Patent Publication Number: US-2012033194-A1

Title: Decision method and storage medium

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a decision method and a storage medium. 
     2. Description of the Related Art 
     In recent years, as semiconductor device micropatterning technology has progressed, it has become difficult to transfer (resolve) a pattern onto a substrate (for example, a wafer). In an exposure apparatus, super-resolution technologies such as modified illumination (off-axis illumination) and OPC (Optical Proximity Correction) are used to cope with the semiconductor device micropatterning. An effective light source (illumination shape) that illuminates an original (a mask or a reticle) is known to affect the pattern resolution. Japanese Patent Laid-Open No. 2009-302206 proposes a technique of sequentially setting (changing) parameters that define the effective light source for illuminating the original and evaluating (measuring) the dimension of the pattern image to be formed on the substrate, thereby deciding the effective light source optimum for the original pattern. In addition, to measure the dimension of the pattern image, “SPIE 2009 7274-033” proposes a technique of setting a plurality of evaluation lines for a pattern element to be measured and measuring the edge on the evaluation lines of a resist pattern corresponding to the pattern element by using a scanning electron microscope (SEM). 
     However, since the pattern resolution is affected by the effective light source, the pattern element to be measured may remain unresolved, that is, the image of the pattern element to be measured and the image of another pattern element may remain unseparated until the effective light source is decided. In the related arts, since it is impossible to correctly evaluate whether the pattern element to be measured is resolved, the dimension of the pattern image is measured based on the misrecognized edge of a resist pattern (that is, the pattern element image) corresponding to the unresolved pattern element. The present inventor has found that in such a case, since the evaluation function to be used to decide the effective light source discontinuously changes in accordance with the measurement result based on the misrecognized edge, the effective light source optimization cannot converge, and the effective light source cannot be decided. 
     SUMMARY OF THE INVENTION 
     The present invention provides a technique advantageous in evaluating the dimension of a pattern image in consideration of whether the images of a plurality of pattern elements included in a pattern are separately formed. 
     According to one aspect of the present invention, there is provided a decision method of causing a computer to decide an exposure condition to be set in an exposure apparatus including an illumination optical system that illuminates a pattern including a plurality of pattern elements, and a projection optical system that projects the pattern onto a substrate, including a first step of setting a first line to be used to evaluate dimensions of images of the pattern elements on the image plane of the projection optical system, a second step of setting a second line to be used to evaluate whether the images of the pattern elements are resolved on the image plane of the projection optical system, a third step of obtaining a distance between intersections of the first line and contours of the images of the pattern elements by obtaining the image of the pattern formed on the image plane of the projection optical system, a fourth step of determining whether there exist intersections of the second line and the contours of the images of the pattern elements to evaluate whether the images of the pattern elements are resolved, a fifth step of evaluating the obtained image of the pattern by setting a value of the distance obtained in the obtaining the distance as an evaluation value upon determining, in the fourth step, that there exist no intersections, and setting an outlier different from the value of the distance obtained in the obtaining the distance as the evaluation value upon determining, in the fourth step, that there exist the intersections, and a sixth step of deciding the exposure condition based on an evaluation result in the fifth step such that the image of the pattern formed on the image plane of the projection optical system satisfies a criterion for evaluation. 
     Further aspects of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a flowchart for explaining an evaluation method according to an embodiment of the present invention. 
         FIG. 2  is a view for explaining a dimension evaluation line segment and a resolution evaluation line segment according to the embodiment. 
         FIGS. 3A and 3B  are views showing the contours of mask pattern images formed on the image plane of a projection optical system upon illuminating the mask pattern shown in  FIG. 2 . 
         FIGS. 4A and 4B  are views for explaining a case in which a plurality of resolution evaluation line segments are set. 
         FIG. 5  is a schematic block diagram showing the arrangement of an information processing apparatus which executes a decision method according to an embodiment of the present invention. 
         FIG. 6  is a flowchart for explaining the decision method according to the embodiment of the present invention. 
         FIG. 7  is a view showing an example of a mask pattern in the decision method shown in  FIG. 6 . 
         FIG. 8  is a view for explaining parameters that define an effective light source. 
         FIGS. 9A to 9C  are views showing the contours of mask pattern images formed on the image plane of the projection optical system upon illuminating the mask pattern shown in  FIG. 7 . 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. Note that the same reference numerals denote the same members throughout the drawings, and a repetitive description thereof will not be given. 
     In this embodiment, a “dimension evaluation line segment (first line)” indicates a line segment set along the measurement direction at a place to measure the dimension on (an image formed on) the image plane of a projection optical system. A “resolution evaluation line segment (second line)” indicates a line segment set to determine whether a pattern element to be measured out of pattern elements included in a pattern is resolved. Note that “resolution” means that the image of the pattern element to be measured and the image of another pattern element are separately formed. In this embodiment, it means that the images of two pattern elements are separately formed. “Measurement” means obtaining the distance between two points of a pattern image (that is, the image of a pattern). 
       FIG. 1  is a flowchart for explaining an evaluation method according to an embodiment of the present invention. This evaluation method evaluates a pattern image formed on the image plane of a projection optical system that projects a pattern including a plurality of pattern elements onto a substrate. The evaluation method of this embodiment is implemented by, for example, supplying a program capable of executing the steps shown in  FIG. 1  to an information processing apparatus (computer) via a network or a recording medium and causing the information processing apparatus to read out and execute the program stored in a storage medium such as a memory. 
     In step S 102 , a dimension evaluation line segment is set on the image plane of the projection optical system. More specifically, a dimension evaluation line segment is set to intersect target pattern elements on the image plane corresponding to two of a plurality of pattern elements included in a mask pattern so as to evaluate the dimension between images corresponding to the two pattern elements. In this embodiment, as shown in  FIG. 2 , the dimension of the end gap between a pattern element PC 1  and a pattern element PC 2  that are target pattern elements is measured in a mask pattern corresponding to a VLSI circuit. In this case, a line segment PQ connecting a point P(x 1 ,y 1 ) and a point Q(x 2 ,y 2 ) is set as the dimension evaluation line segment. 
     In step S 104 , a resolution evaluation line segment is set on the image plane of the projection optical system. More specifically, a resolution evaluation line segment is set between the target pattern elements to intersect the dimension evaluation line segment set in step S 102  so as to evaluate whether the images of the two pattern elements are separately formed (whether the pattern elements are resolved). In this embodiment, as shown in  FIG. 2 , a line segment RS connecting a point R(x 3 ,y 3 ) and a point S(x 4 ,y 4 ) is set as a resolution evaluation line segment between the pattern element PC 1  and the pattern element PC 2  to intersect the line segment PQ serving as the dimension evaluation line segment. Note that in this embodiment, the line segment RS serving as the resolution evaluation line segment is set to be perpendicular to the line segment PQ serving as the dimension evaluation line segment at its center point (a point that equally divides the line segment PQ). However, the present invention is not limited to this. The resolution evaluation line segment may be set at any place where degradation in the pattern image resolving power along the dimension evaluation line segment conspicuously appears. 
     In step S 106 , the mask pattern image formed on the image plane of the projection optical system is obtained. The mask pattern image can be obtained by, for example, illuminating the mask pattern arranged on the object plane of the projection optical system and causing an image sensor (CCD) arranged on the image plane of the projection optical system to sense (the intensity of) light that has passed through the mask pattern. In this embodiment, the mask pattern image is obtained as image information. The image information represents the two-dimensional arrangement of the signals of the pixels of the image sensor. Note that (the image information representing) the mask pattern image can also be calculated using optical simulations. 
     In step S 108 , the contour (contour image) of the mask pattern image obtained in step S 106  is extracted. In this embodiment, image processing is performed to binarize the image information obtained in step S 106 , and the boundary line of the binary values is extracted as the contour of the mask pattern image.  FIGS. 3A and 3B  are views showing the contours of mask pattern images formed on the image plane of a projection optical system upon illuminating the mask pattern shown in  FIG. 2 . Note that  FIG. 3A  shows a case in which the images corresponding to the pattern elements PC 1  and PC 2  are separately formed (that is, the pattern elements PC 1  and PC 2  are resolved).  FIG. 3B  shows a case in which the images corresponding to the pattern elements PC 1  and PC 2  are not separately formed (that is, the pattern elements PC 1  and PC 2  are not resolved). Note that  FIGS. 3A and 3B  also illustrate the pattern elements PC 1  and PC 2  converted into the dimension on the image plane in consideration of the scaling factor of the projection optical system. 
     In step S 110 , the distance between the intersections of the dimension evaluation line segment set in step S 102  and the contours of the images corresponding to the two pattern elements is obtained in the direction along the dimension evaluation line segment (that is, the dimension between the images corresponding to the two pattern elements is measured). For example, in  FIG. 3A , an intersection P′(x 5 ,y 5 ) of (the extension line of) the line segment PQ serving as the dimension evaluation line segment and the contour of the image corresponding to the pattern element PC 1  and an intersection Q′(x 6 ,y 6 ) of the line segment PQ and the contour of the image corresponding to the pattern element PC 2  are specified first. Note that if there are two or more intersections of the line segment PQ and each of the contours of the images corresponding to the two pattern elements PC 1  and PC 2 , two intersections closer to the center point of the line segment PQ serving as the dimension evaluation line segment are specified as the intersections of the dimension evaluation line segment and the contours of the images corresponding to the two pattern elements. As the dimension of the end gap between the pattern element PC 1  and the pattern element PC 2 , a distance D P′,Q′  in the direction along the line segment PQ between the two intersections is obtained by 
         D   P′D′ =√{square root over (( x 5- x 6) 2 +( y 5- y 6) 2 )}{square root over (( x 5- x 6) 2 +( y 5- y 6) 2 )}  (1)
 
     On the other hand, in  FIG. 3B , an intersection P″(x 7 ,y 7 ) of (the extension line of) the line segment PQ serving as the dimension evaluation line segment and the contour of the image corresponding to the pattern element PC 1  and an intersection Q″(x 8 ,y 8 ) of the line segment PQ and the contour of the image corresponding to the pattern element PC 2  are specified first. Then, a distance D P″,Q″  in the direction along the line segment PQ between the two intersections is obtained by 
         D   P″Q″ =√{square root over (( x 7- x 8) 2 +( y 7- y 8) 2 )}{square root over (( x 7- x 8) 2 +( y 7- y 8) 2 )}  (2)
 
     If the pattern elements PC 1  and PC 2  are not resolved, the distance D P″,Q″  is erroneously obtained as the end gap between the pattern element PC 1  and the pattern element PC 2  to be measured, as described above. In other words, the dimension of the mask pattern image is measured based on the misrecognized edge. As a result, the mask pattern image cannot correctly be evaluated because of the measurement result based on the misrecognized edge. 
     In step S 112 , it is evaluated (determined) whether the two pattern elements are separately formed, that is, whether the two pattern elements are resolved. More specifically, it is determined whether intersections exist of the resolution evaluation line segment set in step S 104  and the contours of the images corresponding to the two pattern elements in the mask pattern image formed on the image plane of the projection optical system. For example, in  FIG. 3A , since no intersections exist of the line segment RS and the contours of the images corresponding to the two pattern elements PC 1  and PC 2 , they are determined to be resolved. On the other hand, in  FIG. 3B , since intersections R′(x 9 ,y 9 ) and S′(x 10 ,y 10 ) exist of the line segment RS and the contours of the images corresponding to the two pattern elements PC 1  and PC 2 , they are determined to be unresolved. Note that if the two pattern elements are resolved (that is, if no intersections exist), the process advances to step S 114 . If the two pattern elements are not resolved (that is, if intersections exist), the process advances to step S 116 . 
     In step S 114 , the value (the measurement result in step S 110 ) of the distance in the direction along the dimension evaluation line segment between the intersections of the dimension evaluation line segment set in step S 102  and the contours of the images corresponding to the two pattern elements is set as the evaluation value. In this embodiment, the value of the distance D P′,Q′  in the direction along the line segment PQ between the two intersections is set as the evaluation value when evaluating the pattern image. 
     In step S 116 , the value (the measurement result in step S 110 ) of the distance in the direction along the dimension evaluation line segment between the intersections of the dimension evaluation line segment set in step S 102  and the contours of the images corresponding to the two pattern elements is weighted and set as the evaluation value. For example, examine a case in which the dimension of the end gap between the pattern element PC 1  and the pattern element PC 2  that are target pattern elements is almost “0”. In this case, a value obtained by multiplying the distance D P″,Q″  between the two intersections in the direction along the line segment PQ by a large value such as “100” is set as the evaluation value. Alternatively, the value of the distance D P″,Q″  may be weighted to invalidate it when evaluating the mask pattern image (for example, the distance D P″,Q″  is replaced with a value representing a measurement error in advance). Note that the weighted value includes not only, for example, a value obtained by multiplying the measurement result in step S 110  by a predetermined coefficient but also a value obtained by adding an offset to that value. That is, the evaluation value in step S 116  need only be a numerical value (outlier) representing that the images of the two pattern elements are unresolved. 
     In step S 118 , the mask pattern image (that is, the mask pattern image obtained in step S 108 ) formed on the image plane of the projection optical system is evaluated based on the evaluation value set in step S 114  or S 116 . 
     As described above, in this embodiment, it is possible to evaluate whether the pattern elements included in the mask pattern are resolved. The mask pattern image can correctly be evaluated based on the evaluation value when the pattern elements are resolved and that when they are not resolved. 
     In this embodiment, the dimension between the images corresponding to the two pattern elements is measured (S 110 ) before determining whether the two pattern elements are resolved (S 112 ). However, the dimension between the images corresponding to the two pattern elements may be measured (S 110 ) after determining whether the two pattern elements are resolved (S 112 ). 
     In this embodiment, only one resolution evaluation line segment (line segment RS) is set in step S 104 . However, a plurality of resolution evaluation line segments may be set. For example, examine a case in which the dimension of the end gap between a pattern element PC 3  and a pattern element PC 4  that are target pattern elements is evaluated (measured) in the mask pattern shown in  FIG. 4A . In this case, the line segment PQ connecting the points P and Q is set as the dimension evaluation line segment. A plurality of line segments R 0 S 0  , . . . , RnSn are set as resolution evaluation line segments to be perpendicular to the line segment PQ at a plurality of points that equally divide the line segment PQ.  FIG. 4B  is a view showing the contour of the mask pattern image formed on the image plane of the projection optical system upon illuminating the mask pattern shown in  FIG. 4A . Note that  FIG. 4B  also illustrates the pattern elements PC 3  and PC 4  converted into the dimension on the image plane in consideration of the scaling factor of the projection optical system. Referring to  FIG. 4B , concerning the line segments indicated by bold lines out of the plurality of line segments R 0 S 0  , . . . , RnSn, intersections with respect to the images corresponding to the pattern elements PC 3  and PC 4  exist. However, concerning the line segments (for example, a line segment RkSk (0≦k≦n) indicated by thin lines out of the plurality of line segments R 0 S 0  , . . . , RnSn, no intersections exist with respect to the images corresponding to the pattern elements PC 3  and PC 4 . Hence, a plurality of resolution evaluation line segments are generally set. In step S 112 , it is determined for each of the plurality of resolution evaluation line segments whether there exist intersections with respect to the contours of the images corresponding to the two pattern elements. If at least one of the plurality of resolution evaluation line segments has no intersections with respect to the contours of the images corresponding to the two pattern elements, they are determined to be resolved. On the other hand, if all of the plurality of resolution evaluation line segments have intersections with respect to the contours of the images corresponding to the two pattern elements, they are determined to be unresolved. 
     An example will be explained below in which the evaluation method of this embodiment is applied to a decision method of deciding exposure conditions (the effective light source and the like) to be set in an exposure apparatus including an illumination optical system for illuminating a pattern including a plurality of pattern elements, and a projection optical system for projecting the pattern onto a substrate. Note that the effective light source is the distribution of light intensities to be formed on the pupil plane of the illumination optical system. 
       FIG. 5  is a schematic block diagram showing the arrangement of an information processing apparatus  500  which executes the decision method according to an embodiment of the present invention. The information processing apparatus  500  is an optical simulator which searches for exposure conditions with which the pattern image formed on the image plane of the projection optical system almost has the target dimension. The information processing apparatus  500  includes a control unit  502 , a storage unit  504 , a bridge  506 , an output interface  508 , a network interface  510 , and an input interface  512 . The control unit  502 , the storage unit  504 , the output interface  508 , the network interface  510 , and the input interface  512  are connected to the bridge  506  via buses. 
     A display  522  is connected to the output interface  508 . An input device  524  is connected to the input interface  512 . The network interface  510  is connected to a network such as a LAN to communicate data to another information processing apparatus. The main controller of the exposure apparatus and the like are also connected to the network interface  510 . 
     The control unit  502  includes a CPU (Central Processing Unit), a DSP (Digital Signal Processor), an FPGA (Field Programmable σate Array), and a microcomputer. The storage unit  504  includes memories such as a ROM and a RAM. The input device  524  includes a mouse and a keyboard. 
     The control unit  502  executes programs (software codes) stored in the storage unit  504 , thereby causing the information processing apparatus  500  to function as an apparatus for executing processing or a method according to the programs. The result of processing according to the programs is output to devices such as the display  522  and the main controller of the exposure apparatus via the output interface  508 . The storage unit  504  stores data (layout data, data (numerical aperture (NA) and aberration information) associated with the projection optical system, and data (effective light source information and the like) associated with the illumination optical system) necessary for executing the decision method of this embodiment. These data are provided to the information processing apparatus  500  via, for example, the network interface  510  and stored in the storage unit  504 . 
       FIG. 6  is a flowchart for explaining the decision method according to the embodiment of the present invention. This decision method repeats obtaining a mask pattern image and measuring the dimension of the measurement target of the mask pattern image every time the exposure conditions change. The pattern elements included in the mask pattern may be unresolved under certain exposure conditions. However, the decision method of this embodiment can decide exposure conditions optimum for the mask pattern by correctly evaluating the mask pattern image based on the evaluation value when the pattern elements are resolved and that when they are not resolved. 
     Note that in this embodiment, the mask pattern includes a plurality of pattern elements PC which are tilted with respect to the Y-axis direction and arrayed in the X-axis direction, as shown in  FIG. 7 . More specifically, the mask pattern shown in  FIG. 7  includes nine pattern elements PC at a pitch Pitch of 100 nm, each having a line width W of 50 nm, a height Height of 400 nm, and a tilt W 2  of 150 nm with respect to the Y-axis. Such a pattern can increase the number of bits per unit area of memory cells. Note that the mask is a halftone mask (halftone phase shift mask), the phase difference between the pattern elements and the background is π(180°), the transmittance of the pattern elements is 6%, and that of the background is 100%. In the mask pattern shown in  FIG. 7 , the short between the ends deteriorate the yield. Hence, in this embodiment, the exposure conditions are decided such that the dimension of the end gap between the pattern elements PC satisfies the criterion for evaluation. 
     In step S 601 , initial exposure conditions are set. The exposure conditions are various conditions settable in an exposure apparatus when performing exposure, and include, for example, the NA of the projection optical system, the wavelength of exposure light, the type of the immersion liquid, the refractive index of the resist to be applied to the substrate, and the effective light source (illumination shape). In this embodiment, the NA of the projection optical system is 1.35, the wavelength λ of exposure light is 193 nm, the immersion liquid is pure water, the refractive index of the resist to be applied to the substrate is 1.79, and the effective light source is quadrupole illumination as the initial exposure conditions. In this embodiment, the target of exposure condition decision is the effective light source while the remaining exposure conditions such as the NA of the projection optical system and the exposure light wavelength are fixed to the initial exposure conditions. Note that parameters that define the quadrupole illumination serving as the effective light source are the σ-outer (σa), annular ratio (σratio=(σb/σa)), the aperture angle (φ1 [degree] of the pole in the X-axis direction, and the aperture angle (φ2 [degree] of the pole in the Y-axis direction, as shown in  FIG. 8 . These parameters can be set within the ranges of 0.7≦σa≦0.98, 0.65≦σratio 0.8, 50≦(σ1≦130, and 0≦φ2≦50, respectively. In this example, σa=0.95, σratio=0.737, (φ1=110, and (φ2=20 were set. 
     Step S 602  is the same as step S 102 . In this embodiment, a plurality of line segments P 2     —     1 Q 2     —     1 , . . . , P 2     —     17 Q 2     —     17  parallel to a line segment P 2 Q 2  shown in  FIG. 7  are set as dimension evaluation line segments (see  FIGS. 9A to 9C ). 
     Step S 604  is the same as step S 104 . In this embodiment, a line segment R 2 S 2  is set as a resolution evaluation line segment between the target pattern elements (pattern elements PC 5  and PC 6 ) to intersect the plurality of line segments (dimension evaluation line segments) P 2     —     1 Q 2     —     1 , . . . , P 2     —     17 Q 2     —     17 . 
     Step S 606  is the same as step S 106 . In this embodiment, the information processing apparatus  500  executes an optical simulation to obtain, as image information, the intensity distribution (that is, the mask pattern image) the light that has passed through the mask pattern shown in  FIG. 7  forms on the image plane of the projection optical system. 
     Step S 608  is the same as step S 108 . In this embodiment, a slice level is decided on the intensity distribution obtained in step S 606  such that a line segment T 2 U 2  (see  FIG. 7 ) has the same dimension (50 nm) as that of the mask pattern. The contour line of the intensity distribution at that time is extracted as the contour of the mask pattern image. Note that the contour of the mask pattern image is extracted without processing the intensity distribution in this case. However, the contour of the mask pattern image may be extracted after processing the intensity distribution using a process model that expresses the exposure or development characteristic of the resist. 
     Step S 610  is the same as step S 110 .  FIGS. 9A to 9C  are views showing the contours of mask pattern images formed on the image plane of the projection optical system upon illuminating the mask pattern shown in  FIG. 7 . Note that  FIGS. 9A and 9B  illustrate cases in which the images corresponding to the pattern elements PC 5  and PC 6  are separately formed (that is, the pattern elements PC 5  and PC 6  are resolved).  FIG. 9C  illustrates a case in which the images corresponding to the pattern elements PC 5  and PC 6  are not separately formed (that is, the pattern elements PC 5  and PC 6  are not resolved). Note that  FIGS. 9A to 9C  also illustrate the pattern elements PC 5  and PC 6  converted into the dimension on the image plane in consideration of the scaling factor of the projection optical system. 
     Referring to  FIG. 9A , concerning line segments P 2     —     k Q 2     —     k  (7≦k≦15) out of the plurality of line segments (dimension evaluation line segments) P 2     —     1 Q 2     —     1 , . . . , P 2     —     17 Q 2     —     17  intersections with respect to the contours of the images corresponding to the two pattern elements PC 5  and PC 6  exist. First, intersections P′ 2     —     k , of (the extension line of) the line segments P 2     —     k Q 2     —     k  and the contour of the image corresponding to the pattern element PC 5  and intersections Q 2     —     k of the line segments P 2     —k   Q 2     —k    and the contour of the image corresponding to the pattern element PC 6  are specified. The minimum one of distances D P′2     —     kQ′2     —     k (7≦k≦15) in the direction along the dimension evaluation line segments between the intersections of the line segment P 2     —     k Q 2     —     k  and the contours of the images corresponding to the two pattern elements PC 5  and PC 6  is obtained. Hence, in this embodiment, a distance D P′2     —     9Q′2     —     9  is obtained as the dimension of the end gap between the pattern element PC 5  and the pattern element PC 6 . When the exposure condition (effective light source) changes, the mask pattern image formed on the image plane of the projection optical system also changes. Hence, in  FIG. 9B , a distance D P″2     —10     Q″2     —     10  is obtained as the dimension of the end gap between the pattern element PC 5  and the pattern element PC 6 . Note that in this embodiment, since focus is placed on the dimension of the end gap between the pattern elements, the minimum value of the measurement results of the plurality of dimension evaluation line segments is used. However, the present invention is not limited to this. 
     On the other hand, the mask pattern image as shown in  FIG. 9C  (the pattern elements PC 5  and PC 6  are not resolved) may be formed on the image plane of the projection optical system. Referring to  FIG. 9C , concerning line segments P 2     —     m Q 2     —     m  (m=7, 10≦m≦15) out of the plurality of line segments (dimension evaluation line segments) P 2     —     1 Q 2     —     1 , . . . , P 2     —     17 Q 2     —     17 , intersections with respect to the contours of the images corresponding to the two pattern elements PC 5  and PC 6  exist. In  FIG. 9C , a distance D P ′″ 2     —     10Q′″2     —     10  is obtained as the dimension of the end gap between the pattern element PC 5  and the pattern element PC 6 . Note that the distance D P′″2     —     10Q ′″ 2     —     10  is not the dimension of the end gap between the pattern element PC 5  and the pattern element PC 6  in fact. 
     Step S 612  is the same as step S 112 . In  FIGS. 9A and 9B , since there exist no intersections of the line segment (resolution evaluation line segment) R 2 S 2  and the contours of the images corresponding to the two pattern elements PC 5  and PC 6 , they are determined to be resolved. In  FIG. 9C , since there exist intersections R′″ 2  and S′″ 2  of the line segment RS and the contours of the images corresponding to the two pattern elements PC 5  and PC 6 , they are determined to be unresolved. Note that if the two pattern elements are resolved (that is, if no intersections exist), the process advances to step S 614 . If the two pattern elements are not resolved (that is, if intersections exist), the process advances to step S 616 . 
     Step S 614  is the same as step S 114 . In this embodiment, the measurement result (the distance D P′2     —     9Q′2     —     9  or the distance D P″2     —     10Q″2     —     10 ) in step S 610  is set as the evaluation value. 
     Step S 616  is the same as step S 116 . In this embodiment, the measurement result (the distance D P′″2     —     10Q′″2     —     10 ) in step S 610  is weighted and set as the evaluation value. 
     In step S 618 , the mask pattern image (that is, the mask pattern image obtained in step S 608 ) formed on the image plane of the projection optical system is evaluated based on the evaluation value set in step S 614  or S 616 . 
     In step S 620 , the difference ΔL between the evaluation value set in step S 614  or S 616  and the target dimension of the mask pattern is calculated based on the evaluation result in step S 618 . The dimension is evaluated for a plurality of line segments AB, CD, and T 2 U 2 , as shown in  FIG. 7 , although only the dimension of the end gap between the pattern elements has been described so far. Let L 1  be the measurement result of the dimension of the end gap, L 2 , L 3 , and L 4  be the measurement results of the plurality of line segments AB, CD, and T 2 U 2 , and L 01 , L 02 , L 03 , and L 04  be the target dimensions. In this case, the difference ΔL between the evaluation value and the target dimension of the mask pattern is given by 
     
       
         
           
             
               
                 
                   
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     In step S 622 , it is determined whether the difference ΔL calculated in step S 620  satisfies the criterion for evaluation (that is, whether the deviation from the target dimension falls within the allowable range). If the difference ΔL does not satisfy the criterion for evaluation, the process advances to step S 624 . If the difference ΔL satisfies the criterion for evaluation, the process advances to step S 626 . 
     In step S 624 , the exposure condition is reset, and the process returns to step S 606 . In step S 626 , the initial exposure condition set in step S 601  or the exposure condition reset in step S 624  is decided as the exposure condition to be set in the exposure apparatus. 
     In this embodiment, it is possible to evaluate in this way whether the pattern elements included in the mask pattern are resolved, and thus correctly evaluate the mask pattern image based on the evaluation value when the pattern elements are resolved and that when they are not resolved. As a result, even when such an exposure condition that keeps the pattern elements unresolved until exposure condition decision is set, convergence of effective light source optimization is never impeded, and an effective light source suitable for the mask pattern can be decided. 
     In addition, the evaluation method of this embodiment is applicable to a technique of evaluating the dimension of a resist pattern formed on a substrate using a scanning electron microscope (SEM). There is known a technique of, when manufacturing a semiconductor device, testing the exposure margin by performing exposure while changing the exposure amount and the defocus amount in the exposure apparatus. Since the evaluation target includes a resist pattern corresponding to an unresolved pattern, applying the evaluation method of the embodiment enables correct evaluation of the exposure margin. For example, examine a case in which the dimension of a resist pattern formed on a substrate for exposure margin evaluation in correspondence with a plurality of exposure amounts and defocus amounts is continuously measured using an SEM. In this case, applying the evaluation method of the embodiment makes it possible to evaluate whether the pattern elements included in the mask pattern are resolved (that is, whether a resist pattern corresponding to the pattern elements is formed). As a result, even when the pattern elements are not resolved, the dimension of the resist pattern corresponding to the plurality of exposure amounts and defocus amounts can correctly be evaluated. It is therefore possible to correctly evaluate the exposure margin. 
     For the sake of comparison with the embodiment, other evaluation methods will be examined. For example, the evaluation method may be executed to determine that a pattern is not resolved when the measurement result for a dimension evaluation line segment is deviated from a reference value by a predetermined value or more. Such an evaluation method is effective for the mask pattern image shown in  FIG. 3B . For the mask pattern image shown in  FIG. 9C , however, it is difficult to correctly evaluate whether the pattern is resolved because the distance D P′″2     —     10Q′″2     —     10  is not necessarily deviated from the reference value by a predetermined value or more. 
     The evaluation method may be executed to determine that a pattern is not resolved when the measurement results for a plurality of dimension evaluation line segments do not smoothly change with respect to the coordinates. However, it is difficult for this evaluation method to identify which has caused the change of the measurement result for the plurality of dimension evaluation line segments, the pattern shape or the unresolved pattern. 
     Note that when the pattern is not resolved, as shown in  FIG. 3B , the intensity distribution along the dimension evaluation line segment represents “bright-dark-bright”. When the pattern is resolved, as shown in  FIG. 3A , the intensity distribution along the dimension evaluation line segment represents “dark-bright-dark”. Hence, the evaluation method may be executed to evaluate, in accordance with whether the intensity near the gap is convex or concave with respect to the intensity of the contour of the pattern image, whether a pattern is resolved. In a case where there is the end gap which is resolved in a position shifted from the end gap of interest along the dimension evaluation line segment, such an evaluation method cannot perform a correct resolution evaluation, and is not suitable. 
     The evaluation method may be executed to evaluate, by detecting the number of mask pattern images, whether a pattern is resolved. However, it is difficult to specify the positional relationship between a dimension evaluation line segment and a resolved pattern (or an unresolved pattern). 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent application No. 2010-178077 filed on Aug. 6, 2010, which is hereby incorporated by reference herein in its entirety.