in the first embodiment with reference to  FIG. 5 , the pellicle film  33  causes the phase of the light to change by the multiple reflections between the first surface S 1  and the second surface S 2 . As for the components of the light output from the second surface S 2 , not only the phase but also the intensity changes according to the number of the reflections between the first surface S 1  and the second surface S 2 . In other words, the pellicle film  33  causes the phase and the intensity of the light to change by the multiple reflections. When the light exits from the second surface S 2  of the pellicle film  33 , the intensity of this light changes depending on the thickness of the pellicle film  33 , the refractive index of the material making the pellicle film  33 , and the incident angle of the incident light. 
     The change in the intensity of the light depending on the incident angle of the exposure light acts in the same manner as the lens apodization acts. More particularly, the presence of the pellicle film  33  formed on the reticle  13  causes not only the wavefront error, as described in the first embodiment, but also the change in the lens apodization. The change in the lens apodization may cause a change in the image intensity depending on the density of the mask patterns  32 , etc. The larger the numerical aperture of the projection optical system is, to the larger extent the lens apodization due to the pellicle film  33  changes. 
     The lens apodization of the projection lens  15  of the exposure apparatus  10  (hereinafter, “first lens apodization”) is measured at Step S 31  illustrated in  FIG. 10 . The lens apodization of the projection lens  15  is an optical property of the exposure apparatus  10 , and is called “first optical property”. The first optical property is acquired by the measurement at Step S 31 . More particularly, the lens apodization is measured by using a light that is polarized in the same manner as the exposure light to be used for the exposure by the exposure apparatus  10 , at Step S 31 . When measuring the lens apodization, the exposure apparatus  10  is arranged, for example, almost as illustrated in  FIG. 7  except that the wavefront sensor  21  is replaced by a CCD camera. 
     A difference between the first lens apodization and a second lens apodization is calculated as a difference in the transmittance distributions (hereinafter, “difference distribution”). The second lens apodization is a target lens apodization, for example, a lens apodization of the exposure apparatus based on an optical proximity correction (OPC) model. The second lens apodization is a target optical property of the exposure apparatus  10 , and is called “second optical property”. The difference between the first optical property representing the first lens apodization and the second optical property representing the second lens apodization is acquired at Step S 32 . 
     The properties of the pellicle film  33  are decided based on the difference acquired at Step S 32 , at Step S 33 . More particularly, such properties are calculated that the difference distribution calculated at Step S 32  is offset to almost zero by the change in the transmittance distribution due to the pellicle film  33 . The dependence of the transmittance of the pellicle film  33  on the incident angle can be controlled by adjusting the optical coefficients and the thickness of the pellicle film  33  to appropriate values. 
       FIG. 11  is a graph of a relation among transmittance of the pellicle film  33 , incident angle of the light to the pellicle film  33 , and thickness of the pellicle film  33 . The vertical axis represents the transmittance; the horizontal axis represents a parameter M·n·sin θ, where M is magnification of the projection lens  15 , n is refractive index of the medium between the projection lens  15  and the process object  16 , and θ is incident angle of the light to the pellicle film  33 . Assume, for example, that the magnification M of the projection lens  15  is ¼ and the medium between the projection lens  15  and the process object  16  is water. A curve line A in the figure is the transmittance distribution where the thickness of the pellicle film  33  is 730 nanometers; a curve line B is for the thickness of 770 nanometers; a curve line C is for the thickness of 830 nanometers; and a curve line D is for the thickness of 890 nanometers. 
       FIG. 12  is a schematic diagram for explaining the calculation for the properties of the pellicle film  33 . A broken line and a full line illustrated in an upper graph of the figure are the first lens apodization and the second lens apodization, respectively. The difference distribution between the distribution represented by the full line and the distribution represented by the broken line is calculated at Step S 32 . A full line illustrated in a lower graph of the figure is the second lens apodization the same as illustrated in the upper graph. A broken line illustrated in the lower graph is the lens apodization in the exposure apparatus  10  when the pellicle with a value decided at Step S 33  in the thickness is used as the pellicle film  33 . In this manner, the exposure apparatus  10  obtains the lens apodization closer to the second lens apodization by adjusting the thickness of the pellicle film  33  to such a value that the difference distribution between the first lens apodization and the second lens apodization can be offset. It is allowable to adjust the refractive index of the material making the pellicle film  33  instead of the thickness of the pellicle film  33  as the properties of the pellicle film  33  at Step S 33 . As the properties of the pellicle film  33 , at least one between the film thickness and the refractive index of the material making the pellicle film  33  is selectable. 
     A pellicle having the properties decided at Step S 33  is formed on the reticle  13  as the pellicle film  33  at Step S 34 . The exposure is performed via the reticle  13  including the pellicle film  33  that is formed at Step S 34 , at Step S 35 . The exposure is performed via the pellicle film  33  having the properties decided at Step S 33 , at Step S 35 . Thus, the exposure process goes to end. In the third embodiment, the mask patterns  32  formed on the reticle  13  can be projected in the high-resolution and high-precision manner. Moreover, because the reticle that is fabricated based on the OPC model the same as is used for the exposure apparatus is available as the reticle  13 , the required time to prepare the reticle  13  is shorten. The drop in the required time to prepare the reticle  13  makes it possible to reduce the fabrication costs of the semiconductor device. 
     Although the properties of the pellicle film  33  are decided based on the lens apodization of the projection lens  15  in the exposure process according to the third embodiment, it is allowable to decide the properties based on some other factors such as the imaging properties. The imaging properties include, for example, the dimension error of the image that is projected through the projection lens  15 . The dimension error depends on degree of the density, cycle, size of the mask patterns  32 , etc. In this case, the mask patterns  32  can also be projected in the high-resolution and high-precision manner by adjusting the properties of the pellicle film  33 . 
     Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.