Determination method, exposure method, information processor, program, exposure device, and article manufacturing method

Abstract

To provide a technique advantageous in correcting a variation of imaging characteristics of a projection optical system with high accuracy.SOLUTION: A determination method determines a coefficient expressing a variation amount of imaging characteristics per unit light energy to be imparted to a projection optical system, to be used in a model formula expressing a variation in imaging characteristics of the projection optical system. The determination method includes steps of: conducting a measurement of imaging characteristics; and determining a coefficient according to a measured value obtained by the measurement and an estimated value of imaging characteristics obtained using the model formula. The model formula includes: an exposure model formula expressing a variation of the imaging characteristics while conducting an exposure of a substrate; and a measurement model formula expressing a variation of the imaging characteristics while conducting the measurement. An estimated value of the imaging characteristics while conducting the exposure of the substrate is obtained using the exposure model formula, and an estimated value of the imaging characteristics while conducting the measurement is obtained using the measurement model formula.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a determination method, an exposure method, an information processing device, a program, an exposure apparatus, and an article manufacturing method. [Background technology]

[0002] An exposure apparatus is an apparatus that transfers a pattern on a mask (reticle) onto a photosensitive substrate (plate) via a projection optical system in the manufacturing process of semiconductor devices, liquid crystal display devices, etc. For example, an exposure apparatus used in the manufacture of liquid crystal display devices has a projection optical system equipped with optical elements such as multiple lenses and mirrors that reflect exposure light and irradiate it onto the substrate.

[0003] When the exposure process continues for a long time, the optical elements that make up the projection optical system absorb part of the exposure light, and the energy of the absorbed light is converted into heat, gradually increasing the temperature of the optical elements, their holding members, and the gas surrounding them. When the temperature of the gas in the optical path rises, the refractive index of that space changes, causing changes in the optical characteristics. For this reason, fluctuations in the imaging characteristics due to the state of exposure energy irradiation of the projection optical system are calculated using a model formula that includes correction coefficients with variables such as exposure dose, exposure time, and non-exposure time, and the fluctuations in the imaging characteristics are corrected based on the results of this calculation.

[0004] During the time period when no light is incident on the projection optical system between the end of an exposure and the start of the next exposure, the temperature of the projection optical system decreases, causing fluctuations in imaging characteristics. Patent Document 1 discloses a method for determining the amount of fluctuation in imaging characteristics based on the light irradiation time of the projection optical system, taking into account increases and decreases in the temperature of the projection optical system. Patent Document 2 discloses a method for suppressing fluctuations in imaging characteristics and maintaining a desired imaging state when exposure is performed while alternating between multiple exposure conditions. Patent Document 2 also discloses a method for correcting fluctuations in imaging characteristics due to absorption of illumination light energy in the projection optical system when multiple exposures are performed on a single substrate while changing mask patterns. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Special Publication No. 04-047807 [Patent Document 2] Japanese Patent Application Publication No. 11-150053 Summary of the Invention [Problem to be solved by the invention]

[0006] However, in recent years, exposure has been performed with high energy (high dose, high transmittance masks), which means that the fluctuations in imaging characteristics per unit time are large. Therefore, in order to capture these fluctuations, the intervals between measurements of optical characteristics are shortened and correction coefficients are calculated. However, it has been discovered that predicted values ​​calculated using correction coefficients obtained in this way deviate from the actual measured values. The reason for this is that the amount of energy during measurement is much smaller than during exposure, and the higher the energy during exposure, the greater the fluctuations in imaging characteristics during measurement, in the opposite direction to those during exposure. This fluctuation cannot be ignored when calculating correction coefficients.

[0007] The present invention provides an advantageous technique for correcting fluctuations in the imaging characteristics of a projection optical system with high precision. [Means for solving the problem]

[0008] According to one aspect of the present invention, there is provided a method for determining a coefficient that represents an amount of variation in imaging characteristics per unit light energy applied to a projection optical system in an exposure apparatus that performs an exposure operation to expose a substrate via a projection optical system, the coefficient being used in a model equation that represents variation in imaging characteristics of the projection optical system, the method comprising the steps of: measuring the imaging characteristics based on measurement light that has passed through the projection optical system at a predetermined timing during an exposure operation period in which the exposure operation is performed sequentially on a plurality of substrates; and determining the coefficient based on a measurement value obtained by the measurement and a predicted value of the imaging characteristics obtained using the model equation, wherein the model equation includes an exposure model equation that represents variation in the imaging characteristics while the substrate is being exposed, and a measurement model equation that represents variation in the imaging characteristics while the measurement is being performed, and the predicted value of the imaging characteristics while the substrate is being exposed is obtained using the exposure model equation, and the predicted value of the imaging characteristics while the measurement is being performed is obtained using the measurement model equation. [Effects of the Invention]

[0009] According to the present invention, it is possible to provide an advantageous technique for correcting fluctuations in the imaging characteristics of a projection optical system with high precision. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram showing the configuration of an exposure apparatus. [Figure 2] 10A and 10B are diagrams showing an example of changes over time in the imaging characteristics of a projection optical system. [Figure 3] 10A and 10B are diagrams showing examples of focus measurement values ​​and corrections thereof; [Figure 4] 10A and 10B are diagrams showing examples of measurement results of the amount of fluctuation in imaging characteristics due to differences in measurement intervals. [Figure 5] 10 is a flowchart showing a method for determining a correction coefficient. [Figure 6] 4 is a flowchart showing an exposure process in the first embodiment. [Figure 7] 10 is a flowchart showing an exposure process in the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments do not limit the scope of the invention claimed. Although multiple features are described in the embodiments, not all of these multiple features are necessarily essential to the invention, and multiple features may be combined arbitrarily. Furthermore, in the accompanying drawings, the same reference numerals are used to designate the same or similar components, and redundant explanations will be omitted.

[0012] First Embodiment FIG. 1 is a diagram showing an example of the configuration of an exposure apparatus 100 according to an embodiment. In this specification and the drawings, directions are indicated in an XYZ coordinate system in which the horizontal plane is the XY plane. A plate stage 30 (described below) holds a plate 36 on the holding surface of the plate stage 30 (plate chuck 35) so that the surface of the plate 36 is parallel to the horizontal plane (XY plane). Therefore, in the following, the directions that are perpendicular to each other in a plane along the holding surface of the plate stage 30 are referred to as the X-axis and Y-axis, and the direction perpendicular to the X-axis and Y-axis is referred to as the Z-axis. Furthermore, in the following, the directions parallel to the X-axis, Y-axis, and Z-axis in the XYZ coordinate system are referred to as the X-direction, Y-direction, and Z-direction, respectively, and the directions of rotation around the X-axis, Y-axis, and Z-axis are referred to as the θX-direction, θY-direction, and θZ-direction, respectively.

[0013] In the following, exposure apparatus 100 is assumed to be configured as a scanning exposure apparatus for manufacturing liquid crystal panels. In Fig. 1, optical axis 11 of projection optical system 10 extends in the Z direction, and the scanning direction of a mask (reticle) and a plate (substrate) during scanning exposure is the Y direction.

[0014] The exposure apparatus 100 is equipped with a mask stage 20 above the projection optical system 10 in the Z direction and a plate stage 30 below it. The mask stage 20 and the plate stage 30 are each capable of moving independently in a fixed direction. The mask stage 20 holds and scans a mask 21, while the plate stage 30 holds and scans a plate 36. The scanning positions of the mask stage 20 and the plate stage 30 can be measured by a laser interferometer 50.

[0015] The mask stage 20 carries a mask 21 having a pattern to be projected. The exposure apparatus 100 also includes, above the mask stage 20, an observation optical system 40 that can observe the patterns formed on the mask 21 and the plate 36 via the projection optical system 10, and an illumination optical system 41.

[0016] Plate stage 30 has a Y stage 32 and an X stage 33 arranged on main body base 31, and further has a θZ stage 34 arranged on Y stage 32 and X stage 33. Furthermore, plate chuck 35 is arranged on θZ stage 34, and plate 36, which is the substrate to be processed, is held by plate chuck 35. Y stage 32 is a stage that moves in the Y direction, X stage 33 is a stage that moves in the X direction, and θZ stage 34 is a stage that moves in the Z direction and the θZ direction. θZ stage 34 may be configured as a separate Z stage that moves in the Z direction and a rotation stage that moves in the θZ direction.

[0017] Z sensors 37 and 38 (plate height measurement sensors) measure the position in the Z direction from the surface of plate 36 or plate chuck 35. The measurement value is used to control θZ stage 34.

[0018] The main control unit 60 may include an optical property measurement unit 61, an optical property correction unit 62, an optical property calculation unit 63, and a data storage unit 64. The main control unit 60 performs focus measurement, prediction and correction of focus fluctuation, and control of the mask stage 20 and the plate stage 30. The main control unit 60 may be configured as a computer (information processing device) including a CPU, memory, etc.

[0019] An example of focus measurement in exposure apparatus 100 will now be described.

[0020] Focus measurement marks (not shown) are formed on the surfaces of the mask 21 and the plate chuck 35, and each mark has position information in the X and Y directions. In one example, these focus measurement marks are photoelectric sensors, and the Z position at which the amount of light entering the sensor is at its maximum is the best focus position.

[0021] Because there is a positional difference in the Z direction between the plate 36 and the measurement mark on the plate chuck 35, the main control unit 60 (optical property measurement unit 61) measures this positional difference in advance using the Z sensors 37 and 38. The measured positional difference is designated as "measurement value A." Next, the optical property measurement unit 61 drives the mask stage 20 and the plate chuck 35 to the focus measurement position for focus measurement. After driving is complete, the optical property measurement unit 61 performs height measurement using the Z sensors 37 and 38. Thereafter, the optical property measurement unit 61 irradiates measurement light from the illumination optical system 41 toward the focus measurement mark. The optical property measurement unit 61 receives the measurement light that has passed through the projection optical system 10 at the focus measurement mark and measures the light intensity based on the received measurement light. Then, the focus is measured as an imaging characteristic of the projection optical system 10 as follows.

[0022] After the measurement is completed, the optical property measurement unit 61 repeats height measurement and light intensity measurement while slightly moving the θZ stage 34 until the peak (maximum value) of the light intensity is obtained, and then determines the height position when the light intensity reaches its maximum value. The height position determined here is referred to as "measurement value B." Since measurement value B indicates the best focus value on the plate chuck 35, the difference between measurement value B and measurement value A can be determined as the best focus value on the plate 36.

[0023] Next, a model formula for the fluctuation of the imaging characteristics of the projection optical system 10 due to exposure energy irradiation according to this embodiment and a correction coefficient for compensating for the fluctuation of the imaging characteristics for each exposure condition, which is used to quantify the model formula, will be described.

[0024] Figure 2 shows an example of the change over time in the imaging characteristics of the projection optical system 10. In Figure 2, the horizontal axis represents time t, and the vertical axis represents the amount of fluctuation F in the imaging characteristics of the projection optical system 10. The amount of fluctuation in the imaging characteristics of the projection optical system 10 at the initial stage (i.e., before exposure) is denoted as F0.

[0025] In Figure 2, "exposure time" refers to the exposure operation period during which the exposure operation is performed, and "non-exposure time" refers to the non-exposure operation period following the exposure operation period during which the exposure operation is not performed. The "exposure operation period" refers to the period from the start of the exposure operation for the first plate among multiple plates to the end of the exposure operation for the last plate. The "exposure operation period" also includes the period between shots during which no exposure is actually performed and the plate exchange period.

[0026] 2, when exposure starts at time t0, the imaging characteristics fluctuate over time and converge to a constant fluctuation amount F1 at time t1 (saturation characteristics). After time t1, even if exposure light is incident on the projection optical system 10, the thermal energy absorbed by the projection optical system 10 and the thermal energy released from the projection optical system 10 reach an equilibrium state, so the fluctuation amount of the imaging characteristics does not change from F1. Hereinafter, F1 will also be referred to as the maximum fluctuation amount. Then, when exposure is stopped at time t2, the fluctuation amount of the imaging characteristics returns to its initial state over time and becomes the initial fluctuation amount F0 of the imaging characteristics at time t3.

[0027] 2 are equivalent to the time constants in the heat transfer characteristics of the projection optical system 10. These time constants are values ​​specific to the projection optical system 10.

[0028] Next, we will explain how to calculate the maximum variation F1 of the imaging characteristics shown in Fig. 2. If the variation of the imaging characteristics per unit exposure energy is K and the parameters of the exposure conditions (exposure time, exposure amount, scanning speed, exposure area information, etc.) that determine the actual exposure energy are Q, the maximum variation F1 of the imaging characteristics can be expressed by the following equation:

[0029] F1 = K × Q (1)

[0030] Here, if the amount of fluctuation in the imaging characteristics at a certain time k is F(k), the amount of fluctuation F(k+1) in the imaging characteristics after exposure for a time Δt from time k is approximated by the following equation using the maximum amount of fluctuation F1 and time constants TS1 and TS2.

[0031] F(k+1)=F(k)+F1×(1-e (-Δt / TS1) ) ···(2)

[0032] When no exposure is performed for a time Δt from time k, the amount of fluctuation F(k+1) in the imaging characteristics is approximated by the following equation.

[0033] F(k+1)=F(k)×e (-Δt / TS2) ···(3)

[0034] By modeling the curve showing the fluctuation characteristics of the imaging characteristics of the projection optical system 10 shown in Figure 2 using the functions of equations (1), (2), and (3), it is possible to predict the fluctuations in the imaging characteristics of the projection optical system 10 that fluctuate due to exposure heat. However, the forms of equations (1), (2), and (3) are merely examples, and other equations may be used for modeling. Furthermore, multiple models may be used.

[0035] The parameter Q in equation (1) can include, for example, any of the exposure time, exposure amount, and scanning speed. K, which represents the amount of fluctuation in imaging characteristics per unit amount of light (per unit light energy), is called the correction coefficient. By combining the parameter Q and the correction coefficient K, the maximum fluctuation amount F1 in equation (1) can be calculated.

[0036] The correction coefficient K must be calculated for each exposure condition because changing the exposure condition changes the energy density distribution of the light incident on the projection optical system 10, which in turn changes the amount of fluctuation in the imaging characteristics of the projection optical system 10.

[0037] The following describes the focus as an example of an imaging characteristic of the projection optical system 10. The optical characteristic calculation unit 63 calculates a predicted value of the amount of focus variation based on the parameters stored in the data storage unit 64. The calculation by the optical characteristic calculation unit 63 is repeated sequentially for each plate. The optical characteristic correction unit 62 corrects the amount of focus variation by driving the plate stage 30 (θZ stage 34) in a direction parallel to the optical axis 11 (Z direction) so that it matches the amount of focus variation obtained from this calculation.

[0038] The optical property measurement unit 61 measures the focus, thereby obtaining the measurement value shown in Fig. 3. After that, the optical property calculation unit 63 calculates a predicted value of the amount of focus fluctuation based on the parameters stored in the data storage unit 64, and the optical property correction unit 62 corrects the plate stage 30 based on the calculated predicted value.

[0039] At a predetermined timing during the exposure operation period, the imaging characteristics are measured based on the measurement light passing through the projection optical system 10. Measurements are performed at multiple timings at predetermined time intervals (measurement intervals) during the exposure operation period, before the plate is exposed. Figure 4 shows an example of the measurement results of the amount of variation in the imaging characteristics due to differences in measurement intervals. In Figure 4, the horizontal axis represents time t, and the vertical axis represents the amount of variation F in the measured imaging characteristics of the projection optical system 10. The imaging characteristics of the projection optical system 10 are assumed to have saturation characteristics as shown in Figure 2. In recent years, exposures have been performed with high energy (high doses and masks with high transmittance), resulting in large variations in the imaging characteristics per unit time. To capture such variations, the measurement interval is set short during the first interval of the exposure operation period and long during the second interval after the first interval, and correction coefficients are calculated using these intervals. The imaging characteristics in this case are shown as "Measurement Interval 1." The imaging characteristics shown as "Measurement Interval 2" are those obtained with a constant measurement interval, as in the past.

[0040] It was found that when a correction coefficient was calculated from the imaging characteristics obtained at "measurement interval 1" and a predicted value was calculated from the imaging characteristics obtained at "measurement interval 2," the error between the predicted value and the measured value became large. The reason for this is that the amount of energy during measurement is much smaller than during exposure, and the higher the amount of energy during exposure, the greater the fluctuation in the imaging characteristics during measurement in the opposite direction to that during exposure. In this embodiment, the correction coefficient is calculated with high precision by taking into account the fluctuation in the imaging characteristics during measurement, as explained below.

[0041] 5 is a flowchart showing a method for determining a correction coefficient in this embodiment. In S501, the main control unit 60 sets the exposure conditions when calculating the correction coefficient. The exposure conditions include, for example, a mask and an exposure area. Then, in S502, the main control unit 60 (optical characteristic measurement unit 61) performs an initial measurement (initial focus measurement) of the imaging characteristics before the exposure operation for the first plate is started.

[0042] In S503, the main control unit 60 performs exposure under the set exposure conditions. In S504, the main control unit 60 determines whether a predetermined measurement interval set in the exposure conditions has elapsed. If the measurement interval has not elapsed, the process returns to S503 and exposure continues. If the measurement interval has elapsed, the process proceeds to S505, where the main control unit 60 (optical property measurement unit 61) performs measurement (focus measurement) before exposure of the next plate. The obtained measurement value is stored in the data storage unit 64 in association with the exposure time in S503 and the measurement time in S505. In S506, the main control unit 60 determines whether a specified time preset by the user has elapsed since the start of exposure in S503. If the specified time has not elapsed, the process returns to S503 and exposure continues. If the specified time has elapsed, the process proceeds to S507, where the main control unit 60 determines whether the number of measurements in S505 has reached the specified number preset by the user. If the specified number has not been reached, the process returns to S503 and exposure continues. If the specified number of times has been reached, the process proceeds to S508.

[0043] In S508, the main control unit 60 (optical characteristic calculation unit 63) calculates (determines) correction coefficients. The optical characteristic calculation unit 63 determines the correction coefficients based on the predicted values ​​of the imaging characteristics obtained using the measured values ​​stored in the data storage unit 64 and the associated exposure times and measurement times, using the model formulas (4), (5), (6), and (7) shown below. For example, the correction coefficients are determined so as to minimize the residual between the measured values ​​and the predicted values. The determined correction coefficients are stored in the data storage unit 64.

[0044] A1 = K1 × Q1 (4) A2 = K2 × Q2 (5) F1(k)=F(k)+A1×(1-e -Δt1 / TS1 ) ···(6) F(k+1)=F1(k)+A2×(1-e -Δt2 / TS2 ) ···(7) where A1 is the maximum fluctuation amount of the imaging characteristics during exposure, TS1 is the time constant, K1 is the amount of variation in imaging characteristics per unit exposure energy, Q1 is the parameter of the exposure condition that determines the actual exposure energy. A2 is the maximum fluctuation of the imaging characteristics during measurement. TS2 is the time constant, K2 is the amount of variation in imaging characteristics per unit of measurement energy, Q2 is the parameter that determines the actual measured energy. F(k) is the amount of fluctuation in the imaging characteristics at time k. F1(k) is the amount of change in the imaging characteristics after exposure for time Δt1 from F(k), F(k+1) is the amount of change in the imaging characteristics after measuring time Δt2 from F1(k). The parameters Q1 and Q2 may include, for example, any of the exposure time, exposure amount, and scanning speed. K1 and K2, which represent the amount of fluctuation in the imaging characteristics per unit amount of light (per unit light energy), are called correction coefficients.

[0045] The model equations of the imaging characteristics of the projection optical system 10 described above include an exposure model equation and a measurement model equation. The exposure model equation is a model equation that represents fluctuations in the imaging characteristics while the substrate is being exposed, i.e., while the projection optical system 10 is being irradiated with exposure light. The measurement model equation is a model equation that represents fluctuations in the imaging characteristics while measurement is being performed. The exposure model equation is expressed by equation (6), and the measurement model equation is expressed by equation (7). The predicted values ​​of the imaging characteristics while the substrate is being exposed are obtained using the exposure model equation, and the predicted values ​​of the imaging characteristics while measurement is being performed are obtained using the measurement model equation.

[0046] 6 shows a flowchart of the exposure process in this embodiment. In S601, the main control unit 60 reads out and sets correction coefficients suited to the exposure conditions from the data storage unit 64. In S602, the main control unit 60 (optical property calculation unit 63) calculates a predicted correction amount based on the set correction coefficients. In S603, the main control unit 60 (optical property correction unit 62) corrects and drives the plate stage 30 (adjusts the position of the plate) using the calculated predicted correction amount. Thereafter, in S604, the main control unit 60 performs exposure processing.

[0047] Second Embodiment In the first embodiment described above, a procedure was shown in which correction coefficients were calculated in advance (FIG. 5), a predicted correction amount was calculated using the calculated correction coefficients, and corrective driving was performed (FIG. 6). In contrast, in the second embodiment, a procedure will be described in which a predicted correction amount is calculated while the correction coefficients are being calculated, and corrective driving is performed. With this method, it is not necessary to calculate the correction coefficients in advance, and it is possible to calculate the correction coefficients while production is being performed.

[0048] 7 shows a flowchart of the exposure process in this embodiment. In S701, the main control unit 60 sets the exposure conditions when calculating the correction coefficients. In S702, the main control unit 60 (optical characteristic measurement unit 61) performs an initial measurement.

[0049] In S703, the main control unit 60 (optical property calculation unit 63) determines whether or not the predicted correction amount can be calculated. This determination is made, for example, by determining whether the number of calculations of the correction coefficient exceeds a predetermined number. If the predicted correction amount can be calculated, in S704 the optical property calculation unit 63 calculates the predicted correction amount. In S705, the optical property correction unit 62 corrects and drives the plate stage 30 using the calculated predicted correction amount. Thereafter, in S706, the main control unit 60 performs exposure processing. If it is determined in S703 that the predicted correction amount cannot be calculated, the process proceeds to S705. In S705, the optical property correction unit 62 corrects and drives the plate stage 30 using the final measurement value measured by the optical property measurement unit 61 as the correction amount. Thereafter, in S706, the main control unit 60 performs exposure processing.

[0050] Next, in S707, the main controller 60 determines whether the predetermined measurement interval set in the exposure conditions has elapsed. If the measurement interval has not elapsed, the process proceeds to S710. In S710, the main controller 60 determines whether the exposure has ended, i.e., whether there are any more substrates to be exposed. If the exposure has not ended, the process returns to S703; if the exposure has ended, the process ends.

[0051] If the measurement interval has elapsed in S707, the process proceeds to S708, and the main control unit 60 (optical property measurement unit 61) performs measurement (focus measurement) before the exposure of the next plate. The obtained measurement value is stored in the data storage unit 64 in association with the exposure time in S706 and the measurement time in S708. In S709, the main control unit 60 (optical property calculation unit 63) calculates correction coefficients according to equations (4), (5), (6), and (7) exemplified in the first embodiment. The calculated correction coefficients are stored in the data storage unit 64. Thereafter, the process proceeds to S710.

[0052] The length of the measurement interval determined in S707 may be set for each time constant. The measurement interval may also be determined according to the difference between the predicted correction amount and the measured value. These methods for determining the measurement interval are merely examples, and the measurement interval may be determined by other methods. By making the measurement interval variable in this way, it becomes possible to obtain correction coefficients so as to maintain the correction accuracy of the imaging characteristics.

[0053] In the above-described embodiment, focus has been described as a specific example of the imaging characteristic of the projection optical system. However, the imaging characteristic may include not only focus but also at least one of magnification, field curvature, distortion, astigmatism, spherical aberration, and coma. When the imaging characteristic is focus, as in the above example, the main controller 60 adjusts the position of the plate (substrate) (drives the plate stage 30) based on the results of prediction using the model formula. When the imaging characteristic is magnification, field curvature, distortion, astigmatism, spherical aberration, or coma, the main controller 60 adjusts the imaging characteristic of the projection optical system 10 based on the results of prediction using the model formula. Such adjustments may be performed by driving at least one of the optical elements constituting the projection optical system 10 and the mask stage 20.

[0054] <Embodiment of an article manufacturing method> The article manufacturing method according to an embodiment of the present invention is suitable for manufacturing articles such as microdevices, such as semiconductor devices, and elements having microstructures. The article manufacturing method according to this embodiment includes a step of forming a latent image pattern on a photosensitive agent applied to a substrate using the above-described exposure apparatus (a step of exposing the substrate), and a step of developing the substrate on which the latent image pattern has been formed. Furthermore, this manufacturing method includes other well-known steps (oxidation, film formation, vapor deposition, doping, planarization, etching, resist stripping, dicing, bonding, packaging, etc.). The article manufacturing method according to this embodiment is advantageous over conventional methods in at least one of article performance, quality, productivity, and production cost.

[0055] (Other embodiments) The present invention can also be realized by supplying a program that realizes one or more functions of the above-described embodiments to a system or device via a network or a storage medium, and having one or more processors in the computer of the system or device read and execute the program. It can also be realized by a circuit (e.g., ASIC) that realizes one or more functions.

[0056] The disclosure of this specification includes at least the following determination method, exposure method, information processing device, program, exposure apparatus, and article manufacturing method. (Item 1) 1. A method for determining a coefficient that represents an amount of fluctuation in imaging characteristics per unit light energy applied to a projection optical system, the coefficient being used in a model equation that represents fluctuations in imaging characteristics of a projection optical system in an exposure apparatus that performs an exposure operation to expose a substrate via the projection optical system, the method comprising: measuring the imaging characteristics based on measurement light that has passed through the projection optical system at a predetermined timing during an exposure operation period in which the exposure operation is performed sequentially on a plurality of substrates; determining the coefficients based on the measured values ​​obtained by the measurement and the predicted values ​​of the imaging characteristics obtained using the model formula; and the model formula includes an exposure model formula that represents a variation in the imaging characteristics while the substrate is being exposed, and a measurement model formula that represents a variation in the imaging characteristics while the measurement is being performed, the predicted value of the imaging characteristic during the exposure is obtained using the exposure model equation, and the predicted value of the imaging characteristic during the measurement is obtained using the measurement model equation; A method for determining whether a (Item 2) 2. The determination method according to item 1, wherein the measurement is performed at a plurality of timings at predetermined time intervals during the exposure operation period, before the substrate is exposed. (Item 3) The determination method described in item 2, characterized in that the predetermined time interval is set to be short in a first section of the exposure operation period and long in a second section after the first section, based on the saturation characteristics of the imaging characteristics assumed in advance of the projection optical system. (Item 4) 4. The determination method according to any one of items 1 to 3, further comprising a step of performing an initial measurement of the imaging characteristics before the exposure operation for the first substrate of the plurality of substrates is started. (Item 5) 5. The method according to any one of items 1 to 4, wherein the imaging characteristics include at least one of focus, magnification, field curvature, distortion, astigmatism, spherical aberration, and coma. (Item 6) An exposure method for performing an exposure operation to expose a substrate via a projection optical system, comprising: determining a coefficient representing a variation in the imaging characteristics per unit light energy applied to the projection optical system, the coefficient being used in a model equation representing a variation in the imaging characteristics of the projection optical system; adjusting the position of the substrate or adjusting the imaging characteristics of the projection optical system based on the fluctuations in the imaging characteristics of the projection optical system obtained from the model equation in which the coefficients have been determined, and then exposing the substrate; and The step of determining the coefficients comprises: measuring the imaging characteristics based on measurement light that has passed through the projection optical system at a predetermined timing during an exposure operation period in which the exposure operation is performed sequentially on a plurality of substrates; determining the coefficients based on the measured values ​​obtained by the measurement and the predicted values ​​of the imaging characteristics obtained using the model formula; Including, the model formula includes an exposure model formula that represents a variation in the imaging characteristics while the substrate is being exposed, and a measurement model formula that represents a variation in the imaging characteristics while the measurement is being performed, the predicted value of the imaging characteristic during the exposure is obtained using the exposure model equation, and the predicted value of the imaging characteristic during the measurement is obtained using the measurement model equation; An exposure method characterized by: (Item 7) 6. An information processing device that executes the determination method according to any one of items 1 to 5. (Item 8) 6. A program for causing an information processing device to execute the determination method according to any one of items 1 to 5. (Item 9) An exposure apparatus that exposes a substrate via a projection optical system, a measurement unit that receives measurement light that has passed through the projection optical system and measures the imaging characteristics of the projection optical system based on the received measurement light; a control unit that predicts, using a model formula, fluctuations in imaging characteristics caused by the projection optical system absorbing light energy, adjusts the position of the substrate or the imaging characteristics of the projection optical system based on the results of the prediction, and then exposes the substrate; and the model formula includes an exposure model formula that represents a variation in the imaging characteristics while exposure of a substrate is being performed, and a measurement model formula that represents a variation in the imaging characteristics while measurement is being performed by the measurement unit, the control unit uses the exposure model formula to determine a predicted value of the imaging characteristic during the exposure, and uses the measurement model formula to determine a predicted value of the imaging characteristic during the measurement by the measurement unit. An exposure apparatus characterized by: (Item 10) Item 6. Exposing a substrate using the exposure method; developing the exposed substrate; and manufacturing an article from the developed substrate.

[0057] The invention is not limited to the above-described embodiments, and various changes and modifications can be made without departing from the spirit and scope of the invention. Accordingly, the following claims are appended to apprise the public of the scope of the invention. [Explanation of symbols]

[0058] 10: projection optical system, 20: mask stage, 21: mask, 30: plate stage, 36: plate, 60: main control unit, 100: exposure apparatus

Claims

1. 1. A method for determining a coefficient representing an amount of variation in an imaging characteristic per unit of light energy applied to a projection optical system in an exposure apparatus that performs an exposure operation to expose a substrate via a projection optical system, comprising the steps of: measuring the imaging characteristics based on measurement light that has passed through the projection optical system at a predetermined timing during an exposure operation period in which the exposure operations are sequentially performed on a plurality of substrates; determining the coefficients based on measured values ​​obtained by the measurement and predicted values ​​of the imaging characteristics obtained by calculation; having the predicted value of the imaging characteristic is determined using information representative of a variation in the imaging characteristic while the substrate is being exposed and information representative of a variation in the imaging characteristic while the measurement is being performed; A method for determining whether or not a

2. 2. The method according to claim 1, wherein the measurement is performed at a plurality of timings at predetermined time intervals during the exposure operation period, before exposure of the substrate.

3. 3. The method according to claim 2, wherein the specified time interval is set to be short in a first section of the exposure operation period and to be long in a second section following the first section, based on a saturation characteristic of the imaging characteristics assumed in advance of the projection optical system.

4. 2. The method of claim 1, further comprising the step of performing an initial measurement of the imaging characteristic before the exposure operation for a first substrate of the plurality of substrates is started.

5. 2. The method of claim 1, wherein the imaging characteristics include at least one of focus, magnification, field curvature, distortion, astigmatism, spherical aberration, and coma.

6. 1. An exposure method for performing an exposure operation of exposing a substrate through a projection optical system, comprising: determining a coefficient representing a variation in imaging characteristics per unit light energy applied to the projection optical system; adjusting a position of the substrate or adjusting the imaging characteristics of the projection optical system based on a variation in the imaging characteristics of the projection optical system obtained by using the coefficient, and then exposing the substrate; having The step of determining the coefficients comprises: measuring the imaging characteristics based on measurement light that has passed through the projection optical system at a predetermined timing during an exposure operation period in which the exposure operations are sequentially performed on a plurality of substrates; determining the coefficients based on measured values ​​obtained by the measurement and predicted values ​​of the imaging characteristics obtained by calculation; Including, the predicted value of the imaging characteristic is determined using information representative of a variation in the imaging characteristic while the substrate is being exposed and information representative of a variation in the imaging characteristic while the measurement is being performed; 13. An exposure method comprising:

7. An information processing apparatus that executes the determination method according to any one of claims 1 to 5.

8. A program for causing an information processing device to execute the determination method according to any one of claims 1 to 5.

9. An exposure apparatus that exposes a substrate through a projection optical system, comprising: a measurement unit that receives measurement light that has passed through the projection optical system and measures an imaging characteristic of the projection optical system based on the received measurement light; a control unit that predicts a variation in imaging characteristics caused by the projection optical system absorbing light energy, adjusts the position of the substrate or adjusts the imaging characteristics of the projection optical system based on the result of the prediction, and then exposes the substrate; having the control unit determines a result of the prediction using information representing a variation in the imaging characteristics while an exposure of a substrate is being performed and information representing a variation in the imaging characteristics while a measurement is being performed by the measurement unit. An exposure apparatus comprising:

10. exposing a substrate using the exposure method according to claim 6; developing the exposed substrate; and producing an article from the developed substrate.

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