Method of making a mask pattern

[0002] 1. Field of the Invention

[0003] The present invention relates to a method for making a mask pattern, and more particularly to a method for making a mask pattern by correcting the size of a hole diameter of a mask for forming a contact hole.

[0004] 2. Description of the Background Art

[0005] Making of a contact hole is indispensable in fabrication of LSI, and low precision of the hole diameter of a contact hole (hereinafter called contact hole diameter) leads to a contact failure previously control of the contact hole diameter has been attempted by correcting the mask pattern for forming a contact hole.

[0006] FIG. 24 is a flowchart showing a conventional technique of correcting the hole diameter of a mask (hereinafter called mask hole diameter) for forming a contact hole.

[0007] First, while making a mask pattern by using CAD, a check card is prepared. A check card is a collection of process flow for fabricating an LSI, specifying when to use which mask, when to make or remove which layer, etc.

[0008] Conventionally, by trial fabrication of LSI using a designed mask, the section of the LSI was observed by a microscope, and the actual contact hole diameter was measured. When the contact hole diameter was larger than a desired value, the mask hole diameter was designed smaller, and when the contact hole diameter was smaller than a desired value, the mask hole diameter was designed larger, and thus the mask pattern was corrected by such feedback.

[0009] For example, using a mask hole diameter designed to fabricate a contact hole diameter of 0.5 μm, if the actually fabricated contact hole diameter is 0.4 μm, the mask hole diameter is designed so as to fabricate a contact hole diameter of 0.6 μm. Or, if the fabricated contact hole diameter is 0.6 μm, the mask hole diameter is designed so as to fabricate a contact hole diameter of 0.4 μm.

[0010] It is, however, not practical to execute this step for all contact holes. In the LSI, there are hundreds of thousands of contact holes on one chip.

[0011] In such circumstances, it is also attempted to loosen the design rule of the LSI. The contact hole diameter depends not only on the mask hole diameter, but also on the undulations of the region for forming the contact hole, and therefore when the undulations of the region are moderate, the precision of the contact hole diameter is enhanced. Accordingly, for example, if forming of lithographic pattern is possible at 0.5 μm, then by designing the LSI by the 1 μm rule, undulations in the region for forming the contact hole are set to moderate, and hence the precision of the contact hole diameter may be enhanced. It, however, requires a wide area for realizing the LSI, and the transmission characteristic of the element deteriorates.

[0012] A first aspect of the invention relates to a method of making a mask pattern, by correcting a mask pattern used for providing an actual pattern in a processing region of an object, comprising steps of (a) making the mask pattern, (b) judging undulations of the object, (c) predicting dimensions of the actual pattern depending on the degree of the undulations, and (d) correcting by giving a correction amount to the dimensions of the mask pattern, depending on the result of the step (c).

[0013] A second aspect of the invention relates to a method of making a mask pattern of the first aspect, wherein the actual pattern is provided by forming a resist on the object, and shaping the resist depending on the mask pattern, and the step (c) includes steps of (c-1) determining the film thickness increment or decrement of the resist in the processing region, on the basis of the film thickness of the resist when the object is flat, and (c-2) predicting, on the basis of the film thickness increment or decrement, that the direction of deviation of the dimensions of the actual pattern when the processing region is concave as compared with the actual pattern when the processing region is flat, and the direction of the dimensions of the actual pattern when the processing region is convex as compared with the actual pattern when the processing region is flat are reverse to each other, and that the dimensions of the actual pattern are deviated larger when the degree of undulations of the processing region is greater as compared with when the processing region is flat.

[0014] A third aspect of the invention relates to a method of making a mask pattern of the second aspect, wherein a surface shape of the object is recognized as a surface height, relative to a foundation region expanding at least in a first direction and a second direction reverse to the first direction, and the step (b) includes steps of (b-1) determining the surface height by simulation, (b-2) specifying the position of the processing region in the foundation region, (b-3) setting a first region expanding in the first direction from the processing region, and a second region expanding in the second direction from the processing region, (b-4) detecting whether a first state of the surface height tending to increase relative to the first direction or a second state tending to decrease relative to the first direction is present, in both the first and second regions, on the basis of the result of the step (b-1), and (b-5) judging undulations about the first and second directions in the processing region on the basis of the result of the step (b-4).

[0015] A fourth aspect of the invention relates to a method of making a mask pattern of the third aspect, wherein the step (b-4), respectively in the first and second regions, has steps of (b-4-1) determining a position for taking the maximum value of the surface height, (b-4-2) determining a position for taking the minimum value of the surface height, (b-4-3) determining a shape height by subtracting the surface height of the processing region from the maximum value, (b-4-4) determining a shape depth by subtracting the minimum value from the surface height of the processing region, (b-4-5) judging a presence of the first state when the shape height is greater than the shape depth, and (b-4-6) judging a presence of the second state when the shape height is smaller than the shape depth.

[0016] A fifth aspect of the invention relates to a method of making a mask pattern of the fourth aspect, wherein the step (b-4-5) comprises, when the shape height is greater than the shape depth, a step of (b-4-5-1) taking the shape height as a first value, the step (b-4-6) comprises, when the shape height is smaller than the shape depth, a step of (b-4-6-1) taking the value multiplying the shape depth by (−1) as the first value, the step (c-1) has steps of (c-1-1) obtaining an altitude amount at an intermediate value of the first value of the first region and the first value of the second region, and (c-1-2) determining the film thickness increment or decrement on the basis of the altitude amount, and the absolute value of the film thickness increment or decrement is greater when the absolute value of the altitude amount is greater, and the sign of the altitude amount and the sign of the film thickness increment or decrement are different from each other, in the step (c-1-2).

[0017] A sixth aspect of the invention relates to a method of making a mask pattern of the fifth aspect, wherein the step (c-1-1) comprises a step of (c-1-1-1) obtaining an slope amount at an intermediate value of the value of dividing the first value in the first region by the second value in the first region, and the value of dividing the first value in the second region by the second value in the second region, and the film thickness increment or decrement is determined also on the basis of the slope amount in the step (c-1-2), and the absolute value of the film thickness increment or decrement is greater when the absolute value of the slope amount is greater.

[0018] A seventh aspect of the invention relates to a method of making a mask pattern of the fourth aspect, wherein the step (b-4-5) comprises, when the shape height is greater than the shape depth, steps of (b-4-5-1) taking the shape height as a first value, and (b-4-5-2) taking the distance along the first direction between the processing region and the position obtained in the step (b-4-1) as a second value, the step (b-4-6) comprises, when the shape height is smaller than the shape depth, steps of (b-4-6-1) taking the value multiplying the shape depth by (−1) as the first value, and (b-4-6-2) taking the distance along the first direction between the processing region and the position determined in the step (b-4-2) as the second value, the step (c-1) has steps of (c-1-1) obtaining an altitude amount at either the first value in the first region or the first value in the second region, on the basis of the magnitude relation between a third value obtained by dividing the first value in the first region by the second value in the first region, and a fourth value obtained by dividing the first value in the second region by the second value in the second region, and (c-1-2) determining the film thickness increment or decrement on the basis of the altitude amount, and the absolute value of the film thickness increment or decrement is greater when the absolute value of the altitude amount is greater in the step (c-1-2), and the sign of the altitude amount and the sign of the film thickness increment or decrement are different from each other.

[0019] An eighth aspect of the invention relates to a method of making a mask pattern of the seventh aspect, wherein the step (c-1-1) comprises a step of (c-1-1-1) taking either the third value or the fourth value as the slope amount, on the basis of the magnitude relation of the third value and the fourth value, and the film thickness increment or decrement is determined also on the basis of the slope amount in the step (c-1-2), and the absolute value of the film thickness increment or decrement is greater when the absolute value of the slope amount is greater.

[0020] A ninth aspect of the invention relates to a method of making a mask pattern of the second aspect, wherein the step (c-2) includes a step of (c-2-1) determining a pattern increment or decrement deviated when compared with the actual pattern in the case that the dimension of the actual pattern is flat in the processing region, on the basis of the film thickness increment or decrement, and an index showing a characteristic to an irradiation ray for photosensitizing the resist.

[0021] A tenth aspect of the invention relates to a method of making a mask pattern of the third aspect, wherein the foundation range further expands in a third direction orthogonal to the first and second directions, and a fourth direction opposite to the third direction, a third region expanding from the processing region in the third direction, and a fourth region expanding from the processing region in the fourth region are further set in the step (b-3), presence or absence of the first state and the second state with respect to the third direction is further detected in the third and fourth regions in the step (b-4), undulations about the third and fourth directions in the processing region are further judged in the step (b-5), and the dimension of the actual pattern about the third and fourth directions is also predicted, together with the dimension of the actual patter about the first and second directions in the step (c-1).

[0022] An eleventh aspect of the invention relates to a method of making a mask pattern of the second aspect, wherein the surface shape of the object is understood as a surface height to a foundation region expanding in direction I and direction J orthogonal thereto, and the step (b) includes steps of (b-1) determining the surface height by simulation, (b-2) specifying the position of the processing region in the foundation range, (b-3) setting a first region expanding in a positive direction from the processing region, and a second region expanding in a negative direction from the processing region, with respect to the direction I and direction J, respectively, (b-4) detecting whether the surface height is in a first state in increasing tendency or in a second state in decreasing tendency, about the positive direction, in the first and second regions, with respect to the direction I and direction J, respectively, on the basis of the result of the step (b-1), and (b-5) judging undulations about the direction I and direction J of the processing region on the basis of the result of the step (b-4).

[0023] A twelfth aspect of the invention relates to a method of making a mask pattern of the eleventh aspect, wherein the step (b-4) has, respectively in the first and second regions, steps of (b-4-1) determining a position for taking the maximum value of the surface height, (b-4-2) determining a position for taking the minimum value of the surface height, (b-4-3) determining a shape height by subtracting the surface height of the processing region from the maximum value, (b-4-4) determining a shape depth by subtracting the minimum value from the surface height of the processing region, (b-4-5) judging the presence of the first state when the shape height is greater than the shape depth, and (b-4-6) judging the presence of the second state when the shape height is smaller than the shape depth.

[0024] A thirteenth aspect of the invention relates to a method of making a mask pattern of the twelfth aspect, wherein the step (b-4-5) comprises, when the shape height is greater than the shape depth, steps of (b-4-5-1) taking the shape height as a first value, and (b-4-5-2) taking the distance along the first direction between the processing region and the position obtained in the step (b-4-1) as a second value, the step (b-4-6) comprises, when the shape height is smaller than the shape depth, steps of (b-4-6-1) taking the value multiplying the shape depth by (−1) as the first value, and (b-4-6-2) taking the distance along the first direction between the processing region and the position determined in the step (b-4-2) as the second value, the step (c-1) comprises steps of (c-1-1) obtaining, respectively about the direction I and direction J, an altitude amount candidate at either the first value in the first region or the first value in the second region, on the basis of the magnitude relation between a third value obtained by dividing the first value in the first region by the second value in the first region, and a fourth value obtained by dividing the first value in the second region by the second value in the second region, (c-1-2) taking, respectively about the direction I and direction J, either the third value or the fourth value as a slope amount candidate, on the basis of the magnitude relation between the third value and the fourth value, (c-1-3) taking the altitude amount candidate corresponding to the one with the greatest absolute value among the plural altitude amount candidates as the altitude amount, and (c-1-4) determining the film thickness increment or decrement on the basis of the altitude amount, and the absolute value of the film thickness increment or decrement is greater when the absolute value of the altitude amount is greater in the step (c-1-4), and the sign of the altitude amount and the sign of the film thickness increment or decrement are different from each other.

[0025] A fourteenth aspect of the invention relates to a method of making a mask pattern of the thirteenth aspect, wherein the step (c-1-3) comprises a step of (c-1-3-1) taking the one with the greatest absolute value among the plural slope amount candidates as the slope amount, and the film thickness increment or decrement is determined also on the basis of the slope amount in the step (c-1-4), and the absolute value of the film thickness increment or decrement is greater when the absolute value of the slope amount is greater.

[0026] A fifteenth aspect of the invention relates to a method of making a mask pattern of the thirteenth aspect, wherein the steps (b-3), (b-4), (c-1-1), and (c-1-2) are executed also in first and second directions orthogonal to each other in a stretching plane of the direction I and direction J, crossing at an equal angle with both the direction I and direction J.

[0027] A sixteenth aspect of the invention relates to a method of making a mask pattern of the first aspect, wherein the mask pattern is edited on a screen in the step (d), and a caution is visually alerted on the screen at a position where the absolute value of the correction amount exceeds a specific upper limit.

[0028] A seventeenth aspect of the invention relates to a method of making a mask pattern of the second aspect, wherein the step (c-1) includes:

[0029] (c-1-1) a resist application simulation step for simulating the mode of the resist being disposed on the object.

[0030] An eighteenth aspect of the invention relates to a method of making a mask pattern of the second aspect, wherein the step (c-2) has steps of (c-2-1) determining an equal strength plane by performing strength distribution simulation on irradiation ray for photosensitizing the resist, and (c-2-2) estimating the shape of the resist when the resist is developed, from the equal strength plane.

[0031] A nineteenth aspect of the invention relates to a method of making a mask pattern of the first aspect, wherein the actual pattern is provided by forming a resist on the object, and shaping the resist according to the mask pattern, and the step (c) includes a step of simulating the shaping.

[0032] In the invention, meanwhile, “mask pattern” refers to the data for controlling whether or not the resist is exposed, including the data for controlling the particle rays directly drawn on the resist.

[0033] According to the mask pattern making method of the first aspect of the invention, predicting the effect of the surface shape of the object on the dimension of the actual pattern, it is fed back to the mask pattern.

[0034] Therefore, a mask pattern to obtain the actual pattern in the dimensions of the desired value can be made without actually processing the object.

[0035] According to the mask pattern making method of the second aspect of the invention, a thicker resist is formed when the degree of concavity in the processing region is stronger, and a thinner resist is formed when the degree of convexity is stronger. When the resist is thicker, the irradiation ray for changing the developing characteristic of the resist, for example, the light is absorbed more. Since the resist receives the irradiation ray from the opposite side of the processing region, the area of the resist receiving the irradiation ray passing through the mask pattern becomes smaller as going toward the processing region.

[0036] Therefore, the effectively masked region in the processing region expands, and the interval of the regions to be masked becomes narrower, so that the dimensions of the actual pattern can be predicted.

[0037] According to the mask pattern making method of the third aspect of the invention, when the first region (I₀⁺) is in the first state (D⁺), and the second region (I₀⁻) is in the second state (D⁻), the surface height increases as going toward the processing region along the first direction, and the surface height decreases after passing through the processing region, so that the processing region can be judged to be convex.

[0038] To the contrary, when the first region (I₀⁺) is in the second state (D⁻), and the second region (I₀⁻) is in the first state (D⁺), the surface height decreases as going toward the processing region along the first direction, and the surface height increases after passing through the processing region, so that the processing region is judged to be concave.

[0039] Therefore, the undulations in the processing region can be easily judged by simulation without trial fabrication.

[0040] According to the mask pattern making method of the fourth aspect of the invention, in the first and second regions, presence of the first or second state is judged by taking note of the maximum value and minimum value of the shape of the object.

[0041] Therefore, the undulations in the processing region are judged macroscopically, without being affected by a slight error in simulation of the shape of the object.

[0042] According to the mask pattern making method of the fifth aspect of the invention, the altitude amount is determined in consideration of both the first value of the first region and the first value of the second region.

[0043] Therefore, the altitude amount is determined depending on the degree of change of the processing shape of the first and second regions for determining the undulations, and the film thickness increment or decrement is set depending on the magnitude of the altitude amount, so that the effect of the first aspect can be easily obtained while considering the contribution of the processing shape of both first and second regions to the thickness of the resist.

[0044] According to the mask pattern making method of the sixth aspect of the invention, the slope amount is determined in consideration of both the first value of the first region and the first value of the second region.

[0045] Therefore, the film thickness increment or decrement is set depending not only on the magnitude of the altitude amount but also on the slope amount, so that the mask pattern can be correctly more precisely while considering the contribution of the processing shape of both first and second regions to the thickness of the resist.

[0046] According to the mask pattern making method of the seventh aspect of the invention, the third value refers to the degree of change, including the sign, of the shape of the object in the first region. The fourth value refers to the degree of change, including the sign, of the shape of the object in the second region.

[0047] Therefore, the altitude amount is determined depending on the degree of change of the processing shape of both first and second regions for determining undulations, and the film thickness increment or decrement is set depending on the magnitude of the altitude amount, so that the effect of the fourth aspect can be easily obtained while considering which one of the contribution of the processing shape of the first and second regions is dominant for the thickness of the resist.

[0048] According to the mask pattern making method of the eighth aspect of the invention, the slope amount refers to the degree of change, including the sign, of the shape of the object in the first and second regions.

[0049] Therefore, the film thickness increment or decrement is set not only on the magnitude of the altitude amount, but also on the slope amount, so that the mask pattern can be corrected more precisely.

[0050] According to the mask pattern making method of the ninth aspect of the invention, the irradiation ray is absorbed more when the resist is thicker, depending on the characteristic of the resist.

[0051] Therefore, by determining the pattern increment or decrement on the basis of the index, the prediction at step (c) of the first aspect can be realized.

[0052] According to the mask pattern making method of the tenth aspect of the invention, the dimensions of actual patterns are predicted respectively in two directions orthogonal to each other, so that the mask pattern can be corrected in consideration of these two directions.

[0053] Therefore, a rectangular pattern having parallel sides in two directions orthogonal to each other can be corrected easily.

[0054] According to the mask pattern making method of the eleventh aspect of the invention, undulations are judged respectively in two directions orthogonal to each other, so that the mask pattern can be corrected in consideration of these two directions.

[0055] Therefore, an more accurately mask pattern correction can be done easily.

[0056] According to the mask pattern making method of the twelfth aspect of the invention, in the first and second regions, presence of the first or second states is judged by taking note of the maximum value and minimum value of the shape of the object.

[0057] Therefore, the undulations of the processing region are judged macroscopically, without being affected by a slight error in simulation of the shape of the object.

[0058] According to the mask pattern making method of the thirteenth aspect of the invention, the third value refers to the degree of change, including the sign, of the shape of the object in the first region. The fourth value refers to the degree of change, including the sign, of the shape of the object in the second region.

[0059] Therefore, the altitude amount is determined depending on the degree of change of the processing shape of both first and second regions for determining undulations, and the film thickness increment or decrement is set depending on the magnitude of the altitude amount, so that the effect of the eleventh aspect can be easily obtained while considering which one of the contribution of the processing shape of the first and second regions is dominant for the thickness of the resist.

[0060] According to the mask pattern making method of the fourteenth aspect of the invention, the slope amount refers to the degree of change, including the sign, of the shape of the object in the first and second regions.

[0061] Therefore, the film thickness increment or decrement is set not only on the magnitude of the altitude amount, but also on the slope amount, so that the mask pattern can be corrected more precisely.

[0062] According to the mask pattern making method of the fifteenth aspect of the invention, undulations are judged in four directions mutually crossing at 45 degrees each, and step (c) is executed with the undulations relating to the direction of the greatest degree of undulations.

[0063] Therefore, the undulations are judged in more directions, so that the mask pattern can be correctly more precisely.

[0064] According to the mask pattern making method of the sixteenth aspect of the invention, the caution is visually alerted on the screen, so that the position requiring an excessive amount of correction can be easily known.

[0065] Therefore, the mask pattern can be corrected by easy operation.

[0066] According to the mask pattern making method of the seventeenth aspect of the invention, the film thickness of the resist is accurately determined in the resist application simulation step.

[0067] Therefore, the film thickness of the resist can be determined accurately, so that the dimensions of the actual pattern can be also predicted more accurately.

[0068] According to the mask pattern making method of the eighteenth aspect of the invention, the shape after development of the resist can be accurately determined in the strength distribution simulation step.

[0069] According to the mask pattern making method of the nineteenth aspect of the invention, the shape of the resist can be accurately determined in the simulation step.

[0070] Therefore, the shape of the resist can be determined accurately, and hence the dimensions of the actual pattern can be predicated more accurately.

[0071] It is therefore an object of the present invention to solve the problems and provide a technique for correcting the mask pattern without loosening the design rule or measuring all contact hole diameters.

[0072] These and other objects, features, aspects and advantages of the present invention will become more apparent from the following description of the present invention when taken in conjunction with the accompanying drawings.

[0073] FIG. 1 is a flowchart explaining a first preferred embodiment of the invention.

[0074] FIG. 2 is a perspective view explaining the concept used in shape simulation.

[0075] FIG. 3 is a perspective view explaining the concept used in shape simulation.

[0076] FIG. 4 is a contour map showing an example of result of shape simulation.

[0077] FIG. 5 is a sectional view of a semiconductor element explaining a basic idea of the first preferred embodiment of the invention.

[0078] FIGS. 6 to 8 are flowcharts explaining the first preferred embodiment of the invention.

[0079] FIG. 9 is a concept diagram explaining the first preferred embodiment of the invention.

[0080] FIG. 10 is a flowchart explaining the first preferred embodiment of the invention.

[0081] FIGS. 11 to 13 are graphs explaining the first preferred embodiment of the invention.

[0082] FIG. 14 is a concept diagram explaining the first preferred embodiment of the invention.

[0083] FIGS. 15 and 16 are flowcharts explaining the first preferred embodiment of the invention.

[0084] FIG. 17 is a graph schematically showing the first preferred embodiment of the invention.

[0085] FIG. 18 is a flowchart explaining the first preferred embodiment of the invention.

[0086] FIG. 19 is a sectional view explaining the first preferred embodiment of the invention.

[0087] FIGS. 20 and 21 are flowcharts explaining the first preferred embodiment of the invention.

[0088] FIG. 22 is a schematic diagram explaining a third preferred embodiment of the invention.

[0089] FIG. 23 is a schematic diagram explaining a fourth preferred embodiment of the invention.

[0090] FIG. 24 is a flowchart showing a background art.

[0091] (A-1) General Description

[0092] FIG. 1 is a flowchart showing a first preferred embodiment of the invention. A mask pattern M for LSI fabrication is prepared by using a CAD for layout (step S1), while a check card K is prepared by using a system for manufacturing line control (step S2). Afterwards, according to the check card K, the shape obtained through the process of etching, deposition, and reflow is simulated, and undulations of the region or forming contact holes are determined (step S3).

[0093] Furthermore, on the basis of the surface shape (undulations) determined at step S3, the contact hole diameter obtained when the mask hole diameter fabricated at step S1 is predicted (step S4). According to the result of prediction, the mask pattern M is corrected to mask pattern M′ as for mask hole diameter (step S5). Later, using this mask pattern M′, a trial product of LSI can be manufactured (step S6). If it is also necessary to correct the check card K, a corrected check card K′ can be obtained before step S6.

[0094] As for shape simulation at step S3, a known art can be employed. For example, a three-dimensional shape simulation is described in “3D Lithography, Etching, and Deposition Simulation (SAMPLE-3D)” (E. W. Scheckler et al., VLSI Technology Digest, pp. 97-98, 1991). The present applicant also disclosed a shape simulation method in Japanese Patent Laid-open Gazette No. 4-133326.

[0095] FIG. 2 and FIG. 3 are perspective views showing the concept employed in the shape simulation. The region for shape simulation is divided into orthogonal meshes as shown in FIG. 2. In each rectangular parallelepiped cell divided by orthogonal meshes, the existence rate of substance is calculated. For example, when the region is divided by three mutually orthogonal axes I, J, K, the substance height H (I_c, J_c) in K direction at a specific position (I_c, J_c) on a plane stretched in directions I, J is determined by the sum of the substance existence rate a_p(0≦a_p≦1) of the cell existing at position (I_c, J_c, K_p) (p=1, 2, 3, . . . )

[0096] H (I_c, J_c)=Σa_p·Δk_p

[0097] where Δk_p: width in direction K of the cell existing at position (I_c, J_c, K_p).

[0098] While updating the specific position (I_c, J_c) on the plane stretched in directions I, J, by determining its height H (I_c, J_c), a plane shape can be simulated.

[0099] FIG. 4 is a contour map showing an example of result of shape simulation. Such contour map is obtained by performing shape simulation. In FIG. 4, contour lines are drawn at intervals of 0.03 μm in regions having expansions of 14.5 μm and 12.5 μm in direction I and direction J, respectively.

[0100] FIG. 5 is a sectional view of a semiconductor element showing a basic idea of step S4. On a silicon substrate, a LOCOS film is formed selectively, and a gate electrode is provided above the silicon substrate where the LOCOS film is not formed. On the silicon substrate, a silicon oxide film is formed, and further a BPSG film is formed by reflow.

[0101] In the semiconductor element having a sectional profile as shown in FIG. 5, when forming contact holes by piercing the BPSG film, the resist is selectively removed after once forming a resist on the BPSG film. That is, by shaping the resist, its base surface of BPSG film is patterned. By etching the BPSG film according to this pattern, contact holes can be provided.

[0102] Meanwhile, owing to the presence of LOCOS film and gate electrode, the BPSG film has undulations. The result obtained at step S3 expresses the undulations. Because of the presence of undulations in the base, the film thickness of the resist is not uniform.

[0103] In FIG. 5, the BPSG film is formed relatively flat on the LOCOS film, and the resist is formed at film thickness x₀. On the other hand, the BPSG film enclosed by the LOCOS film and gate electrode has a concave portion, and the film thickness x⁺ of the resist formed in this area is greater than the film thickness x₀. To the contrary, the BPSG film formed near the gate electrode has a convex portion, and the film thickness x⁻ of the resist formed in this area is smaller than the film thickness x₀.

[0104] Such deviation in the film thickness of the resist induces deviation of pattern obtained by shaping the resist. The thicker the resist, the more is absorbed the irradiation ray (for example, light) for varying the developing characteristic of the resist. Light is emitted to the resist from the opposite side of the BPSG film, that is, from above in FIG. 5, and therefore the area of the resist receiving the light passing through the mask pattern is decreased as going toward the BPSG film.

[0105] For example, in any one of the flat part, concave part, and convex part shown in FIG. 5, suppose to shape the resist by using the mask pattern showing transmission of light at diameter D. For example, the diameter of the pattern given by the resist to the BPSG film in the flat part is d₀. When the resist is of positive type, the diameter d⁺ of the pattern given by the resist to the BPSG film in the concave part is smaller than the diameter d₀. To the contrary, the diameter d⁻ of the pattern given by the resist to the BPSG film in the convex part is greater than d₀.

[0106] Such effect of the resist film thickness on the diameter of the pattern given to the BPSG film is, as a matter of course, more manifest when the degree of concave or convex property is greater.

[0107] In the light of such tendency, at step S4, the contact hole diameter is predicted from the surface shape of the base of the resist such as the BPSG film.

[0108] At step S5, when the contact hole diameter predicted at step S4 is greater than the desired diameter, the mask hole diameter is corrected smaller depending on the degree. To the contrary, when the predicted contact hole diameter is smaller than the desired diameter, the mask hole diameter is corrected larger depending on the degree.

[0109] The invention is intended to correct the mask pattern in such procedure, and it is neither necessary to loosen the design rule, nor necessary to measure all contact hole diameters.

[0110] (A-2) Detail of step S4

[0111] FIG. 6 and FIG. 7 are flowcharts showing the detail of step S3 and step S4. Step S100 corresponds to step S3, and steps S200 to S1000 denote the detail of step S4.

[0112] At step S100, as explained above, shape simulation is performed. Referring to FIG. 5, a plane orthogonal to the thickness direction of the resist is taken on a plane stretched in directions I, J (plane IJ). The surface of the object A corresponds to the BPSG film. Hence, height H (I, J) indicates the surface shape of the BPSG film.

[0113] At step S200, the position (I₀, J₀) for forming a contact hole is specified. This is to inspect the undulations at this position.

[0114] Consequently, at step S300, presence or absence of undulations at the position (I₀, J₀) in various directions is inspected. This is to inspect the presence or absence of undulations not only in direction I and direction J, but in mutually orthogonal first and second directions within a plane stretched in directions I, J, intersecting at equal angle (45 deg., 135 deg.) in both direction I and direction J.

[0115] Next, at step S400, the operation is advanced to step S500 when undulations are confirmed in any one of these four directions, and to step S900 when undulations are not observed in any direction.

[0116] At step S500, concerning each direction in which presence of undulations is confirmed, the altitude amount candidate ΔH_pand slope amount candidate ΔH/L]_p(p=I, J, 1, 2) are determined. These values indicate the degree of undulations, and are described in detail in the next section.

[0117] At step S600, on the basis of the altitude amount candidate and slope amount candidate, the film thickness increment or decrement ΔX from the film thickness X₀on a flat surface of the resist film thickness at position (I₀, J₀) is determined. Referring to FIG. 5, for example, the differences between thicknesses x⁺, x⁻, and X₀are determined. They are determined, as explained in the preceding section, according to the tendency that the resist is formed thick in the concave portion, and thin in the convex portion.

[0118] Further at step S700, the diameter increment or decrement Δd from the set value d of the contact hole diameter is determined. Referring to FIG. 5, for example, the differences between diameters d⁺, d⁻ and d₀are determined. They are determined, as explained in the preceding section, according to the tendency that the actual contact hole diameter is smaller when the resist is thicker.

[0119] At step S800, consequently, on the basis of the diameter increment or decrement Δd, the set value of mask hole diameter is corrected. Herein, the diameter increment or decrement Δd is subtracted from the actual size D of the mask actually fabricated as mask pattern. When the mask pattern is used in a reticle enlarged more than the actual size, of course, the correction is done according to the rate of enlargement. Furthermore, when exposing by directly drawing an electron beams on the resist, the mask pattern is the data for determining the rate of deflection of electron beams, and in such a case the degree of deflection is corrected according to the diameter increment or decrement Δd.

[0120] All such correction of mask hole diameter is done on the contact hole. That is, if there is still another contact hole to be investigated at step S900, the contact hole of notice is updated to return to step S200, and when correction of all contact holes is over, the correction process is over. Thereafter, step S5 is executed.

[0121] (A-3) Detail of step S300

[0122] FIG. 8 is a flowchart showing the detail of step S300. Here is shown only an example of inspection for presence or absence of undulations in direction I. In direction J and first and second directions, undulations are inspected similarly.

[0123] First at step S310, regions I₀⁺, I₀⁻ are set for the contact hole forming position (I₀, J₀).

[0124] FIG. 9 is a concept diagram showing the mode of specifying the position (I₀, J₀) on the plane IJ. If the position Q for actually forming the contact hole is not located at the center of the orthogonal mesh used in shape simulation, the center of the orthogonal mesh in which the position Q is present is regarded as the position (I₀, J₀).

[0125] At step S300, undulations are judged in a region having a specific expanse nearly centered at position (I₀, J₀). Herein, undulations are judged in 100 cells spreading by 10 blocks each in direction I and direction J. For example, when one orthogonal cell has a width of 0.5 μm in direction I and direction J, undulations are judged in a region of 5 μm square nearly centered at position (I₀, J₀).

[0126] Back to FIG. 8, the explanation is continued by limiting to the case of judging undulations only in direction I. The region I₀⁺ is an area including the position (I₀, J₀), and belonging to the increasing direction of I (hereinafter called I⁺ direction), with J₀being invariable. That is, it may be expressed as follows:

[0127] I₀⁺={(I₀, J₀), (I₀+1, J₀), . . . (I₀+N, J₀)}

[0128] Similarly, the region I₀⁻ is an area including the position (I₀, J₀), and belonging to the decreasing direction of I (hereinafter called I⁻ direction), with J₀being invariable. That is, it may be expressed as follows:

[0129] I₀⁻={(I₀, J₀), (I₀−1, J₀), . . . (I₀−N, J₀)}

[0130] At step S320, the regions I₀⁺, I₀⁻ are judged to be in the state D⁺, D⁻ or not. The judging method is described specifically in the next section, but roughly speaking, the state D⁺ refers to the case in which H (I, J₀) tends to increase in the I⁺ direction, and the state D⁻ refers to the case in which H(I, J₀) tends to decrease in the I⁺ direction. In FIG. 9, the region I₀⁻ is in the state D⁻, and the region I₀⁺ is in the state D⁺.

[0131] At step S330 to step S380, according to the result of step S320, it is judged whether the vicinity of H (I₀, J₀) is concave or convex, that is, presence or absence of undulations at position (I₀, J₀) is judged.

[0132] First, at step S330, both regions I₀⁺ and I₀⁻ are judged to be equally in state D⁺, or equally in state D⁻. When this condition is satisfied, concerning the I⁺ direction, H (I₀, J₀) is either in the monotonously increasing tendency (in the case of state D⁺) or in the monotonously decreasing tendency (in the case of state D⁻). Therefore, advancing to step S380, it is judged that undulations are absent at position (I₀, J₀). In other directions (direction J, first direction, second direction), undulations are judged, thereby advancing to step S400.

[0133] If the condition is not satisfied at step S330, advancing to step S340, the regions I₀⁺, I₀⁻ are judged to be respectively in state D⁺ and state D⁻. When this condition is satisfied, concerning the I⁺ direction, H (I, J₀) is judged nearly to be concave (step S350), and undulations are also judged in other directions (direction J, first direction, second direction), thereby advancing to step S400.

[0134] If the condition is not satisfied at step S340, advancing to step S360, the regions I₀⁺, I₀⁻ are judged to be respectively in state D⁻ and state D⁺. When this condition is satisfied, concerning the I⁺ direction, H (I, J₀) is judged nearly to be convex (step S370), and undulations are also judged in other directions (direction J, first direction, second direction), thereby advancing to step S400.

[0135] The case in which the condition of step S360 is not satisfied is the case in which at least one of regions I₀⁺ and I₀⁻ is neither in state D⁺ nor in state D⁻, and in such state, undulations are judged to be absent (step S380).

[0136] (A-4) Detail of step S320

[0137] FIG. 10 is a flowchart showing the detail of step S320. Shown here is only an example of specifying the states D⁺, D⁻ in the region I₀⁻. In the region I₀⁻, similarly, the states D⁺, D⁻ are judged. Of course, when step S300 is executed in other direction, for example, direction J, at step S320, the states D⁺, D⁻ are judged in the regions J₀⁺ (={(I₀, J₀), (I₀, J₀+1), . . . (I₀, J₀+N)}), J₀⁻(={(I₀, J₀), (I₀, J₀−1), . . . (I₀, J₀−N)}).

[0138] First, at step S321, the position (I_IM⁺, J₀) taking the maximum value in region I₀⁺, and the position (I_Im⁺, J₀) taking the minimum value are determined. In the example shown in FIG. 9, the maximum value is taken at position (I₀+2, J₀), and the minimum value, at position (I₀, J₀).

[0139] Next, at step S322, H_IM⁺ is determined by subtracting the height H (I₀, J₀) at position (I₀, J₀) from the maximum value in the region I₀⁺, and H_Im⁺ is determined by subtracting the minimum value from the height H (I₀, J₀) at position (I₀, J₀). That is, on the basis of the height H (I₀, J₀) at position (I₀, J₀), the height H_IM⁺ of the maximum value, and the depth H_Im⁺ of the minimum value are determined.

[0140] FIG. 11 to FIG. 13 are graphs for explaining the manner of determining ΔH_I⁺, L_I⁺ at step S323. FIG. 11 refers to the case of H_IM⁺>H_Im⁺, FIG. 12, the case of H_IM⁺<H_Im⁺, and FIG. 13, the case of H_IM⁺=H_Im⁺.

[0141] If H_IM⁺>H_Im⁺, ΔH_I⁺ is taken equally to H_IM⁺, and L_I⁺ is determined as the absolute value of I₀−I_IM⁺. FIGS. 11(a) shows the case of I_IM⁺<I_Im⁺, and (b) is the case of I_IM⁺>I_Im⁺.

[0142] If H_IM⁺<H_Im⁺, ΔH_I⁺ is taken equally to −H_Im⁺, and L_I⁺ is determined as the absolute value of I₀−I_Im⁺. FIGS. 12(a) shows the case of I_IM⁺<I_Im⁺, and (b) is the case of I_IM⁺>I_Im⁺.

[0143] If H_IM⁺=H_Im⁺, L_I⁺ is either the absolute value of I₀−I_IM⁺ or the absolute value of I₀−I_IM⁺, whichever the smaller. When L_I⁺ is the absolute value of I₀−I_IM⁺, that is, when the distance from position (I₀, J₀) to position (I_Im⁺, J₀) is longer than the distance from position (I₀, J₀) to position (I_IM⁺, J₀), ΔH_I⁺ is taken equally to H_IM^{+. When L}_I⁺ is the absolute value of I₀−I_Im⁺, that is, when the distance from position (I₀, J₀) to position (I_Im⁺, J₀) is shorter than the distance from position (I₀, J₀) to position (I_IM⁺, J₀), ΔH_I⁺ is taken equally to −H_Im⁺. FIGS. 13(a) refers to the case of I_IM⁺<I_Im⁺, and (b) is the case of I_IM⁺>I_Im⁺.

[0144] Being thus determined, the sign of ΔH_I⁺ indicates increase or decrease along the I⁺ direction in region I₀⁺, and by dividing ΔH_I⁺ by L_I⁺ (that is, by determining ΔH_I⁺/L_I⁺), a rough tendency of increase or decrease along in the I⁺ direction in the region I₀⁺ is shown. In other words, undulations smaller than H_IM⁺, H_Im⁺ are not taken into consideration. Therefore, the tendency of increase or decrease of thickness of the resist provided on the base is not influenced by a slight error of the base shape which may occur in shape simulation.

[0145] At step S324, the status in the region I₀⁺ is judged by the sign of ΔH_I⁺. That is, when ΔH_I⁺>0, the region I₀⁺ is judged to be in state D⁺, and when ΔH_I⁺<0, the region I₀⁺ to be in state D⁻.

[0146] FIG. 14 is a concept diagram showing the mode of judging presence or absence of undulations, which corresponds to steps S330 to S380. For example, as shown in FIG. 14(a), when the state in the region I₀⁺ is D⁺ and the state in the region I₀⁻ is D⁻, it is judged that a concave portion is present at position (I₀, J₀). As shown in FIG. 14(b), when the state in the region I₀⁺ is D⁻ and the state in the region I₀⁻ is D⁺, it is judged that a convex portion is present at position (I₀, J₀).

[0147] Of course, when all heights in the region I₀⁺ are equal to the height H (I₀, J₀), it results in ΔH_I⁺=0, which corresponds neither to the state D⁺ nor to D⁻. This is the case when the condition at step S360 is not satisfied.

[0148] (A-5) Detail of step S500

[0149] FIG. 15 is a flowchart showing the detail of step S500. It only shows an example of determining the altitude amount candidate and slope amount candidate concerning direction I. In other direction J, first and second directions, the altitude amount candidate and slope amount candidate are determined similarly.

[0150] At step S510, it is determined whether the slope in the region I₀⁺ or the slope in the region I₀⁻ for forming undulations contributes more to determination of the resist film thickness at position (I₀, J₀). It is supposed herein that the milder slope determines the resist film thickness more dominantly.

[0151] When the absolute value of the slope ΔH_I⁺/L_I⁻ in the region I₀⁺ is greater than the absolute value of the slope ΔH_I⁻/L_I⁻ in the region I₀⁻, ΔH_I⁻ is taken as the altitude amount candidate ΔH_I. On the other hand, when the absolute value of the slope ΔH_I⁺/L_I⁺ in the region I₀⁺ is smaller than the absolute value of the slope ΔH_I⁻/L_I⁻ in the region I₀⁻, ΔH_I⁺is taken as the altitude amount candidate ΔH_I.

[0152] Similarly, when the absolute value of the slope ΔH_I⁺/L_I⁺ in the region I₀⁺is greater than the absolute value of the slope ΔH_I⁻/L_I⁻ in the region I₀⁻, ΔH/L]_Iis ΔH_I⁻/L_I⁻. On the other hand, when the absolute value of the slope ΔH_I⁺/L_I⁺ in the region I₀⁺ is smaller than the absolute value of the slope ΔH_I⁻/L_I⁻ in the region I₀⁻, ΔH/L]_Iis ΔH_I⁺/L_I⁺.

[0153] Of course, the steeper slope may determine the resist film thickness more dominantly, depending on other conditions than the shape of the base, such as the kind of the base, kind of the resist, and mutual relation of the base and resist, or an intermediate value of ΔH_I⁺/L_I⁺ and ΔH_I⁻/L_I⁻, or an intermediate value of ΔH_I⁺ and ΔH_I⁻ (for example, average) may be also used.

[0154] At step S500, in the direction in which presence of undulations is confirmed among direction I, direction J, first and second directions, the altitude amount candidate ΔHp, and slope amount candidate ΔH/L]_p(p=I, J, 1, 2) are determined.

[0155] (A-6) Detail of step S600

[0156] FIG. 16 is a flowchart showing the detail of step S600. First, at step S610, the maximum absolute value among ΔH/L]_I, ΔH/L]_J, ΔH/L]₁, and ΔH/L]₂, is determined as the slope amount ΔH/L. The symbol MAX ( ) means the maximum with the parentheses. When the slope ΔH/L is, for example, the slope amount candidate ΔH/L]_I, the altitude amount candidate ΔH_Iis taken as the altitude amount ΔH.

[0157] Next, at step S620, the film thickness increment or decrement Δx is determined. Herein, supposing

[0158] Δx=−ΔH{1−exp{−(ΔH/L)/η}]  (1)

[0159] the film thickness increment or decrement Δx is determined. In formula (1), relaxation factor η (0<η) is introduced. At the right side, (−ΔH) is multiplied, and the film thickness increment or decrement Δx is determined as a positive number if a concave portion is present, or the film thickness increment or decrement Δx is determined as a negative number if a convex portion is present.

[0160] FIG. 17 is a graph showing schematically the relation between the absolute value of the film thickness increment or decrement Δx and the slope amount ΔH/L. The greater the slope amount ΔH/L, that is, the more manifest the degree of undulations, the greater becomes the absolute value of the film thickness increment or decrement Δx. That is, at the resist film thickness, the deviation of x to x₀is large. But the degree of deviation is alleviated as the relaxation factor η is greater. Therefore, by employing formula (1), the effect of other factors than the base shape, such as the characteristic of the resist and mutual relation of the base and resist, can be considered by the relaxation factor η. For example, the relaxation factor η is set below about 0.5.

[0161] FIG. 18 is a flowchart showing step S630 which can be replaced with step S620. At step S630, the film thickness increment or decrement Δx is evaluated more easily than at step S620. Herein, supposing

[0162] Δx=−ΔH·S  (2)

[0163] the film thickness increment or decrement Δx is determined. In formula (2), relaxation factor S (0<S) is introduced, and it is evaluated only by the altitude amount ΔH and relaxation factor S. Same as in formula (1), at the right side, (−ΔH) is multiplied, and the film thickness increment or decrement Δx is determined as a positive number if a concave portion is present, or the film thickness increment or decrement Δx is determined as a negative number if a convex portion is present. The relaxation factor S is set at, for example, about 0.2.

[0164] (A-7) Detail of step S700

[0165] FIG. 19 is a sectional view explaining a method of determining the diameter increment or decrement Δd from the film thickness increment or decrement. In FIG. 19(a), the resist is formed on a flat area, and its film thickness is x₀, in (b), the resist is formed in a concave portion, and its film thickness is x⁺ (>x₀), and in (c) the resists is formed on a convex portion, and its film thickness is x⁻ (<x₀).

[0166] In FIG. 19(a), the relation between the actual size D of the mask actually fabricated as mask pattern and the contact hole diameter d₀is expressed as follows in terms of parameter θ:

[0167] tan θ=(D−d₀)/2x₀  (3)

[0168] here the parameter θ is an intrinsic value for the resist determined by the characteristic of the resist, for example, the transmissivity of the irradiated light.

[0169] Hence, in FIGS. 19(b) and (c), introducing the parameter θ also introduced in formula (3), the formula (4)

[0170] tan θ={D−(d₀+Δd)}/2(x₀+Δx)  (4)

[0171] is established. In FIG. 19, the upward direction is positive, and downward direction is negative. In FIG. 19(b), the film thickness increment or decrement Δx is positive, and the diameter increment or decrement Δd at this time is negative. In FIG. 19(c), the film thickness increment or decrement Δx is negative, and the diameter increment or decrement Δd at this time is positive.

[0172] From formulas (3) and (4), the diameter increment or decrement Δd is determined as follows.

[0173] Δd=−2Δx·tanθ  (5)

[0174] FIG. 20 is a flowchart showing the detail of step S700, and the process according to formula (5) is executed at step S710.

[0175] Of course, instead of step S710, other process may be done for determining the diameter increment or decrement Δd on the basis of the film thickness increment or decrement Δx.

[0176] (A-8) Modified example of first preferred embodiment

[0177] Various modifications are possible in the first preferred embodiment. Instead of analyzing in all of direction I, direction J, first and second directions, only the pair of mutually orthogonal direction I and direction J, or the pair of first and second directions may be analyzed.

[0178] Or, for example, the contact hole diameter may be predicted by two-dimensional analysis for considering the base shape only in the direction I and height. In this case, the shape simulation at step S3 is done two-dimensionally, and the height of the object A at step S100 may be expressed as the function H(I) of I only. The position for forming a contact hole at step S300 is specified as (1₀), and at step S300, therefore, presence or absence of undulations is inspected only in direction I.

[0179] Therefore, at step S400, presence or absence of undulations is investigated in direction I, and at step S500, therefore, only the altitude amount candidate ΔH_Iand slope amount candidate ΔH/L]_Iare determined. At step S610, the altitude amount candidate ΔH_Iis taken as the altitude amount ΔH, and the slope amount candidate ΔH/L]_Iis taken as the slope amount ΔH/L.

[0180] When step S4 is promoted only by two-dimensional analysis in this way, if the film thickness increment or decrement Δx is determined further by using formula (2), it is not necessary to determine the slope amount ΔH/L nor slope amount candidate ΔH/L]_I. The reason is as follows.

[0181] At step S630, the slope amount ΔH/L is not employed, and it is not necessary at step S610 to compare the slope amount candidates ΔH/L]_pfor determining the altitude amount ΔH. Therefore, at step S500, it is not necessary to determine the slope amount candidate ΔH/L]_I. FIG. 21 is a flowchart showing the step S520 for composing step S500 in such a case.

[0182] It is thus advantageous that the required process is less when analyzing two-dimensionally.

[0183] On the other hand, by performing two-dimensional analysis in direction I and direction J, the diameter increment or decrement Δd_Iin direction I, and the diameter increment or decrement Δd_Jin direction J can be determined individually. Such method of determining is preferable especially when the contact hole is rectangular, having sides parallel to direction I and sides parallel to direction J.

[0184] In the first preferred embodiment, at step S600, employing the relaxation factors η and S, the film thickness increment or decrement Δx was determined. However, by the resist coating shape simulation, the resist film thickness can be determined, and accordingly the film thickness increment or decrement Δx can be determined.

[0185] Such resist application shape simulation is known, and is disclosed, for example, in “Spin Coating Over Topography,” L. M. Peurrung and D. B. Graves, IEEE transactions on semiconductor manufacturing, Vol. 6, No. 1, pp. 72-76 (1993).

[0186] By thus using the resist coating shape simulation, the film thickness increment or decrement Δx is determined in consideration of the resist viscosity, and therefore the diameter increment or decrement Δd of higher precision for actual deviation of the contact hole diameter can be obtained.

[0187] In the first preferred embodiment, at step S700, the diameter increment or decrement Δd was determined by using parameter θ showing the resist characteristic. After determining the film thickness increment or decrement (or film thickness x=x₀+Δx) by the technique disclosed in the first preferred embodiment or second preferred embodiment, the light intensity distribution simulation may be done on the resist, and the contact hole diameter may be estimated from the surface (equal intensity surface) having a specific light intensity. Such technique is also useful because the resist is changed in the dissolution characteristic in the developing solution depending on the light exceeding the specific intensity and the shape of the resist developed and left over is determined.

[0188] For example, when the light intensity distribution is expressed by percentage, the resist receiving the light intensity of more than 15 percent is supposed to be dissolved by development, and the equal intensity surface of 15 percent is determined and the boundary contacting with it on the base may be determined as the shape of the contact hole.

[0189] Such light intensity distribution simulation is known, and is disclosed, for example, in “Partially Coherent Imaging In Two Dimensions and the Theoretical Limits of Projection Printing in Microfabrication,” B. J. Lin, IEEE transactions on electron devices, Vol. ED-27, No. 5, pp. 931-938 (1980), or “Modeling Aerial Images in Two and Three Dimensions,” M. Yeung, Proc. of Kodak ME Seminar Interface 85, pp. 115-126 (1986). In particular, the calculation technique of light intensity distribution inside the resist is disclosed in “Modeling Latent Image Formation in Photolithography Using the Helmholtz Equation,” H. P. Urbach and D. A. Bernald, SPIE Vol. 1264, Optical/Laser Microlithography III, pp. 278-293 (1990).

[0190] FIG. 22 is a schematic diagram for explaining a practical technique for determining the shape of contact hole from various equal intensity surfaces obtained by the light intensity distribution simulation. At the position (I₀, J₀, KB (I₀, J₀)) at the boundary of the resist and the base of BPSG film immediately beneath the contact hole position (I₀, J₀), the light intensity is investigated to be if more than the specified intensity (for example, 15 percent) or not. Herein, KB (I₀, J₀) refers to the position of the boundary of the base and BPSG film, which may be represented by the height H (I₀, J₀) in the first preferred embodiment.

[0191] For example, if the equal intensity surface β indicated in FIG. 22 is an equal intensity surface more than the specified intensity, it is natural that the light is emitted from above the resist, and therefore the light intensity is considered to be more than the specified intensity above the equal intensity surface β, and hence the light intensity at position (I₀, J₀, KB) is judged to be more than the specified intensity (for example, 15 percent).

[0192] Next, from the position (I₀, J₀, KB) along the boundary of the resist and base, an equal intensity surface of specified intensity is searched in direction I and direction J, and the distance b in direction I and distance a in direction J from the position (I₀, J₀, KB) to the specified equal intensity surface are determined. The distances a and b thus determined represent the contact hole diameter.

[0193] If the light intensity at position (I₀, J₀, KB (I₀, J₀)) is less than the specified intensity, if the resist is developed, the bottom of the contact hole does not reach up to the boundary surface of the resist and the base, and hence the contact hole diameter is judged to be 0.

[0194] In the third preferred embodiment, only the equal intensity surface for determining the dissolution characteristic of the resist is obtained, but it is also possible to obtain the shape of the resist left over after development by simulating the development process. Such simulation of development process is known, and is disclosed, for example, by the present applicant in Japanese Patent Laid-open Gazette No. 4-133326 and U.S. Pat. No. 5,293,557.

[0195] FIG. 23 is a schematic diagram explaining a practical method of determining the shape of contact hole from various equal intensity surfaces obtained by light intensity distribution simulation. The position (I₀, J₀, KB (I₀, J₀)) is same as in the third preferred embodiment. The shape of the resist left over after development is indicated by surface α.

[0196] If there is a base (BPSG) at position (I₀, J₀, KB), the surface a is searched from the position (I₀, J₀, KB) in direction I and direction J along the boundary of the resist and base, and distance b in direction I and distance a in direction J from the position (I₀, J₀, KB) to surface α are determined. Thus obtained distances a and b represent the contact hole diameter.

[0197] If a resist is present at position (I₀, J₀, KB), as a result of development of the resist, the bottom of the contact hole does not reach up to the boundary of the resist and base, and hence the contact hole diameter is judged to be 0.

[0198] An upper limit Δd_maxmay be provided in the absolute value of the diameter increment or decrement Δd determined at step S700. When the absolute value of the diameter increment or decrement Δd exceeds the upper limit Δd_max, the contact hole to be formed at position (I₀, J₀) may be judged to be defective.

[0199] At step S5, on the layout editor screen for designing the mask pattern M′, the caution may be alerted by flickering, or displaying in a specific appealing color, such as white, yellow, sky blue and yellowish green. Thus, the mask pattern can be corrected by easy operation.

[0200] The invention may be applied not only in control of the contact hole diameter of semiconductor device, but also in fine processing in forming impurity region such ion implantation. Evidently, it may be also applied in fine processing of micromachine.

[0201] While the invention has been shown and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous modifications and variations can be devised without departing from the scope of the invention.