JP2000232057A - Simulation method for resist pattern and formation method for pattern - Google Patents

Abstract

PROBLEM TO BE SOLVED: To predict variations in dimension and outline of a resist pattern with less data capacity in a short calculation time by introducing calculation for average photosensitive agent concentration distribution on a resist thin film flat surface, by considering influence of standing-wave effect depending on film thickness, refractive index, photosensitive parameter, etc., of resist in a substrate to be exposed. SOLUTION: A mask pattern form, wave length of exposure light, the number of openings of a lens, a lighting condition and a condition of defocus in a data input part 12 are inputted to a light intensity distribution simulator of a processor part 13 to calculate distribution of exposure light applied to a surface of a substrate to be exposed containing a resist layer. Then conditions of quantity of light exposure, film thickness of resist, refractive index, photosensitive parameter, etc., in the data input part 12 are inputted to an average photosensitive agent concentration distribution simulator of the processor part 13, and surface conditions of light intensity distribution of the light intensity distribution simulator is utilized to calculate average photosensitive agent concentration distribution in the resist, and dimension and outline of a resist pattern to be formed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical lithography technique used for manufacturing semiconductor integrated circuits and liquid crystal panels, and more particularly to a method for simulating a contour of a resist pattern formed on a substrate to be exposed and using the method. The present invention relates to a simulation system, a method of designing a layer structure of a substrate to be exposed, and a method of designing a mask pattern.

[0002]

2. Description of the Related Art The following calculation method has been used to predict the shape of a resist pattern formed by optical lithography by simulation.

The first method is a method of predicting the size and contour of a pattern formed by applying a slice level to a light intensity distribution applied to a wafer surface (conventional method 1). The light intensity distribution can be obtained, for example, by using Kodak Microelectronics Seminar Interface '85 (Kodak Microelectronics Seminar Interface).
Modeling Aeri Images in Two and Three Dimensions at Microelectronics Seminar Interface '85
al Images in Two and Three Dimensions)
And the like. In this method, the calculation time is short, and the calculation space is a two-dimensional space parallel to the surface of the substrate to be exposed, so that the data capacity is small, and it is possible to cope with a large-scale pattern over a wide area.

A second method is a method of predicting a pattern shape to be formed by performing a light intensity distribution calculation, a photosensitive agent concentration distribution calculation, a bake diffusion calculation, and a development calculation (conventional method 2). As a simulator using this method, UC
From B (University of California Berkley), IEE Transactions on Electronton Devices, ED 26 (1979)
(IEEE Transactions on Electron Devices, vol.
ED-26, No. 4, April, 1979) A General Simulator for VLSI Lithography and Etching Processing Part One Application to Projection Lithography (A General Simulator for VLSI Lith)
ography and Etching Processes: Part I-App
SAMPLE and SAMPLE described in papers entitled “Lication to Projection Lithography”
-3D and FINLE T
echnologies Inc.) from Inside Prolith (FINLETe)
CHNologies Inc.)) and PROLITH and PROLITH-3D described in a book and the like have been published. Conventional method 2 considers the influence of various parameters of optical lithography, and
It is possible to determine a dimensional shape.

[0005] A third method is based on an aggregate parameter model, the details of which are lithography for buoy.
L.S.I. Chapter 2 V.L.S.
Eye Electronics Microstructure Science Academic Press New York 19
87 (Chapter 2, Lithography for VLSI, VLSIEl
ectronics-Microstructure Science, RKWatts and
NGEinspruch, eds., Academic Press (New Yor
k: 1987)) by Lumped Paramete Model for Optical Lithography
r Model for Optical Lithography) (conventional method 3). This model is based on a simple model for the development speed and a developmental expression for the development process. The effect of development can be considered in a short calculation time.

A fourth method is a simplified method of representing a resist process, and is described in the proceeding of SPII optical microlithography.
2726 (1996) (Proceeding of SPIE, O
Approximate Models for Resist Processing Effects in ptical Microlithography, Vol.2726, 1996)
Resist Processing Effects) (conventional method 4). Simplify the effect of development,
It can be calculated in a short calculation time.

[0007] Optical proximity correction (OP
One of the attempts to perform C) is simulation-based OPC
And, for example, the Proceeding of SPIE Optical Microlithography, Vol. 2726 (1996)
SPIE, Optical Microlithography, vol.2726, 199
6) The Mathematical and CAD Framework for Proximity Collection (Mathematical and CAD Framework for
Proximity Correction). This is a method of correcting the shape of a mask pattern so that a desired pattern is formed based on the light intensity distribution calculated by the conventional method 1.

As another attempt to perform OPC using the conventional method 1, there is a rule-based OPC, which is described in Proceeding of SPIE Optical Laser Microlithography, Vol. 2197 (1).
994) (Proceeding of SPIE, Optical / Laser Mi)
Automated Optical Proximity Collection A Rules Based Approach (crolithography, vol.2197, 1994) (Automated
optical proximity correction-a rules-base
d approach) based on a method described in a paper etc.

A method for directly estimating a pattern shape from a photosensitive agent concentration distribution in a resist is disclosed in Japanese Patent Laid-Open No. Hei 10-25661.
No. 20 discloses this.

[0010]

The problems of the above conventional method for estimating the resist pattern shape are as follows.

In the conventional method 1, it is impossible to predict a change in the pattern shape depending on the resist film thickness, the underlayer structure, the antireflection film and the like.

In the conventional method 2, although the cross-sectional shape of the resist pattern can be obtained, the calculation time is long and the data capacity is large because of the three-dimensional calculation. It is difficult to calculate with

In the conventional methods 3 and 4, the effect of development can be considered, but the change in the resist pattern size and contour due to the effect of the standing wave effect which depends on the resist film thickness, the underlayer structure, the antireflection film, etc. can not predict.

On the other hand, in the simulation-based OPC and the rule-based OPC for performing the optical proximity effect correction based on the above-mentioned conventional method 1, the standing wave effect that depends on the resist film thickness of the substrate to be exposed, the underlayer structure, the antireflection film, and the like. It is not possible to correct the mask pattern shape so as to obtain a desired resist pattern contour in consideration of the influence of the above.

Further, the method described in Japanese Patent Application Laid-Open No. H10-256120 has problems that the method of determining the threshold value is not generalized and that the data capacity is reduced.

An object of the present invention is to reduce the size and contour of a resist pattern due to the effect of a standing wave effect which depends on the setting conditions of a resist film thickness, an underlayer structure, an antireflection film and the like with a short calculation time and a small data capacity. Is to provide a simulation method capable of predicting

Another object of the present invention is to use this simulation method, taking into account the effects of the standing wave effect which depends on the resist film thickness of the substrate to be exposed, the underlayer structure, the antireflection film and the like. An object of the present invention is to provide a method for designing a resist film thickness of a substrate to be exposed and a layer structure and a film thickness of an underlayer, an antireflection film and the like so that a good pattern can be formed.

Still another object of the present invention is to form a good pattern in consideration of the effect of the standing wave effect which depends on the resist film thickness of the substrate to be exposed, the underlayer structure, the antireflection film and the like. An object of the present invention is to provide a method for designing a mask pattern.

[0019]

In order to solve the above problems, the present invention provides a method of forming a resist on a substrate to be exposed.
Refractive index / photosensitive parameter, layer structure / thickness / complex refractive index of underlayer, and thickness / complex refractive index of antireflection film,
The calculation of the average photosensitizer concentration distribution on the plane of the resist thin film is introduced in consideration of the effect of the standing wave effect depending on the like.

That is, the simulation method of the present invention comprises the steps of: inputting a mask pattern shape, a wavelength of exposure light, a numerical aperture of a lens, illumination conditions, and defocus conditions;
The process of calculating the distribution of exposure light applied to the surface of the substrate to be exposed including the resist layer, the amount of exposure, the resist film thickness, refractive index, and photosensitive parameters, the structure, thickness, complex refractive index, and reflection of the underlying layer Inputting the conditions of the thickness / complex refractive index of the prevention film and the complex refractive index of the substrate, and calculating the photosensitive agent concentration distribution in the resist layer, and averaging the photosensitive agent concentration distribution in the depth direction of the resist layer. Calculating an average photosensitizer density distribution, obtaining a developing speed as a function of the photosensitizer density based on the input parameters, obtaining a photosensitizer density threshold corresponding to a predetermined developing speed, Applying a photosensitizer concentration threshold value to the average photosensitizer concentration distribution, numerically calculating a pattern outline after development of the resist, and displaying the pattern outline obtained by the calculation. I do.

Of these, the calculation of the photosensitive agent concentration is as follows.
IEE Transactions on
Electroton Devices ED Volume 22 (1975)
(IEEE Transactions on Electron Devices, vol.
ED-22, No. 7, July, 1975) Characterization of positive photoresist (Ch
First, according to Dill's photosensitive model described in a paper entitled "Aracterization of Positive Photoresist", the concentration distribution M (x, y,
z), and then, as shown in FIG. 2, for the point (x, y), M (z = z _d ) from the upper surface of the resist (z = 0) to the interface between the resist and the underlayer (z = z _d ). (x, y, z) are averaged, and the average photosensitizer concentration M _m (x, y) is obtained by Expression 1.

[0022]

(Equation 1)

Here, z _d is the resist film thickness. This operation is performed for (x, y) in the entire calculation area.

Next, M _m (x, y), we apply a photosensitizer concentration threshold M _th, the case of a positive resist M _m (x,
y) If <M _th , the resist is removed by development and M _m
(X, y)> M _th If even after development the resist is assumed to remain, to calculate the resist pattern dimensions and contours. In the case of a negative resist, this relationship is reversed.

Here, the threshold value of the photosensitive agent concentration is determined by the above Di.
II, Developing Model, or Journal of Electrochemical Society, Volume 134 (1987) (Jo
urnal of Electrochemical Society, vol. 134,
No. 1, January, 1987) Development of Positive Photoresist (Development
The value of the photosensitizer concentration at the inflection point of the development speed curve in the dependence of the development speed on the photosensitizer concentration obtained by Mack's development model and the like described in a paper entitled "Positive Photoresists".

However, when the inflection point is not between 0 and 1 in the photosensitive agent density value, the threshold value disclosed in Japanese Patent Application Laid-Open No. H10-256120, A value whose calculated dimension substantially matches the experimental value is used as the threshold value. This threshold value may be adopted when the inflection point is between the photosensitizer density values of 0 and 1.

In this calculation method, as shown in FIG. 6, the calculation time is about 1/9 to 1/10 as compared with the conventional method 2 for calculating all main steps of optical lithography. In this calculation method, M (x, y) is calculated for a certain (x, y) value.
Immediately after obtaining y, z), the data that must be stored in the calculation process in order to obtain M _m (x, y) by averaging in the depth direction (z direction) of the resist layer according to Equation 1 above. Is not a three-dimensional array M (x, y, z) but a two-dimensional array M _m (x, y). Therefore, the data memory in the computer has almost the same order as the calculation of the light intensity distribution of the conventional method 1.

For example, for a square area of 2.56 μm on a side, the mesh division width in the x and y directions, horizontal to the resist layer, is 0.01 μm, and the depth direction of the resist layer (z direction).
Is assumed to be 120 divisions, since the light intensity distribution calculation in the conventional method 1 is a two-dimensional array, the required number of nodes is 25
6 × 256 = 65536. Further, in this calculation method, if the division of the exposure amount is 103 in addition to the nodes 65536 of the two-dimensional array, the data of the photosensitive agent density table is (the number of divisions of the exposure amount = 103) × (z direction). Number of divisions =
120) to be given by 120). Therefore, the number of nodes required in this calculation method is 65536 + 1236
0 = 77896.

On the other hand, since the conventional method 2 requires a three-dimensional array, the required number of nodes is 256 × 256 × 12
0 = 7864320.

As described above, when the calculation method of the present invention is used, the resist film thickness of the substrate to be exposed, the underlayer structure, and the layers such as the anti-reflection film can be obtained in a substantially as large area as the light intensity distribution calculation of the conventional method 1. In consideration of the influence of the structure, it becomes possible to predict the pattern size and contour formed by optical lithography.

[0031]

DESCRIPTION OF THE PREFERRED EMBODIMENTS As an example of the present invention, a pattern formation by KrF excimer laser lithography will be mainly described here. Also, needless to say, the present invention is not limited by the following embodiments.

(Embodiment 1) FIG. 1 shows a flowchart of a method for simulating a contour of a resist pattern according to the present invention. In the simulation method shown in FIG. 1, in the coordinate system, as shown in FIG. 2, directions parallel to the surface of the substrate to be exposed are x and y coordinates, and directions perpendicular to the surface of the substrate to be exposed are z coordinates.

First, a light intensity distribution I (x, y) applied to the surface of the substrate to be exposed is calculated (Process 1). Next, for a certain (x, y) value, a photosensitive agent concentration distribution M (x, y, z) in the resist layer is calculated, and the average photosensitive agent concentration distribution M _m (x, y) is calculated by the above equation (1). ) Is calculated. This operation is performed for (x, y) in the entire calculation area (process 2). The size and contour of the resist pattern to be formed are calculated by applying the photosensitive agent concentration threshold M _th obtained from the development speed curve and the like to the distribution of M _m (x, y) obtained in the process 2. Processing 3). The I (x, y) obtained in the processing 1, the M _m (x, y) obtained in the processing 2, and the resist pattern dimensions and contour obtained in the processing 3 are displayed (processing 4).

FIG. 3 shows an outline of a simulation system based on the simulation method of the present invention. This system includes a data input unit 12, an arithmetic processing unit 13, and a graph display unit 14. In the light intensity distribution simulation, the data input unit 12 inputs the wavelength of the exposure light, the illumination condition, the numerical aperture of the lens, the mask pattern, and the data of the defocus. The light intensity distribution applied to the surface of the substrate to be exposed through the apparatus is calculated, and a graph display unit 14 is provided.
To display the light intensity distribution on the screen. Regarding the average photosensitive agent concentration distribution simulation, first, the data input unit 12
Enter the exposure conditions, the resist film thickness, the refractive index, the exposure parameters, the thickness of the underlayer, the complex refractive index, the thickness of the antireflection film, the complex refractive index, and the complex refractive index of the substrate. .

Next, the arithmetic processing section 13 uses the light intensity distribution on the surface of the substrate to be exposed obtained by the light intensity distribution simulator as a surface condition, and the average photosensitive agent concentration distribution in the resist and the average photosensitive agent concentration distribution by the average photosensitive agent concentration distribution simulator. Calculate the size and contour of the resist pattern to be formed. Finally, the graph display unit 14 displays the average photosensitizer concentration distribution and the size and contour of the formed resist pattern.

Next, the results of an investigation on the defocus dependency of the dimensional change caused by the standing wave effect using this simulation method will be described.

Here, the dependence of the pattern size on the resist film thickness when a 0.30 μm line / space pattern (binary mask) was transferred to a chemically amplified positive resist using a KrF excimer laser as a light source was calculated. The conditions of the optical calculation were such that the wavelength of the exposure light was λ = 0.248 μm, the numerical aperture NA of the lens was 0.50, and the illumination was ordinary illumination with σ = 0.60. The conditions for calculating the average photosensitive agent concentration distribution are as follows: exposure dose: Dose = 170 mJcm ⁻² , resist: APEX-E (S
The photosensitive parameters of Dill are A
= −0.01 μm ⁻¹ , B = 0.362 μm ⁻¹ , C = 0.0
033 cm ² / mJ, the refractive index of the resist is N _Resist = 1.7
4. The complex refractive index of the substrate Si is n _Si = 1.56-i · 3.
565. The photosensitizer concentration threshold is Mac
M _th = 0.80 obtained by the k model was used.

FIG. 7 shows the dependency of the resist pattern dimension CD on the resist film thickness calculated under the above conditions (swing and swing).
Curve). The amplitude of the swing curve was 0.096 μm when the defocus df was 0.0 μm, and 0.134 μm when the defocus df was 0.5 μm. From FIG. 7, it was found that under the conditions of the present example, there was a resist film thickness having a constant dimension regardless of the change in defocus.

FIG. 8 shows the dependence of the swing curve amplitude ΔCD on the defocus under the above conditions. As the defocus increased, the value of ΔCD also increased, and the slope of the curve became steeper. Δ when defocus is 0.6 μm
The CD was 0.159 μm, which was about 1.66 times that of the best focus.

FIG. 9 shows the dependency of the maximum value M _m (x _max ) and the minimum value M _m (x _min ) of the average photosensitive agent concentration M _m (x) at a certain resist film thickness on the resist film thickness under the above conditions. The results obtained in are shown. Here, the pitch direction of the line / space pattern is the x direction, and x _max and x _min are:
It is assumed that M _m (x) is the x coordinate at which the maximum and the minimum are obtained.

Comparing FIG. 9 with FIG. 7, M _m (x _max ) and M _m (x _max ) are obtained when the resist pattern dimension CD to be formed has a maximum resist film thickness regardless of the defocus value.
_m (x _min ) was maximized, and M _m (x _max ) and M _m (x _min ) were minimized at the resist film thickness at which CD was minimized. Under the conditions of this embodiment, M _m (x _min ) has a larger change with respect to the resist film thickness, and M _m (x _max ) has a larger change with respect to defocus.

Here, the maximum value M _m (x
_max ) and the minimum value M _m (x _min ) are applied to the equation of the optical contrast to define the equation of the average photosensitive agent density contrast as the following equation (2).

[0043]

(Equation 2)

FIG. 10 shows the dependency of the average photosensitizer density contrast Count _Mm obtained by the _{equation 2 on} the resist film thickness. When FIG. 10 is compared with FIG. 7, the Count _Mm is maximum and minimum when the resist pattern size is the minimum and maximum resist film thickness. Defocus is 0.5 μm
_Had lower Count _Mm .

As described above, it has been shown by the average photosensitive agent density model that the width of dimensional variation increases due to the influence of defocus and the average photosensitive agent density contrast decreases.
Further, under the conditions of the present embodiment, the resist film thickness z _d (for example, z _d = 0.83
0 μm), it was shown that the resist film thickness can be set so as to minimize the influence of dimensional fluctuation due to defocus.

(Embodiment 2) In Embodiment 2, an example will be described in which the threshold value of the photosensitive agent concentration is set based on the dependency of the developing speed on the photosensitive agent concentration. Here, an i-line resist whose development parameters are well known is targeted. In the above-mentioned Dill's development model, the dependency of the development speed on the photosensitive agent concentration M is given by Equation 3.

[0047]

(Equation 3)

FIG. 4 shows that the developing speed parameter is E ₁ = 5.
96 shows the result of calculating the developing speed of the resist in which E ₂ = −1.19 and E ₃ = −2.27. As shown in FIG. 4, the inflection point of the curve is around the photosensitive agent concentration of 0.3. Therefore, the threshold value M _th of the photosensitive agent concentration of this resist was set to 0.3.

Next, an example of a simulation of pattern formation using this resist will be described. The mask pattern was a 0.36 μm isolated hole pattern. The condition of the light intensity distribution calculation is that the wavelength of the exposure light λ = 0.365μ
m, numerical aperture of the lens NA = O. 55, illumination is σ = 0.3
, And the defocus df = 0.0 μm. The condition for calculating the average photosensitive agent density distribution is that the exposure amount Dose = 1
50 mJ / cm ² , Dill's photosensitive parameter is A = 0.7
4 μm ⁻¹ , B = 0.20 μm ⁻¹ , C = 0.012 cm ² / m
J, the refractive index n _{Resist of the} resist was 1.72, and the complex refractive index n _Si of the substrate Si was 6.50-i · 2.61.

FIG. 5 shows the average photosensitizer concentration distribution obtained under the above conditions. In FIG. 5, the contour lines are M
_m (x, y) = 0.9, 0.8, 0.7, 0.6,.
5, 0.4, 0.3 and 0.2. Here, the contour line of 0.3 corresponding to the threshold value is displayed thick, and represents the contour of the pattern to be formed. Here, since the resist is a positive resist, the value of M _m (xy) is 0.3.
The following places correspond to the areas where the resist is removed.
FIG. 5A shows the resist film thickness z _{d at} which the hole size is maximized.
FIG. 2B shows the case where the resist film thickness z _d = 1.06 μm at which the hole size is minimized. By applying the threshold value 0.3 set using FIG. 4 to the average photosensitizer concentration distribution shown in FIG. 5, the hole contour formed in consideration of the influence of the resist film thickness could be predicted.

Next, the calculation time will be described. It is assumed that the mask pattern is a 0.40 μm line / space pattern. The calculation conditions were the same as in the example shown in FIG. 5 except for the mask pattern. The development time was 90 s. FIG. 6 shows the CPU (Central P
The results obtained by measuring the dependence of the calculation area length on the processing area length using a large-scale computer M-880 (manufactured by Hitachi, Ltd.) are shown.
Although the CPU time varies slightly depending on the length of the calculation region, the present calculation method does not require the cross-sectional shape of the pattern, but the conventional method 2 for calculating all the main steps of optical lithography.
Could be calculated in about 1/9 to 1/10 of the time. By such a short calculation, the pattern contour to be formed could be predicted in consideration of the effect of the standing wave effect depending on the resist film thickness of the substrate to be exposed, the underlayer structure, the antireflection film, and the like.

(Embodiment 3) In Embodiment 3, the effect of the antireflection film on the substrate to be exposed is examined by the simulation method shown in Embodiment 1.

FIG. 11 shows a substrate to be exposed which is handled in this embodiment. Here, the complex refractive index of the TARC layer 16 is 1.7.
9-i · 0.47, the complex refractive index of the BARC layer 18 is 1.
79-i · 0.47, and the complex refractive index of the SiO 2 layer 22 was 1.51-i · 0.0. The mask pattern is a 0.28 μm isolated hole pattern (transmittance 6.0).
% Opening pattern on a halftone mask).

The calculation conditions of the light intensity distribution applied to the surface of the substrate to be exposed are as follows: exposure wavelength λ = 0.248 μm, lens numerical aperture NA = 0.60, coherence factor σ = 0.
40 (normal illumination) and defocus df = 0.0. The conditions for calculating the average photosensitizer concentration distribution are as follows:
Dose = 200 mJ / cm ^2, and all other necessary input parameters were assumed to be the same as in the first embodiment.

In order to evaluate the effects of the upper antireflection film TARC layer 16 and the lower antireflection film BARC layer 18 on the layer structures 1 and 2 shown in FIG.
None, without BARC (Case 1) "," with TARC
No BARC (Case 2) "," No TARC / BAR "
Dependence of formed hole size on resist film thickness (swing curve) in four cases of "with C (case 3)" and "with TARC / with BARC (case 4)"
Was calculated. The result is shown in FIG. Then, the influence of the difference in the layer structure and the difference in the intra-film interference effect due to the presence or absence of the antireflection film on the formed hole diameter was examined.

When there is no anti-reflection film (Case 1), the dimensional fluctuation caused by the standing wave effect is large in any layer structure.
In addition, the resist film thickness at which the size becomes maximum and minimum is different when the layer structure is different. Dimension fluctuation range (Swing ・
The curve amplitude) is 0.062 μm in the case of the layer structure 1,
In the case of the layer structure 2, it could be predicted to be 0.064 μm.

In case 2, the size shifted to the larger one. The dimensional variation with respect to the resist film thickness is much smaller than in Case 1. Swing curve amplitude is layered structure 1.
In each case of the layer structure 2, the thickness was 0.006 μm.

In case 3, the dimension shifted to the smaller one. Dimensional variation width for resist film thickness change is case 1
Considerably smaller, but slightly larger than Case 2. The amplitude of the swing curve is 0.01 for the layer structure 1.
5 μm, and 0.011 μm in the case of the layer structure 2.

In case 4, the dimensions have shifted to smaller ones. The width of the dimensional variation is the smallest among the four antireflection conditions. The amplitude of the swing curve is 0.002 μm in each of the layer structures 1 and 2.

As described above, the effect of the antireflection film could be quantitatively evaluated as the dimensional variation in consideration of the effect of the standing wave effect by the simulation method shown in the first embodiment.

(Embodiment 4) In Embodiment 4, the layout method using a negative resist is examined by using the simulation method shown in Embodiment 1, and exposure is performed so that desired pattern dimensions and contours are obtained. A method for setting the resist film thickness of the substrate will be described.

The conditions for calculating the light intensity distribution applied to the surface of the substrate to be exposed are as follows: exposure wavelength λ = 0.248 μm, lens numerical aperture NA = 0.45, illumination σ = 0.3, defocus df = 0.0 μm. The conditions for calculating the average photosensitive agent concentration distribution were as follows: exposure dose: Dose = 180 mJ / cm ² , resist: chemically amplified negative resist XP-8843, photosensitive parameters of Dill: A = −0.92 μm ⁻¹ , B = 1. 55
μm ⁻¹ , C = 0.0020 cm ² / mJ, the refractive index of the resist is n _Resist = 1.76, and the complex refractive index of the substrate Si is n _Si =
1.56-i · 3.565. The threshold value of the photosensitizer concentration used was M _th = 0.90.

FIG. 13 shows the mask pattern used here. In FIG. 13, as shown in the figure, a white polygon is an opening mask having a phase of 0 °, a polygon hatched by oblique lines is an opening mask having a phase of 180 °, and the other portions are light shielding portions. FIG. 14 shows a layer structure of a wafer to which this pattern is transferred. The layer structure A and the layer structure B are arranged adjacent to each other as shown in FIG.

FIG. 16 shows the result of a simulation of the layout pattern formation using a negative resist under the above conditions, using an average photosensitive agent concentration model. The contour lines of the average photosensitive agent concentration are 0.95 and 0.9 in order from the outside.
0, 0.85, 0.80, 0.75, 0.70, 0.6
5, 0.60. The contour line of 0.90 corresponding to the threshold value is shown in bold, and represents the contour of the formed resist pattern. Here, since the resist is of a negative type, a portion where the average photosensitizer concentration is 0.90 or less corresponds to a region where the resist remains.

FIG. 16A shows the case where the resist film thickness z _d = 0.745 μm in which the dimensions of the layer structure A and the layer structure B match. At this time, the patterns formed on the layer structure A and the layer structure B both had the same dimensions. On the other hand, FIG.
In the case of the resist film thickness z _d = 0.760 μm at which the difference between the pattern dimensions formed on the layer structure A and the layer structure B is maximized. In this case, the pattern size formed on the layer structure A was small, and the pattern size formed on the layer structure B was large.

As described above, the resist film thickness can be set so as to suppress a dimensional difference due to a difference in layer structure.

(Embodiment 5) In the fifth embodiment, using the simulation method shown in the first embodiment, an image distortion depending on the substrate structure is predicted, and a mask pattern shape correcting method for correcting this distortion is used. Is shown.

The mask pattern to be calculated is shown in FIG.
And a rectangular pattern having a vertical length of 1.0 μm and a line width of 0.26 μm. Here, the white area is an aperture mask that transmits light, and the hatched area represents a chrome film that does not transmit light. There are two types of layer structures on the substrate to which the mask pattern is transferred, as shown in FIG. 14, which are arranged adjacent to each other as shown in FIG. The resist film thickness was set to z _d = 0.792 μm. Other conditions for light intensity distribution calculation and average photosensitizer concentration distribution calculation are as follows:
It was assumed to be the same as Example 3.

FIG. 19A shows the average photosensitive agent density distribution obtained by the simulation (in the case of a mask pattern before correction).
Shown in The line width on the layer structure B is smaller. In this case, in order to form a desired pattern, the line width of a portion to be transferred on the layer structure B may be corrected widely as shown in FIG. Here, the white area is an aperture mask that transmits light, and the hatched area represents a chrome film that does not transmit light. FIG. 19 (b) (in the case of a corrected mask pattern) shows the average photosensitive agent density distribution when the pattern thus corrected is transferred. By correcting the line width of the pattern transferred to the layer structure B, the difference in the pattern size due to the difference in the layer structure could be suppressed.

[0070]

The photosensitive agent concentration distribution in the resist thin film in the substrate to be exposed contains information on the standing wave effect in the resist layer which depends on the thickness of the resist, the structure of the underlayer, and the conditions of the antireflection film and the like. It is included. By averaging this photosensitive agent concentration distribution in the depth direction of the resist layer, it is possible to predict the dimensional fluctuation caused by the standing wave effect. It can be predicted that they differ depending on conditions such as. Using this simulation method, the layer structure of the substrate to be exposed can be designed so that a desired pattern can be formed. This simulation method can be used as a tool for proximity effect correction in consideration of the influence of the layer structure of the substrate to be exposed.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a simulation method according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram showing modeling of a resist pattern line width.

FIG. 3 is a block diagram showing a configuration of a simulation system according to the present invention.

FIG. 4 is a diagram showing the dependency of a developing speed on a photosensitive agent concentration.

FIG. 5 is an explanatory diagram showing contour lines of an average photosensitive agent concentration and a contour of a formed resist pattern.

FIG. 6 is a diagram showing dependence of CPU time on a calculation area length.

FIG. 7 is a view showing the dependency of the resist pattern dimension on the resist film thickness.

FIG. 8 is a view showing the defocus dependency of a dimensional variation width.

FIG. 9 is a diagram showing the dependency of the maximum value and the minimum value of the average photosensitive agent concentration on the resist film thickness.

FIG. 10 is a graph showing the dependence of the average photosensitive agent concentration contrast on the resist film thickness.

FIG. 11 is a cross-sectional view illustrating an example of a layer structure of a substrate to be exposed.

FIG. 12 is a diagram showing the dependence of the formed hole size on the resist film thickness.

FIG. 13 is a plan view showing a layout pattern.

FIG. 14 is a cross-sectional view illustrating a layer structure of a substrate to be exposed.

FIG. 15 is a plan view showing an arrangement of a layer structure on a substrate to be exposed.

FIG. 16 is a diagram showing contour lines of an average photosensitive agent concentration distribution and a contour of a formed resist pattern.

FIG. 17 is a plan view showing a mask pattern shape before correction.

FIG. 18 is a plan view showing a mask pattern shape after correction.

FIG. 19 is a diagram showing contour lines of an average photosensitive agent concentration and a contour of a formed resist pattern.

[Explanation of symbols]

Reference numeral 5: upper layer film, 6: resist layer, 7: lower layer film, 8: Si substrate, 9: exposure light, 10: contour line of photosensitive agent concentration, 11: average photosensitive agent concentration distribution, 12: data input section, 13: arithmetic operation Processing unit, 14: Graph display unit, 16: Upper anti-reflective coating (T
ARC), 17: resist layer, 18: lower antireflection film (BARC), 22: SiO ₂ layer, 23: Si substrate, 2
4 ... layer structure A, 25 ... layer structure B

 ──────────────────────────────────────────────────続 き Continued on the front page F term (reference) 2H096 AA25 LA17 LA19 LA30 5B046 AA07 DA01 GA01 JA04 5F046 CB05 DA01 DA02 DA14 DB05 DB10 DB14 JA21 JA22 LA14 LA18

Claims (11)

[Claims] In a simulation method for irradiating an energy ray having pattern information on a resist thin film formed on a substrate to be exposed and predicting a contour of a resist pattern obtained after a development process, a mask pattern shape, energy ray Inputting a wavelength, a numerical aperture of a lens, illumination conditions, and defocus conditions; calculating an energy ray distribution applied to the surface of the substrate to be exposed including the resist thin film; Inputting conditions of thickness, refractive index, photosensitive parameters, structure, thickness, complex refractive index of the underlayer, thickness, complex refractive index of the antireflection film, and complex refractive index of the substrate; Calculate the agent concentration distribution,
Calculating the average photosensitizer concentration distribution by averaging the photosensitizer concentration distribution in the depth direction of the resist layer; obtaining a developing speed as a function of the photosensitizer concentration based on input parameters; Obtaining a corresponding photosensitizer concentration threshold; and numerically calculating a pattern contour after development of the resist by applying the photosensitizer concentration threshold to the average photosensitizer concentration distribution. Displaying a contour of the patterned pattern. 2. The simulation method according to claim 1, wherein the energy beam having the pattern information is an energy beam that transmits through a mask and forms a mask pattern projected image on a substrate to be exposed via a projection lens. A method of simulating a contour of a resist pattern. 3. The simulation method according to claim 1, wherein the step of determining the photosensitive agent concentration threshold value comprises the step of: determining a photosensitive agent concentration value at an inflection point of a developing speed curve indicating a developing agent speed dependency on the photosensitive agent concentration. Setting a threshold value as a threshold value. 4. The simulation method according to claim 1, wherein the step of determining the photosensitive agent concentration threshold value sets the threshold value such that a dimension obtained by calculation at a given exposure dose matches an experimental value. A method for simulating a resist pattern. 5. A simulation system for irradiating an energy beam having pattern information on a resist thin film formed on a substrate to be exposed and predicting a contour of a resist pattern obtained after a development process, wherein a mask pattern shape, an energy beam Means for inputting the wavelength, numerical aperture of the lens, illumination conditions, and defocus conditions; means for calculating the distribution of energy rays applied to the surface of the substrate to be exposed including the resist layer; Means for inputting conditions of thickness, refractive index, photosensitive parameters, structure, thickness, and complex refractive index of the underlayer, thickness and complex refractive index of the antireflection film, and complex refractive index of the substrate; Means for calculating an agent concentration distribution, averaging the photosensitive agent concentration distribution in the depth direction of the resist layer to calculate an average photosensitive agent concentration distribution; Means for determining a developing speed as a function of density; means for determining a photosensitizer concentration threshold corresponding to a predetermined developing speed; and applying the photosensitizer density threshold to the average photosensitizer density distribution to obtain the resist. A resist pattern simulation system, comprising: means for numerically calculating a pattern outline after development; and means for displaying a pattern outline obtained by the calculation. 6. A step of calculating a contour of a resist pattern formed by an existing mask pattern by the simulation method according to claim 1 in consideration of a resist film thickness, an underlayer structure, an antireflection film, and the like. Setting the layer structure and the thickness of each layer of the substrate to be exposed including the resist layer, the underlayer, and the antireflection film by comparing the calculation results with desired dimensions and contours. To design a substrate to be exposed. 7. The method for designing a substrate to be exposed according to claim 6, wherein the area irradiated by one opening pattern has two areas.
The process of comparing the pattern dimensions and contours on each substrate structure when crossing over more than one type of substrate structure, and the table of the calculation results of the correlation between the pattern dimensions and the layer structure and film thickness, from the table of the pattern dimensions on each substrate structure Setting a layer structure, a film thickness, and the like of the substrate to be exposed so that the contour has desired dimensions and contours. 8. A substrate to be exposed and a semiconductor device designed by the method for designing a substrate to be exposed according to claim 6. 9. A step of calculating dimensions and contours of a resist pattern formed by an optical lithography technique in consideration of the influence of a resist film thickness, an underlayer, an antireflection film, etc., by the simulation method according to claim 1. Based on the table of the calculation results of the correlation between the pattern dimensions and the layer structure, the film thickness, and the opening mask shape, the mask opening pattern shape is deformed and designed so as to obtain the desired resist pattern size and contour. And a method of designing a mask pattern. 10. The mask pattern designing method according to claim 9, wherein one opening pattern is transferred to two areas.
In the case of extending over a plurality of types of substrate structures, a process of comparing the pattern dimensions on each substrate and a table of a calculation result of a correlation between the pattern dimensions and the layer structure, the film thickness, and the opening mask shape are used. Deforming the shape of the mask opening pattern so as to obtain the pattern dimensions and contours. 11. A mask designed by the mask pattern designing method according to claim 9.