KR20180129625A - Determination method, exposure method, information processing apparatus, program, and article manufacturing method - Google Patents

Abstract

The purpose of the present invention is to provide a determination method which is favorable in the determination of a coefficient indicating saturated values of the imaging properties used in a model formula showing variations in imaging properties of a projection optical system. According to the present invention, the determination method determines the coefficient indicating the saturated values of the imaging properties used in the model formula showing variations in the imaging properties of the projection optical system in an exposure apparatus for transferring patterns of a mask to a substrate through the projection optical system. The determination method comprises: a first process of obtaining a first coefficient indicating the saturated values of the imaging properties based on a plurality of measurement values obtained by measuring the imaging properties a plurality of times, and prediction values of the imaging properties in initiating light exposure of the substrate obtained from the model formula; a second process of determining whether a difference between the first coefficient and a second coefficient indicating the saturated values of the imaging properties used in the model formula memorized in the exposure apparatus is within an allowable range or not; a third process of renewing the coefficient so that the first coefficient is used in the model formula when the difference is within the allowable range; and a fourth process of comparing a first evaluation value of the first coefficient obtained from the prediction values with a second evaluation value of the second coefficient obtained from the prediction values of the imaging properties obtained from the model formula in obtaining the second coefficient, when the difference is not within the allowable range, and, if the first evaluation value is less than the second evaluation value, renewing the coefficient by using the first coefficient as a temporary coefficient, and if the first evaluation value is not less than the second evaluation value, not renewing the coefficient.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an information processing method, an information processing method, an information processing method, a determination method, an exposure method, an information processing apparatus,

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

There has been used an exposure apparatus for projecting (reducing projection) a pattern of a mask (reticle) onto a substrate coated with a resist (photosensitive agent) and transferring the pattern of the mask (reticle) when manufacturing a fine semiconductor device such as an LSI or a super LSI. As the mounting density of the semiconductor device is improved, the pattern is further required to be finer, and with the development of the resist process, the resolution of the exposure apparatus is being improved. As a technique for improving the resolving power of the exposure apparatus, there are a shortening of the wavelength of exposure light and an increase in the numerical aperture (NA) of the projection optical system. However, when the resolution is improved in this way, since the depth of focus of the projection optical system becomes shallow, it is important to improve the focus accuracy of fitting the surface of the substrate to the image plane (focal plane) of the projection optical system.

As one of the important performances of the exposure apparatus, there is a superposition accuracy of each pattern transferred to the substrate through a plurality of processes. The imaging characteristics (focus, magnification, distortion aberration, astigmatism, wavefront aberration, etc.) of the projection optical system are important factors affecting the superposition accuracy. In recent years, the pattern used in the super LSI tends to become finer, and there is a growing demand for improvement in superimposing accuracy.

In the exposure apparatus, when the exposure is repeated, the projection optical system absorbs a part of the energy of the exposure light and is heated. Thereafter, heat radiation causes variation in the imaging characteristics of the projection optical system (thermal aberration and exposure aberration). Such fluctuation of the imaging characteristic of the projection optical system causes a factor of lowering the overlapping accuracy. Therefore, a technique for compensating for the fluctuation of the imaging characteristic of the projection optical system by the irradiation of the exposure light to the projection optical system has been proposed in Japanese Patent Application Laid-Open Nos. 63-16725 and 2828226.

For example, Japanese Unexamined Patent Publication No. 63-16725 discloses a method of calculating a variation amount of an imaging characteristic of a projection optical system by a model formula using exposure amount, exposure time, and non-exposure time as parameters, (Adjustment) of the imaging characteristic of the optical system is disclosed. Such a model expression has a correction coefficient unique to the projection optical system for every imaging characteristic, and the correction coefficient changes depending on the light source distribution formed on the pupil plane of the projection optical system. For this reason, Japanese Patent No. 2828226 proposes a technique capable of satisfactorily correcting variations in imaging characteristics even when the distribution of light sources formed on the pupil plane of the projection optical system changes. In Japanese Patent No. 2828226, a correction coefficient corresponding to each light source distribution formed on the pupil plane of the projection optical system is stored. When the light source distribution is changed, a correction coefficient corresponding to such light source distribution is read, The variation amount of the imaging characteristic of the optical system is calculated.

In the prior art, in order to predict the fluctuation of the imaging characteristic of the projection optical system during exposure, the imaging characteristic of the projection optical system is measured a plurality of times during exposure, and a correction coefficient is obtained from the measurement result. When the exposure is performed under the same exposure conditions (illumination mode, mask, etc.) after calculating the correction coefficient, the imaging characteristic of the projection optical system is not measured during exposure, and the variation of the projection optical system is predicted using the correction coefficient.

However, when the imaging characteristic of the projection optical system is measured plural times during exposure, if the influence of the exposure aberration caused by the exposure immediately before the projection optical system remains in the projection optical system, a correction coefficient including an error is obtained. Therefore, before the correction coefficient is obtained, that is, before the imaging characteristic of the projection optical system is measured plural times during exposure, sufficient cooling (waiting) time for excluding the influence of the exposure aberration must be ensured, and the productivity is lowered.

The present invention provides a determination method advantageous for determining a coefficient indicating a saturation value of an imaging characteristic used in a model equation that expresses a variation in the imaging characteristic of a projection optical system.

A determination method as one aspect of the present invention is a method of determining a coefficient representing a saturation value of the imaging characteristic used in a model expression that represents fluctuation of the imaging characteristic of the projection optical system in an exposure apparatus that transfers a pattern of a mask onto a substrate via a projection optical system The method comprising the steps of: determining, based on a plurality of measured values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model formula, And a second coefficient indicating a saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus is within an allowable range A second step of determining whether or not the difference is in the allowable range, A third step of updating the coefficient to be used in the model equation; and a third step of, when the difference does not fall within the allowable range, obtaining the first evaluation value and the second coefficient of the first coefficient obtained from the predicted value The second evaluation value of the second coefficient obtained from the predicted value of the imaging characteristic obtained from the model expression is compared with the first evaluation value, and when the first evaluation value is less than the second evaluation value, And a fourth step of updating the coefficient and not updating the coefficient if the first evaluation value is equal to or more than the second evaluation value.

Other objects or other aspects of the present invention will be apparent from the following description of preferred embodiments with reference to the accompanying drawings.

1 is a schematic view showing a configuration of an exposure apparatus.
Fig. 2 is a view showing an example of variation of aberration of the projection optical system. Fig.
Fig. 3 is a diagram showing an example of variation of aberration of the projection optical system. Fig.
4 is a diagram showing an example of variation of aberration of the projection optical system.
5A and 5B are diagrams for explaining the reason why correction coefficients can not be obtained accurately.
Fig. 6 is a flowchart for explaining a determination method as one aspect of the present invention.
7 is a diagram showing an example of a predicted value of the imaging characteristic (focus) of the projection optical system.
8A and 8B are diagrams for explaining weighting coefficients.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. In the drawings, the same reference numerals are used to denote the same members, and redundant explanations are omitted.

1 is a schematic view showing a configuration of an exposure apparatus 1. Fig. The exposure apparatus 1 exposes a substrate. Specifically, the exposure apparatus 1 is a lithography apparatus that transfers a pattern of a mask (reticle) to a substrate via a projection optical system in a step-and-scan manner. However, the exposure apparatus 1 may employ a step-and-repeat method or other exposure method.

The exposure apparatus 1 includes an illumination optical system 104 for illuminating a mask 109 using light from a light source unit 101, a projection optical system 110, a substrate stage 116). The exposure apparatus 1 also has an opening drive 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 . The exposure apparatus 1 further includes a light source control unit 102, a lighting 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 an out-of-atom region having a wavelength of about 248 nm. The light source unit 101 also includes a narrow-talk module, a monitor module, a shutter, and the like. The negotiating module is composed of a front mirror constituting a resonator, a diffraction grating for narrowing the wavelength (exposure wavelength), a prism, and the like, and the monitor module is constituted by a spectroscope and a detector for monitoring the stability of the wavelength and the spectrum width .

The light source control unit 102 controls the gas exchange operation in the light source unit 101, the wavelength stabilization operation of the light emitted from the light source unit 101, the discharge application voltage in the light source unit 101, and the like. In the present embodiment, the light source control unit 102 controls the light source unit 101 under the control of the main control unit 125, instead of controlling the light source unit 101 alone.

The light emitted from the light source unit 101 is incident on 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). This optical integrator forms a plurality of secondary light sources in order to illuminate the mask 109 with a uniform illumination distribution.

The aperture stop 105 included in the illumination optical system 104 has an opening of a substantially circular shape. The illumination control unit 108 controls the illumination optical system 104 so that the diameter of the aperture of the aperture stop 105 and the numerical aperture NA of the illumination optical system 104 become a predetermined value under the control of the main control unit 125. [ Respectively. Since the value of 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 (sigma value), the illumination control unit 108 controls the aperture stop 105, The σ value can be adjusted (set).

On the optical path of the illumination optical system 104, a half mirror 106 for reflecting (extracting) a part of the light illuminating the mask 109 is disposed. On the optical path of the light reflected by the half mirror 106, a photosensor 107 for ultraviolet light is disposed. The photosensor 107 generates an output corresponding to the intensity of the light illuminating the mask 109 (i.e., the exposure energy). The output of the photosensor 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 output 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 in a mask stage (not shown). The mask stage holds the mask 109 and moves in the three-dimensional direction (in the direction of the optical axis of the projection optical system 110 and in the plane orthogonal to the optical axis) using, for example, a linear motor or the like. The pattern of the mask 109 is transferred to the substrate 115 by scanning the mask 109 and the substrate 115 because the exposure apparatus 1 employs the step-and-scan method.

The projection optical system 110 includes a plurality of optical elements (lenses and the like) and reduces the pattern of the mask 109 to a predetermined reduction magnification? (For example,? = 1/4) In a short region of the screen.

On the pupil plane (the Fourier transform plane with respect to the mask 109) of the projection optical system 110, an aperture stop 111 having an approximately circular opening is disposed. The aperture drive unit 112 includes a motor and the like and drives the aperture stop 111 so that the diameter of the aperture of the aperture stop 111 becomes a predetermined value. The lens driving unit 113 uses an air pressure, a piezoelectric element, or the like to drive an optical element constituting the projection optical system 110, in this embodiment, a part of the lens (for example, a field lens) In the direction of the optical axis. The projection control section 114 controls the aperture drive section 112 and the lens drive section 113 under the control of the main control section 125. [ In the present embodiment, the fluctuation of various aberrations of the projection optical system 110 is reduced by driving the lenses constituting the projection optical system 110, and the magnification (projection magnification) is well maintained to reduce the distortion error.

The substrate 115 is a substrate on which a pattern of the mask 109 is projected (transferred). The substrate 115 is coated with a photoresist (photosensitive agent). The substrate 115 includes a wafer, a glass plate, and other substrates.

The substrate stage 116 holds the substrate 115 and moves in the three-dimensional direction (within the plane of the optical axis of the projection optical system 110 and in the plane orthogonal to the optical axis) using, for example, a linear motor or the like. The position of the substrate stage 116 in the plane orthogonal to the optical axis of the projection optical system 110 is detected by measuring the distance to the moving mirror 117 fixed on the substrate stage 116 by the laser interferometer 118 . 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 To a predetermined position).

The 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 direction of the optical axis of the projection optical system 110 (that is, the height of the surface of the substrate 115). The projection optical system 121 emits light (non-exposure light) that does not sensitize the photoresist applied to the substrate 115, and condenses it at each position on the substrate 115. Light reflected at each position of the substrate 115 is incident on the detection optical system 122. A plurality of photodetecting elements for position detection are disposed in the detecting optical system 122 in correspondence with the light reflected at each position of the substrate 115. [ Specifically, the plurality of light-receiving elements are arranged so that the light-receiving surface of each light-receiving element and the reflection point on the substrate 115 are substantially conjugate with each other via the imaging optical system. Therefore, the positional deviation of the substrate 115 in the direction of the optical axis of the projection optical system 110 is detected as the positional deviation of the light incident on the respective light-receiving elements arranged in the detection optical system 122. [

The measuring unit 123 is disposed on the upper surface side of the projection optical system 110, in this embodiment, on the substrate stage 116. [ The measuring unit 123 detects the light passing through the projection optical system 110 and measures the imaging characteristic of the projection optical system 110. The measuring section 123 includes, for example, a light shielding plate having a pinhole for passing light from the projection optical system 110, and a photoelectric conversion element for detecting light passing through the pinhole.

The main control unit 125 is constituted by a computer (information processing apparatus) including a CPU, a memory and the like and is connected to a light source control unit 102, a lighting control unit 108, a projection control unit 114, a stage control unit 120, , And controls the entire exposure apparatus 1 (each section of the exposure apparatus 1). Further, in the present embodiment, the main control unit 125 can also have a function of determining a correction coefficient used in a model expression that expresses fluctuation of the imaging characteristic of the projection optical system 110, as will be described later.

Here, a model expression for expressing the fluctuation of the imaging performance of the projection optical system 110 by the irradiation of the exposure light, and a correction coefficient for compensating the fluctuation of the imaging characteristic for each exposure condition used for quantifying the model expression . In this embodiment, it is assumed that the imaging characteristic of the projection optical system 110 includes at least one of focus, magnification, distortion aberration, astigmatism, spherical aberration, coma aberration, and wavefront aberration. Further, the wavefront aberration can be expressed as each term developed in the Zernike polynomial, as is well known in the art. In some cases, these are collectively referred to as " aberration ".

Fig. 2 is a view showing an example of a variation (a change with time) of the aberration of the projection optical system 110. Fig. 2, the horizontal axis represents time t, and the vertical axis represents aberration amount F at a certain elevation of the projection optical system 110. In FIG. ? F represents the aberration variation amount of the projection optical system 110, and the aberration variation amount? F is different for each image height. In addition, the initial number (before exposure) of the projection optical system 110 is F0.

Referring to Fig. 2, when the exposure starts from the time t0, the aberration fluctuates with the elapse of time, and is stabilized at a constant number of vehicles (maximum variation) F1 at time t1. Even after the time t1, even when light (exposure light) enters 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 , The aberration amount does not change from F1. Then, when the exposure ends at time t2, the aberration returns to the initial state with the passage of time, and becomes the initial number vehicle F0 at time t3.

The time constant TS1 shown in Fig. 2 is the time constant of the heat transfer characteristic of the projection optical system 110. Fig. 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 also for each aberration of the projection optical system 110, for example, during maintenance of the exposure apparatus 1.

The maximum variation F1 of the aberration shown in Fig. 2 is obtained by using the aberration variation amount K per unit light amount (unit exposure energy) and the actual exposure energy Q determined from parameters such as exposure time, exposure amount, scanning speed, (1).

F1 = K x Q ... (One)

The number of vehicles at a certain time is _denoted by? F _k . In this case, in the state in which exposure is performed, the aberration amount? F _{k + 1} after elapse of the time? T from a certain time is approximated by the following formula (2) using the maximum variation amount F1 and the time constant TS1. Likewise, in the state in which no exposure is performed, the aberration amount? F _{k + 1} after elapse of time? T from a certain time is approximated by the following expression (3).

? F _{k + 1} =? F _k + F ₁ (1-exp (-Δt / TS 1)) (2)

? F _{k + 1} =? F _k × exp (-Δt / TS ₁ ) (3)

The variation of the aberration of the projection optical system 110 shown in Fig. 2 (the curve shown in Fig. 2) is modeled by using the equations (1), (2) and (3). However, the formulas (1), (2) and (3) are only examples in this embodiment, and may be modeled by using other formulas.

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

The maximum variation F1 used in equation (2) represents the saturation value of the aberration of the projection optical system 110, which is a correction coefficient 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 expressions having different time constants.

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

When the exposure conditions are changed, the energy density distribution of the light (exposure light) incident on the projection optical system 110 changes, so the aberration variation amount of the projection optical system 110 and its dependence on the image height change. 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 illuminating the mask 109, and the like.

A case is considered in which correction coefficients are obtained for different exposure conditions, for example, the first exposure condition and the second exposure condition. In this case, in order to obtain the correction coefficient with high accuracy, a sufficient cooling (waiting) time can be ensured until the influence of the residual aberration under the different exposure conditions is eliminated, for example, as shown in Fig. However, by providing a cooling time, productivity is lowered. 3 is a diagram showing an example of variation of the aberration of the projection optical system 110. As shown in Fig. 3, the horizontal axis represents time, and the vertical axis represents aberration (aberration) of the projection optical system 110. In 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 The variation of the aberration is indicated.

The formulas (1) to (3) also hold between other exposure conditions. Therefore, for example, as shown in Fig. 4, if the correction coefficient in the immediately preceding job for the first exposure condition is accurately obtained, the correction coefficient in each exposure condition can be accurately obtained even if the cooling time is omitted . However, if there is an error in the correction coefficient in the immediately preceding job of the first exposure condition, as shown in Fig. 4, if the cooling time is omitted, the correction coefficient in each exposure condition can not be obtained accurately. 4 is a diagram showing an example of variation of the aberration of the projection optical system 110. Fig. In Fig. 4, the horizontal axis represents time, and the vertical axis represents aberration (aberration) 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 in each of the first exposure condition, the second exposure condition, and the third exposure condition.

Here, the reason why the correction coefficient in an exposure condition can not be accurately obtained when there is an error in the correction coefficient in a job immediately before an exposure condition will be described. First, for ease of understanding, the case where there is no error in the correction coefficient in the immediately preceding job will be described.

Here, for example, the imaging characteristic of the projection optical system 110 during the exposure of one lot, more specifically, the focus is measured plural times, and the exposure time of one lot is set to 400 seconds. The time constant TS1 is set to one type and is set to 200 seconds. At the start of exposure (t = 0), the predicted value of the focus of the projection optical system 110 by the previous job is 15 nm. Since these predicted values are predicted using the equations (1) to (3), if there is no error in the correction coefficients, there is no error in the predicted values at the start of exposure. 5A shows measured values when the focus of the projection optical system 110 is actually measured at the start of exposure.

Assuming that the predicted value at a certain time after exposure is DELTA F2 and the predicted value at the next time after exposure is DELTA F3, the exposure model equation and the non-exposure model equation are selected by using equations (2) and , The following equation is obtained.

? F2 =? F1 + F1 (1-exp (-Δt / TS1))

? F3 =? F2 (1-exp (-Δt / TS1))

The correction coefficient (maximum variation F1) is obtained by substituting ΔF1 = 15 nm into this equation and fitting the plurality of measurement values obtained by measuring the focus of the projection optical system 110 a plurality of times. In this case, the correction coefficient is 100 nm.

Next, a case is considered where there is an error in the correction coefficient in the immediately preceding job, that is, when there is an error (prediction error) in the predicted value at the start of exposure. Assuming that 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 on the solid line curve in Fig. In this case, since? F1 = 30 nm is substituted for the above formula, the correction coefficient is 115 nm.

For these other correction coefficients, equation (2) when? F1 = 0 is shown in Fig. 5B. As apparent from Fig. 5B, when there is a prediction error, a correction coefficient including an error is obtained, so that a curve having a large change with respect to the true correction coefficient is obtained. In this way, when there is a prediction error, as a result, a wrong correction coefficient is obtained.

Therefore, in the present embodiment, in the determination method for determining the correction coefficient used in the model expression that expresses the fluctuation of the imaging characteristic of the projection optical system 110, there is a method of stepping up the accuracy of the correction coefficient while shortening the cooling time .

FIG. 6 is a flowchart for explaining a determination method for determining a correction coefficient used in a model expression that represents a variation in imaging characteristic of the projection optical system 110 in the present embodiment. This determination method can be executed by the main control unit 125 or by an information processing apparatus outside the exposure apparatus 1. [

(Second coefficient) corresponding to the exposure condition of the exposure performed in the exposure apparatus 1 in step S1. These correction coefficients are stored in advance in the exposure apparatus 1 (the memory of the main control unit 125 and the memory of the exposure apparatus 1).

S2, a predicted value of the imaging characteristic of the projection optical system 110 at the start of exposure is obtained. This predicted value corresponds to the residual of the fluctuation of the imaging characteristic of the projection optical system 110 in the exposure prior to the present exposure (exposure to be performed from now). 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 exposure acquired in S2 becomes close to zero. However, in the present embodiment, in order to shorten the cooling time, the predicted value of the imaging characteristic of the projection optical system 110 at the start of exposure acquired in S2 is not zero.

In S3, exposure is started. In S4, while the exposure apparatus 1 is performing exposure of the substrate 115, the imaging characteristics of the projection optical system 110 are measured a plurality of times to acquire a plurality of measured values. For example, as described above, the measuring unit 123 measures the imaging characteristic of the projection optical system 110 a plurality of times (for example, when the substrate 115 is exchanged) between exposure and exposure of one lot do.

(1) to (3) on the basis of the predicted value of the imaging characteristic of the projection optical system 110 at the start of exposure acquired at S2 and the plurality of measured values acquired at S4 in S5 A correction coefficient (first coefficient) is obtained (first step).

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

The correction coefficient (first coefficient) obtained in S5 is set in the exposure apparatus 1 in S7, that is, the correction coefficient obtained in S5 is stored in the exposure apparatus 1 Second coefficient) (third step). Accordingly, when the exposure is performed under the same exposure conditions, the imaging characteristic of the projection optical system 110 is predicted using the correction coefficient obtained in S5 without measuring the imaging characteristic of the projection optical system 110 plural times (S4) It is possible to perform exposure. Therefore, it is not necessary to measure the imaging characteristic of the projection optical system 110 a plurality of times in one lot exposure, so that it is possible to suppress deterioration of the throughput.

(Second coefficient) obtained from the predictive value obtained from the model equation when obtaining the first evaluation value of the correction coefficient (first coefficient) obtained from the predictive value obtained in S2 and the correction coefficient obtained in S1 in S8, Compare the values. In the present embodiment, it is determined whether the first evaluation value is less than the second evaluation value and whether the first evaluation value is greater than or equal to the second evaluation value. At this time, the second evaluation value is stored in advance in the exposure apparatus 1 in association with the correction coefficient (second coefficient) acquired in S1.

More specifically, the evaluation value indicating the reliability of the correction coefficient is a value obtained by subtracting the predicted value? F1 at the start of exposure and the predicted value? Is obtained by? F1. Specifically, the evaluation value V is expressed by the absolute value of the linear sum of the weighting coefficient set for each of the plurality of time constants and the predicted value? F1, as shown in the following equation (4).

V = | ΔF1_TS1 × weight_TS1 + ΔF1_TS2 × weight_TS2 + ΔF1_TS3 × weight_TS3 | (4)

Since the predicted value? F1 is predicted from the fluctuation of the imaging characteristic of the projection optical system 110 in the previous exposure condition using the equation (3), a predicted value is obtained for each time constant. These predicted values are? F1_TS1,? F1_TS2 and? F1_TS3. In this case, the time constant is assumed to be three types. Further, the weight_TS1, the weight_TS2, and the weight_TS3 are weighting factors preset in the exposure apparatus 1 for each time constant.

Here, a case where an error (prediction error) exists in the predicted value? F1 is considered. The predicted value? F1 is predicted using equation (3) in the immediately preceding job. FIG. 7 shows the case where the predicted value? F1 has a prediction error and the case where the predicted value? F1 has no prediction error. In Fig. 7, the vertical axis represents the focus of the projection optical system 110, and the horizontal axis represents time. From the characteristics of the equation (3), the prediction error A depends on the prediction value B when there is a prediction error, and as the prediction value B becomes smaller, the prediction error A also becomes smaller. By providing a sufficient cooling time, the predicted value B can be infinitely close to zero. Accordingly, the prediction error A also becomes zero, and when the correction coefficient is obtained from this state, the correction coefficient does not include an error.

The weighting coefficient in the equation (4) will be described. In the case where there is an error in a component with a long time constant and in a case where there is an error in a component with a short time constant, the influence of variation in the imaging characteristic of the projection optical system 110 in one lot The effects are different.

If there is an error in the predicted value at the start of exposure, the correction coefficient obtained from such a predicted value also includes an error. As shown in Figs. 8A and 8B, the long time constant is set to 200 seconds and the short time constant is set to 5000 seconds. 8A and 8B, the vertical axis represents the focus of the projection optical system 110, and the horizontal axis represents time. The true correction coefficient is set to 100 nm in both the long time constant and the short time constant, and the error of the correction coefficient is set to 50 nm in both the long time constant and the short time constant. As can be seen from Figs. 8A and 8B, it can be seen that the prediction error in one lot has a large effect on the short time constant.

Therefore, as described above, it is necessary to set a weighting factor according to the size of the time constant. The evaluation amount V corresponds to the influence of the prediction error in the predetermined exposure period by the correction coefficient (correction coefficient including the error) obtained in S5 in consideration of the influence of the time constant. Therefore, the larger the value, the easier the error is to be made, so that the reliability of the correction coefficient can be judged to be 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 higher than the correction coefficient (second coefficient) stored in the exposure apparatus 1. Therefore, in S9, the correction coefficient used in the model expression, that is, the correction coefficient stored in the exposure apparatus 1, is updated with the correction coefficient obtained in S5 as a temporary coefficient (fourth step). However, since the correction coefficient obtained in S5 does not satisfy the condition in S6, it becomes a temporary correction coefficient. Therefore, when exposure is performed under the same exposure conditions, exposure is performed using the correction coefficient updated in S9 or the correction coefficient obtained in S1. In step S9, the evaluation value is updated to the evaluation value (first evaluation value) of the correction coefficient (first coefficient) obtained in S5, along with the update of the correction coefficient.

If the first evaluation value is equal to or larger than the second evaluation value in S8, the correction coefficient used in the model expression is not updated, and the process proceeds to S1 (fourth process).

In this way, in the present embodiment, the accuracy of the correction coefficient can be efficiently improved by employing the correction coefficient with high reliability while reducing the cooling time. Further, in exposure, the fluctuation of the imaging characteristic of the projection optical system 110 is predicted from the model equation (correction process) in which correction coefficients are determined in this manner. The aperture driving unit 112 and the lens driving unit 113 adjust the imaging characteristics of the projection optical system 110 and change the position of the substrate 115 based on the fluctuation of the imaging characteristics of the projection optical system 110 , And exposes the substrate 115 (exposure step). Such an exposure method constitutes one aspect of the present invention.

The method of manufacturing an article in the embodiment of the present invention is suitable for producing articles such as devices (semiconductor devices, magnetic storage media, liquid crystal display elements, etc.). Such a manufacturing method includes a step of exposing a substrate coated with a photosensitizer using a light exposure apparatus 1 (the above-described exposure method), and a step of developing the exposed photosensitizer. Further, a circuit pattern is formed on the substrate by performing an etching process, an ion implantation process, and the like on the substrate using the pattern of the developed photosensitive agent as a mask. These steps of exposure, development, etching, and the like are repeated to form a circuit pattern composed of a plurality of layers on the substrate. In a later step, the substrate on which the circuit pattern is formed is subjected to dicing, and chip mounting, bonding, and inspecting steps are performed. Such a manufacturing method may also include other known processes (oxidation, deposition, deposition, doping, planarization, resist stripping, etc.). The method of manufacturing an article in the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article, compared with the conventional method.

(Other Embodiments)

The present invention can be realized by supplying a program or a program for realizing one or more functions of the above embodiments to a system or an apparatus via a network or a storage medium and by reading one or more programs in the computer of the system or apparatus It is also possible to execute the processing. Further, it can be realized by a circuit (for example, an ASIC) that realizes one or more functions.

Although the preferred embodiments of the present invention have been described above, it is needless to say that the present invention is not limited to these embodiments, and various modifications and changes are possible within the scope of the present invention.

Claims (10)

There is provided a determination method for determining a coefficient indicating a saturation value of the imaging characteristic used in a model equation representing variation in imaging characteristics of the projection optical system in an exposure apparatus that transfers a pattern of a mask onto a substrate via a projection optical system,
A first coefficient indicating a saturation value of the imaging characteristic on the basis of a plurality of measured values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation, A first step of obtaining a first-
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 equation stored in the exposure apparatus falls within an allowable range,
A third step of updating the coefficient so that the first coefficient is used for the model expression when the difference falls within the allowable range;
Which is obtained from the predicted value of the imaging characteristic obtained from the model expression when the second coefficient is obtained and the first evaluation value of the first coefficient obtained from the predictive value when the difference does not fall within the allowable range, The first evaluation value is compared with the second evaluation value of the coefficient to update the coefficient with the first coefficient as a temporary coefficient when the first evaluation value is less than the second evaluation value, Value, the fourth step of not updating the coefficient.
The method according to claim 1,
The model equation includes a plurality of time constants,
Wherein each of the first evaluation value and the second evaluation value includes an absolute value of a linear sum of the weighting coefficient set for each of the plurality of time constants and the predicted value.
3. The method according to claim 1 or 2,
And the second evaluation value is stored in the exposure apparatus.
The method of claim 3,
And in the fourth step, when the first evaluation value is less than the second evaluation value, the second evaluation value is updated with the first evaluation value as a temporary evaluation value.
The method according to claim 1,
Wherein the model formula includes an exposure model expression that indicates a variation of the imaging characteristic while the exposure apparatus is performing exposure of the substrate and a exposure model expression that expresses a variation of the imaging characteristic after the exposure apparatus finishes exposure of the substrate Exposure model equation,
Wherein in the first step, the predicted value is obtained using the non-exposure model equation.
The method according to claim 1,
Wherein the imaging characteristic includes at least one of a focus, a magnification, a distortion aberration, an astigmatism, and a wavefront aberration.
An exposure method for exposing a substrate using an exposure apparatus that transfers a pattern of a mask onto a substrate via a projection optical system,
A determining step of determining a coefficient indicating a saturation value of the imaging characteristic used in a model equation representing a variation in imaging characteristic of the projection optical system;
And an exposure step of exposing the substrate by adjusting an imaging characteristic of the projection optical system or changing a position of the substrate on the basis of a fluctuation of an imaging characteristic of the projection optical system obtained from the model equation in which the coefficient is determined,
The above-
A first coefficient indicating a saturation value of the imaging characteristic on the basis of a plurality of measured values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation, A first step of obtaining a first-
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 equation stored in the exposure apparatus falls within an allowable range,
A third step of updating the coefficient so that the first coefficient is used for the model expression when the difference falls within the allowable range;
Which is obtained from the predicted value of the imaging characteristic obtained from the model expression when the second coefficient is obtained and the first evaluation value of the first coefficient obtained from the predictive value when the difference does not fall within the allowable range, The first evaluation value is compared with the second evaluation value of the coefficient to update the coefficient with the first coefficient as a temporary coefficient when the first evaluation value is less than the second evaluation value, Value, the coefficient is not updated.
There is provided an information processing apparatus for determining a coefficient indicating a saturation value of the imaging characteristic used in a model expression for expressing a variation in imaging characteristic of the projection optical system in an exposure apparatus for transferring a pattern of a mask onto a substrate via a projection optical system,
A first coefficient indicating a saturation value of the imaging characteristic on the basis of a plurality of measured values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation, Is obtained,
It is determined whether or not a difference between the first coefficient and a second coefficient indicating a saturation value of the imaging characteristic used in the model equation stored in the exposure apparatus falls within an allowable range,
Updating the coefficient so that the first coefficient is used in the model expression when the difference falls within the allowable range,
Which is obtained from the predicted value of the imaging characteristic obtained from the model expression when the second coefficient is obtained and the first evaluation value of the first coefficient obtained from the predictive value when the difference does not fall within the allowable range, The first evaluation value is compared with the second evaluation value of the coefficient to update the coefficient with the first coefficient as a temporary coefficient when the first evaluation value is less than the second evaluation value, Value, the coefficient is not updated.
A determination method for determining a coefficient indicating a saturation value of the imaging characteristic used in a model expression that represents a variation in imaging characteristic of the projection optical system in an exposure apparatus that transfers a pattern of a mask to a substrate via a projection optical system, A program stored in a medium for execution,
The program causes the information processing apparatus to execute:
A first coefficient indicating a saturation value of the imaging characteristic on the basis of a plurality of measured values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation, A first step of obtaining a first-
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 equation stored in the exposure apparatus falls within an allowable range,
A third step of updating the coefficient so that the first coefficient is used for the model expression when the difference falls within the allowable range;
Which is obtained from the predicted value of the imaging characteristic obtained from the model expression when the second coefficient is obtained and the first evaluation value of the first coefficient obtained from the predictive value when the difference does not fall within the allowable range, The first evaluation value is compared with the second evaluation value of the coefficient to update the coefficient with the first coefficient as a temporary coefficient when the first evaluation value is less than the second evaluation value, Value is equal to or greater than a predetermined value, the coefficient is not updated.
A determining step of determining a coefficient indicating a saturation value of the imaging characteristic used in a model equation representing a variation in imaging characteristic of a projection optical system for projecting a pattern of a mask onto a substrate;
An exposure step of adjusting the imaging characteristic of the projection optical system or changing the position of the substrate based on the variation of the imaging characteristic of the projection optical system obtained from the model formula in which the coefficient is determined,
Forming a pattern of the photosensitive agent by developing the photosensitive agent of the exposed substrate;
Forming a pattern on the substrate based on the developed pattern of the photosensitive agent, and processing the substrate on which the pattern is formed to produce an article,
The above-
A first coefficient indicating a saturation value of the imaging characteristic on the basis of a plurality of measured values obtained by measuring the imaging characteristic a plurality of times and a predicted value of the imaging characteristic at the start of exposure of the substrate obtained from the model equation, A first step of obtaining a first-
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 equation stored in the exposure apparatus falls within an allowable range,
A third step of updating the coefficient so that the first coefficient is used for the model expression when the difference falls within the allowable range;
Which is obtained from the predicted value of the imaging characteristic obtained from the model expression when the second coefficient is obtained and the first evaluation value of the first coefficient obtained from the predictive value when the difference does not fall within the allowable range, The first evaluation value is compared with the second evaluation value of the coefficient to update the coefficient with the first coefficient as a temporary coefficient when the first evaluation value is less than the second evaluation value, Value, the fourth step of not updating the coefficient.

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