JP2010040553A - Position detecting method, program, position detection device, and exposure device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position detecting method attaining high throughput and accuracy. <P>SOLUTION: A set of some markers is repeatedly selected from the limited number of markers indicating position information of a plurality of shot regions SA arrayed on an object at a probability proportional to a set of predetermined probability distributions defined on the limited number of markers. Each position of a set of markers when an index indicative of an error from a predetermined model for defining the array of a plurality of cell regions is minimized is measured from the selected predetermined set of markers. A value of a parameter of the model expressing strain is estimated from each position of the measured set of markers by an importance weighting least square method. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a position detection method, a program, a position detection apparatus, and an exposure apparatus for aligning a substrate when projecting and exposing a pattern image onto a photosensitive substrate in a manufacturing process of a semiconductor element or a liquid crystal display element.

  In the manufacture of semiconductor elements and liquid crystal display elements, an image of a fine pattern formed on a photomask or reticle (hereinafter referred to as a reticle) using an exposure apparatus is applied to a semiconductor wafer coated with a photosensitive agent such as a photoresist, Projection exposure is performed on a substrate such as a glass plate (hereinafter referred to as a wafer).

  The reticle pattern is projected and exposed by aligning the reticle and wafer with high precision using, for example, a step-and-repeat exposure apparatus and overlaying the pattern already formed on the wafer. The The requirement for the accuracy of this alignment has become stricter with the miniaturization of the pattern, and various ideas have been made for the alignment.

  The alignment of the reticle generally uses exposure light. As reticle alignment, for example, exposure light is irradiated onto an alignment mark (hereinafter referred to as a marker) drawn on the reticle, image data of the marker imaged by a CCD camera or the like is subjected to image processing, and the mark position is measured. There is a VRA (Visual Reticle Alignment) method.

  On the other hand, examples of the wafer alignment method include an LSA (Laser Step Alignment) method, an FIA (Field Image Alignment) method, and an LIA (Laser Interferometric Alignment) method. The VRA method is a method of irradiating a laser beam with a dot array marker on a wafer and detecting the mark position using light diffracted or scattered by the mark. The FIA method is a method of detecting the position of a marker by illuminating with light having a wide wavelength bandwidth using a halogen lamp or the like as a light source, and processing image data of the marker imaged by a CCD camera or the like. The LIA method is a method of irradiating a marker on a diffraction grating on a wafer with laser light having a slightly different frequency from two directions, causing the two diffracted lights to interfere with each other, and measuring the position of the marker from its phase. .

  In these optical alignments, first, the marker detection process on the reticle is performed, and the position coordinates of the marker on the reticle are measured. Next, the marker on the wafer is detected and the position coordinates of the marker on the wafer are measured to obtain the position (partition area) of the shot to be overlaid. Then, based on the position coordinates of the markers on the reticle and the position coordinates of the markers on the wafer, the wafer is moved by the wafer stage so that the reticle pattern image overlaps the shot position, and the reticle pattern image is projected and exposed. To do.

  As a conventional method of approximating the error, there is an enhanced global alignment (EGA) method in which the error amount is approximated by affine transformation when obtaining the superimposed shot position from the measurement result of the marker on the wafer. . The approximation of the error amount in the EGA method is based on the assumption of an affine transformation model that the shot arrangement is mainly determined by the expansion / contraction, rotation, and shift of the wafer. There is at least one marker on the wafer for every shot, but measuring all the markers is not ideal because it reduces throughput (processing capacity per unit time). The shot to be measured is preferably selected so that the expected overlay error is minimized, in other words, the overlay accuracy is the best. It is known that the optimum selection under the assumption that the shot arrangement is approximated with sufficient accuracy by the affine transformation model is to measure shots on the outer periphery of the wafer.

  However, in recent years, higher order distortion of the shot arrangement has become a problem as the required alignment accuracy increases. Therefore, it is necessary to approximate the shot arrangement with a higher-order model having a higher degree of freedom. However, in order to achieve high accuracy, it is necessary to perform more measurements according to the degree of freedom of the model.

  Therefore, for example, a method for achieving both high accuracy and high throughput has been proposed. For example, in order to cope with the individuality of the previous layer device that can cause higher-order distortion, many shots are measured only for the wafer at the head of the lot, and subsequent wafers are processed with the same higher-order distortion as the head wafer. There has been proposed a method of superimposing on the assumption that there is. In addition, a method has been proposed in which a change in higher-order components is detected by a model selection method, and the model and the number of measurement points are changed based on the result. In this way, when using a higher-order model, it is ideal to select a measurement shot so that the overlay accuracy is the best, as in the case of affine transformation.

  However, since the selection of measurement shots is not obvious, the conventional method performs shot selection so that measurement shots are distributed as uniformly as possible. Therefore, the conventional method cannot always exhibit ideal performance in terms of both high accuracy and high throughput.

  As described above, for example, traditional active learning can be applied to the problem of achieving both high accuracy and high throughput (see, for example, Non-Patent Document 1). In the active learning described in Non-Patent Document 1, a model error index that is expected when a shot is measured is formulated, and a shot is selected so as to minimize the formulated model error index. . For example, measuring an outer periphery of a wafer when an affine transformation model is used is based on a traditional active learning method.

  Also, when using a higher-order model, traditional active learning can be applied as well, but it is not optimal for the following reasons. In other words, the traditional active learning evaluation criteria is derived under the assumption that the model can approximate the actual shot array with good accuracy, and the model can approximate the actual shot array with good accuracy. Only optimal for.

  On the other hand, in aligning the exposure apparatus, it is necessary to minimize the number of measurement shots in order to achieve high throughput, and it is necessary to limit the complexity of the model accordingly. Therefore, when using higher-order models, it is not optimal to apply traditional active learning because assumptions for applying traditional active learning are not satisfied.

  Thus, an evaluation standard that can be used when traditional active learning cannot be applied has also been proposed (see, for example, Non-Patent Document 2). However, this method can be used when the measurement coordinates can be freely selected, specifically, when the measurement coordinates can be freely selected from an infinite number of shots, so the optimum shot set is selected from a finite number of markers. It cannot be applied to the method to do.

  In addition, a method that can select an optimal shot set from a finite number of markers has been proposed (see, for example, Non-Patent Document 3). However, this method does not provide good overlay accuracy.

JP 2006-108533 A Fedorov, V.V. Theory of optimal experiments. New York: Academic Press. (1972) Sugiyama, M. Active learning in approximately linear regression based on conditional expectation of generalization error. Journal of Machine Learning Research, vol.7 (Jan), pp.141-166 (2006) Takafumi Kanamori: Pool-based active learning with optimal sampling distribution and its information geometrival interpretation. Neurocomputing 71 (1-3): 353-362 (2007)

  Accordingly, the present invention solves the above-described conventional problems, and provides a position detection method, a program, and a position detection apparatus and an exposure apparatus to which the position detection method can be applied that can achieve both high throughput and high accuracy. The purpose is to provide.

  In the position detection method according to the present invention, the array of the plurality of partition regions is defined by measuring the finite number of markers from the finite number of markers serving as position information of the plurality of partition regions arranged on the object. Based on the first step of measuring each position of the set of some markers that minimizes the index indicating the accuracy when the parameters of the predetermined model are estimated, and the plurality of positions based on the positions of the measured set of markers And a second step of estimating the value of the parameter of the model expressing the distortion of the divided area by the importance-weighted least square method.

  Further, the program according to the present invention defines the arrangement of the plurality of partitioned areas by measuring the finite number of markers from the finite number of markers serving as position information of the plurality of partitioned areas arranged on the object. Based on the first step of measuring each position of the set of some markers that minimizes the index indicating the accuracy when the parameters of the predetermined model are estimated, and the plurality of positions based on the positions of the measured set of markers This is to cause the information processing apparatus to execute a process including a second step of estimating the value of the parameter of the model expressing the distortion of the divided area by the importance-weighted least square method.

  Furthermore, the position detection device according to the present invention measures the finite number of markers from a finite number of markers serving as position information of the plurality of partitioned regions arranged on the object, thereby determining the arrangement of the plurality of partitioned regions. A measuring unit for measuring each position of a set of some markers that minimizes an index indicating accuracy when a parameter of a predetermined model to be defined is estimated, a first step, and a set of markers measured by the measuring unit An estimation unit that estimates a parameter value of a model that expresses the distortion of the plurality of partition regions based on each position by the importance-weighted least square method.

  Furthermore, the exposure apparatus according to the present invention measures the finite number of markers by measuring the finite number of markers from the finite number of markers serving as position information of the plurality of exposure target regions arranged on the wafer. A measurement unit that measures each position of a set of some markers that minimizes an index indicating accuracy when estimating a parameter of a predetermined model that defines an array, and each position of the set of markers measured by the measurement unit Based on the parameter value of the model that represents the distortion of the plurality of exposure target areas based on the importance weight-weighted least square method and the parameter value estimated by the estimation unit. A drive unit that drives the wafer so that the exposure target region is a predetermined exposure position, and a plurality of exposure target regions of the wafer driven by the drive unit. Te, and a radiation unit for irradiating the light for light exposure.

  According to the present invention, a shot that minimizes an index indicating accuracy when a parameter of a predetermined model that defines an array of a plurality of partitioned regions is estimated by measuring the finite number of markers from a finite number of markers is selected. Therefore, it is possible to achieve both high throughput and high accuracy.

  Hereinafter, specific embodiments to which the present invention is applied will be described with reference to the drawings. FIG. 1 shows an exposure apparatus to which the present invention is applied. The exposure apparatus 1 according to the present embodiment is an index (expected) indicating accuracy when a parameter of a predetermined model that defines the arrangement of a plurality of partitioned regions is estimated by measuring the finite number of markers from a finite number of markers. It is possible to achieve both high throughput and high accuracy by selecting shots that minimize the error.

  The exposure apparatus 1 includes a light source 2, a reflecting mirror 4, a wavelength selection filter 5, a fly eye integrator 6, a reticle blind 7, a reflecting mirror 8, a lens system 9, a reticle 10, a projection optical system 11, a wafer 12, a stage 13, and a moving mirror. 14, a laser interference system 20, a stage drive unit 21, a reticle alignment sensor 31, a wafer alignment sensor 32, a reference mark member 33, an alignment control system 35, a stage control system 36, and a main control system 37.

  The light source 2 is composed of, for example, an ultrahigh pressure mercury lamp or an excimer laser. The illumination light emitted from the light source 2 is reflected by the reflecting mirror 4 and enters the wavelength selection filter 5.

  The wavelength selection filter 5 passes only light having a wavelength necessary for exposure. The illumination light that has passed through the wavelength selection filter 5 is adjusted to a light flux having a uniform intensity distribution by the fly eye integrator 6 and reaches the reticle blind 7.

  The reticle blind 7 adjusts the illumination range on the reticle 10 by illumination light by changing the size of the opening S. The illumination light that has passed through the opening S of the reticle blind 7 is reflected by the reflecting mirror 8 and enters the lens system 9, and an image of the opening S of the reticle blind 7 is formed on the reticle 10 by the lens system 9. The desired range of the reticle 10 is illuminated.

  An image existing in the illumination range of the reticle 10 is formed on a wafer 12 coated with a resist by the projection optical system 11. For example, the image existing in the illumination range of the reticle 10 includes a shot pattern or a marker image. Thus, the pattern image of the reticle 10 is exposed to a specific area of the wafer 12.

  The wafer 12 is held on the stage 13 by, for example, vacuum suction. The stage 13 has, for example, a known structure in which a pair of blocks movable in directions orthogonal to each other are overlapped.

For example, as shown in FIG. 2, on the wafer 12, a plurality of shot areas SA _p is the center position and C _p are regularly arranged and formed. Each shot area SA _p, by is applied through it to the step (processing including exposure processing and development processing) the same manufacturing process, the chip pattern is formed. Each shot area SA _p is divided by street lines with a predetermined width extending in the α direction and the β direction, and a wafer mark (hereinafter referred to as a marker) MX _p on the street line in contact with each shot area SA _p . MY _p is formed. These markers MX _p and MY _p are, for example, as shown in FIG. 2, in which three linear patterns are arranged at a predetermined pitch in the X direction and the Y direction, respectively. It is formed as a pattern. In the following description, it is assumed that marker measurement is performed for the markers MX _p and MY _p .

  Note that the shape of the mark formed on the wafer 12 is not limited to the one-dimensional mark as shown in FIG. 2. For example, a plurality of direct patterns extending in the α direction and a plurality of linear patterns extending in the β direction are appropriately combined. It may be a mark for two-dimensional measurement. The shape of the mark may be a two-dimensional measurement mark (for example, a cross mark) formed by appropriately combining a single linear pattern extending in the α direction and a single linear pattern extending in the β direction, or other configuration. The mark may be used.

  Returning to FIG. 1, the stage 13 is driven by a stage drive unit 21 such as a motor, so that the position in the stage movement coordinate system moves. As a result, the shot position on the wafer 12 overlapping the exposure field of the projection optical system 11 is adjusted. The position of the stage 13 in the stage moving coordinate system is detected by the laser interference system 20 toward the moving mirror 14 fixed to the stage 13. The measurement value in the laser interference system 20 is sent to the stage control system 36.

  Further, a reference mark member 33 having a surface having the same height as the surface of the wafer 12 is fixed on the stage 13. A mark serving as a reference for alignment is formed on the surface of the reference mark member 33.

  The reticle alignment sensor 31 and the wafer alignment sensor 32 are for aligning the reticle 10 and the wafer 12. The reticle alignment sensor 31 and the wafer alignment sensor 32 determine the reference position in each alignment sensor by measuring the mark on the reference mark member 33.

  The reticle alignment sensor 31 measures the positional relationship (shift amount) between the marker formed on the reticle 10 and the reference mark or wafer 12 on the reference mark member 33 observed through the projection optical system 11. As the reticle alignment sensor 31, for example, a TTR (through-the-reticle) method can be used. In particular, an LSA method using a He-Ne laser or the like, an LIA method, or an exposure light alignment method using exposure light. preferable. When the projection optical system 11 for KrF (krypton fluoride) and ArF (argon fluoride) excimer lasers is employed, the exposure light alignment method is preferable because of the chromatic aberration of the projection optical system 11. The reason why the exposure light alignment method is preferable is that the wavelengths of the He—Ne laser and the KrF / ArF excimer laser are greatly different. As described above, in the exposure light alignment method, for example, the positional relationship between the marker and the reference mark member 33 is directly observed by displaying the marker and the reference mark member 33 on the monitor using an imaging device (CCD). It becomes possible.

  On the other hand, as the wafer alignment sensor 32, an off-axis type sensor can be used. As an alignment method of the off-axis wafer alignment sensor 32, for example, an FIA method, an LSA method, an LIA method, or an exposure light alignment method using exposure light can be applied.

  In the alignment process, the position of the marker formed on the wafer is detected using the reticle alignment sensor 31 or the wafer alignment sensor 32. Based on the detection result, the pattern formed in the previous process on the shot area of the wafer 12 and the pattern on the reticle 10 are accurately aligned.

  The alignment control system 35 processes a detection signal from the reticle alignment sensor 31 or the wafer alignment sensor 32. The alignment control system 35 is controlled by the main control system 37.

  The stage control system 36 controls the stage drive unit 21 based on the measurement value sent from the laser interference system 20. Further, the stage control system 36 supplies information on measured values in the laser interference system 20 to the main control system 37. The stage control system 36 receives the alignment result from the main control system 37 and controls the stage driving unit 21 based on the alignment result to expose the shot.

  The main control system 37 is a general computer (information processing apparatus) composed of, for example, a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like. This is the part that supervises the control over. The main control system 37 can execute a position detection processing program, which will be described in detail later, by hardware, software, or a combined configuration of both. For example, software processing can be executed by installing a program that records a processing sequence into a memory in a computer incorporated in dedicated hardware, or by installing a program on a general-purpose computer that can perform various processes. It is.

  The main control system 37 controls the stage control system 36 based on the measurement value information in the laser interference system 20 supplied from the stage control system 36.

  Next, an example of the processing operation in the exposure apparatus 1 will be described with reference to the flowchart shown in FIG. Note that the various processes described below are not only executed in time series according to the description, but may be executed in parallel or individually as required by the processing capability of the apparatus that executes the processes.

  In step S1, reticle 10 is loaded on a reticle stage (not shown).

  In step S2, the main control system 37 executes a reticle alignment process. Specifically, the main control system 37 positions the reference mark member 33 on the stage 13 at a predetermined position (hereinafter referred to as a reference position) directly below the projection optical system 11 via the stage drive unit 21. Subsequently, the main control system 37 detects a relative position between the pair of reticle marks on the reticle 10 corresponding to the pair of reference marks on the reference mark member 33 by the pair of reticle alignment sensors 31. The main control system 37 stores the detection result by the reticle alignment sensor 31 and the measured value of the laser interference system 20 at the time of detection in a memory (not shown).

  In step S3, baseline measurement is performed. Specifically, the stage control system 36 returns the stage 13 to the reference position, and the reference mark on the reference mark member 33 is detected by the wafer alignment sensor 32. The main control system 37 calculates the distance between the baseline of the wafer alignment sensor 32, that is, the projection center of the reticle pattern and the detection center (index center) of the wafer alignment sensor 32.

  In step S4, the main control system 37 initializes the wafer number.

  In step S5, the main control system 37 loads the wafer 12 onto a wafer holder (not shown) on the stage 13 via a wafer loader (not shown).

  In step S6, the main control system 37 performs wafer alignment processing. In this wafer alignment process, the arrangement of shot areas on the wafer 12 in the coordinate system of the stage 13 is estimated, and the center positions of all shot areas are calculated. Specifically, as will be described in detail later, when the main control system 37 measures the marker formed on the wafer 12, the index indicating the error of the model that defines the arrangement of the shot areas is minimized. A set of markers is selected, and the selected marker set is measured.

  In step S7, the main control system 37 sets the first shot area as an exposure target area.

  In step S8, the main control system 37 positions the operation start position. Specifically, the main control system 37 sets the position of the wafer 12 to be an acceleration start position for exposing the shot area on the wafer 12 based on the array coordinates of the shot area calculated in step S6. Here, the main control system 37 drives the stage 13 via the stage control system 36 and the stage drive unit 21. Further, the main control system 37 moves the reticle stage via the stage control system 36 and a reticle stage drive unit (not shown) so that the position of the reticle 10 becomes the acceleration start position.

  In step S9, the main control system 37 executes an exposure process. Specifically, the main control system 37 starts relative scanning between the stage 13 and the reticle stage, and when both stages reach their respective target scanning speeds and reach a constant speed synchronous state, the reticle is illuminated by illumination light from the light source 2. The ten pattern areas are illuminated and scanning exposure is started.

  In step S10, the main control system 37 determines whether exposure has been performed on all shot areas by referring to a counter value, for example.

  In step S11, the main control system 37 increments the counter value and sets the next shot area as an exposure target area, thereby executing the process of step S8 again.

  In step S <b> 12, the main control system 37 instructs unloading of the wafer 12. Thereby, the wafer 12 is unloaded from, for example, the wafer holder and then transferred to a coater / developer (not shown) connected inline to the exposure apparatus 1 by a wafer transfer system (not shown). .

  In step S13, the main control system 37 determines whether exposure of all the wafers 12 in the lot has been completed. If the main control system 37 determines that the exposure of all the wafers 12 in the lot has been completed, the main control system 37 ends the exposure process, and if it determines that the exposure of all the wafers 12 has not been completed, The process of S5 is executed again.

  Next, details of the wafer alignment process in step S6 will be described.

The coordinates (vertical position and horizontal position) on the design value of the shot are x = (x ₁ , x ₂ ) ^T, and the deviation from the design value is (δx ₁ , δx ₂ ) ^T. That is, the actual shot position is given by (x ₁ + δx ₁ , x ₂ + δx ₂ ) ^T. Note that the subscript T represents transposition. In the following, attention is paid to one component of the minute deviation amount (δx ₁ , δx ₂ ) ^T , and this minute deviation amount is assumed to be y. A model expressing shot distortion can be expressed by the following equation (8), for example.

  Here, in order to construct a more accurate model, the basis functions may be increased. For example, if a model includes up to a quadratic function, it is expressed as in equation (10).

However, optimal overlay accuracy cannot be realized with a marker set (measurement point set) optimized for an affine transformation model. Therefore, in the exposure apparatus 1 according to the present embodiment, a marker set is selected by the following procedure. That is, the main control system 37, a finite number of markers _MX p to be a positional information of the plurality of shot areas SA _p arranged in a wafer 12, from MY _p, the predetermined defined marker _MX p, on MY _p probability A set of predetermined markers MX _p and MY _p is repeatedly selected with a probability proportional to the set of distributions. The main control system 37 uses the marker MX for minimizing an index indicating the accuracy when a parameter of a predetermined model that defines the arrangement of the plurality of shot areas SA _p is estimated from the set of the selected markers MX _p and MY _p. A set of _p and MY _p is selected. Subsequently, the main control system 37 measures each position in the coordinate system of the stage 13 of the set of selected markers MX _p and MY _p . Then, the main control system 37 defines the arrangement of the plurality of shot areas SA _p by using the positions of the designed markers MX _p and MY _p and the measured positions of the markers MX _p and MY _p . (8) The value of the parameter of the model formula expressing the distortion defined by the formula is estimated by statistical processing (specifically, a weighted least square method).

  Hereinafter, an example of a process of selecting a marker set will be described with reference to the flowchart shown in FIG. The main control system 37 selects an optimum measurement shot (marker set) by the process described below.

  First, in step S20, the main control system 37 calculates a t × t matrix U whose components are values defined by the following equation (11). Assume that the set of basis functions is determined in advance.

Specifically, (12) the set of all shots a value defined by the equation, i.e., a value defined by equation (12), and respective position information of the shot area SA _p arranged on the wafer 12 The entire marker set.

Further, the value defined by the equation (13) is set as a measurement point set, that is, a predetermined marker set to be selected. Incidentally, for example, (13) measurement points defined by the equation set is possible to determine when the sequence of the shot areas SA _p on the wafer 12 has been designed.

  In step S21, the main control system 37 sets the predetermined marker set (sample) defined by the above expression (13) from the set of all shots defined by the expression (12) and the probability defined by the expression (14). Select with probability proportional to the set of distributions.

  Specifically, in order to create a set of probability distribution candidates on the set of all shots defined by the equation (12), for example, the following equation (15) is calculated for a given γ ≧ 0.

  Here, the value of γ in the above-described equation (14) characterizes the equation (14). That is, γ dominates the shape of the probability distribution. In the exposure apparatus 1, it is desirable to perform calculations for all γ in order to achieve high measurement accuracy. However, if the exposure apparatus 1 performs calculations for all γ in this way, a great amount of calculation time is required, so that the optimum value of γ cannot be searched quickly. Therefore, in the exposure apparatus 1 according to the present embodiment, it is desirable to finely search around γ = 0.5 in order to achieve high accuracy and shorten the time of wafer alignment processing. In the exposure apparatus 1, for example, by calculating a marker set corresponding to the value of γ defined by the following equation (16), the set of the entire shot is compared (when γ = 0). Thus, high measurement accuracy can be obtained and calculation time can be shortened.

In step S22, the main control system 37 calculates an (n ^tr × t) matrix X _γ defined by, for example, equation (17).

In step S23, the main control system 37 calculates a diagonal matrix W _γ of (n ^tr × n ^tr ) defined by, for example, equation (18). Here, W is a diagonal matrix having the weight w as a diagonal component.

In step S24, the main control system 37 calculates a matrix L _γ defined by equation (19) using, for example, the matrix calculated by equations (17) and (18).

  In step S25, the main control system 37 calculates a value defined by equation (20) using the matrix calculated by equations (11) and (19) described above.

Here, CV _w (γ) defined by the equation (20) defines the arrangement of the plurality of shot areas SA _p by measuring the finite number of markers from the selected set of predetermined markers (8 This is an index indicating the accuracy in estimating the parameters of the model expressing the distortion of the shot area defined by the equation (1).

  Subsequently, in step S26, the main control system 37 determines whether or not the calculations in steps S22 to S25 have been performed for all γ in γ in the equation (14). For example, when the main control system 37 determines that calculation has been performed for all γ defined by the equation (15), the main control system 37 executes the process of step S27. On the other hand, when the main control system 37 determines that calculation has not been performed for all γ defined by the equation (15), it executes the process of step S21 again.

  In step S27, the main control system 37 selects a set (sample) of markers corresponding to γ when the value defined by equation (20) is minimized as a set of measurement points. It should be noted that the processing up to step S27 is preferably calculated in advance offline.

  In step S28, the main control system 37 measures the position of the measurement point set selected in step S27. As described above, the main control system 37 can achieve high alignment accuracy and high throughput by selecting a measurement point set corresponding to γ when the value defined by the equation (20) is minimized. it can. That is, the exposure apparatus 1 can achieve both high accuracy and high throughput.

In step S29, the main control system 37 estimates (21) defining an array of a plurality of shot areas SA _p defined by equation (8) the value of the parameter of a predetermined model defined by the formula (theta) . That is, the parameter value in equation (21) is represented by a linear combination of the selected measurement point set value y, and the solution of the normal equation is determined by the least square method.

  In the formula (21), y is expressed as (22), for example.

  That is, the parameter value defined by the equation (21) is determined by the importance-weighted least square method as defined by the equation (23) in order to improve the estimation accuracy of the parameter value. .

  Here, w (x) is the importance and is defined by equation (24).

In the equation (24), (p _te (x)) is a test input density, and (p _tr (x)) is a training input density. The training input density (p _tr (x)) is determined from a predetermined marker set defined by the above-described equation (13). In the importance weighted least squares method (OWLS), training data having a high test input density and a low training input density are strongly weighted. That is, according to the importance weighted least squares method, training data that does not resemble test data is excluded, and data that resembles test data is automatically selected. That is, by using the importance-weighted least square method, the calculation accuracy can be further improved as compared with the case of using the ordinary least square method (OLS: Ordinary Least Squares). (For the importance-weighted least square method, see, for example, the following non-patent literature. H. Shimodaira. Improving predictive inference under covariate shift by weighting the log-likelihood function. Journal of Statistical Planning and Inference, 90 (2) : 227-244,2000.)

[Evaluation Test 1]
Subsequently, a result of simulation using the above-described algorithm will be described.
In this simulation, the input dimension d is set to 1, and the target function to be learned is expressed by the following equation (25).

  In the equation (25), γ (x) is a value defined by the following equation (26).

  In the formula (26), z is a value defined by the following formula (27).

  Here, γ (x) defined by equation (26) is a cubic polynomial, and was selected to satisfy the following equations (28) and (29).

In this simulation, for each of the following algorithms of Example 1 and Comparative Examples 1 to 3, mean square errors were observed when δ was 0, 0.03, and 0.06. In addition, the number of trials (n _tr ) was set to 100, and the value defined by the following equation (30) was set to Gaussian noise that is iid (independent identical distribution). Here, iid refers to a sequence of random variables that are independent of each other and have the same distribution.

The Gaussian noise defined by equation (30) was treated as an unknown value with an average value = 0 and σ (standard deviation) = 0.3. Further, P _te (x) is a Gaussian distribution with an average value = 0.2 and σ = 0.4, and this P _te (x) is also treated as unknown.

In addition, 1000 test input points (n _te = 1000) were extracted independently from the test input distribution. For learning, a second-order polynomial model defined by the following equation (31) was used.

[Example 1]
In Example 1, the measurement point set corresponding to γ defined by Equation (16) was selected in Equation (14). The importance-weighted least square method (OWLS) was used to estimate the value of the parameter defined by equation (21).

[Comparative Example 1]
Comparative Example 1 was performed in the same manner as in Example 1 except that an optimal value of γ was selected from a set of probability distributions defined by the following equation (32).

[Comparative Example 2]
In Comparative Example 2, instead of the equation (20), a measurement point set corresponding to γ defined by the equation (16) is selected based on the following equation (33). It carried out like Example 1 except having used the square method (OLS).

In the equation (33), the matrix L _O is represented as the following equation (34). (For details, see Non-Patent Document 1, Cohn, DA, Ghahramani, Z., Jordan, MI (1996). Active learning with statistical models. JAIR, 4, 129-145., Fukumizu, K. (2000). Statistical. active learning in multilayer perceptrons. See IEEE TNN, 11, 17-26.)

[Comparative Example 3]
In Comparative Example 3, a marker was uniformly selected from a set of measurement points corresponding to random γ, that is, on the wafer. Further, the least square method (OLS) was used for estimation of the parameter value.

[Evaluation result 1]
Regarding Example 1, Comparative Example 1, Comparative Example 2, and Comparative Example 3, Table 1 shows the results of the mean square error when δ is 0, 0.03, and 0.06.

  That is, as shown in Table 1, the mean square error is 2.03 ± 1.81 in Example 1, 2.56 ± 2.10 in Comparative Example 1, and in Comparative Example 2 when δ = 0. 1.87 ± 1.85, and in Comparative Example 3, it was 3.30 ± 2.64. From this result, it can be seen that substantially the same results are obtained in Example 1 and Comparative Example 2. Moreover, in Example 1, it turns out that a better result than the comparative example 1 and the comparative example 3 is obtained.

  Further, when δ = 0.03, in Example 1, 2.04 ± 1.85, in Comparative Example 1, 2.62 ± 2.16, in Comparative Example 2, 2.60 ± 2.45, comparison In Example 3, it was 3.40 ± 3.02. From this result, in Example 1 and Comparative Example 1, almost the same result was obtained as compared to when δ = 0, but in Comparative Example 2, the result was significantly larger than when δ = 0. You can see that it got worse.

  Further, when δ = 0.06, in Example 1, 2.15 ± 2.26, in Comparative Example 1, 2.78 ± 2.65, in Comparative Example 2, 4.80 ± 4.15, comparison In Example 3, it was 3.86 ± 3.98. From this result, in Example 1 and Comparative Example 1, almost the same result was obtained as compared to when δ = 0, but in Comparative Example 2, the result was significantly larger than when δ = 0. You can see that it got worse. That is, when δ = 0.06, in Comparative Example 2, the error was significantly increased. In Comparative Example 2, the result was worse than Comparative Example 3.

  From these results, it can be seen that the first example shows higher robustness to the model error than the case of the first to third comparative examples.

[Evaluation Test 2]
Subsequently, the alignment of the wafer was evaluated using the exposure apparatus 1 shown in FIG. Specifically, the number of trials is set to 100, and the data of 220 continuous wafers are shifted in the horizontal direction and the vertical direction (mean square error) using the secondary model defined by the above-described equation (10). ) Was observed. The number of samples was 20. That is, 20 markers provided on the wafer were selected.

[Example 2]
In Example 2, it carried out similarly to Example 1.

[Comparative Example 4]
In Comparative Example 4, the same operation as in Comparative Example 1 was performed.

[Comparative Example 5]
In Comparative Example 5, the same operation as in Comparative Example 2 was performed.

[Comparative Example 6]
In Comparative Example 6, the same operation as in Comparative Example 3 was performed.

[Comparative Example 7]
In Comparative Example 7, 20 markers on the outer periphery of the wafer were selected.

[Evaluation result 2]
Table 2 shows the results of Evaluation Test 2 regarding Example 2 and Comparative Examples 4 to 7.

  That is, as shown in Table 2, each mean square error was as follows. That is, the mean square error is 1.93 ± 0.89 in Example 2, 2.09 ± 0.98 in Comparative Example 4, and 1.96 in Comparative Example 5. In the case of ± 0.91, Comparative Example 6, it was 2.32 ± 1.15, and in the case of Comparative Example 7, it was 2.13 ± 1.08.

  As described above, according to the second embodiment, when 20 markers on the wafer are selected for the secondary model, the prediction error of the alignment of all the markers is selected uniformly. Compared with (Comparative Example 6), about 16.8% can be reduced. In addition, according to the present invention, the prediction error of the alignment of all the markers can be reduced by about 9.3% compared to the case where 20 markers on the outer periphery of the wafer are selected (Comparative Example 7).

It is a figure which shows the example of 1 structure of the exposure apparatus which concerns on this embodiment. It is a figure which shows an example of the shot area | region on the shot area | region on a wafer, and this. It is a flowchart which shows an example of processing operation in the exposure apparatus which concerns on this embodiment. It is a flowchart which shows an example of a wafer alignment process.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 Exposure apparatus, 2 Light source, 4 Reflecting mirror, 5 Wavelength selection filter, 6 Fly eye integrator, 7 Reticle blind, 8 Reflecting mirror, 9 Lens system, 10 Reticle, 11 Projection optical system, 12 Wafer, 13 Stage, 14 Moving mirror , 20 Laser interference system, 21 Stage drive unit, 31 Reticle alignment sensor, 32 Wafer alignment sensor, 33 Reference mark member, 35 Alignment control system, 36 Stage control system, 37 Main control system

Claims (7)

When the parameters of a predetermined model that prescribes the array of the plurality of partition regions are estimated from the finite number of markers that are the positional information of the plurality of partition regions arranged on the object A first step of measuring each position of a set of some markers that minimizes an index indicating accuracy;
A second step of estimating, based on each position of the measured marker set, a parameter value of a model that expresses distortion of the plurality of partition regions by an importance-weighted least square method; . In the first step, from a finite number of markers serving as position information of the plurality of partitioned areas defined by equation (1), a probability proportional to a set of predetermined probability distributions defined by equation (2) is used. , Selecting a plurality of sets of the partial markers defined by the equation (3), measuring each position of the marker set when minimizing the index defined by the equation (4),
The parameter value of the model expressing the distortion defined by the equation (6) is estimated in the second step when each position of the measured marker set is defined by the equation (5). Position detection method.

  3. The position detection method according to claim 2, wherein the set of the partial markers is one when the value γ characterizing the equation (2) is about 0.5. The position detection method according to claim 2, wherein the set of some markers is a value when the value γ characterizing the equation (2) is defined by the equation (7).

When the parameters of a predetermined model that prescribes the array of the plurality of partition regions are estimated from the finite number of markers that are the positional information of the plurality of partition regions arranged on the object A first step of measuring each position of a set of some markers that minimizes an index indicating accuracy;
A second step of estimating, based on each position of the measured marker set, a parameter value of a model that expresses distortion of the plurality of partition regions by an importance-weighted least square method; For causing the information processing apparatus to execute the program. When the parameters of a predetermined model that prescribes the array of the plurality of partition regions are estimated from the finite number of markers that are the positional information of the plurality of partition regions arranged on the object A measurement unit that measures each position of a set of some markers that minimizes an index indicating accuracy;
A position detection unit comprising: an estimation unit configured to estimate a value of a parameter of a model expressing distortion of the plurality of partitioned regions based on each position of the set of markers measured by the measurement unit using an importance-weighted least square method apparatus. A parameter of a predetermined model that prescribes the arrangement of the plurality of exposure target regions was estimated from a finite number of markers serving as position information of the plurality of exposure target regions arranged on the wafer. A measurement unit that measures each position of a set of some markers that minimizes the index indicating the accuracy of the case,
Based on each position of the set of markers measured by the measurement unit, an estimation unit that estimates the value of a parameter of a model expressing distortion of the plurality of exposure target regions by an importance weighted least square method;
A driving unit that drives the wafer based on the parameter value estimated by the estimating unit so that the plurality of exposure target regions are at predetermined exposure positions;
An exposure apparatus comprising: an irradiation unit that irradiates a plurality of exposure target areas of the wafer driven by the driving unit with light for exposure.

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