JP2011009575A - Exposure device, adjusting method, and method of manufacturing device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide novel technique for finding an adjustment amount of an optical element while taking into consideration uncertainty of an optical characteristic value caused by that an optical element which varies the optical characteristic value is adjusted.SOLUTION: An exposure device which exposes a substrate through a pattern of a reticle includes a projection optical system which includes the optical element for having at least one of the position, posture and shape adjusted, and projects light from the pattern on the substrate, an adjustment part which adjusts at least one of the position, posture and shape of the optical element, and a control part which calculates the adjustment amount of the optical element by quadratic programming or quadratic cone programming so that a value of a target function including a variable representing logical variation in optical characteristic value of the projection optical system when the optical element is adjusted in accordance with an adjustment amount of the optical element provided for the adjustment part and uncertainty of variation in optical characteristic value of the projection optical system caused owing to an adjustment error when the adjustment part adjusts the optical element satisfies an allowable level, and controls the adjustment part based upon the calculated adjustment amount.

Description

  The present invention relates to an exposure apparatus, an adjustment method, and a device manufacturing method.

  An exposure apparatus is used when a fine semiconductor device such as a semiconductor memory or a logic circuit is manufactured by using a photolithography technique. The exposure apparatus projects a pattern formed on a reticle (mask) onto a substrate such as a wafer via a projection optical system and transfers the pattern.

  The projection optical system measures the optical characteristics (various aberrations, etc.) of the projection optical system, and calculates an adjustment amount (correction amount) for adjusting the optical characteristics of the projection optical system based on the measured optical characteristics. The adjustment is performed through the process and the process of adjusting the projection optical system based on the calculated adjustment amount.

  Many optical characteristics to be adjusted change in proportion to the adjustment amount of each element (for example, an optical element such as a lens), and it is required to minimize the absolute value thereof. Therefore, a technique for determining the adjustment amount of each element using linear programming has been proposed (see Patent Document 1).

  On the other hand, the optical characteristic to be adjusted is represented by a weighted square sum of the wavefront aberration coefficient at each point in the image plane (exposure area), such as the square of the RMS (Root Mean Square) value of the wavefront aberration. Characteristics are also included. Therefore, under the linear constraint equation, the primary evaluation value (optical characteristic value represented by a linear function of the adjustment amount of each optical element) and the secondary evaluation value (2 of the adjustment amount of each optical element). There has also been proposed a technique for optimizing the optical characteristic value expressed by the following function in a well-balanced manner (see Patent Document 2).

JP 2002-367886 A JP 2005-268451 A

  However, even if the adjustment amount determined in Patent Document 1 or Patent Document 2 is given as a target value to the adjustment unit that adjusts each optical element, there is a tolerance between the actual adjustment amount and the target value. . Therefore, when a sensitive optical element that greatly changes the optical characteristics even with a small adjustment amount is adjusted, the optical characteristics of the projection optical system may be deteriorated.

  The present invention has been made in view of such problems of the prior art, and takes into account the uncertainties of optical characteristic values that arise from adjusting optical elements that change optical characteristic values. The purpose is to provide a simple technique.

  In order to achieve the above object, an exposure apparatus according to one aspect of the present invention is an exposure apparatus that exposes a substrate through a pattern of a reticle, and is an optical element that can adjust at least one of position, posture, and shape A projection optical system that projects light from the pattern onto the substrate, an adjustment unit that adjusts at least one of the position, posture, and shape of the optical element, and the adjustment of the optical element that is provided to the adjustment unit The projection optics caused by a variable representing a theoretical change in the optical characteristic value of the projection optical system when the optical element can be adjusted according to the amount, and an adjustment error when the adjustment unit adjusts the optical element Calculating the adjustment amount of the optical element using quadratic programming or quadratic cone programming so that the value of the objective function including the uncertainty of the change in the optical characteristic value of the system satisfies an allowable level, Calculated key And having a control unit for controlling the adjustment portion based on the amount.

  Further objects and other aspects of the present invention will become apparent from the preferred embodiments described below with reference to the accompanying drawings.

  According to the present invention, for example, it is possible to provide a new technique for obtaining the adjustment amount of the optical element in consideration of the uncertainty of the optical characteristic value generated by adjusting the optical element that changes the optical characteristic value. .

It is a schematic perspective view which shows the structure of the exposure apparatus as 1 side surface of this invention. FIG. 2 is a diagram schematically showing an example of a movable direction (drive direction) of an optical element included in a reticle, a wafer, and a projection optical system whose position can be adjusted in the exposure apparatus shown in FIG. 1. 3 is a flowchart for explaining automatic adjustment of optical characteristics of a projection optical system in the exposure apparatus shown in FIG. 2 is a flowchart for explaining automatic adjustment of a projection optical system in the exposure apparatus shown in FIG.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described with reference to the accompanying drawings. In addition, in each figure, the same reference number is attached | subjected about the same member and the overlapping description is abbreviate | omitted.

  FIG. 1 is a schematic perspective view showing a configuration of an exposure apparatus 1 as one aspect of the present invention. In this embodiment, the exposure apparatus 1 is a projection exposure apparatus that exposes the pattern of the reticle 10 onto the wafer 40 by a step-and-scan method. However, the exposure apparatus 1 can also apply a step-and-repeat method and other exposure methods.

  The exposure apparatus 1 includes an illumination optical system (not shown), a reticle stage 20 that holds a reticle 10, a projection optical system 30, a wafer stage 50 that holds a wafer 40, laser interferometers 60a, 60b, and 60c, and a measurement unit. 70, an adjustment unit 80, and a control unit 90.

An illumination optical system (not shown) illuminates the reticle 10 on which a circuit pattern is formed using a light beam from a light source such as a KrF excimer laser having a wavelength of about 248 nm, an ArF excimer laser having a wavelength of about 193 nm, or an F ₂ laser having a wavelength of about 157 nm. .

  The reticle 10 has a circuit pattern and is supported and driven by the reticle stage 20. Diffracted light emitted from the reticle 10 is projected onto the wafer 40 via the projection optical system 30.

  The reticle stage 20 supports the reticle 10 and moves the reticle 10 using, for example, a linear motor. The reticle stage 20 is controlled by the control unit 90 and has a function of adjusting at least one of the position and posture of the reticle 10.

  The projection optical system 30 is an optical system that includes a plurality of optical elements (for example, optical elements such as a lens and an aperture stop) and projects the pattern of the reticle 10 onto the wafer 40. Some of the optical elements included in the projection optical system 30 are configured to be adjustable by the adjusting unit 80 at least one of position, posture, and shape.

  The wafer 40 is a substrate onto which the pattern of the reticle 10 is projected (transferred). However, the wafer 40 can be replaced with a glass plate or other substrate.

  The wafer stage 50 supports the wafer 40 and moves the wafer 40 using, for example, a linear motor. The wafer stage 50 is controlled by the control unit 90 and has a function of adjusting at least one of the position and posture of the wafer 40.

  The laser interferometers 60 a to 60 c are arranged in the vicinity of the wafer stage 50 and measure the position of the wafer stage 50.

  The measuring unit 70 measures the optical characteristics of the exposure apparatus 1, particularly the optical characteristics of the projection optical system 30. The measurement unit 70 includes, for example, an interferometer and a light intensity sensor, and has a function of measuring wavefront aberration at each point in the exposure area of the projection optical system 30. The measurement unit 70 also has a function of measuring distortion (distortion) as an aberration of the projection optical system 30. Here, the distortion is an amount representing how much the actual image height on the image plane is deviated from the ideal image height, and can be measured at each point on the image plane (within the exposure area). is there. The measurement unit 70 can be applied with any configuration known in the art, and a detailed description of the structure and operation is omitted here.

  The adjustment unit 80 is controlled by the control unit 90 and adjusts at least one of the position, posture, and shape of some of the optical elements included in the projection optical system 30. The adjustment unit 80 includes an actuator, and includes, for example, a mechanism that drives in the optical axis direction (Z-axis direction shown in FIG. 1), a direction perpendicular to the optical axis direction, a mechanism that drives a support unit that supports the optical element, and an optical element. And a mechanism for applying stress (force to push the optical element or force to pull the optical element).

  The control unit 90 includes a CPU and a memory (not shown) and controls the operation of the exposure apparatus 1. For example, the control unit 90 controls the scanning speed of the reticle stage 20 and the wafer stage 50. In the present embodiment, the control unit 90 uses the quadratic programming method or the quadratic cone programming method to adjust the adjustment amount of the optical element of the projection optical system 30 by the adjusting unit 80 based on the measurement result of the measuring unit 70. calculate. For example, as will be described later, the control unit 90 includes a variable representing a theoretical change in the optical characteristic value of the projection optical system 30 when the optical element can be adjusted according to the adjustment amount given to the adjustment unit 80, and the projection An objective function including the uncertainty of the change in the optical characteristic value of the optical system 30 is generated. Then, the control unit 90 calculates the adjustment amount of the optical element by using the quadratic programming method or the quadratic cone programming method so that the value of the objective function satisfies the allowable level. Note that the uncertainty of the change in the optical characteristic value of the projection optical system 30 is caused by an adjustment error when the optical element is adjusted. Furthermore, the control unit 90 controls the adjustment unit 80 based on the adjustment amount of the optical element of the projection optical system 30 calculated using the quadratic programming method or the quadratic cone programming method.

  FIG. 2 is a diagram schematically illustrating an example of the movable direction (drive direction) of the optical element 302 and 304 included in the reticle 10, the wafer 40, and the projection optical system 30 that can be adjusted in position. The position of the reticle 10 is adjusted in the direction of six degrees of freedom (that is, the directions of arrows X1, Y1, Z1, ωX1, ωY1, and ωZ1) via the reticle stage 20 controlled by the control unit 90. Similarly, the position of the wafer 40 is adjusted in the six degrees of freedom direction (that is, the directions of arrows X4, Y4, Z4, ωX4, ωY4, and ωZ4) via the wafer stage 50 controlled by the control unit 90. The position of the optical element 302 is adjusted in the direction of six degrees of freedom (that is, the directions of arrows X2, Y2, Z2, ωX2, ωY2, and ωZ2) via a drive mechanism 80a as the adjustment unit 80 controlled by the control unit 90. . Similarly, the optical element 304 is positioned in a 6-degree-of-freedom direction (that is, the directions of arrows X3, Y3, Z3, ωX3, ωY3, and ωZ3) via a drive mechanism 80b as an adjustment unit 80 controlled by the control unit 90. Adjusted.

  Hereinafter, a method for adjusting the optical characteristics (such as wavefront aberration) of the projection optical system 30 will be described. FIG. 3 is a flowchart for explaining the automatic adjustment of the optical characteristics of the projection optical system 30 in the exposure apparatus 1. Note that the automatic adjustment of the optical characteristics of the projection optical system 30 is realized by the control unit 90 controlling the respective units of the exposure apparatus 1 in an integrated manner.

  Referring to FIG. 3, in S <b> 1002, the distortion of the projection optical system 30 is measured via the measurement unit 70. Similarly, in S1004, the wavefront aberration is measured for each of the H measurement points in the exposure area of the projection optical system 30 via the measurement unit 70.

Next, in S1006, the wavefront aberration at the measurement point h in the exposure area of the projection optical system 30 measured in S1004 is expanded with J Zernike orthogonal functions, and each Zernike coefficient Z _ih is calculated.

  Next, the optical characteristic value of the projection optical system 30 is calculated from the Zernike coefficient (wavefront aberration coefficient) for each measurement point h of the projection optical system 30 calculated in S1006. Specifically, in S1008, a type I optical characteristic value having first-order characteristics with respect to wavefront aberration amounts such as line width asymmetry, field curvature, and astigmatism is calculated. Such an optical characteristic value is represented by a linear function of the adjustment amount of the optical elements 302 and 304 constituting the projection optical system 30 and is referred to as a primary optical characteristic value in the present embodiment. In S1010, the square value of the j-th Zernike coefficient at the measurement point h of the projection optical system 30 and the optical characteristic value represented by the product sum of the weight coefficients for each Zernike component, for example, the square of the wavefront aberration RMS value, etc. M types of optical characteristic values having secondary characteristics with respect to the amount of wavefront aberration are calculated. Such an optical characteristic value is represented by a quadratic function of adjustment amounts of the optical elements 302 and 304 constituting the projection optical system 30, and is referred to as a secondary optical characteristic value in the present embodiment.

  Here, the primary optical characteristic value, the secondary optical characteristic value, and the distortion will be described. Note that subscripts h, i, j, k, and m used below are defined by Equations 1 to 5.

The i-th primary optical characteristic value y _ih at the measurement point h in the exposure area of the projection optical system 30 is expressed by a linear combination of Zernike coefficients as shown in Equation 6. In addition, when the adjustment amount of each adjustment point (the optical elements 302 and 304 in the present embodiment) is changed, the j-th Zernike coefficient Z _{jh at the} measurement point h is the k-th adjustment as shown in Equation 7. It is represented by a linear combination of the adjustment amounts _xk of the places. In Equation 6, a _ij is the degree of influence of the j-th Zernike coefficient on the i-th primary optical characteristic value. In Equation 7, Z _0jh is an initial value of the j-th Zernike coefficient at the measurement point h, and b _hjk is the influence of the adjustment amount x _k of each adjustment unit on the j-th Zernike coefficient at the measurement point h. Degree. The adjustment location is not limited to the optical elements 302 and 304, and may include, for example, the reticle stage 20, the wafer stage 50, and the like.

  Equation 8 is derived from Equation 6 and Equation 7.

At this time, the uncertainty py _ih of the primary optical characteristic value y _ih generated by adjusting (manipulating) each adjustment point is defined by Equation 9. However, in Equation 9, qy _ihk is the uncertainty of the primary optical characteristic value y _ih generated by adjusting the k th adjustment location, and e _k adjusts (manipulates) the k th adjustment location. This variable indicates whether or not to adjust (non-operation). The uncertainty qy _ih of the primary optical characteristic value y _ih is obtained by multiplying the optical characteristic sensitivity at the k-th adjustment position by an adjustment tolerance.

Further, the distortion u _{h at} the measurement point h of the projection optical system 30 is also a primary optical characteristic value expressed by a linear function with respect to the adjustment amount x _k of the k-th adjustment location. Therefore, when the adjustment amount at the adjustment point is changed, the distortion u _{h at} the measurement point h is expressed by a linear combination of the adjustment amount x _{k at} the k-th adjustment point as shown in Equation 10. In Equation 10, u _0h is an initial value of distortion at the measurement point h, and c _hk is the degree of influence of the adjustment amount x _k of each adjustment point on the distortion at the measurement point h.

At this time, the uncertainty pu _h of the distortion u _h generated by adjusting each adjustment point is defined by Equation 11. However, in Equation 11, qu _hk is the uncertainty of distortion u _h generated by adjusting the k th adjustment point.

On the other hand, the m-th secondary optical characteristic value w _{mh at} the measurement point h of the projection optical system 30 is expressed by Equation 12. In Equation 12, d _jm is the degree of influence of the jth Zernike coefficient on the mth secondary optical characteristic value.

From Expression 7 and Expression 12, Expression 13 representing M secondary optical characteristic values W _mh at the measurement point h of the projection optical system 30 is derived.

At this time, the uncertainty pw _mh of the secondary optical characteristic value w _mh generated by adjusting each adjustment point is defined by Equation 14. However, in Equation 13, qw _mhk is the uncertainty of the secondary optical characteristic value w _mh generated by adjusting the k th adjustment location.

Further, since the physical limit exists in the adjusting amount x _k of the adjustment locations, adjusting amount x _k of each adjustment portion is represented by equation 15. However, in Equation 15, L _k is the lower limit value of the adjustment amount at the k th adjustment location, and U _k is the upper limit value of the adjustment amount at the k th adjustment location.

In Expressions 6 to 15, y _ih , u _h , x _k and e _k are unknown. On the other hand, Z _jh , Z _0ij , a _ij , b _hjk , u _0h , c _hk , d _jm , L _k , U _k , py _ih , pu _h , pw _mh , qy _ihk , qu _hk and qw _mhk are known. is there.

In step S1012, an objective function for obtaining the adjustment amount of each adjustment point, and a constraint condition expression for the primary optical characteristic value, distortion, and secondary optical characteristic value are generated. Specifically, as shown in Equations 16 to 23, the linear optical programming method using dummy variables proposed in Patent Document 1 is used for the adjustment range of the primary optical characteristic value, the distortion, and the adjustment amount of each adjustment portion. Generate constraint expression. Therefore, Equations 16 to 23 are constraint equations for the optimization problem. Note that t _{1i on} the right side of Equation 16 and t _{2 on} the right side of Equation 18 are dummy variables corresponding to the upper limit value of the primary optical characteristic value.

On the other hand, in order to minimize the secondary optical characteristic value expressed by the weighted _square sum of the Zernike coefficient, the upper limit Z _ajh of the absolute value of the j-th Zernike coefficient at the measurement point h of the projection optical system 30 is _expressed by Equation 24. And Expression 25.

As is clear from Equations 24 and 25, the upper limit Z _ajh is always non-negative.

Here, the constraint condition expressions shown in Expressions 26 to 28 are added. T _{3m on} the right side of Expression 26 and Expression 27 is a dummy variable corresponding to the upper limit value of the secondary optical characteristic value.

Moreover, the upper limit value of the uncertainty of the optical characteristic value generated when the adjustment location is adjusted is expressed by the following mathematical formulas 29 to 31. Note that s _{1i on} the right side of Equation 29 is a dummy variable corresponding to the upper limit value of the uncertainty of the primary optical characteristic value. S _{2 on} the right side of Equation 30 is a dummy variable corresponding to the upper limit value of distortion uncertainty. S _{3m on} the right side of Equation 31 is a dummy variable corresponding to the upper limit value of the uncertainty of the secondary optical characteristic value.

In this way, if the objective function to be minimized is expressed by Equation 32, the following constraint quadratic programming problem is generated. Here, Y _i is an allowable value of the i-th primary optical characteristic value, U is an allowable value of distortion, and W _m is an allowable value of the m-th secondary optical characteristic value.

  In S1014, optimization calculation is performed on the constrained quadratic programming problem generated in S1012 using a constrained quadratic programming calculation program (constraint quadratic programming solver), and each adjustment location (optical elements 302 and 304). The adjustment amount is calculated. In the objective function expressed by Equation 32, in order to optimize each optical characteristic of the projection optical system 30 with good balance, each optical characteristic value may be normalized by dividing by an allowable value. Accordingly, any optical characteristic value is permitted when the evaluation amount is 1 or less, and is not permitted when the evaluation value exceeds 1, and a plurality of aberrations can be minimized in a balanced manner.

  In S1016, each adjustment location is adjusted based on the adjustment amount of each adjustment location calculated in S1014. Specifically, the position, posture, shape, and the like of each of the optical elements 302 and 304 of the projection optical system 30 are adjusted via the adjustment unit 80. Thereby, the optical characteristic of the projection optical system 30 is adjusted (that is, the aberration of the projection optical system 30 is corrected).

  As described above, according to the method for adjusting the optical characteristics of the projection optical system 30 in the present embodiment, the element adjustment is performed in consideration of the uncertainty of the optical characteristic value generated by adjusting the element that changes the optical characteristic value. The amount can be determined. In addition, the optical characteristic value for each point in the exposure area (that is, the entire exposure area) is set to an appropriate range (that is, an allowable range) including whether or not to adjust the element, even though it is a very simple process. It is possible to obtain the adjustment amount of each part for maintaining the above.

As described above, the adjustment amount x _k of the adjustment locations, which is a control variable, the adjustment amount of the wafer stage 50 (e.g., adjusting the amount of focus adjustment and alignment adjustment) can also be included. Therefore, even when the wavefront aberration at each point in the exposure area of the projection optical system 30 includes a defocus component, the adjustment method of the projection optical system 30 according to the present embodiment is affected by the defocus component. The amount of adjustment at each adjustment point can be obtained without any problem. Similarly, even when an alignment component is included in the distortion of each point in the exposure area of the projection optical system 30, according to the adjustment method of the projection optical system 30 of the present embodiment, the alignment component is not affected. The amount of adjustment at each adjustment point can be obtained.

  Moreover, as shown in FIG. 4, you may perform the automatic adjustment of the optical characteristic of the projection optical system 30 using a secondary cone planning method. FIG. 4 is a flowchart for explaining the automatic adjustment of the optical characteristics of the projection optical system 30 in the exposure apparatus 1. Measurement of distortion of the projection optical system 30 (S1002), measurement of wavefront aberration of the projection optical system 30 (S1004), calculation of Zernike coefficients (S1006), calculation of primary optical characteristic values (S1008), and secondary optical characteristics The value calculation (S1010) is as described above.

  In S1012A, an objective function for obtaining an adjustment amount at each adjustment location, and a constraint condition expression for the primary optical characteristic value, distortion, and secondary optical characteristic value are generated. Specifically, Formula 16 to Formula 31 are transformed into the following equivalent formulas (Formula 33 to Formula 45). As a result, a secondary cone planning problem is generated.

Here, in Expressions 33 to 45, X, B _hm , α _hm, and β _hm are expressed by Expressions 46 to 49 below.

  In S1014A, the second-order cone planning problem generated in S1012A is subjected to optimization calculation using a second-order cone programming calculation program (secondary cone planning solver), and each adjustment location (optical elements 302 and 304). The adjustment amount is calculated.

  In S1016, each adjustment location is adjusted based on the adjustment amount of each adjustment location calculated in S1014A. Specifically, the position, posture, shape, and the like of each of the optical elements 302 and 304 of the projection optical system 30 are adjusted via the adjustment unit 80. Thereby, the optical characteristic of the projection optical system 30 is adjusted (that is, the aberration of the projection optical system 30 is corrected).

  As described above, even when the second-order cone programming method is used, the adjustment amount of the element can be obtained in consideration of the uncertainty of the optical characteristic value generated by adjusting the element that changes the optical characteristic value.

  In the exposure, the light beam emitted from the light source illuminates the reticle 10 by the illumination optical system. The light beam reflecting the pattern of the reticle 10 is imaged on the wafer 40 by the projection optical system 30. At this time, the projection optical system 30 is adjusted so that the optical characteristics in the exposure region are optimized by the adjustment method described above, and therefore the pattern of the reticle 10 is projected onto the wafer 40 with excellent imaging performance. Can do. Therefore, the exposure apparatus 1 can provide a high-quality device (semiconductor element, LCD element, imaging element (CCD, etc.), thin film magnetic head, etc.) with high throughput and high cost efficiency. Such a device includes a step of exposing a substrate (wafer, glass plate, etc.) coated with a photoresist (photosensitive agent) using the exposure apparatus 1, a step of developing the exposed substrate, and other known steps. , Manufactured by going through.

  As mentioned above, although preferable embodiment of this invention was described, it cannot be overemphasized that this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

Claims (8)

An exposure apparatus that exposes a substrate through a reticle pattern,
A projection optical system that includes an optical element capable of adjusting at least one of position, posture, and shape, and that projects light from the pattern onto the substrate;
An adjustment unit for adjusting at least one of the position, posture and shape of the optical element;
A variable representing a theoretical change in an optical characteristic value of the projection optical system when the optical element can be adjusted according to an adjustment amount of the optical element given to the adjustment unit; and The adjustment amount of the optical element is set to a quadratic programming method or 2 so that the value of the objective function including the uncertainty of the change in the optical characteristic value of the projection optical system caused by the adjustment error when adjusted is satisfied. A control unit that calculates using a next cone programming method, and controls the adjustment unit based on the calculated adjustment amount;
An exposure apparatus comprising:   Whether the objective function performs the uncertainty by adjusting the optical element value by the adjustment unit and the change of the optical characteristic value of the projection optical system caused by an adjustment error when the adjustment unit adjusts the optical element. The exposure apparatus according to claim 1, wherein the exposure apparatus includes a product term with a variable representing whether or not. The adjustment unit includes an actuator,
The uncertainty is caused by an adjustment error caused when the optical element is adjusted according to the adjustment amount of the optical element given by the actuator when the adjustment amount of the optical element is given to the actuator. The exposure apparatus according to claim 1, wherein the exposure apparatus is a change in optical characteristic value.   The optical characteristic value is an optical characteristic value represented by a linear combination of wavefront aberration coefficients, a distortion value as an aberration of the projection optical system, and an optical characteristic value represented by a weighted square sum of wavefront aberration coefficients. 4. The exposure apparatus according to claim 1, further comprising at least one of a square of the wavefront aberration RMS value. 5.   5. The exposure apparatus according to claim 4, wherein the wavefront aberration coefficient is a Zernike coefficient. A method for adjusting a projection optical system, which includes an optical element capable of adjusting at least one of position, posture, and shape, and projects light from a reticle pattern onto a substrate,
The projection caused by a variable representing a theoretical change in the optical characteristic value of the projection optical system when the optical element can be adjusted according to the adjustment amount of the optical element and an adjustment error when adjusting the optical element A generating step for generating an objective function including an uncertainty of a change in an optical characteristic value of the optical system;
A calculation step of calculating the adjustment amount of the optical element using a quadratic programming method or a quadratic cone programming method so that the value of the objective function generated in the generating step satisfies an allowable level;
An adjustment step of adjusting the optical element based on the adjustment amount calculated in the calculation step;
The adjustment method characterized by having.   The uncertainty is caused by an adjustment error when the optical element is adjusted in accordance with the adjustment amount of the optical element given to the actuator that adjusts the optical element when the adjustment amount of the optical element is given to the actuator that adjusts the optical element. The adjustment method according to claim 1, wherein the adjustment is a change in an optical characteristic value of the projection optical system. Exposing the substrate using the exposure apparatus according to any one of claims 1 to 5,
Developing the exposed substrate;
A device manufacturing method characterized by comprising:

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