Method of correcting mask pattern and mask, method of exposure, apparatus thereof, and photomask and semiconductor device using the same

A method of correcting a mask pattern of a photo-mask used in a photo-lithographic process includes deforming the mask pattern to account for distortions in the pattern that will be caused during projection of the pattern by the photo-lithographic equipment so that the pattern image as transferred by the equipment matches a desired design pattern despite the distortions caused by the equipment. The method includes the steps of simulating a transfer image obtained by projecting a mask pattern through the exposure equipment under predetermined transfer conditions; arranging evaluation points on the transfer image; comparing the evaluation points of the simulated transfer image with the desired design pattern; and deforming the initial mask pattern in accordance with the differences between the simulated transfer image and the desired pattern. The method may also include repeating the foregoing steps to decrease the differences between the transfer pattern and the desired pattern. The evaluation points are arranged at corners and at predetermined intervals along the sides of the transfer pattern.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method of correcting a mask pattern 
which causes a mask pattern of a photomask used when producing a 
semiconductor device etc. to deform so as to give a transfer image close 
to a desired design pattern, a correction apparatus working this method of 
correction, a photomask obtained by this method of correction, an exposure 
method for performing exposure using a photomask having such a corrected 
mask pattern, a semiconductor device produced by photo-lithography using a 
photomask having such a corrected mask pattern, and an apparatus for 
production of a photomask and an apparatus for production of a 
semiconductor device using this method of correction. 
2. Description of the Related Art 
In the production of a semiconductor device etc., the process for 
transferring a mask pattern to a resist material on a semiconductor wafer 
is referred to as the photo-lithographic process. 
In recent years, along with the increasing miniaturization of the 
semiconductor devices produced, the design rule has become smaller and 
lithography is being performed near the theoretical limit of resolution. 
This fact is leading to the disadvantages of a deterioration of the 
performance of the semiconductor device due to deformation of the transfer 
pattern and reduction of yield due to bridging (error connection) and 
disconnection of the patterns. Accordingly, the mask patterns have been 
optimized by trial and error so as to obtain the desired resist pattern. 
The practice has been to prepare mask patterns to which have been added a 
plurality of modification patterns for a design pattern, find the transfer 
patterns by simulation in transfer experiments, and add the modification 
pattern giving the transfer pattern closest to the design pattern to the 
mask pattern. 
In recent years, light proximity effect correction techniques by which mask 
patterns have been automatically optimized by computer, have been 
developed. In the light proximity effect correction, the mask pattern 
deformed so as to improve the transfer image to match with the input 
design pattern has been sought by computations. 
However, it suffers from the following disadvantages in the related art. In 
the trial and error method, it takes tremendous time and work to find the 
optimal mask pattern. Therefore, this can only be used for limited 
patterns. Accordingly, it cannot be used for irregular patterns such as 
ASICs(Applied Specific Integrated Circuits). Further, in the trial and 
error method, the number of mask patterns which can be evaluated is 
limited. Therefore, there is the possibility of overlooking a better mask 
pattern and the precision of correction of the mask pattern is limited. 
Therefore, in recent years, technologies for automatically correcting mask 
patterns have been developed. These have had the following disadvantages, 
however. 
First, the corrected mask pattern would sometimes cause a deterioration in 
the processing margin, that is, the exposure margin and the focal depth. 
Therefore, the correction might conversely cause a deterioration in the 
yield, making use for actual processes impossible. 
Further, one method of correction is to find the distribution of light 
intensity using simulation of the light intensity, use the contour lines 
obtained by slicing by the threshold value of the same as the transfer 
image, and correct this to the optimal mask pattern. In this method, 
however, no consideration is given to the resist process, so the contour 
lines obtained by slicing the distribution of light intensity do not match 
the resist image obtained by the actual process and thus the resist image 
is not sufficiently corrected. 
Further, depending on the method of correction, due to the excessive 
correction of the corners of the pattern or the ends of the line patterns 
etc., distortion would occur at other portions, bridging (miss-connection) 
of the resist pattern would occur when the amount of exposure or focal 
position fluctuated, or mask patterns difficult to fabricate would be 
produced. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide a means and method for 
enabling calculation of a mask pattern so as to give a resist pattern 
close to the design pattern and thereby produce a high performance device 
with a high yield. According to one aspect of the present invention, there 
is provided a method of correcting a mask pattern wherein the mask pattern 
of a photomask used in a photo-lithography step is made to deform so as to 
give a transfer image close to a desired design pattern, the method of 
correcting a mask pattern comprises: an evaluation point arranging step 
for arranging a plurality of evaluation points along the outer periphery 
of the desired design pattern; a simulation step for simulating a transfer 
image obtained at exposure under predetermined transfer conditions using a 
photomask of a design pattern with evaluation points; a comparison step 
for comparing for each evaluation point the difference between the 
simulated transfer image and the design pattern; and a deformation step 
for deforming the design pattern in accordance with the differences 
compared for each evaluation point so that the differences become smaller. 
The evaluation point arranging step arranges the evaluation points at the 
corners of the desired design pattern and arranges the evaluation points 
at predetermined intervals at the sides of the pattern. 
Or, the evaluation point arranging steps arranges the evaluation points at 
the corners of the desired design pattern, adds a predetermined number of 
evaluation points at predetermined narrow intervals from the corners at 
the sides of the pattern, and arranges the evaluation points at 
predetermined wide intervals at remaining portions of the sides away from 
the corners. 
Or, the evaluation point arranging step does not add evaluation points at 
the small sides of the design pattern of less than predetermined lengths, 
does not add evaluation points at the corners near the small sides, and 
arranges the evaluation points at predetermined intervals at the other 
corners and sides. 
Or, the evaluation point arranging step arranges the evaluation points at 
the corners of the design pattern not at the boundaries of predetermined 
repeating regions and arranging the evaluation points at predetermined 
intervals at the sides of the pattern not at the boundaries of 
predetermined repeating regions. 
Or, the evaluation point arranging step arranges the evaluation points at 
the corners of the design pattern not at the boundaries of predetermined 
repeating regions and arranging the evaluation points at predetermined 
intervals at the sides of the pattern not at the boundaries of 
predetermined repeating regions. 
Or, the evaluation point arranging step arranges the evaluation points at 
the corners of the design pattern, adds evaluation points at the 
substantially midpoints of short sides of the pattern smaller than a 
predetermined width, and arranges the evaluation points at predetermined 
intervals at the other sides of the pattern. 
Or, the evaluation point arranging step arranges the evaluation points at 
the corners of the design pattern except corners of the pattern adjoining 
sides shorter than a predetermined length, adds evaluation points at 
relatively large intervals at the ends adjoining the sides shorter than a 
predetermined length at sides of the pattern longer than a predetermined 
length and arranges evaluation points at predetermined intervals at the 
sides of the pattern longer than the predetermined length. 
Preferably, a design pattern deformed in the deformation step is used to 
repeat at least once the process from the simulation step to deformation 
step. 
Preferably, the simulation step simulates transfer images under a plurality 
of transfer conditions based on combinations of a plurality of amounts of 
exposure of preset exposure margins and a plurality of focal positions 
within a preset range of focal depths to obtain a plurality of transfer 
images, the comparison step compares for each evaluation point the 
difference with the design pattern for each of the plurality of transfer 
patterns to calculate a plurality of differences for each evaluation 
point, and the deformation step deforms the design pattern so that the 
plurality of differences for each evaluation point become smaller by a 
predetermined criteria. 
Preferably, the simulation step calculates a two-dimensional light 
intensity on a substrate based on the design pattern and exposure 
conditions, calculates and cumulatively adds the effects on the exposure 
energy of any noted position on the two-dimensional plane of the substrate 
by the light intensity at a plurality of positions surrounding that any 
noted position based on the light intensity at the surrounding positions 
and the distance between the noted position and surrounding positions so 
as to calculate the latent image-forming intensity at that any noted 
position, finds the distribution of the latent image-forming intensity at 
the two-dimensional plane of the substrate, determines the threshold value 
of the latent image-forming intensity corresponding to the amount of 
exposure and development conditions, finds the contour lines of the 
threshold value for the distribution of latent image-forming intensity, 
and calculates the pattern defined by the contour lines as the transfer 
image. 
Preferably, the deformation step moves the boundary lines of the mask 
pattern near the evaluation points by exactly the magnitude of the 
magnitude of the difference compared for each evaluation point multiplied 
by a certain coefficient in a reverse direction to the difference. 
Preferably, the coefficient is larger than 0 and less than 1. 
Preferably, the evaluation point arranging step arranges a plurality of 
evaluation points along the outer periphery of the desired design pattern 
and sets target points separate from the evaluation points at 
predetermined evaluation points, the comparison step compares for each 
evaluation point the difference between the simulated transfer image and 
the design pattern at positions where just the evaluation points are set 
and compares the difference between the target points and transfer image 
at positions where the target points are set, and the deformation step 
deforms the design pattern in accordance with the difference compared for 
each evaluation point or for each target point so that the difference 
becomes smaller. 
Preferably, the target points are set corresponding to the evaluation 
points positioned at the projecting corners or recessed corners of the 
design pattern, the target points being determined at the inside of the 
corners at the projecting corners and the target points being determined 
at the outside of the corners at the recessed corners. 
According to another aspect of the invention, there is provided a photomask 
having a mask pattern corrected using the method of correction of a mask 
pattern as set forth above, 
According to another aspect of the invention, there is provided a method of 
exposure for performing exposure using a photomask having a mask pattern 
corrected using the method of correction of a mask pattern as set forth 
above. 
According to another aspect of the invention, there is provided a 
semiconductor device produced by photo-lithography using a photomask 
having a mask pattern corrected using the method of correction of a mask 
pattern as set forth above. 
According to another aspect of the invention, there is provided an 
apparatus for correction of a mask pattern wherein the mask pattern of a 
photomask used in a photo-lithography step is made to deform so as to give 
a transfer image close to a desired design pattern, the apparatus for 
correction of a mask pattern comprising an evaluation point arranging 
means for arranging a plurality of evaluation points along the outer 
periphery of the desired design pattern, a simulating means for simulating 
a transfer image obtained at exposure under predetermined transfer 
conditions using a photomask of a design pattern with evaluation points, a 
comparing means for comparing for each evaluation point the difference 
between the simulated transfer image and the design pattern, and a 
deforming means for deforming the design pattern in accordance with the 
differences compared for each evaluation point so that the differences 
become smaller, the evaluation point arranging means arranging the 
evaluation points at the corners of the desired design pattern and 
arranging the evaluation points at predetermined intervals at the sides of 
the pattern; arranging the evaluation points at the corners of the desired 
design pattern, adding a predetermined number of evaluation points at 
predetermined narrow intervals from the corners at the sides of the 
pattern, and arranging the evaluation points at predetermined wide 
intervals at remaining portions of the sides away from the corners; not 
adding evaluation points at the small sides of the design pattern of less 
than predetermined lengths, not adding evaluation points at the corners 
near the small sides, and arranging the evaluation points at predetermined 
intervals at the other corners and sides; arranging the evaluation points 
at the corners of the design pattern not at the boundaries of 
predetermined repeating regions and arranging the evaluation points at 
predetermined intervals at the sides of the pattern not at the boundaries 
of predetermined repeating regions; arranging the evaluation points at the 
corners of the design pattern, adding evaluation points at the 
substantially midpoints of short sides of the pattern smaller than a 
predetermined width, and arranging the evaluation points at predetermined 
intervals at the other sides of the pattern; or arranging the evaluation 
points at the corners of the design pattern except corners of the pattern 
adjoining sides shorter than a predetermined length, adding evaluation 
points at relatively large intervals at the ends adjoining the sides 
shorter than a predetermined length at sides of the pattern longer than a 
predetermined length and arranging evaluation points at predetermined 
intervals at the sides of the pattern longer than the predetermined 
length. 
Preferably, a design pattern deformed by the deforming means is used to 
repeat at least once the process from the simulation step to deformation 
step. 
Preferably, the simulating means has a means for simulating transfer images 
under a plurality of transfer conditions based on combinations of a 
plurality of amounts of exposure of preset exposure margins and a 
plurality of focal positions within a preset range of focal depths to 
obtain a plurality of transfer images, the comparing means has a means for 
comparing for each evaluation point the difference with the design pattern 
for each of the plurality of transfer patterns to calculate a plurality of 
differences for each evaluation point, and the deforming means has a means 
for deforming the design pattern so that the plurality of differences for 
each evaluation point become smaller by a predetermined criteria. 
Preferably, the simulating means has a means for calculating a 
two-dimensional light intensity on a substrate based on the design pattern 
and exposure conditions, a means for calculating and cumulatively adding 
the effects on the exposure energy of any noted position on the 
two-dimensional plane of the substrate by the light intensity at a 
plurality of positions surrounding that any noted position based on the 
light intensity at the surrounding positions and the distance between the 
noted position and surrounding positions so as to calculate the latent 
image-forming intensity at that any noted position, a means for finding 
the distribution of the latent image-forming intensity at the 
two-dimensional plane of the substrate, a means for determining the 
threshold value of the latent image-forming intensity corresponding to the 
amount of exposure and development conditions, a means for finding the 
contour lines of the threshold value for the distribution of latent 
image-forming intensity, and a means for calculating the pattern defined 
by the contour lines as the transfer image. 
Preferably, the deforming means moves the boundary lines of the mask 
pattern near the evaluation points by exactly the magnitude of the 
magnitude of the difference compared for each evaluation point multiplied 
by a certain coefficient in a reverse direction to the difference. 
Preferably, the coefficient is larger than 0 and less than 1. 
According to another aspect of the invention, there is provided an 
apparatus for production of a photomask having an apparatus for correction 
of a mask pattern as set forth above and a drawing means for drawing a 
photomask of a mask pattern corrected by the apparatus for correction of a 
mask pattern. 
According to another aspect of the invention, there is provided an 
apparatus for production of a semiconductor device having an apparatus for 
correction of a mask pattern as set forth above and an exposing means for 
performing exposure using a photomask of a mask pattern corrected by the 
apparatus for correction of a mask pattern.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Below, an explanation will be made of embodiments of the present invention. 
EXAMPLE 1 
A schematic block diagram of an apparatus for correction of a mask pattern 
according to the present example is given in FIG. 1, and a schematic flow 
chart of the method of correction thereof is shown in FIG. 2. 
As shown in FIG. 1, the apparatus for correction of a mask pattern 
according to the present example has an inputting means 2, a design 
pattern storing means 4, a transfer condition storing means 6, an 
evaluation point arranging means 8, a simulating means 10, a comparing 
means 12, a deforming means 14, a correction pattern storing means 16, a 
repeating means 18, and an outputting means 20. 
The inputting means 2 is not particularly limited so far as it can input 
the design pattern, the transfer conditions, etc. A keyboard, a touch 
panel, etc. can be mentioned. Where the design pattern, transfer 
conditions, etc. are input in the form of electric signals, the inputting 
means 2 can be a wired or wireless input terminal as well. Further, where 
design pattern, transfer conditions, etc. stored in a recording medium 
such as a floppy disk are input, the inputting means 2 is constituted by a 
disk drive or the like. Further, as the outputting means 20, a cathode ray 
tube (CRT), a liquid crystal display device, or the like which can display 
at least a corrected design pattern on a screen can be used. Further, as 
the outputting means 20, it is also possible to adopt an outputting means 
such as a printer or an XY plotter which can draw at least the corrected 
design pattern on paper, film, or other substrates. 
The other means 4, 6, 10, 12, 14, 16, and 18 shown in FIG. 1 are 
constituted by program information which is stored in a recording means 
such as an operating circuit, a random access memory (RAM), a read only 
memory (ROM), an optical recording medium, or the like, and processed by a 
central processing unit (CPU) of a computer. 
The mode of operation of the device shown in FIG. 1 will be explained based 
on the flow chart shown in FIG. 2. 
At step S10 shown in FIG. 2, the design pattern and the transfer conditions 
are stored in the design pattern storing means 4 and the transfer 
condition storing means 6 of the apparatus for correction shown in FIG. 1 
from the inputting means 2 shown in FIG. 1, respectively. One example of 
the design pattern is shown in FIG. 11. 
The transfer conditions are conditions concerning for example a wavelength 
.lambda. of the light used for the exposure, the numerical aperture NA, 
the apparent size .sigma. (partial coherence) of the light source or a 
distribution of the transmission rate of the light source, distribution of 
a phase and transmission rate of an exit pupil, and defocused condition. 
At step S11 shown in FIG. 2, a plurality of evaluation points are prepared 
along an outer periphery of the design pattern. The preparation of the 
evaluation points is carried out by the evaluation point arranging means 8 
based on the design pattern stored in the design pattern storing means 4 
shown in FIG. 1. For example, as shown in FIG. 35, the evaluation points 
30 are imparted based on the following rules along the outer periphery of 
the design pattern 32. 
rul 1: Evaluation points are added to the corners of the design pattern. 
rul 2: A predetermined number of evaluation points are added at the sides 
at predetermined small intervals starting from the corners and then 
further evaluation points are added at the sides at predetermined large 
intervals. 
rul 3: Evaluation points are not added at corners next to very small sides, 
and evaluation points are not added to the very small sides. 
rul 4: Sides next to repeating regions are not recognized as sides. 
rul 5: Evaluation points are added to the midpoint of relatively small 
sides in sides to which the evaluation points are to be added. 
rul 6: Evaluation points are added at relatively large intervals at sides 
of corners next to very small sides where no evaluation points are added. 
In the above rules, the intervals of the evaluation points, the lengths of 
the very small sides, etc. can be freely set according to the design rule 
of the pattern, exposure conditions, pattern shape, etc. 
At step S12 shown in FIG. 2, a transfer resist pattern (transfer image) is 
calculated by the simulating means 10 shown in FIG. 1. As the simulating 
means 10, use can be made of for example a commercially available light 
intensity simulation system which can simulate the transfer image by input 
of the exposure conditions and the design pattern. One part of the 
transfer image resulting from the simulation is indicated by numeral 34 of 
FIG. 4. 
At step S13 shown in FIG. 2, a deviation (difference) of the resist edge 
with respect to the design pattern is calculated for each evaluation point 
30 by the comparing means 12 shown in FIG. 1. The direction of measurement 
of the deviation of the resist edge position of the design pattern at this 
time is made the orthogonal direction with respect to a boundary line 
(edge) of the design pattern 32 as shown in FIG. 4A at positions other 
than the corners of the pattern, the outward direction of the design 
pattern 32 is defined as the positive direction and the inward direction 
thereof is defined as a negative direction. Further, at the corners of the 
design pattern 32, the direction of measurement of the deviation is made 
the direction of the sum of the directional vectors of the two sides 
constituting the corners, and similarly the outward direction of the 
pattern is determined to be the positive direction. 
At step S14 shown in FIG. 2, the design pattern 32 is deformed and 
corrected by the deforming means 14 shown in FIG. 1 in accordance with the 
deviations (differences) compared for every evaluation point 30 so that 
the differences become smaller. A schematic view of the deforming and 
correcting method is shown in FIG. 4B. 
AS shown in FIGS. 4A and 4B, at the deformation and correction of the 
design pattern 32, the boundary lines (including not only the evaluation 
points, but also the boundary lines near them) of the mask pattern in the 
vicinity of the evaluation points 30 are moved exactly by amounts obtained 
by multiplying the amounts of differences by a constant coefficient in a 
reverse direction of the deviations (differences) compared for every 
evaluation point 30. The coefficient is preferably larger than 0 and less 
than 1 and further preferably 0.10 to 0.50. When this coefficient is too 
large, an excessive deformation and correction occur, and there is an 
apprehension that the transfer image will not become closer to the design 
pattern but conversely will become more different from it even by the 
repeated calculation mentioned later. Note that, it is possible for the 
coefficient to be constant for all evaluation points or different for 
specific evaluation points. One example of a design pattern corrected in 
this way is shown in FIG. 14. 
The corrected design pattern is stored in the correction pattern storing 
means 16 shown in FIG. 1. Where a good corrected pattern is obtained by 
the series of operations, at step S15 shown in FIG. 2, a corrected mask 
pattern is obtained. The corrected mask pattern is output onto the screen 
or sheet or film by the outputting means 20 shown in FIG. 1. 
Note that, preferably, upon receipt of the signal of the repeating means 18 
shown in FIG. 1, steps S12 to S14 shown in FIG. 2 are repeated at least 
one or more times by using the simulating means 10, the comparing means 
12, and the deforming means 14 based on the corrected design pattern 
stored in the correction pattern storing means 16. At this time, the 
positions of the evaluation points 30 acting as the reference are not 
changed. Namely, based on the corrected design patterns the transfer input 
is found again, deviation (differences) between that transfer image and 
the reference point is found, and the corrected design pattern is deformed 
and corrected again based on the difference. By repeating these 
operations, the transfer image will gradually approach the initial design 
pattern (positions of the evaluation points). 
In the correction apparatus and correction method of the present example, 
the mask pattern of the photomask can be automatically deformed so as to 
obtain a transfer image near the desired design pattern without regard as 
to the design pattern. Accordingly, if photo-lithographic processing is 
carried out by using a photomask having a corrected design pattern 
obtained by the present example, a resist pattern which is near the 
initial design pattern as much as possible can be obtained, and bridging, 
disconnection, or the like do not occur. As a result, a semiconductor 
device with good electrical characteristics can be produced with a high 
manufacturing yield. 
EXAMPLE 2 
In the present example, the correction of the design pattern is carried out 
in a similar manner to the first example except the following means is 
used as the simulating means 10 shown in FIG. 1 performing step S12 shown 
in FIG. 2. 
The simulating means 10 used in the present example is not a technique for 
simply finding the two-dimensional light intensity distribution based on 
the exposure conditions and design pattern and calculating the lines of 
the light intensity distribution above a predetermined threshold value as 
the transfer image. 
As shown in FIG. 3, in the present example, the information concerning the 
design pattern (step S19) and the transfer conditions are simulated by the 
light intensity simulation (step S20). The two-dimensional light intensity 
distribution on the substrate, such as a semiconductor wafer, is found at 
step S21. Note that, it is also possible if the light intensity 
distribution is found by using an actual light intensity measuring device. 
After the two-dimensional light intensity distribution is found, at step 
S22, the latent image-forming intensity is calculated. The latent 
image-forming intensity distribution is found at step S23. 
Below, a detailed explanation will be made of the processing in the 
calculation of the latent image-forming intensity. 
In the calculation of the latent image-forming intensity, for example, a 
latent image-forming intensity Mj0 at a point j0 on a wafer plane shown in 
FIG. 5 is determined by considering the influence of the light intensities 
at a point j0 and a point jn (n is an integer satisfying 
0.ltoreq.n.ltoreq.24) located at the periphery of the point j0. Here, the 
influence Mj0jn of the light intensity at the point jn is defined as in 
the following Equation (1): 
EQU M.sub.j0jn =f(rn)*g(1(jn)) (1) 
In the above Equation (1), rn indicates a distance between the point j0 and 
the point jn, and f(rn) is indicated by the following Equation (2): 
EQU f(rn)=K*exp(-rn.sup.2 /.alpha..sup.2) (2) 
Note, in Equation (2), the following Equation (3) is satisfied. Namely, 
Equation (2) is defined by using a Gaussian function. 
##EQU1## 
Further, in Equation (1), g(I(jn)) is defined by the following Equation (4) 
: 
EQU g(1(jn))=I(jn) (4) 
Namely, the influence Mj0jn of the light intensity at the point jn is a 
value obtained by multiplying the distance rn between the point j0 and the 
point jn by the light intensity I(jn) of the point jn. 
In the calculation of the latent image-forming intensity, for example in 
the case shown in FIG. 5, the latent image-forming intensity Mj0 is found 
by cumulatively adding the influence Mj0jn of the light intensity at the 
points jn with respect to the exposure energy at the points j0. 
At this time, for example, the size of the wafer is infinite in the 
two-dimensional direction. When considering the influence of the light 
intensity from the infinite number of points jn 
(-.infin..ltoreq.n.ltoreq..infin.) arranged in a predetermined pattern, 
Mj0 is indicated by the following Equation (5): 
##EQU2## 
Here, when Equations (2) and (4) are introduced into Equation (5), Mj0 is 
defined by Equation (6): 
##EQU3## 
In the calculation of the latent image-forming intensity, the Mj0 at the 
points arranged on a two-dimensional plane on the wafer in a predetermined 
pattern is calculated by the above procedure. The distribution of the 
latent image-forming intensity on a two-dimensional plane is found based 
on the result of the calculation. 
Next, the contour lines with which the latent image-forming intensity 
becomes the threshold value are found at step S24 shown in FIG. 3 in the 
distribution of the latent image-forming intensity found by the above 
procedure. The pattern defined by the contour lines is used as the resist 
pattern at step S25. At this time, the threshold value is determined in 
accordance with for example the amount of exposure and the development 
conditions. 
An example of the optimum calculation method of the threshold value Eth and 
the constant .alpha. used in the simulation will be shown next. 
A plurality of resist patterns are calculated based on various exposure 
times and defocused conditions. The processing shown in FIG. 6 is carried 
out by using the calculated resist patterns. 
Here, the latent image-forming intensity R(x,y) in the latent image-forming 
intensity distribution is defined by for example the following Equation 
(7). In Equation (7), a is a constant. 
##EQU4## 
Step S1: In the resist pattern calculated by the simulation method shown in 
FIG. 3, line widths are found at a plurality of positions. At this time, 
the line in question is given a wide range of line widths. 
Step S2: A transfer experiment is actually carried out by using the mask 
pattern and exposure conditions the same as those of this simulation 
method, and the line width of the line corresponding to the line in 
question at step S1 is found. 
Step S3: The difference in the line widths of the plurality of lines found 
at steps S1 and S2 by the method of calculation of the resist pattern and 
the transfer experiment is found. 
Step S4: The squared value of the difference found at step S3 is found. 
This squared value is cumulatively added for a plurality of lines to find 
a cumulative value. 
Step S5: The constant .alpha. and the threshold value Eth giving the 
smallest cumulative value found at step S4 are calculated. At this time, 
the simulation shown in FIG. 3 and processing of steps S1 to S4 of FIG. 6 
are carried out by using for example the predetermined constant .alpha. 
and the threshold value Eth as an initial value, the cumulative value of 
step S4 shown in FIG. 6 in the previous processing and the cumulative 
value of step S4 in the current processing are compared, and the constant 
.alpha. and the threshold value Eth used for the processing to be carried 
out next are determined so that the difference of these cumulative values 
is made smaller. Then, by using this constant .alpha. and the threshold 
value Eth, the simulation of FIG. 3 and the processing of steps S1 to S4 
of FIG. 6 are carried out again. This procedure is repeated so as to find 
the constant .alpha. and the threshold value Eth giving the minimum 
difference of the cumulative values. 
Step S6: The simulation shown in FIG. 3 mentioned before is carried out by 
using Equation (7) in which the constant .alpha. and Eth are made the 
values calculated at step S5. 
Using the method shown in FIG. 6, it is possible to suitably set the 
constant .alpha. and Eth in the above Equation (7) for performing the 
simulation shown in FIG. 3. For this reason, the accuracy of the 
simulation shown in FIG. 3 can be further improved. 
Note that, in the above Example 2, it is also possible if the contact 
.alpha. and the Eth are calculated so that the maximum value of the 
difference of the line widths between the resist pattern obtained by the 
resist pattern calculating method and the resist pattern found by the 
experiment becomes the smallest for the line widths at a plurality of 
corresponding positions. 
Further, in the present example, the case of using a Gaussian function in 
Equations (2) and (3) used in the calculation of the latent image-forming 
intensity (step S22 shown in FIG. 3) was explained by way of an example, 
but this function is not particularly limited so far as it becomes the 
maximum when the distance rn is zero and becomes zero when the distance rn 
is infinitely large. 
Further, in the present example, in the calculation of the latent 
image-forming intensity of step S22 shown in FIG. 3, the latent 
image-forming intensity was defined by using the product of the light 
intensity and the distance, but it is also possible if the latent 
image-forming intensity is defined by the product of a power of the light 
intensity and the distance. 
In this case, the latent image-forming intensity Mj0 is defined by for 
example the following Equation (8). 
##EQU5## 
Further, in the present example, a case where the exposure was carried out 
by using an i-ray was explained by way of example, but the present 
invention can also be applied to the case where the pattern formation is 
carried out by using for example an X-ray or electron beam (EB). 
In the present example, the distribution of the latent image-forming 
intensity used when finding the resist pattern was determined by 
considering not only the light intensity of the point noted, but also the 
influence by the light intensity of the points on its periphery, therefore 
a more correct calculation of the resist pattern (transfer image) can be 
carried out. 
Next, the fact that a result near the actual transfer resist pattern is 
obtained by performing the simulation shown in FIG. 3 is shown. 
In this example, the constant .alpha. in Equation (6) was defined as 0.131 
and Eth was defined as 197.01. 
Further, in this example, in an L/S transfer experiment, the exposure was 
actually carried out for an i-ray positive resist of a company A by using 
an i-ray having a wavelength .lambda. of 365 nm and under an exposure 
condition of a numerical aperture NA of 0.50 and an apparent size .sigma. 
of 0.68 while changing the defocused condition and exposure time. 
FIG. 8A is a correspondence table of the line width (measured by 
SEM:Scanning type Electron Microscope) found in the L/S transfer 
experiment at different defocused conditions and exposure times, the line 
width (present procedure) found by using the resist pattern calculating 
method of this example, and the difference between the line width (present 
procedure) and the line width (SEM). 
FIG. 8B is a graph in which the line width (present procedure) and the line 
width (SEM) shown in FIG. 8A are plotted on the ordinate and the exposure 
time is plotted on the abscissa. 
From the results of the experiment shown in FIG. 8A, 3.sigma. became equal 
to 0.0153 in the present example. 
Contrary to this, a resist pattern was prepared by using the conventional 
resist pattern calculating method not using the calculation of the latent 
image-forming intensity. At this time, when finding the resist pattern 
from the distribution of the light intensity, the threshold value Eth was 
determined to be 193.54. 
Further, in the present comparative example, in the L/S transfer 
experiment, the exposure was actually carried out for an i-ray positive 
resist of the company A by using an i-ray having a wavelength .lambda. of 
365 nm and under exposure conditions of a numerical aperture NA of 0.50 
and an apparent size .sigma. of 0.68 while changing the defocused 
conditions and exposure times. 
FIG. 9A is a correspondence table of the line width (SEM) found in the L/S 
transfer experiment at different defocused conditions and exposure times, 
the line width (conventional procedure) found by using the resist pattern 
calculating method of the present comparative example, and the difference 
between the line width (conventional procedure) and the line width (SEM). 
FIG. 9B is a graph in which the line width (conventional procedure) and the 
line width (SEM) shown in FIG. 9A are plotted on the ordinate and the 
exposure time is plotted on the abscissa. 
From the results of the experiment shown in FIG. 9A, 3.sigma. became equal 
to 0.0313 in the present comparative example. 
When comparing the results shown in FIGS. 8A and 8B (present example) and 
the results shown in FIGS. 9A and 9B (comparative example), it was 
confirmed that the 3.sigma. according to the present example was about a 
half of that of the comparative example and that the precision of the 
simulation shown in FIG. 3 was good. 
EXAMPLE 3 
In the present example, the design pattern was corrected in a similar 
manner as with Example 1 or Example 2 except target points were set in 
addition to the evaluation points at step S11 shown in FIG. 2 carried out 
by the evaluation point arranging means 8 shown in FIG. 1. 
Below, an explanation will be made of only the portions different from that 
of the examples mentioned before. 
In the present example, as shown in FIG. 10, a target point 36 is set 
corresponding to an evaluation point 30 located in a projecting corner or 
a recessed corner of a design portion 32. The target point 36 is set 
inside of the corner (for example -0.08 .mu.m) in the case of a projecting 
corner, and the target point 36 is set outside of the corner portion (for 
example +0.08 .mu.m) in case of a recessed corner. 
In the present example, in the comparing step of step S13 shown in FIG. 2 
the difference a between the simulated transfer image 34 and the design 
pattern 32 is compared for every evaluation point 30 at the positions 
where only the evaluation points 30 are set and the difference b between 
the target point 36 and the transfer image 34 is compared at the positions 
where the target points 36 are set. Then, in the deforming step of step 
S14 shown in FIG. 2, the design pattern 32 is deformed according to the 
differences a and b compared for every evaluation point 30 or every target 
point 36 so that the differences become smaller with the evaluation points 
30 (not the target points) as the reference. 
For example, in the case of a projecting corner or a recessed corner of the 
design pattern 32, when evaluation points 30 are located at these corners, 
if the correction of the mask pattern were carried out to make the 
transfer image approach the evaluation points 30 per se, there would be 
the apprehension that the transfer image will move away from the design 
pattern 32 at the positions other than the corner portions. 
In the method of correction of the mask pattern according to the present 
example, for example, since the target points 36 are set inside of the 
corners in the case of projecting corners, the target points 36 are set 
outside of the corners in the case of recessed corners, and the design 
pattern 32 is corrected so that the transfer image 34 approaches these 
target points 36, the transfer image 34 can be brought closer to the 
design pattern in an excellent manner. As a result, bridging, 
disconnection, or the like between parts of the pattern can be effectively 
prevented. 
EXAMPLE 4 
In the present example, the design pattern was corrected in a similar 
manner as Example 1, Example 2, or Example 3 except the simulation carried 
out at step S12 shown in FIG. 2 was carried out under a plurality of 
transfer conditions by using the simulating means 10 shown in FIG. 1. 
Below, an explanation will be made of only the portions different from 
those of the examples mentioned before. 
Namely, in the present example, in the simulation step, transfer images are 
simulated by using a plurality of transfer conditions based on the 
combination of a plurality of amounts of exposure of a preliminarily set 
exposure margin and a plurality of focal positions within a range of a 
preliminarily set depth of focus so as to obtain a plurality of transfer 
images. Then, in the comparing step of step S13 shown in FIG. 2, the 
difference from the design pattern is compared for every evaluation point 
for each of the plurality of transfer images so as to calculate a 
plurality of differences for every evaluation point. Then, in the 
deforming step of step S14 shown in FIG. 2, the design pattern is deformed 
so that the plurality of differences for every evaluation point become 
smaller compared with a predetermined reference. 
The predetermined reference in the deforming step is for example a 
reference that gives the smallest average value of the plurality of 
differences for every evaluation point. 
Further, as another predetermined reference, a reference that gives the 
smallest difference between the maximum difference and the minimum 
difference among the plurality of differences for every evaluation point 
may be mentioned. 
Further, as still another predetermined reference, a reference that gives 
the smallest square average of the plurality of differences for every 
evaluation point may be mentioned. 
By the method of correction of the mask pattern according to the present 
example, since transfer images of transfer conditions changed within the 
range of the processing margin are considered (processing margin is 
considered), the processing margin such as the exposure margin or depth of 
focus is no longer deteriorated based on the corrected mask pattern. As a 
result, if the photo-lithography is carried out by using the photomask of 
this mask pattern, the manufacturing yield is improved. 
EXAMPLE 5 
In the present example, the invention is applied to a case where a pattern 
of a 0.32 .mu.m rule is exposed under conditions of an exposure wavelength 
.lambda. of 365 nm, a numerical aperture NA of 0.5, and an apparent size 
.sigma. of 0.68. 
FIG. 11 shows the design pattern used in the present example. 
First, as shown in FIG. 12, evaluation points were arranged at all corners 
of the design pattern. A predetermined number of further evaluation points 
were added to the sides of the pattern at predetermined small intervals 
starting from the corners, then further evaluation points were arranged at 
the sides at predetermined large intervals in the remaining areas far from 
the corners. The small interval of the evaluation points was about 0.16 
.mu.m and the large interval was about 0.32 .mu.m. 
Next, the distribution of light intensity obtained when a mask of this 
design pattern was transferred as is under a focused condition was found. 
The contour lines sliced at the threshold value Eth were found as the 
resist image (FIG. 13). Note, the threshold value Eth is set so that L in 
FIG. 13 becomes 0.32 pm. 
Subsequently, the amount of deviation of the resist edge position from the 
evaluation point was found with respect to the edges (corners and sides) 
of the resist image at all evaluation points. At the evaluation points 
other than the corners, as shown in FIG. 4, the direction of measurement 
of the deviation of the edge position at this time was made the orthogonal 
direction with respect to the edge and the outward direction of the 
pattern was made the positive direction. At the corner points, this was 
made the direction of the sum of the directional vectors of the two sides 
forming the corner, and similarly the outside of the pattern was made the 
positive direction. 
Note, at the corner evaluation points, in order to prevent excessive 
correction of the pattern later, the target value of the amount of 
deviation of the edge was made -0.07 .mu.m for the outwardly projecting 
corners and was made +0.07 .mu.m for the outwardly recessed corners and 
the difference of these target values and the amount of deviation of the 
evaluation point of the edge position was found. 
In this way, the side of the mask pattern in the vicinity of each 
evaluation point was moved in a reverse direction to the obtained amount 
of deviation of the edge so as to obtain the corrected mask pattern. Here, 
the amount of movement of the sides of the pattern was made an amount 
obtained by multiplying the amount of deviation by 0.25. 
Further, these procedures were carried out again by maintaining the 
position of the evaluation point as is and making the corrected mask 
pattern the pattern input. 
By repeating this procedure four times, the mask pattern of FIG. 14 was 
obtained. 
By this correction, it was possible to successfully reduce the 3.sigma. of 
the edge deviation at each evaluation point, which was 0.101 .mu.m if the 
mask was the design pattern as it was, to 0.034 .mu.m. The resist pattern 
under a focused condition obtained by the mask of FIG. 14 is shown in FIG. 
15. It shows that a very good resist pattern is obtained in comparison 
with FIG. 13 before the correction. 
By using the present mask, a semiconductor device having good electrical 
characteristics can be produced with a high manufacturing yield. 
COMATIVE EXAMPLE 1 
In Comparative Example 1, processing for correction of the mask pattern was 
carried out in a similar manner to Example 5 except that, in the method of 
arranging the evaluation points of the above Example 5, the evaluation 
points were arranged along the edge of the pattern at constant intervals 
of about 0.16 .mu.m. 
FIG. 16 shows the evaluation points added to the design pattern; FIG. 17 
shows the mask pattern obtained by the correction; and FIG. 18 shows the 
transfer resist pattern. 
When comparing Example 5 and Comparative Example 1, an equivalent transfer 
image is obtained, but the number of the evaluation points is smaller in 
Example 5 and therefore the calculation time becomes shorter. Also, the 
number of shapes used in the mask is reduced. In this way, by using the 
technique shown in the example, it is possible to correct the light 
proximity effect at a low cost. 
EXAMPLE 6 
In Example 6, the invention is applied to a case where a pattern of a 0.35 
.mu.m rule is exposed under conditions of an exposure wavelength .lambda. 
of 365 nm, a numerical aperture NA of 0.50, and an apparent size .sigma. 
of 0.68. 
FIG. 19 shows the design pattern used in the present example. 
First, as shown in FIG. 20, the evaluation points were generated for the 
sides of the design pattern. At this time, evaluation points 30 were 
respectively arranged at the corners of the pattern, further evaluation 
points 30 were added to the substantially midpoints of the short sides 32a 
of the pattern shorter than a predetermined width, and further evaluation 
points 30 were arranged at predetermined intervals at the other sides of 
the pattern. In this case, the predetermined width was about 0.53 .mu.m. 
Further, at the time of arrangement of the evaluation points, no evaluation 
points were arranged at the boundaries 32b of the repeat regions of the 
pattern. 
Next, the distribution of light intensity obtained when the mask of this 
design pattern was transferred as is under a focused condition was found, 
and the contour lines sliced at the threshold value Eth were found as the 
resist image (FIG. 21). Note, the threshold value Eth is set so that L in 
FIG. 21 becomes 0.4 .mu.m. 
Subsequently, the amount of deviation of the resist edge position from the 
evaluation point was found with respect to the edges (corners and sides) 
of the resist image at all evaluation points. At the evaluation points 
other than the corners, the direction of measurement of the deviation of 
the edge position at this time was made the orthogonal direction with 
respect to the edge and the outward direction of the pattern was made the 
positive direction. At the corner points, this was made the direction of 
the sum of the directional vectors of the two sides forming the corner, 
and similarly the outside of the pattern was made the positive direction. 
Note, at the corner evaluation points, in order to prevent excessive 
correction of the pattern later, the target value of the amount of 
deviation of the edge was made -0.07 .mu.m for the outwardly projecting 
corners and was made +0.07 .mu.m for the outwardly recessed corners and 
the difference of these target values and the amount of deviation of the 
evaluation point of the edge position was found. 
In this way, the side of the mask pattern in the vicinity of each 
evaluation point was moved in a reverse direction to the obtained amount 
of deviation of the edge so as to obtain the corrected mask pattern. Here, 
the amount of movement of the sides of the pattern was made an amount 
obtained by multiplying the amount of deviation by 0.35. 
Further, these procedures were carried out again by maintaining the 
position of the evaluation point as is and making the corrected mask 
pattern the pattern input. 
By repeating this procedure 10 times, the mask pattern of FIG. 22 was 
obtained. 
By this correction, it was possible to successfully reduce the 3.sigma. of 
the edge deviation at each evaluation point, which was 0.104 .mu.m if the 
mask was the design pattern as it was, to 0.009 .mu.m. The resist pattern 
under a focused condition obtained by the mask of FIG. 22 is shown in FIG. 
23. It shows that a very good resist pattern is obtained in comparison 
with FIG. 21 before the correction. 
By using the present mask, a semiconductor device having good electrical 
characteristics can be produced with a high manufacturing yield. 
COMATIVE EXAMPLE 2 
In Comparative Example 2, the processing for correction of the mask pattern 
was carried out in a similar manner to Example 6 except that evaluation 
points were arranged at the corners and sides of the design pattern at 
predetermined intervals (for example 0.175 .mu.m), that is, the evaluation 
points 30 were added even at portions other than the midpoints of the 
short sides 32a of the pattern shorter than the predetermined width in 
Example 6. 
FIG. 24 shows the evaluation points added to the design pattern; FIG. 25 
shows the mask pattern obtained by the correction; and FIG. 26 shows the 
transfer resist pattern. 
In Comparative Example 2, since the evaluation points are not arranged at 
the midpoints of the line ends at the points 32a in the figure, while the 
line widths at the evaluation points are corrected, protrusions of the 
pattern occur at the midpoint of the line ends (refer to FIG. 27). 
Contrary to this, in Example 6, since the evaluation points are arranged 
at the midpoints of the line ends, no protrusions occur (refer to FIG. 
28). In this way, by using the method of the present example, the 
correction precision of the pattern of the line ends can be improved. 
EXAMPLE 7 
In Example 7, the invention is applied to a case where a pattern of a 0.35 
.mu.m rule is exposed under conditions of an exposure wavelength .lambda. 
of 365 nm, a numerical aperture NA of 0.50, and an apparent size .sigma. 
of 0.68. 
FIG. 29 shows the design pattern used in the present example. 
First, as shown in FIG. 30, the evaluation points were generated for the 
corners and sides of the design pattern. At this time, in the present 
example, evaluation points were not added to the very small sides 32c of 
the desired design pattern smaller than a predetermined length and, at the 
same time, evaluation points were not added to the corners 32d next to the 
very small sides. Evaluation points were arranged at the other corners and 
sides at predetermined intervals, respectively. The predetermined length 
was about 0.3 .mu.m or less in the present example. Further, the slanted 
side 32e was assumed to be a stepped pattern, and one evaluation point was 
arranged per horizontal line of each step. Further, the evaluation points 
were not arranged at the sides at the boundaries 32b of the repeating 
regions. 
Next, the distribution of light intensity obtained where the mask of this 
design pattern was transferred as is under a focused condition was found, 
and the contour lines sliced at the threshold value Eth were found as the 
resist image (FIG. 31). Note, the threshold value Eth is set so that L in 
FIG. 31 becomes 0.35 .mu.m. 
Subsequently, the amount of deviation of the resist edge position from the 
evaluation point was found with respect to the edges (corners and sides) 
of the resist image at all evaluation points. At the evaluation points 
other than the corners, the direction of measurement of the deviation of 
the edge position at this time was made the orthogonal direction with 
respect to the edge and the outward direction of the pattern was made the 
positive direction. At the corner points, this was made the direction of 
the sum of the directional vectors of the two sides forming the corner, 
and similarly the outside of the pattern was made the positive direction. 
Note, at the corner evaluation points, in order to prevent excessive 
correction of the pattern later, the target value of the amount of 
deviation of the edge was made -0.07 .mu.m for the outwardly projecting 
corners and was made +0.07 .mu.m for the outwardly recessed corners and 
the difference of these target values and the amount of deviation of the 
evaluation point of the edge position was found. 
In this way, the side of the mask pattern in the vicinity of each 
evaluation point was moved in a reverse direction to the obtained amount 
of deviation of the edge so as to obtain the corrected mask pattern. Here, 
the amount of movement of the sides of the pattern was made an amount 
obtained by multiplying the amount of deviation by 0.25. 
Further, these procedures were carried out again by maintaining the 
position of the evaluation point as is and making the corrected mask 
pattern the pattern input. 
By repeating this procedure 8 times, the mask pattern of FIG. 32 was 
obtained. 
By this correction, it was possible to successfully reduce the 3.sigma. of 
the edge deviation at each evaluation point, which was 0.079 .mu.m if the 
mask was the design pattern as it was, to 0.028 .mu.m. The resist pattern 
under a focused condition obtained by the mask of FIG. 32 is shown in FIG. 
33. It shows that a very good resist pattern is obtained in comparison 
with FIG. 31 before the correction. 
By using the present mask, a semiconductor device having good electrical 
characteristics can be produced with a high manufacturing yield. 
EXAMPLE 8 
In Example 8, the invention is applied to a case where a pattern of a 
polycrystalline silicon layer of a memory device of a 0.35 .mu.m rule is 
exposed on a positive Novolak resist under conditions of an exposure 
wavelength .lambda. of 365 nm, a numerical aperture NA of 0.50, and an 
apparent size .sigma. of 0.68. 
FIG. 34 shows the design pattern used in the present example. 
First, as shown in FIG. 35, the evaluation points were generated for the 
sides of the design pattern. At this time, in the present example, the 
evaluation points were not added to the very small sides 32c of that 
desired design pattern shorter than a predetermined length and, at the 
same time, evaluation points were not added to the corners 32d next to the 
very small sides. Evaluation points were arranged at the other corners and 
sides at predetermined intervals. The predetermined length was about 0.3 
.mu.m or less in the present example. Further, the slanted side 32e was 
assumed to be a stepped pattern, and one evaluation point was arranged per 
horizontal line of each step. Further, the evaluation points were not 
arranged at the sides at the boundaries 32b of the repeating regions. 
Next, the distribution of light intensity obtained where the mask of this 
design pattern was transferred as is under a focused condition was found, 
this was subjected to the convolution integration as shown by Equation 
(6), and the contours line obtained by slicing this convolution at the 
threshold value Eth were found as the resist image (FIG. 36). Note, the 
threshold value Eth is set so that L in FIG. 36 becomes 0.35 .mu.m. 
Further, the depth of focus necessary in the lithographic process was 
determined to .+-.0.75 .mu.m, and the convolution of the light intensity 
distribution and Gaussian function at a 0.75 .mu.m defocus was found, and 
the contour lines sliced at the above Eth were found (FIG. 37). 
Further, the exposure margin necessary in the lithographic process was made 
.+-.10%, the contour lines sliced at the height Eth.sup.- obtained when 
decreasing Eth by 10% in the two convolutions were found as the resist 
image where the exposure amount was increased by +10%, and the contour 
lines sliced at the height of Eth.sup.+ obtained by increasing Eth by 10% 
were found as the resist image where the exposure amount was reduced by 
10%, respectively. By this, a total of six resist images were calculated, 
i.e., for the focused condition and 0.75 .mu.m defocus in terms of the 
focal position and for the optimum exposure amount, 10% overdose, and -10% 
underdose in terms of the exposure amount. 
Subsequently, the amounts of deviation of the resist edge positions from 
the evaluation points were found at all evaluation point for the edges of 
the six resist images. At the evaluation points other than the corners, 
the direction of measurement of the deviation of the edge position at this 
time was made the orthogonal direction with respect to the edge and the 
outward direction of the pattern was made the positive direction. At the 
corner points, this was made the direction of the sum of the directional 
vectors of the two sides forming the corner, and similarly the outside of 
the pattern was made the positive direction. 
The average value of the amounts of deviation of the edges under the six 
conditions was found for every evaluation point obtained in this way. 
Note, at the corner evaluation points, in order to prevent excessive 
correction of the pattern later, the target value of the amount of 
deviation of the edge was made -0.07 .mu.m for the outwardly projecting 
corners and was made +0.07 .mu.m for the outwardly recessed corners and 
the difference of these target values and the amount of deviation of the 
evaluation point of the edge position was found. The average value of 
these was found. 
In this way, the side of the mask pattern in the vicinity of each 
evaluation point was moved in a reverse direction to the obtained amount 
of deviation of the edge so as to obtain the corrected mask pattern. Here, 
the amount of movement of the sides of the pattern was made an amount 
obtained by multiplying the amount of deviation by 0.25. 
Further, these procedures were carried out again by maintaining the 
position of the evaluation point as is and making the corrected mask 
pattern the pattern input. 
By repeating this procedure four times, the mask pattern of FIG. 38 was 
obtained. 
By this correction, it was possible to successfully reduce the 3.sigma. of 
the amounts of edge deviation in the resist patterns of the combinations 
of the two types of focal positions of the focused condition and 0.75 
.mu.m defocus and the three types of exposure amounts of the optimum 
exposure amount, 10% overdose, and -10% underdose, which was 0.291 .mu.m 
if the mask was the design pattern as it was, to 0.132 .mu.m in the 
present example. The resist patterns obtained under a focused condition 
and 0.75 .mu.m defocus obtained by the mask of FIG. 38 are shown in FIG. 
39 and FIG. 40. It is shown that very good resist patterns in comparison 
with FIGS. 36 and 37 before the correction are obtained. 
By using the mask obtained by the method according to the present example, 
a semiconductor device having good electrical characteristics can be 
produced with a high manufacturing yield. 
Note that, the present invention is not limited to the above examples. The 
exposure conditions are not limited to the values disclosed in the 
examples. Also, the photoresist to be used is not limited to the ones in 
the examples, and the mask pattern is not limited to those of the 
examples. 
Further, as the exposure method, it is also possible to use the modified 
illumination method and pupil filtering method. Also, the mask to be used 
can be a phase shift mask such as a halftone system or the Levenson system 
and is not limited to the present examples. 
As explained above, the present invention enables the calculation of a mask 
pattern that solves the problems of the related art and gives a resist 
pattern near the design pattern, whereby a means of producing a high 
performance design with a high manufacturing yield can be provided.