JP6554141B2 - Determination method, exposure method, information processing apparatus, program, and article manufacturing method - Google Patents

Description

  The present invention relates to a determination method, an exposure method, an information processing apparatus, a program, and an article manufacturing method.

  When manufacturing fine semiconductor devices such as LSIs and VLSIs, an exposure apparatus is used that transfers (projects for reduction) the pattern of a mask (reticle) onto a substrate coated with a resist (photosensitive agent) for transfer. Yes. With the improvement of the mounting density of semiconductor devices, further miniaturization of patterns is required, and along with the development of the resist process, measures to improve the resolution of the exposure apparatus are being advanced. Techniques for improving the resolving power of the exposure apparatus include shortening the wavelength of exposure light and increasing the numerical aperture (NA) of the projection optical system. However, since the depth of focus of the projection optical system becomes shallow if the resolution is improved in this way, it is important to improve the focus accuracy to make the surface of the substrate coincide with the imaging plane (focal plane) of the projection optical system.

  Further, one of the important performances of the exposure apparatus is the overlay accuracy of each pattern transferred to the substrate through a plurality of steps. The imaging characteristics (focus, magnification, distortion, astigmatism, wavefront aberration, etc.) of the projection optical system are important factors that affect the overlay accuracy. In recent years, patterns used in VLSI are becoming increasingly finer, and accordingly, there is an increasing demand for improving overlay accuracy.

  In the exposure apparatus, when exposure is repeated, the projection optical system absorbs a part of the energy of the exposure light and is heated, and then dissipates heat, thereby changing the imaging characteristics of the projection optical system (thermal aberration, exposure aberration ) Occurs. Such fluctuations in the imaging characteristics of the projection optical system are factors that reduce the overlay accuracy. In view of this, a technique has been proposed for compensating for variations in the imaging characteristics of the projection optical system due to exposure light exposure to the projection optical system (see Patent Documents 1 and 2).

For example, in Patent Document 1, the fluctuation amount of the imaging characteristic of the projection optical system is calculated by a model formula having an exposure amount, an exposure time, a non-exposure time, etc. as variables, and the projection optical system A technique for correcting (adjusting) imaging characteristics is disclosed.
The model formula has a correction coefficient specific to the projection optical system for each imaging characteristic, and the correction coefficient changes depending on the light source distribution formed on the pupil plane of the projection optical system. Therefore, Patent Document 2 proposes a technique capable of satisfactorily correcting the fluctuation of the imaging characteristic even if the light source distribution formed on the pupil plane of the projection optical system changes. In Patent Document 2, a correction coefficient corresponding to each light source distribution formed on the pupil plane of the projection optical system is stored, and when the light source distribution is changed, the correction coefficient corresponding to the light source distribution is read and projected. The fluctuation amount of the imaging characteristics of the optical system is calculated.

Japanese Patent Publication No. 63-16725 Japanese Patent No. 28828226

  In the prior art, in order to predict fluctuations in the imaging characteristics of the projection optical system during exposure, the imaging characteristics of the projection optical system are measured a plurality of times during exposure, and a correction coefficient is obtained from the measurement results. When exposure is performed under the same exposure conditions (illumination mode, mask, etc.) after obtaining the correction coefficient, the projection optical system is not measured using the correction coefficient without measuring the imaging characteristics of the projection optical system during exposure. Predict fluctuations.

  However, when the imaging characteristics of the projection optical system are measured a plurality of times during exposure, if the influence of the exposure aberration due to the previous exposure remains on the projection optical system, a correction coefficient including an error is obtained. . Therefore, before obtaining the correction coefficient, that is, before measuring the imaging characteristics of the projection optical system a plurality of times during exposure, it is necessary to ensure a sufficient cooling (standby) time for eliminating the influence of the exposure aberration. In other words, productivity is reduced.

  The present invention has been made in view of such problems of the prior art, and is an advantageous determination method for determining a coefficient indicating a saturation value of an imaging characteristic used in a model formula representing a fluctuation of an imaging characteristic of a projection optical system. For illustrative purposes.

  In order to achieve the above object, a determination method according to one aspect of the present invention is a model equation that represents a variation in imaging characteristics of a projection optical system in an exposure apparatus that transfers a mask pattern onto a substrate via the projection optical system. A determination method for determining a coefficient indicating a saturation value of the imaging characteristic used in a plurality of measurement values obtained by measuring the imaging characteristic a plurality of times, and the substrate obtained from the model formula A first step of obtaining a first coefficient indicating a saturation value of the imaging characteristic based on the predicted value of the imaging characteristic at the start of exposure, the first coefficient, and the exposure apparatus are stored in the exposure apparatus A second step of determining whether a difference between the second equation and the second coefficient indicating a saturation value of the imaging characteristic used in the model equation is within an allowable range, and the difference is within the allowable range; The first coefficient is A third step of updating the coefficient so as to determine the first evaluation value of the first coefficient obtained from the predicted value and the second coefficient when the difference is not within the allowable range In comparison with the second evaluation value of the second coefficient obtained from the predicted value of the imaging characteristics obtained from the model formula, if the first evaluation value is less than the second evaluation value, A fourth step of updating the coefficient using a first coefficient as a temporary coefficient and not updating the coefficient if the first evaluation value is equal to or greater than the second evaluation value.

  Further objects or other aspects of the present invention will be made clear by the preferred embodiments described below with reference to the accompanying drawings.

  According to the present invention, for example, it is possible to provide an advantageous determination method for determining a coefficient indicating a saturation value of an image formation characteristic used in a model expression representing a change in image formation characteristic of a projection optical system.

It is the schematic which shows the structure of exposure apparatus. It is a figure which shows an example of the fluctuation | variation of the aberration of a projection optical system. It is a figure which shows an example of the fluctuation | variation of the aberration of a projection optical system. It is a figure which shows an example of the fluctuation | variation of the aberration of a projection optical system. It is a figure for demonstrating the reason a correction coefficient cannot be calculated | required correctly. It is a flowchart for demonstrating the determination method as 1 side surface of this invention. It is a figure which shows an example of the predicted value of the imaging characteristic (focus) of a projection optical system. It is a figure for demonstrating a weighting coefficient.

  Hereinafter, preferred embodiments of the present 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 diagram showing the configuration of the exposure apparatus 1. The exposure apparatus 1 is a lithography apparatus that exposes a substrate, specifically, transfers a mask (reticle) pattern to the substrate via a projection optical system by a step-and-scan method. However, the exposure apparatus 1 can also apply a step-and-repeat method or another exposure method.

  The exposure apparatus 1 includes an illumination optical system 104 that illuminates the mask 109 using light from the light source unit 101, a projection optical system 110, and a substrate stage 116 that holds and moves the substrate 115. The exposure apparatus 1 also includes an aperture driving unit 112, a lens driving unit 113, a laser interferometer 118, a light projecting optical system 121, a detection optical system 122, and a measuring unit 123. Further, the exposure apparatus 1 includes a light source control unit 102, an illumination control unit 108, a projection control unit 114, a stage control unit 120, and a main control unit 125.

  The light source unit 101 includes, for example, a pulse light source in which a gas such as KrF or ArF is sealed, and emits light in the far ultraviolet region having a wavelength of about 248 nm. The light source unit 101 also includes a narrowing module, a monitor module, a shutter, and the like. The narrowing module comprises a front mirror constituting a resonator, a diffraction grating for narrowing the wavelength (exposure wavelength) and a prism, and the monitor module monitors the wavelength stability and the spectral width. It consists of a spectroscope and a detector.

  The light source control unit 102 controls a gas exchange operation in the light source unit 101, a wavelength stabilization operation of light emitted from the light source unit 101, a discharge applied voltage in the light source unit 101, and the like. In the present embodiment, the light source control unit 102 does not control the light source unit 101 alone, but controls the light source unit 101 under the control of the main control unit 125.

  The light emitted from the light source unit 101 enters the illumination optical system 104. The light incident on the illumination optical system 104 is shaped into a predetermined beam shape through a beam shaping optical system (not shown), and is incident on an optical integrator (not shown). Such an optical integrator forms a large number of secondary light sources in order to illuminate the mask 109 with a uniform illuminance distribution.

  The aperture stop 105 included in the illumination optical system 104 has a substantially circular opening. The illumination control unit 108 controls each part of the illumination optical system 104 so that the diameter of the opening of the aperture stop 105 and the numerical aperture (NA) of the illumination optical system 104 have predetermined values under the control of the main control unit 125. Control. Since the ratio of the numerical aperture of the illumination optical system 104 to the numerical aperture (NA) of the projection optical system 110 is the coherence factor (σ value), the illumination control unit 108 controls the diameter of the aperture of the aperture stop 105. Thus, the σ value can be adjusted (set).

  On the optical path of the illumination optical system 104, a half mirror 106 for reflecting (extracting) part of the light that illuminates the mask 109 is disposed. A photo sensor 107 for ultraviolet light is disposed on the optical path of the light reflected by the half mirror 106. The photosensor 107 generates an output corresponding to the intensity of light illuminating the mask 109 (ie, the exposure energy). The output of the photo sensor 107 is converted into exposure energy per pulse by an integration circuit (not shown) that performs integration for each pulse emission of the light source unit 101, and is input to the main control unit 125 via the illumination control unit 108. .

  The mask 109 is an original plate having a pattern (circuit pattern) to be transferred to the substrate 115, and is held by a mask stage (not shown). The mask stage holds the mask 109 and moves in a three-dimensional direction (in the plane perpendicular to the optical axis direction and the optical axis of the projection optical system 110) using, for example, a linear motor. Since the exposure apparatus 1 employs a step-and-scan method, the pattern of the mask 109 is transferred to the substrate 115 by scanning the mask 109 and the substrate 115.

  The projection optical system 110 includes a plurality of optical elements (such as lenses), and reduces the pattern of the mask 109 by a predetermined reduction ratio β (for example, β = 1/4) and projects it on (the shot area of) the substrate 115 .

  On the pupil plane of the projection optical system 110 (Fourier transform plane with respect to the mask 109), an aperture stop 111 having a substantially circular aperture is disposed. The aperture driving unit 112 includes a motor and the like, and drives the aperture stop 111 such that the diameter of the aperture of the aperture stop 111 has a predetermined value. In addition, the lens driving unit 113 is an optical element constituting the projection optical system 110 using air pressure or a piezoelectric element, and in the present embodiment, a part of the lens (for example, a field lens) Drive in the axial direction. The projection control unit 114 controls the aperture driving unit 112 and the lens driving unit 113 under the control of the main control unit 125. In the present embodiment, by driving the lens constituting the projection optical system 110, the fluctuation of various aberrations of the projection optical system 110 is reduced, and the magnification (projection magnification) is maintained well to reduce distortion errors.

  The substrate 115 is a substrate onto which the pattern of the mask 109 is projected (transferred). A photoresist (photosensitive agent) is applied to the substrate 115. The substrate 115 includes a wafer, a glass plate, and other substrates.

  The substrate stage 116 holds the substrate 115, and moves in a three-dimensional direction (in the plane orthogonal to the optical axis direction of the projection optical system 110 and the optical axis) using, for example, a linear motor or the like. By measuring the distance to the moving mirror 117 fixed to the substrate stage 116 with the laser interferometer 118, the position of the substrate stage 116 in the plane orthogonal to the optical axis of the projection optical system 110 is detected. The stage control unit 120 controls the position of the substrate stage 116 based on the measurement result of the laser interferometer 118 under the control of the main control unit 125 (for example, the substrate stage 116 is moved to a predetermined position).

  The light projection optical system 121 and the detection optical system 122 constitute a focus detection system for detecting the position of the substrate 115 in the optical axis direction of the projection optical system 110 (that is, the height of the surface of the substrate 115). The light projecting optical system 121 projects light (non-exposure light) that does not sensitize the photoresist applied to the substrate 115 and focuses it on each position on the substrate 115. The light reflected at each position of the substrate 115 enters the detection optical system 122. In the detection optical system 122, a plurality of light receiving elements for position detection are arranged corresponding to the light reflected at each position of the substrate 115. Specifically, the plurality of light receiving elements are arranged such that the light receiving surface of each light receiving element and the reflection point on the substrate 115 are substantially conjugate via the imaging optical system. Therefore, the positional deviation of the substrate 115 in the optical axis direction of the projection optical system 110 is detected as the positional deviation of the light incident on each light receiving element arranged in the detection optical system 122.

  The measurement unit 123 is disposed on the image plane side of the projection optical system 110, in the present embodiment, the substrate stage 116. The measuring unit 123 detects the light having passed through the projection optical system 110 and measures the imaging characteristics of the projection optical system 110. The measurement unit 123 includes, for example, a light shielding plate having a pinhole that allows the light from the projection optical system 110 to pass, and a photoelectric conversion element that detects the light that has passed through the pinhole.

  The main control unit 125 is configured by a computer (information processing device) including a CPU, a memory, and the like. The main control unit 125 includes a light source control unit 102, an illumination control unit 108, a projection control unit 114, a stage control unit 120, and the like. The whole (each part of the exposure apparatus 1) is controlled. In the present embodiment, the main control unit 125 can also have a function of determining a correction coefficient used in a model formula representing a change in imaging characteristics of the projection optical system 110, as will be described later.

  Here, a model expression that represents the variation of the imaging performance of the projection optical system 110 due to the irradiation of the exposure light, and a correction for compensating the variation of the imaging characteristic for each exposure condition used to quantify the model equation. The coefficient will be described. In the present embodiment, the imaging characteristics of the projection optical system 110 include at least one of focus, magnification, distortion, astigmatism, spherical aberration, coma and wavefront aberration. The wavefront aberration can be expressed as each term obtained by developing the wavefront shape with a Zernike polynomial, as is well known in the art. In addition, these may be collectively referred to as “aberration”.

  FIG. 2 is a view showing an example of the fluctuation (change over time) of the aberration of the projection optical system 110. In FIG. 2, the horizontal axis indicates time t, and the vertical axis indicates the aberration amount F at a certain image height of the projection optical system 110. ΔF indicates the aberration fluctuation amount of the projection optical system 110, and the aberration fluctuation amount ΔF takes a value that differs for each image height. Further, the initial aberration amount of the projection optical system 110 (that is, before exposure) is F0.

  Referring to FIG. 2, when the exposure is started from time t0, the aberration fluctuates with time and stabilizes at a constant aberration amount (maximum fluctuation amount) F1 at time t1. After time t1, even if light (exposure light) is incident on the projection optical system 110, the thermal energy absorbed by the projection optical system 110 and the thermal energy emitted from the projection optical system 110 reach an equilibrium state Therefore, the amount of aberration does not change from F1. When the exposure ends at time t2, the aberration returns to the initial state with the passage of time, and reaches the initial aberration amount F0 at time t3.

  2 is a time constant of the heat transfer characteristic of the projection optical system 110. These time constants are values unique to the projection optical system 110, and are different values for each aberration. Therefore, the time constant is acquired for each projection optical system 110 and for each aberration of the projection optical system 110, for example, during maintenance of the exposure apparatus 1.

  The maximum fluctuation amount F1 of the aberration shown in FIG. 2 is the actual exposure energy Q determined from the aberration fluctuation amount K per unit light quantity (unit exposure energy) and parameters such as exposure time, exposure amount, scanning speed, exposure area information and the like. Is represented by the following formula (1).

F1 = K × Q (1)
The amount of aberration at a certain time is represented by ΔF _k . In this case, in the exposure state, the aberration amount ΔF _{k + 1} after a lapse of time Δt from a certain time is approximated by the following equation (2) using the maximum fluctuation amount F1 and the time constant TS1. Ru. Similarly, in a state where exposure has not been performed, the aberration amount ΔF _{k + 1} after a lapse of time Δt from a certain time is approximated by the following equation (3).

ΔF _{k + 1} = ΔF _k + F1 × (1-exp (−Δt / TS1)) (2)
ΔF _{k + 1} = ΔF _k × exp (−Δt / TS1) (3)
The variation of the aberration of the projection optical system 110 shown in FIG. 2 (curve shown in FIG. 2) is modeled using Equation (1), Equation (2) and Equation (3). However, Formula (1), Formula (2), and Formula (3) are an example in this embodiment, and you may model using another Formula.

  The model formula representing the variation in aberration of the projection optical system 110 includes an exposure model formula expressed by formula (2) and a non-exposure model formula expressed by formula (3). The exposure model equation represents the fluctuation of the aberration of the projection optical system 110 during the irradiation of the exposure light to the projection optical system 110, that is, the fluctuation of the aberration of the projection optical system 110 during the exposure. The non-exposure model equation represents the fluctuation of the aberration of the projection optical system 110 in a state in which the irradiation of the exposure light to the projection optical system 110 is stopped, that is, the fluctuation of the aberration of the projection optical system 110 after the completion of the exposure.

  The maximum fluctuation amount F1 used in the equation (2) represents a saturation value of the aberration of the projection optical system 110, and is a correction coefficient to be described later. The correction coefficient is acquired for each aberration of the projection optical system 110, and may be predicted by a plurality of model equations having different time constants.

  Here, the correction coefficient is predicted using a plurality of time constants TS1, TS2, and TS3 different from one another. For each model equation of the plurality of time constants TS1, TS2, and TS3, let F_TS1, F_TS2, and F_TS3 be the predicted values of aberration of the projection optical system 110 at a certain time. In this case, the predicted value of the aberration of the projection optical system 110 is the sum of predicted values for each model formula (F_TS1 + F_TS2 + F_TS3). Here, although the aberration of the projection optical system 110 is predicted by three model equations, the present invention is not limited to this.

  When the exposure condition is changed, the energy density distribution of light (exposure light) incident on the projection optical system 110 is changed, so that the aberration fluctuation amount of the projection optical system 110 and the image height dependency thereof are changed. Therefore, the correction coefficient must be obtained for each exposure condition. Here, the exposure conditions include, for example, the shape of the effective light source, the pattern of the mask 109, the illumination area for illuminating the mask 109, and the like.

  Consider the case where correction coefficients are determined for different exposure conditions, for example, each of the first exposure condition and the second exposure condition. In this case, in order to obtain the correction coefficient with high accuracy, for example, as shown in FIG. 3, a sufficient cooling (waiting) time may be secured until the influence of the residual aberration under different exposure conditions disappears. However, productivity is lowered by providing a cooling time. FIG. 3 is a diagram illustrating an example of aberration variation of the projection optical system 110. In FIG. 3, the horizontal axis indicates time, and the vertical axis indicates the aberration (aberration amount) of the projection optical system 110. FIG. 3 shows the variation of the aberration of the projection optical system 110 when the substrate 115 is exposed under the first exposure condition, and the variation of the aberration of the projection optical system 110 when the substrate 115 is exposed under the second exposure condition. Has been.

  In addition, Expressions (1) to (3) are also established between different exposure conditions. Therefore, for example, as shown in FIG. 4, if the correction coefficient in the job immediately before the first exposure condition is correctly determined, the correction coefficient in each exposure condition can also be correctly determined even if the cooling time is omitted. . However, when there is an error in the correction coefficient in the job immediately before the first exposure condition, as shown in FIG. 4, if the cooling time is omitted, the correction coefficient under each exposure condition can not be obtained correctly. FIG. 4 is a diagram illustrating an example of the variation in aberration of the projection optical system 110. In FIG. 4, the horizontal axis indicates time, and the vertical axis indicates the aberration (aberration amount) of the projection optical system 110. FIG. 4 shows variations in the aberration of the projection optical system 110 when the substrate 115 is exposed under each of the first exposure condition, the second exposure condition, and the third exposure condition.

  Here, when there is an error in the correction coefficient in a job immediately before a certain exposure condition, the reason why the correction coefficient under a certain exposure condition can not be obtained correctly will be described. In order to facilitate understanding, a case where there is no error in the correction coefficient in the immediately preceding job will be described first.

  Here, for example, the imaging characteristics of the projection optical system 110 during the exposure of one lot, specifically, the focus is measured a plurality of times, and the exposure time of one lot is 400 seconds. Also, the time constant TS1 is of one type and is 200 seconds. The predicted value of the focus of the projection optical system 110 by the immediately preceding job at the start of exposure (t = 0) is 15 nm. Since the predicted value is predicted using the equations (1) to (3), if there is no error in the correction coefficient, the predicted value at the start of exposure will also have no error. The measured value when the focus of the projection optical system 110 is actually measured at the start of exposure is shown in FIG.

  Assuming that the predicted value at a certain time after exposure is ΔF 2 and the predicted value at the next time after exposure is ΔF 3, equations (2) and (3) are used (ie, exposure model equation and non-exposure model equation By using properly), the following formula is obtained.

ΔF2 = ΔF1 + F1 × (1−exp (−Δt / TS1))
ΔF3 = ΔF2 × (1-exp (−Δt / TS1))
Substituting ΔF1 = 15 nm into such an equation, and fitting a plurality of measurement values obtained by measuring the focus of the projection optical system 110 a plurality of times, thereby obtaining a correction coefficient (maximum variation F1). In this case, the correction coefficient is 100 nm.

  Next, it is assumed that there is an error in the correction coefficient in the immediately preceding job, that is, there is an error (prediction error) in the predicted value at the start of exposure. Here, if the prediction error is 15 nm, as shown in FIG. 5A, the predicted value at the start of exposure (t = 0) is 30 nm. Even if there is an error in the predicted value, the amount of variation between the measured values does not change. Therefore, a correction coefficient is obtained for the predicted value with the solid curve in FIG. In this case, in order to substitute ΔF1 = 30 nm into the above equation, the correction coefficient is 115 nm.

  Equation (2) when ΔF 1 = 0 is shown in FIG. 5B for such different correction coefficients. As is clear from FIG. 5B, when there is a prediction error, a correction coefficient including the error is obtained, so that the curve has a large change with respect to the true correction coefficient. Thus, when there is a prediction error, an incorrect correction coefficient is obtained as a result.

  Therefore, in the present embodiment, in the determination method for determining the correction coefficient used in the model formula representing the fluctuation of the imaging characteristic of the projection optical system 110, the accuracy of the correction coefficient is gradually improved while shortening the cooling time. Suggest a method.

  FIG. 6 is a flowchart for explaining a determination method for determining a correction coefficient used in a model formula representing a change in imaging characteristics of the projection optical system 110 in the present embodiment. The determination method may be executed by the main control unit 125 or may be executed by an information processing apparatus outside the exposure apparatus 1.

  In S1, a correction coefficient (second coefficient) corresponding to the exposure condition of the exposure performed by the exposure apparatus 1 is acquired. The correction coefficient is stored in advance in the exposure apparatus 1 (a memory of the main control unit 125 or a storage device of the exposure apparatus 1).

  In S2, a predicted value of the imaging characteristics of the projection optical system 110 at the start of exposure is acquired. The predicted value corresponds to the residual of the fluctuation of the imaging characteristic of the projection optical system 110 in the exposure before the main exposure (the exposure to be performed). If the cooling time is sufficiently provided from the end of the previous exposure, the predicted value of the imaging characteristic of the projection optical system 110 at the start of the exposure acquired in S2 approaches zero. However, in the present embodiment, in order to reduce the cooling time, the predicted value of the imaging characteristic of the projection optical system 110 at the start of the exposure acquired in S2 is not zero.

  In S3, exposure is started. In S4, while the exposure apparatus 1 performs exposure of the substrate 115, the imaging characteristics of the projection optical system 110 are measured a plurality of times to obtain a plurality of measurement values. For example, as described above, the measurement unit 123 measures the imaging characteristics of the projection optical system 110 a plurality of times between exposure of one lot and exposure (for example, at the time of replacement of the substrate 115).

  In S5, Formulas (1) to (3) are used based on the predicted values of the imaging characteristics of the projection optical system 110 at the start of exposure obtained in S2 and the plurality of measurement values obtained in S4. Thus, a correction coefficient (first coefficient) is obtained (first step).

  In S6, it is determined whether the correction coefficient obtained in S5 is to be updated as the final correction coefficient used in the model expression. Specifically, the absolute value of the difference between the correction coefficient obtained in S1 (the second coefficient stored in advance in the exposure apparatus 1) and the correction coefficient obtained in S5 (the first coefficient) falls within the allowable range. It is determined whether it is (second step). The allowable range is stored in advance in the exposure apparatus 1. If the absolute value of the difference between the correction coefficient acquired in S1 and the correction coefficient obtained in S5 is within the allowable range, the process proceeds to S7. If the absolute value of the difference between the correction coefficient acquired in S1 and the correction coefficient obtained in S5 is not within the allowable range, the process proceeds to S8.

  In S7, the correction coefficient (first coefficient) determined in S5 is set in the exposure apparatus 1, that is, the correction coefficient stored in the exposure apparatus 1 such that the correction coefficient determined in S5 is used in the model equation. (2nd coefficient) is updated (3rd process). As a result, when exposure is performed under the same exposure conditions, the imaging characteristics of the projection optical system 110 are not measured multiple times (S4), and the projection optical system 110 is connected using the correction coefficient obtained in S5. It is possible to perform exposure while predicting image characteristics. Accordingly, since it is not necessary to measure the imaging characteristics of the projection optical system 110 a plurality of times in one lot of exposure, a reduction in throughput can be suppressed.

  In S8, the first evaluation value of the correction coefficient (first coefficient) obtained from the predicted value obtained in S2, and the correction coefficient obtained from the predicted value obtained from the model formula when obtaining the correction coefficient obtained in S1 The second evaluation value of the second coefficient) is compared. In the present embodiment, it is determined whether the first evaluation value is less than the second evaluation value or whether the first evaluation value is equal to or more than the second evaluation value. The second evaluation value is stored in advance in the exposure apparatus 1 in association with the correction coefficient (second coefficient) acquired in S1.

  The first evaluation value and the second evaluation value, specifically, the evaluation value indicating the reliability of the correction coefficient, are predicted values ΔF1 at the start of exposure and S2 obtained at the time of obtaining the correction coefficient obtained in S1. It is calculated | required by prediction value (DELTA) F1 acquired by (1). Specifically, the evaluation value V is represented by the absolute value of the linear sum of the weighting factor set to each of the plurality of time constants and the predicted value ΔF1, as shown in the following equation (4).

V = | ΔF1_TS1 × weighting_TS1 + ΔF1_TS2 × weighting_TS2ΔF1_TS3 × weighting_TS3 | (4)
In order to predict the predicted value ΔF1 from the fluctuation of the imaging characteristic of the projection optical system 110 under the previous exposure condition using the equation (3), the predicted value is obtained for each time constant. Such predicted values are ΔF1_TS1, ΔF1_TS2, and ΔF1_TS3. Here, three types of time constants are assumed. Further, weight_TS1, weight_TS2 and weight_TS3 are weight coefficients that are preset in the exposure apparatus 1 for each time constant.

  Here, consider a case where there is an error (prediction error) in the predicted value ΔF1. The predicted value ΔF1 is predicted using Expression (3) in the immediately preceding job. The case where there is a prediction error in the predicted value ΔF1 and the case where there is no prediction error in the predicted value ΔF1 are shown in FIG. In FIG. 7, the vertical axis indicates the focus of the projection optical system 110, and the horizontal axis indicates the time. From the characteristic of Equation (3), the prediction error amount A depends on the prediction value B when there is a prediction error, and the prediction error amount A decreases as the prediction value B decreases. By providing a sufficient cooling time, the predicted value B can be made as close to zero as possible. As a result, the prediction error amount A approaches zero, and if a correction coefficient is obtained from this state, the correction coefficient does not include an error.

  The weighting coefficient in equation (4) will be described. Depending on the size of the time constant used in the model equation, the imaging characteristics of the projection optical system 110 in one lot may differ depending on whether there is an error in the long time constant component or the short time constant component. The effect on the fluctuation of

  If there is an error in the predicted value at the start of exposure, the correction coefficient obtained from the predicted value will also contain an error. As shown in each of FIGS. 8A and 8B, the long time constant is 200 seconds, and the short time constant is 5000 seconds. In FIGS. 8A and 8B, the vertical axis indicates the focus of the projection optical system 110, and the horizontal axis indicates the time. The true correction coefficient is 100 nm for both the long time constant and the short time constant, and the error of the correction coefficient is 50 nm for both the long time constant and the short time constant. As is clear from FIGS. 8A and 8B, it can be seen that a short time constant has a larger influence on the prediction error amount in one lot.

  Therefore, as described above, it is necessary to set the weighting factor according to the size of the time constant. The evaluation amount V corresponds to the influence degree of the prediction error in a predetermined exposure period by the correction coefficient (correction coefficient including an error) obtained in S5 in consideration of the influence of the time constant. Therefore, since the larger the value is, the easier it is to give an error, it can be judged that the reliability of the correction coefficient is low.

  Returning to FIG. 6, in S8, when the first evaluation value is less than the second evaluation value, the process proceeds to S9. In this case, the correction coefficient (first coefficient) obtained in S5 is more reliable than the correction coefficient (second coefficient) stored in the exposure apparatus 1. Therefore, in S9, using the correction coefficient obtained in S5 as a temporary coefficient, the correction coefficient used in the model equation, that is, the correction coefficient stored in the exposure apparatus 1 is updated (fourth step). However, since the correction coefficient obtained in S5 does not satisfy the condition in S6, it is a temporary correction coefficient. Therefore, when performing exposure under the same exposure conditions next time, exposure is performed using the correction coefficient updated in S9 or the correction coefficient acquired in S1. In S9, along with the update of the correction coefficient, the evaluation value is also updated to the evaluation value (first evaluation value) of the correction coefficient (first coefficient) obtained in S5.

  In S8, when the first evaluation value is equal to or greater than the second evaluation value, the process proceeds to S1 without updating the correction coefficient used in the model equation (fourth step).

  Thus, in the present embodiment, it is possible to efficiently improve the accuracy of the correction coefficient by adopting a highly reliable correction coefficient while shortening the cooling time. Further, in the exposure, the fluctuation of the imaging characteristic of the projection optical system 110 is predicted from the model equation in which the correction coefficient is determined in this manner (determination step). Then, based on fluctuations in the imaging characteristics of the projection optical system 110, the imaging characteristics of the projection optical system 110 are adjusted by the aperture driving unit 112 and the lens driving unit 113 and the position of the substrate 115 is changed to expose the substrate 115. Do (exposure step). Such an exposure method also constitutes one aspect of the present invention.

  The method of manufacturing an article according to the embodiment of the present invention is suitable for manufacturing an article such as a device (semiconductor element, magnetic storage medium, liquid crystal display element, etc.), for example. Such a manufacturing method includes a step of exposing a substrate coated with a photosensitive agent and a step of developing the exposed substrate using the exposure apparatus 1 (the exposure method described above). In addition, such a manufacturing method may include other known steps (oxidation, film formation, deposition, doping, planarization, etching, resist peeling, dicing, bonding, packaging, etc.). The method for manufacturing an article in the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article as compared with the conventional method.

  The present invention supplies a program that implements one or more functions of the above-described embodiments to a system or apparatus via a network or a storage medium, and one or more processors in a computer of the system or apparatus read the program. It can also be realized by processing to be executed. It can also be realized by a circuit (for example, ASIC) that realizes one or more functions.

  Although the preferred embodiments of the present invention have been described above, it goes without saying that the present invention is not limited to these embodiments, and various modifications and changes can be made within the scope of the present invention.

1: Exposure apparatus 109: Mask 110: Projection optical system 115: Substrate 125: Main controller

Claims (10)

In an exposure apparatus for transferring a mask pattern onto a substrate via a projection optical system, a determination method for determining a coefficient indicating a saturation value of the imaging characteristic used in a model expression representing a fluctuation of an imaging characteristic of the projection optical system There,
Based on a plurality of measurement values obtained by measuring the imaging characteristics a plurality of times and a predicted value of the imaging characteristics at the start of exposure of the substrate obtained from the model equation, A first step for obtaining a first coefficient indicating a saturation value;
A second step of determining whether a difference between the first coefficient and a second coefficient indicating a saturation value of the imaging characteristic used in the model formula stored in the exposure apparatus is within an allowable range; ,
A third step of updating the coefficients such that the first coefficient is used in the model equation if the difference is within the tolerance range;
The first evaluation value of the first coefficient obtained from the predicted value when the difference is not within the allowable range, and the imaging characteristics obtained from the model equation when the second coefficient is obtained Comparing the second evaluation value of the second coefficient obtained from the predicted value, and updating the coefficient using the first coefficient as a temporary coefficient if the first evaluation value is less than the second evaluation value; If the first evaluation value is greater than or equal to the second evaluation value, a fourth step not updating the coefficient;
A determination method characterized by having: The model formula includes a plurality of time constants,
Each of the first evaluation value and the second evaluation value includes an absolute value of a linear sum of a weighting coefficient set to each of the plurality of time constants and the predicted value. Determination method described in.   The method according to claim 1, wherein the second evaluation value is stored in the exposure apparatus.   In the fourth step, if the first evaluation value is less than the second evaluation value, the second evaluation value is updated using the first evaluation value as a temporary evaluation value. Described method of description. The model equation is an exposure model equation representing the fluctuation of the imaging characteristics while the exposure device is exposing the substrate, and the imaging characteristics after the exposure device completes the exposure of the substrate. Including a non-exposure model formula representing variation,
The determination method according to any one of claims 1 to 4, wherein the predicted value is determined using the non-exposure model equation in the first step.   The determination method according to any one of claims 1 to 5, wherein the imaging characteristic includes at least one of focus, magnification, distortion, astigmatism, and wavefront aberration. An exposure method for exposing the substrate using an exposure apparatus that transfers a mask pattern to the substrate via a projection optical system,
A determination step of determining a coefficient indicating a saturation value of the imaging characteristic used in a model expression representing a variation of the imaging characteristic of the projection optical system;
The adjustment of the imaging characteristic of the projection optical system or the change of the position of the substrate is performed based on the fluctuation of the imaging characteristic of the projection optical system obtained from the model equation whose coefficient is determined, and the substrate is exposed. And an exposure process,
The determination step
Based on a plurality of measurement values obtained by measuring the imaging characteristics a plurality of times and a predicted value of the imaging characteristics at the start of exposure of the substrate obtained from the model equation, A first step for obtaining a first coefficient indicating a saturation value;
A second step of determining whether a difference between the first coefficient and a second coefficient indicating a saturation value of the imaging characteristic used in the model formula stored in the exposure apparatus is within an allowable range; ,
A third step of updating the coefficients such that the first coefficient is used in the model equation if the difference is within the tolerance range;
The first evaluation value of the first coefficient obtained from the predicted value when the difference is not within the allowable range, and the imaging characteristics obtained from the model equation when the second coefficient is obtained Comparing the second evaluation value of the second coefficient obtained from the predicted value, and updating the coefficient using the first coefficient as a temporary coefficient if the first evaluation value is less than the second evaluation value; If the first evaluation value is greater than or equal to the second evaluation value, a fourth step not updating the coefficient;
An exposure method comprising:   An information processing apparatus that executes the determination method according to any one of claims 1 to 6.   A program for causing an information processing apparatus to execute the determination method according to any one of claims 1 to 6. Exposing the substrate using the exposure method according to claim 7;
Developing the exposed substrate;
Producing an article from the developed substrate;
A method for producing an article comprising:

Images