Patent Publication Number: US-9891525-B2

Title: Exposure method, exposure apparatus, and article manufacturing method

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an exposure method, an exposure apparatus, and an article manufacturing method. 
     Description of the Related Art 
     Various devices, for example, a semiconductor device and a flat panel display (liquid crystal display device) are manufactured through a photolithography process. The photolithography process includes an exposure process in which a pattern of an original referred to as a “mask” or a “reticle” is projected and exposed to a substrate such as a glass plate or a wafer coated with photosensitizer referred to as “resist”. In recent years, improvement of the focus accuracy, which indicates accuracy of matching a substrate surface with an imaging plane of a projection optical system, and improvement of alignment accuracy, which indicates accuracy of accurately superposing pattern layers formed through a plurality of processes, and the like have been important in order to improve exposure accuracy so as to meet a demand for further miniaturization of the pattern. 
     In this context, when an exposure light is continuously irradiated to the projection optical system for a long time, heat is generated by absorbing a part of the exposure energy, and as a result, imaging performance (focus, magnification, distortion, astigmatism, wave front aberration, etc.) changes, and focus and alignment errors that cannot be ignored may occur. In contrast, an exposure method that successfully adjusts the change of the imaging performance even when an illumination condition of the exposure light changes and the heat-generation distribution of a lens in the projection optical system changes, has been proposed. Japanese Patent No. 2828226 discloses an exposure method in which a correction coefficient of the imaging performance corresponding to a light source image distribution state of the illumination light is stored, corresponding correction information is read out when the light source image distribution state is changed, and the correction is performed on the basis of the information. However, in the exposure method disclosed in the Japanese Patent No. 2828226, immediately after the change of the illumination condition, the temperature distribution occurring due to the illumination conditions before the change remains in the projection optical system. Thus, there may be cases where an offset in accordance with the amount of influence of the absorption of the illumination light before the change occurs in the imaging performance under the illumination condition after the change. Accordingly, Japanese Patent No. 3395280 discloses an exposure method in which the occurrence of the offset of the imaging performance immediately after the change of the illumination condition is eliminated by correcting the correction amount of the imaging performance on the basis of an accumulated energy amount according to the illumination condition before the change. 
     In this context, when the exposure is continued under the illumination condition after the change, the temperature distribution in the lens in the vicinity of a pupil plane of the projection optical system becomes a transient state in which the influence under the illumination condition before the change and the influence under the illumination condition after the change are overlapped. In contrast, in the exposure method disclosed in the Japanese Patent No. 3395280, because the correction amount of the imaging performance is corrected by focusing only on the offset amount immediately after the change of the illumination condition, it is difficult to accurately calculate the change amount in such a transient state. 
     In contrast, for example, there is a method for performing exposure while controlling the imaging performance of the projection optical system under a new illumination condition, after stopping the exposure until influence of the change amount of the imaging performance becomes small when the illumination condition is changed corresponding to the original or its pattern. Here, “until influence of the change amount of the imaging performance becomes small” refers to the point at which the change amount of the imaging performance, which is due to absorption of the illumination light of the projection optical system under the illumination condition before the change, becomes a predetermined allowable value or less. This can also be called the point in time at which the influence on the imaging performance of the energy amount accumulated in the projection optical system before the change becomes negligible. According to this method, exposure is not performed under the transient state when the illumination condition is changed, and thus, the imaging performance of the projection optical system can be strictly controlled for each illumination condition. However, in this method, because it is necessary to stop the exposure each time the illumination condition and the pattern of the original (that is, illumination distribution in the pupil plane of the projection optical system (light source image distribution) changes)), throughput of the exposure apparatus decreases. Additionally, as another method, in the transient state after the change of the illumination condition, it is assumed that exposure is performed while successively measuring the imaging performance of the projection optical system by using a reference mark on a stage that holds the substrate, and correcting the imaging performance as needed based on this measurement result. However, it is necessary to perform the measurement of the imaging performance after temporarily stopping the exposure also in this method, and a decrease of the throughput cannot be avoided. 
     SUMMARY OF THE INVENTION 
     The present invention provides, for example, an exposure method that is advantageous in improving exposure accuracy. 
     The present invention is an exposure method that performs exposure processing in which light from a light source is irradiated to an original, a pattern of the original is projected to a substrate via a projection optical system to expose the substrate, comprising: a first exposure step of performing the exposure processing by irradiating the projection optical system by a first pupil plane illumination distribution of the projection optical system; a second exposure step of performing the exposure processing by irradiating the projection optical system by the second pupil plane illumination distribution that is different from the first pupil plane illumination distribution, after the first exposure step; a change amount obtaining step of obtaining a change amount of an imaging performance of the projection optical system in a condition of the second pupil plane illumination distribution, with respect to the imaging performance of the projection optical system in the first exposure step in which the irradiation is performed in the first pupil plane illumination distribution; and a correction amount obtaining step of obtaining a correction amount for correcting the imaging performance of the projection optical system in the second exposure step, by using the change amount obtained in the change amount obtaining step, wherein, in the second exposure step, the exposure processing is performed by correcting the imaging performance of the projection optical system using the obtained correction amount. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a configuration of an exposure apparatus according to one embodiment of the present invention. 
         FIG. 2  is a graph illustrating a change with the passage of time of the imaging performance of a projection optical system due to the exposure. 
         FIG. 3A  illustrates a pupil plane illumination distribution of the projection optical system for each illumination condition. 
         FIG. 3B  illustrates a pupil plane illumination distribution of the projection optical system for each illumination condition. 
         FIG. 4A  illustrates a luminous flux for each illumination condition. 
         FIG. 4B  illustrates a luminous flux for each illumination condition. 
         FIG. 5  is a graph illustrating the change of the imaging performance in one embodiment. 
         FIG. 6  is a graph illustrating a calculation model of the change of the imaging performance in one embodiment. 
         FIG. 7  is a graph illustrating a correction amount of the imaging performance in one embodiment. 
         FIG. 8  is a flowchart illustrating a parameter acquisition process in one embodiment. 
         FIG. 9  is a graph illustrating measurement timing in the parameter acquisition process. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Hereinafter, embodiments for performing the present invention will be described with reference to drawings and the like. 
     First, a description will be given of a configuration of an exposure apparatus according to one embodiment of the present invention. The exposure apparatus is an apparatus that exposes a pattern formed on an original such as a reticle onto a substrate to be treated by a step-and-step method or a step-and-repeat method, and in the present invention, the exposure method is not particularly limited. Hereinafter, as an example, the exposure apparatus according to the present embodiment is a projection exposure apparatus used in a lithography process in the manufacturing process of a semiconductor device, and that exposes (transfers) an image of the pattern formed on a reticle R onto a wafer W (onto the substrate) by a scanning exposure method. 
       FIG. 1  is a schematic diagram illustrating a configuration of an exposure apparatus  100  according to the present embodiment. Note that, in each drawing, the Z-axis is parallel to the optical axis of a projection optical system  110 , the Y-axis is in a scanning direction of the wafer W during exposure in the same plane perpendicular to the Z-axis (or the relative moving direction between the reticle R and the wafer W), and the X-axis is in the non-scanning direction orthogonal to the Y-axis. The exposure apparatus  100  includes an illumination optical system  104 , a reticle stage  109 , a projection optical system  110 , a wafer stage  116 , and a control unit  115 . 
     The illumination optical system  104  adjusts a luminous flux from a laser light source  101 , and illuminates the reticle R. The laser light source  101  is, for example, a pulse laser light source that emits a laser light and is filled with gas such as KrF or ArF. Additionally, the laser light source  101  includes a front mirror that configures a resonator, a diffraction grating that narrows exposure wavelength, a narrowing module including a prism or the like, a monitor module including a spectrometer and a detector that monitors the stability of the wavelength and spectral width, and a shutter. A beam emitted from the laser light source  101  is shaped into a predetermined beam shape by a beam shaping optical system (not illustrated) under the illumination optical system  104 , incident to an optical integrator (not illustrated), and a plurality of secondary light sources for illuminating the reticle R with a uniform illumination distribution is formed. Additionally, the illumination optical system  104  includes an aperture diaphragm  105 , a half mirror  106 , and a photo sensor  107 . The aperture diaphragm  105  has a substantially circular-shaped opening, and can set not only the diameter of the opening but also the number of the openings (NA) of the illumination optical system  104  to a desired value. Here, the aperture diaphragm  105  can form annular illumination if the opening is formed so as to have an annular shape. The half mirror  106  is disposed on the optical path of the illumination optical system  104 , and reflects and removes a part of the exposure light that illuminates the reticle R. The photo sensor  107  is a detector for ultraviolet lights, and outputs a value that can lead exposure energy (the intensity of the exposure light) based on the light reflected and removed by the half mirror  106 . Specifically, the output of the photo sensor  107  is converted to the exposure energy per one pulse by an integration circuit (not illustrated) that performs integration for each pulse emission from the laser light source  101 . 
     The reticle R is, for example, a quartz glass original, formed with a pattern to be transferred to the wafer W (for example, a circuit pattern). The reticle stage (original holder)  109  is movable in each of the X and Y axial directions while holding the reticle R. The projection optical system  110  projects light passed through the reticle R (circuit pattern image) onto the wafer W at a predetermined magnification R (for example, ¼ times). Additionally, the projection optical system  110  includes an aperture diaphragm  111  and a lens drive device  113 . The aperture diaphragm  111  has a substantially circular shaped opening, disposed on the pupil plane of the projection optical system  110  (Fourier transform plane with respect to the reticle R), and a drive unit  112  such as a motor can adjust the diameter of the opening. The lens drive device (optical element drive unit)  113  allows a field that configures a part of a lens (optical element) system in the projection optical system  110  to move along the optical axis of the projection optical system  110  by using, for example, air pressure or a piezoelectric element, or allows deforming the lens itself. 
     The wafer W is a substrate made of, for example, monocrystalline silicon, coated with a resist (photosensitizer) on the surface. The wafer stage (substrate holder)  116  holds the wafer W via a wafer chuck (not illustrated), and is movable in each of the X, Y, and Z axial directions (ωx, ωy, ωz that are respective rotational directions thereof may be included). The XY plane position of the wafer stage  116  is determined at a laser interferometer  118  by measuring the distance from a moving mirror  117  that is fixed to the wafer stage  116 . The plane position of the wafer W in the optical axis direction (focus plane position) is determined by the measurement by a focus detection device. The focus detection device includes a light projection optical system  121  and a detection optical system  122 . The light projection optical system  121  projects a plurality of luminous fluxes consisting of non-exposure light that does not expose the resist onto the wafer W. Each luminous flux is focused on the wafer W and reflected, and the detection optical system  122  detects the luminous flux reflected on the wafer W. The detection optical system  122  includes a plurality of position detection light receiving elements (not illustrated) corresponding to each reflected luminous flux, and is configured such that the light receiving surface of the light receiving element and the reflection point of each luminous flux on the wafer W become substantially conjugated by an imaging optical system (not illustrated). Subsequently, the surface positional shift of the wafer W in the optical axis direction of the projection optical system  110  is measured as a positional shift of the incident luminous flux on the light receiving element. 
     The control unit  115  is configured by, for example, a computer, connected to each element of the exposure apparatus  100  via a line, and can control the operation and adjustment of each element in accordance with a program, and the like. The control unit  115  includes a main control device  103 , a laser control device  102 , an illumination system control device  108 , a projection lens control device  114 , and a stage control device  120 . The main control device  103  is connected to each control device in the control unit  115 , and performs the control of the entire exposure apparatus  100 . The laser control device  102  executes, for example, the gas exchange operation control of the laser light source  101 , the control for wavelength stabilization, or the control of a discharge applying voltage. Note that, in the present embodiment, these controls are not single controls directed only by the laser control device  102 , and shall be executed by the direction from the main control device  103 . The illumination system control device  108  is one of the switching units that enables switching a plurality of illumination conditions (the number of openings of the illumination optical system  104 , the number of openings of the projection optical system  110 , the annular illumination, oblique illumination, and the like), and controls the diameter of the opening of the aperture diaphragm  105  under the illumination optical system  104 . Here, because a value of ratio of the number of openings of the illumination optical system  104  with respect to the number of openings of the projection optical system  110  is a coherence factor (G value), the illumination system control device  108  can set G value by controlling the diameter of the opening. Note that, as a switching unit, in addition, there is a mechanism (control device) that changes the reticle R having a different pattern shape, or changes the irradiation area of the reticle R. Additionally, the illumination system control device  108  transmits the value of the exposure energy converted based on the output of the photo sensor  107  to the main control device  103 . The projection lens control device  114  calculates the change of the imaging performance of the projection optical system  110  based on a model formula described below, and determines the amount to be corrected. The lens drive device  113  drives the lens in the projection optical system  110  based on the correction amount determined by the projection lens control device  114 , and can suppress the change of the imaging performance of the projection optical system  110 . The stage control device  120  makes the laser interferometer  118  detect the position of the wafer stage  116 , controls a drive device  119  such as a motor, and moves the wafer stage  116  to a predetermined XY plane position. 
     Next, a description will be given of a model formula for the imaging performance change of the projection optical system  110  caused by the exposure in the present embodiment (irradiation of exposure light to the projection optical system  110  by the laser light source  101 ), and a correction amount to be used to quantify the model formula (correction coefficient). In this context, examples of the imaging performance of the projection optical system  110  include focus, magnification, distortion aberration (distortion), astigmatism, or field curvature. 
       FIG. 2  is a graph that exemplifies a typical change with the passage of time (change characteristic) of the imaging performance of the projection optical system due to the exposure. In  FIG. 2 , the horizontal axis indicates time t, the vertical axis indicates a change amount ΔF of the imaging performance in an image height of the projection optical system. Note that the change amount ΔF is different for each image height. First, when the exposure starts from time t 0  as setting the initial change amount ΔF of the projection optical system to zero, the imaging performance changes with time, and eventually stabilizes at a constant value (the maximum change amount) F 1 . This state indicates that energy is absorbed in the projection optical system and becomes heat, and heat energy released from the projection optical system reach an equilibrium state, and subsequently, even if exposure light is continuously irradiated, the change amount ΔF does not change from the maximum change amount F 1 . Subsequently, when the exposure stops, the change amount ΔF decreases with time, and eventually returns to the initial value zero. 
     Here, the maximum change amount F 1  is represented by formula (1) by the using change amount (exposure coefficient) K of the imaging performance per unit light amount (unit exposure energy) and actual exposure energy Q calculated based on various conditions including the exposure amount, the scanning speed, or the exposure area information.
 
 F 1= K×Q   (1)
 
     First, in a case where the exposure starts from time t′ 0 , the change amount ΔF(t) of the imaging performance after time t′ 0  is approximated as in formula (2) by using the maximum change amount F 1  and time constant T 1  that represents the speed of heating.
 
Δ F ( t )= F 1×(1−exp(−( t−t′   0 )/ T 1))  (2)
 
     Additionally, the change after stopping the exposure at time t′ 1  is approximated as in formula (3) by using ΔF(t′ 1 ) at time t′ 1  and the time constant T 2  that represents the speed of heat release.
 
Δ F ( t )=Δ F ( t′   1 )×exp(−( t−t′   1 )/ T 2)  (3)
 
     Moreover, in a case where the exposure resumes at time t′ 2 , the change after time t′ 2  is represented by formula (4).
 
Δ F ( t )=Δ F ( t′   1 )×exp(−( t−t′   1 )/ T 2)+ F 1×(1−exp(−( t−t′   2 )/ T 1))  (4)
 
     Here, the first term on the right side of the formula (4) is the same as the right side of the formula (3). Additionally, with regards to the second term on the right side of the formula (4), t′ 2  is given instead of t′ 0  in the right side of the formula (2). That is, it is possible to take into consideration the formula (4) as a linear sum of a tendency of releasing heat of the lens in the projection optical system after time t′ 1  and a tendency of heating of the lens after time t′ 2 . Additionally, in a case where time (t−t′ 1 ) is sufficiently large, the formula (4) is consistent with the formula (2) because the first term on the right side is negligible. This means that the influence of heat caused by the exposure is negligible if a sufficient time has elapsed after the completion of the exposure. 
     Accordingly, it is possible to predict the change of the imaging performance of the projection optical system caused by the exposure by modeling the change characteristic curves shown in  FIG. 2  by using a function shown in the formulae (1) to (4). However, the formulas (1) to (4) are examples, and modeling may be carried out by using another approximation. 
     Additionally, the change amount K of the imaging performance per unit light amount described above, and the time constants T 1  and T 2  change depending on the exposure conditions. This is because, in different exposure conditions, the distributions of the energy density of light that is incident to the projection optical system (see  FIGS. 3A  and B below) are different, as a result, distribution of the temperature change and time characteristic of the projection optical system change, so that the change amount and time characteristic of the imaging performance also change. Here, as the exposure conditions, for example, there are illumination conditions, the pattern of the reticle R (presence or absence of a phase shifter, periodicity, fineness, etc.), or the illumination area of the reticle. 
     In contrast, when the illumination conditions are different, not only the temperature distribution occurring in the lens in the projection optical system, but also the influence of the temperature distribution on the imaging performance is different. That is, when the illumination conditions are different, even if the temperature distributions of the lens are identical, the degrees of the influences on the imaging performance are different. This is because the influence of the temperature distribution of the lens on the imaging performance changes depending on the part of the lens through which the luminous flux passes. Hereinafter, as an example, a case in which the exposure apparatus is used by switching between two types of illumination conditions, that is, an illumination condition A that corresponds to a condition in which there is a first pupil plane illumination distribution in the projection optical system  110 , and an illumination condition B that corresponds to a condition in which there is a second pupil plane illumination distribution in the projection optical system  110 , will be assumed. 
     First, a description will be given of the difference of each illumination condition.  FIG. 3  is a schematic diagram illustrating the pupil plane illumination distribution (energy density distribution of light on the pupil plane) of the projection optical system  110  with respect to each illumination condition, wherein  FIG. 3A  illustrates the first pupil plane illumination distribution according to the illumination condition A, and  FIG. 3B  illustrates a second pupil plane illumination distribution according to the illumination condition B. In the drawings, an area  301  indicates a pupil area of the projection optical system  110 . An area  302  indicates an area where light mainly passes through in a case where the exposure processing under the illumination condition A (first exposure processing) is performed. Additionally, an area  303  indicates an area where light mainly passes through in a case where the exposure processing under the illumination condition B (second exposure processing) is performed. Note that the illumination condition A is what is referred to as conventional illumination, and the illumination condition B is what is referred to as annular illumination. 
       FIGS. 4A and 4B  are schematic diagrams illustrating the difference of the passing position of luminous flux in the projection optical system  110  according to each illumination condition, wherein  FIG. 4A  illustrates the luminous flux under the illumination condition A, and  FIG. 4B  illustrates the luminous flux under the illumination condition B. Note that, in the projection optical system  110 , optical elements other than a lens  401  near the pupil are not illustrated. First, under the illumination condition A, in the lens  401 , because a luminous flux  402  passes through the central portion of the lens, the central portion of the lens is heated during exposure. Additionally, the temperature distribution of this portion influences the imaging performance. In contrast, the temperature distribution of the lens periphery where the luminous flux does not pass thorough does not influence the imaging performance (or hardly influences it). Next, under the illumination condition B, in the lens  401 , because a luminous flux  403  passes through the lens periphery, the lens periphery is heated during exposure. Additionally, the temperature distribution of this portion influences the imaging performance. In contrast, the temperature distribution of the central portion of the lens where the luminous flux does not pass through does not influence the imaging performance (or hardly influences it). Accordingly, the heated portion of the lens is different between the illumination condition A and the illumination condition B. Additionally, the portions of the lens influencing the imaging performance are different. Note that, although the lens  401  near the pupil of the projection optical system  110  is emphasized here, even in the optical elements other than the lens  401 , areas where the luminous flux passes through are different depending under the illumination conditions in a similar way. 
     Next, a specific description will be given of a method of performing exposure while switching between two types of the illumination conditions.  FIG. 5  is a graph illustrating a change with the passage of time (change characteristic) of the imaging performance of the projection optical system due to the exposure while switching the illumination conditions. In  FIG. 5 , the horizontal axis indicates time t, the vertical axis indicates the change amount ΔF of the imaging performance in an image height of the projection optical system. Here, the exposure is performed under the illumination condition A in a section between time t 0  and t 1 , performed under the illumination condition B in a section between time t 2  and t 3 , and performed under the illumination condition A again in a section from time t 4 . Additionally, the exposure temporarily stops in order to switch the illumination conditions, in the section between time t 1  and t 2 , and in the section between time t 3  and t 4 . 
     Here, in the section of t 0 ≦t&lt;t 2 , the change amount ΔF can be calculated by using the formulas (2) and (3). However, the change amount ΔF discontinuously changes at the moment of the change from the illumination condition A to the illumination condition B at the time t 2 . This discontinuity is due to the offset that occurs in response to the amount influenced by the absorption of the illumination light before the change when the area of the lens where the luminous flux passes through is switched. Moreover, the lens temperature distribution after the time t 2  transitions to a state in which a tendency of releasing heat of the temperature distribution caused under the illumination condition A and a tendency of heating thereof caused under the illumination condition B are overlapped. Originally, the change of the imaging performance in a state in which the tendency of releasing heat and the tendency of heating are overlapped can be represented by a linear sum of heat release characteristics of the imaging performance change represented by the formula (3) and the heating characteristic of the imaging performance change represented by the formula (2). Therefore, the change in the imaging performance after the time t 2  can be accurately determined by respectively determining both characteristics. 
     Here, the change amount ΔF after the time t 2  must take into consideration the influence of the lens temperature distribution in the area where the luminous flux under the illumination condition B passes through. Accordingly, the heat release characteristic of the imaging performance change caused under the illumination condition A should also be the subject of evaluation with respect to the lens temperature distribution of the area where the luminous flux under the illumination condition B passes through. However, although the change amount ΔF in the section of t 0 ≦t&lt;t 2  shown in  FIG. 5  takes into consideration the influence of the lens temperature distribution in the area where the luminous flux under the illumination condition A passes through, it does not take into consideration the influence of the lens temperature distribution in the area where the luminous flux under the illumination condition B passes through. Hence, it is impossible to determine the heat release characteristic of the imaging performance change caused under the illumination condition A after switching the illumination at the time t 2 , consequently, it is impossible to accurately determine the change amount ΔF after the time t 2 . Note that the same applies when the illumination conditions are changed from the illumination condition B to the illumination condition A at the time t 4 . This means that the change amount ΔF of the imaging performance while switching the illumination conditions cannot be accurately determined only by the calculation models represented by the formulas (1) to (4). 
     Accordingly, in the present embodiment, the change in the imaging performance is taken into consideration by using two models: a first model that represents the influence on the imaging performance of the temperature distribution with respect to the luminous flux under the illumination condition A, and a second model that represents the influence on the imaging performance of the temperature distribution with respect to the luminous flux under the illumination condition B. The reason that the change amount ΔF of the imaging performance while switching the illumination conditions cannot be accurately determined only by the above calculation models is due to the fact that the lens area of the projection optical system where the luminous flux passes through are different depending under the illumination conditions. That is, the change amount ΔF in the section of t 0 ≦t&lt;t 2 , and the change amount ΔF in the section of t 2 ≦t&lt;t 4  represent the influence of the temperature distribution in the different lens areas, and they respectively change according to different models. Accordingly, when the calculation model is divided for each illumination condition, the continuity of the calculation model can be maintained even after changing the illumination conditions. Hereinafter, as an example, a variable unit that makes the imaging performance of the projection optical system  110  variable serves as the lens drive device  113 , and the projection lens control device  114  serving as a change amount deriving process derives the change amount ΔF of the projection optical system  110  as described below. However, the variable unit that makes the imaging performance of the projection optical system  110  variable is not limited to the lens drive device  113 , and the reticle stage  109  or the wafer stage  116  may be used and, for example, the main control device  103  may execute the change amount deriving process. 
       FIG. 6  is a graph that illustrates a calculation model (imaging performance model) that represents the change with the passage of time of the imaging performance of the projection optical system  110  due to the exposure in the present embodiment. Note that performing exposure while switching between two types of the illumination conditions is the same as precondition in  FIG. 5 . In the drawing, ΔF A  shown by solid lines is a first change amount that represents the influence on the imaging performance of the temperature distribution with respect to the luminous flux under the illumination condition A, that is, the first model in the present embodiment. In contrast, ΔF B  also shown by solid lines is a second change amount that represents the influence on the imaging performance of the temperature distribution with respect to the luminous flux under the illumination condition B, that is, a second model in the present embodiment. Note that, at the time t 0 , the change amounts ΔF A  and ΔF B  are both zero. 
     First, each of the change amounts ΔF A  and ΔF B  in the section in which the exposure processing is performed under the illumination condition A from the time t 0  to t 1  (t 0 ≦t≦t 1 ) (first exposure process) are represented by formulae (5) and (6), based on the formula (2).
 
Δ F   A ( t )=Δ F   AA ( t )= F 1 AA ×(1−exp(−( t−t   0 )/ T 1 AA ))  (5)
 
Δ F   B ( t )=Δ F   BA ( t )= F 1 BA ×(1−exp(−( t−t   0 )/ T 1 BA ))  (6)
 
     Here, ΔF XY  represents the influence of the temperature distribution caused under the illumination condition Y on the imaging performance with respect to the luminous flux of the illumination condition X. Here, the change amount ΔF A  is calculated using two parameters, F 1   AA  and T 1   AA , as represented by the formula (5). In contrast, the change amount ΔF B  is calculated using two parameters, F 1   BA  and T 1   BA , as represented by the formula (6). As such, the change amount ΔF A  and the change amount ΔF B  are calculated by different parameters. This is because this reflects that the lens portions that influence the imaging performance are different for each illumination condition. 
     Next, each of the change amounts ΔF A  and ΔF B  in the exposure stop section between the time t 1  and t 2  (t 1 &lt;t&lt;t 2 ) is represented by formulas (7) and (8) based on the formula (3). 
                           Δ   ⁢           ⁢       F   A     ⁡     (   t   )         =       ⁢     Δ   ⁢           ⁢       F   AA     ⁡     (   t   )                     =       ⁢     Δ   ⁢           ⁢       F   AA     ⁡     (     t   1     )       ×     exp   ⁡     (         -     (     t   -     t   1       )       /   T     ⁢           ⁢     2   AA       )                       (   7   )                       Δ   ⁢           ⁢       F   B     ⁡     (   t   )         =       ⁢     Δ   ⁢           ⁢       F   BA     ⁡     (   t   )                     =       ⁢     Δ   ⁢           ⁢       F   BA     ⁡     (     t   1     )       ×     exp   ⁡     (         -     (     t   -     t   1       )       /   T     ⁢           ⁢     2   BA       )                       (   8   )               
As shown in the formulae (7) and (8), the change amount ΔF A  and the change amount ΔF B  are calculated by different parameters (T 2   AA  and T 2   BA ).
 
     Next, the change amounts ΔF A  and ΔF B  in the section where exposure processing is performed under the illumination condition B between the time t 2  and t 3  (t 2 &lt;t≦t 3 ) (second exposure process) are represented by formula (9) and (10) respectively.
 
Δ F   A ( t )=Δ F   AA ( t )+Δ F   AB ( t )  (9)
 
Δ F   B ( t )=Δ F   BA ( t )+Δ F   BB ( t )  (10)
 
However, ΔF AA  and ΔF AB  are represented by formulas (11) and (12) respectively.
 
Δ F   AA ( t )=Δ F   AA ( t )×exp(−( t−t   1 )/ T 2 AA )  (11)
 
Δ F   AB ( t )= F 1 BB ×(1−exp(−( t−t   2 )/ T 1 AB ))  (12)
 
In contrast, ΔF BA  and ΔF BB  are respectively represented by formulae (13) and (14).
 
Δ F   BA ( t )=Δ F   BA ( t   1 )×exp(−( t−t   1 )/ T 2 BA )  (13)
 
Δ F   BB ( t )= F 1 BB ×(1−exp(−( t−t   2 )/ T 1 BB )  (14)
 
     Here, in a manner similar to ΔF AA  in the formula (7), ΔF AA  in the formula (11) represents the tendency of decreasing the temperature distribution under the illumination condition A after the time t 1 . In contrast, ΔF AB  in the formula (12) represents the tendency of increasing the temperature distribution under the illumination condition B after the time t 2 . Subsequently, the change amount ΔF A  is represented by a linear sum thereof. The reason for the establishment of this linear sum is that ΔF AA  and ΔF AB  both represent the influence on the luminous flux under the illumination condition A. Additionally, ΔF BA  in formula (13) represents the tendency of decreasing temperature distribution under the illumination condition A after the time t 1 , in a manner similar to ΔF BA  in the formula (8). In contrast, ΔF BB  in the formula (14) represents the tendency of increasing the temperature distribution under the illumination condition B after the time t 2 . Subsequently, the change amount ΔF B  is represented by these linear sums. The reason for the establishment of this linear sum is that ΔF BA  and ΔF BB  both represent the influence on the luminous flux under the illumination condition B. Note that ΔF BA  and ΔF BB  in the section of t 2 &lt;t≦t 3  are shown by dashed lines in  FIG. 6 . Thus, if the imaging performance with respect to the luminous flux under the illumination condition A and the imaging performance with respect to the luminous flux under the illumination condition B are handled as different models, the change of the imaging performance can be accurately determined even after changing the illumination conditions. 
     Next, each of the change amounts ΔF A  and ΔF B  in the exposure stop section from the time t 3  to t 4  (t 3 &lt;t≦t 4 ) is represented by formulas (15) and (16).
 
Δ F   A ( t )=Δ F   AA ( t )+Δ F   AB ( t )  (15)
 
Δ F   B ( t )=Δ F   BA ( t )+Δ F   BB ( t )  (16)
 
However, ΔF AA  and ΔF AB  are represented by formulae (17) and (18) respectively.
 
Δ F   AA ( t )=Δ F   AA ( t   1 )×exp(−( t−t   1 )/ T 2 AA )  (17)
 
Δ F   AB ( t )=Δ F   AB ( t   3 )×exp(−( t−t   3 )/ T 2 AB )  (18)
 
In contrast, ΔF BA  and ΔF BB  are represented by formulae (19) and by (20) respectively.
 
Δ F   BA ( t )=Δ F   BA ( t   1 )×exp(−( t−t   1 )/ T 2 BA )  (19)
 
Δ F   BB ( t )=Δ F   BB ( t   3 )×exp(−( t−t   3 )/ T 2 BB )  (20)
 
     Here, the ΔF AA  in the formula (17) represents the tendency of decreasing the temperature distribution under the illumination condition A after the time t 1 , in a manner similar to ΔF AA  in the formulas (7) and (11). In contrast, the ΔF AB  in the formula (18) represents the tendency of decreasing the temperature distribution under the illumination condition B after the time t 3 . The change amount ΔF A  is represented by the linear sum of these two models. Additionally, the ΔF BA  in the formula (19) represents the tendency of decreasing the temperature distribution under the illumination condition A after the time t 1 , in a manner similar to ΔF BA  in the formulas (8) and (13). In contrast, the ΔF BB  in the formula (20) indicates the tendency of decreasing the temperature distribution under the illumination condition B after the time t 3 . The change amount ΔF B  is represented by the linear sum of these two models. 
     Subsequently, each of the change amounts ΔF A  and ΔF B  in the section where the exposure processing is performed under the illumination condition A after the time t 4  (t 4 &lt;t) is represented by formulas (21) and (22)
 
Δ F   A ( t )=Δ F   AA ( t )+Δ F   AB ( t )+Δ F′   AA ( t )  (21)
 
Δ F   B ( t )=Δ F   BA ( t )+Δ F   BB ( t )+Δ F′   BA ( t )  (22)
 
However, ΔF AA , ΔF AB , and ΔF′ AA  are represented by formulae (23), (24), and (25) respectively.
 
Δ F   AA ( t )=Δ F   AA ( t   1 )×exp(−( t−t   1 )/ T 2 AA )  (23)
 
Δ F   AB ( t )=Δ F   AB ( t   3 )×exp(−( t−t   3 )/ T 2 AB )  (24)
 
Δ F′   AA ( t )= F 1 AA ×(1−exp(−( t−t   4 )/ T 1 AA ))  (25)
 
In contrast, ΔF BA , ΔF BB , and ΔF′ BA  are represented by formulae (26), (27), and (28) respectively.
 
Δ F   BA ( t )=Δ F   BA ( t   1 )×exp(−( t−t   1 )/ T 2 BA )  (26)
 
Δ F   BB ( t )=Δ F   BB ( t   3 )×exp(−( t−t   3 )/ T 2 BB )  (27)
 
Δ F′   BA ( t )= F 1 BA ×(1−exp(−( t−t   4 )/ T 1 BA ))  (28)
 
     Here, ΔF AA  in the formula (23) is identical to ΔF AA  in the formula (17). Similarly, ΔF AB  in the formula (24) is identical to ΔF AB  in the formula (18). In contrast, ΔF′ AA  represents the tendency of increasing the temperature distribution under the illumination condition A after the time t 4 . The change amount ΔF A  is represented by the linear sum of these three models. Note that ΔF′ AA  and ΔF AB  in t 4 ≦t are shown by dashed lines in  FIG. 6 . ΔF BA  in the formula (26) is identical to ΔF BA  in the formula (19). Similarly, ΔF BB  in the formula (27) is identical to ΔF BB  in the formula (20). In contrast, ΔF′ BA  represents the tendency of increasing the temperature distribution under the illumination condition A after the time t 4 . The change amount ΔFE is represented by the linear sum of these three models. 
     Note that although the change amount ΔF A  represented by the formula (21) and the change amount ΔF B  represented by the formula (22) are respectively the sum of the three models, when the illumination condition is further changed and the exposure is continued, the number of models that take the sum increases, and the calculation formula for ΔF A  and ΔF B  becomes complicated. However, when the elapsed time from the time t 1  is sufficiently large with respect to the time constant T 2   AA , that is, (t−t 1 )&gt;&gt;T 2   AA , ΔF AA  can be regarded as zero. Accordingly, the section of t 4 &lt;t and (t−t 1 )&gt;&gt;T 2   AA , ΔF A  can be represented by the sum of the two models represented by formula (29) based on the formula (21).
 
Δ F   A ( t )=Δ F   AB ( t )+Δ F′   AA ( t )  (29)
 
Similarly, in the section of t 4 &lt;t and (t−t 1 )&gt;&gt;T 2   BA , ΔF B  can be represented by the sum of the two models represented by formula (30), based on the formula (22).
 
Δ F   B ( t )=Δ F   BB ( t )+Δ F′   BA ( t )  (30)
 
     Thus, even when exposure is performed while changing the illumination conditions, it is not necessary to determine a model that represents the influence regarding all of the exposures performed in the past. If only the exposure performed within a time T L  in the past influences the imaging performance, in the calculation of the change of the imaging performance at time t, only the influence of the exposure after the time (t−T L ) needs to be taken into consideration and the complexity of the formula of the change amounts ΔF A  and ΔF B  can be suppressed. Here, the time T L  may be optionally determined based on the accuracy requested for the calculation. For example, in a case where the error in calculations needs to be suppressed within 1% of the maximum change amount, the value of the time T L  may be set to 4.5 to 5 times or more than the time constant T 2 . 
     Next, a description will be given of a correction method of the imaging performance of the projection optical system  110  in the present embodiment.  FIG. 7  is a graph that illustrates a correction amount C of the imaging performance with respect to the imaging performance model shown in  FIG. 6 . In the section of t 0 ≦t≦t 1  and t 4 ≦t, because the exposure processing is performed under the illumination condition A, the correction amount C is derived so as to offset the change amount ΔF A  of the imaging performance with respect to the illumination condition A. In contrast, in the section of t 2 ≦t≦t 4 , because the exposure processing is performed under the illumination condition B, the correction amount C is derived so as to offset the change amount ΔF B  of the imaging performance with respect to the illumination condition B. That is, the relation shown in formulae (31) to (33) is established.
 
 t   0   ≦t≦t   1   :C ( t )=−Δ F   A ( t )  (31)
 
 t   2   ≦t≦t   3   :C ( t )=−Δ F   B ( t )  (32)
 
 t   4   ≦t:C ( t )=−Δ F   A ( t )  (33)
 
     The projection lens control device  114  derives the correction amount C as described above as the correction amount deriving process. Subsequently, the projection lens control device  114  drives the lens drive device  113  so as to change the imaging performance only by the correction amount C, and can offset the change of the imaging performance of the projection optical system  110 . Note that if the reticle stage  109  or the wafer stage  116  is employed as a variable unit that makes the imaging performance of the projection optical system  110  variable instead of the lens drive device  113 , for example, the main control device  103  executes the correction amount deriving process. 
     Note that in the sections t 1 &lt;t&lt;t 2  and t 3 &lt;t&lt;t 4 , because the exposure processing is not performed, it is not necessary to correct the imaging performance. Additionally, in each section represented by the formulae (31) to (33), the change amount ΔF B  is used for the correction only in the section t 2 ≦t≦t 3 , and in other sections, it makes no contribution to the correction amount C, and therefore is not required. Accordingly, the projection lens control device  114  may determine ΔF B  at the time of t 2  for the first time based on the formula (8), without determining the change amount ΔF B  in the section, for example, t 0 ≦t&lt;t 2 . However, in the calculations for that case, the history information of the exposure performed in the past is required, and the projection lens control device  114  records the history information in advance. Moreover, the projection lens control device  114  may constantly perform the calculation of the change amount ΔF B , regardless of whether or not it contributes to the correction, and this is also applied to the change amount ΔF A . 
     Next, a description will be given of a method for acquiring parameters that specify the change of the imaging performance of the projection optical system  110  in the present embodiment, that is, parameters used for deriving the imaging performance model. Here, in order to specify the change of the imaging performance, four types of maximum change amount, F 1   AA , F 1   AB , F 1   BA , and F 1   BB  are required, and thus, four types of K AA , K AB , K BA , and K BB  are also required for the change amount K of the imaging performance per unit light amount. Additionally, four types are similarly required for the time constants T 1  and T 2 . To summarize the set of parameters, a first parameter includes K AA , T 1   AA , and T 2   AA . Similarly, a second parameter includes K AB , T 1   AB , and T 2   AB , a third parameter includes K BA , T 1   BA , and T 2   BA , and a fourth parameter includes K BB , T 1   BB , and T 2   BB . 
       FIG. 8  is a flowchart that illustrates a flow of the acquisition process of parameters. Additionally,  FIG. 9  is a graph that illustrates the change of the imaging performance of the projection optical system  110  during the acquisition process, and the timing of the imaging performance measurement included in the acquisition process. In  FIG. 9 , white circles indicate the timing for performing the imaging performance measurement under the illumination condition A, whereas, x-marks indicate the timing for performing the imaging performance measurement under illumination condition B. Note that, because of a state having no change in the imaging performance due to the exposure at the beginning of the acquisition process, ΔF A =0, and ΔF B =0. 
     In the beginning, the main control device  103  performs the measurement process related to the heating characteristic. First, the main control device  103  makes the illumination system control device  108  set the illumination condition to the illumination condition A (step S 101 ). Next, the main control device  103  directs measuring the imaging performance under the illumination condition A (step S 102 ). Here, as the measurement methods, for example, the pattern for the measurement is exposed onto the wafer W, and the line width and the like of the pattern are measured by separately using a measurement device, or they are directly measured by using a sensor (not illustrated) disposed on the wafer stage  116 . At this time, it is desirable that the measurement time is sufficiently short with respect to the speed of change of the imaging performance, and an exposure energy irradiated to the projection optical system  110  is sufficiently small with respect to the exposure energy during dummy exposure in step S 106 , which is the subsequent step. Next, the main control device  103  makes the illumination system control device  108  set (switch) the illumination condition under the illumination condition B (step S 103 ). Next, the main control device  103  directs measuring the imaging performance under the illumination condition B (step S 104 ). Next, the main control device  103  determines whether or not the measurement process related to the heating characteristic will be ended, specifically, determines whether or not the measurement by the predetermined number of times has been ended (step S 105 ). At this time, when the main control device  103  determines that the measurement has not ended by the predetermined number of times (NO), it again sets (switches) the illumination condition to the illumination condition A (step S 106 ), and continuously directs performing the dummy exposure for a predetermined time (step S 107 ). Here, the dummy exposure refers to exposure that irradiates the exposure light to the projection optical system  110  separately from the normal exposure, in order to provide a heat load to the projection optical system  110 . That is, each measurement of the imaging performance under the illumination condition A or the illumination condition B related to the heating characteristic here is performed under the condition in which thermal load is provided under the illumination condition A. Subsequently, after the end of step S 106 , the main control device  103  returns to step S 102 , and repeats the imaging performance measurement, and the like. In contrast, in step S 105 , when the main control device  103  determines that the measurement has ended by the predetermined number of times (YES), the process is forwarded to the measurement process related to the subsequent heat release characteristic. 
     Next, the main control device  103  executes the measurement process related to the heat release characteristic. First, the main control device  103  waits for a predetermined time in a state in which light is not irradiated to the projection optical system  110  (step S 108 ). Next, the main control device  103  directs repeating the setting of the illumination condition (switching) and the measurement of the imaging performance (steps S 109  to S 112 ) in a state similar to steps S 101  to S 104 . Next, the main control device  103  determines whether or not the measurement process related to the heat release characteristic will end, and specifically, determines whether or not the measurement has ended by the predetermined number of times (step S 113 ). At this time, when the main control device  103  determines that the measurement has not ended by the predetermined number of times (NO), the process returns to step S 108 , and the main control device  103  directs repeating the measurement of the imaging performance and the like. In contrast, in step S 113 , when the main control device  103  determines that the measurement has ended by the predetermined number of times (YES), the process proceeds to step S 114 . 
     Next, the main control device  103  executes the calculation process of parameter (step S 114 ). At this time, the main control device  103  can calculate K AA  and T 1   AA  from the measurement results of the imaging performance under the illumination condition A in step S 102 , and can calculate K BA , T 1   BA  from the measurement results of the imaging performance under the illumination condition B in step S 104 . Additionally, the main control device  103  can calculate T 2   AA  from the measurement results of the imaging performance under the illumination condition A in step S 110 , and can calculate T 2   BA  from the measurement results of the imaging performance under the illumination condition B in step S 112 . 
     In contrast, if the main control device  103  executes a similar process after interchanging the illumination condition A and the illumination condition B in step S 106  among processes shown in  FIG. 8 , the following parameters can also be calculated. Specifically, the main control device  103  can calculate K AB  and T 1   AB  from the measurement results of the imaging performance under the illumination condition A and can calculate K BB  and T 1   BB  from the measurement results of the imaging performance under the illumination condition B in the heating characteristic measurement process. Additionally, the main control device  103  can calculate T 2   AB  from the measurement results of the imaging performance under the illumination condition A and can calculate T 2   BB  from the measurement results of the imaging performance under the illumination condition B in the heat release characteristic measurement process. Subsequently, when the parameter calculation process of step S 114  ends, the parameter acquisition process ends. 
     Note that a flow of the measurement process shown in  FIG. 8  is an example of the determination of each measurement end in step S 105  and step S 113  may be determined based on whether or not the change of the measured imaging performance is saturated. Additionally, the heat release characteristic can be predicted from the measurement results related to the heating characteristic, instead of implementing the measurement related to the heat release characteristic of the subsequent step S 108 . For example, T 2   AA  may be identical to the time constant T 1   m  of the heating characteristic, instead of determining T 2   AA  from the measurement results related to heat release characteristic. 
     Additionally, in the above description, a method for determining each parameter by the measurement of the imaging performance is exemplified. However, the present invention is not limited thereby, and for example, it may be possible that each parameter is determined by simulation in advance, and the change amount of the imaging performance is derived by using the acquired parameters. 
     Thus, in the exposure method according to the present embodiment, for example, in a case where exposure is continued while changing the illumination conditions, with respect to the change of the imaging performance of the projection optical system  110 , a correction amount for correcting the imaging performance is determined by taking into consideration in advance not only the illumination condition at that time, but also the influence on other illumination conditions. Accordingly, in particular, it is possible to determine more accurately the correction value in the transient state where the influence under the illumination condition before the change and the influence under the illumination condition after the change overlap. Additionally, in the exposure method according to the present embodiment, it is not necessary to stop the exposure each time the illumination condition changes in order to eliminate the discontinuous state or transient state when illumination conditions are changed, so that exposure can be performed under a high-accuracy imaging performance without losing productivity. 
     As described above, according to the present embodiment, it is possible to provide the exposure method and the exposure apparatus that are advantageous in improving the exposure accuracy. 
     Note that, in the above description, although the case of switching between two types of illumination conditions is exemplified, it may be possible to switch among three or more types of illumination conditions. In that case, the exposure method similar to the above examples is applicable by increasing the number of models and the number of parameters that represent the influence on the imaging performance, depending on the number (type) of the illumination conditions. Here, the more the illumination condition increases, the more the number of models and the number of parameters increases, and then a configuration of the formula becomes complicated. Accordingly, in order to avoid complicating the configuration of the formula, the determination of the model and parameter is only targeted to a few typical illumination conditions. Subsequently, with respect to the other illumination conditions, it may be possible that a closer one is selected from among the typical illumination conditions, and the number of models and the number of parameters same as that are used. Alternatively, a plurality of closer ones from among the typical illumination conditions are selected, and the number of model and the number of parameter may be calculated by interpolation calculations. 
     (Article Manufacturing Method) 
     An article manufacturing method according to an embodiment of the present invention is preferred in manufacturing an article such as a micro device such as a semiconductor device or the like, an element or the like having a microstructure, or the like. The article manufacturing method may include a step of forming a latent image pattern on an object (e.g., exposure process) using the aforementioned exposure apparatus; and a step of developing the object on which the latent image pattern has been formed in the previous step. Furthermore, the article manufacturing method may include other known steps (oxidizing, film forming, vapor depositing, doping, flattening, etching, resist peeling, dicing, bonding, packaging, and the like). The device manufacturing method of this embodiment has an advantage, as compared with a conventional device manufacturing method, in at least one of performance, quality, productivity and production cost of a device. 
     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. 2014-224877 filed Nov. 5, 2014, which is hereby incorporated by reference herein in its entirety.