Abstract:
A mask pattern data generating method is disclosed, which comprises preparing mask pattern data which corresponds to a design pattern including a pair of line patterns formed of two line patterns, and disposing an auxiliary pattern which is un-transferable to a resist film at a center of a space region between the pair of line patterns, in which the disposing of the auxiliary pattern includes obtaining a shape of the auxiliary pattern which meets formulae in which a width in the short edge direction of the auxiliary pattern, a space width between the auxiliary pattern and one of the pair of line patterns, a wavelength of an exposure light emitted by a projection aligner using a photo mask at exposure, and a numerical apertures of a projection lens of the projection aligner are defined as parameters, and disposing the obtained auxiliary pattern at the center of the space region.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2004-316418, filed Oct. 29, 2004, the entire contents of which are incorporated herein by reference.  
       BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention relates to a method of generating mask pattern data on a mask pattern to be transferred to a substrate, a method of manufacturing a photo mask, and a method of manufacturing a semiconductor device.  
         [0004]     2. Description of the Related Art  
         [0005]     With downsizing of a device pattern, there is a demand for obtaining a resolution close to a theoretical limit which depends on a wavelength of optical beam. To realize this demand, a variety of phase shift masks are proposed as masks. In addition, as an exposure method, there is proposed an oblique incidence illumination technique in which a light incident onto a mask is inclined from an optical axis by an angle which corresponds to the numerical aperture of an objection lens system of a projection exposure apparatus. There is proposed another exposure method in which a phase shift mask and an oblique incidence illumination are combined with each other.  
         [0006]     Both of the phase shift mask and the oblique incidence illumination technique are intended to enhance a resolution by utilizing a phase difference between the adjacent patterns. With this technology, a high resolution can be obtained with respect to a highly periodic and simple pattern such as an L/S (Line-and-Space) pattern. However, a satisfactory resolution cannot be obtained with respect to a random pattern contained in a device pattern.  
         [0007]     In recent years, there is proposed a mask obtained by arranging in a random pattern region an un-transferable auxiliary pattern which cannot be transferred on a substrate. Also, there is proposed an exposure method using the mask. For example, in Jpn. Pat. Appln. KOKAI Publication No. 7-140639, there is disclosed a mask for use in projection exposure using the oblique incidence illumination, wherein the mask includes a pattern to be transferred and an un-transferable pattern. In the case where the to-be-transferred pattern has periodicity (that is, in the case where the pattern is periodically arranged at a fixed pitch), an un-transferable auxiliary pattern or patterns are provided in such a manner that the periodicity is maintained. On the other hand, in the case where the to-be-transferred pattern does not have periodicity (that is, in the case where the pattern is arranged to be isolated), an un-transferable auxiliary pattern or patterns are provided in such a manner that a periodicity is imparted to the to-be-transferred pattern. When λ is defined as a wavelength of the illumination light and NA is a numerical aperture of the projection lens, in the case where the to-be-transferred pattern formed of a light transmitting section (or a light shielding section) has a periodicity and a width of the to-be-transferred pattern is equal to or greater than λ/2 NA, one or more un-transferable auxiliary patterns formed of a light transmitting section (or a light shielding section) are provided, at pitches of 0.8×λ/2 NA to 1.4×λ/2 NA from an edge of the mask transmitting section (or a light shielding section), at an end of the periodic disposition of the to-be-transferred pattern. On the other hand, in the case where the to-be-transferred pattern formed of a light transmitting section has no-periodicity and is thus isolated, and a width of the to-be-transferred pattern is equal to or greater than λ/2 NA, one or more un-transferable auxiliary patterns formed of a light transmitting section (or a light shielding section) are provided, at pitches of 0.8×λ/2 NA to 1.4×λ/2 NA from an edge of the pattern, at one side or both sides of the to-be-transferred pattern.  
         [0008]     In the above prior art disclosed in Jpn. Pat. Appln. KOKAI Publication No. 7-140639, in the case where the pattern is formed at one type of comparatively simple pitches, the technology is effective. However, an actual device, for example, a select gate and its vicinity of a NAND-type flash memory ( FIGS. 1 and 13 ), comprises patterns with a variety of pitches: a region p 1  of a pattern with a fine periodicity, a region p 2  of a pattern adjacent to the region p 1  and having a periodicity longer than that of the region p 1 , and a region p 3  of a pattern whose periodicity is longer than that of the region p 2 . Patterns whose lithography margin is insufficient and which is to be provided with an auxiliary pattern are line patterns  11  and  12  in  FIG. 1  and line patterns  11 ,  12  and  8  in  FIG. 13 . In the patterns shown in, for example,  FIG. 13 , when the oblique incidence illumination is used, a line width variation in edge portions E 1  and E 2  of the line patterns  11  and  12  having lowest periodicity is large.  
         [0009]     With the conventional method of adding an auxiliary pattern, it is impossible to determine how the auxiliary pattern is deposited with respect to a pattern with a complicated arrangement such as the line pattern  11  or  12 .  
         [0010]     In addition, in the pattern of the select gate of the NAND-type flash memory, as shown in  FIG. 13 , a contact portion locally exists. In other words, a region having more non-periodic patterns than other pattern regions exists. Thus, a low-resolution problem occurs. With the patterns shown in  FIG. 13 , a sufficient resolution margin cannot be obtained with respect to a local portion  10  of the line patterns  8  and  9 .  
         [0011]     As described above, in the prior art of improving the margin by adding an un-transferable auxiliary pattern, it is impossible to determine how an auxiliary pattern should be disposed. Hence, there has not been successfully solved the low-margin problem in a pattern region which requires downsizing, in particular, in a non-periodic pattern region in a cell region of a device.  
       BRIEF SUMMARY OF THE INVENTION  
       [0012]     According to an aspect of the present invention, there is provided a mask pattern data generating method of generating mask pattern data of a mask pattern to be depicted on a photo mask, based on a design pattern, for use in projection by an oblique incidence illumination, the method comprising: 
        preparing mask pattern data which corresponds to a design pattern including a pair of line patterns formed of two line patterns adjacent to each other in a short edge direction; and     disposing an auxiliary pattern which is un-transferable to a resist film at a center portion of a space region between the pair of line patterns, in which the disposing of the auxiliary pattern includes obtaining a shape of the auxiliary pattern which meets formulae in which a width in the short edge direction of the auxiliary pattern, a space width between the auxiliary pattern and one of the pair of line patterns, a wavelength of an exposure light emitted by a projection aligner using a photo mask at exposure, and a numerical apertures of a projection lens of the projection aligner are defined as parameters, and disposing the obtained auxiliary pattern at the center portion of the space region between the pair of line patterns.        
 
         [0015]     According to another aspect of the present invention, there is provided a photo mask manufacturing method of manufacturing a photo mask by using mask pattern data, in which the mask pattern data corresponds to a design pattern including a pair of line patterns formed of two line patterns adjacent to each other in a short edge direction; the mask pattern data is added with an auxiliary pattern which is un-transferable to a resist film; the auxiliary pattern is disposed at a center portion of a space region between the pair of line patterns; and the auxiliary pattern has a shape which meets formulae in which a width in the short edge direction of the auxiliary pattern, a space width between the auxiliary pattern and one of the pair of line patterns, a wavelength of an exposure light emitted by a projection aligner using a photo mask at exposure, and a numerical apertures of a projection lens of the projection aligner are defined as parameters.  
         [0016]     According to a further aspect of the present invention, there is provided a semiconductor device manufacturing method of manufacturing a semiconductor device, by carrying out an oblique incidence illumination to a photo mask to project a pattern formed on the photo mask to a resist film formed on a substrate, in which  
         [0017]     the photo mask is manufactured by using mask pattern data corresponding to a design pattern including a pair of line patterns formed of two line patterns adjacent to each other in a short edge direction; the mask pattern data is added with an auxiliary pattern which is un-transferable to a resist film; the auxiliary pattern is disposed at a center portion of a space region between the pair of line patterns; and the auxiliary pattern has a shape which meets formulae in which a width in the short edge direction of the auxiliary pattern, a space width between the auxiliary pattern and one of the pair of line patterns, a wavelength of an exposure light emitted by a projection aligner using a photo mask at exposure, and a numerical apertures of a projection lens of the projection aligner are defined as parameters. 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING  
       [0018]      FIG. 1  is a diagram showing a design pattern of a select gate and its vicinity of a NAND-type flash memory to be referred to in association with a first embodiment of the present invention;  
         [0019]      FIG. 2  is a diagram showing a pattern in which an auxiliary pattern  14  has been disposed with respect to the design pattern shown in  FIG. 1 ;  
         [0020]      FIG. 3  is a characteristic diagram showing a defocus dependency of an image intensity taken along the line II-II of a pattern shown in  FIG. 2  in which the auxiliary pattern  14  is arranged;  
         [0021]      FIG. 4  is a characteristic diagram used as a reference to the characteristic diagram shown in  FIG. 3 , which shows a defocus dependency of an image intensity taken along the line II-II of the pattern shown in  FIG. 2  in the case where the auxiliary pattern  14  is not arranged in the pattern of  FIG. 2 ;  
         [0022]      FIG. 5  is a characteristic diagram showing a defocus dependency of an image intensity of a specific portion, i.e., a select gate portion, taken along the line II-II of the pattern shown in  FIG. 2  in which the auxiliary pattern  14  is arranged;  
         [0023]      FIG. 6  is a characteristic diagram used as a reference to the characteristic diagram shown in  FIG. 5 , which shows a defocus dependency of an image intensity in a specific portion, i.e., a select gate portion, taken along the line II-II of the pattern shown in  FIG. 2  in the case where the auxiliary pattern is not arranged in the pattern of  FIG. 2 ;  
         [0024]      FIG. 7  is a diagram showing a light source used in the first embodiment of the present invention, in which four fan-shaped light portions are symmetrically disposed;  
         [0025]      FIG. 8  is a diagram showing a pattern disposition used for obtaining a disposition rule of an auxiliary pattern according to the first embodiment of the present invention;  
         [0026]      FIG. 9  shows a simulation image of a pattern shown in  FIG. 8 , obtained by transfer when an auxiliary pattern width Sw=70 nm in the pattern shown in  FIG. 8 ;  
         [0027]      FIG. 10  shows a simulation image of a pattern shown in  FIG. 8 , obtained by transfer when an auxiliary pattern width Sw=68 nm in the pattern shown in  FIG. 8 ;  
         [0028]      FIG. 11  shows a simulation image of a pattern shown in  FIG. 8 , obtained by transfer when an auxiliary pattern width Sw=65 nm in the pattern shown in  FIG. 8 ;  
         [0029]      FIG. 12  is a diagram showing a relationship between the auxiliary pattern width Sw and a space width St (distance) Sd between the auxiliary pattern and the adjacent pattern, obtained in accordance with the first embodiment of the present invention;  
         [0030]      FIG. 13  is a diagram showing a design pattern of a select gate and its vicinity of a NAND-type flash memory to be referred to in association with a second embodiment of the present invention;  
         [0031]      FIG. 14  is a diagram showing a pattern obtained by adding auxiliary patterns  17 ,  18 , and  19  to the design pattern shown in  FIG. 13 ;  
         [0032]      FIG. 15  is a diagram showing a part of the pattern shown in  FIG. 14 , in which numerical dimensions are added;  
         [0033]      FIG. 16  shows a simulation image of a resist pattern obtained by transferring the pattern shown in  FIG. 13 ; and  
         [0034]      FIG. 17  shows a simulation image used as a reference to the simulation image shown in  FIG. 16 , the simulation image of the resist pattern being obtained by transferring the pattern shown in  FIG. 13  when the auxiliary patterns  17  and  18  are not added. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0035]     Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.  
       FIRST EMBODIMENT  
       [0036]     The inventors of the present application have invented a technique of adding an auxiliary pattern to a pattern in which the periodicity of pattern arrangement is lowered to affect the exposure margin, or adding an auxiliary pattern in accordance with a distance between a pattern edge and its adjacent pattern edge.  
         [0037]     Specifically, the inventors of the present application focused attention to a portion of a line pattern of a select gate and its vicinity of a NAND-type flash memory, at which the exposure margin is lowered and the resolution is degraded.  
         [0038]      FIG. 1  is a design pattern of a select gate and its vicinity of a NAND-type flash memory.  
         [0039]     In the line pattern of the select gate and its vicinity of a NAND type flash memory, as shown in  FIG. 1 , there exist a pattern region p 1 , a pattern region p 2  adjacent to the pattern p 1 , and a pattern region p 3  adjacent to the pattern p 2 . In the pattern region p 1 , line patterns are repeatedly disposed at a small pattern pitch, and there is a demand for the severest design rule with regard to the pattern shown in  FIG. 1 . The line patterns repeatedly disposed at the small pitch in the pattern region p 1  correspond to patterns of series-connected memory cells of the NAND type flash memory. In the pattern region p 2 , only one line pattern is disposed at a pattern pitch which is slightly greater than the pattern pitch in the pattern region p 1 . There is some case where some line patterns are repeatedly disposed in the pattern region p 2 . In the pattern region p 3 , only one line pattern is disposed at a pattern pitch which is significantly greater than the pattern pitch in the pattern region p 1 . In the pattern region p 3 , two line patterns may be repeatedly disposed. The line patterns including the pattern region p 1 , the pattern region p 2 , and the pattern region p 3  are repeatedly disposed at a further greater pitch P, with a space width Sc between the line patterns. In this case, there has been a problem that an exposure margin is lowered with respect to the line patterns in the regions p 2  and p 3 .  
         [0040]     In the present embodiment, with respect to such a complicated device pattern, there has been invented a technique of adding an auxiliary pattern for ensuring a required exposure margin while taking consideration so that a design rule of the size of the auxiliary pattern becomes not extremely sever from the viewpoint of manufacturing a mask.  
         [0041]     A detailed description will be described below by way of example of a pattern of a select gate and its vicinity of the NAND-type flash memory cells shown in  FIG. 1 .  
         [0042]      FIG. 2  shows an example of adding to the pattern shown in  FIG. 1  an auxiliary pattern according to the present embodiment. In  FIG. 2 , the L/S patterns (Line/Space pattern) of the region p 1  have a pitch of 140 nm (L/S=70 nm/70 nm), and are repeatedly arranged. The L/S pattern of the region p 2  has a pitch of 164 nm (L/S=82 nm/82 nm), and is singly, not repeatedly, disposed. The L/S pattern of the region p 3  has a pitch of 290 nm (L/S=200 nm/90 nm), and is singly, not repeatedly, disposed. A width of a region between the adjacent NAND-type flash memory cells, i.e., width Sc of the space between the region p 3  of a NAND-type flash memory cell and the region p 3  of a NAND-type flash memory cell adjacent to that NAND-type flash memory cell is Sc=335 nm.  
         [0043]     It is problematic that the exposure margin of the line patterns  11  and  12  is small. In particular, there is a problem that a line width variation of edges E 1  and E 2  in the line patterns  11  and  12  is large.  
         [0044]     In order to solve these problems, the inventors of the present application added an un-transferable auxiliary pattern  14  having a width Sw in a space of the width Sc, which is not transferred to a resist film by exposure. The auxiliary pattern  14  is disposed at the center of the space between the line pattern  11  and the line pattern  12 .  
         [0045]      FIG. 3  shows characteristics indicating a defocus dependency of an image intensity taken along the line II-II shown in  FIG. 2  showing a NAND cell pattern in which an auxiliary pattern is disposed.  FIG. 4  shows, as a reference against the characteristic diagram shown in  FIG. 3 , a characteristic diagram indicating a defocus dependency of an image intensity taken along the line II-II shown in  FIG. 2  showing a NAND cell pattern in the case where no auxiliary pattern is disposed. In addition,  FIG. 5  shows an enlarged diagram showing a portion of the characteristic diagram of the defocus dependency of the image intensity shown in  FIG. 3 , which portion corresponds to a select gate portion of the NAND cell pattern.  FIG. 6  shows, as a reference against the characteristic diagram shown in  FIG. 5 , an enlarged diagram showing a portion of the characteristic diagram of the defocus dependency of the image intensity shown in  FIG. 4 , which portion corresponds to a select gate portion of the NAND cell pattern.  
         [0046]     The width Sw of the auxiliary pattern  14  applied in the embodiment is 75 nm, and the auxiliary pattern  14  is disposed at the center of the space width Sc. In addition, an optical condition for exposure is such that exposure light is an ArF excimer laser beam, an exposure wavelength λ is λ=193 nm, and a numerical apertures NA=0.83. An illumination condition is such that use is made of a light source, as shown in  FIG. 7 , having a fan-shaped light portion which is symmetrical in four directions, in consideration of importance of the resolution of a fine pattern in a direction of 0 degree and in a direction of 90 degrees (inner σ=0.7, outer σ=0.9, and fan aperture angle of 40 degrees). In addition, ΔL=40 nm is defined with respect to ΔL indicating a blurring quantity of an optical image serving as a process factor.  
         [0047]     Here, the boundary line indicated by the broken line shown in  FIGS. 3, 4 ,  5  and  6  indicates an exposure intensity (edge optical intensity) for resolving an L/S pattern (L/S=70 nm/70 nm) in the region p 1  of the NAND cell pattern. It is desirable that, with respect to this boundary line, the image intensity at the light portion is high and the image resolution at the dark portion is low.  
         [0048]     It should be noted that, from the characteristic diagram shown in  FIG. 3 , a condition is established such that the auxiliary pattern is not transferred to a resist film although the size Sw of the auxiliary pattern is 75 nm which is greater than a design rule (specifically, p 1 / 2 =70 nm) of a cell portion. Further, when comparison is made among the characteristic diagrams of  FIGS. 3, 4 ,  5  and  6 , it is found that the lowering of the image intensity of a portion corresponding to the line pattern  11  at the dark portion is significantly improved by disposing the auxiliary pattern  14 . In addition, the lowering of the image intensity in the space between the line pattern  11  and a line pattern  15  shown in  FIG. 2  can also be suppressed, thus improving a total margin of the select gate portion.  
         [0049]     Next, the inventors of the present application have studied a condition of an auxiliary pattern width Sw and a space width St between the auxiliary pattern and its adjacent line pattern in order to obtain a specific design rule on the auxiliary pattern disposed in a cell region which requires downsizing of the device pattern as shown in  FIG. 1 . In the device pattern, in many cases, a condition is defined depending on a portion at which its periodicity is lost. Therefore, an attempt was made to attain a condition that an auxiliary pattern is not transferred, including a local pattern region shown in  FIG. 8 . A detailed description will be described below.  
         [0050]      FIG. 8  shows a pattern used for obtaining a disposition rule of an auxiliary pattern. The pattern shown in  FIG. 8  differs from the design pattern shown in  FIG. 1  in that the line patterns  11  and  12  are broken on the midway thereof to provide a space of a width Sb=750 nm. With the pattern shown in  FIG. 8 , an auxiliary pattern is transferred more easily than with the pattern disposition shown in  FIG. 2 . The inventors of the present application carried out an exposure simulation, while changing the space width St between the auxiliary pattern and its adjacent line pattern and the width Sw of the short edge of the auxiliary pattern. This simulation was carried out under the same condition as that used for obtaining the characteristics shown in  FIGS. 3, 4 ,  5  and  6 .  
         [0051]     FIGS.  9  to  11  show a simulation result of an influence due to the pattern region shown in  FIG. 8  on an auxiliary pattern of the width Sw when the mask pattern is exposed. FIGS.  9  to  11  show the results when Sw=70 nm, Sw=68 nm, and Sw=65 nm, respectively. That is,  FIG. 9  shows a simulation image of a pattern shown in  FIG. 8 , obtained when an auxiliary pattern width Sw=70 nm in the pattern shown in  FIG. 8 .  FIG. 10  shows a simulation image of a pattern shown in  FIG. 8 , obtained when an auxiliary pattern width Sw=68 nm in the pattern shown in  FIG. 8 .  FIG. 11  shows a simulation image of a pattern shown in  FIG. 8 , obtained when an auxiliary pattern width Sw=65 nm in the pattern shown in  FIG. 8 . In FIGS.  9  to  11 , white solid line indicates a resist pattern image at an exposure dose of Just dose ±10%, Just dose denoting a dose by which L/S=70 nm/70 nm is obtained so that the cell portion of the region p 1  is desirably formed at Just Focus and thus as designed. Here, the space width Sc is 300 nm.  
         [0052]     From these simulation results, it is found that, at a portion at which the line pattern  11  and the line pattern  12  have their periodicity, an auxiliary pattern is not transferred to a resist film even when the auxiliary pattern width Sw is any of Sw=70 nm, Sw=68 nm, and Sw=65 nm. It is also found that, even at a portion at which the periodicity is lost, the auxiliary pattern is not transferred in the case where the auxiliary pattern width Sw=65 nm. However, it is found that, at a portion at which the periodicity is lost, the auxiliary pattern is transferred to the resist film in the case where the auxiliary pattern width Sw is 70 nm or 68 nm. Namely, these simulation results show that it is necessary to determine the auxiliary pattern width Sw, taking the pattern line periodicity into consideration. However, in consideration of a correlation between an actually carried out exposure test and the above simulation results, it has been confirmed that a resist film whose width is smaller than 20 nm formed on a substrate by exposure is removed from the surface of the substrate by a developing process. Thus, it is determined that an auxiliary pattern, which forms a resist film image having a width smaller than 20 nm by exposure on the substrate, is not transferred to the resist film. Since in the case of  FIG. 10 , the width of the resist film obtained by exposure was 20 nm, then a condition that the auxiliary pattern was not transferred to the resist film was defined such that the auxiliary pattern is smaller than 68 nm.  
         [0053]     However, it is possible to set a width of the auxiliary pattern to be greater than the above auxiliary pattern width, by contriving a method of disposing an auxiliary pattern. For example, in the above example, it is possible to introduce advantageous effects of the auxiliary pattern by gradually reducing the size of the auxiliary pattern as the line patterns  11  and  12  come close to portions at which periodicity is lost, though the design of the auxiliary pattern becomes slightly complicated.  
         [0054]     Next, with regard to a relationship between the space width St and the auxiliary pattern width Sw, the inventors of the present application performed simulations to obtain a specific disposition condition that the auxiliary pattern cannot not be transferred and the exposure margins of the adjacent pattern and its further adjacent pattern can be improved, where the space width St between the auxiliary pattern and its adjacent pattern is applied as a parameter St, and is given by St=(Sc−Sw)/2, see  FIG. 8 .  
         [0055]      FIG. 12  shows a relationship between the width Sw of an auxiliary pattern and the space distance St between the auxiliary pattern and its adjacent pattern to improve an exposure margin of the above-described adjacent pattern. The width Sw and the space distance St were indicated by being normalized based on the numerical aperture NA and wavelength λ of the exposure apparatus. In  FIG. 12 , plots indicate results of Sw and St obtained by the above exposure simulation. The solid line indicates a relationship between Sw and St obtained from the result. However, with respect to the above simulation result, in actual exposure, it is believed that variation in order of ±0.06 is found at a value normalized by λ/NA depending on an exposure device to be used or a resist process performance to be used. In  FIG. 12 , two broken lines indicate variation of ±0.06 at a value normalized at λ/NA with respect to the above solid line.  
         [0056]     In the graph of  FIG. 12 , it is found that a region D (i.e., a left-side region of the left-side broken line) is a region in which advantageous effect of the embodiment is attained. That is, in the region D, the auxiliary pattern is not transferred. On the other hand, in a region E (i.e., a right-side region of the right-side broken line), the auxiliary pattern is transferred, and thus, is a region in which disposition of an auxiliary pattern is not suitable. Further, a region F between the regions D and E is a region in which there is a high possibility that an auxiliary pattern is transferred in accordance with an exposure process to be used. If the transfer of the auxiliary pattern is suppressed in the region F, advantageous effect of oblique incidence exposure is greatly attained in the region F as compared with that in the region D. Thus, the improvement of an exposure margin can be expected with regard to the region F.  
         [0057]     In addition, in a region B shown in  FIG. 12  (in which Sw is equal to or greater than 0.37 in normalized dimensions), the auxiliary pattern is transferred without dependency on the space width St. On the other hand, in a region C shown in  FIG. 12  (in which Sw is equal to or smaller than 0.25 in normalized dimensions), the width of the auxiliary pattern is small as compared with a cell size, and thus, a restriction on manufacturing a mask occurs.  
         [0058]     From the foregoing, it is found that the auxiliary pattern width Sw may meet: 
 
0.23 ≦Sw /(λ/ NA )≦0.35  (1) 
 
 and the space width St between the auxiliary pattern and its adjacent line pattern may meet: 
 
 St /(λ/ NA )≧3.97 Sw− 0.74  (2) 
 
         [0059]     As described above, with the embodiment, regarding the problem that a pattern exposure margin is lowered in a non-periodic region of an actual device pattern, in particular, in a cell pattern, especially, in a region where patterns having a plurality of periodicities are adjacent to each other, attention is focused only to the space width St between the auxiliary pattern and its adjacent pattern (i.e., a target pattern whose margin is to be improved), and the auxiliary pattern width Sw and the space width St are set so as to meet Formulae (1) and (2), thereby making it possible to set an auxiliary pattern capable of achieving the improvement of an exposure margin.  
         [0060]     In this manner, with respect to a non-periodic pattern in a cell pattern in which a sufficient exposure margin is not successfully obtained conventionally, remarkable improvement of the exposure margin is achieved due to the advantageous effect of an un-transferable auxiliary pattern.  
         [0061]     While the embodiment has primarily described a mask on which an auxiliary pattern has been disposed, it is possible to apply the embodiment to the mask pattern data generating method. That is, determination is made as to whether or not an auxiliary pattern can be disposed on a line pattern as a target from a relationship between the width Sw of the auxiliary pattern and the space width St between the auxiliary pattern and its adjacent pattern, by using the above Formulae 1 and 2, making it possible to generate the auxiliary pattern.  
       SECOND EMBODIMENT  
       [0062]     Hereinafter, a second embodiment describes that a technique of disposing an auxiliary pattern used in the first embodiment can be applied to a region of a complicated pattern shown in  FIG. 13 .  
         [0063]     Regarding the pattern region shown in  FIG. 13 , an auxiliary pattern is disposed, as shown in  FIGS. 14 and 15 , based on the relation shown in formulae (1) and (2).  
         [0064]     In  FIG. 14 , reference numerals  17  and  18  each designate an auxiliary pattern (i.e., a pattern forming a transmitting section). In addition, reference numeral  19  denotes an auxiliary pattern of 70 nm in width.  FIG. 15  shows a portion of  FIG. 14 , detailed numerical dimensions being added. An exposure condition and patterns of the regions p 1  to p 3  are the same as those according to the first embodiment.  
         [0065]     The inventors of the present application disposed auxiliary patterns  17  and  18  so as to meet formulae (1) and (2), while the dimensions in the short edge direction of the auxiliary patterns  17  and  18  are defined as Sw, as shown in  FIG. 14 .  
         [0066]      FIG. 16  shows a resist pattern image of the mask pattern shown in  FIGS. 14 and 15 , obtained by simulation. For comparison with the resist pattern image shown in  FIG. 16 ,  FIG. 17  shows a resist pattern image of the mask pattern shown in  FIGS. 14 and 15 , in the case where the auxiliary patterns  17  and  18  are not disposed. The white solid line indicates a resist pattern image at an exposure dose of Just dose ±10%, Just dose denoting a dose by which L/S=70 nm/70 nm is obtained so that the cell portion of the region p 1  is desirably formed at Just Focus and thus as designed.  
         [0067]     From the resist pattern images shown in  FIGS. 16 and 17 , it has been confirmed that the disposed auxiliary patterns  17  and  18  meet a condition that the auxiliary patterns  17  and  18  are not transferred. Moreover, due to advantageous effect of the auxiliary pattern, the line pattern  8  and the line pattern  9  shown in  FIG. 13 , in particular, a pattern in a region  10  of these line patterns  8  and  9  can be formed without short-circuiting, and the exposure margin has been remarkably improved.  
         [0068]     As described above, to cope with a problem with exposure margin degradation of a pattern in an non-periodic region of an actual device pattern, in particular, in a cell pattern, especially, in a region where a plurality of patterns having a plurality of periodicities are adjacent to each other, according to the second embodiment, while the short edge direction dimensions of the auxiliary pattern width disposed in a complicated pattern region in a two-dimensional manner are defined as Sw, attention is focused on only the auxiliary pattern width Sw and the space width St between the auxiliary pattern and the adjacent pattern (i.e., a target pattern whose margin is to be improved), and the auxiliary pattern width Sw and the space width St are set so as to meet the above formulae (1) and (2), thereby making it possible to set an auxiliary pattern capable of achieving the improvement of the exposure margin. In this manner, with respect to the non-periodic pattern in the cell pattern as well, in which a sufficient exposure margin has not been successfully obtained, remarkable improvement of the exposure margin can be achieved due to advantageous effect of an auxiliary pattern whose image is not transferred.  
         [0069]     While each of the above embodiments has described a mask on which an auxiliary pattern has been disposed, the mask can be used in manufacturing a semiconductor device.  
         [0070]     The embodiments can be applied to a method of generating mask pattern data. That is, determination is made as to whether or not an auxiliary pattern can be disposed on a line pattern as a target from a relationship between the width Sw of the auxiliary pattern and the space width St between the auxiliary pattern and its adjacent pattern, by using the above Formulae (1) and (2), making it possible to generate the auxiliary pattern.  
         [0071]     A photo mask can be manufactured by using the mask pattern data generated by using the mask pattern data generating method described in each of the above embodiments. In addition, the manufactured photo mask can be used in manufacturing a semiconductor device. A sufficient exposure margin can be obtained by using the manufactured photo mask, thus improving the yield of the semiconductor device. It is preferable that the mask pattern data generating method described in each of the embodiments is applied to a design pattern of a semiconductor device or a liquid crystal display to generate a pattern for manufacturing a photo mask. Then, the manufactured photo mask for manufacturing the semiconductor device and the manufactured photo mask for manufacturing the liquid crystal display are radiated in use by the oblique incidence illumination system to project the patterns formed on the photo mask on a resist pattern formed on the substrate.  
         [0072]     In each of the above embodiments, an auxiliary pattern is disposed to a design pattern. However, without being limited thereto, an auxiliary pattern may be disposed to a design pattern in which optical proximity effect correction and/or process proximity effect correction has been carried out.  
         [0073]     Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.