JPH0982614A - Method and device for control of pattern measurements - Google Patents

Abstract

PROBLEM TO BE SOLVED: To suppress the irregularity in line width of a pattern by a method wherein the irregularity of pattern measurements is computed from the thickness distribution and the standing-wave effect of the resist film on the surface of a wafer, and the angular velocity condition of the wafer within the range of an allowable value is computed by comparing said measurement irregularity and the allowable value. SOLUTION: The distribution of thickness H of a resist film on the surface of a wafer is computed based on the continuous condition shown in the formula I (Step 11). The irregularity in pattern measurement is computed by the formula II taking into consideration of said thickness distribution of the resist film and the effect of standing-wave (Steps 12 and 13). The angular velocity of the wafer when a rotary painting operation is conducted is computed so as to obtain the allowable value or smaller (Step 16) by comparing the obtained irregularity in pattern measurement and the allowable value (Step 14). In the formula I, λ=(3Ω<2> )<1/3> = 3(pw<2> w<3> r<0> )/(rhf)}<1/3> , x=(r-r<0> )/w indicates the thickness distribution, and the x in the formula II indicates film thickness, the n indicates the reference index of film, c indicates the wavelength of exposure, and a, b, c and d indicate the constant of standing wave regression.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pattern size control method and a control device for predicting the sizes of various patterns formed on a semiconductor device.

[0002]

2. Description of the Related Art In recent years, with the progress of higher integration of VLSI, higher precision pattern forming technology is required. The accuracy is generally ± 10 of the design rule.
%. For example, design rule is 0.35μm ultra-L
The SI requires a line width uniformity of ± 0.035 μm.

The following items can be cited as causes of the deterioration of the accuracy. (1) Variation of resist film thickness, (2) Standing wave effect, (3) Variation of resist dissolution rate, (4) Variation of various resist material properties, (5) Exposure equipment optical and mechanical Variation, (6) reticle line width variation, (7) etching variation, (8)
Variation in light reflectance of substrate (or variation in thickness of film formed on substrate surface), (9) Step due to underlying pattern, (10) Effect of acid / alkali in atmosphere (especially in case of chemically amplified resist) ). Of the above, (1) to (4) and (10)
Causes a line width variation in the photolithography process. The present invention intends to solve the problems (1) and (2), which is the fluctuation of the pattern line width due to the local fluctuation of the resist film thickness caused by the step difference in the underlying layer. Considering such factors of line width variation, the design rule is 0.35μ.
In the VLSI of m, the film thickness uniformity of the resist film is required to be 5 nm or less.

On the other hand, as a factor of the variation of the pattern line width, (2) the standing wave effect is mentioned. The standing wave effect is a phenomenon in which the light incident on the resist interferes with the reflected light from the underlayer, and the sensitivity changes at a cycle corresponding to the exposure wavelength and the refractive index of the resist. Therefore, the pattern line width varies. In order to suppress this, for example, the interference between the incident light and the reflected light may be reduced, and as a means therefor, there is an overcoat antireflection film. The overcoat antireflection film is a film in which a transparent film is formed on the surface of the resist film by coating, and the light whose phase is inverted by the transparent film interferes in the direction of canceling the standing wave.

[0005]

The required uniformity of the film thickness can be realized when the film is formed on a flat substrate surface. However, a step is actually formed on the surface of the substrate, and the step causes a film thickness variation more than an allowable value.

Further, as shown in the explanatory view regarding the standing wave effect of FIG. 14, the line width of the pattern fluctuates at a constant cycle as the thickness of the resist film increases. The figure also includes the effect of the bulk effect. In general, the film thickness of the resist is adjusted to the top a of the peak portion of the standing wave curve C in which the line width variation due to the standing wave is small. This is because the position of point a has the widest allowable range with respect to film thickness variation.

However, since the local variation of the resist film thickness is large in the vicinity of the step, it has been unclear which point of the standing wave curve the film thickness is in the vicinity of the step. Furthermore, it has been difficult to achieve the required line width uniformity of the pattern even if the above antireflection film is used. Thus, it was not possible to suppress the local variation in the line width of the pattern, and it was not possible to even predict the line width distribution of the pattern. Therefore, there is a strong demand for establishment of a method for predicting this local pattern line width variation and a method for suppressing it.

It is an object of the present invention to provide a pattern dimension control method and control device which are excellent in suppressing line width variations of patterns.

[0009]

SUMMARY OF THE INVENTION The present invention is a pattern dimension control method and control device which are designed to achieve the above object.

A first method for controlling the pattern size is the first means, in which the thickness H of the resist film formed on the surface of a wafer having a step on the surface and rotating at a set angular velocity is set to (1
It is represented by the formula 1).

[0011]

H = 1 + aexp (−λx) + bexp (λx / 2) cos (√3λx / 2) + cexp (λx / 2) sin (√3λx / 2) (11) [(11) λ = (3Ω²)^1/3= {3 (ρω²w
^Threer₀) / (Γhf)} ^1/3, X = (rr₀) / W
, Ρ: resist density, ω: wafer angular velocity, w:
Width of wafer step difference, r: distance from wafer center, r
₀: Distance between wafer center and step center, γ: Resist table
Surface tension, hf: Registration of wafer flat position away from step
Strike film thickness)

Then, the thickness distribution of the resist film is obtained by obtaining the continuous condition of the equation (11). Then, by the second means, the dimension y of the pattern formed by the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect, is obtained by the equation (12).

[0013]

Equation 12] y = (aχ + b) sin (4nπχ / λ c + c) + dχ + e ··· (12) [(12) wherein, chi: resist film thickness, n: the refractive index of the film, lambda _c: exposure Wavelength, a, b, _C , d, e: Represents constants for standing wave regression]

Subsequently, the third means calculates the dimension variation from the obtained pattern dimension y. Then, the fourth means determines whether or not the dimensional variation is larger than a preset allowable value. If the dimensional variation is larger than the allowable value as a result of this determination, the fifth means changes the angular velocity of the wafer set by the first means to set a new angular velocity, and the first and subsequent steps are repeated. Give instructions. On the other hand, when the dimensional variation is less than or equal to the allowable value, the sixth means determines the wafer angular velocity set by the first means as the wafer angular velocity in the spin coating method.

In the first pattern size control method,
The first means calculates the thickness distribution of the resist film in consideration of the step difference on the wafer surface, and the second means calculates the thickness distribution of the resist film and the standing wave effect in consideration of the pattern size (for example, the line size). By obtaining the width, the dimension of the pattern corresponding to the surface shape of the wafer can be obtained. Then, the dimensional variation is obtained from the dimensions of the pattern, and when the dimensional variation is smaller than the allowable value, the condition at that time is the angular velocity condition of the wafer. Therefore, the resist film thickness within which the dimensional variation of the pattern falls within the allowable range is obtained.
On the other hand, when the dimensional variation is large, a new angular velocity of the wafer when the resist film is formed by spin coating is set, and the first and subsequent steps are performed again at the new angular velocity.
Therefore, the angular velocity that minimizes the dimensional variation is determined. As a result, the resist film thickness that minimizes the dimensional variation can be obtained.

The first pattern size control device has the following configuration. That is, a map creation storage unit for creating a map of the underlayer shape of the wafer is provided. Then, based on each position on the wafer stored in this, the thickness of the resist film formed by the spin coating method is calculated, and the thickness of the resist film in the wafer surface is calculated based on the thickness of the resist film at each position. A film thickness distribution calculation unit for creating a thickness distribution is provided. Further, the size of the pattern formed by the resist film having the above-mentioned film thickness distribution is calculated by including the fluctuation state due to the standing wave effect, and the dimensional variation is calculated from the difference between the pattern size value and the design size value of the pattern. A required dimensional variation calculation unit is provided. A determining unit is provided to determine whether or not the obtained dimensional variation is larger than a preset allowable value. If the determination unit determines that the dimensional variation is larger than the allowable value, a rotation condition instruction unit that sets a new rotation condition of the wafer and instructs the new rotation condition to the film thickness distribution calculation unit is provided. Further, a coating device instructing unit is provided to instruct the spin coating device about the rotation condition of the wafer when it is determined that the dimensional variation is less than or equal to the allowable value.

In the first pattern size control device,
Since the film thickness distribution calculation unit is provided, the thickness distribution of the resist film in the wafer surface is created in consideration of the underlayer shape of the wafer. The size of the pattern to be calculated is calculated by including the fluctuation state due to the standing wave effect, and the variation of the pattern size in the thickness of each resist film is further obtained. Therefore, the dimensional variation of the pattern corresponding to the film thickness distribution can be obtained. Since the determination unit and the rotation condition instruction unit are provided, the magnitude of the obtained dimensional variation and the preset allowable value is determined, and if the dimensional variation is large, the rotation condition instruction unit sets a new rotation condition. . Then, again, the thickness distribution calculation unit calculates the thickness distribution of the resist film. As a result, the thickness of the resist film within which the dimensional variation of the pattern is within the allowable value can be obtained.

The second pattern dimension control method is similar to the first pattern dimension control method, and the first to fourth means are used.
Do even the means. Then, as a result of the judgment by the fourth means, if the dimensional variation is larger than the allowable value, the fifth means is performed. That is, the area Aa where the dimensional variation is larger than the allowable value is compared with the area Ab indicating the limit value of the area where the dimensional variation is larger than the allowable value to determine which is larger. Then, as a result of the judgment by the fifth means, when the area Aa> the area Ab, the sixth means is performed. That is, the angular velocity of the wafer set by the first means is changed to issue a command to repeat the first and subsequent steps. On the other hand, as a result of the judgment by the fifth means, when the area Aa ≤ the area Ab,
In the seventh means, a region having a large dimensional variation is a region where formation of an actual pattern (that is, a pattern functioning as an element) is prohibited. Further, as a result of the judgment by the fourth means, when the dimensional variation is less than or equal to the allowable value, the eighth means determines the area in which the dimensional variation is less than or equal to the allowable value as the real pattern formation area.

In the second pattern size control method,
Similar to the first pattern size control method, the size of the pattern corresponding to the surface shape of the wafer is obtained. Then, the fourth means determines whether or not the dimensional variation is larger than the allowable value. Further, the fifth means determines the size of the area Aa in which the dimensional variation is larger than the allowable value and the area Ab indicating the limit value of the area in which the dimensional variation is larger than the allowable value. ＞ If the size is Ab, the sixth
The means changes the angular velocity of the wafer set by the first means, and issues a command to repeat the first and subsequent steps. Therefore, the area is at least the area Aa ≦ the area Ab. On the other hand, when the area Aa ≦ the area Ab, the area where the dimensional variation is large is the area where the formation of the actual pattern is prohibited by the seventh means. Therefore, the actual pattern formation prohibited area is within the above limit value. On the other hand, the area in which the dimensional variation is small is the area where the actual pattern is formed by the eighth means. As a result, the actual pattern is provided only in the area where the dimensional variation is small, and the actual pattern is not provided in the area where the dimensional variation is large, for example, the dummy pattern is provided.

The second pattern size control device has the following configuration. That is, a map creation storage unit, a film thickness distribution calculation unit, and a dimension variation calculation unit, which are similar to those of the first pattern size control device, are provided. The dimension variation calculation unit is provided with a determination unit that divides a region in which the dimension variation is larger than a preset allowable value and a region in which the dimension variation is equal to or smaller than the allowable value. further,
For the area where the dimensional variation is larger than the allowable value, the judgment unit indicates the area Aa where the dimensional variation is larger than the allowable value and the limit value of the area where the dimensional variation is larger than the allowable value. An area determination unit is provided for comparing the area Ab with which area is larger. When the area Aa> the area Ab is judged by the area judging unit,
A rotation condition instructing unit is provided for setting a new rotation condition for the wafer and instructing the film thickness distribution calculating unit about the new rotation condition. Further, the area determination section is provided with a prohibited area instruction section for instructing the pattern design apparatus to prohibit the placement of the actual pattern in the area of the area Aa when it is determined that the area Aa ≤ the area Ab. There is. On the other hand, the judging section is provided with an actual pattern area instructing section for instructing the pattern designing apparatus to recognize the arrangement of the actual patterns in the area where the dimensional variation is equal to or less than the allowable value.

In the second pattern size control device,
Similar to the first pattern size controller, the pattern size variation corresponding to the resist film thickness distribution can be obtained. Since the determination unit is provided, it is divided into an area in which the dimensional variation is larger than a preset allowable value and an area in which the dimensional variation is less than or equal to the allowable value. Further, since the area judgment unit and the actual pattern area instruction unit corresponding to the division of the judgment unit are provided, the area judgment unit determines the area Aa in which the dimensional variation is larger than the allowable value and the dimensional variation is the allowable value. It is judged which is larger by comparing with the width Ab indicating the limit value of the area that becomes larger. Further, since the rotation condition instructing section and the prohibited area instructing section corresponding to the judgment of the area judging section are provided, the area judging section determines the area A
When it is determined that a> width Ab, the rotation condition instructing unit determines the new rotation condition of the wafer (for example, rotation speed, angular velocity, etc.).
Is set and the new rotation condition is instructed to the film thickness distribution calculator. On the other hand, the area determination unit determines the area Aa ≤ area A
If it is determined to be b, the prohibited area designating unit instructs the pattern design apparatus to prohibit the formation of the actual pattern in the area where the dimensional variation is large. As a result, a pattern that functions as an element is not provided in the region where the dimensional variation is large. On the other hand, with respect to the area classified as the area in which the dimensional variation is equal to or less than the allowable value, the actual pattern area instructing section instructs the pattern design apparatus to recognize the arrangement of the actual pattern. As a result, the actual pattern is arranged only in the area where the dimensional variation is small.

In the third method of controlling the pattern size, the first means causes the pattern generator to generate the set mask pattern. After that, like the first to fourth means in the first pattern dimension control method, the second means for obtaining the resist film thickness distribution, the third means for obtaining the pattern dimension y, and the dimension variation are obtained. Fourth
The means and the fifth means for determining whether or not the dimensional variation is less than or equal to the allowable value are sequentially performed. Then, as a result of the judgment by the fifth means, the sixth means is performed when the dimensional variation is larger than the allowable value. That is, the dimensions of the mask pattern of the pattern generator generated by the first means are corrected to define the dimensions of the new mask pattern, and the instruction for repeating the first and subsequent steps is instructed. On the other hand, as a result of the judgment by the fifth means, if the dimensional variation is smaller than the allowable value, the seventh means is performed. That is, the dimension value of the mask pattern set by the first means is used as the dimension of the mask pattern for manufacturing the mask pattern.

In the third pattern dimension control method,
Similar to the first pattern size control method, the size of the pattern corresponding to the surface shape of the wafer is determined in consideration of the standing wave effect. Then, the dimension variation is obtained from the dimension of the pattern, and when the dimension variation is smaller than the allowable value, the condition at that time is the dimension of the mask pattern.
Therefore, the dimensions of the mask pattern within which the variation in the dimensions of the pattern falls within the allowable range can be obtained. On the other hand, if the dimensional variation is larger than the allowable value, the first
The dimensions of the mask pattern of the pattern generator generated by the means are corrected to define the dimensions of the new mask pattern, and the first means and subsequent steps are performed again with the dimensions of the mask pattern. Therefore, the dimension of the mask pattern that minimizes the dimensional variation is determined. As a result, the dimension of the mask pattern that minimizes the dimensional variation is obtained.

The third pattern size control device has the following configuration. That is, the map creation storage unit, the film thickness distribution calculation unit, the dimension variation calculation unit, and the determination unit, which are similar to those of the first pattern size control device, are provided. Further, a pattern generator for generating a mask pattern is provided. The dimensional variation calculator calculates by including the fluctuation state due to the standing wave effect caused by the exposure using the mask pattern generated by the pattern generator. Further, there is provided a correction instructing unit that corrects the dimensions of the mask pattern when the dimensional variation is larger than the allowable value and instructs the pattern generator to provide a new mask pattern. Further, a mask pattern designating unit is provided for designating a mask pattern generated by the pattern generator to the mask drawing device when the dimensional variation is equal to or less than the allowable value.

In the third pattern size control device,
Almost the same as the control device for the first pattern size,
The dimensional variation of the pattern corresponding to the film thickness distribution of the resist film in consideration of the base shape of the wafer can be obtained. Since the determination unit is provided, the magnitude of the obtained dimensional variation and the preset allowable value is determined. Further, since the correction instructing unit and the mask pattern instructing unit corresponding to the judgment of the judging unit are provided, the correction instructing unit sets a new mask pattern dimension when the dimensional variation is large, and the new mask pattern dimension is set. Is instructed by the pattern generator, and the dimensional variation calculation unit calculates the dimensional variation of the pattern again. Then, the process is repeated until the dimensional variation becomes equal to or less than the allowable value, and as a result, the dimension of the mask pattern with less dimensional variation of the pattern is obtained. on the other hand,
The mask pattern instructing unit, when it is determined that the dimensional variation is equal to or less than the allowable value, instructs the mask pattern dimension at that time to the mask drawing apparatus. Therefore, it becomes possible to draw a mask pattern with which the dimensional variation of the pattern of the resist film is minimized.

The fourth pattern dimension control method is the first means, in which the resist film thickness hf _i (i = 1, 2, ..., At a flat position apart from the step formed on the wafer).
m) is specified. Next, by the second means, the thickness of the resist film is set to i = 1 type, and by the third means, the thickness H of the resist film formed by spin coating under the conditions is calculated as described in (11) above.
The thickness distribution of the resist film is obtained by expressing the same condition as the formula and determining the continuity condition of this formula. Then, in the fourth means, the dimension y of the pattern made of the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect, is
It is calculated by the same formula as the above formula (12). Then fifth
By means of means, dimensional variation is obtained from the obtained pattern dimension value. Then, the sixth means determines whether i = m, and i ≠
In the case of m, the seventh means sets i = i + 1 and instructs to repeat the third to sixth means. On the other hand, i
= M, the eighth means measures the thickness hf _{i of} each resist film.
The relationship between (i = 1, 2, ..., M) and the dimensional variation of the pattern at the thickness hf _i is obtained. Then, with the ninth means, from the relationship between the thickness of the resist film and the dimensional variation,
The thickness of the resist film formed on the wafer has the smallest film thickness variation.

In the fourth pattern dimension control method,
Corresponding to each resist film thickness, from the resist film thickness distribution obtained by considering the surface condition of the wafer and the standing wave effect,
The dimension of the pattern corresponding to the surface shape of the wafer is obtained, and the dimension variation is obtained from the dimension of the pattern. Therefore, from the relationship between the resist film thickness and the dimensional variation, the resist film thickness with the smallest dimensional variation can be obtained.

A fifth pattern dimension control method is the first means, in which the resist film thickness hf _i (i = 1, 2, ..., At a flat position apart from the step formed on the wafer).
m) is specified. Next, by the second means, the thickness of the resist film is set to i = 1 type, and by the third means, the thickness H of the resist film formed by spin coating under the conditions is calculated as described in (11) above.
The thickness distribution of the resist film is obtained by expressing the same condition as the formula and determining the continuity condition of this formula. Then, in the fourth means, the dimension y of the pattern made of the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect, is
It is calculated by the same formula as the above formula (12). Then fifth
By means of means, dimensional variation is obtained from the obtained pattern dimension value. Next, the sixth means obtains the size of the prohibited area in which the dimensional variation becomes larger than a preset allowable value. Then, the seventh means determines whether i = m, and when i ≠ m, the eighth means sets i = i + 1 and the third to seventh
Instruct to repeat the procedure. On the other hand, when i = m, the thickness of each resist film hf _i (i =
, 1, ..., M) and the size of the prohibited area in the thickness hf _i . Then, the tenth means determines the thickness of the resist film formed on the wafer to be the smallest film thickness of the forbidden region, based on the relationship between the thickness of the resist film and the size of the forbidden region.

In the fifth pattern dimension control method,
Corresponding to each resist film thickness, from the resist film thickness distribution obtained by considering the surface condition of the wafer and the standing wave effect,
The dimension of the pattern corresponding to the surface shape of the wafer is obtained, and the dimension variation is obtained from the dimension of the pattern. Further, the size of the prohibited area in which the dimensional variation is larger than a preset allowable value is obtained. Therefore, from the relationship between the resist film thickness and the size of the forbidden region, the resist film thickness that minimizes the size of the forbidden region can be obtained.

[0030]

BEST MODE FOR CARRYING OUT THE INVENTION An example of a first embodiment relating to a pattern dimension control method of the present invention will be described with reference to the flowchart of FIG. 1 and the explanatory view of the surface shape of a wafer in FIG.

Here, as shown in FIG. 2, a step S (for example, width =) is formed on the surface of the wafer 101 by the spin coating method.
A case will be described in which the resist film 111 is formed on the surface of the wafer 101 having w and height = δ. Then, from the center direction of the wafer 101 toward the outer peripheral direction,
The top of the step is Sui, the bottom of the step is Sb, and the top of the step is Suo.

As shown in FIG. 1, the first means S11 forms a resist film on the surface of the wafer rotating at a set angular velocity by, for example, a spin coating method. The thickness H of the resist film is expressed by the equation (13).

[0033]

H = aexp (−λx) + bexp (λx / 2) cos (√3λx / 2) + cexp (λx / 2) sin (√3λx / 2) (13) [wherein (13) λ = (3Ω²)^1/3= {3 (ρω²w
^Threer₀) / (Γhf)} ^1/3, X = (rr₀) / W
, Ρ: resist density, ω: wafer angular velocity, w:
Width of wafer step difference, r: distance from wafer center, r
₀: Distance between wafer center and step center, γ: Resist table
Surface tension, hf: Registration of wafer flat position away from step
Strike film thickness)

From the above equation (13), the thickness H ₁ of the resist film including the step above the step above Sui is (14)
It is expressed like a formula.

[0035]

H ₁ = b ₁ exp (λx / 2) cos (√3λx / 2) + c ₁ exp (λx / 2) sin (√3λx / 2) + 1 + s (14) [wherein (14) , S = δ / hf represents the height of the step S standardized by the thickness of the resist film]

The thickness H ₂ of the resist film on the bottom of the step Sb is expressed by the equation (15).

[0037]

H ₂ = a ₂ exp (−λx) + b ₂ exp (λx / 2) cos (√3λx / 2) + c ₂ exp (λx / 2) sin (√3λx / 2) +1 (15) )

Further, the thickness H ₃ of the resist film including the step above Suo on the step is expressed by the equation (16).

[0039]

[Equation 16] H ₃ = a ₃ exp (−λx) + 1 + s (16)

Here, exp (-λx), exp (λx / 2) cos (√3λ) in the above equations (14) to (16).
x / 2), exp (λx / 2) sin (√3λx / 2)
As shown in the equations (17) to (19), ψ ₁ ,
Replace with ψ ₂ , ψ ₃ .

[0041]

## EQU17 ## exp (-λx) = ψ ₁ (17)

[0042]

(18) exp (λx / 2) cos (√3λx / 2) = ψ ₂ (18)

[0043]

## EQU19 ## exp (λx / 2) sin (√3λx / 2) = ψ ₃ (19)

Therefore, the above equations (14) to (16) are
Expressions (20) to (22) are given.

[0045]

H ₁ = b ₁ ψ ₂ + c ₁ ψ ₃ + 1 + s (20)

[0046]

[Equation 21] H ₂ = a ₂ ψ ₁ + b ₂ ψ ₂ + c ₂ ψ ₃ +1 (21)

[0047]

[Equation 22] H ₃ = a ₃ ψ ₁ + 1 + s (22)

The continuous condition at the step is (2
Equations (0) to (22), equations (20) to (22) that have been differentiated once, and equations (20) to (22) that have been differentiated twice are used to determine the continuous condition at the step portion. Obtained by solving as simultaneous equations. That is, equation (20)
The expression obtained by differentiating the expression (22) once is expressed as the expressions (23) to (25).

[0049]

Equation 23] _{H 1 '(x) = b} 1 ψ' 2 + c 1 ψ '3 ··· (23)

[0050]

H ₂ '= a ₂ ψ ₁ ' + b ₂ ψ ₂ '+ c ₂ ψ ₃ ' (24)

[0051]

[Equation 25] H ₃ '= a ₃ ψ ₁ ' (25)

Further, the expressions obtained by differentiating the expressions (20) to (22) twice are expressed as the expressions (26) to (28).

[0053]

[Equation 26] H ₁ "(x) = b ₁ ψ" ₂ + c ₁ ψ " ₃ (26)

[0054]

[Expression 27] H ₂ "= a ₂ ψ ₁ " + b ₂ ψ ₂ "+ c ₂ ψ ₃ " (27)

[0055]

[Equation 28] H ₃ '= a ₃ ψ ₁ "... (28)

Therefore, the step top Sui and the step bottom Sb
The continuous conditions at the step between and are the following formulas (29) to (31).
It looks like an expression.

[0057]

(29) b ₁ ψ ₂ + c ₁ ψ ₃ + s = a ₂ ψ ₁ + b ₂ ψ ₂ + c ₂ ψ ₃ (29)

[0058]

B ₁ ψ ′ ₂ + c ₁ ψ ′ ₃ = a ₂ ψ ₁ ′ + b ₂ ψ ₂ ′ + c ₂ ψ ₃ ′ (30)

[0059]

[Expression 31] b ₁ ψ " ₂ + c ₁ ψ" ₃ = a ₂ ψ ₁ "+ b ₂ ψ ₂ " + c ₂ ψ ₃ "(31)

Further, the continuous conditions for the step difference between the step bottom Sb and the step upper part Suo are expressed by the following equations (32) to (34).

[0061]

[Expression 32] a ₂ ψ ₁ + b ₂ ψ ₂ + c ₂ ψ ₃ = a ₃ ψ ₁ + s (32)

[0062]

[Expression 33] a ₂ ψ ₁ ′ + b ₂ ψ ₂ ′ + c ₂ ψ ₃ ′ = a ₃ ψ ₁ ′ (33)

[0063]

[Expression 34] a ₂ ψ ₁ "+ b ₂ ψ ₂ " + c ₂ ψ ₃ "= a ₃ ψ ₁ " (34)

For example, the above equations (29) to (34) are changed to 6
When the continuous condition at x = ± 1/2 is obtained as an original simultaneous equation, a ₂ , a ₃ , b ₂ , b ₃ , c ₁ , c ₃ are given by the following equations (35) to (40). become.

[0065]

A ₂ = s / 3exp (λ / 2) (35)

[0066]

A ₃ = s / 3exp (λ / 2) −s / 3exp (−λ / 2) (36)

[0067]

B ₂ = 2s · cos (√3λ / 4) / 3exp (λ / 4) (37)

[0068]

B ₁ = 2 [cos (√3λ / 4) / 3exp (λ / 4) -cos (-√3λ / 4) / 3exp (-λ / 4)] (38)

[0069]

C ₁ = 2s [sin (√3λ / 4) / 3exp (λ / 4) -sin (-√3λ / 4) / 3exp (-λ / 4)] (39)

[0070]

C ₂ = 2s · sin (√3λ / 4) / 3exp (λ / 4) (40)

As a result, the above a ₂ , a ₃ , b ₂ , b ₃ ,
By substituting c ₁ and c ₃ into the equations (20) to (22), the step upper part is on Sui, the step bottom part is on Sb, and the step upper part is on Sb.
H ₁ , H ₂ , and H representing the thickness distribution of each resist film on uo
₃ is obtained.

For example, the thickness distribution of the resist film is obtained under the following conditions. The position x of the width w of the underlying step S of the wafer is x = ± 1/2, the height of the step δ = ψ ₁ , the density of the resist ρ = 1.05 g / cm ³ , the surface tension of the resist γ = 29.3 mN / m, the resist film thickness hf at a flat position on the wafer away from the step =
1.0 μm, wafer rotation speed R = 2200 rpm (rotation condition),

As a result, the thickness distribution shown in FIG. 3 was obtained.
In the figure, the vertical axis shows the thickness of the resist film, and the horizontal axis shows the position x of the width w of the underlying step S of the wafer. As shown in FIG. 3, the thickness distribution of the resist film at the step S takes into consideration the influence of the underlying step. Therefore, a distribution state almost equal to the thickness distribution of the resist film obtained by measuring the thickness of the actually applied resist film was obtained.

Next, the second means S12 is performed. here,
The pattern dimension y, which is formed by the resist film 111 and fluctuates due to the thickness distribution of the resist film 111 and the standing wave effect, is obtained by the equation (41).

[0075]

Y = (aχ + b) sin (4nπχ / λ _c + c) + dχ + e (41) [wherein (41), χ: thickness of resist film, n: refractive index of film, λ _c : exposure Wavelength, a, b, _C , d, e: Represents constants for standing wave regression]

That is, the film thickness at a predetermined position of the resist film thickness distribution represented by H ₁ , H ₂ , and H ₃ is given by the above (4)
By substituting for χ in the equation 1), the pattern dimension y at the predetermined position, that is, the line width of the pattern is obtained.

Next, the third means S13 is performed. here,
Dimensional variation is determined from the value of the pattern dimension y obtained above. Here, the dimensional variation is, for example, simply a maximum value y _max of the pattern dimension y and a minimum value y of the pattern dimension y.
Difference from _min . Alternatively, it may be the difference from the average value of the pattern dimensions of multiple calculation points.
Variations in pattern dimensions may be defined.

Next, the fourth means S14 is performed. here,
It is determined whether or not the above dimensional variation is larger than a preset allowable value.

In the above judgment, when the dimensional variation is larger than the allowable value (Yes), the fifth means S1.
By 5, indicate that performed above by changing the angular velocity omega of the wafer set in the first means S11 newly set the angular velocity omega _{new new,} repeated unit of the angular velocity omega _{new new} said first means S11 or later as omega To do.

On the other hand, in the above judgment, when the dimensional variation is less than or equal to the allowable value (No), the sixth means S16.
Thus, the angular velocity ω of the wafer set by the first means S11 is set as the angular velocity of the wafer in the spin coating method.

In the pattern dimension control method described in the first embodiment, the first means S11 determines the resist film thickness distribution from the equations (20) to (22) in consideration of the step difference on the wafer surface. . Then, in the second means S12, the thickness distribution of the resist film obtained and the standing wave effect are taken into consideration (4
Since the dimension of the pattern (for example, the line width) is obtained from the equation 1), the dimension of the pattern corresponding to the surface shape of the wafer can be obtained. Then, the third means S13 obtains a dimensional variation from the dimensions of the pattern, and the fourth means S14 determines whether or not the dimensional variation is larger than the allowable value. If the dimensional variation is large, the resist is applied by spin coating. set the new angular velocity omega _{new new} wafer when forming the film, from doing the new angular velocity omega _{new new} again a first means S11 or later as omega, calculated allowable value or less of the angular velocity omega is. on the other hand,
When the dimensional variation is small, the condition at that time is the angular velocity ω of the wafer. Therefore, the thickness of the resist film is obtained so that the dimensional variation is equal to or less than the allowable value.

Although the angular velocity of the wafer is used in the above control method, the same control can be performed by using the rotational speed of the wafer, for example.

Here, an example in which the line width distribution of the pattern is obtained by the above method of controlling the pattern size is shown in the relationship diagram between the line width of the pattern and the base step in FIG. FIG. 4 shows the line width distribution of a line pattern having a line width of 0.35 μm, which is obtained, for example, under the following conditions. Wafer step difference width w = 150 μm, resist film thickness hf at a flat position on the wafer away from the step =
0.79 μm (however, phase shift is not taken into consideration), height (depth) of stepped portion δ = ψ ₁ = 0.19 μm, distance from wafer center r ₀ = 35.5 mm, wafer rotational speed R = 2200 rpm, shrinking coefficient σ = 0.47, resist surface tension γ = 29.3 mN / m, resist density ρ = 1.05 g / cm ³ , standing wave regression constant a = −0.044221, standing wave Regression constant b = 0.078897, standing wave regression constant c = 2.3209, standing wave regression constant d = 0.1539, standing wave regression constant e = 0.18729, wafer angular velocity ω = 73.3π rad / s.

The results are shown in the relationship diagram between the line width of the pattern and the underlying step in FIG. In the figure, the vertical axis represents the line width, the horizontal axis represents the position x of the width w of the underlying step S of the wafer, and the position x of the width w of the underlying step S is x = ± 1/2. As shown in FIG. 4, under the above conditions, the line width variation is 0.02.
It became 5 μm. On the other hand, as a result of actually spin-coating a resist on the wafer under the above conditions and patterning the resist film, the actually measured line width variation is 0.02.
It was 4 μm. As described above, it was found that the line width variation obtained by the pattern size control method is almost equal to the actual line width variation. Therefore, it is possible to sufficiently predict the line width variation of the pattern size by the above pattern size control method.

Further, when the control method of the first embodiment described with reference to FIG. 1 is operated, the optimum film thickness of the resist film is expected to be the standard film thickness + 0.013 μm, and the pattern dimension ( That is, the variation of the pattern line width) was 0.02 μm. On the other hand, since the conventional line width variation was ± 0.035 μm, it was a significant improvement compared to that.

Next, an example of the first embodiment relating to the pattern size control apparatus of the present invention will be described with reference to the schematic block diagram of FIG.

As shown in FIG. 5, the pattern size control device 1 is provided with a map creation storage section 11 which creates a map of the underlayer shape by storing the position on the wafer and the underlayer shape at that position. . The map creation storage unit 11 divides the wafer surface into, for example, a minute lattice shape, and stores, for example, the depth of the stepped portion with respect to the surface of the wafer as the base shape of each lattice point. As a result, the base shape on the entire surface of the wafer is stored. The method of creating the base shape map on the wafer surface is not limited to the above method, and the base shape map may be created by another method.

A film thickness distribution calculation unit 12 is connected to the map creation storage unit 11. This film thickness distribution calculator 12
Calculates the thickness of the resist film formed by the spin coating method based on the base shape at each position on the wafer stored in the map creation storage unit 11. As the method, for example, the calculation may be performed as described in the first embodiment of the pattern dimension control method. Then, based on the thickness of the resist film at each position on the wafer, a thickness distribution of the resist film within the wafer surface is created.

Further, a dimensional variation calculator 13 is connected to the film thickness distribution calculator 12. The dimension variation calculation unit 13 calculates the dimension of the pattern formed by the resist film, including the fluctuation state due to the standing wave effect. The calculation method may be the same as that described in the first embodiment of the pattern size control method, for example. Further, for example, the difference between the maximum value y _max of the pattern dimension y and the minimum value y _min of the pattern dimension y is calculated to obtain the dimension variation. Alternatively, it may be a difference from the average value of the pattern dimensions of a plurality of calculation points, and the variation of the pattern dimensions may be defined by other criteria.

The dimensional variation calculator 13 includes a judgment unit 1
4 are connected. The determination unit 14 determines whether or not the dimensional variation is larger than a preset allowable value.

The determination section 14 includes a rotation condition instruction section 15
And the coating device command unit 16 are connected. The rotation condition instructing unit 15 functions when the determination unit 14 determines that the dimensional variation is larger than the allowable value, and sets a new rotation condition (for example, rotation speed, angular velocity, etc.) of the wafer, The new rotation condition is instructed to the film thickness distribution calculator 12. As an example of setting the new rotation condition,
The new rotation condition is set by, for example, adding a preset correction amount to the old rotation condition.

On the other hand, the coating device commanding section 16 instructs the spin coating apparatus 31 on the rotation condition of the wafer when the judging section 14 judges that the dimensional variation is less than or equal to the allowable value. Specifically, for example, the wafer 101
Is instructed to the control device 34 that controls the rotation of the motor 33 that rotates the wafer chuck 32 of the spin coating device 31 on which is mounted.

In the pattern size control apparatus according to the first embodiment, since the film thickness distribution calculating section 12 is provided,
The thickness distribution of the resist film in the wafer surface is created in consideration of the base shape of the wafer, particularly the step shape.

Further, since the dimensional variation calculation unit 13 is provided, the thickness distribution of the resist film at the predetermined position of the resist film obtained by the film thickness distribution calculation unit 12 and the standing wave effect generated by the film thickness Put the fluctuation state,
The dimensions of the pattern formed by exposure and development are calculated. Furthermore, the variation in the pattern dimension depending on the thickness of each resist film is required. Therefore, the dimensional variation of the pattern corresponding to the thickness distribution of the resist film can be obtained. Since the determination unit 14 is provided, the magnitude relation between the obtained dimensional variation and the preset allowable value is determined. Then, if the dimensional variation is large, the rotation condition instructing unit 15 sets a new rotation condition, and again, under the new rotation condition,
The thickness distribution calculator 12 calculates the thickness distribution of the resist film.

Therefore, the rotation condition instruction unit 15, the film thickness distribution calculation unit 12, the size variation calculation unit 13, and the determination unit 14 operate until the determination unit 14 reduces the pattern dimension variation to the allowable value or less. Will be done. In this way, the thickness of the resist film in which the dimensional variation of the pattern is within the allowable range is obtained.

The pattern size control device 1 may be configured so that each of the above-mentioned components functions within one arithmetic unit as long as it has the functions of each of the above-described components. That is, it is also possible to configure by an electronic computer having the hardware configuration as described above.

Next, an example of the second embodiment relating to the pattern dimension control method of the present invention will be described with reference to the flowchart of FIG.

As shown in FIG. 6, the thickness H of the resist film formed on the surface of the wafer having a step on the surface by the spin coating method by the first means S21 has been described in the first embodiment. The thickness distribution of the resist film is obtained by obtaining the same condition [Equation (13)] and obtaining the continuity condition of the equation.

Then, in the second means S22, the second means (S1 in the first embodiment of the method for controlling the pattern size) is used.
In the same manner as described in 2), in the resist film, the dimension y of the pattern, which varies depending on the thickness distribution of the resist film and the standing wave effect, is calculated by the equation (41).

Then, in the third means S23, the third means (S1 in the first embodiment of the method for controlling the pattern size).
In the same manner as described in 3), the dimensional variation of the pattern is obtained from the value of the obtained pattern dimension y.

Then, in the fourth means S24, the fourth means (S1 in the first embodiment of the method for controlling the pattern size).
In the same manner as described in 4), it is determined whether or not the above dimensional variation is larger than a preset allowable value.

Next, as a result of the judgment by the fourth means S24, if the dimensional variation is larger than the allowable value, the fifth
Means S25 is performed. In the fifth means S25, the area Aa in which the dimensional variation is larger than the allowable value is compared with the area Ab indicating the limit value of the area in which the dimensional variation is larger than the allowable value, and whichever is larger. To judge.

As a result of the judgment by the fifth means S25, if the area Aa> the area Ab, it means that, for example, even the dummy pattern cannot be arranged. Therefore, by performing the sixth means S26, the wafer rotation conditions set by the first means S21 (for example, angular velocity,
The number of revolutions) is changed and a command is issued to repeat the first means S21 and thereafter.

On the other hand, as a result of the judgment by the fifth means S25, on the other hand, when the area Aa ≦ the area Ab, the seventh means S2
The area in which the dimensional variation becomes large by performing step 7 is the area in which the formation of the actual pattern is prohibited. For example, a dummy pattern is arranged in such a prohibited area.

As a result of the judgment by the fourth means S24, if the dimensional variation is less than the allowable value, the eighth means S28 is carried out to set the area Aa as a real pattern formation area.

In the pattern size control method described in the second embodiment, the first and second means S21 and S22 correspond to the surface shape of the wafer as in the pattern size control method of the first embodiment. Find the dimensions of the pattern. Then, since the pattern dimensional variation is obtained by the third means S23, the pattern dimensional variation corresponding to the surface shape of the wafer can be obtained.

Then, in the fourth means S24, it is judged whether or not the dimensional variation is larger than the allowable value. And the fifth
In step S25, the area Aa in which the dimensional variation is larger than the allowable value is compared with the area Ab indicating the limit value in the area in which the dimensional variation is larger than the allowable value to determine which is larger. To do. For example, when the area Aa> the area Ab, the sixth means S26 changes the wafer rotation conditions (for example, angular velocity, rotation speed, etc.) set by the first means S21, and the first means S21. It issues a command to repeat the following. The rotation condition is changed, for example, by adding a preset correction amount. On the other hand, for example, when the area Aa ≦ the area Ab, in the seventh means S27, the area in which the dimensional variation becomes large is the area in which the formation of the actual pattern is prohibited. On the other hand, the area in which the dimensional variation is small is identified as the area where the actual pattern is formed by the eighth means S28.

As a result, the actual pattern is provided only in the area where the dimensional variation is small, and the actual pattern is not provided in the area where the dimensional variation is large, for example, the dummy pattern is provided. Therefore, the effective dimensional variation of the actual pattern is reduced.

When the control method of the first embodiment described with reference to FIG. 6 is operated, it is 10 μm from the base step S.
The areas up to are areas where the formation of actual patterns is prohibited. When the pattern layout was performed excluding the prohibited region and the line width variation of the formed pattern was examined, the line width variation was 0.010 μm. On the other hand, the line width variation due to the conventional pattern layout is ± 0.0
Since it was 35 μm, it was a great improvement compared with it.

Next, an example of the second embodiment relating to the pattern size control apparatus of the present invention will be described with reference to the schematic block diagram of FIG. In the figure, the same components as those explained in FIG.

As shown in FIG. 7, the pattern size control device 2 includes a map creation storage unit 11 and a film thickness distribution calculation unit 1.
2, a dimensional variation calculation unit 13, and a determination unit 14 are provided. These map creation storage unit 11, film thickness distribution calculation unit 12, dimensional variation calculation unit 13, and determination unit 14
Has the same function as that of the pattern size control device (1) of the first embodiment. Therefore, the detailed description is
Please refer to the description of the embodiment.

An area judgment section 17 and an actual pattern area instruction section 18 are connected to the judgment section 14. Further, the rotation condition instruction unit 15 and the prohibited area instruction unit 19 are connected to the area determination unit 17.

The area judgment unit 17 allows the area width Aa in which the dimensional variation is larger than the allowable value and the dimensional variation when the dimensional variation is judged by the judging unit 14 to be larger than the allowable value. The size is judged by comparing with the width Ab indicating the limit value of the area larger than the value.

When the judgment unit 14 judges that the dimensional variation is smaller than the allowable value, the real pattern area designating unit 18 sets the real pattern (ie,
The pattern forming region functions as an element.

The rotation condition instructing section 15 sets a new rotation condition (for example, rotation speed, angular velocity, etc.) of the wafer when the area judging section 17 judges that the area Aa is larger than the area Ab. Then, the new rotation condition is instructed to the film thickness distribution calculator 12. As an example of a method for setting the new rotation condition, the new rotation condition is set by adding a preset correction amount to the old rotation condition, for example. Although not shown here, the instruction of the new rotation condition is, for example, the wafer (101) as in the control device of the first embodiment.
Is instructed to the control device (34) that controls the rotation of the motor (33) that rotates the wafer chuck (32) of the spin coating device (31) on which is mounted.

When the area judging section 17 judges that the area Aa ≦ the area Ab, the prohibited area instructing section 19 gives an instruction to prohibit the formation of an actual pattern in an area having a large dimensional variation. This is performed by the pattern design device 41.

Like the pattern size control device (1), the pattern size control device 2 is provided with the film thickness distribution calculation part 12 and the size variation calculation part 13 to adjust the thickness distribution of the resist film. Correspondingly, the dimensional variation of the pattern is obtained.

Since the determination unit 14 is provided, the magnitude of the obtained dimensional variation and the preset allowable value is determined. Further, since the area determination unit 17 and the actual pattern area instruction unit 18 are connected to the determination unit 14, the area determination unit 17
Thus, the area Aa in which the dimensional variation is larger than the allowable value is compared with the area Ab indicating the limit value of the area in which the dimensional variation is larger than the allowable value, and it is determined which is larger.

The area determination unit 17 includes a rotation condition instruction unit 1
5 is connected to the prohibited area designating section 19,
When the area determination unit 17 determines that the area Aa is larger than the area Ab, the rotation condition instruction unit 15 sets a new rotation condition (for example, rotation speed, angular velocity, etc.) of the wafer and sets the new rotation condition. The film thickness distribution calculator 12 is instructed. On the other hand, when the area judging section 17 judges that the area Aa ≦ the area Ab, the prohibited area instructing section 19 gives the pattern designing device 41 an instruction to prohibit the formation of an actual pattern in an area having a large dimensional variation. To do. As a result, the pattern that functions as the element pattern is not provided in the region where the dimensional variation is large.

On the other hand, when the judging section 14 judges that the dimensional variation is smaller than the allowable value, the actual pattern area instructing section 18 gives an instruction to arrange the actual pattern in the area. As a result, the actual pattern is arranged only in the area where the dimensional variation is small.

Note that the pattern size control device 2 may have a configuration in which each of the above-described components is made to function in one arithmetic device as long as it has the functions of each of the above-described components. That is, it is also possible to configure by an electronic computer having the hardware configuration as described above.

Next, an example of the third embodiment relating to the pattern dimension control method of the present invention will be described with reference to the flow chart of FIG.

As shown in FIG. 8, in the first means S31, the set mask pattern is generated by the pattern generator.

Then, in the second means S32, the thickness H of the resist film formed on the surface of the wafer having a step on the surface by the spin coating method is set to the first means (S) of the first embodiment.
The thickness distribution of the resist film is obtained by expressing by the same equation as that described in 11) [Equation (13)] and determining the continuous condition of the equation.

Then, in the third means S33, by the same method as described in the second means (S12) of the above-mentioned first embodiment, the thickness distribution of the resist film and the stationary state generated by the exposure using the above mask pattern. The dimension y of the pattern, which fluctuates due to the wave effect, is calculated by the equation (41).

Subsequently, in the fourth means S34, the dimensional variation is obtained based on the obtained value of the pattern dimension y, in the same manner as described in the third means (S13) of the first embodiment.
Here, the dimensional variation is simply obtained, for example, as a difference between the maximum value y _max of the pattern dimension y and the minimum value y _min of the pattern dimension y. For example, the difference between the average value of the pattern dimensions of a plurality of calculation points is obtained. Alternatively, the variation of the pattern dimensions may be defined by other criteria.

Then, in the fifth means S35, it is determined whether or not the dimensional variation is larger than a preset allowable value, as described in the fourth means (S14) of the first embodiment. .

When it is judged by the fifth means S35 that the dimensional variation is larger than the allowable value (Yes), the sixth means S36 is carried out. That is, the first means S
The size of the mask pattern of the pattern generator generated in 31 is corrected to define the size of a new mask pattern, and the new mask pattern size is used to instruct to repeat the first and subsequent steps. As an example of the correction method, the correction amount set in advance is added to the dimension of the old mask pattern.

On the other hand, when the fifth means S35 determines that the dimensional variation is less than or equal to the allowable value (No), the seventh means S37 is performed, that is, the mask pattern set by the first means S31 is set. The dimension value is the mask pattern dimension used for manufacturing.

In the pattern dimension control method of the third embodiment, the standing wave effect is taken into consideration and the wafer surface shape is handled in the same manner as described in the pattern dimension control method of the first embodiment. The dimensions of the pattern that you made can be found. And
Dimensional variations are obtained from the dimensions of the pattern. If the dimensional variation is smaller than the allowable value, the dimension value of the mask pattern at that time becomes the dimension of the mask pattern used for manufacturing. Therefore, the dimensions of the mask pattern within which the variation in the dimensions of the pattern falls within the allowable range can be obtained. On the other hand, when the dimensional variation is larger than the allowable value, the sixth means S36 corrects the dimensions of the mask pattern generated by the pattern generator to define the dimensions of the new mask pattern, and the newly defined mask. The first means S31 and subsequent steps are performed again according to the pattern size. Therefore, the dimension of the mask pattern that minimizes the dimensional variation is determined. Therefore, the dimensions of the mask pattern that minimize the dimensional variation can be obtained.

When the control method of the third embodiment described with reference to FIG. 8 was operated, the distribution of the line width variation of the mask pattern was the reverse of the distribution of the dimension variation of the resist film pattern. Under the conditions obtained by operating the above control method, the dimensional variation of the pattern obtained by patterning the resist film, that is, the line width variation of the pattern was 0.005 μm. On the other hand, the line width variation due to the conventional pattern layout is ± 0.035.
Since it was μm, it was a great improvement compared with it.

Next, an example of the third embodiment relating to the pattern size control apparatus of the present invention will be described with reference to the schematic configuration diagram of FIG. In this figure, the same components as those described in FIG. 5 are designated by the same reference numerals.

As shown in FIG. 9, the pattern size control device 3 includes a map creation storage unit 11 and a film thickness distribution calculation unit 1.
2, a dimensional variation calculation unit 13, and a determination unit 14 are provided. These map creation storage unit 11, film thickness distribution calculation unit 12, dimensional variation calculation unit 13, and determination unit 14
The connection state of is the same as that of the pattern size control device (1) of the first embodiment. The functions of the map creation storage unit 11 and the film thickness distribution calculation unit 12 are the same as those of the first
This is the same as that of the pattern size control device (1) of the embodiment.

A pattern generator 51 for generating a mask pattern is connected to the dimensional variation calculator 13. The dimension variation calculation unit 13 receives the information about the mask pattern from the pattern generator 51. Further, the size of the pattern formed by the resist film is calculated in consideration of the fluctuation state due to the standing wave effect generated by the exposure using the mask pattern generated by the pattern generator 51.
Then, the dimensional variation is obtained from the obtained dimensional value. For example, the calculation may be performed as described in the first embodiment of the pattern dimension control method. Furthermore, for example,
The difference between the maximum value y _max of the pattern dimension y and the minimum value y _min of the pattern dimension y is calculated to obtain the dimension variation. Alternatively, it may be a difference from the average value of the pattern dimensions of a plurality of calculation points, and the variation of the pattern dimensions may be defined by other criteria.

In addition, the judgment unit 14 includes the correction instruction unit 2
0 and the mask pattern instruction unit 21 are connected, and the correction instruction unit 20 is connected to the pattern generator 51. The judgment unit 14 judges whether or not the dimensional variation is less than or equal to the allowable value.

The correction instruction section 20 functions when the dimensional variation is larger than the allowable value, corrects the dimension M of the mask pattern generated by the pattern generator 51, and
The size M _new of the corrected mask pattern is designated as M and is instructed to the pattern generator 51. The correction amount is based on a preset correction amount.

The mask pattern designating section 21 functions when the dimensional variation is equal to or less than the allowable value, and serves to designate the dimension M of the mask pattern generated by the pattern generator 51 to the mask drawing device 61.

In the pattern size control device 3, as in the pattern size control device (1), since the film thickness distribution calculation part 12 and the dimension variation calculation part 13 are provided, the thickness distribution of the resist film can be improved. Correspondingly, the dimensional variation of the pattern is obtained.

Since the determination unit 14 is provided, the magnitude of the obtained dimensional variation and the preset allowable value is determined. Further, since the correction instruction unit 20 and the mask pattern instruction unit 21 are connected to the determination unit 14, the correction instruction unit 21
By this, when the dimensional variation is large, a new mask pattern dimension is set, the new mask pattern dimension is instructed to the pattern generator 51, and the dimensional variation calculation unit 13 calculates the dimensional variation of the pattern again. Then, the process is repeated until the dimensional variation becomes equal to or less than the allowable value, and as a result, the dimension of the mask pattern with less dimensional variation of the pattern is obtained. On the other hand, the determination unit 1
When it is determined by 4 that the dimensional variation is less than or equal to the allowable value, the mask pattern instruction unit 21 instructs the mask drawing device 61 on the mask pattern dimension. Therefore, it is possible to draw a mask pattern in which the dimensional variation of the pattern made of the resist film is minimized.

The pattern size control device 3 may have a configuration in which each of the above-described components is made to function in one arithmetic unit as long as it has the function of each of the above-described components. That is, it is also possible to configure by an electronic computer having the hardware configuration as described above.

Next, an example of the fourth embodiment relating to the pattern dimension control method of the present invention will be described with reference to the flowchart of FIG.

As shown in FIG. 10, in the first means S41,
When a resist film is formed on the surface of a wafer having a step on the surface by a spin coating method, the thickness h of the resist film formed at a flat position on the wafer away from the step
Define f _i (i = 1, 2, ..., M).

Then, in the second means S42, the thickness of the resist film is set to i = 1 type.

Subsequently, in the third means S43, the thickness H of the resist film formed on the surface of the wafer having a step on the surface is set to the pattern size by the spin coating method under the condition that the thickness hf _i of the resist film is obtained. The thickness distribution of the resist film is obtained by the equation (13), which is the same as that described in the first means (S11) in the first embodiment of the control method of FIG. .

Then, in the fourth means S44, the second means (S1 in the first embodiment of the method for controlling the pattern dimension) is used.
In the same manner as described in 2), the dimension y of the pattern, which fluctuates due to the thickness distribution of the resist film obtained above and the standing wave effect, is obtained by the equation (41).

Then, in the fifth means S45, the third means (S1 in the first embodiment of the method for controlling the pattern size) is used.
In the same manner as described in 3), the dimensional variation of the pattern is obtained from the value of the obtained pattern dimension y.

Then, the sixth means S46 judges whether i = m.

Here, in the judgment of the sixth means S46, if i ≠ m (No), the seventh means S47.
Then, i = i + 1 is set, and it is instructed to repeat the third means S43 to the sixth means S46.

On the other hand, in the determination of the sixth means S46, if i = m (Yes), the eighth means S4
8, the thickness hf _i of each resist film (i = 1, 2, ...
, M) and the dimensional variation of the pattern at the thickness hf _i .

Then, in the ninth means S49, the thickness of the resist film having the smallest pattern size variation is determined as the resist film thickness formed on the wafer from the relationship between the pattern size variation and the resist film thickness. To do. As an example of how to obtain the thickness of the resist film in which the pattern dimension variation becomes the smallest, the values of the pattern dimension variation are sequentially compared, and the resist film thickness when the pattern dimension variation value becomes the smallest You should ask.

In the fourth embodiment of the method for controlling the pattern size, the third means S43 to the fourth means S44 are used to correspond to the resist film thicknesses set by the first means S41.
The dimension y of the pattern corresponding to the surface shape of the wafer is determined from the thickness distribution of the resist film obtained by considering the surface state of the wafer and the standing wave effect. Then, the fifth means S45 obtains the dimension variation from the obtained dimension y of the pattern. Then, by repeating the third means S43 to the seventh means S47 until i = m, the eighth means S48 obtains the relationship between the dimensional variation of the pattern and the resist film thickness. Further, by the ninth means S49, the thickness of the resist film having the smallest dimensional variation can be obtained.

The relationship between the pattern dimension variation (line width variation) and the resist film thickness was obtained by the method described in the fourth embodiment of the pattern dimension control method. The result is shown in FIG. In FIG. 11, the vertical axis represents the line width variation of the pattern, and the horizontal axis represents the resist film thickness. Here, the thickness of the resist film (λ: exposure wavelength, n =
1, 2, ...) indicates the position where the value of 6.50 on the horizontal axis is the bottom of the trough where the film thickness variation due to the standing wave effect occurs.
The position where the value on the horizontal axis is 6.50 indicates the position where the film thickness variation due to the standing wave effect is at the top of the peak. As shown in the figure, it was found that the minimum line width variation of the pattern was at the position of 7.05.

Next, an example of the fifth embodiment relating to the pattern dimension control method of the present invention will be described with reference to the flowchart of FIG.

As shown in FIG. 12, in the first means S51,
When a resist film is formed on the surface of a wafer having a step on the surface by a spin coating method, the thickness h of the resist film formed at a flat position on the wafer away from the step
Define f _i (i = 1, 2, ..., M).

Then, in the second means S52, the thickness of the resist film is set to i = 1 type.

Subsequently, in the third means S53, the thickness H of the resist film formed on the surface of the wafer having a step on the surface is measured by the spin coating method under the condition that the thickness hf _i of the resist film is obtained. The thickness distribution of the resist film is obtained by the equation (13), which is the same as that described in the first means (S11) in the first embodiment of the control method of FIG. .

Then, in the fourth means S54, the second means (S1 in the first embodiment of the pattern dimension control method).
In the same manner as described in 2), the dimension y of the pattern, which fluctuates due to the thickness distribution of the resist film obtained above and the standing wave effect, is obtained by the equation (41).

Then, in the fifth means S55, the third means (S1 in the first embodiment of the method for controlling the pattern size).
In the same manner as described in 3), the dimensional variation of the pattern is obtained from the value of the obtained pattern dimension y.

Then, in the sixth means S56, the forbidden area in which the above-mentioned dimensional variation becomes larger than the preset allowable value is obtained, and the size of the forbidden area is obtained. The prohibited area here is defined, for example, as an area formed when a pattern is formed on a wafer in a state where the pattern exceeds an allowable value of variation in pattern dimensions. The size of the prohibited area is defined as, for example, the length of a continuous portion formed in a state in which the allowable value of the variation in the pattern dimension is exceeded.

Then, in the seventh means S57, it is determined whether i = m.

Here, in the judgment of the seventh means S57, if i ≠ m (No), the eighth means S58.
Then, i = i + 1 is set, and it is instructed to repeat the third means S53 to the seventh means S57.

On the other hand, in the determination of the seventh means S57, if i = m (Yes), the ninth means S5
9, the thickness hf _i of each resist film (i = 1, 2, ...
, M) and the size of the prohibited area at the thickness hf _i .

Then, in the tenth means S60, from the relationship between the size of the forbidden area and the thickness of the resist film, the thickness of the resist film that minimizes the size of the forbidden area is set to the thickness of the resist film formed on the wafer. Satoshi As an example of how to determine the thickness of the resist film that minimizes the size of the prohibited area, the values of the sizes of the prohibited areas are sequentially compared, and the resist film when the value of the size of the prohibited area becomes the smallest The thickness of

In the fifth embodiment of the pattern size control method, the third means S53 to the fourth means S54 are used to correspond to the resist film thicknesses set by the first means S51.
The dimension y of the pattern corresponding to the surface shape of the wafer is determined from the thickness distribution of the resist film obtained by considering the surface state of the wafer and the standing wave effect. Then, by the fifth means S55, dimensional variation is obtained from the obtained pattern dimension y. Then, by repeating the third means S53 to the eighth means S58 until i = m, the ninth means S59 obtains the relationship between the size of the prohibited region and the resist film thickness. Further, by the tenth means S60, the thickness of the resist film which minimizes the size of the prohibited area is obtained.

The relationship between the prohibited area and the thickness of the resist film was obtained by the method described in the fifth embodiment of the pattern dimension control method. The result is shown in FIG. FIG.
In the figure, the vertical axis represents the prohibited area, and the horizontal axis represents the resist film thickness. Here, the thickness of the resist film (λ: exposure wavelength, n =
1, 2, ...) indicates the position where the value of 6.50 on the horizontal axis is the bottom of the valley where the sensitivity fluctuation due to the standing wave effect is,
The position where the value on the horizontal axis is 7.00 indicates the position where the sensitivity variation due to the standing wave effect is the top of the mountain portion. As shown in the figure, it was found that the minimum size of the prohibited area was at the position where the thickness of the resist film was 7.15.

[0166]

As described above, according to the invention of claim 1, the first means obtains the thickness distribution of the resist film in consideration of the step difference on the wafer surface, and the second means calculates the thickness of the resist film. Since the size of the pattern is obtained in consideration of the distribution of the height and the effect of standing waves, the size of the pattern corresponding to the step on the wafer surface can be obtained. Further, by obtaining the dimensional variation by the third means, and by comparing the dimensional variation of the pattern with the allowable value by the fourth means and thereafter, the angular velocity condition of the wafer which falls within the allowable value range is obtained. The thickness will be required. Therefore, since it is possible to obtain the resist film thickness within which the dimensional variation of the pattern is within the allowable value, it is possible to form the pattern with high accuracy.

According to the second aspect of the present invention, since the film thickness distribution calculation unit is provided, it is possible to create the resist film thickness distribution within the wafer surface in consideration of the underlayer shape of the wafer, resulting in dimensional variation. Since the calculation unit is provided, it is possible to calculate the size of the pattern in accordance with the thickness distribution of the resist film, including the fluctuation state due to the standing wave effect, and to correspond to the thickness distribution of the resist film. It is possible to obtain the variation in pattern dimensions. Further, since the determination unit and the rotation condition instruction unit for instructing the film thickness distribution calculation unit are provided,
The new rotation condition can be set by the rotation condition instructing unit until the dimensional variation is within the allowable value, and the dimensional variation can be calculated by the film thickness distribution calculating unit and the dimensional variation calculating unit. Therefore, the rotation condition of the wafer within which the dimensional variation of the pattern is within the allowable value is obtained, and the thickness of the resist film can be obtained based on the condition.

According to the third aspect of the invention, similarly to the first aspect of the invention, the thickness distribution of the resist film is obtained in consideration of the step difference on the wafer surface, and the pattern is taken into consideration in consideration of the standing wave effect. Is obtained, the pattern dimension corresponding to the step on the wafer surface can be obtained. Furthermore, by obtaining the dimensional variation by the third means and comparing the dimensional variation of the pattern with the allowable value after the fourth means, the area of the area in which the dimensional variation is larger than the allowable value and the dimensional variation from the allowable value are obtained. By comparing the size of the region in which the maximum value increases with the width indicating the limit value, the size of the region is determined to determine the region where the formation of the actual pattern is prohibited and the region where the actual pattern is formed. Therefore, since it is possible to form an actual pattern in a region where the dimensional variation is within the allowable value, it is possible to form a highly accurate pattern.

According to the invention of claim 4, since the film thickness distribution calculating part and the dimensional variation calculating part are provided, the resist film in consideration of the underlayer shape of the wafer is formed in the same manner as in the invention of claim 2. The size of the pattern corresponding to the film thickness distribution can be calculated by including the fluctuation state due to the standing wave effect. Further, it is possible to obtain the variation of the pattern dimension corresponding to the thickness distribution of the resist film. Further, since a rotation condition instructing unit that gives an instruction to the determination unit, the region determination unit, and the film thickness distribution calculation unit is provided, at least the region in which the dimensional variation is larger than the allowable value is excluded and is equal to or less than the preset limit value. Becomes Therefore, a pattern that functions as an element is not provided in a region that is equal to or less than the limit value and that has a large dimensional variation. On the other hand, an actual pattern area designating section is provided that functions when the dimensional variation is divided into areas where the dimensional variation is below the allowable value. You can Therefore, it is possible to reduce the dimensional variation of the actual pattern, and improve the dimensional accuracy of the actual pattern.

According to the invention of claim 5, the dimension of the pattern corresponding to the step on the wafer surface can be obtained in the same manner as the invention of claim 1. Further, by obtaining the dimensional variation by the fourth means and comparing the dimensional variation of the pattern with the permissible value by the fifth and subsequent means, it becomes possible to obtain the dimensions of the mask pattern within the range of the permissible value.
Therefore, it is possible to obtain a mask pattern size that minimizes the pattern size variation, and thus it is possible to form a highly accurate pattern.

According to the invention of claim 6, since the film thickness distribution calculating portion and the dimension variation calculating portion are provided, the resist film in consideration of the underlying shape of the wafer is formed in the same manner as in the invention of claim 2. The size of the pattern corresponding to the film thickness distribution can be calculated by including the fluctuation state due to the standing wave effect. Further, since the judgment unit and the correction instructing unit for instructing the pattern generator of the dimensions of the mask pattern are provided, the dimensions of the new mask pattern are reset by the correction instructing unit until the dimensional variation is within the allowable value, and the film is formed. The thickness distribution calculation unit and the dimension variation calculation unit can calculate to obtain the dimension variation of the repetitive pattern. Thereby,
Since it is possible to obtain the dimensions of the mask pattern with a small variation in the dimensions of the pattern, it is possible to draw a mask pattern in which the variations in the dimensions of the pattern made of the resist film are within the allowable value by the pattern generator. Therefore, it is possible to reduce the dimensional variation of the pattern and improve the dimensional accuracy of the pattern.

According to the seventh aspect of the present invention, the surface shape of the wafer is determined based on the resist film thickness distribution and the standing wave effect obtained in consideration of the surface condition of the wafer in correspondence with each resist film thickness. Since the dimension of the corresponding pattern is obtained, the dimension variation can be obtained from the dimension of the pattern. Therefore, from the relationship between the resist film thickness and the dimensional variation, it is possible to obtain the resist film thickness with the smallest dimensional variation. Therefore, it is possible to obtain the resist film thickness that minimizes the dimensional variation of the pattern, which enables highly accurate pattern formation.

According to the eighth aspect of the present invention, the surface shape of the wafer is determined from the resist film thickness distribution and the standing wave effect obtained in consideration of the surface condition of the wafer in correspondence with each resist film thickness. Since the dimension of the corresponding pattern is obtained, the dimension variation and its distribution can be obtained from the dimension of the pattern. Furthermore, it is possible to obtain the size of the prohibited area in which the dimensional variation of the pattern is larger than a preset allowable value. Therefore, from the relationship between the resist film thickness and the size of the prohibited area, it is possible to obtain the resist film thickness that minimizes the size of the prohibited area. Therefore,
Since it is possible to obtain the resist film thickness that minimizes the size of the prohibited area, it is possible to form a highly accurate pattern with high density.

[Brief description of drawings]

FIG. 1 is a flow chart of a first embodiment relating to a control method of the present invention.

FIG. 2 is an explanatory diagram of a wafer surface shape.

FIG. 3 is a diagram showing the relationship between the thickness of a resist film and the level difference of a base.

FIG. 4 is a relationship diagram between a line width of a pattern and a base step.

FIG. 5 is a schematic configuration diagram of a first embodiment relating to a control device of the present invention.

FIG. 6 is a flowchart of a second embodiment relating to the control method of the present invention.

FIG. 7 is a schematic configuration diagram of a second embodiment relating to the control device of the present invention.

FIG. 8 is a flowchart of a third embodiment relating to the control method of the present invention.

FIG. 9 is a schematic configuration diagram of a third embodiment related to the control device of the present invention.

FIG. 10 is a flow chart of a fourth embodiment according to the control method of the present invention.

FIG. 11 is a relationship diagram between the line width variation of a pattern and the thickness of a resist film.

FIG. 12 is a flow chart of a fifth embodiment according to the control method of the present invention.

FIG. 13 is a relationship diagram between a prohibited area and the thickness of a resist film.

FIG. 14 is an explanatory diagram of a standing wave effect.

[Explanation of symbols]

 1-3 Pattern Dimension Control Device 11 Map Creation Storage Unit 12 Film Thickness Distribution Calculation Unit 13 Dimensional Variation Calculation Unit 14 Judgment Unit 15 Rotation Condition Indication Unit 16 Coating Device Indication Unit 17 Area Judgment Unit 18 Actual Pattern Area Indication Unit 19 Prohibited Area Instructing unit 20 Correction instructing unit 21 Mask pattern instructing unit 31 Spin coating device 41 Pattern designing device 51 Pattern generator 61 Mask drawing device

[Procedure amendment]

[Submission date] October 4, 1995

[Procedure amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0064

[Correction method] Change

[Correction contents]

For example, the above equations (29) to (34) are changed to 6
When the continuous condition at x = ± _1/2 is calculated as a simultaneous equation, a ₂ , a ₃ , b ₂ , b ₁ , c ₁ , c ₂ are given by the following equations (35) to (40). become.

[Procedure amendment 2]

[Document name to be amended] Statement

[Correction target item name]

[Correction method] Change

[Correction contents]

[0068]

B ₁ = 2s [cos (√3λ / 4) / 3exp (λ / 4) -cos (-√3λ / 4) / 3exp (-λ / 4)] (38)

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0071

[Correction method] Change

[Correction contents]

As a result, the above a ₂ , a ₃ , b ₂ , b ₁ ,
Substituting c ₁ and c ₂ into the equations (20) to (22), the upper part of the step is on Sui, the lower part of the step is on Sb, and the upper part of the step is S.
H ₁ , H ₂ , and H representing the thickness distribution of each resist film on uo
₃ is obtained.

Claims (8)

[Claims] 1. The thickness H of a resist film formed on the surface of a wafer having a step on the surface and rotating at a set angular velocity is expressed as follows: H = 1 + aexp (-λx) + bexp (λx / 2 ) cos (√3λx / 2) + cexp (λx / 2) sin (√3λx / 2) ··· (1) [(1) ^{where, λ = (3Ω 2) 1/3} = {3 (ρω 2 w ³
_{r 0) / (γhf)}} 1/3, x = ( represents the _{r-r 0) / w,} ρ: density of the resist, omega: wafer of the angular velocity, w: wafer underlying step width, r: a wafer center Distance from,
r ₀ is the distance between the center of the wafer and the center of the step, γ is the surface tension of the resist, hf is the resist film thickness at a flat position on the wafer away from the step], and the continuous condition of the equation (1) is obtained. The first means for obtaining the thickness distribution of the resist film, and the dimension y of the pattern formed by the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect. during equation 2 y = (aχ + b) sin (4nπχ / λ c + c) + dχ + e ··· (2) [(2), chi: resist film thickness, n: the refractive index of the film, lambda _c: exposure wavelength , A, b, _C , d, e: representing constants of standing wave regression], a third means for obtaining dimensional variation from the obtained pattern dimension y, and the dimensional variation is preset. Means for judging whether or not it is larger than the allowable value And, when the dimensional variation is larger than the allowable value, changing the angular velocity of the wafer set by the first means to newly set the angular velocity, and instructing to repeat the first and subsequent steps. 5 means, when the dimensional variation is less than or equal to the allowable value, the first
6. A pattern dimension control method comprising: a sixth means for setting a wafer angular velocity set by the means as a wafer angular velocity of a spin coating method. 2. A map creation storage unit that creates a map of the base shape by storing a position on the wafer and the base shape of the wafer at the position, and at each position on the wafer stored in the map creation storage unit. A film thickness distribution calculation unit that calculates a thickness of a resist film formed by a spin coating method and creates a thickness distribution of the resist film in the wafer surface based on the thickness of the resist film at each position, A dimension variation calculation unit that calculates the dimension of the pattern formed by the resist film by including the variation state due to the standing wave effect, and obtains the dimension variation from the difference between the obtained dimension value and the design dimension value of the pattern; A determination unit that determines whether the variation is greater than a preset allowable value; and a wafer when the determination unit determines that the dimensional variation is greater than the allowable value. When a new rotation condition is set and the new rotation condition is instructed to the film thickness distribution calculation unit by the rotation condition instruction unit, and the determination unit determines that the dimensional variation is less than or equal to the allowable value, A pattern dimension control device, comprising: a coating device instructing unit for instructing a spin coating device on a wafer rotation condition. 3. A thickness H of a resist film formed by a spin coating method on a surface of a wafer having a step is expressed by the following formula: H = 1 + aexp (-λx) + bexp (λx / 2) cos (√ 3λx / 2) + cexp (λx / 2) sin (√3λx / 2) ··· (3) [(3) ^{where, λ = (3Ω 2) 1/3} = {3 (ρω 2 w 3
_{r 0) / (γhf)}} 1/3, x = ( represents the _{r-r 0) / w,} ρ: density of the resist, omega: wafer of the angular velocity, w: wafer underlying step width, r: a wafer center Distance from,
r ₀ is the distance between the center of the wafer and the center of the step, γ is the surface tension of the resist, hf is the resist film thickness at a flat position on the wafer away from the step, and the continuous condition of the equation (3) is obtained. The first means for obtaining the thickness distribution of the resist film, and the dimension y of the pattern formed by the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect, during y = (aχ + b) sin (4nπχ / λ c + c) + dχ + e ··· (4) [(4), chi: resist film thickness, n: the refractive index of the film, lambda _c: the exposure wavelength, a , B, _C , d, e: representing constants of standing wave regression], a third means for obtaining dimensional variation from the obtained pattern dimension value, and a predetermined tolerance for the dimensional variation. Areas larger than the value and less than the allowable value A fourth means for dividing the area into areas, and as a result of the judgment made by the fourth means, for the area in which the dimensional variation is larger than the allowable value, the area Aa in which the dimensional variation is larger than the allowable value. And a width Ab, which is a preset width and indicates a limit value of a region in which the dimensional variation is larger than an allowable value, and a fifth means for determining which is wider; As a result of the judgment by the means, when the area Aa> the area Ab, the angular velocity of the wafer set by the first means is changed and a command for repeatedly performing the first and subsequent steps is issued.
And the seventh means for setting the area of the area Aa as an area for prohibiting the formation of the actual pattern when the area Aa is less than the area Ab as a result of the judgment by the fifth means. A pattern dimension control method comprising: an eighth means for setting an area where the dimension variation is equal to or less than the allowable value as an actual pattern formation area. 4. A map creation storage unit for creating a map of a base shape by storing a position on the wafer and a base shape of the wafer at the position, and at each position on the wafer stored in the map creation storage unit. A film thickness distribution calculation unit that obtains the thickness of the resist film and creates a thickness distribution of the resist film in the wafer surface based on the thickness of the resist film at each position, and the dimensions of the pattern formed by the resist film Calculating the fluctuation state due to the standing wave effect to calculate the dimensional variation from the difference between the obtained dimensional value and the design dimensional value of the pattern, and a dimensional variation calculating unit that determines the dimensional variation from a preset allowable value. A determination unit that divides a region that becomes larger and a region that is less than or equal to the allowable value, and a region that has a greater dimensional variation than the allowable value that is determined by the determination unit. The width Aa of the area in which the size is larger than the allowable value is compared with the width Ab that indicates the limit value of the area that is the preset size and in which the dimensional variation is larger than the allowable value. And a region determining unit that determines whether the region Aa is greater than the region Ab, a new rotation condition of the wafer is set, and the new rotation condition is calculated by the film thickness distribution calculation. When the area Aa ≤ area Ab is judged by the rotation condition instruction section for instructing the area and the area judging section, the pattern designing apparatus is instructed to prohibit the arrangement of the actual pattern in the area having the area Aa. A prohibited area instruction section for performing and an actual pattern area instruction section for instructing the pattern design apparatus to recognize the placement of the actual pattern for the area classified by the determination section and having a dimensional variation of not more than an allowable value are provided. Characterized by The control device of the over down dimension. 5. A first means for generating a set mask pattern by a pattern generator, and a thickness H of a resist film formed by spin coating on the surface of a wafer having a step on the surface, H = 1 + aexp (−λx) + bexp (λx / 2) cos (√3λx / 2) + cexp (λx / 2) sin (√3λx / 2) (5) [wherein λ = (3Ω ² ) ^1/3 = {3 (ρω ² w ³
_{r 0) / (γhf)}} 1/3, x = ( represents the _{r-r 0) / w,} ρ: density of the resist, omega: wafer of the angular velocity, w: wafer underlying step width, r: a wafer center Distance from,
r ₀ is the distance between the center of the wafer and the center of the step, γ is the surface tension of the resist, hf is the resist film thickness at a flat position on the wafer away from the step], and the continuous condition of the equation (5) is obtained. By means of the second means for obtaining the thickness distribution of the resist film formed on the wafer surface, and by the standing wave effect generated by the exposure using the mask pattern and the resist pattern. The dimension y of the pattern formed by the resist film is expressed as follows: y = (aχ + b) sin (4nπχ / λ _c + c) + dχ + e (6) [wherein, χ: thickness of resist film] , N: refractive index of film, λ _c : exposure wavelength, a, b, _C , d, e: standing wave regression constant], and a dimension from the obtained pattern dimension value. The fourth means for obtaining the variation and the above-mentioned dimensional variation Fifth means for determining whether or not the deviation is less than or equal to an allowable value, and the size of the mask pattern of the pattern generator generated by the first means when the dimensional variation is greater than the allowable value by the fifth means. Sixth means for correcting and defining a new mask pattern dimension and instructing to repeat the first and subsequent steps; and when the dimensional variation is less than or equal to the allowable value by the fifth means, 7. A pattern dimension control method comprising: a mask pattern dimension for mask pattern manufacturing, wherein the dimension value of the mask pattern is set by one means. 6. A map creation storage section for creating a map of a base shape by storing a position on the wafer and a base shape of the wafer at the position, and at each position on the wafer stored in the map creation storage section. A film thickness distribution calculation unit that obtains a resist film thickness and creates a resist film thickness distribution within the wafer surface based on the resist film thickness at each position; a pattern generator that generates a mask pattern; The dimension of the pattern formed by the resist film is calculated by including the fluctuation state due to the standing wave effect generated by the exposure using the mask pattern, and the dimension variation is calculated from the difference between the obtained dimension value and the design dimension value of the pattern A dimensional variation calculation unit to be obtained, a determination unit that determines whether or not the dimensional variation is less than or equal to a permissible value, and a case where the dimensional variation is greater than the permissible value. A correction instruction unit for correcting the dimensions of the mask pattern generated by the pattern generator and instructing the corrected mask pattern to the pattern generator, and generating in the pattern generator when the dimensional variation is less than or equal to the allowable value. And a mask pattern designating unit for designating the mask pattern to the mask drawing device. 7. When a resist film is formed on the surface of a wafer having a step on the surface by a spin coating method,
First means for defining the thickness hf _i (i = 1, 2, ..., M) of the resist film formed at a flat position on the wafer away from the step; = 1 and a second means for the type eyes, the thickness H of the resist film formed on the wafer by spin coating under the condition that a thickness hf _i of the resist film
Where H = 1 + aexp (−λx) + bexp (λx / 2) cos (√3λx / 2) + cexp (λx / 2) sin (√3λx / 2) (7) [(7) Expression ^{among, λ = (3Ω 2) 1/3} = {3 (ρω 2 w 3
_{r 0) / (γhf)}} 1/3, x = ( represents the _{r-r 0) / w,} ρ: density of the resist, omega: wafer of the angular velocity, w: wafer underlying step width, r: a wafer center Distance from,
r ₀ is the distance between the center of the wafer and the center of the step, γ is the surface tension of the resist, hf is the resist film thickness at a flat position on the wafer away from the step], and the continuous condition of the equation (7) is obtained. By means of a third means for obtaining the thickness distribution of the resist film, and the dimension y of the pattern formed by the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect. during y = (aχ + b) sin (4nπχ / λ c + c) + dχ + e ··· (8) [(8), chi: resist film thickness, n: the refractive index of the film, lambda _c: the exposure wavelength, a , B, _C , d, e: Representing constants of standing wave regression], and a fifth means for obtaining dimensional variation from the obtained pattern dimension value, and it is determined whether i = m. A sixth means for performing the above, and in the case of i ≠ m, i = i + 1 A seventh means for instructing to repeat from unit to said sixth means, in the case of i = m, the thickness hf _i of each of the resist film (i =
, 2, ..., M) and the eighth means for obtaining the relationship between the dimensional variation of the pattern at the thickness hf _i, and the relationship between the thickness and the dimensional variation of the resist film, the film having the smallest dimensional variation. 9. A pattern dimension control method comprising: a ninth means for setting the thickness to be the thickness of a resist film formed on the wafer. 8. When a resist film is formed on the surface of a wafer having a step on the surface by a spin coating method,
First means for defining the thickness hf _i (i = 1, 2, ..., M) of the resist film formed at a flat position on the wafer away from the step; = 1 and a second means for the type eyes, the thickness H of the resist film formed on the wafer by spin coating under the condition that a thickness hf _i of the resist film
H = 1 + aexp (−λx) + bexp (λx / 2) cos (√3λx / 2) + cexp (λx / 2) sin (√3λx / 2) (9) [(9) Expression ^{among, λ = (3Ω 2) 1/3} = {3 (ρω 2 w 3
_{r 0) / (γhf)}} 1/3, x = ( represents the _{r-r 0) / w,} ρ: density of the resist, omega: wafer of the angular velocity, w: wafer underlying step width, r: a wafer center Distance from,
r ₀ is the distance between the center of the wafer and the center of the step, γ is the surface tension of the resist, hf is the resist film thickness at a flat position on the wafer away from the step], and the continuous condition of the equation (9) is obtained. By means of a third means for obtaining the thickness distribution of the resist film, and the dimension y of the pattern formed by the resist film, which varies depending on the thickness distribution of the resist film and the standing wave effect. Y = (aχ + b) sin (4nπχ / λ _c + c) + dχ + e (10) [wherein (10), χ: thickness of resist film, n: refractive index of film, λ _c : exposure wavelength, a , B, _C , d, e: represents constants of standing wave regression], a fifth means for obtaining dimensional variation from the obtained pattern dimension value, and a predetermined tolerance for the dimensional variation. The size of the prohibited area that becomes larger than the value Sixth means for obtaining, Seventh means for judging whether i = m, and, if i ≠ m, set i = i + 1, and give an eighth instruction to repeat the steps from the third means to the seventh means. And i = m, the thickness hf _i (i =
1, 2, ..., M) and the ninth means for obtaining the relationship between the size of the prohibited area at the thickness hf _i and the relationship between the thickness of the resist film and the size of the prohibited area. And a resist film formed on the wafer to have a thickness of the resist film having the smallest thickness.