JP2005064369A - Optimization method, exposure method, optimization device, exposure device, manufacturing method for device and program therefor, and information recording medium therefor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To optimize data selection used for a predetermined process. <P>SOLUTION: In a step 403, the reference vector map of a correction quantity vector when performing an EGA treatment by using all of the measured values of candidate marks on an EGA measuring shot region, is prepared; in a step 407, the vector map of the correction quantity vector when performing the EGA treatment for each of combinations excluding the portion of the number of expected skip shots, is prepared. Then, in a step 409, correlation coefficients between vector maps are calculated, and the combination that the correlation coefficient is lower than a threshold after a step 411 and also residual errors in the EGA treatment are reduced is employed as the combination of the shot region used for the EGA treatment. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to an optimization method, an exposure method, an optimization apparatus, an exposure apparatus, a device manufacturing method, a program, and an information recording medium, and an optimization method for optimizing selection of a plurality of data used for a predetermined process , An exposure method using the optimization method, an optimization device that optimizes selection of a plurality of data used in a predetermined process, an exposure device including the optimization device, the exposure method, and the exposure device The present invention relates to a device manufacturing method, a program for causing a computer to execute the optimization method, and an information recording medium on which the program is recorded.

  In a lithography process for manufacturing a semiconductor element, a liquid crystal display element, or the like, a wafer or glass on which a pattern formed on a mask or a reticle (hereinafter collectively referred to as “reticle”) is coated with a resist or the like via a projection optical system An exposure apparatus that transfers onto a substrate such as a plate (hereinafter collectively referred to as a “wafer”), such as a step-and-repeat reduction projection exposure apparatus (so-called stepper), or a step-and- A sequential movement type projection exposure apparatus (hereinafter abbreviated as “exposure apparatus”) such as a scanning scanning exposure apparatus (so-called scanning stepper) is mainly used.

  When manufacturing a semiconductor element or the like, different circuit patterns are stacked and formed on a wafer in several layers. However, if the overlay accuracy between the layers is poor, the circuit characteristics may be inconvenient. In such a case, the chip does not satisfy the desired characteristics, and in the worst case, the chip becomes a defective product, which decreases the yield. Therefore, in the exposure process, it is important to accurately superimpose and transfer the reticle on which the circuit pattern is formed and the pattern already formed on each shot area on the wafer.

  For this reason, in the exposure process, an alignment mark is previously attached to each of a plurality of shot areas on the wafer, and a stage coordinate system of the wafer stage on which the wafer is placed (a coordinate system that defines the movement of the wafer stage, Usually, the position (coordinate value) of the alignment mark on the laser interferometer (defined by the measuring axis) is detected. Thereafter, based on the position information of the mark and the position information of the projection position of the known reticle pattern (this is measured in advance), the positional relationship between each shot area and the projection position of the reticle pattern is obtained. (Wafer alignment measurement) is performed.

  There are roughly two types of wafer alignment. One is a die-by-die (D / D) alignment method in which alignment is detected by detecting an alignment mark for each shot area on the wafer. The other is a global alignment method in which each shot area is aligned by detecting alignment marks of only a few shot areas on the wafer and obtaining the regularity of the arrangement of the shot areas. At present, the global alignment method is mainly used in the device manufacturing line in consideration of the throughput. In particular, at present, an enhanced global alignment (EGA) method for accurately specifying the regularity of the arrangement of shot areas on a wafer by a statistical method has become mainstream (see, for example, Patent Document 1 and Patent Document 2). ).

  The EGA method measures the position coordinates of only a plurality of (three or more required, usually about 7 to 15) shot areas previously selected as specific shot areas on one wafer, and these measured values. After calculating the position coordinates (arrangement of shot areas) of all shot areas on the wafer using statistical calculation processing (such as least square method), the wafer stage is stepped according to the calculated arrangement of shot areas It is. This EGA method has the advantage that the measurement time is short and an averaging effect can be expected for random measurement errors.

Here, a statistical processing method performed by the EGA method will be briefly described. Design arrangement coordinates of m (an integer of m ≧ 3) specific shot areas (also called “sample shot areas” or “alignment shot areas”) on the wafer are (X _n , Y _n ) (n = 1, 2,..., M), and a linear model as shown in the following equation (1) is assumed with respect to the deviation (ΔX _n , ΔY _n ) from the design array coordinates.

さらに、ｍ個のサンプルショット領域の各々の実際の配列座標の設計上の配列座標からのずれ（計測値）を（Δｘ_n、Δｙ_n）としたとき、このずれと上記線形モデルで仮定される設計上の配列座標からのずれとの残差（フィッティング残差）の二乗和の平均Ｅは次式（２）で表される。

Further, when the deviation (measured value) of the actual arrangement coordinates of each of the m sample shot areas from the designed arrangement coordinates is (Δx _n , Δy _n ), this deviation is assumed in the linear model. The average E of the sum of squares of the residual (fitting residual) from the deviation from the design array coordinates is expressed by the following equation (2).

そこで、この式を最小にするようなパラメータａ、ｂ、ｃ、ｄ、ｅ、ｆを最小二乗法などの統計演算により求めれば良い。ＥＧＡ方式では、上記の如くして算出されたパラメータａ〜ｆと設計上の配列座標とに基づいて、ウエハ上の全てのショット領域のステージ座標系上の配列座標が算出されることになる。

Therefore, the parameters a, b, c, d, e, and f that minimize this equation may be obtained by statistical calculation such as the least square method. In the EGA method, the arrangement coordinates on the stage coordinate system of all shot areas on the wafer are calculated based on the parameters a to f calculated as described above and the arrangement coordinates on the design.

  By the way, in the above-mentioned EGA type wafer alignment, measurement values with extremely low accuracy may be mixed due to the influence of a mark defect or the like. In such a case, the influence of the measurement values with low accuracy is reduced. It is preferable to calculate the parameters a to f in order to accurately obtain the array coordinates of the shot area. Conventionally, the following method has been proposed as a method for reducing the influence of such an inaccurate measurement value.

  As a first method, a threshold value is set for the fitting residual from the calculated statistical model, measurement values whose absolute value is greater than or equal to the threshold value are excluded, and the model is calculated using only the remaining measurement values. There is a method of reworking (see, for example, Patent Document 3).

  As a second method, the number of exclusions is determined in advance, models are assumed as many as the number of combinations that form a set of (measured number−excluded number), and standard deviations (fitting residuals) of measured values corresponding to these models are assumed. ) Is an index value (for example, probability density function) of the probability of the model, and there is a method of adopting a model that takes a weighted average by the index value of the certainty (see, for example, Patent Document 4).

  However, in the first method, the fitting error itself used for threshold determination has already been affected by measurement values with poor accuracy, and the influence of measurement with poor accuracy on the calculation result can be completely eliminated. There is inconvenience that we cannot do it.

  In addition, considering the degree of variation in the absolute value of the fitting residual, it is necessary to set a larger value as the threshold, and there is a high probability that the measurement value that should originally be excluded may not be excluded, It becomes difficult to achieve effective processing.

  On the other hand, in the second method, there is no such difficulty in changing the threshold value, and qualitatively so-called jump shots (shot regions having a particularly large alignment error compared to alignment errors (measurement errors) of other shot regions). Can reduce the effects of However, in this second method, it is difficult to set a model, and if the model deviates from the actual one, the calculation result may be deteriorated.

Thus, in EGA, various methods have been proposed so far for properly excluding measurement marks to be excluded or optimizing the number and position of measurement marks used for calculation. No means has yet been found to comprehensively solve the above concerns.
JP-A 61-44429 JP-A-62-84516 JP-A-8-97123 International Publication No. 00/49367 Pamphlet

  The present invention has been made under such circumstances, and a first object thereof is to provide an optimization method capable of optimizing selection of data used for a predetermined process.

  A second object of the present invention is to provide an exposure method capable of realizing highly accurate exposure.

  A third object of the present invention is to provide an optimization device capable of optimizing selection of data used for predetermined processing.

  A fourth object of the present invention is to provide an exposure apparatus capable of realizing highly accurate exposure.

  A fifth object of the present invention is to provide a device manufacturing method capable of improving the productivity of a highly integrated device.

  A sixth object of the present invention is to provide a program that can be executed by a computer and that can optimize a predetermined process, and an information recording medium on which the program is recorded.

  The invention according to claim 1 is an optimization method for optimizing selection of a plurality of data used for a predetermined process, and is a first method used for the predetermined process from among a plurality of first data candidates. A first step of creating a plurality of candidate combinations of one data; and a plurality of second data created when the predetermined processing is performed using the first data candidates included in each of the created combinations. A second step of calculating correlation information indicating a degree of correlation between the data group consisting of the reference data group and a reference data group consisting of a plurality of reference data by a predetermined correlation calculation; and based on the calculated correlation information, the first step And a third step of determining a first data combination to be used for the predetermined process from a plurality of combinations of data candidates.

  According to this, in the first step, a plurality of combinations of first data candidates are created from among a plurality of first data candidates used for a predetermined process. In the second step, the correlation between the reference data group and a data group composed of a plurality of second data created when a predetermined process is performed using the first data candidates included in the created combination Correlation information indicating the degree is calculated by a predetermined correlation calculation. Further, in the third step, based on the calculated correlation value, a combination of first data used for a predetermined process is determined from a plurality of combinations of candidates for the first data.

  That is, in the present invention, for example, if a data group including inaccurate data or a data group including only accurate data is used as a reference data group, each of several combinations of first data candidates and its combination Each correlation information with the reference data group serves as a guideline (index) of how much inaccurate data or accurate data is included in the combination. Therefore, by referring to the calculated correlation information, it is possible to determine a combination of first data that makes the processing result of the predetermined process good from among combinations of candidates for the first data. Therefore, if the predetermined processing is executed using the combination of the first data determined in the third step, the processing result of the predetermined processing can be improved and used for the predetermined processing. Optimization of data selection is realized.

  In this case, as in the optimization method according to claim 2, the predetermined correlation calculation may be a vector correlation calculation for calculating the correlation information by regarding each second data as a vector quantity. As in the optimization method according to claim 3, the predetermined correlation calculation may be a scalar correlation calculation for calculating the correlation information by regarding each second data as a scalar quantity.

  The optimization method according to any one of claims 1 to 3, wherein all of the plurality of first data candidates are used prior to the second step, as in the optimization method according to claim 4. A fourth step of creating a data group composed of a plurality of second data created when the predetermined processing is performed, and in the second step, the data group created in the fourth step is It can be used as the reference data group.

  In this case, as in the optimization method according to claim 5, in the third step, when there is a combination satisfying a predetermined condition, the combination is used as a plurality of first data used for the predetermined process. When there is no combination that satisfies the predetermined condition, all of the plurality of first data candidates can be used as the first data used for the predetermined process.

  In this case, as in the optimization method described in claim 6, the correlation information may include a correlation coefficient between the data group including the plurality of second data and the reference data group.

  In this case, as in the optimization method according to claim 7, the predetermined condition may include that the correlation coefficient is lower than a predetermined threshold.

  The predetermined condition is that the correlation coefficient is lower than the predetermined threshold because the data obtained when the predetermined processing is performed using all data (reference data) including the defective data and the defect This is because it is considered that the correlation with the data group obtained when the predetermined processing is performed using the remaining data as a result of optimal rejection of the data is low.

  In the optimization method according to claim 6, as in the optimization method according to claim 8, the predetermined condition is determined in the second step among a plurality of combinations created in the first step. The calculated correlation coefficient is the lowest combination.

  9. The optimization method according to claim 7 or 8, wherein, as in the optimization method according to claim 9, the predetermined condition is determined by using a plurality of first data candidates included in the combination. It further includes that the accuracy index of the processing result when the processing is performed is better than the accuracy index of the processing result when the predetermined processing is performed using all of the plurality of first data candidates. It can be.

  The optimization method according to any one of claims 6 to 9, wherein the correlation coefficient is normalized by an average value of the second data as in the optimization method according to claim 10. It can be a correlation coefficient.

  The optimization method according to any one of claims 1 to 10, wherein, as in the optimization method according to claim 11, in the first step, a predetermined value is selected from all candidates of the plurality of first data. By removing a number of first data candidates, a plurality of combinations of the first data candidates can be created.

  The invention according to claim 12 is an optimization method for optimizing selection of a plurality of data used for a predetermined process, and a new first combination is added to the combination of the plurality of first data used for the predetermined process. A first step of creating a temporary combination of first data by adding one data candidate; and when the predetermined process is performed using the first data included in the created temporary combination Created when the predetermined processing is performed using the first data included in the combination of the first data before adding the candidate of the first data and the data group composed of the plurality of second data to be created A second step of calculating correlation information indicating a degree of correlation with a data group composed of a plurality of second data by a predetermined correlation calculation; a predetermined condition is satisfied based on the calculated correlation information In the case, the first day An optimization method comprising: a candidate, third step and to add to the combination of the first data.

  According to this, in the first step, a temporary combination of the first data is created by adding a candidate for the first data to the combination of the first data. In the second step, correlation information indicating the degree of correlation between the data groups of the second data before the addition of the first data candidate and after the addition is calculated. Further, in the third step, if a predetermined condition is satisfied based on the calculated correlation information, the first data candidate is added to the first data combination. In this way, based on the correlation information, it is possible to prevent the first data candidate with low accuracy from being added to the combination of the first data, and to convert the first data candidate into the first data. Whether or not to add is determined one by one. Therefore, in the present invention, the number of first data used for the predetermined process can be optimized. Therefore, if the predetermined processing is executed using the finally determined combination of the first data, the processing result of the predetermined processing can be improved.

  In this case, as in the optimization method according to claim 13, the first step, the second step, and the third step are repeated until the value indicated by the correlation information is equal to or greater than a predetermined value. It can be done.

  14. The optimization method according to claim 12 or 13, wherein, as in the optimization method according to claim 14, the predetermined correlation calculation is a vector for calculating the correlation information using each second data as a vector quantity. It is good also as a correlation calculation, and the said predetermined correlation calculation is a scalar correlation calculation which calculates the said correlation information by making each said 2nd data into a scalar quantity like the optimization method of Claim 15. It's also good.

  The optimization method according to any one of claims 12 to 15, wherein, as in the optimization method according to claim 16, the correlation information is added to the combination before the candidate for the first data is added. Performing the predetermined process using a data group composed of a plurality of second data created when the predetermined process is performed using the included first data and the first data included in the temporary combination It is possible to include a correlation coefficient with a data group composed of a plurality of second data created in the case of

  In this case, as in the optimization method according to claim 17, the predetermined condition can include that the correlation coefficient calculated in the second step is not equal to or greater than the first threshold value.

  In this case, as in the optimization method according to claim 18, the predetermined condition is that the correlation coefficient calculated in the second step is not less than or equal to a predetermined second threshold smaller than the first threshold. May further be included.

  The optimization method according to claim 17 or 18, wherein, as in the optimization method according to claim 19, the predetermined condition is determined by using the first data included in the created temporary combination. The accuracy index of the processing result when the processing is performed is the accuracy index of the processing result when the predetermined processing is performed using the first data included in the combination before adding the candidate for the first data It can be further included.

  The optimization method according to any one of claims 16 to 19, wherein the correlation coefficient is normalized by an average value of the second data as in the optimization method according to claim 20. It can be a correlation coefficient.

  The optimization method according to any one of claims 1 to 20, wherein the predetermined process defines a moving position of a moving body on which an object is placed, as in the optimization method according to claim 21. A process of detecting a plurality of error information relating to a deviation between the first coordinate system and a second coordinate system defined by an array of a plurality of regions formed on the object, wherein the plurality of first data candidates are The measurement value of the position information on the first coordinate system of at least a part of the plurality of regions may be used.

  In this case, as in the optimization method according to claim 22, the second data is a correction amount from a design value in the position information on the first coordinate system of each of the plurality of regions based on the error information. 24. As in the optimization method according to claim 23, the second data includes positional information on the first coordinate system of each of the plurality of regions corrected based on the error information. And a residual between the measured value of the position information on the first coordinate system.

  In the optimization method according to any one of claims 1 to 20, as in the optimization method according to claim 24, the predetermined process is a process of detecting flatness of a surface of an object, The plurality of first data candidates are measured values of the surface height of the object at different measurement points on the surface of the object, and the second data is the surface height of the object at each measurement point. The height at each of the measurement points on the curved surface indicating the surface of the object can be determined based on the measured value of the height.

  According to a twenty-fifth aspect of the present invention, the measurement values of the position information of the marks respectively attached to the plurality of regions formed on the substrate are used as first data candidates, respectively. Executing the optimization method according to claim 1 and extracting the position information of the mark as the first data from the position information of the plurality of marks; based on the position information of the extracted mark, Detecting a plurality of pieces of error information indicating a deviation between a first coordinate system defining a movement position of a moving body on which the substrate is placed and a second coordinate system defined by an arrangement of the plurality of regions; And a step of transferring a predetermined pattern to the substrate while controlling the position of the substrate based on the result.

  According to this, the measurement value of the position information of the mark formed on the substrate as the first data is extracted and extracted by using the optimization method according to any one of claims 21 to 23. Since the transfer is performed in a state where the position control of the substrate is performed based on the measurement value of the mark position information, highly accurate exposure can be realized.

  According to a twenty-sixth aspect of the invention, the optimization method according to the twenty-fourth aspect is executed by using, as the first data candidates, the measurement values of the surface height of the substrate at a plurality of different measurement points on the surface of the substrate. And extracting the measurement value of the surface height of the substrate as first data from the measurement values of the surface height of the substrate at the plurality of measurement points; A step of obtaining the flatness of the substrate based on a measured value of the surface height of the substrate; a step of transferring a predetermined pattern to the substrate while performing position control of the substrate based on the obtained flatness; An exposure method comprising:

  According to this, using the optimization method according to claim 24, the measurement value of the surface height of the substrate at each measurement point as the first data is extracted, and the measurement value of the extracted surface height of the substrate is extracted. Based on the above, since the transfer is performed in a state where the position control of the substrate is performed, it is possible to realize highly accurate exposure.

  A twenty-seventh aspect of the present invention is a device manufacturing method including a lithography process, wherein the exposure is performed using the exposure method according to the twenty-fifth or twenty-sixth aspect. In such a case, since exposure is performed using the exposure method according to claim 25 or 26, both high exposure accuracy and high throughput can be realized, so that the productivity of a highly integrated device is improved. be able to.

  The invention according to claim 28 is an optimizing device for optimizing selection of a plurality of data used for a predetermined process, and is a first apparatus used for the predetermined process from among a plurality of first data candidates. A creation device for creating a plurality of combinations of candidates for one data; data comprising a plurality of second data created when the predetermined processing is performed using candidates for the first data included in the created combinations An arithmetic unit that calculates correlation information indicating a degree of correlation between the group and a reference data group including a plurality of reference data by a predetermined correlation calculation; and is used for the predetermined process based on the calculated correlation information. And a determination device that determines a combination of the first data.

  According to this, a plurality of combinations of the first data candidates are created from the plurality of first data candidates used for the predetermined process by the creation device. Then, a correlation value between a reference data group and a data group composed of a plurality of second data created when a predetermined process is performed by using the first data candidate included in the created combination by the arithmetic device Is calculated by a predetermined correlation calculation. Further, the determination device determines a combination of the first data used for the predetermined processing based on the calculated correlation value.

  Therefore, a data group including inaccurate data, a data group of highly accurate data, or the like is set as a reference data group by an arithmetic device, and the determination device determines, for example, that reference data group most frequently. It is possible to determine a combination of first data candidates having a low correlation or a high correlation, and a combination of the first data that makes a predetermined processing result good. Therefore, if the predetermined process is executed using the combination of the first data determined by the determination device, the processing result of the predetermined process can be improved.

  In this case, as in the optimization device according to claim 29, the predetermined correlation calculation may be a vector correlation calculation for calculating the correlation information by regarding each second data as a vector quantity. In the optimization apparatus according to claim 30, the predetermined correlation calculation may be a scalar correlation calculation that calculates the correlation information by regarding each second data as a scalar quantity.

  The optimization device according to any one of claims 28 to 30, wherein, when there is a combination that satisfies a predetermined condition, as in the optimization device according to claim 31, the determination device includes the combination. Is a combination of a plurality of first data used for the predetermined process, and if there is no combination that satisfies the predetermined condition, all the candidates for the first data are used for the first process. The correlation information may include a correlation coefficient between the data group including the plurality of second data and the reference data group.

  In this case, as in the optimization device according to claim 32, the predetermined condition may include that the correlation coefficient obtained by the arithmetic device is lower than a predetermined threshold. As in the optimization method described in 33, the predetermined condition includes a combination having a lowest correlation coefficient calculated in the arithmetic device among a plurality of combinations created by the creating device. It's also good.

  The optimization device according to any one of claims 31 to 33, wherein the correlation coefficient is normalized by an average value of the second data as in the optimization device according to claim 34. It can be a correlation coefficient.

  The invention described in claim 35 is an optimizing device for optimizing selection of a plurality of data used in a predetermined process, wherein a new first combination of the plurality of first data used in the predetermined process is added. A creation device that creates a temporary combination of first data by adding one data candidate; and created when the predetermined processing is performed using the first data included in the created temporary combination Generated when the predetermined process is performed using the first data included in the combination of the first data before adding the candidate for the first data and the data group including the plurality of second data. A calculation device that calculates correlation information indicating a correlation value with a data group composed of a plurality of second data by a predetermined correlation calculation; and when a predetermined condition is satisfied based on the calculated correlation information Is the first day An optimization apparatus comprising: a candidate, additional devices and to add to the combination of the first data.

  According to this, the provisional combination of the first data is created by adding the candidate for the first data to the combination of the first data by the creation device. And the correlation information which shows the correlation degree between the data groups of the 2nd data before adding the candidate of the 1st data and after adding by the arithmetic unit is calculated. Furthermore, when a predetermined condition is satisfied based on the correlation information calculated by the adding device, the candidate for the first data is added to the combination of the first data. In this way, based on the correlation information, it is possible to prevent the first data candidates with low accuracy from being added to the combination of the first data, and determine the first data candidates one by one. Therefore, the number of first data used for the predetermined process can be optimized.

  In this case, as in the optimization device according to claim 36, the creation of the temporary combination by the creation device and the correlation information by the arithmetic device until the value indicated by the correlation information becomes a predetermined value or more. And the addition by the additional device can be repeatedly executed.

  37. The optimization device according to claim 35 or 36, wherein, as in the optimization device according to claim 37, the predetermined correlation calculation is a vector for calculating the correlation information using each second data as a vector quantity. It is good also as a correlation calculation, and the said predetermined correlation calculation is a scalar correlation calculation which calculates the said correlation information by making each said 2nd data into a scalar quantity like the optimization apparatus of Claim 38. It's also good.

  The optimization apparatus according to any one of claims 35 to 38, wherein the correlation information is included in the combination before adding the candidate for the first data, as in the optimization apparatus according to claim 39. When the predetermined process is performed using the first data included in the provisional combination and the data group composed of a plurality of second data created when the predetermined process is performed using the first data It can be said that it is a correlation coefficient with the data group which consists of several 2nd data produced in (1).

  In this case, as in the optimization device according to claim 40, the predetermined condition is calculated by the arithmetic device that the value indicated by the correlation information calculated by the arithmetic device is not equal to or greater than a first threshold value. The value indicated by the correlation information is not less than or equal to the second threshold value smaller than the first threshold value, and the processing result when the predetermined process is performed using the first data included in the created temporary combination. The accuracy index is at least 1 better than the accuracy index of the processing result when the predetermined processing is performed using the first data included in the combination before adding the first data candidate. One can be included.

  41. The optimization device according to claim 39 or 40, wherein, as in the optimization device according to claim 41, the correlation coefficient is a correlation coefficient normalized by an average value of the second data. Can be.

  The optimization apparatus according to any one of claims 28 to 41, wherein the predetermined process defines a movement position of a moving body on which an object is placed, as in the optimization apparatus according to claim 42. A process for detecting a plurality of pieces of error information indicating a deviation between a first coordinate system and a second coordinate system defined by an array of a plurality of regions formed on the object, wherein the plurality of first data candidates Can be measured values of position information on the first coordinate system of at least a part of the plurality of regions.

  In this case, as in the optimization device according to claim 43, the second data is a correction amount from a design value related to position information on the first coordinate system of each of the plurality of regions based on the error information. 45. As in the optimization device according to claim 44, the second data includes positional information on the first coordinate system of each of the plurality of regions corrected based on the error information. And a residual between the measured value of the position information on the first coordinate system.

  In the optimization apparatus according to any one of claims 28 to 41, as in the optimization apparatus according to claim 45, the predetermined process is a process for detecting flatness of a surface of an object, and the plurality of the first processes. The data candidate is a measurement value of the surface height of the object at a plurality of different measurement points on the surface of the object, and the second data is a measurement value of the surface height of the object at each measurement point. The height at each measurement point on the curved surface indicating the surface of the object can be determined based on the height.

  In the invention according to claim 46, from the position information of the plurality of marks, the measurement values of the position information of the marks respectively attached to the plurality of regions formed on the substrate are used as first data candidates. 45. The optimization apparatus according to any one of claims 42 to 44, which extracts position information of a mark as the first data; and the substrate is placed based on the position information of the extracted mark. A detection device for detecting a plurality of pieces of error information indicating a deviation between a first coordinate system for defining a moving position of the moving body and a second coordinate system defined by an array of the plurality of regions; and a detection result of the detection device And a transfer device that transfers a predetermined pattern to the substrate while controlling the position of the substrate based on the above.

  According to this, it is possible to detect a deviation between the first coordinate system and the second coordinate system using the mark position information extracted by the optimization device according to any one of claims 42 to 44. Since the predetermined pattern can be transferred onto the substrate based on the deviation, high-accuracy exposure can be realized.

  According to a 47th aspect of the present invention, measurement values of the surface height of the substrate at a plurality of different measurement points on the surface of the substrate are respectively used as first data candidates, and the surface height of the substrate at the plurality of measurement points. 46. The optimization apparatus according to claim 45, wherein a measurement value of the surface height of the substrate as first data is extracted from the measurement values of height; and the surface height of the substrate at each of the extracted measurement points An exposure apparatus comprising: a calculation device for obtaining flatness of the substrate based on the measured value; and a transfer device for transferring a predetermined pattern to the substrate while performing position control of the substrate based on the detection result. is there.

  According to this, the flatness of the substrate can be obtained using the measured value of the surface height of the substrate extracted by the optimization device according to claim 45, and the predetermined pattern is formed on the substrate based on the flatness. Since it can be transferred to the top, high-precision exposure can be realized.

  The invention according to claim 48 is a program for causing a computer to execute a process of optimizing selection of a plurality of data used in a predetermined process, wherein the predetermined process is selected from a plurality of first data candidates. A first procedure for creating a plurality of first data candidate combinations used for the first data; a plurality of first data created when the predetermined processing is performed using the first data candidates included in the created combination A second procedure for calculating correlation information indicating a degree of correlation between a data group composed of two data and a reference data group composed of a plurality of reference data by a predetermined correlation operation; and based on the calculated correlation information, And a third procedure for determining a combination of first data to be used for predetermined processing.

  When this program is installed in the computer, the computer executes the above steps. Thus, the optimization method according to claim 1 is executed by the computer. Therefore, similarly to the first aspect, it is possible to optimize selection of data used for the predetermined processing.

  In this case, as in the program according to claim 49, in the second procedure, as the predetermined correlation calculation, the computer performs a vector correlation calculation for calculating the correlation information by regarding each second data as a vector quantity. 52. As in the program according to claim 50, in the second procedure, in the second procedure, as the predetermined correlation calculation, a scalar correlation that calculates the correlation information by regarding each second data as a scalar quantity. It is good also as making a computer perform a calculation.

  52. In the program according to any one of claims 48 to 50, as in the program according to claim 51, prior to the second procedure, the predetermined data is obtained using all of the plurality of first data candidates. A fourth procedure for creating a data group consisting of a plurality of second data created when processing is performed is further executed by the computer, and the data group created in the fourth procedure is used as the reference data group, The second procedure can be executed by the computer.

  In this case, as in the program according to claim 52, if there is a combination that satisfies a predetermined condition, the combination is a combination of a plurality of first data used for the predetermined process, and the predetermined condition is If there is no combination to satisfy, the third procedure can be executed by the computer so that all the candidates for the first data are the first data used for the predetermined processing.

  53. The program according to claim 51, wherein, as in the program according to claim 53, the correlation information includes a correlation coefficient between a data group composed of the plurality of second data and the reference data group. can do.

  In this case, as in the program according to claim 54, the predetermined condition includes that an index value of the correlation degree included in the correlation information calculated in the second procedure is lower than a predetermined threshold value. 55. As in the program according to claim 55, the predetermined condition includes a correlation degree included in the correlation information calculated in the second procedure among a plurality of combinations created in the first procedure. It is good also as including that it is the combination with the lowest index value.

  56. In the program according to claim 54 or 55, as in the program according to claim 56, the predetermined condition is obtained by performing the predetermined process using a plurality of first data candidates included in the combination. It is further included that the accuracy index of the processing result in this case is better than the accuracy index of the processing result when the predetermined processing is performed using all of the plurality of first data candidates. it can.

  The invention according to claim 57 is a program for causing a computer to execute a process of optimizing the selection of a plurality of data used in a predetermined process, wherein a combination of the first data includes a first data candidate. A first procedure for creating a tentative combination of first data by adding, and a plurality of items created when the predetermined processing is performed using the first data included in the created tentative combination A plurality of data created when the predetermined process is performed using the first data included in the combination of the first data before adding the first data candidate and the data group composed of the second data A second procedure for calculating correlation information indicating a degree of correlation with the data group including the second data by a predetermined correlation calculation; and when a predetermined condition is satisfied based on the calculated correlation information, The first de A program causing a computer to execute the; other candidates, the third procedure and to add to the combination of the first data.

  When this program is installed in the computer, the computer executes the above steps. Thus, the optimization method according to claim 12 is executed by the computer. Therefore, similarly to the twelfth aspect, it is possible to optimize selection of data used for the predetermined processing.

  In this case, as in the program according to claim 58, the first procedure, the second procedure, and the third procedure are repeated until the value indicated by the correlation information is equal to or greater than a predetermined value. Can be executed.

  59. In the program according to claim 57 or 58, as in the program according to claim 59, the predetermined correlation calculation is a vector correlation calculation for calculating the correlation information using the second data as a vector quantity. The predetermined correlation calculation may be a scalar correlation calculation that calculates the correlation information using each second data as a scalar quantity, as in the program according to claim 60.

  The program according to any one of claims 57 to 60, wherein, as in the program according to claim 61, the correlation information uses the first data included in the combination before adding the candidate for the first data. A plurality of second data created when the predetermined process is performed using a data group composed of a plurality of second data created when the predetermined process is performed and the first data included in the temporary combination. It is a correlation coefficient with a data group consisting of two data, and the predetermined condition may include that the value indicated by the correlation information calculated in the second procedure is not greater than or equal to a first threshold value. .

  In this case, as in the program according to claim 62, the predetermined condition is an accuracy index of a processing result when the predetermined processing is performed using the first data included in the created temporary combination. And an accuracy index of a processing result when the predetermined processing is performed using the first data included in the combination before adding the first data candidate is further included. be able to.

  A 63rd aspect of the present invention is a computer-readable information recording medium on which the program according to any one of 48th to 62nd aspects is recorded.

<< First Embodiment >>
A first embodiment of the present invention will be described below with reference to FIGS.

  FIG. 1 shows a schematic configuration of an exposure apparatus 100 according to the first embodiment to which the optimization method and the exposure method of the present invention are applied. The exposure apparatus 100 is a step-and-scan projection exposure apparatus. The exposure apparatus 100 includes an illumination system 10, a reticle stage RST on which a reticle R as a mask is mounted, a projection optical system PL, a wafer stage WST as a moving body on which a wafer W as an object is mounted, an alignment detection system AS. , And a main control device 20 that performs overall control of the entire apparatus.

  The illumination system 10 includes, for example, a light source, an illuminance uniformizing optical system including an optical integrator, a relay lens, a variable ND filter, a variable field stop (reticle blind or masking) as disclosed in Japanese Patent Laid-Open No. 6-349701. (Also referred to as a blade) and a dichroic mirror or the like (both not shown). As the optical integrator, a fly-eye lens, a rod integrator (an internal reflection type integrator), a diffractive optical element, or the like is used.

In the illumination system 10, on the reticle R on which a circuit pattern or the like is drawn, a slit-shaped illumination area (a rectangular illumination area elongated in the X-axis direction) defined by the reticle blind is substantially uniform by the illumination light IL. Illuminate with illuminance. Here, as the illumination light IL, far ultraviolet light such as KrF excimer laser light (wavelength 248 nm), ArF excimer laser light (wavelength 193 nm), vacuum ultraviolet light such as F ₂ laser light (wavelength 157 nm), or the like is used. . As the illumination light IL, it is also possible to use an ultraviolet bright line (g-line, i-line, etc.) from an ultra-high pressure mercury lamp.

  On reticle stage RST, reticle R is fixed, for example, by vacuum suction. Reticle stage RST is XY perpendicular to the optical axis of illumination system 10 (corresponding to optical axis AX of projection optical system PL described later) by a reticle stage drive unit (not shown) using a linear motor, a voice coil motor or the like as a drive source. It can be driven minutely in a plane and can be driven at a scanning speed specified in a predetermined scanning direction (here, the Y-axis direction which is the left-right direction in FIG. 1).

  The reticle stage RST is formed with a reflecting surface composed of a moving mirror or the like facing the X-axis direction and the Y-axis direction that reflects the laser light, and the position of the reticle stage RST within the stage moving surface is on the reflecting surface. A reticle laser interferometer (hereinafter, referred to as “reticle interferometer” or simply “interferometer”) 16 that irradiates laser light is always detected with a resolution of about 0.5 to 1 nm, for example. Here, actually, a reticle X interferometer having a length measuring axis along the X axis direction and a reticle Y interferometer having a length measuring axis along the Y axis direction are provided. Is typically shown as a reticle interferometer 16. At least one of the reticle Y interferometer and the reticle X interferometer, for example, the reticle Y interferometer, is a two-axis interferometer having two measurement axes, and the reticle stage RST is based on the measurement value of the reticle Y interferometer. In addition to the Y position, the rotation amount (yawing amount) in the θz direction (rotation direction around the Z axis) can also be measured. Position information (including rotation information such as yawing amount) of reticle stage RST from reticle interferometer 16 is supplied to stage controller 19 and main controller 20 via this. The stage control device 19 drives and controls the reticle stage RST via a reticle stage drive unit (not shown) based on the position information of the reticle stage RST in response to an instruction from the main control device 20.

  Above the reticle R, a pair of reticle alignment detection systems 22 (however, in FIG. 1, the reticle alignment detection system 22 on the back side of the drawing is not shown) are arranged at a predetermined distance in the X-axis direction. Although not shown here, each reticle alignment detection system 22 includes an epi-illumination system for illuminating the detection target mark with illumination light having the same wavelength as the illumination light IL, and the detection target mark. And a detection system for capturing an image. The detection system includes an imaging optical system and an image sensor, and an imaging result (that is, a mark detection result by the reticle alignment detection system 22) by this detection system is supplied to the main controller 20. In this case, a deflection mirror (not shown) for guiding the detection light from the reticle R to the reticle alignment detection system 22 is movably arranged, and when an exposure sequence is started, based on a command from the main controller 20. The deflecting mirrors are retracted out of the optical path of the illumination light IL integrally with the reticle alignment detection system 22 by a driving device (not shown).

  The projection optical system PL is disposed below the reticle stage RST in FIG. 1, and the direction of the optical axis AX is the Z-axis direction. As the projection optical system PL, a birefringent optical system having a predetermined reduction magnification (for example, 1/5 or 1/4) is used. Therefore, when the illumination area of the reticle R is illuminated by the illumination light IL from the illumination system 10, a reduced image (partial inverted image) of the illumination area portion of the circuit pattern of the reticle R is passed through the projection optical system PL through the wafer W. The light is projected onto the projection area in the field of view of the projection optical system PL conjugate to the illumination area above, and transferred to the resist layer on the surface of the wafer W.

  Wafer stage WST is arranged on a base (not shown) below projection optical system PL in FIG. Wafer holder 25 is placed on wafer stage WST. A wafer W is fixed on the wafer holder 25 by, for example, vacuum suction.

  Wafer stage WST is rotated by X, Y, Z, θz (rotation direction around Z axis), θx (rotation direction around X axis), and θy (rotation direction around Y axis) by wafer stage drive unit 24 in FIG. ) Of 6 stages of freedom. Regarding the θz direction, wafer stage WST (specifically, wafer holder 25) may be configured to be rotatable, or yawing error of wafer stage WST may be corrected by rotation on reticle stage RST side. good.

  Wafer stage WST is formed with a reflecting surface composed of a moving mirror or the like facing in the X-axis direction and Y-axis direction for reflecting laser light, and the position of wafer stage WST is arranged outside and on the reflecting surface. For example, a wafer laser interferometer (hereinafter referred to as “wafer interferometer” or simply “interferometer”) 18 that irradiates laser light is constantly detected with a resolution of about 0.5 to 1 nm. In practice, an interferometer having a length measuring axis in the X-axis direction and an interferometer having a length measuring axis in the Y-axis direction are provided, but these are typically shown as a wafer interferometer 18 in FIG. Has been. These interferometers are composed of multi-axis interferometers having a plurality of measurement axes, and in addition to the X and Y positions of wafer stage WST, rotation (yawing (θz rotation that is rotation around the Z axis)), pitching (X axis) Rotation around (θx rotation) and rolling (θy rotation around Y axis)) can also be measured. In response to an instruction from main controller 20, stage controller 19 drives and controls wafer stage WST via wafer stage driver 24 based on the position information of wafer stage WST, and is held on wafer stage WST. The position of the wafer W is controlled.

  A reference mark plate FM is fixed in the vicinity of wafer W on wafer stage WST. The surface of the reference mark plate FM is set to substantially the same height as the surface of the wafer W, and at least a pair of reticle alignment reference marks, a reference mark for baseline measurement of the alignment detection system AS, and the like are provided on this surface. Is formed.

  The alignment detection system AS is an off-axis alignment sensor disposed on the side surface of the projection optical system PL. As this alignment detection system AS, for example, a broadband detection light beam that does not sensitize a resist on a wafer is irradiated onto a target mark, and an image of the target mark formed on a light receiving surface by reflected light from the target mark is not shown. An image processing type FIA (Field Image Alignment) type sensor that captures an image of an index using an imaging device (CCD) or the like and outputs an image pickup signal thereof is used. In addition to the FIA system, a target mark is irradiated with coherent detection light, and scattered light or diffracted light generated from the target mark is detected, or two diffracted lights (for example, of the same order) generated from the target mark. Of course, it is possible to use an alignment sensor for detecting the interference by using them alone or in combination as appropriate. The imaging result of the alignment detection system AS is output to the main controller 20.

  In FIG. 1, the control system is mainly configured by a main control device 20 and a stage control device 19 subordinate thereto. The main control device 20 includes a so-called microcomputer (or workstation) including a CPU (central processing unit), a main memory, and the like, and controls the entire device.

  The main controller 20 includes, for example, a storage device including a hard disk, an input device including a pointing device such as a keyboard and a mouse, and a display device such as a CRT display (or a liquid crystal display) (all not shown), A drive device 46 for an information recording medium such as a CD (Compact Disc), a DVD (Digital Versatile Disc), an MO (Magneto-Optical Disc), or an FD (Flexible Disc) is connected externally. An information recording medium (hereinafter referred to as a CD) set in the drive device 46 has a program corresponding to a processing algorithm at the time of wafer alignment and exposure operations shown in the flowchart described later (hereinafter, “specific” for convenience). Other programs, and databases attached to these programs are recorded.

  The main controller 20 executes processing according to the above-described specific program so that, for example, the exposure operation is accurately performed, and controls, for example, synchronous scanning of the reticle R and the wafer W, step movement (stepping) of the wafer W, and the like. To do.

Specifically, the main controller 20 synchronizes with the reticle R being scanned in the + Y direction (or −Y direction) at the speed V _R = V via the reticle stage RST, for example, during scanning exposure. Through wafer stage WST, wafer W has a velocity V _W = β · V (β is the projection magnification from reticle R to wafer W) in the −Y direction (or + Y direction) with respect to the projection region conjugate with the illumination region. Based on the measurement values of the reticle interferometer 16 and the wafer interferometer 18 obtained through the stage control device 19 so as to be scanned, the reticle stage drive unit and wafer stage drive unit (not shown) are passed through the stage control device 19. The position and speed of reticle stage RST and wafer stage WST are controlled via 24 respectively. Further, at the time of stepping, main controller 20 uses wafer stage WST via stage controller 19 and wafer stage drive unit 24 based on the measurement value of wafer interferometer 18 obtained via stage controller 19. Control the position of the.

  Furthermore, the exposure apparatus 100 of the first embodiment supplies an imaging light beam for forming a plurality of slit images toward the best imaging surface of the projection optical system PL from an oblique direction with respect to the optical axis AX direction. A grazing incidence multipoint focus detection system comprising an irradiation system (not shown) and a light receiving system (not shown) that receives each reflected light beam of the imaging light beam on the surface of the wafer W through a slit. ing. As this multipoint focus detection system, one having the same configuration as that disclosed in, for example, Japanese Patent Laid-Open No. 6-283403 is used, and the output of this multipoint focus detection system is supplied to the main controller 20. Yes. Main controller 20 moves wafer stage WST in the Z-axis direction and the tilt direction (θx rotation, θy rotation) via stage control device 19 and wafer stage drive unit 24 based on the wafer position information from this multipoint focus detection system. To drive.

  Next, an operation performed when the exposure apparatus 100 according to the first embodiment configured as described above performs the exposure process for the second layer (second layer) and subsequent layers on the wafer W will be described. .

First, as a premise, as shown in FIG. 2A, 51 shot areas SA formed by the processing steps up to the previous layer are formed on the wafer W that is the exposure target of the second and subsequent layers. _p (p = 1 to 51) is arranged. Furthermore, as shown in FIG. 2 (B) is an enlarged view of the wafer W shown in FIG. 2 (A), with the shot area SA _p, predetermined width between shot regions adjacent to each other, for example, about 100μm width A wafer alignment X mark (wafer X mark) MX _p and a wafer alignment Y mark (wafer Y mark) MY _p are respectively formed on the street lines. As the wafer X mark MX _p , for example, a line and space mark whose periodic direction is the X axis direction is used, and as the wafer Y mark MY _p , for example, a line and space mark whose periodic direction is the Y axis direction is used. Then, the X position of the wafer X mark MX _p (that is, the position at which the line and space mark is equally divided in the arrangement direction) coincides with the X coordinate of the shot area SA _p (center C _p ) by design, and the wafer Y The Y position of the mark MY _p (that is, the position where the line and space mark is equally divided in the arrangement direction) is designed to coincide with the Y coordinate of the shot area SA _p (center C _p ). That is, in design, the position coordinates of the shot area SA _p (center C _p ) are obtained from the X position of the wafer X mark MX _p and the Y position of the wafer Y mark MY _p . In FIG. 2B, a mark having three line patterns is used as an example of these marks, but the number of line patterns may be any number and may not be a line pattern. Further, the number of shot areas on the wafer W is not limited to 51.

On this wafer W, in order to form a shot region of a new layer, a photoresist is applied to transfer and form a circuit pattern of the shot region. Shot areas of the new layer, on the shot area SA _p on the wafer W shown in FIG. 2 (A), needs to be formed by overlapping. In order to increase the overlay accuracy, EGA type wafer alignment (hereinafter, abbreviated as “EGA” or “EGA processing”) is performed in the first embodiment.

In EGA, some shot areas are selected as measurement shot areas (hereinafter referred to as “EGA measurement shot areas”) out of all shot areas SA _p shown in FIG. 2A, and the selected measurement shots are selected. Wafer X mark MX _p and wafer Y mark MY _p attached to the area are detected by alignment detection system AS, and on the stage coordinate system (first coordinate system) that defines the movement position of wafer stage WST based on the detection result. The positions (array coordinates) of the wafer X mark MX _p and the wafer Y mark MY _p are calculated. As described above, the positions of these marks indicate the X position and the Y position of the EGA measurement shot area. In EGA, the shot area on the wafer is based on the position information of the plurality of EGA measurement shot areas. Information on the deviation between the arrangement coordinate system (wafer coordinate system, second coordinate system), which is a coordinate system defined by the SA _p arrangement, and the stage coordinate system (EGA parameters a, b, c, d, e, f) are obtained by statistical calculation processing, and the arrangement coordinates on the stage coordinate system of the shot area SA _p are obtained based on the information regarding the deviation. The information on the deviation between the wafer coordinate system and the stage coordinate system is essential information for improving the overlay accuracy described above. When overlay exposure is performed, the position of the stage is taken into consideration. Control is performed.

But in practice, the deviation and the exposure position in the previous step, the deformation of the wafer W by the process, the formation state of the shot area SA _p, there are slight variations in each region, all the shot areas SA _p They are not necessarily arranged in a regular and regular grid pattern. In such a case, for example, when a shot area (so-called jump shot area) having a large variation in formation state with respect to many other shot areas is selected as the EGA measurement shot area, the EGA measurement shot area is obtained by EGA. Deviation between the wafer coordinate system to be defined and the most likely wafer coordinate system to be originally defined increases, and eventually the overlay accuracy between the shot area SA _p of the new layer and the shot area SA _p decreases. It will end up. Therefore, in EGA, an important point is which shot area to select as the EGA measurement shot area.

Therefore, in the first embodiment, shot regions (SA ₅ , SA ₆ , SA ₁₂ , SA ₁₃ , SA ₃₉ , SA ₄₀ , SA ₄₆ , SA near the outer periphery of the wafer W shown in FIG. ₄₇ ) is a candidate for an EGA measurement shot area to be measured by the alignment detection system AS. If it is determined that there is a jump shot area in the shot area, the jump shot area is used as an EGA measurement shot area. Exclude (reject) from the area.

It should be noted that the probability that such a jump shot area is included in the EGA measurement shot area can be regarded as substantially the same for a wafer that has undergone a similar process, for example, a wafer in one lot. Therefore, in the first embodiment, the number of jump shot areas excluded from the EGA measurement shot area (the number of expected jump shots) is set to a predetermined number (for example, one). However, in the first embodiment, when it is determined that the shot area SA _p is accurately formed, for example, in an ideal lattice shape, and the wafer state is good and there is almost no jump shot area, the shot area to be excluded is excluded. It is assumed that EGA is performed using position information of all candidates in the EGA measurement shot area.

Further, information regarding the shot area on the wafer W as described above, for example, the shot number of the EGA measurement shot area, the design position coordinates of each shot area SA _p , the number of exclusions from the EGA measurement shot area, etc. Assume that it is stored in a storage device.

  Next, regarding the processing algorithm of the CPU in the main controller 20 when performing the exposure processing including EGA, which is executed according to the specific program, refer to other drawings as appropriate along the flowcharts of FIGS. While explaining.

  First, as a premise, it is assumed that the specific program and other programs in the CD-ROM set in the drive device 46 are installed in the storage device of the main control device 20, and further, reticle alignment and baseline measurement thereof. It is assumed that a program such as processing is loaded from the storage device into the main memory by the CPU inside the main control device 20.

  As shown in FIG. 3, first, in step 301, reticle R is loaded on reticle stage RST using a reticle loader (not shown). When this reticle loading is completed, in step 303 → step 305 → step 307, reticle alignment, baseline measurement, and wafer loading are executed as follows according to the above-described reticle alignment, baseline measurement, and wafer loading processing program. To do.

  That is, the reference mark plate FM on the wafer stage WST is positioned at a predetermined position directly below the projection optical system PL (hereinafter referred to as “reference position” for convenience), and a pair of first reference marks on the reference mark plate FM; The relative position of the pair of reticle alignment marks on the reticle R corresponding to the first reference mark is detected using the pair of reticle alignment detection systems 22 described above. Then, the detection result of the reticle alignment detection system 22 and the measurement values of the interferometers 16 and 18 at the time of detection are stored in the main memory. Next, wafer stage WST and reticle stage RST are moved in opposite directions along the Y-axis direction by a predetermined distance, respectively, and another pair of first reference marks on reference mark plate FM and its first reference A relative position with another pair of reticle alignment marks on the reticle R corresponding to the mark is detected using the pair of reticle alignment detection systems 22 described above. Then, the detection result of the reticle alignment detection system 22 and the measurement values of the interferometers 16 and 18 at the time of detection are stored in the main memory. Next, in the same manner as described above, the relative positional relationship between another pair of first reference marks on the reference mark plate FM and the reticle alignment mark corresponding to the first reference mark may be further measured. .

  Then, using the information on the relative positional relationship between the at least two pairs of first reference marks and the corresponding reticle alignment marks obtained in this way, and the measured values of the interferometers 16 and 18 at the time of each measurement, The relative positional relationship between the reticle stage coordinate system defined by the measurement axis of the interferometer 16 and the wafer stage coordinate system defined by the measurement axis of the interferometer 18 is obtained. Thereby, reticle alignment is completed.

  Next, in step 305, baseline measurement is performed. Specifically, wafer stage WST is returned to the above-mentioned reference position, moved from the reference position by a predetermined amount, for example, the design value of the baseline, in the XY plane, and then moved onto reference mark plate FM using alignment detection system AS. The second reference mark is detected (the measured value of the wafer interferometer 18 is stored in the main memory). Information on the relative positional relationship between the detection center of the alignment detection system AS and the second reference mark obtained at this time, a pair of first reference marks previously measured when the wafer stage WST was positioned at the reference position, and the first reference mark Information on the relative positional relationship between the pair of reticle alignment marks corresponding to the reference mark, the measured value of the wafer interferometer 18 at the time of each measurement, the design value of the baseline, and the first and second known reference marks and second Based on the positional relationship with the reference mark, the base line of the alignment detection system AS, that is, the distance (positional relationship) between the projection center of the reticle pattern and the detection center (index center) of the alignment detection system AS is calculated.

  Next, in step 307, the control unit of the wafer loader (not shown) is instructed to load the wafer W. Thereby, wafer W is loaded onto wafer holder 25 on wafer stage WST by the wafer loader. Here, in the first embodiment, prior to the loading of the wafer W, the wafer W relative to the wafer stage WST is aligned by a pre-alignment apparatus (not shown) so that the stage coordinate system and the wafer coordinate system coincide to a certain extent. It is assumed that the rotational deviation and the center position deviation are substantially adjusted. Also, here, information relating to the wafer W stored in the storage device is read into the main memory.

  When such a series of preparation operations are completed, the above-described reticle alignment and baseline measurement processing programs are unloaded from the main memory, and the above-described specific program is loaded into the main memory. Thereafter, in accordance with this specific program, the optimization method of the first embodiment, that is, the EGA process including the reject process of the jump shot area in the EGA measurement shot area in the subroutine 309, and the exposure for each shot area on the wafer W To do.

  Before executing this subroutine 309, a search alignment mark (not shown) provided on the wafer W (an alignment mark shown in FIG. 2B may be used as the search alignment mark) is detected. The system AS is detected with a low magnification, and based on the position information of the search alignment mark, so-called search alignment is performed in which the shift amount of the stage coordinate system rotation component and offset component is obtained with rough accuracy. May be.

FIG. 4 shows a flowchart of the subroutine 309. In the subroutine 309, as shown in FIG. 4, first, in step 401, EGA mark measurement is performed. Specifically, from the storage device, information on the EGA measurement shot area (the EGA measurement shot area is SA ₅ , SA ₆ , SA ₁₂ , SA ₁₃ , SA ₃₉ , SA ₄₀ , SA ₄₆ , SA ₄₇ , The design position information of these shot areas is read out. Then, the wafer X mark MX _p and the wafer Y mark MY _p attached to the shot area that is a candidate for the EGA measurement shot area are sequentially positioned in the detection visual field of the alignment detection system AS, and these marks are aligned with the alignment detection system AS. Let it be detected. In the following description, the shot areas SA ₅ , SA ₆ , SA ₃₉ , SA ₄₀ , SA ₄₇ , SA ₄₆ , SA ₁₃ , SA ₁₂ are designated as shot areas G ₁ , G ₂ , G ₃ , G ₄ , G ₅ , respectively. G _6, and G _7, G _8. The subscript G does not necessarily mean the mark measurement order, and the mark measurement order is set to shorten the measurement time.

Based on the detection result sent from the alignment detection system AS (for example, a signal corresponding to peripheral image data including those marks) and the measurement value of the wafer interferometer 18 at the time of detection, the position coordinates on the stage coordinate system Get the measured value. Furthermore, for example, by template matching, evaluation of mirror image symmetry by scanning a window with a predetermined width, and other appropriate detection processing (image processing) with respect to the image data as the detection result described above, The position information of these marks is obtained, and the position (measurement value) of the wafer X mark MX _p and wafer Y mark MY _{p on} the stage coordinate system is obtained from the position information and the measurement value of the wafer interferometer 18 described above. These measurement values are used as the measurement values at the positions of the shot areas G ₁ , G ₂ , G ₃ , G ₄ , G ₅ , G ₆ , G ₇ , G ₈ , that is, as the first data candidates. Used.

Next, in step 403, using the measurement values of the candidate G ₁ ~G ₈ all EGA measurement shot area, the correction amount of the position information of the shot area that is created when performing the EGA process as the predetermined processing A vector map of vectors is created as a reference vector map. Specifically, the evaluation function E of the above equation (2) is minimized by using the measured values of the position information of all candidates of the EGA shot area measured in step 401 (that is, all of the plurality of first data candidates). The values of parameters a, b, c, d, e, and f are obtained. Then, based on the values of the obtained parameters a, b, c, d, e, and f, the correction amount of the position coordinate in the stage coordinate system in each of the EGA measurement shot areas G _{1 to} G ₈ is obtained. Since this process is disclosed in, for example, Japanese Patent Laid-Open No. 61-44429, detailed description thereof is omitted. The vector map of each correction amount vector created here becomes a reference data group composed of a plurality of reference data, and this reference vector map is used as a reference data group in the subsequent processing.

FIG. 5A shows an example of a reference vector map in each EGA measurement shot area candidate obtained in this way. In FIG. 5A, correction amounts obtained as a result of EGA processing are displayed as vectors (hereinafter referred to as “correction amount vectors”) S _{1 to} S ₈ . In step 403, thus created reference vector map, i.e. in the case of performing EGA process using all candidate EGA measurement shot area, the correction amount vector S in each EGA measurement shot area G ₁ ~G _{8 1 to} S ₈ (actually, the X component and the Y component of the correction amount vector) are stored in the storage device.

Returning to FIG. 4, in the next step 405, EGA calculation is performed for the combination excluding the number of expected jump shots. In the first embodiment, as described above, the number of shot areas to be rejected in advance is set to a predetermined number, and the predetermined number is stored in the storage device. Here, first, the number is read from the storage device. Let that number be r. In the first embodiment, all combinations of shot areas obtained when only r are excluded from each EGA measurement shot area (eight in the first embodiment) are stored in the EGA measurement shot area. Create multiple candidates. Here, since the number of EGA measurement shot areas is eight and the number of shot areas to be excluded is r, a combination of ₈ C _r EGA measurement shot area candidates is created. Further, EGA processing is executed for each created combination, and the evaluation function E of the above equation (2) is minimized based on the position information of the shot area included in the combination (first data candidate included in the combination). The values of parameters a, b, c, d, e, and f are calculated for each combination.

In step 407, based on the values of the obtained parameters a, b, c, d, e, and f, the correction amount vector (second value) of the position coordinate of the stage coordinate system in each of the EGA measurement shot areas G _{1 to} G ₈ is used. Data) is executed for each combination excluding the number of expected jump shots, and a vector map of correction amount vectors for each combination is created.

In FIG. 5B, EGA processing is performed on the combination of EGA measurement shot areas obtained by rejecting a predetermined number of shot areas from the EGA measurement shot area in this way, using position information of the combination. An example of the correction amount vector in each of the EGA measurement shot area candidates G _{1 to} G ₈ obtained at times is shown. In FIG. 5B, the correction amounts of the shot areas G _{1 to} G ₈ are displayed as vectors T _{1 to} T ₈ . A vector map of correction amount vectors of each combination created here is a data group composed of a plurality of second data. These vector maps are stored in a storage device.

Returning to FIG. 4, in the next step 409, the shot areas G _{1 to} G created when the EGA process is performed using all the candidates of the reference vector map calculated in step 403, that is, the EGA measurement shot area. A correlation coefficient between the standard vector map (reference data group) of the correction amount vector corresponding to ₈ and the vector map of each combination (data group consisting of the second data) calculated in step 407 is calculated for each combination. To do. Specifically, first, the reference vector map (correction amount vectors S _{1 to} S ₈ ) calculated in step 403 is read from the storage device. Then, all vector maps (correction amount vectors T _{1 to} T ₂ ) calculated in step 407 are read out. Further, the standard deviation σ _S0 of the correction vector S _{1 to} S ₈ of the reference vector map is obtained for each combination using the following equation. In the following formula, for generalization, the number of EGA measurement shot area candidates is set to N instead of 8, and in the following description, the number of EGA measurement shot area candidates is assumed to be N. In addition, (*) _x and (*) _y indicate a component in the X-axis direction and a component in the Y-axis direction of the vector in parentheses.

そして、ステップ４０７で求めた各組合せのベクトルマップの補正量ベクトルＴ₁〜Ｔ_Nの標準偏差σ_T0を、次式を用いて求める（補正量ベクトルＴ₁〜Ｔ_Nの大きさは、ショット領域の組合せによってそれぞれ異なるため、標準偏差σ_T0の値も、ショット領域の組合せによって異なる）。

Then, the standard deviation σ _T0 of the correction amount vectors T _{1 to} T _N of the vector map of each combination obtained in step 407 is obtained using the following equation (the magnitude of the correction amount vectors T _{1 to} T _N is the shot region). _Therefore , the value of the standard deviation σ _T0 also differs depending on the combination of shot areas).

さらに、基準ベクトルマップと、各組合せのベクトルマップとの共分散（内積和）ρ_V0を、次式を用いて組合せ毎に求める。

Further, a covariance (sum of inner products) ρ _V0 between the reference vector map and the vector map of each combination is obtained for each combination using the following equation.

ここで、上記式（５）におけるθ_iは、図６に示されるように、同じショット領域Ｇ_Nに対応する基準ベクトルマップの補正量ベクトルと各組合せのベクトルマップの補正量ベクトル同士の成す角度である。

Angle Here, theta _i is in the above formula (5), formed by the way, the correction amount vector between the vector map of the correction amount vector and each combination of reference vector map corresponding to the same shot area G _N shown in FIG. 6 It is.

Then, based on the calculation results of the above formulas (3), (4), and (5), using the following formula, the correlation information indicating the correlation between the reference vector map and the vector map of each combination is used. Correlation coefficient C _V0 is obtained for each combination. This correlation coefficient C _V0 is obtained by calculating a vector map of correction amount vectors obtained when EGA processing is performed using all EGA measurement shot area candidates, and the remaining EGA measurement shots when a predetermined number of shot areas are rejected. This is a scale indicating how much correlation there is with the vector map of correction vector obtained when EGA processing is performed using a combination of regions. The larger the value, the higher the correlation between the two, and the smaller the value, the lower the correlation between the two.

In the next step 411, among the combinations of EGA measurement shot area candidates, combinations of EGA measurement shot area candidates whose correlation coefficient C _V0 obtained in step 409 is lower than a predetermined threshold are extracted.

Next, in step 413, it is determined whether or not a combination having a correlation coefficient C _V0 value lower than a predetermined threshold value is extracted in step 411. If the determination is affirmative, the process proceeds to step 415, and if the determination is negative, the process proceeds to step 419. That the value of the correlation coefficient C _V0 is lower than the predetermined threshold means that the EGA processing is performed using the vector map of the correction amount vector obtained when the EGA processing is performed with the combination and all candidates of the EGA measurement shot area. This means that the reference vector map of the correction amount vector obtained when the correction is performed is significantly different. When the combination is created, the rejected EGA measurement shot area candidate may be a jump shot area. The nature will be high. Here, in step 411, it is assumed that only one combination whose correlation coefficient C _V0 is lower than a predetermined threshold has been extracted, and the processing proceeds to step 415.

  In step 415, the residual error created when the EGA process is executed with the combination of the extracted EGA measurement shot areas is the residual error created when the EGA process is performed using all EGA measurement shot area candidates. It is determined whether or not the error is reduced. If the determination is positive, the process proceeds to step 417, and if the determination is negative, the process proceeds to step 419. Here, the residual error is a fitting residual in the EGA processing, and this fitting residual is one of accuracy indexes of the processing result when the EGA processing is performed. This fitting error can be obtained by executing the above equation (2). Here, it is assumed that the determination is affirmed, and the process proceeds to proceed to step 417.

In step 417, the extracted combination for EGA parameters obtained previously in step 405 a, on the basis of b, c, d, e, a f, the sequence on the stage coordinate system of all the shot areas SA _p on the wafer W The coordinates are calculated as a result of the current EGA processing. After step 417 ends, the processing of subroutine 309 ends.

On the other hand, if the determination in step 413 or step 415 is negative, in step 419 to be executed thereafter, it is determined that there are no shot areas to be rejected in G _{1 to} G ₈ , and all EGA measurement shot area candidates are present. , On the basis of the EGA parameters a, b, c, d, e, and f already obtained in step 403, the array coordinates on the stage coordinate system of all shot areas on the wafer W are converted into the current EGA processing results. Calculate as After step 419 ends, the processing of subroutine 309 ends.

  After completion of the subroutine 309, the process returns to step 311 in FIG. 3, and in the next step 311, 1 is set in the counter j indicating the array number of the shot area, and the first shot area is set as the exposure target area. Note that the position information reflecting the result of the EGA processing of the subroutine 309 is used for the position information of the first shot area used for positioning of the wafer stage WST at this time.

  In step 313, the position of the wafer W is used to expose the exposure target area on the wafer W based on the alignment coordinates of the exposure target area calculated in the EGA process (step 417 or 419 in FIG. 4). Wafer stage WST is moved to the acceleration start position, and reticle stage RST is moved so that the position of reticle R is the acceleration start position.

  In step 315, relative scanning of reticle stage RST and wafer stage WST is started. When both stages reach their respective target scanning speeds and reach a constant speed synchronization state, the pattern area of the reticle R starts to be illuminated by the illumination light IL from the illumination system 10, and scanning exposure is started. Then, different areas of the pattern area of the reticle R are sequentially illuminated with the illumination light IL, and the scanning exposure is completed when the illumination on the entire pattern area is completed. Thereby, the pattern of the reticle R is reduced and transferred to the exposure target area on the wafer W via the projection optical system PL.

  In step 317, with reference to the counter value j, it is determined whether or not exposure has been performed on all shot areas. Here, since j = 1, that is, only the first shot area has been exposed, the determination in step 317 is denied and the routine proceeds to step 319.

  In step 319, the value of the counter j is incremented (+1), the next shot area is set as the exposure target area, and the process returns to step 313.

  Thereafter, the processing and determination of step 313 → step 315 → step 317 → step 319 are repeated until the determination in step 317 is affirmed.

  When the transfer of the pattern to all the shot areas on the wafer W is completed, the determination in step 317 is affirmed, and the process proceeds to step 321.

  In step 321, a wafer loader (not shown) is instructed to unload the wafer W. As a result, the wafer W is unloaded from the wafer holder 25 by a wafer loader (not shown) and then transferred to a coater / developer (not shown) connected inline to the exposure apparatus 100 by a wafer transfer system (not shown). Is done. Thereby, the exposure processing operation ends.

  If another wafer is to be exposed, the processing from step 307 may be repeated.

  As is apparent from the above description, in the first embodiment, the main control device 20 corresponds to the optimization device creation device, arithmetic device, and determination device of the present invention. That is, the function of the creation device is realized by the processing of Step 405 and Step 407 (FIG. 4) performed by the CPU of the main control device 20, and the function of the arithmetic device is realized by the processing of Step 409 (FIG. 4). The function of the determination device is realized by the processing in step 419 (FIG. 4). However, it goes without saying that the present invention is not limited to this.

As described above in detail, according to the first embodiment, in Step 405, a plurality of combinations of EGA measurement shot area candidates are created from the EGA measurement shot area candidates used for EGA processing. The EGA calculation is performed for each combination. In step 407, a vector map of correction amount vectors created for combinations ( _N C _r ) excluding the number of expected jump shots (r), and a reference for correction amount vectors as reference data groups created in step 403 A correlation coefficient with the vector map is calculated by vector correlation calculation. Further, in step 413 to step 419, a combination of EGA measurement shot areas used for EGA processing is determined based on the calculated correlation value, and the shot area SA _{p on} the stage coordinate system is determined based on the determined combination. Calculate array coordinates.

  That is, in the first embodiment, in step 403, a reference vector map obtained when EGA processing is performed using all EGA measurement shot areas including the EGA measurement shot area to be rejected, and in step 409, Based on the correlation information with the vector map for the combination excluding the number of expected jump shots, the combination of EGA measurement shot areas that makes the processing result of the EGA processing good can be determined. Therefore, if the EGA processing is executed using the determined combination of EGA measurement shot areas, the processing result of the EGA processing can be improved. That is, according to the first embodiment, it is possible to optimize selection of data (EGA measurement shot area position information) used for EGA processing.

  If a plurality of combinations are extracted in step 411, in step 417, a combination having the smallest residual error (fitting error) may be selected from the extracted combinations.

Further, in the first embodiment, in step 411, a combination in which the value of the correlation coefficient C _V0 obtained in step 409 is lower than a predetermined threshold is extracted. However, the present invention is not limited to this. _{Alternatively,} the combination having the lowest correlation coefficient C _V0 may be extracted.

Further, instead of step 411, the combination having the smallest value of the covariance (sum of inner products) ρ _{V0 represented by} the equation (5) is selected, and the shot area excluded at the time of creating the combination is set as the jump shot area. May be.

  In the first embodiment, the standard deviation, covariance (sum of inner products), and correlation coefficient of the vector map are calculated using the above equations (3), (4), (5), and (6). Although calculated, the following formula (7), formula (8), formula (9) (formula (10)), and formula (11) may be used instead.

  However, (PHI) is shown by following Formula.

  That is, the above formulas (7) and (8) are standard deviations of the vector map standardized by the average value of the correction amount vector, and the formula (9) is standardized by the average value of the correction amount vector. The reference vector map and the covariance (sum of inner products) of each combination. Equation (11) is a correlation coefficient based on the standard deviation and covariance that are standardized.

  In the first embodiment, the correlation between the vector maps is obtained by the vector correlation calculation. However, the correction amount obtained as a result of the EGA processing is regarded as a scalar amount of each axis instead of a vector. The EGA measurement shot area may be optimized by obtaining the correlation between the scalar quantity data groups, that is, the scalar maps, by the scalar correlation calculation shown.

Here, σ _T0 and σ _S0 are standard deviations, and the same values as those calculated using the above formulas (3) and (4) can be used.

  As described above, in the first embodiment, the data (second data) obtained as a result of the EGA process may be regarded as a vector, and the optimization process may be performed by a vector correlation operation. It may be regarded as a quantity, and optimization processing may be performed by scalar correlation calculation.

  In the first embodiment, the number of shot areas to be rejected is fixed. However, the present invention is not limited to this, and the processes of steps 401 to 419 in FIG. 4 are repeated by sequentially changing the shot areas to be rejected. As a result, a combination of shot areas with the least residual error may be adopted as a combination of EGA measurement shot areas.

<< Second Embodiment >>
Next, a second embodiment of the present invention will be described with reference to FIG. In the second embodiment, the optimization method and the exposure method according to the present invention are performed using the same or equivalent exposure apparatus as that of the first embodiment. Therefore, in the following, from the viewpoint of preventing repeated description, the same reference numerals as those in the first embodiment are used for these devices and the respective components, and the processing contents are different from those in the first embodiment. Only the EGA processing of the subroutine 309 shown in FIG.

Also in the second embodiment, EGA measurement shot area candidates are shot areas SA ₅ , SA ₆ , SA ₁₂ , SA ₁₃ , SA ₃₉ , SA ₄₀ , SA _{46 shown in FIG.} , SA ₄₇ . In the second embodiment, a shot area that is likely to be a jump shot area and a shot area that is not likely to be a jump shot area are determined statistically or empirically from the EGA measurement shot area candidates. It is assumed that the EGA measurement shot areas are G ₁ , G ₂ , G ₃ , G ₄ , G ₅ , G ₆ , G ₇ , and G ₈ , respectively, in the order in which the EGA measurement shot areas are less likely to become jump shot areas.

In the subroutine 309, as shown in FIG. 7, first, in step 701, a mark is measured. Here, first, from the storage device, the first EGA measurement shot area, that information on the shot area G _1, for example, reads the position information on the design, based on the information in the first EGA measurement shot area G ₁ Wafer stage WST is moved so that attached wafer X mark MX _p and wafer Y mark MY _p are positioned in the detection field of alignment detection system AS. Based on the detection result sent from the alignment detection system AS (for example, a signal corresponding to peripheral image data including those marks) and the measurement value of the wafer interferometer at the time of detection, the position coordinate on the stage coordinate system Get the measured value. Furthermore, for example, by template matching, evaluation of mirror image symmetry by scanning a window with a predetermined width, and other appropriate detection processing (image processing) with respect to the image data as the detection result described above, The position information of these marks is obtained, and the position (measurement value) of the wafer X mark MX _p and wafer Y mark MY _{p on} the stage coordinate system is obtained from the position information and the measurement value of the wafer interferometer 18 described above. Next, in step 703, it is determined whether or not mark measurement of (specified number-1) or more shot areas has been performed. If the determination is affirmative, the process proceeds to step 705, and if the determination is negative, the process returns to step 701. Here, since only the mark attached to the _first EGA measurement shot area G ₁ has been measured, the determination is denied and the processing returns to step 701.

Thereafter, in step 703, the process from step 701 to step 703 is performed until the determination is affirmed, that is, until mark measurement of (specified number −1) or more shot areas (G ₂ , G ₃ ,...) Is performed. Repeatedly executed.

When the measurement of (specified number-1) marks is completed and the determination in step 703 is affirmative, the process proceeds to step 705, where EGA calculation is performed based on the mark position information of the shot area measured so far. The values of the parameters a, b, c, d, e, and f that minimize the evaluation function E of the above formula (2) at that time are obtained. Then, based on the values of the obtained parameters a, b, c, d, e, and f, the correction amount of the position coordinate in the stage coordinate system in each of the EGA measurement shot region candidates G _{1 to} G ₈ is determined, and the correction amount vector Create a vector map of The created vector map is stored in the storage device.

  In the next step 707, the mark attached to one EGA measurement shot area candidate that has not yet been measured is measured, and in step 709, the mark of the shot area that has been measured so far, including the measurement value of the mark, is measured. The EGA calculation is performed again using the measurement values, and a vector map at that time is created. The vector map created here is also stored in the storage device. The vector map created in step 705 is referred to as “previous vector map”, and the vector map created in step 709 is referred to as “current vector map”.

In the next step 711, a correlation value between the current vector map and the previous vector map is calculated. Here, as in the first embodiment, the equations (3), (4), and (5) are calculated, and the standard deviation σ _S0 of the current vector map and the standard deviation σ of the previous vector map are calculated. The covariance ρ _V0 between _{T0 and the} vector map is obtained, and finally the correlation coefficient C _V0 of each vector map is calculated using the equation (6).

In the next step 713, it is determined whether or not the correlation coefficient C _V0 calculated in step 711 is greater than or equal to a specified upper limit value (first threshold value). If the correlation coefficient C _V0 is high, it indicates that there is almost no change in the previous vector map and the current vector map, and the processing result of the EGA processing does not change even if the number of measurement points is increased further. It is shown that. Therefore, if the determination is affirmed, the EGA process is performed only on the currently measured EGA measurement shot area, and the process proceeds to step 725 to calculate the array coordinates. If the determination is negative, the newly measured EGA measurement is performed. Since it is necessary to determine whether or not the mark in the shot area is used for EGA processing, the process proceeds to step 715. Here, the description will be continued on the assumption that the correlation coefficient C _V0 is not equal to or higher than the upper limit value and proceeds to step 715.

In the next step 715, it is determined whether or not the correlation coefficient C _V0 is equal to or less than a specified lower limit value (second threshold value). Here, when the determination is negative, that is, when it is determined that the correlation coefficient C _V0 is not less than the specified lower limit value, the vector map generated when the mark of the shot area measured this time is added. Since the change does not exceed the degree, it can be determined that the mark measured this time is not a jump shot area mark. Therefore, if the determination is negative, the process proceeds to step 721, where it is determined that the EGA measurement shot area (current shot area) measured this time is not rejected (that is, used for EGA processing). Then, the process proceeds to step 723.

On the other hand, if the determination in step 715 is affirmative and the correlation coefficient C _V0 is determined to be equal to or less than the specified lower limit value, the change in the vector map that occurs when the mark measured this time is added is It can be judged that it is a large one that exceeds. Accordingly, since the mark of the shot area (current shot area) measured this time is highly likely to be a mark of the jump shot area, the process proceeds to step 717 at that time. Here, the description will proceed assuming that the correlation coefficient C _V0 is equal to or less than the specified lower limit value and the process proceeds to step 717.

  In the next step 717, it is determined whether or not the residual error as the accuracy index of the EGA processing is increased from the EGA processing in the previous combination of EGA measurement shot areas. Again, as the residual error, the fitting residual shown in the above equation (2) can be used as in the first embodiment. That is, here, if the residual error is increased by using the mark of the EGA measurement shot area (current shot area) measured this time as a mark used for EGA processing, the process proceeds to step 719, and in step 719, The current shot area is rejected without using the mark measured in step 707 in the EGA processing. On the contrary, if the residual error is reduced by using the mark of the EGA measurement shot area measured this time as a mark used for the EGA processing, the accuracy index is good in step 721. In step 707, it is determined that the shot area (current shot area) to be measured is used as the EGA measurement shot area.

After executing step 719 or step 721, the process proceeds to step 723. In step 723, it is determined whether or not the shot area mark measurement has been executed for the designated number. If the determination is positive, the process proceeds to step 725, and if the determination is negative, the process returns to step 707. Here, since eight shot areas G _{1 to} G ₈ are selected as candidates for the EGA measurement shot area, the specified number is 8, and it is determined whether or not the number of measured shot areas exceeds 8. The standard. Here, the number of shot areas that have been measured has not yet reached 8, and the description will be continued assuming that the process returns to step 707.

  Thereafter, until the designated number of shot areas are measured and the determination in step 723 or step 713 is affirmed, step 707 → step 709 → step 711 → step 713 → step 715 → step 717 (executed depending on the determination in step 715) The process of step 719 (or step 721) → step 723 is repeated.

  If the determination is affirmative in step 723 or the determination is affirmative in step 713, the process proceeds to step 725. In step 725, all shot areas on the wafer W are determined based on the EGA parameters a, b, c, d, e, and f already obtained in step 709 or step 705 for all EGA measurement shot area candidates. The arrangement coordinates on the stage coordinate system are calculated. After step 725 ends, the process of subroutine 309 ends.

  As is apparent from the above description, in the second embodiment, the main control device 20 corresponds to the optimization device creation device, arithmetic device, and additional device of the present invention. That is, the function of the creation device is realized by the processing of Step 701 to Step 709 in FIG. 7 performed by the CPU of the main control device 20, the function of the arithmetic device is realized by the processing of Step 711, and Steps 713 to 723 are performed. By the processing, the function of the additional device is realized. However, it goes without saying that the present invention is not limited to this.

According to the second embodiment, in Step 707 and Step 709, a temporary combination of EGA measurement shot areas is created by adding EGA measurement shot area candidates to the combination of EGA measurement shot areas. In step 711, the degree of correlation between the correction amount vector map before the addition of the EGA measurement shot area candidate and the correction amount vector map of the provisional combination of the EGA measurement shot area after the addition is calculated. A correlation coefficient C _V0 is calculated as correlation information to be shown.

In step 721, if the calculated correlation coefficient C _V0 satisfies a predetermined condition, or if the residual error value that is an accuracy index of the EGA processing result has not increased, the EGA measurement shot area Are added to the combination of EGA measurement shot areas. In this way, the jump shot area can be prevented from being added to the combination of EGA measurement shot areas based on the correlation coefficient C _{V0 and the} like, and the EGA measurement shot area candidates can be jumped one by one. Since it is determined whether or not it is a shot area, the number of EGA measurement shot areas used for EGA processing can also be optimized.

  In the second embodiment, as in the first embodiment, the standard deviation of the vector map using the above formula (3), formula (4), formula (5), and formula (6), Covariance (sum of inner products) and correlation coefficient were calculated, but instead of these equations, the above equation (7), equation (8), equation (9) (equation (10)), and equation (11) were used. May be. That is, the above (7), formula (8), formula (9) (formula (10)), and formula (11) are the standard deviation and covariance (inner product) of the vector map normalized by the average value of the correction amount vectors. Sum), the correlation coefficient.

  Further, in the second embodiment, the correlation of the vector map is obtained by the vector correlation calculation. However, the correlation may be obtained by the scalar correlation calculation as in the first embodiment. That is, in the second embodiment, the correction amount data obtained by the EGA process may be regarded as a vector, and the optimization process may be performed by a vector correlation operation. The data may be regarded as a scalar amount to the last, Optimization processing may be performed by scalar correlation calculation.

  In the second embodiment, in the loop processing from step 701 to step 703, marks attached to a predetermined number of shot areas that are always used for EGA calculation are measured, but those marks are rejected. However, when the residual error decreases, the mark may be rejected.

  In each of the above embodiments, the correlation of the correction amount vector of each EGA measurement shot area is calculated. However, the present invention is not limited to this, and the vector map (or scalar map) of the fitting residual vector in each shot area after correction is calculated. The combination of EGA measurement shot areas (position information data thereof) may be optimized based on the correlation between the two.

Further, in each of the above embodiments, the correlation calculation of the correction amount for the EGA measurement shot region is performed. However, optimization is performed based on the correction amount of all the shot regions SA _{1 to} SA ₅₁ and the correlation of the fitting residuals. You can go. In order to perform optimization based on the fitting errors of all shot areas, it is necessary to measure the positions of all shot areas on the stage coordinate system in advance.

  Further, in each of the above embodiments, the case where the present invention is applied to a normal EGA system has been described. However, the present invention can be applied to a so-called weighted EGA system disclosed in detail in, for example, Japanese Patent Laid-Open No. 5-304077. Alternatively, the present invention can be applied to a so-called in-shot multipoint EGA method disclosed in, for example, Japanese Patent Laid-Open No. 6-349705.

  In the weighted EGA method, position coordinates on a stage coordinate system of at least three sample shot areas selected in advance among a plurality of shot areas on a wafer are measured. Next, for each shot area on the wafer, a predetermined value that is defined in advance according to the distance between the shot area (its center point) and each of the sample shot areas (its center point) or on the shot area and the wafer. And weighting each of the position coordinates on the stage coordinate system of the sample shot area according to the distance between the target point and the distance between the target point and each of the sample shot areas. The position coordinates on the stage coordinate system of each of the plurality of shot areas on the wafer are determined by performing a statistical calculation (such as a least square method or a simple averaging process) using the plurality of position coordinates. Then, based on the determined position coordinates, each of a plurality of shot areas arranged on the wafer is aligned with a predetermined reference position in the stage coordinate system. Even in this weighted EGA method, by applying the present invention, if the jump shot area is rejected and the weighted EGA is performed on the EGA measurement shot area other than the jump shot area, it is possible to further improve the overlay accuracy.

  Further, in the shot multi-point EGA method, a plurality of alignment marks are detected for each sample shot region to obtain a plurality of X and Y coordinates, respectively, to cope with expansion / contraction, rotation, etc. of the wafer used in the EGA method. In addition to the wafer parameters, the position information of each shot area, for example, the coordinate value, is obtained using a model function including at least one of shot parameters (chip parameters) corresponding to rotation error, orthogonality, and scaling of the shot area. calculate. Then, based on the determined position coordinates, each of a plurality of shot areas arranged on the wafer is aligned with a predetermined reference position in the stage coordinate system. Even in this in-shot multipoint EGA method, the optimum rejection of the jump shot region by applying the present invention exhibits a sufficient effect. In this case, optimum rejection can be performed for each alignment mark.

  The present invention can also be applied to a secondary EGA as disclosed in JP-A-5-114545. In addition, the present invention can be applied to higher-order EGA of third or higher order.

  Furthermore, in the above embodiments, it is assumed that the EGA method is used. However, any alignment method (for example, die-by-die (D / D) alignment) may be used, and an alignment mark is attached to each shot area. For example, a plurality of alignment marks formed discretely around the periphery of the wafer may be used.

  In each of the above embodiments, it is assumed that the EGA method is used. However, any alignment method may be used as long as the alignment method selects an alignment mark to be measured from alignment marks that are candidates for measurement. Can be applied. For example, the present invention can also be applied to an alignment system that can detect a plurality of diffraction order lights, as disclosed in International Publication No. WO98 / 39689.

  In each of the above embodiments, the FIA type alignment sensor is used as the alignment detection system AS. However, as described above, the laser beam is irradiated onto the alignment mark in the form of dots on the wafer W and is diffracted by the mark. Alternatively, the present invention can be applied to an LSA (Laser Step Alignment) type alignment sensor that detects a mark position using scattered light, or an alignment sensor that appropriately combines the alignment sensor and the FIA method. is there. In addition, for example, an alignment sensor that irradiates a mark on the surface to be detected with a coherent detection light and causes two diffracted lights (for example, the same order) generated from the mark to interfere with each other is used alone, or the FIA method, the LSA. Of course, it is possible to apply the present invention to an alignment sensor appropriately combined with a method.

  The alignment detection system may be an on-axis method (for example, a TTL (Through The Lens) method). In addition, the alignment detection system is not limited to the one that detects the alignment mark in a state where the alignment mark is almost stationary in the detection visual field of the alignment detection system. Relative movement may be used (for example, the aforementioned LSA system or homodyne LIA system). In the case where the detection light and the alignment mark are moved relative to each other, it is desirable that the relative movement direction is the same as the movement direction of the wafer stage WST when detecting each of the alignment marks.

  In each of the above embodiments, the present invention is applied to EGA. However, the present invention is not limited to this. For example, the present invention can also be applied to processing for measuring the flatness (flatness) of a wafer as an object. is there.

For example, first, the wafer surface height is measured at a plurality of different measurement points on the wafer surface. Then, an approximate curved surface of the wafer is obtained by the least square method or the like using measured values at all measurement points i (i = 1 to N). Further, determine the height of the approximate curve at all measurement points, the respective values with T _i. Then, the measurement values at some arbitrary measurement points are rejected from all the measurement points 1 to N, and the approximate curved surface of the wafer is again obtained by the least square method or the like using the measurement values at the remaining measurement points. The height S _i of the approximate curved surface of each measurement point i is obtained.

Then, the following equations (14) and (15) are calculated to perform a scalar correlation operation to obtain a correlation coefficient C _F0 .

ここで、σ_T0、σ_S0は、各計測点ｉの各近似曲面の高さＴ_i、Ｓ_iの標準偏差である。

Here, σ _T0 and σ _S0 are standard deviations of the heights T _i and S _i of each approximate curved surface at each measurement point i.

  In this way, it is possible to obtain a curved surface showing the flatness of the wafer by excluding the measurement value of the measurement point i with low accuracy from the process of measuring the flatness of the wafer. Therefore, it is possible to achieve high exposure accuracy by transferring the pattern while controlling the position of the wafer in the Z-axis direction relative to the projection optical system PL with reference to the curved surface obtained with high accuracy. Become.

  In each of the above-described embodiments, the case where the present invention is applied to a step-and-scan type scanning exposure apparatus has been described. However, the scope of the present invention is not limited to this. That is, it can be suitably applied to a step-and-repeat method, a step-and-stitch method, a mirror projection aligner, a photo repeater, and the like. Further, the projection optical system PL may be any of a refraction system, a catadioptric system, and a reflection system, and may be any one of a reduction system, an equal magnification system, and an enlargement system.

Further, although the light source of the exposure apparatus to which the present invention is applied is a KrF excimer laser, an ArF excimer laser, or an F ₂ laser, other pulse laser light sources in the vacuum ultraviolet region may be used. In addition, as the illumination light for exposure, for example, a fiber doped with, for example, erbium (or both erbium and ytterbium) with a single wavelength laser beam oscillated from a DFB semiconductor laser or a fiber laser. Harmonics that are amplified by an amplifier and wavelength-converted to ultraviolet light using a nonlinear optical crystal may be used.

  An illumination optical system, a projection optical system, and an alignment detection system AS composed of a plurality of lenses are incorporated in the exposure apparatus main body, optically adjusted, and a reticle stage and wafer stage made up of a large number of mechanical parts are arranged in the exposure apparatus main body. The exposure apparatus according to each of the above-described embodiments can be manufactured by attaching wirings and pipes and performing general adjustment (electrical adjustment, operation check, etc.). The exposure apparatus is preferably manufactured in a clean room where the temperature, cleanliness, etc. are controlled.

  The present invention is not limited to an exposure apparatus for manufacturing a semiconductor, but is used for manufacturing a display including a liquid crystal display element. An exposure apparatus for transferring a device pattern onto a glass plate and a device used for manufacturing a thin film magnetic head. The present invention can also be applied to an exposure apparatus that transfers a pattern onto a ceramic wafer, an exposure apparatus used for manufacturing an image sensor (CCD, etc.), an organic EL, a micromachine, and a DNA chip. Further, in order to manufacture reticles or masks used in not only microdevices such as semiconductor elements but also light exposure apparatuses, EUV exposure apparatuses, X-ray exposure apparatuses, electron beam exposure apparatuses, etc., glass substrates or silicon wafers, etc. The present invention can also be applied to an exposure apparatus that transfers a circuit pattern. Here, in an exposure apparatus using DUV (far ultraviolet) light, VUV (vacuum ultraviolet) light, or the like, a transmission type reticle is generally used. As a reticle substrate, quartz glass, fluorine-doped quartz glass, fluorite, Magnesium fluoride or quartz is used. Further, in a proximity type X-ray exposure apparatus or an electron beam exposure apparatus, a transmission mask (stencil mask, membrane mask) is used, and a silicon wafer or the like is used as a mask substrate.

  Further, the optimization method according to the present invention is not limited to the exposure apparatus, and the present invention is not limited to the present invention as long as a plurality of marks on the object are sequentially detected and a predetermined process using the detection results of these marks is performed. The same effect can be obtained by applying.

<Device manufacturing method>
Next, an embodiment of a device manufacturing method using the exposure apparatus 100 described above in a lithography process will be described.

  FIG. 8 shows a flowchart of a manufacturing example of a device (a semiconductor chip such as an IC or LSI, a liquid crystal panel, a CCD, a thin film magnetic head, a micromachine, etc.). As shown in FIG. 8, first, in step 801 (design step), device function / performance design (for example, circuit design of a semiconductor device) is performed, and pattern design for realizing the function is performed. Subsequently, in step 802 (mask manufacturing step), a mask on which the designed circuit pattern is formed is manufactured. On the other hand, in step 803 (wafer manufacturing step), a wafer is manufactured using a material such as silicon.

  Next, in step 804 (wafer processing step), using the mask and wafer prepared in steps 801 to 803, an actual circuit or the like is formed on the wafer by lithography or the like, as will be described later. Next, in step 805 (device assembly step), device assembly is performed using the wafer processed in step 804. Step 805 includes processes such as a dicing process, a bonding process, and a packaging process (chip encapsulation) as necessary.

  Finally, in step 806 (inspection step), inspections such as an operation confirmation test and a durability test of the device created in step 805 are performed. After these steps, the device is completed and shipped.

  FIG. 9 shows a detailed flow example of step 804 in the semiconductor device. In FIG. 9, in step 811 (oxidation step), the surface of the wafer is oxidized. In step 812 (CVD step), an insulating film is formed on the wafer surface. In step 813 (electrode formation step), an electrode is formed on the wafer by vapor deposition. In step 814 (ion implantation step), ions are implanted into the wafer. Each of the above steps 811 to 814 constitutes a pre-processing process in each stage of the wafer processing, and is selected and executed according to a necessary process in each stage.

  At each stage of the wafer process, when the above pre-process is completed, the post-process is executed as follows. In this post-processing process, first, in step 815 (resist formation step), a photosensitive agent is applied to the wafer. Subsequently, in step 816 (exposure step), the circuit pattern of the mask is transferred to the wafer using the exposure apparatus 100 of each of the above embodiments. Next, in step 817 (development step), the exposed wafer is developed, and in step 818 (etching step), the exposed member other than the portion where the resist remains is removed by etching. In step 819 (resist removal step), the resist that has become unnecessary after the etching is removed.

  By repeatedly performing these pre-processing steps and post-processing steps, multiple circuit patterns are formed on the wafer.

  If the device manufacturing method of this embodiment described above is used, the exposure apparatus 100 of each of the above embodiments is used in the exposure step (step 816), so that highly accurate exposure can be realized. As a result, it becomes possible to produce a device with a higher degree of integration.

  As described above, according to the optimization method and apparatus, the exposure method and apparatus, the program, and the information recording medium of the present invention, it is possible to optimize predetermined processing such as the above-described EGA alignment and perform high-precision overlay. It is suitable for exposure, and the device manufacturing method of the present invention is suitable for the production of microdevices.

1 is a view showing a schematic configuration of an exposure apparatus according to a first embodiment of the present invention. FIG. 2A is a diagram showing the arrangement of shot areas on the wafer, and FIG. 2B is a diagram showing the arrangement of alignment marks on the wafer. It is a flowchart which shows the process algorithm of CPU of the main control apparatus in the case of the exposure process in the exposure apparatus which concerns on the 1st Embodiment of this invention. It is a flowchart which shows the subroutine of the EGA process in the 1st Embodiment of this invention. FIG. 5A is a diagram showing an example of a reference vector map when EGA processing is performed using all candidates of the EGA measurement shot area, and FIG. 5B rejects a predetermined number of shot areas. It is a figure which shows an example of the vector map at the time of performing an EGA process using the remaining EGA measurement shot area | region when it did. It is a figure which shows the inner product sum of the vector in an EGA measurement shot area | region. It is a flowchart which shows the subroutine of the EGA process in the 2nd Embodiment of this invention. It is a flowchart for demonstrating embodiment of the device manufacturing method which concerns on this invention. It is a flowchart which shows the detail of step 804 of FIG.

Explanation of symbols

20 ... main control unit (optimization apparatus, generating apparatus, computing device, determining device, creation device, additional devices), 100 ... exposure apparatus, AS ... alignment detection system, MX _p, MY _p ... alignment marks (marks), G _{1 to} G ₈ , SA _{1 to} SA ₅₁ ... Shot area, W... Wafer (object), WST... Wafer stage (moving body).

Claims (63)

An optimization method for optimizing selection of a plurality of data used for a predetermined process,
A first step of creating a plurality of combinations of first data candidates used for the predetermined process from among a plurality of first data candidates;
A data group composed of a plurality of second data and a reference data group composed of a plurality of reference data created when the predetermined processing is performed using the first data candidates included in each of the created combinations. A second step of calculating correlation information indicating a degree of correlation with a predetermined correlation calculation;
A third step of determining, based on the calculated correlation information, a first data combination to be used for the predetermined process from a plurality of combinations of the first data candidates.   2. The optimization method according to claim 1, wherein the predetermined correlation calculation is a vector correlation calculation for calculating the correlation information by regarding each second data as a vector quantity.   2. The optimization method according to claim 1, wherein the predetermined correlation calculation is a scalar correlation calculation for calculating the correlation information by regarding each second data as a scalar quantity. Prior to the second step,
A fourth step of creating a data group composed of a plurality of second data created when the predetermined processing is performed using all of the plurality of first data candidates;
In the second step,
The optimization method according to claim 1, wherein the data group created in the fourth step is used as the reference data group. In the third step,
When there is a combination that satisfies a predetermined condition, the combination is a combination of a plurality of first data used for the predetermined process,
5. The optimization method according to claim 4, wherein when there is no combination that satisfies the predetermined condition, all of the plurality of first data candidates are set as first data used for the predetermined process.   6. The optimization method according to claim 5, wherein the correlation information includes a correlation coefficient between the data group including the plurality of second data and the reference data group. The predetermined condition is:
The optimization method according to claim 6, further comprising: the correlation coefficient being lower than a predetermined threshold. The predetermined condition is:
The optimization method according to claim 6, comprising: a combination having a lowest correlation coefficient calculated in the second step among the plurality of combinations created in the first step. . The predetermined condition is:
The accuracy index of the processing result when the predetermined processing is performed using a plurality of first data candidates included in the combination is performed using the plurality of first data candidates. The optimization method according to claim 7, further comprising: being better than the accuracy index of the processing result at the time.   The optimization method according to claim 6, wherein the correlation coefficient is a correlation coefficient normalized by an average value of the second data. In the first step,
11. A plurality of combinations of the first data candidates are created by removing a predetermined number of first data candidates from all of the plurality of first data candidates. The optimization method according to one item. An optimization method for optimizing selection of a plurality of data used for a predetermined process,
A first step of creating a temporary combination of first data by adding new first data candidates to a plurality of first data combinations used in the predetermined process;
A data group consisting of a plurality of second data created when the predetermined processing is performed using the first data included in the created temporary combination, and before adding the candidate for the first data Correlation information indicating a degree of correlation with a data group composed of a plurality of second data created when the predetermined processing is performed using the first data included in the combination of the first data, and a predetermined correlation calculation A second step calculated by:
And a third step of adding a candidate for the first data to the combination of the first data when a predetermined condition is satisfied based on the calculated correlation information.   The optimization according to claim 12, wherein the first step, the second step, and the third step are repeatedly executed until a value indicated by the correlation information is equal to or greater than a predetermined value. Method.   The optimization method according to claim 12 or 13, wherein the predetermined correlation calculation is a vector correlation calculation for calculating the correlation information using each second data as a vector quantity.   14. The optimization method according to claim 12 or 13, wherein the predetermined correlation calculation is a scalar correlation calculation that calculates the correlation information using each second data as a scalar quantity. The correlation information is
A data group composed of a plurality of second data created when the predetermined processing is performed using the first data included in the combination before adding the candidate for the first data, and the temporary combination The correlation coefficient with the data group which consists of several 2nd data produced when the said predetermined | prescribed process is performed using the included 1st data is included, The any one of Claims 12-15 characterized by the above-mentioned. The optimization method according to item. The predetermined condition is:
The optimization method according to claim 16, further comprising: the correlation coefficient calculated in the second step is not greater than or equal to a first threshold value. The predetermined condition is:
The optimization method according to claim 17, further comprising: the correlation coefficient calculated in the second step is not less than or equal to a predetermined second threshold value smaller than the first threshold value. The predetermined condition is:
The accuracy index of the processing result when the predetermined processing is performed using the first data included in the created temporary combination is included in the first combination before adding the first data candidate. The optimization method according to claim 17, further comprising: being better than an accuracy index of a processing result when the predetermined processing is performed using data.   The optimization method according to any one of claims 16 to 19, wherein the correlation coefficient is a correlation coefficient normalized by an average value of the second data. The predetermined processing includes a plurality of deviations between a first coordinate system that defines a moving position of a moving body on which an object is placed and a second coordinate system that is defined by an array of a plurality of regions formed on the object. Is a process for detecting error information of
21. The plurality of first data candidates are measured values of position information on the first coordinate system of at least a part of the plurality of regions. Optimization method.   The optimization method according to claim 21, wherein the second data is a correction amount from a design value in position information on the first coordinate system of each of the plurality of regions based on the error information. .   The second data is a residual between the position information on the first coordinate system of each of the plurality of regions corrected based on the error information and the measurement value of the position information on the first coordinate system. The optimization method according to claim 21, wherein: The predetermined process is a process of detecting the flatness of the surface of the object,
The plurality of first data candidates are measured values of the surface height of the object at different measurement points on the surface of the object,
The second data is a height at each measurement point on a curved surface indicating a surface of the object, which is obtained based on a measurement value of the surface height of the object at each measurement point. The optimization method as described in any one of Claims 1-20. The optimization method according to any one of claims 21 to 23, wherein measurement values of position information of marks respectively attached to a plurality of regions formed on a substrate are used as first data candidates, respectively. Extracting the mark position information as the first data from the position information of the plurality of marks;
Based on the extracted position information of the mark, a deviation between the first coordinate system that defines the movement position of the moving body on which the substrate is placed and the second coordinate system that is defined by the arrangement of the plurality of regions is determined. Detecting a plurality of error information to indicate;
And a step of transferring a predetermined pattern to the substrate while controlling the position of the substrate based on the detection result. 25. The optimization method according to claim 24, wherein the measurement values of the surface height of the substrate at different measurement points on the surface of the substrate are respectively candidates for first data, and the optimization method according to claim 24 is performed. Extracting the measurement value of the surface height of the substrate as the first data from the measurement value of the surface height of the substrate;
Obtaining the flatness of the substrate based on the measurement value of the surface height of the substrate at each of the extracted measurement points;
And a step of transferring a predetermined pattern to the substrate while controlling the position of the substrate based on the calculated flatness. In a device manufacturing method including a lithography process,
27. A device manufacturing method, wherein in the lithography step, exposure is performed using the exposure method according to claim 25 or 26. An optimization device that optimizes selection of a plurality of data used in a predetermined process,
A creation device that creates a plurality of combinations of first data candidates used for the predetermined process from among a plurality of first data candidates;
A data group composed of a plurality of second data created when the predetermined processing is performed using a candidate for the first data included in the created combination, and a reference data group composed of a plurality of reference data An arithmetic unit that calculates correlation information indicating the degree of correlation by a predetermined correlation calculation;
And a determination device that determines a combination of first data used for the predetermined processing based on the calculated correlation information.   The optimization device according to claim 28, wherein the predetermined correlation calculation is a vector correlation calculation for calculating the correlation information by regarding each second data as a vector quantity.   29. The optimization apparatus according to claim 28, wherein the predetermined correlation calculation is a scalar correlation calculation that calculates the correlation information by regarding each second data as a scalar quantity. The determination device includes:
When there is a combination that satisfies a predetermined condition, the combination is a combination of a plurality of first data used for the predetermined process,
When there is no combination that satisfies the predetermined condition, all of the plurality of first data candidates are set as the first data used for the predetermined process,
31. The optimization apparatus according to claim 28, wherein the correlation information includes a correlation coefficient between a data group including the plurality of second data and the reference data group. The predetermined condition is:
32. The optimization device according to claim 31, further comprising: a correlation coefficient obtained by the arithmetic device being lower than a predetermined threshold value. The predetermined condition is:
32. The optimization apparatus according to claim 31, further comprising: a combination having a lowest correlation coefficient calculated by the arithmetic apparatus among a plurality of combinations generated by the generation apparatus.   The optimization device according to any one of claims 31 to 33, wherein the correlation coefficient is a correlation coefficient normalized by an average value of the second data. An optimization device that optimizes selection of a plurality of data used in a predetermined process,
A creation device that creates a temporary combination of first data by adding new first data candidates to a plurality of first data combinations used in the predetermined processing;
A data group consisting of a plurality of second data created when the predetermined processing is performed using the first data included in the created temporary combination, and before adding the candidate for the first data Correlation information indicating a correlation value with a data group composed of a plurality of second data created when the predetermined processing is performed using the first data included in the combination of the first data, and a predetermined correlation calculation An arithmetic unit that calculates by:
An optimization device comprising: an addition device that adds the candidate for the first data to the combination of the first data when a predetermined condition is satisfied based on the calculated correlation information.   Until the value indicated by the correlation information becomes a predetermined value or more, the creation of the temporary combination by the creation device, the calculation of the correlation information by the calculation device, and the addition by the addition device are repeatedly executed. 36. The optimizing device according to claim 35.   37. The optimization apparatus according to claim 35 or 36, wherein the predetermined correlation calculation is a vector correlation calculation for calculating the correlation information using each second data as a vector quantity.   37. The optimization apparatus according to claim 35 or 36, wherein the predetermined correlation calculation is a scalar correlation calculation that calculates the correlation information using each second data as a scalar quantity. The correlation information is
A data group composed of a plurality of second data created when the predetermined processing is performed using the first data included in the combination before adding the candidate for the first data, and the temporary combination The correlation coefficient with a data group composed of a plurality of second data created when the predetermined processing is performed using the included first data. The optimization apparatus as described in the item. The predetermined condition is:
The value indicated by the correlation information calculated by the arithmetic device is not equal to or greater than the first threshold;
The value indicated by the correlation information calculated by the arithmetic device is not less than or equal to a second threshold value smaller than the first threshold value;
The accuracy index of the processing result when the predetermined processing is performed using the first data included in the created temporary combination is included in the first combination before adding the first data candidate. 40. The optimization apparatus according to claim 39, comprising at least one of being better than an accuracy index of a processing result when the predetermined processing is performed using data.   41. The optimization apparatus according to claim 39 or 40, wherein the correlation coefficient is a correlation coefficient normalized by an average value of the second data. The predetermined processing indicates a deviation between a first coordinate system that defines a moving position of a moving body on which an object is placed and a second coordinate system that is defined by an array of a plurality of regions formed on the object. It is a process to detect multiple error information,
The candidate for the plurality of first data is a measurement value of position information on the first coordinate system of at least a part of the plurality of regions, according to any one of claims 28 to 41. Optimization device.   43. The optimization device according to claim 42, wherein the second data is a correction amount from a design value related to position information on the first coordinate system of each of the plurality of regions based on the error information. .   The second data is a residual between the position information on the first coordinate system of each of the plurality of regions corrected based on the error information and the measurement value of the position information on the first coordinate system. 43. The optimization device according to claim 42, wherein: The predetermined process is a process of detecting the flatness of the surface of the object,
The plurality of first data candidates are measured values of the surface height of the object at different measurement points on the surface of the object,
The second data is a height at each measurement point on a curved surface indicating a surface of the object, which is obtained based on a measurement value of the surface height of the object at each measurement point. The optimization device according to any one of claims 28 to 41. Measurement values of the position information of the marks respectively attached to the plurality of regions formed on the substrate are used as first data candidates, and the mark data as the first data is selected from the position information of the plurality of marks. 45. The optimization device according to any one of claims 42 to 44, which extracts position information;
Based on the extracted position information of the mark, a deviation between the first coordinate system that defines the movement position of the moving body on which the substrate is placed and the second coordinate system that is defined by the arrangement of the plurality of regions is determined. A detection device for detecting a plurality of error information shown;
An exposure apparatus comprising: a transfer device that transfers a predetermined pattern to the substrate while performing position control of the substrate based on a detection result of the detection device. Measurement values of the surface height of the substrate at a plurality of different measurement points on the surface of the substrate are used as first data candidates, respectively, from among the measurement values of the surface height of the substrate at the plurality of measurement points, 46. The optimization apparatus according to claim 45, wherein a measurement value of the surface height of the substrate as one data is extracted;
A calculation device for obtaining flatness of the substrate based on a measurement value of the surface height of the substrate at each of the extracted measurement points;
An exposure apparatus comprising: a transfer device that transfers a predetermined pattern to the substrate while performing position control of the substrate based on the detection result. A program for causing a computer to execute processing for optimizing selection of a plurality of data used for predetermined processing,
A first procedure for creating a plurality of combinations of first data candidates used for the predetermined processing from a plurality of first data candidates;
A data group composed of a plurality of second data created when the predetermined processing is performed using a candidate for the first data included in the created combination, and a reference data group composed of a plurality of reference data A second procedure for calculating correlation information indicating the degree of correlation by a predetermined correlation calculation;
A program for causing the computer to execute a third procedure for determining a combination of first data used for the predetermined processing based on the calculated correlation information. In the second procedure,
49. The program according to claim 48, wherein the computer executes a vector correlation calculation for calculating the correlation information by regarding each second data as a vector quantity as the predetermined correlation calculation. In the second procedure,
49. The program according to claim 48, causing the computer to execute a scalar correlation calculation for calculating the correlation information by regarding each second data as a scalar quantity as the predetermined correlation calculation. Prior to the second step,
Causing the computer to further execute a fourth procedure for creating a data group composed of a plurality of second data created when the predetermined processing is performed using all of the plurality of first data candidates,
The program according to any one of claims 48 to 50, wherein the computer is caused to execute the second procedure using the data group created in the fourth procedure as the reference data group. When there is a combination that satisfies a predetermined condition, the combination is a combination of a plurality of first data used for the predetermined process,
When there is no combination that satisfies the predetermined condition, the computer is caused to execute the third procedure so that all of the plurality of first data candidates are used as the first data used for the predetermined process. The program according to claim 51.   52. The program according to claim 51, wherein the correlation information includes a correlation coefficient between the data group composed of the plurality of second data and the reference data group. The predetermined condition is:
54. The program according to claim 53, comprising: the correlation coefficient calculated in the second procedure being lower than a predetermined threshold value. The predetermined condition is:
54. The program according to claim 53, comprising: a combination having a lowest correlation coefficient calculated in the second procedure among a plurality of combinations created in the first procedure. The predetermined condition is:
The accuracy index of the processing result when the predetermined processing is performed using a plurality of first data candidates included in the combination is performed using the plurality of first data candidates. The program according to claim 54 or 55, further comprising: being better than an accuracy index of a processing result at the time. A program for causing a computer to execute processing for optimizing selection of a plurality of data used for predetermined processing,
A first procedure for creating a temporary combination of first data by adding first data candidates to the first data combination;
A data group consisting of a plurality of second data created when the predetermined processing is performed using the first data included in the created temporary combination, and before adding the candidate for the first data Correlation information indicating a degree of correlation with a data group composed of a plurality of second data created when the predetermined processing is performed using the first data included in the combination of the first data, and a predetermined correlation calculation A second procedure calculated by:
A program for causing a computer to execute a third procedure of adding a candidate for the first data to the combination of the first data when a predetermined condition is satisfied based on the calculated correlation information.   58. The computer according to claim 57, wherein the computer repeatedly executes the first procedure, the second procedure, and the third procedure until a value indicated by the correlation information is equal to or greater than a predetermined value. Program.   59. The program according to claim 57 or 58, wherein the predetermined correlation calculation is a vector correlation calculation for calculating the correlation information using each second data as a vector quantity.   59. The program according to claim 57 or 58, wherein the predetermined correlation calculation is a scalar correlation calculation for calculating the correlation information using each second data as a scalar quantity. The correlation information is
A data group composed of a plurality of second data created when the predetermined processing is performed using the first data included in the combination before adding the candidate for the first data, and the temporary combination A correlation coefficient with a data group consisting of a plurality of second data created when the predetermined processing is performed using the included first data;
The predetermined condition is:
The program according to any one of claims 57 to 60, wherein the value indicated by the correlation information calculated in the second procedure includes that the value is not equal to or greater than a first threshold value. The predetermined condition is:
The accuracy index of the processing result when the predetermined processing is performed using the first data included in the created temporary combination is included in the first combination before adding the first data candidate. 62. The program according to claim 61, further comprising: being better than an accuracy index of a processing result when the predetermined processing is performed using data. An information recording medium readable by a computer on which the program according to any one of claims 48 to 62 is recorded.

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