Patent Publication Number: US-7596776-B2

Title: Light intensity distribution simulation method and computer program product

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2006-094847, filed Mar. 30, 2006, the entire contents of which are incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a light intensity distribution simulation method for obtaining a distribution of light intensity on a substrate surface at a time of exposure in the lithography process and computer program product. 
   2. Description of Related Art 
   For miniaturization of a pattern formed on a wafer, it is attempted to increase a numerical aperture NA of an exposure apparatus used for pattern forming. Therefore, an incident angle of light to a photomask and a wafer has been more increased. The incident angle of light especially to a surface of the photomask is so increased as to affect the pattern forming unfavorably. 
   The photomask comprises a pattern film having a film thickness such as a light shielding portion or a phase shifter portion. Because of a sidewall of the pattern film, a part which is not irradiated with the light generates in an aperture of the photomask. As a result, there arises a problem called shadowing in which an effective aperture ratio of the photomask fluctuates. 
   In consideration of the problem, in order to predict a pattern formed on a wafer according to a simulation, it is necessary to calculate the light diffraction phenomena generated in the aperture strictly based on a three-dimensional structure of a photomask. However, the calculation of diffraction phenomena based on the three-dimensional structure takes an immense time even with a high performance computer (for example, refer to Jpn. Pat. Appln. KOKAI Publication No. 7-29813). 
   BRIEF SUMMARY OF THE INVENTION 
   According to an aspect of the present invention, there is provided a light intensity distribution simulation method for predicting an intensity distribution of light on a substrate when a pattern formed on a photomask is irradiated with light in which a shape distribution of an effective light source is defined, by using an illumination optical system, and the light which passes through the photomask is projected on the substrate through a projection optical system, the method comprising: extracting a plurality of point light sources from the shape distribution of the effective light source; entering the light which is emitted from each of the plurality of point light sources in the pattern on the photomask; calculating an effective shape for each of the plurality of point light sources, the effective shape being a pattern obtained by excluding a part which is not irradiated with the light directly due to a sidewall of a pattern film including the pattern from a design shape of an aperture of the pattern; and calculating a distribution of a diffraction light generated in the pattern for each of the plurality of point light sources by using the effective shape calculated for each of the plurality of point light sources. 
   According to an aspect of the present invention, there is provided a computer program product for predicting an intensity distribution of light on a substrate when a photomask comprising a pattern is irradiated with light in which a shape distribution of an effective light source is defined, by using an illumination optical system, and the light which passes through the photomask is projected on the substrate through a projection optical system, the computer program product configured to store program instructions for execution on a computer system enabling the computer system to perform: an instruction for extracting a plurality of point light sources from the shape distribution of the effective light source; an instruction for entering light in the pattern of the photomask, the light being emitted from each of the plurality of point light sources; an instruction for calculating an effective shape for each of the plurality of point light sources, the effective shape being a shape obtained by excluding a part from a design shape of an aperture of the pattern, the part being failed to be irradiated with the light directly due to a sidewall of a pattern film including the pattern; and an instruction for calculating a distribution of diffraction light generated in the pattern for each of the plurality of point light sources by using the effective shape calculated for each of the plurality of point light sources. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       FIG. 1  is a block diagram showing a light intensity distribution simulation system according to a first embodiment of the invention; 
       FIG. 2  is a first schematic view of an exposure apparatus subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 3  is a second schematic view of an exposure apparatus subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 4  is a first cross-sectional view of a photomask subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 5  is a second cross-sectional view of a photomask subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 6  is a first schematic view of an effective light source subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 7  is a first schematic view of an aperture of the photomask subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 8  is a first graph of transmittance of the photomask subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 9  is a second schematic view of the effective light source subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 10  is a second schematic view of the aperture of the photomask subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 11  is a second graph showing transmittance of the photomask subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 12  is a first graph showing diffraction light amplitude intensity according to the first embodiment of the invention; 
       FIG. 13  is a first graph showing diffraction light amplitude intensity modulation ratio according to the first embodiment of the invention; 
       FIG. 14  is a second graph showing the diffraction light amplitude intensity according to the first embodiment of the invention; 
       FIG. 15  is a second graph showing the diffraction light amplitude intensity modulation ratio according to the first embodiment of the invention; 
       FIG. 16  is a second schematic view of the effective light source subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 17  is a schematic view of a design shape of an aperture and a dummy pattern aperture subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 18  is schematic view of effective shape of the aperture subjected to the light intensity distribution simulation system according to the first embodiment of the invention; 
       FIG. 19  is a flow chart showing a light intensity distribution simulation method according to the first embodiment of the invention; 
       FIG. 20  is a schematic view of a design of an aperture subjected to a light intensity distribution simulation system according to a second embodiment of the invention; 
       FIG. 21  is a first schematic view of a side vector forming the design shape of the aperture subjected to the light intensity distribution simulation system according to the second embodiment of the invention; 
       FIG. 22  is a second schematic view of the side vector forming the design shape of the aperture subjected to the light intensity distribution simulation system according to the second embodiment of the invention; 
       FIG. 23  is a schematic view of a shadow pattern generated in the aperture subjected to the light intensity distribution simulation system according to the second embodiment of the invention; 
       FIG. 24  is a schematic view of an effective shape of the aperture subjected to the light intensity distribution simulation system according to the second embodiment of the invention; 
       FIG. 25  is a flow chart showing a light intensity distribution simulation method according to the second embodiment of the invention; 
       FIG. 26  is a block diagram showing a light intensity distribution simulation system according to a third embodiment of the invention; 
       FIG. 27  is a first schematic view of an effective light source subjected to the light intensity distribution simulation system according to the third embodiment of the invention; 
       FIG. 28  is a flow chart showing a light intensity distribution simulation method according to the third embodiment of the invention; 
       FIG. 29  is a second schematic view of the effective light source subjected to the light intensity distribution simulation system according to the third embodiment of the invention; 
       FIG. 30  is a block diagram showing a light intensity distribution simulation system according to a fourth embodiment of the invention; 
       FIG. 31  is a graph showing a relation between a point light source position and diffraction light intensity ratio according to the fourth embodiment of the invention; 
       FIG. 32  is a flow chart showing a light intensity distribution simulation method according to the fourth embodiment of the invention; 
       FIG. 33  is a block diagram showing a light intensity distribution simulation system according to a fifth embodiment of the invention; 
       FIG. 34  is a schematic view showing diffraction light generated in an aperture of a photomask according to the fifth embodiment of the invention; 
       FIG. 35  is a flow chart showing a light intensity distribution simulation method according to the fifth embodiment of the invention; and 
       FIG. 36  is a view for explaining a computer program product according to embodiment. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Hereinafter, embodiments of the invention will be described referring to the drawings. 
   FIRST EMBODIMENT 
   As shown in  FIG. 1 , a light intensity distribution simulation system according to a first embodiment comprises a central processing unit (CPU)  300   a . The central processing unit  300   a  comprises an incident vector calculator unit  308 , an effective shape calculator unit  309 , and a light intensity calculator unit  351   a.    
   The incident vector calculator unit  308  extracts a plurality of point light sources from an effective light source formed by light which is emitted from an integrator of an exposure apparatus. Further, the incident vector calculator unit  308  calculates an incident vector of each light which is emitted from each of the plurality of point light sources and enter in a photomask including a pattern film having a film thickness. 
   The effective shape calculator unit  309  calculates a movement vector of the light on a plane parallel to the pattern film when the light proceeds the same distance as the film thickness of the pattern film in a direction vertical to the pattern film having a pattern including apertures. Further, the effective shape calculator unit  309  calculates the effective shape excluding a part which cannot be irradiated with light directly due to the sidewall of the pattern film, from a two-dimensional design shape of the apertures provided in the pattern film, for every point light source, using the movement vector. 
   The light intensity calculator unit  351   a  calculates a distribution of the diffraction lights generated in the apertures of the pattern using the effective shape calculated for every point light source, assuming the film thickness of the pattern film is zero 
   One example of the exposure apparatus which is subjected to the light intensity distribution simulation by the light intensity distribution simulation system is shown in  FIG. 2 . 
   The exposure apparatus comprises an illumination optical system  14 , a reticle stage  15  arranged below the illumination optical system  14 , a projection optical system  42  arranged below the reticle stage  15 , and a wafer stage  32  arranged below the projection optical system  42 . 
   The illumination optical system  14  comprises an illumination light source  41  for irradiating the light of a wavelength λ, an integrator  44  arranged under the illumination light source  41 , an aperture diaphragm holder  58  arranged under the integrator  44 , a polarizer  59  for polarizing the light emitted from the illumination light source  41 , a concentration optical system  43  for concentrating light, and a slit holder  54  arranged under the concentration optical system  43 . Here, the integrator  44  is also called fly-eye lens and includes a plurality of lens elements. The light emitted from the integrator  44  forms the effective light source. 
   The reticle stage  15  comprises a reticle XY stage  81 , reticle movable shafts  83   a  and  83   b  provided on the reticle XY stage  81  and a reticle Z-tilting stage  82  connected to the reticle XY stage  81  by the reticle movable shafts  83   a  and  83   b.    
   A reticle stage driving unit  97  is connected to the reticle stage  15 . The reticle stage driving unit  97  scans the reticle XY stage  81  in a horizontal direction. The reticle stage driving unit  97  drives the reticle movable shafts  83   a  and  83   b  in a vertical direction. Therefore, the reticle Z-tilting stage  82  can be positioned in the horizontal direction by the reticle XY stage  81 . Further, the reticle Z-tilting stage  82  may be tilted on a horizontal surface by the reticle movable shafts  83   a  and  83   b . A reticle movable mirror  98  is positioned at the end of the reticle Z-tilting stage  82 . The position of the reticle Z-tilting stage  82  is measured by a reticle laser interferometer  99  which is arranged opposite to the reticle movable mirror  98 . 
   The wafer stage  32  comprises a wafer XY stage  91 , wafer movable shafts  93   a  and  93   b  arranged on the wafer XY stage  91 , and a wafer Z-tilting stage  92  connected to the wafer XY stage  91  by the wafer movable shafts  93   a  and  93   b . A wafer stage driving unit  94  is connected to the wafer stage  32 . The wafer stage driving unit  94  scans the wafer XY stage  91  in the horizontal direction. The wafer stage driving unit  94  drives the wafer movable shafts  93   a  and  93   b  in the vertical direction. Therefore, the wafer Z-tilting stage  92  is positioned in the horizontal direction by the wafer XY stage  91 . The wafer Z-tilting stage  92  may be tilted on the horizontal surface by the wafer movable shafts  93   a  and  93   b . A wafer movable mirror  96  is positioned at the end of the wafer Z-tilting stage  92 . The position of the wafer Z-tilting stage  92  is measured by a wafer laser interferometer  95  which is arranged opposite to the wafer movable mirror  96 . 
   A photomask  5  to be irradiated with light is disposed on the reticle stage  15 .  FIG. 3  schematically shows the state in which light ψ emitted from a point light source (SX, SY) that is a part of an effective light source  40  formed by the light emitted from the integrator  44  is concentrated by the concentration optical system  43  and the concentrated light ψ enters in the photomask  5 . 
   As shown in a cross-sectional view of  FIG. 4 , the photomask  5  comprises a transparent substrate  1  formed of a quartz glass and the like, and a pattern film  100  arranged on a rear surface of the transparent substrate  1 . As shown in  FIGS. 3 and 4 , the pattern film  100  includes apertures  101   a ,  101   b , and  101   c  having a designed aperture size D 0 . The surface of the transparent substrate  1  is exposed in the apertures  101   a  to  101   c . As a material of the pattern film  100 , chromic oxide (CrxOy), chromic fluoride (CrF), molybdenum silicide (MoSi) and the like can be used. Each refractive index n of CrxOy, CrF, and MoSi is about 2.2. Here, a phase difference φ between the light which passes through the pattern film  100  and the light which proceeds in the air, emitted from the transparent substrate  1  is obtained by the following formula (1).
 
Φ=2 π{n×d/λ−n   0   ×d/λ}   (1)
 
   In the formula (1), n shows the refractive index of the pattern film  100 , n 0  shows the refractive index of the air, and d shows the film thickness of the pattern film  100 . 
   When the refractive index n 0  is 1.0 and the wavelength λ of the light is 193 nm, the film thickness d of the pattern film  100  necessary to make the phase difference φ at the angle of 180 degrees is 80 nm. 
   Even when the photomask  5  is not a halftone mask and the pattern film  100  is formed by chrome (Cr), the film thickness d has to be 80 nm. 
   Hereinafter, in order to simplify the description, it is assumed that the pattern film  100  is formed by a light-shielding material such as Cr. 
   Here, it is assumed that the light ψ emitted from the illumination light source  41  shown in  FIG. 2  enters obliquely in the transparent substrate  1  of the photomask  5  at incident angle of the light ψ emitted from each of the point light sources defined at each position of the point light sources as shown in  FIG. 5 , and the obliquely entered light ψ proceeds into the air from the transparent substrate  1  at the refracting angle θ. 
   In this case, although the aperture  101   a  actually has the designed aperture size D 0 , an effective aperture size D E  becomes smaller than the designed aperture size D 0  with respect to the oblique incident light ψ. 
   The effective aperture size D E  is obtained by the following formula (2). 
   Here, the ratio of the effective aperture size D E  and the designed aperture size D 0  shown in the following formula (3) is defined as an aperture size ratio O.R.
 
 D   E   =D   0   −d  tan θ  (2)
 
 O.R.=D   E   /D   0 =1 −d  tan θ/ D   0   (3)
 
   The value of refracting angle θ shown in  FIG. 5  changes according to a numerical aperture NA and a coherence factor C of the optical system of the exposure apparatus shown in  FIG. 2 . In addition, as the miniaturization of the mask pattern of the photomask  5  proceeds, the maximum value θmax of the refracting angle θ tends to become larger. The relation among the maximum refracting angle θmax, the numerical aperture NA, and the coherence factor σ is obtained by the following formula (4) with an inverse number Mag of a demagnification factor of the projection optical system  42 .
 
θmax=arcsin(σNA/ Mag )  (4)
 
   For example, when the coherence factor σ is 0.95, the numerical aperture NA is 1.05, and the inverse number Mag of the demagnification factor is 4, the maximum refracting angle θmax is 14.4 degrees. Further, when the film thickness d of the pattern film  100  is 80 nm and the designed aperture size D 0  is 260 nm, the opening size ratio O.R. is 0.92 according to the formula (3). Such the variation of the aperture size has effect on the diffraction light generated in the photomask, and the influence will be described below. 
   At first, as shown in  FIG. 6 , the film thickness d of the pattern film  100  does not have the effect on the diffraction light, with respect to the light which is emitted from a point light source (0, 0) positioning at the center of the effective light source  40  and enters in the photomask  5  vertically. Therefore, the designed aperture size D 0  of the aperture  101   b  shown in the top view of  FIG. 7  is equal to the effective aperture size D E  and a first transmittance distribution T p  (X) in the vicinity of the aperture  101   b  can be expressed by a first rectangle (rect) function obtained by the following formula (5) as shown in  FIG. 8 .
 
 T   p ( X )= rect ( x/D   0 )  (5)
 
   In this case, ν is put as frequency and a first amplitude intensity distribution E D1 (ν) of the diffraction light generated in the aperture  101   b  is expressed in a first sync (sinc) function obtained by the following formula (6) in which the first rect function obtained by the formula (5) is Fourier transformed. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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   Where, i shows an imaginary number. 
   Contrarily, as shown in  FIG. 9 , the light which is emitted from a point light source (−SX, 0) that is a part of the effective light source  40  and enters obliquely in the photomask  5  cannot illuminate the whole aperture  101   b  due to the side wall  102  of the pattern film  100  having the film thickness d and a shadow occurs in the aperture  101   b . Therefore, the two-dimensional effective aperture size D E  Of the aperture  101   b  shown in the top view of  FIG. 10  becomes smaller than the designed aperture size D 0 . 
   Here, when the incident vector υ of the light entering in the photomask  5  from a point light source (SX, SY) forming the effective light source  40  is obtained by the following formulas (7) to (9), the diffraction phenomenon generated in the aperture  101   b  may be approximated to the diffraction phenomenon generated in the case where a virtual aperture having the film thickness d of 0 and the effective aperture size D E  obtained by the following formula (10) is provided in the pattern film  100  instead of the aperture  101   b.  
 
υ=( SX,SY ,(1− SX   2   −SY   2 ) 1/2 )  (7)
 
|υ|=1  (8)
 
 SX   2   +SX   2   +SY   2 ≦1  (9)
 
 D   E   =D   0   −d  tan(arcsin( SX ))= D   0   −ΔD   (10)
 
   Therefore, a second transmittance distribution T 0  (X) in the vicinity of the aperture  101   b  when the light enters obliquely in the photomask  5  can be shown by a second rectangle (rect) function obtained by the following formula (11), as shown in  FIG. 11 . 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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   In this case, a second amplitude intensity distribution E D2  (ν) of the diffraction light generated in the aperture  101   b  is shown by a second sinc function obtained by the following formula (12) in which a second rect function obtained by the formula (11) is Fourier transformed.
 
 E   D2 (ν)=( D   0   −ΔD )sinc {( D   0   −ΔD )ν} exp {2 πi (Δ D/ 2)ν}  (12)
 
   As shown in the formula (12), the second sinc function includes the imaginary part exp {2πi(ΔD/2)ν}. 
   Therefore, when the light enters in the photomask  5  obliquely, the amplitude intensity of the diffraction light is separated into a real part Re and an imaginary part Im as shown in  FIG. 12 , further, the diffraction light receives an amplitude modulation Δamp obtained by the following formula (13), as shown in  FIG. 13 . 
   In addition,  FIGS. 12 and 13  show the case where the wavelength λ of the light is 193 nm, the numerical aperture NA is 0.92, the coherence factor σ is 0.95, the film thickness d is 80 nm, the designed aperture size D 0  is 360 nm, and the aperture  101   b  is reduced by 1/4 and projected. The amplitude intensity of the diffraction light when the designed aperture size D 0  is 220 nm under the same exposure condition is shown in  FIG. 14  and the modulation ratio of the amplitude intensity of the diffraction light is shown in  FIG. 15 .
 
Δ amp=|E   D1 |−( Re   2   +Im   2 ) 1/2   (13)
 
   Here, a fluctuation estimating unit  307  included in the CPU  300   a  shown in  FIG. 1  calculates each opening size ratio O.R. of the apertures  101   a  to  101   c  by using the formula (3) when the photomask  5  shown in  FIGS. 3 to 5  is put on the exposure apparatus shown in  FIG. 2 . 
   The fluctuation estimating unit  307  shown in  FIG. 1  determines whether the opening size ratio O.R. calculated is 0.95 or less which is an example of an allowance value. 
   In addition, when a plurality of apertures are provided in the photomask  5 , it may determine whether the opening size ratio O.R. of the minimum aperture is not more than the allowance value. 
   The incident vector calculator unit  308  divides the effective light source  40  and extracts a plurality of point light sources (SX, SY). Further, the incident vector calculator unit  308  calculates the incident vector υ of the light which is emitted from the point light source (SX, SY) shown in  FIG. 16  and enters obliquely in the photomask  5  shown in  FIG. 5 , obtained by the formulas (7) to (9). 
   The effective shape calculator unit  309  shown in  FIG. 1  calculates a plurality of effective shapes of the aperture  101   b  corresponding to the respective point light sources. More specifically, the effective shape calculator unit  309  calculates a movement vector V of the light obtained by the following formula (14) on a plane parallel to the pattern film  100  when the light proceeds the same distance as the film thickness d of the pattern film  100  in the direction vertical to the photomask  5  according to the incident vector υ.
 
 V =(− d  tan(arcsin( SX )),− d  tan(arcsin( SY ))  (14)
 
   Here, as shown in  FIG. 17 , the effective shape calculator unit  309  calculates a dummy pattern aperture  111  obtained by parallel moving the design shape  105  of the aperture  101   b  according to the movement vector V obtained by the formula (11). Further, the effective shape calculator unit  309  obtains logical multiplication (AND) of the design shape  105  and the dummy pattern aperture  111 , and calculates the effective shape  121  as shown in  FIG. 18 . When a set of coordinates forming the design shape  105  is shown by A (x, y) and a set of coordinates forming the dummy pattern aperture  111  is shown by A (x+d tan(arcsin (SX)), y+d tan(arcsin (SY))), a set Aeff (x, y) of coordinates forming the effective shape  121  is obtained by the following formula (15).
 
 A   eff ( x,y )= A ( x,y )∩ A ( x+d  tan(arcsin( SX ),  y+d  tan(arcsin( SY ))  (15)
 
   In the above example, although the case of calculating the effective shape  121  from the aperture  101   b  has been shown, the effective shape calculator unit  309  shown in  FIG. 1  calculates a plurality of effective shapes corresponding to a plurality of point light sources respectively in respect to the other apertures  101   a  and  101   c , etc included in the photomask  5 . 
   Assuming that there is no film thickness in the pattern film  100 , the intensity calculator unit  351   a  calculates the light intensity distribution of a projected image of a mask pattern of the photomask  5  imaged on a semiconductor substrate which is disposed on the wafer stage  32  shown in  FIG. 2 , by using the respective effective shapes of the apertures  101   b  corresponding to the respective point light sources. Here, a partial coherent imaging formula obtained by the following formula (16) or (17) is generally used for the light intensity distribution simulation. 
   
     
       
         
           
             
               
                 
                   
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   In the formulas (16) and (17), S shows the intensity distribution of the effective light source, P shows a pupil function of the projection optical system  42 , * shows a complex conjugate, m^ shows a Fourier transform of a complex transmission distribution of the mask pattern, and TCC shows a transfer function called transmittance cross coefficient. 
   According to the formula (16), among the light intensity distribution of the diffraction light generated in the mask pattern, the components which can pass through the pupil are calculated, further, the light amplitude distribution on the image surface is calculated by inverse Fourier transform, and intensity integration is performed according to the intensity distribution of the effective light source. 
   According to the formula (17), a previously calculated TCC and the diffraction light distribution generated in the mask pattern are double integrated and the light intensity distribution on the image surface is calculated. 
   By comparison between the formulas (16) and (17), the formula (16) performs a coherent imaging calculation on the light emitted from each point light source forming the effective light source  40 . Therefore, when the light intensity distribution of the projection image is calculated by using the effective shapes of the aperture  101   b  corresponding to the respective point light sources, the formula (16) is better suited. However, the formula (16) uses an assumption that the intensity distribution of the diffraction light generated in the mask pattern does not depend on the point light source (f, g). Therefore, the light intensity calculator unit  351   a  shown in  FIG. 1  calculates the light intensity distribution of the projection image by using the following formula (18) which is modification of the formula (16).
 
 I ( x,y )=∫ S ( f,g )|∫ P ( f+f   1   ,g+g   1 ){circumflex over ( m )}( f   1   ,g   1   ;f,g )exp(−2 πi ( f   1   x+g   1   y )) df   1   dg   1 | 2   dfdg   (18)
 
   A data storage device  320   a  is connected to the CPU  300   a . The data storage device  320   a  comprises an exposure condition storage unit  302 , a mask pattern storage unit  303 , a division environment storage unit  305 , and an effective shape storage unit  304 . 
   The exposure condition storage unit  302  stores the exposure condition such as the numerical aperture NA of the projection optical system  42 , the coherence factor σ, and an orbicular zone screen factor of the illumination light source  41  in the exposure apparatus shown in  FIG. 2 . 
   The mask pattern storage unit  303  shown in  FIG. 1  stores the design data of the photomask  5  shown in  FIGS. 3 to 5  disposed on the reticle stage  15  of the exposure apparatus shown in  FIG. 2  in the form of CAD data or the like. The design data of the photomask  5  is related to the apertures  101   a ,  101   b , and  101   c  and the film thickness d of the pattern film  100  or the like. 
   The division environment storage unit  305  shown in  FIG. 1  stores the coordinates of a plurality of point light sources (SX, SY) calculated by the incident vector calculator unit  308  and the incident vectors U of the respective lights ψ irradiated from the point light sources (SX, SY). 
   The effective shape storage unit  304  stores the respective effective shapes of the apertures  101   a  to  101   c  calculated by the effective shape calculator unit  309 . 
   An input unit  312 , an output unit  313 , a program memory  330 , and a temporary memory  331  are connected to the CPU  300   a.    
   As the input unit  312 , a pointing device such as a keyboard and a mouse may be used. 
   An image display such as a liquid display and a monitor, and a printer may be used as the output unit  31 . 
   The program memory  330  stores an operating system for controlling the CPU  300   a.    
   The temporary memory  331  sequentially stores an operation result obtained by the CPU  300   a.    
   As the program memory  330  and the temporary memory  331 , a recording medium for recording a program, such as a semiconductor memory, a magnetic disk, an optical disk, an optical magnetic disk, and a magnetic tape may be used. 
   Next, a light intensity distribution simulation method according to the first embodiment will be described by using the flow chart shown in  FIG. 19 . 
   (a) In Step S 50 , the fluctuation estimating unit  307  shown in  FIG. 1  reads out the exposure environment of the exposure apparatus shown in  FIG. 2  from the exposure condition storage unit  302 . In addition, the fluctuation estimating unit  307  shown in  FIG. 1  reads out the design shape of the aperture  101   b  of the photomask  5  including the pattern film  100  having the film thickness d shown in  FIGS. 3 to 5  and an disposed position of the aperture  101   b  when the photomask  5  is disposed on the reticle stage  15 , from the mask pattern storage unit  303 . 
   Next, the fluctuation estimating unit  307  shown in  FIG. 1  calculates the opening size ratio O.R. of the respective apertures  101   a  to  101   c  by using the formula (3) when the photomask  5  shown in  FIGS. 3 to 5  is arranged in the exposure apparatus shown in  FIG. 2 . In addition, the fluctuation estimating unit  307  shown in  FIG. 1  determines whether the calculated opening size ratio O.R. is not more than the allowance value. When the calculated opening size ratio O.R. is not more than the allowance value, the process goes to Step S 100 . When the opening size ratio O.R. which is calculated is more than the acceptable value, the light intensity distribution simulation is performed by conventional method. 
   (b) In Step S 100 , the incident vector calculator unit  308  shown in  FIG. 1  reads out the exposure environment such as the form of the effective light source  40  formed of the light emitted from the integrator  44  shown in  FIG. 2 , from the exposure condition storage unit  302 . 
   Next, the incident vector calculator unit  308  shown in  FIG. 1  divides the effective light source  40  and extracts the plurality of point light sources (SX, SY). In Step S 101 , the incident vector calculator unit  308  reads out the design shape of the aperture  101   b  of the photomask  5  including the pattern film  100  having the film thickness d shown in  FIGS. 3 to 5  and the disposed position of the aperture  101   b  when the photomask  5  is disposed on the reticle stage  15 , from the mask pattern storage unit  303 . 
   The incident vector calculator unit  308  shown in  FIG. 1  calculates the incident vector υ of the light ψ which is emitted from each of the plurality of point light sources (SX, SY) and enters in the photomask  5  as shown in  FIG. 3 . The incident vector υ is obtained by the formulas (7) to (9). The incident vector calculator unit  308  stores the coordinates of the plurality of point light sources (SX, SY) and the incident vector υ of the plurality of lights ψ irradiated from each of the plurality of point light sources (SX, SY) in the division environment storage unit  305 . 
   (c) In Step S 102 , the effective shape calculator unit  309  reads out the coordinates of the plurality of point light sources (SX, SY) and the incident vector υ of the plurality of lights ψ irradiated from each of the plurality of point light sources (SX, SY), from the division environment storage unit  305 . 
   Next, the effective shape calculator unit  309  calculates the movement vector V of the light ψ on the plane parallel with the pattern film  100  when the light ψ emitted from each of the plurality of point light sources (SX, SY) proceeds the same distance as the film thickness d of the pattern film  100  in the vertical direction to the photomask  5  shown in  FIG. 5  according to the incident vector υ. The movement vector V is obtained by the formula (14). 
   (d) In Step S 103 , the effective shape calculator unit  309  calculates the dummy pattern aperture  111  obtained by shifting the design shape  105  of the aperture  101   b  in parallel according to the movement vector V obtained by the formula (11), as shown in  FIG. 17 . In Step S 104 , the effective shape calculator unit  309  obtains logical multiplication (AND) of the design shape  105  and the dummy pattern aperture  111 , and calculates the effective shape  121 , as shown in  FIG. 18 . The effective shape calculator unit  309  stores the calculated effective shape  121  in the effective shape storage unit  304 . 
   (e) In Step S 105 , the light intensity calculator unit  351   a  reads out the effective shape  121  from the effective shape storage unit  304  and reads out the exposure environment of the exposure apparatus shown in  FIG. 2  from the exposure condition storage unit  302 . In addition, the light intensity calculator unit  351   a  shown in  FIG. 1  reads out the design shape of the aperture  101   b  of the photomask  5  including the pattern film  100  shown in  FIGS. 3 to 5  and the disposed position of the aperture  101   b  when the photomask  5  is disposed on the reticle stage  15  from the mask pattern storage unit  303 . 
   Next, the light intensity calculator unit  351   a  substitutes the virtual aperture having the effective shape  121  for the aperture  101   b  having the design shape  105  of the photomask  5  and assumes that the film thickness d of the pattern film  100  is zero. 
   (f) In Step S 106 , the light intensity calculator unit  351   a  calculates distribution of diffraction light in the virtual aperture by using the formula (18). The diffraction light is generated by the light emitted from the point light sources (SX, SY) forming the effective light source  40  entering in the virtual aperture. Further, the light intensity calculator unit  351   a  calculates the light intensity distribution of the projection image of the mask pattern of the photomask  5  imaged on the semiconductor substrate arranged on the wafer stage  32  shown in  FIG. 2 . It also calculates the distribution of the diffraction light generated in the corresponding virtual aperture with respect to the other light emitted from each of the other point light sources (SX, SY), further calculates the light intensity distribution of the projection image. In this way, the light intensity distribution simulation method according to the first embodiment is finished. 
   Heretofore, in order to calculate the intensity distribution of the diffraction light generated in the aperture  101   b  included in the pattern film  100  having the film thickness d as shown in  FIG. 5 , an electromagnetic field on the transparent substrate  1  has been calculated exactly based on the film thickness d. 
   However, there is a problem that a finite difference time domain (FDTD) method takes a long time to calculate the electromagnetic field exactly and that a load of a computer is large. Therefore, it is difficult to feed back the intensity distribution of the calculated diffraction light to OPC. 
   Contrarily, according to the light intensity distribution simulation method of the first embodiment, the effective light source  40  is divided to extract a plurality of point light sources and a plurality of effective shapes of the apertures  101   b  corresponding to the point light sources (SX, SY) are calculated respectively. 
   Here, assuming that the film thickness d of the pattern film is zero, when the amplitude intensity of the diffraction light is calculated in every virtual aperture having each effective shape, the amplitude intensity of the calculated diffraction light reflects the area difference between the design shape and the effective shape caused by the film thickness d of the pattern film  100 . 
   The step for calculating each of the plurality of effective shapes can be performed by graphics processing function of a computer. The load of the computer necessary for the graphics processing is much smaller than the load necessary to calculate the electromagnetic field exactly. 
   Therefore, according to the light intensity distribution simulation method of the first embodiment, an effect on the diffraction phenomenon by the film thickness d of the pattern film can be reflected easily in the calculation result of the light intensity distribution of the projection image. As a result, it is possible to feed back the light intensity distribution simulation result having a high accuracy to OPC more rapidly and to provide the mask pattern data having higher accuracy. 
   Further, OPC processed photomask with the calculation result fed back from the light intensity distribution simulation method according to the first embodiment may realize a good transfer reproducibility with a higher accuracy. As a result, it is possible to provide a semiconductor device with a high accuracy. 
   In addition, the light intensity distribution simulation method according to the first embodiment may be performed by extracting only the aperture having a smaller opening size ratio O.R. in the design rule checking step of the mask data processing. 
   SECOND EMBODIMENT 
   In a second embodiment, the effective shape calculator unit  309  included in the CPU  300   a  shown in  FIG. 1  defines the vertexes of the design shape  105  of the aperture  101   b  shown in  FIG. 20  as a 1 , a 2 , a 3 , and a 4 . 
   As shown in  FIG. 21 , the effective shape calculator unit  309  shown in  FIG. 1  calculates a first side vector v 1  connecting the second vertex a 2  and the first vertex a 1 , a second side vector v 2  connecting the third vertex a 3  and the second vertex a 2 , a third side vector v 3  connecting the fourth vertex a 4  and the third vertex a 3 , and a fourth side vector v 4  connecting the first vertex a 1  and the fourth vertex a 4 . 
   As shown in  FIGS. 22 and 23 , the effective shape calculator unit  309  shown in  FIG. 1  calculates a first shadow pattern  141  which is formed by the first side vector v 1  and the movement vector V obtained by the formula (14), a second shadow pattern  142  which is formed by the second side vector v 2  and the movement vector V, a third shadow pattern  143  which is formed by the third side vector v 3  and the movement vector V, and a fourth shadow pattern  144  which is formed by the fourth side vector v 4  and the movement vector V. 
   The effective shape calculator unit  309  shown in  FIG. 1  obtains logical addition (OR) of the first shadow pattern  141 , the second shadow pattern  142 , the third shadow pattern  143 , and the fourth shadow pattern  144  shown in  FIG. 23  to calculate a composite shadow pattern. 
   The effective shape calculator unit  309  shown in  FIG. 1  obtains logical multiplication (AND) of negative (NOT) of the composite shadow pattern and the design shape  105  to calculate the effective shape  121  of the aperture  101   b  shown in  FIG. 24 . 
   The other modules of the light intensity distribution simulation system shown in  FIG. 1  work in the same way as in the first embodiment, thereby omitting the description. 
   Next, a light intensity distribution simulation method according to the second embodiment will be described by using flow chart shown in  FIG. 25 . 
   (a) Step S 50  and Step S 200  to Step S 202  shown in  FIG. 25  are performed in the same way as Step S 50  and Step S 100  to Step S 102  shown in  FIG. 19 . 
   In Step S 203 , the effective shape calculator unit  309  shown in  FIG. 1  defines the vertexes of the design shape  105  of the aperture  101   b  shown in  FIG. 20  as a 1 , a 2 , a 3 , and a 4 . 
   Next, as shown in  FIG. 21 , the effective shape calculator unit  309  calculates a first side vector v 1  connecting the second vertex a 2  and the first vertex a 1 , a second side vector v 2  connecting the third vertex a 3  and the second vertex a 2 , a third side vector v 3  connecting the fourth vertex a 4  and the third vertex a 3 , and a fourth side vector v 4  connecting the first vertex a 1  and the fourth vertex a 4 . 
   (b) In Step S 204 , as shown in  FIG. 23 , the effective shape calculator unit  309  shown in  FIG. 1  calculates a first shadow pattern  141  which is formed by the first side vector v 1  and the movement vector V, a second shadow pattern  142  which is formed by the second side vector v 2  and the movement vector V, a third shadow pattern  143  which is formed by the third side vector v 3  and the movement vector V, and a fourth shadow pattern  144  which is formed by the fourth side vector v 4  and the movement vector V. 
   Thereafter, the effective shape calculator unit  309  shown in  FIG. 1  obtains the logical addition (OR) of the first shadow pattern  141 , the second shadow pattern  142 , the third shadow pattern  143 , and the fourth shadow pattern  144  shown in  FIG. 23  to calculate the composite shadow pattern. 
   (c) In Step S 205 , the effective shape calculator unit  309  shown in  FIG. 1  obtains the logical multiplication (AND) of the negative (NOT) of the composite shadow pattern and the design shape  105  to calculate the effective shape  121  of the aperture  101   b  shown in  FIG. 24 . 
   Next, the effective shape calculator unit  309  stores the calculated effective shape  121  in the effective shape storage unit  304 . 
   Thereafter, Step S 206  and Step S 207  shown in  FIG. 25  are performed in the same way as Step S 105  and Step S 106  shown in  FIG. 19 , and hence to complete the light intensity distribution simulation method according to the second embodiment. 
   The image processing for decomposing a polygon into vector sequence imposes a little load on the computer. Therefore, according to the light intensity distribution simulation method according to the second embodiment, it is also possible to reflect the effect on the diffraction phenomenon by the film thickness d of the pattern film in the calculation result easily and obtain the light intensity distribution simulation result with high accuracy in shorter time. 
   THIRD EMBODIMENT 
   A light intensity distribution simulation system according to a third embodiment shown in  FIG. 26  is different from the light intensity distribution simulation system shown in  FIG. 1  in that the CPU  300   b  further comprises a thinning-out processing unit  352  and an interpolation processing unit  353 . 
   As shown in  FIG. 27 , the thinning-out processing unit  352  sets a grid of the space (1/m)×NA/λ on the pupil surface of an incident pupil  24  in the effective light source  40 . The thinning-out processing unit  352  performs the thinning-out processing for extracting each portion of the effective light source  40  corresponding to each intersection of the grid as a selected point light source (SXa, SYa). Therefore, in the third embodiment, the effective shape calculator unit  309  shown in  FIG. 26  calculates each extracted effective shape of aperture corresponding to each selected point light source (SXa, SYa). 
   The interpolation processing unit  353  calculates effective shapes of apertures corresponding to unselected point light sources (SXc, SYc) thinned out by the thinning-out processing unit  352 , of the point light sources (SX, SY) forming the effective light source  40 , based on effective shapes of the apertures corresponding to the selected point light sources (SXa, SYa) by interpolation method. 
   Next, a light intensity distribution simulation method according to the third embodiment will be described by using the flow chart shown in  FIG. 28 . 
   (a) Step S 50  shown in  FIG. 28  is performed in the same way as Step S 50  shown in  FIG. 19 . 
   In Step S 300 , the thinning-out processing unit  352  shown in  FIG. 26  reads out the form of the effective light source  40  shown in  FIG. 2  from the exposure condition storage unit  302 . 
   Next, the thinning-out processing unit  352  sets the grid of the space (1/m)×NA/λ in the effective light source  40  as shown in  FIG. 27 . 
   Thereafter, the thinning-out processing unit  352  extracts each portion of the effective light source corresponding to each intersection of the grid as the selected point light source (SXa, SYa). 
   (b) In Step S 301 , as shown in  FIG. 3 , the incident vector calculator unit  308  shown in  FIG. 26  calculates the incident vector υ of the light ψ which is emitted from each of the plurality of selected point light sources (SXa, SYa) and enters in the photomask  5 . The incident vector υ is obtained by the formulas (7) to (9). 
   The incident vector calculator unit  308  stores the coordinates of the plurality of selected point light sources (SXa, SYa) and the incident vectors υ of the plurality of lights ψ emitted from the plurality of selected point light sources (SXa, SYa), in the division environment storage unit  305 . 
   (c) In Step S 302 , the effective shape calculator unit  309  reads out the respective coordinates of the plurality of selected point light sources (SXa, SYa) and the incident vectors υ of the plurality of lights ψ emitted from the plurality of selected point light sources (SXa, SYa), from the division environment storage unit  305 . 
   Next, the effective shape calculator unit  309  calculates the movement vector V of the light ψ on the plane parallel to the pattern film  100  when the light ψ emitted from each of the plurality of selected point light sources (SXa, SYa) proceeds the same distance as the film thickness d of the pattern film  100  according to the incident vector υ in the horizontal direction of the photomask  5  shown in  FIG. 5 . The movement vector V is obtained by the formula (14). 
   (d) Step S 303  and Step S 304  shown in  FIG. 28  are performed in the same way as Step S 103  and Step S 104  shown in  FIG. 19 . 
   In Step S 305 , the interpolation processing unit  353  shown in  FIG. 26  reads out the effective shape of the aperture  101   b  corresponding to each of the plurality of selected point light sources (SXa, SYa) from the effective shape storage unit  304 . 
   Next, the interpolation processing unit  353  calculates effective shapes of apertures corresponding to the unselected point light sources (SXc, SYc) thinned out by thinning-out processing unit  352 , of the plurality of point light sources (SX, SY) forming the effective light source  40 , based on the effective shapes of the apertures corresponding to the of selected point light sources (SXa, SYa) by interpolation method. 
   The interpolation processing unit  353  stores the calculated effective shapes in the effective shape storage unit  304 . 
   Thereafter, Step S 306  and Step S 307  shown in  FIG. 28  are performed in the same way as Step S 105  and Step S 106  shown in  FIG. 19 , and hence to complete the light intensity distribution simulation method according to the third embodiment. 
   According to the light intensity distribution simulation method according to the third embodiment described above, it is possible to reduce the load on the computer necessary for performing Steps S 301  to S 304  as the thinning-out processing of Step S 300  is performed. Therefore, it is possible to shorten a calculation time necessary for performing the simulation. Further, according to the embodiment, it is possible to keep the accuracy of the calculated light intensity as the interpolation processing is performed in Step S 305 . 
   In addition, the method of extracting the plurality of selected point light sources (SXa, SYa) performed by the thinning-out processing unit  352  shown in  FIG. 26  is not limited to the example shown in  FIG. 27 . Since the light emitted from the outer portion of the center of the effective light source  40  is more affected by the film thickness d of the pattern film  100  shown in  FIG. 5 . Therefore, for example, as shown in  FIG. 29 , the select point light sources (SXa, SYa) arranged in a manner that the intervals of the select point light sources (SXa, SYa) reduce toward an edge of an optical axis of the effective light source having diameter of a NA/λ on the incident pupil  24  from a center of the optical axis. In addition, the number of the selected point light sources extracted by the thinning-out processing unit  352  may be set so that the opening size ratio O.R. may be a predetermined value or more. 
   FOURTH EMBODIMENT 
   A light intensity simulation system according to the fourth embodiment is different from the light intensity simulation system shown in  FIG. 1  in that the CPU  300   c  further comprises a loss calculator  354  and a light source modulator unit  355 , as shown in  FIG. 30 . 
   The loss calculator  354  calculates a lost area for each of the plurality of point light sources (SX, SY), in which the lost area is obtained by eliminating the effective shape from the design shape. 
   The light source modulator unit  355  calculates the modulated intensity distribution Sm (f, g) of the effective light source by applying the modulation to the light intensity of the light emitted from each of the plurality of point light sources (SX, SY) based on the lost area. 
   Here, a first amplitude intensity distribution E D1 (ν) of the diffraction light generated in the aperture by the light emitted from the point light source (0, 0) of the center of the effective light source  40  shown in  FIG. 3  is obtained by the formula (6). A second amplitude intensity distribution E D2 (ν) of the diffraction light generated in the aperture by the light emitted from the point light source (−SX, 0) of the effective light source  40  is obtained by the formula (12). Therefore, when the coherency of the light emitted from the illumination light source  41  is not perfect, the relation between the second amplitude intensity distribution E D2 (ν) and the first amplitude intensity distribution E D1 (ν) may be approximated by the following formula (19). Therefore, the intensity of the light emitted from the point light source (SX, SY) may be expressed as the intensity relative to the intensity of the light emitted from the point light source (0, 0).
 
E D2 (ν)÷{(D 0 −ΔD)/D 0 }×E D1   (19)
 
     FIG. 31  shows the relation between the position of the point light source (SX, 0) and the light intensity of the diffraction light generated in the aperture by the light emitted from each point light source (SX, 0). 
   Here, it shows the light intensity of the diffraction light generated in the aperture by the light emitted from each point light source (SX, 0) relatively with the light intensity of the diffraction light generated in the aperture by the light emitted from the point light source (0, 0) as 1. 
   In addition, it shows the respective cases where the designed aperture size D 0  is 400 nm, 500 nm, 600 nm, and 700 nm when the film thickness d of the pattern film  100  is 100 nm. 
   According to the graph shown in  FIG. 31 , it is found that the light intensity of the diffraction light generated in the aperture by the light emitted from the point light source (SX, 0) is further reduced as the point light source (SX, 0) gets further away from the center of the effective light source. 
   Then, the light source modulator unit  355  shown in  FIG. 30  substitutes the decrease in the light intensity of the light emitted from each point light source (SX, SY) of the effective light source for the decrease in the light intensity of the diffraction light and calculates the modulated intensity distribution Sm (f, g) of the effective light source. 
   In addition, when a plurality of apertures are provided in the photomask and each design size is different, the modulated intensity distribution Sm (f, g) of the effective light source may be calculated based on the decrease in the light intensity of the diffraction light generated in the aperture having the same design size as the value defined according to the design rule. 
   The light intensity calculator unit  351   b  assumes that there is no film thickness of the pattern film  100  and calculates the light intensity distribution of the projection image of the mask pattern of the photomask  5  imaged on the semiconductor substrate which is disposed on the wafer stage  32  shown in  FIG. 2 , according to the following formula (20) using the modulated intensity distribution Sm (f, g) of the effective light source, by using the design shape of the aperture  101   b . 
   
     
       
         
           
             
               
                 
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   The data storage device  320   b  shown in  FIG. 30  further comprises a lost area storage unit  321  and an effective light source distribution storage unit  322 . 
   The lost area storage unit  321  stores the lost area calculated by the loss calculator unit  354 . 
   The effective light source distribution storage unit  322  stores the modulated intensity distribution Sm (f, g) of the effective light source calculated by the light source modulator unit  355 . 
   Next, a light intensity distribution simulation method according to the fourth embodiment will be described by using the flow chart shown in  FIG. 32 . 
   (a) Step S 50  and Step S 400  to Step S 404  shown in  FIG. 32  are performed in the same way as Step S 50  and Step S 100  to Step S 102  shown in  FIG. 19 . 
   Next, in Step S 405 , the loss calculator unit  354  shown in  FIG. 30  calculates a lost area for each point light source (SX, SY), in which the lost area is obtained by eliminating the effective shape from the design shape. The loss calculator unit  354  stores the calculated lost area in the lost area storage unit  321 . 
   (b) In Step S 406 , the light source modulator unit  355  reads out the lost area of the aperture corresponding to each point light source (SX, SY) from the lost area storage unit  321 . 
   Next, the light source modulator unit  355  calculates the decreasing amount of the intensity of the diffraction light generated in the aperture by the light emitted from each point light source (SX, SY), which is caused by the lost area. 
   Next, the light source modulator unit  355  substitutes the decrease in the intensity of the light emitted from each point light source (SX, SY) of the effective light source for the decrease in the light intensity of the diffraction light and calculates the modulated intensity distribution Sm (f, g) of the effective light source. 
   The light source modulator unit  355  stores the calculated modulated intensity distribution Sm (f, g) of the effective light source in the effective light source distribution storage unit  322 . 
   (c) In Step S 407 , the light intensity calculator unit  351   b  reads out the exposure environment of the exposure apparatus shown in  FIG. 2  from the exposure condition storage unit  302 . Further, the light intensity calculator unit  351   b  reads out the design shape of the aperture  101   b  of the photomask  5  including the pattern film  100  shown in  FIGS. 3 to 5  and the disposed position of the aperture  101   b  when the photomask  5  is disposed on the reticle stage  15  from the mask pattern storage unit  303 . Next, the light intensity calculator unit  351   b  assumes that the film thickness d of the pattern film  100  is zero. 
   (d) In Step S 408 , the light intensity calculator unit  351   b  reads out the modulated intensity distribution Sm (f, g) of the effective light source from the effective light source distribution storage unit  322 . 
   Next, the light intensity calculator unit  351   b  calculates an intensity distribution of diffraction light generated in the aperture using the formula (20), in which the diffraction light is generated by the light emitted from the point light sources (SX, SY) forming the effective light source  40  entering in the aperture having the design shape, further, the light intensity calculator unit  351   b  calculates the light intensity distribution of the projection image of the mask pattern of the photomask  5  which is imaged on a semiconductor substrate disposed on the wafer stage  32  shown in  FIG. 2 . Similarly, the light intensity calculator unit  351   b  calculates the distribution of the diffraction light generated in the corresponding virtual aperture with respect to the other light emitted from each of the other point light sources (SX, SY), and further calculates the light intensity distribution of the projection image, and hence to complete the light intensity distribution simulation method according to the fourth embodiment. 
   According to the above mentioned light intensity distribution simulation method relating to the fourth embodiment, fluctuation of the effective shape to the each point light source (SX, SY) of the aperture, due to the film thickness d of the pattern film  100 , is substituted with the modulation of the intensity of the light emitted from the each point light source (SX, SY). Therefore, even if assuming the film thickness d of the pattern film  100  is zero, when the light intensity of the diffraction light generated in the aperture having the design shape is calculated, the effect of the film thickness d is reflected in the calculated light intensity. Therefore, it is possible to calculate the light intensity with high accuracy. In addition, once the modulated intensity distribution Sm (f, g) of the effective light source is calculated, it is possible to reflect the effect of the film thickness d in the calculation result of the light intensity of the diffraction light generated in the aperture having the design shape, by using the modulated intensity distribution Sm (f, g) of the effective light source, without calculating the effective shape of the aperture at next time or later. 
   In addition, as shown in  FIG. 31 , the modulation of the intensity of the diffraction light generated in the aperture by the light emitted from each point light source (SX, SY) varies depending on the design size of the aperture. Therefore, the modulated intensity distribution SmL (f, g) of the effective light source is calculated for every aperture of different design size, and then the light intensity distribution of the projection image of the mask pattern of the photomask  5  imaged on a semiconductor substrate disposed on the wafer stage  32  maybe calculated using the following formula (21). 
   
     
       
         
           
             
               
                 
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   In addition, in the formula (21), ΣSmL (f, g) is approximated to S (f, g) and ΣmL (f, g) is approximated to m (f, g). 
   FIFTH EMBODIMENT 
   A light intensity simulation system according to a fifth embodiment is different from the light intensity simulation system shown in  FIG. 30  in that the CPU  300   d  further comprises a pupil function modulator unit  356  as shown in  FIG. 33 . 
   Here, when the photomask  5  shown in  FIG. 34  includes the pattern film  100  of halftone, the intensity distribution of the effective light source is projected on the incident pupil  24  as the intensity distribution of the zero-order diffraction light. In the second embodiment, it has been described that the effect of the film thickness d of the pattern film may be reflected in the simulation result by substituting the decrease in the light intensity of the diffraction light generated in the aperture with the decrease in the intensity of the light emitted from each point light source (SX, SY) of the effective light source. Here, the effect of the film thickness d of the pattern film may be reflected in the simulation result by further substituting the modulated intensity distribution Sm (f, g) of the effective light source with the modulation of the pupil function P (f+f 1 , g+g 1 ). 
   Therefore, the pupil function modulator unit  356  shown in  FIG. 33  calculates Pm (f+f 1 , g+g 1 ) which is modulated pupil function P (f+f 1 , g+g 1 ), based on the modulated intensity distribution Sm (f, g) of the effective light source. 
   Assuming that the film thickness of the pattern film  100  is zero, the light intensity calculator  351   c  calculates the light intensity distribution of the projection image of the mask pattern of the photomask  5  imaged on a semiconductor substrate disposed on the wafer stage  32  shown in  FIG. 2 , by the following formula (22) using the modulated pupil function Pm (f+f 1 , g+g 1 ), using the design shape of the aperture  101   b . 
   
     
       
         
           
             
               
                 
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   The data storage  320   c  shown in  FIG. 33  further comprises a pupil function storage unit  323 . The pupil function storage unit  323  stores the modulated pupil function Pm (f+f 1 , g+g 1 ) which is calculated by the pupil function modulator unit  356 . 
   Next, a light intensity distribution simulation method according to the fifth embodiment will be described by using the flow chart shown in  FIG. 35 . 
   (a) Step S 50  and Step S 500  to Step S 506  shown in  FIG. 35  are performed in the same way as Step S 50  and Step S 400  to Step S 406  shown in  FIG. 32 . 
   In Step S 507 , the pupil function modulator unit  356  reads out the modulated intensity distribution Sm (f, g) of the effective light source from the effective light source distribution storage unit  322 . 
   Next, the pupil function modulator unit  356  calculates Pm (f+f 1 , g+g 1 ) which is modulated pupil function P (f+f 1 , g+g 1 ), based on the modulated intensity distribution Sm (f, g) of the effective light source. The pupil function modulator unit  356  stores the calculated modulated pupil function Pm (f+f 1 , g+g 1 ) in the pupil function storage unit  323 . 
   (b) In Step S 508 , the light intensity calculator  351   c  reads out the exposure environment of the exposure apparatus shown in  FIG. 2  from the exposure condition storage unit  302 . Further, the light intensity calculator  351   c  reads out the design shape of the aperture  101   b  of the photomask  5  including the pattern film  100  shown in  FIGS. 3 to 5  and the disposed position of the aperture  101   b  when the photomask  5  is disposed on the reticle stage  15 , from the mask pattern storage unit  303 . Next, the light intensity calculator  351   c  assumes that the film thickness d of the pattern film  100  is zero. 
   (c) In Step S 509 , the light intensity calculator  351   c  reads out the modulated pupil function Pm (f+f 1 , g+g 1 ) from the pupil function storage unit  323 . 
   Next, the light intensity calculator  351   c  calculates the intensity distribution of the diffraction light in the aperture, in which the intensity distribution is generated by the light emitted from the point light source (SX, SY) forming the effective light source  40  and enters in the aperture having the design shape, and further the light intensity calculator  351   c  calculates the light intensity distribution of the projection image of the mask pattern of the photomask  5  which is imaged on a semiconductor substrate disposed on the wafer stage  32  shown in  FIG. 2 , according to the formula (22). Similarly, as for each light emitted from the other point light sources (SX, SY), the light intensity calculator  351   c  calculates the intensity distribution of the diffraction light generated in the corresponding virtual aperture, and further the light intensity calculator  351   c  calculates the light intensity distribution of the projection image, and hence to complete the light intensity distribution simulation method according to the fifth embodiment. 
   According to the above-mentioned light intensity distribution simulation method according to the fifth embodiment, fluctuation in the effective shape of the aperture, corresponding to each point light source (SX, SY), caused by the film thickness d of the pattern film  100 , is substituted with the modulation of the pupil function P (f+f 1 , g+g 1 ). Therefore, even if assuming the film thickness d of the pattern film  100  is zero, when the light intensity of the diffraction light generated in the aperture having the design shape is calculated, the effect of the film thickness d is reflected in the calculated light intensity. Therefore, it is possible to calculate the light intensity with high accuracy. In addition, once the modulated pupil function Pm (f+f 1 , g+g 1 ) is calculated, it is possible to reflect the effect of the film thickness d in the calculation result of the light intensity of the diffraction light generated in the aperture having the design shape by using the modulated pupil function Pm (f+f 1 , g+g 1 ) without calculating the effective shape of the aperture at next time or later. 
   Instead of modulating the pupil function P (f+f 1 , g+g 1 ), a function TCCm (f+f 1 , g+g 1 ; f 1 , g 1 ) which is modulated transfer function TCC (f+f 1 , g+g 1 ; f 1 , g 1 ) may be used to calculate the light intensity, as shown in the following formulas (23) and (24). Further, by using the modulated transfer function TCCm (f+f 1 , g+g 1 ; f 1 , g 1 ) and applying an optimal coherent approximation (OCA) method used for the calculation of optical proximity correction (OPC), it is possible to shorten the calculation time more. A kernel is generated by OCA development, the light intensity of the projection light is calculated.
 
 I ( x,y )=∫(∫∫ TCC   m ( f+f   1   ,g+g   1   ;f   1   ,g   1 ) {circumflex over (m)} ( f+f   1   ,g+g   1 ){circumflex over ( m )}*( f   1   ,g   1 ) df   1   dg   1 )exp(−2π i ( fx+gy ) dfdg   (23)
 
 TCC   m ( f   1   ,g   1   ;f   2   ,g   2 )=∫∫ S   m ( f,g ) P ( f+f   1   ,g+g   1 ) P ( f+f   2   ,g+g   2 ) dfdg   (24)
 
   The invention is not limited to above embodiments. For example, in the above light intensity distribution simulation method, a change in the polarized light condition generated by the structure of the mask pattern and a waveguide effect generated by the case where the size of the mask pattern becomes the same as the wavelength of the light have not been described. However, the change in the polarized light condition and the waveguide effect may be taken in the above light intensity distribution simulation method so as to improve the calculation accuracy. In addition, the light intensity distribution simulation method may be expressed as sequential processing or operations in time series. Therefore, in order to perform the light intensity distribution simulation method by the CPU  300   a  shown in  FIG. 1 , the light intensity distribution simulation method shown in  FIG. 19  may be realized by the computer program product for specifying a plurality of functions executed by a processor within the CPU  300   a . That is, as is shown in  FIG. 36 , the above-described light intensity distribution simulation method of the embodiments can be realized as a computer program product  32  which stores a program  31  that is to be executed by a system including a computer  30 . For example, the computer program product according to the embodiment is configured to cause the computer  30  to execute the steps (instructions) of  FIG. 19 , the steps (instructions) of  FIG. 25 , the steps (instructions) of  FIG. 28 , the steps (instructions) of  FIG. 32 , or the steps (instructions) of  FIG. 35 . The computer program product is a recording medium or a recording device which may input and output data to and from the CPU  300   a . The recording medium includes a memory, a magnetic disk, an optical disk, and the other program recording device. 
   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.