JPH07239546A - Method for designing translucent film - Google Patents

Abstract

PURPOSE:To provide a method for designing a translucent film capable of recognizing the conventional translucent phase shift film not by indirect information, such as phase difference and transmittance but by more concrete information, such as refractive index, attenuation coefft. and film thickness with exactness and elucidating the permissible ranges thereof. CONSTITUTION:The phase difference phi and transmittance (t) obtd. by multiple reflection calculations using an arbitrary coefft. (k) and film thickness (d) are calculated for an arbitrary refractive index (n) by considering this (n) as a fixed value in the method for designing the translucent film which determines the refractive indexing, attenuation coefft. (k) and film thickness (d) of the translucent film. The error between the desired value and the calculated value for the phase difference phi is reduced to the film thickness (d) and the error between the desired value and the calculated value for the transmittance (t) is reduced to the attenuation constant (k). The refractive index (n), attenuation coefft. (k) and film thickness (d) satisfying the desired phase difference phi and transmittance (t) are rapidly and accurately determined by repeating the multiple reflection calculation and reduction.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a lithographic technique in a manufacturing process of a semiconductor device, and particularly, to determine a refractive index n, an extinction coefficient k and a film thickness d of a semitransparent film used for forming a phase shift mask. Design method for doing.

[0002]

2. Description of the Related Art With the progress of semiconductor technology, semiconductor devices, and thus semiconductor elements, are becoming highly integrated and miniaturized. When manufacturing this semiconductor element, the lithography technique is particularly important as a cornerstone of processing. In the current lithography technology, the mask pattern is transferred to the LSI through the reduction optical system.
A method of projection exposure on a substrate is mainly used.

In such a lithography technique,
The miniaturization is greatly restricted by the exposure wavelength λ, and it has been very difficult to form a pattern of a wavelength or less. This is because in a pattern having almost the same size as the wavelength, interference occurs between adjacent patterns, the light intensity is in a region originally desired to be formed as a dark portion, and the light amount difference between the dark portion and the bright portion hardly occurs. . Therefore, when a pattern is formed on an LSI substrate using an arbitrary wavelength, the minimum line width is 1.
I had no choice but to limit the size to about four times.

By the way, the minimum line width required for recent LSIs is 64 MdRAM, 0.35 μm, and 256 Mm.
It is set to 0.25 μm in dRAM. In order to realize these dimensions by the conventional lithography technique, a KrF laser is used as an exposure light source for a minimum line width of 0.35 μm,
For the minimum line width of 0.25 μm, it becomes necessary to deal with it with an ArF laser. However, when these light sources are used, it is necessary to develop corresponding resists, but these resists are still in the research process, and it takes a considerable time for practical use. Although it is not impossible to replace the exposure light source with EB, the throughput is significantly reduced as compared with the exposure using light, which is not practical. For these reasons, in place of the conventional shortening of the wavelength of the exposure light source, a method of promoting miniaturization without changing the exposure wavelength λ has come to be considered.

As a technique for achieving this purpose, Japanese Patent Laid-Open No. 4 (1999) -242242
There is a halftone type phase shift method which does not require a device design change, as described in Japanese Patent Laid-Open No. 136854. To maximize the effect of this phase shift method,
The phase difference φ and the transmittance t of the light transmitted through the transparent portion and the semi-transmissive film.
It is important to optimize. These optical variables can be easily optimized by simulation or the like.

Conventionally, the semi-transparent phase shift mask is made of a two-layer film, but this method is easy to make because the phase difference φ and the transmittance t are controlled independently. However, in the two-layer structure, an increase in the number of steps has been a problem since the film forming step and the etching step are required twice. Further, when a defect occurs in the lower layer film, there is a problem that it is difficult to correct. On the other hand, Japanese Patent Laid-Open No. 4-136854 also describes a semi-transparent phase shift film having a single layer structure. Similarly, JP-A-4-162039 also discusses a semi-transparent phase shift film having a single layer structure.

In these publications, a single-layer semitransparent phase shift film is formed by mixing a dye into the coated glass. In this method, the transmittance was adjusted with a dye and the phase difference was adjusted with a coated glass. Further, Japanese Unexamined Patent Publication (Kokai) No. 5-127361 also describes a single-layer semitransparent film, but the thickness of the semitransparent film has a phase relationship of 2π ( From the relationship of dn / λ-d / λ) = π, the thickness d is set to d = λ / 2 (n-1).

However, this type of method has the following problems. That is, in the method of forming a single-layer semitransparent phase shift film by mixing a dye in the coated glass, the transmittance was adjusted by the dye and the phase difference was adjusted by the coated glass. This method does not describe a specific method for determining the refractive index, extinction coefficient, and film thickness necessary to obtain the desired transmittance and phase difference, and it is not Was lacking in credibility. On the other hand, the method in which the film thickness of the single-layer semi-transparent film is d = λ / 2 (n−1) does not consider the effect of the extinction coefficient on the phase difference, and the phase shift caused by the multiple reflection. However, the reliability of transmittance and phase difference was lacking.

[0009]

As described above, conventionally, when a semitransparent phase shift film is formed of a single layer, it is essential to match the phase difference φ and the transmittance t to desired values. For this purpose, it is necessary to quickly and rigorously determine the possible relationship among the desired transmittance t and the phase difference φ of the semitransparent film at the exposure wavelength λ with respect to the refractive index n, the extinction coefficient k, and the film thickness d. However, a method of designing a semitransparent film that satisfies this has not yet been proposed.

The present invention has been made in consideration of the above circumstances, and its purpose is to provide a single layer film with an amplitude transmittance t.
It is to provide a method of designing a semitransparent film that can accurately and promptly determine the conditions of the refractive index n, the extinction coefficient k, and the film thickness d of the semitransparent film that satisfy the conditions of the phase difference φ and the phase difference φ. .

[0011]

In order to solve the above problems, the present invention employs the following configurations.

That is, the present invention (claim 1) is a method of designing a semitransparent film for optimally setting the refractive index n, the extinction coefficient k, and the film thickness d of the semitransparent film. Exposure wavelength λ of the semitransparent film for an arbitrary refractive index n at λ
And the initial values of the extinction coefficient k and the film thickness d, the refractive index n of the semitransparent film, the extinction coefficient k, the film thickness d, and the refractive index and the extinction of the substrate and air on which the semitransparent film is formed. Considering the multiple reflection from the coefficient and film thickness, the step of calculating the transmissivity tc of the semitransparent film and the phase difference φc of the light passing through the transparent portion and the semitransparent film, and the calculated transmissivity tc and the phase difference φc are desired. And a step of resetting the extinction coefficient k and the film thickness d from the phase error and the transmittance error obtained by the comparison, respectively. Based on the thickness d and the extinction coefficient k, the calculation process and the comparison process of the transmittance tc and the phase difference φc are performed, and the resetting is performed until both the transmittance tc and the phase difference φc match the desired values φ and t. The step of performing, the step of calculating, and the step of comparing are repeated.

The preferred embodiments of the present invention are as follows.

(1) The initial value of the film thickness d is d = φλ / (360 (n-1)) with respect to the desired phase difference φ (degrees) at the exposure wavelength λ and the refractive index n of the semitransparent film. Will be given in.

(2) The initial value of the film thickness d is d = φλ / (2π (n-1)) with respect to the desired phase difference φ (radian) at the exposure wavelength λ and the refractive index n of the semitransparent film. Will be given in.

(3) The initial value of the extinction coefficient k is calculated and given from the desired transmittance t, the exposure wavelength λ, and the film thickness d of the semitransparent film.

(4) The refractive index n is reset by multiplying the value obtained by dividing the desired value of the phase difference φ by the calculated value by the refractive index n used in the calculation.

(5) For resetting the extinction coefficient k, multiply the logarithm of the desired value of the transmittance t by the calculated value by -λ / 2π,
Further, it is performed by dividing by the extinction coefficient k used in the calculation.

(6) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d are The method includes determining at least one combination.

(7) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d It also includes determining the range of at least one item.

(8) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d It is meant to include determining all ranges.

(9) The desired transmittance t and the phase difference φ are set in appropriate ranges, and the refractive index n is set in the appropriate range. It includes determining the range of the extinction coefficient k and the film thickness d that satisfy the range of the ratio n.

The present invention (claim 2) is a method for designing a semitransparent film for optimally setting the refractive index n, the extinction coefficient k, and the film thickness d of the semitransparent film. Wavelength λ
For an arbitrary extinction coefficient k in, the step of giving initial values of the refractive index n and the film thickness d of the semitransparent film at the exposure wavelength λ; And the transmittance tc of the semitransparent film, the phase difference between the light transmitted through the transparent portion and the semitransparent film, taking into account multiple reflection from the refractive index, extinction coefficient, and film thickness of the substrate on which the semitransparent film is formed. The step of calculating φc, the step of comparing the calculated transmittance tc, the phase difference φc with the desired transmittance t, the phase difference φ, and the refractive index n, respectively, from the phase error and the transmittance error obtained by the comparison. And a step of resetting the film thickness d. Based on the reset refractive index n and the film thickness d, the transmittance tc and the phase difference φc are calculated and compared, and the transmittance tc and the phase difference are compared. The steps of resetting, calculating, and comparing are repeated until both φc and the desired values φ and t match. And wherein the return.

Here, the following are preferred embodiments of the present invention.

(1) The initial value of the film thickness d is the desired transmittance t,
It is calculated and given from the exposure wavelength λ and the extinction coefficient k.

(2) The initial value of the refractive index n is given by n = φλ / 360d + 1 with respect to the desired phase difference φ (degrees) at the exposure wavelength λ and the film thickness d of the semitransparent film.

(3) The initial value of the refractive index n is given by n = φλ / 2πd + 1 with respect to the desired phase difference φ (radian) at the exposure wavelength λ and the film thickness d of the semitransparent film. . (4) The refractive index n is reset by multiplying the value obtained by dividing the desired value of the phase difference φ by the calculated value by the refractive index n used in the calculation.

(5) To reset the film thickness d, multiply the logarithm of the desired value of the transmittance t by the calculated value by -λ / 2π, and divide by the film thickness d used in the calculation. I am going to do it.

(6) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d The method includes determining at least one combination.

(7) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d It also includes determining the range of at least one item.

(8) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d are It is meant to include determining all ranges.

(9) The desired transmittance t and phase difference φ are set in appropriate ranges, and the extinction coefficient k is set in an appropriate range. Extinction coefficient k
It is included to determine the range of the refractive index n and the film thickness d that satisfy the above range.

Further, the present invention (claim 3) is a method of designing a semitransparent film for optimally setting the refractive index n, the extinction coefficient k and the film thickness d of the semitransparent film. Wavelength λ
Exposure wavelength λ of the semitransparent film for an arbitrary film thickness d in
And the initial values of the extinction coefficient k and the refractive index n of the semitransparent film, the extinction coefficient k, the film thickness d, and the refractive index and extinction of the substrate and air on which the semitransparent film is formed. Considering the multiple reflection from the coefficient and film thickness, the step of calculating the transmissivity tc of the semitransparent film and the phase difference φc of the light passing through the transparent portion and the semitransparent film, and the calculated transmissivity tc and the phase difference φc are desired. And the step of resetting the refractive index n and the extinction coefficient k from the phase error and the transmittance error obtained by the comparison, respectively. Based on the rate n and the extinction coefficient k, the steps of calculating and comparing the transmittance tc and the phase difference φc are performed, and reset until both the transmittance tc and the phase difference φc match the desired values φ and t. The step of performing, the step of calculating, and the step of comparing are repeated.

The preferred embodiments of the present invention are as follows.

(1) The initial value of the film thickness d is the desired transmittance t,
It is calculated and given from the exposure wavelength λ and the extinction coefficient k.

(2) The initial value of the refractive index n is given by n = φλ / 360d + 1 with respect to the desired phase difference φ (degree) at the exposure wavelength λ and the film thickness d of the semitransparent film. .

(3) The initial value of the refractive index n is given by n = φλ / 2πd + 1 with respect to the desired phase difference φ (radian) at the exposure wavelength λ and the film thickness d of the semitransparent film. ing. (4) The refractive index n is reset by multiplying the value obtained by dividing the desired value of the phase difference φ by the calculated value by the refractive index n used in the calculation.

(5) To reset the film thickness d, multiply the logarithmic value of the desired value of the transmittance t by the calculated value by -λ / 2π, and further divide by the film thickness d used in the calculation. I am going to do it.

(6) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d The method includes determining at least one combination.

(7) The desired transmittance t and phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d It also includes determining the range of at least one item.

(8) The desired transmittance t and the phase difference φ are set in appropriate ranges, and the transmittance t, the refractive index n satisfying the phase difference φ, the extinction coefficient k, and the film thickness d It is meant to include determining all ranges.

(9) Desired transmittance t and phase difference φ are set in appropriate ranges, and film thickness d is set in an appropriate range. Transmittance t, phase difference φ, film It includes determining the range of the refractive index n and the extinction coefficient k that satisfy the range of the thickness d.

Further, as preferred embodiments in the inventions of claims 1 to 3, the following can be mentioned.

(1) Appropriate ranges of the desired transmittance t and phase difference φ should be determined by the resolution performance of the resist pattern at the time of exposure, the depth of focus, and the image profile obtained by simulation assuming exposure. ing.

(2) The agreement with the desired value means that the desired transmittance t,
The phase difference φ is set to be within a range of desired value ± 0.01 × desired value.

(3) A semitransparent film having a set refractive index n, extinction coefficient k, and film thickness t is formed on a transparent substrate.

(4) A semi-transparent film having a set refractive index n, extinction coefficient k, and film thickness t is formed on a translucent substrate and is processed to include a patterning exposure mask. . (5-1) The semitransparent film having the set refractive index n, extinction coefficient k, and film thickness t is made of Si, SiO, SiN, SiON, SiC,
MoSi, MoSiO, MoSiN, MoSiON, C
rO, CrN, CrON, AlO, AlN, AlNO,
It is characterized in that it is composed of at least one of TiO, TiN, and TiNO.

(5-2) The semitransparent film is such that hydrogen, carbon or a halogen element is further added to the above composition.

(5-3) Refractive index n and extinction coefficient k of the semitransparent film
Is obtained by adjusting the ratio of the above composition.

(5-4) Reactive sputtering, plasma CVD, photo CVD, atmospheric pressure CVD or vapor deposition is used for forming the semitransparent film, and the composition ratio of the semitransparent film is gas composition, pressure or temperature during the reaction. I am trying to get it by adjusting.

(6-1) Using an exposure mask in which a semitransparent film having a set refractive index n, extinction coefficient k, and film thickness t is formed on a transparent substrate and processed to form a pattern. A mask image is formed on a substrate by radiation or the like, and a semiconductor substrate processed based on this image is included.

(6-2) The radiation wavelength is 100 nm to 45 nm.
It is set to either 0 nm.

Further, as an application of the present invention, a semitransparent film having a refractive index n0, an extinction coefficient k0, and a film thickness D, which has a phase difference of 180 degrees at the exposure wavelength λ and satisfies the intensity transmittance T,
When the phase difference φ of the semitransparent film is 180 ± Pe, the intensity transmittance t = T × (1 ± Te), and the film thickness d = D (1 ± De) is within the allowable range, Refractive index n and extinction coefficient k are n = n0 ± λ (5.58Pe + 0.167T-12.7Te-982D)
e−0.68) / 2000D k = k0 ± λ (−0.413Pe + 0.417T + 163Te−312D
We provide semi-transparent film set in the range of e-2.41) / 2000D.

Desirably, the allowable range Pe of the phase difference is 10
It is set to be within the degree. Desirably, the desired intensity transmittance T is set to be 1 to 20%.

Desirably, the ratio Te of the allowable range of the transmittance to the desired transmittance T is set to 0.2 or less.

Desirably, the ratio De of the allowable range of the thickness of the semitransparent film to the desired film thickness D is set to 0.02 or less.

Desirably, there is provided a substrate on which at least a semitransparent film which simultaneously satisfies the refractive index range and the extinction coefficient range shown in the present invention is provided on a transparent substrate.

It is desirable to provide an exposure mask substrate on which at least a pattern formed of a semitransparent film that simultaneously satisfies the refractive index range and the extinction coefficient range shown in the present invention is provided on a transparent substrate. ing.

Desirably, the semitransparent film is Si, SiO, S.
iN, SiON, SiC, MoSi, MoSiO, Mo
SiN, MoSiON, CrO, CrN, CrON, A
It is characterized in that it is composed of at least one composition of 10, AlN, AlNO, TiO, TiN, and TiNO.

Still more preferably, the semitransparent film is such that hydrogen, carbon or a halogen element is added to the composition.

Further preferably, the refractive index n and the extinction coefficient k of the semitransparent film are obtained by adjusting the ratio of the above composition.

Further preferably, reactive sputtering, plasma CVD, photo CVD, atmospheric pressure C are used for forming the semitransparent film.
VD or vapor deposition is used, and the composition ratio of the semitransparent film is obtained by adjusting the gas composition or pressure or temperature during the reaction.

Preferably, a mask substrate for exposure is used, a mask image is formed on the substrate by radiation or the like, and a semiconductor substrate processed based on this image is included.

More preferably, the wavelength of the radiation is 100
nm to 450 nm.

As an application of the present invention, in a semitransparent film having a phase difference of approximately 180 degrees with respect to the exposure wavelength λ, the refractive index n and the extinction coefficient k of the semitransparent film are arbitrary. Average refractive index n0 and average extinction coefficient k obtained by extracting
0 and the average film thickness D are n = n0 ± 0.214λ / D and k = k0 ± 0.115λ / D.

Desirably, there is provided a substrate on which at least a semitransparent film which simultaneously satisfies the range of refractive index and the range of extinction coefficient shown in the present invention is provided on a transparent substrate.

It is desirable to provide an exposure mask substrate on which at least a pattern formed by a semitransparent film that simultaneously satisfies the range of refractive index and the range of extinction coefficient shown in the present invention is provided on a transparent substrate. ing.

Desirably, the semitransparent film is Si, SiO, S.
iN, SiON, SiC, MoSi, MoSiO, Mo
SiN, MoSiON, CrO, CrN, CrON, A
It is characterized in that it is composed of at least one composition of 10, AlN, AlNO, TiO, TiN, and TiNO.

Further preferably, the semitransparent film is made such that hydrogen, carbon or a halogen element is further added to the above composition.

Further preferably, the refractive index n and the extinction coefficient k of the semitransparent film are obtained by adjusting the ratio of the above composition.

Further preferably, reactive sputtering, plasma CVD, photo-CVD, atmospheric pressure C are used for forming the semitransparent film.
VD or vapor deposition is used, and the composition ratio of the semitransparent film is obtained by adjusting the gas composition, pressure or temperature during the reaction.

Preferably, a mask substrate for exposure is used, a mask image is formed on the substrate by radiation or the like, and a semiconductor substrate processed based on this image is included.

More preferably, the wavelength of the radiation is 100
nm to 450 nm.

[0074]

In the following, with respect to the present invention, conditions and a specific method for obtaining a single-layer semitransparent film capable of obtaining a desired transmittance t and a phase difference φ with respect to an opening of a transparent substrate will be described.

When the translucent film is used as a single layer, it is necessary to control the phase of the light passing through the semitransparent film to 180 ° with respect to the phase of the light passing through the transparent portion, and the translucent film is semitransparent. It is necessary to set the transmittance t of the membrane to a desired value.

In order to obtain the maximum resolution with the phase shift mask of the semitransparent film, the optical constants of the semitransparent film must satisfy the following conditions.

To obtain the phase difference φ and the transmittance t of the film, it is very effective to perform multiple interference calculation using the characteristic matrix of the film as described in Applied Optics (Baifukan) by Masao Tsuruta. Is. Considering a case where the refractive index of the semitransparent film is n, the extinction coefficient is k, the film thickness is d, and the exposure light is vertically incident on the semitransparent film, the characteristic matrix of the semitransparent film is as shown in (Equation 1). Can be expressed as

[0078]

[Equation 1] Here, δ is given by (Equation 2).

Δ = 2πnd / λ (Equation 2) Using this characteristic matrix, the electric field E ₀ magnetic field H ₀ on the interface between the semitransparent film and the quartz substrate is the electric field E ₁ magnetic field on the interface between the semitransparent film and the air. With H ₁

[Equation 2] It can be expressed as. By the way, considering that the substrate is sufficiently thick with respect to the exposure wavelength λ and that multiple interference does not occur in the substrate, the tangential components of the electromagnetic field of the transmitted wave on the boundary surface brought close to the substrate side are E ₂ ⁺ and H ₂ ^+. = E ₂ ⁺ Y ₂ , since E 1 = E ₂ ⁺ and H ₁ = H ₂ ⁺ from the boundary condition,

[Equation 3] To get From this, the complex transmittance t ′ can be expressed as (Equation 5).

T ′ = E ₂ ⁺ / E ₀ ⁺ = 2n ₀ / {n ₀ (m11 + n ₂ m12) + (m21 + n ₂ m22)} (Equation 5) Furthermore, when the intensity transmittance t and the phase φ are calculated from t, t = (Real part of t ′) ² + (lie part of t ′) ² (Equation 6) φ = tan ⁻¹ (lie part of t ′ / real part of t ′) (Equation 7) The intensity transmissivity t and the phase φ of the semitransparent film thus obtained and the relative value φ of the intensity transmissivity t and the phase obtained with the air having the same thickness as the semitransparent film are obtained to obtain the semitransparent film. The transmittance t and the phase difference φ when the film is applied to the mask pattern can be obtained.

By the way, in the above calculation, the transmittance t when the refractive index n, the extinction coefficient k, and the film thickness d of the semitransparent film are given,
This is merely a calculation method for the phase difference φ, and a combination of the desired phase difference φ, the refractive index n, the extinction coefficient k, and the film thickness d satisfying the desired transmittance t cannot be obtained. Therefore, in practice, it is necessary to adjust the refractive index n, the extinction coefficient k, and the film thickness d in addition to the above-described multiple reflection calculation. This adjustment makes the refractive index n satisfying the desired transmittance t and phase difference φ. , Is an extremely important factor in determining the extinction coefficient k and the film thickness d.

As an adjusting method, there is a method of simultaneously adjusting three variables of a refractive index n, an extinction coefficient k, and a film thickness d. However, this method is not preferable in terms of calculation efficiency. Because
The dominant factor for the desired phase difference φ is the refractive index n,
Since the film thickness d is the dominant factor for the transmittance t, the extinction coefficient k and the film thickness d are used. Is also an important factor, and therefore the calculated values do not converge or are difficult to converge. In addition, the calculation accuracy may be poor.
The deterioration of calculation accuracy is extremely fatal. For example, in forming a semi-transparent phase shift film, it is necessary to keep the permissible ranges of the refractive index n and the extinction coefficient k within 0.05 with respect to the desired values, and the calculation error was 0.01. Even if you can't ignore it.

Therefore, in the present application, the adjustment of the refractive index n, the extinction coefficient k, and the film thickness d is achieved by any one of the following three methods in order to prevent the deterioration of accuracy and shorten the calculation time. (1) Considering this n as a fixed value for an arbitrary refractive index n, the phase difference φ and the transmittance t obtained by multiple reflection calculation are calculated using the arbitrary extinction coefficient k and the film thickness d, and the phase difference is calculated. φ
The error between the desired value and the calculated value for the film thickness d is reduced, and the error between the desired value and the calculated value for the transmittance t is reduced to the extinction coefficient k. Often, a refractive index n, an extinction coefficient k, and a film thickness d satisfying the desired phase difference φ and transmittance t are obtained.

(2) Considering this k as a fixed value for an arbitrary extinction coefficient k, a phase difference φ and a transmittance t obtained by multiple reflection calculation are calculated using an arbitrary refractive index n and film thickness d. , The difference between the desired value and the calculated value for the phase difference φ is
In addition, by reducing the error between the desired value and the calculated value with respect to the transmittance t to the film thickness d, and performing the multiple reflection calculation and the reduction at least once, the desired phase difference φ and the transmittance t can be quickly and accurately satisfied. The refractive index n, extinction coefficient k, and film thickness d are obtained.

(3) Considering this d as a fixed value for an arbitrary film thickness d, a phase difference φ and a transmittance t obtained by multiple reflection calculation are calculated using an arbitrary refractive index n and extinction coefficient k. , The difference between the desired value and the calculated value for the phase difference φ is
In addition, by reducing the error between the desired value and the calculated value with respect to the transmittance t to the extinction coefficient k, and performing the multiple reflection calculation and the reduction at least once, the desired phase difference φ and the transmittance t can be satisfied quickly and accurately. The refractive index n, the extinction coefficient k, and the film thickness d are calculated.

Preferred modes of (1), (2) and (3) are shown in FIGS. 1, 2 and 3, respectively. Reference numeral 11 in the figure is a means for giving an initial value of the extinction coefficient k and the film thickness d to an arbitrary refractive index n of the semitransparent film at the exposure wavelength λ.
2 is means for giving initial values of the refractive index n and the film thickness d to an arbitrary extinction coefficient k of the semitransparent film at the exposure wavelength λ;
Is a means for giving an initial value of the refractive index n and the extinction coefficient k to an arbitrary film thickness d at the exposure wavelength λ of the semitransparent film, and 20 is the transmissivity tc and phase difference of the semitransparent film in consideration of multiple reflection. φc
, 30 is means for comparing the calculated transmittance tc and phase difference φc with the ideal values t, φ, 41 is a phase error,
Means for resetting the film thickness d and extinction coefficient k respectively from the transmittance error, 42 is a means for resetting the refractive index n and film thickness d from the transmittance error, respectively 43 is a phase error, the transmittance error Are means for resetting the refractive index n and the extinction coefficient k, respectively.

In the initial settings of FIGS. 1 to 3, a desired transmittance t, a refractive index n satisfying a desired phase difference φ, an extinction coefficient k, and a film thickness d.
In order to obtain more quickly, the phase difference φ (which is set to 180 ° in FIGS. 1 to 3 without considering multiple reflections in advance, but when the desired phase difference φ is different from 180 °, Any two of the refractive index n, the extinction coefficient k, and the film thickness d are calculated from the transmittance t, but the calculation formula is not limited to these.

Further, in the resetting of FIGS. 1 to 3, calculation formulas for more promptly obtaining the refractive index n satisfying the desired transmittance t, the phase difference φ, the extinction coefficient k, and the film thickness d are described. However, the calculation formula can be defined as long as it does not deviate from the gist of (1), (2), and (3).

Further, in comparison with the ideal values shown in FIGS. 1 to 3, both desired values ± 0.
It is preferable to interpret that the agreement is within the range of 01 × desired value. The above-mentioned method not only obtains the only refractive index n, extinction coefficient k, and film thickness d that satisfy the desired transmittance and phase difference, but also refracts the transmittance t with a certain width and the phase difference φ. It is also very effective in obtaining a plurality of combinations of the rate n, the extinction coefficient k, and the film thickness.

Usually, the ranges of the transmittance t and the phase difference φ of the semitransparent phase shift film can be determined from the resolution performance obtained at the time of exposure, the depth of focus and the image profile obtained by a simulation assuming the exposure. By replacing the range obtained by these studies with a combination of the refractive index n, the extinction coefficient k, and the film thickness d, it is possible to clarify the orientation when the semitransparent phase shift film is formed.

The present invention will be described in detail below with reference to examples.

(Example 1) In this example, regarding the i-line semitransparent phase shift film, the relationship between the refractive index n satisfying the intensity transmittance of 5% and the phase difference of 180 °, the extinction coefficient k, and the film thickness d was as follows. It is obtained by the invention of claim 1. Here, the calculation mode is the method shown in FIG. 1, and the refractive index is n = 1.5.
It is calculated for each value from 0 to 4.0.

The results obtained in this example are shown in FIG. In the figure, the vertical axis on the left shows the extinction coefficient k, and the vertical axis on the right shows the film thickness d. Figure 4
As described above, the extinction coefficient k and the film thickness d could be determined for each refractive index n.

In the present embodiment, the extinction coefficient k and the film thickness d are obtained by intermittently changing the refractive index n, but it is more preferable that the extinction coefficient k and the film thickness d be continuously changed.

Further, even when the analysis is performed using the invention of claim 2 and the invention of claim 3, the same combination of the refractive index n, the extinction coefficient k, and the film thickness d as in the present embodiment is obtained. I was able to.

In this embodiment, the exposure wavelength is i-line (365n).
m), but the g-line (436
nm), KrF (248 nm), ArF (193 nm)
There is no problem even if applied to such wavelengths.

In this embodiment, the desired intensity transmittance is 5
%, The phase difference is 180 °, but the present invention is not limited to this, but it can be sufficiently applied even in the range of the intensity transmittance of 1% to 20% or the phase difference of 90 to 270 ° depending on the performance at the time of exposure. .

Further, although the refractive index of 1.5 is set as the lower limit, it is not limited to this and any value larger than 1 can be used.

(Embodiment 2) The strength is adjusted by adjusting the nitrogen flow rate in an argon atmosphere with Si as a target so that the relationship among the refractive index n, the extinction coefficient k, and the film thickness d obtained in Embodiment 1 can be obtained. A SiN single-layer semitransparent phase shift film having a transmittance of 5% and a phase difference of 180 ° was formed. At this time, (refractive index, extinction coefficient, film thickness) = (2.9, 0.768, 99.7 nm)
Met.

The translucent substrate on which the semitransparent phase shift film is formed is processed to form a region on the translucent substrate from which the semitransparent phase shift film of 2 μm square is removed, and a semitransparent substrate of 1.75 μm on the translucent substrate. A line & space pattern was formed in which transparent phase shift portions and transparent substrate exposed portions were alternately arranged.

This translucent substrate is used to form an i-line (365 nm) illumination system with a coherent factor σ of 0.4, and is formed on the transferred substrate by a 1/5 reduction projection exposure optical system with a numerical aperture of 0.5. An image was formed on the resist layer and exposed to light to form a hole pattern of 0.4 μm. The depth of focus of this pattern was about 1.5 μm.

Similarly, using this translucent substrate, the i-line (3
(65 nm), an image is formed on the resist layer formed on the transferred substrate by a ⅕ reduction projection exposure optical system with a numerical aperture of 0.5 and exposed to 0.35 μm.
m line & space pattern could be formed. The depth of focus of this pattern was about 2.5 μm.

In this embodiment, a material having SiN in composition is used as the semitransparent film, but the material is not limited to this, and S
iO, SiON, CrO, CrN, CrON, MoSi
O, MoSiN, MoSiON, TiO, TiN, Ti
ON, AlO, AlN, AlON, GaAsO, WSi
It may have O, WSiN, WSiON, or the like in the composition or a part of the composition.

Further, the applied pattern is not limited to the hole pattern and the line & space pattern, but can be applied to an isolated remaining pattern, an isolated pattern, and a combination of these patterns. Further, the applicable size may be any size.

Also, the illumination system at the time of exposure is not limited to these, and an illumination system in which an aperture is provided at a position symmetrical at least four times with respect to the optical axis, or at a position symmetrical at least twice with respect to the optical axis. An illumination system provided with a hole may be used.

(Embodiment 3) In this embodiment, the i-line semitransparent phase shift film has an intensity transmittance of 5 ± 1% and a phase difference of 180.
The relationship among the refractive index n, the extinction coefficient k, and the film thickness d satisfying the condition is obtained by the invention of claim 1. Here, the form of calculation is performed by the method shown in FIG. 1, and the refractive index is n =
It is obtained for each value from 1.5 to 4.0.

The results obtained in this example are shown in FIG. In the figure, the vertical axis on the left shows the extinction coefficient k, and the vertical axis on the right shows the film thickness d. Figure 5
As described above, the ranges of the refractive index n, the extinction coefficient k, and the film thickness d could be determined. The range of the extinction coefficient k with respect to the refractive index n is shown by diagonal lines, and the range of the film thickness d with respect to the refractive index n is shown as a black region (the region is narrow under the conditions of the phase shift film of the present embodiment, and is shown as one line. ). Thus, according to this method,
Even when the phase difference has a range, the allowable range of the refractive index n, the extinction coefficient k, and the film thickness d can be accurately obtained.

In the present embodiment, the extinction coefficient k and the film thickness d were obtained by intermittently changing the refractive index n, but it is more preferable that the extinction coefficient k and the film thickness d be continuously changed.

Further, even when the analysis is carried out using the invention of claim 2 and the invention of claim 3, the same range of the refractive index n, the extinction coefficient k, and the film thickness d as in the present embodiment is obtained. I was able to.

In this embodiment, the exposure wavelength is i-line (365n).
m), but the g-line (436
nm), KrF (248 nm), ArF (193 nm)
There is no problem even if applied to such wavelengths.

In this embodiment, the desired intensity transmittance is set to 5
The phase difference is set to ± 1% and the phase difference is set to 180 °, but the invention is not limited to this, and it can be sufficiently applied even in the range of intensity transmittance of 1% to 20% or phase difference of 90 to 270 ° depending on the performance at the time of exposure. is there.

Further, the refractive index of 1.5 is set as the lower limit, but the present invention is not limited to this, and any value larger than 1 can be used.

Example 4 In this example, the KrF semi-transparent phase shift film has an intensity transmittance of 6% and a phase difference of 180 °.
The relationship among the refractive index n, the extinction coefficient k, and the film thickness d satisfying the above is obtained by the invention of claim 2. Here, the form of calculation is performed by the method shown in FIG. 2, and the extinction coefficient is k =
It is obtained for each value from 0.5 to 1.2.

The results obtained in this example are shown in FIG. In the figure, the left vertical axis shows the refractive index n, and the right vertical axis shows the film thickness d. As shown in FIG. 6, the refractive index n and the film thickness d could be uniquely determined for each extinction coefficient k.

In the present embodiment, the extinction coefficient k is intermittently changed to obtain the refractive index n and the film thickness d, but it is more preferable to continuously change k.

Also, when the analysis is performed using the inventions of claim 1 and claim 3, the same combination of the refractive index n, the extinction coefficient k, and the film thickness d as in the present embodiment is obtained. I was able to.

In this embodiment, the exposure wavelength is set to KrF (248n
m), but it is not limited to this and g line (436n
m), i-line (365 nm), ArF (193 nm) and other wavelengths do not pose any problem.

In this embodiment, the desired intensity transmittance is set to 6
%, The phase difference is 180 °, but the present invention is not limited to this, but it can be sufficiently applied even in the range of the intensity transmittance of 1% to 20% or the phase difference of 90 to 270 ° depending on the performance at the time of exposure. .

Further, although the extinction coefficient of 0.5 is set as the lower limit,
The value is not limited to this, and any value larger than 0 can be used.

(Embodiment 5) The intensity transmittance is adjusted by adjusting the nitrogen flow rate in an argon atmosphere with Si as a target so that the relationship among the refractive index n, the extinction coefficient k, and the film thickness d obtained in Embodiment 4 can be obtained. A 6% SiN single layer semitransparent phase shift film having a phase difference of 180 ° was formed. At this time, (refractive index, extinction coefficient, film thickness) = (2.14, 0.48
1,110.9 nm).

The transparent substrate on which the semitransparent phase shift film is formed is processed to form a 1.2 μm square area on the transparent substrate where the semitransparent phase shift film is removed, and a region on the transparent substrate for 1 μm. A line & space pattern was formed in which translucent phase shift parts and translucent substrate exposed parts were alternately arranged.

Using this translucent substrate, a KrF (248 nm) illumination system with a coherent factor σ = 0.4 is used.
An image was formed on the resist layer formed on the transfer substrate by a 1/4 reduction projection exposure optical system with a numerical aperture of 0.5, and by exposing this image, a 0.3 μm hole pattern could be formed. . The depth of focus of this pattern was about 1.2 μm.

Similarly, using this light-transmissive substrate, KrF having a coherent factor σ = 0.6 and an imperfection region of 0.6σ.
An image is formed on the resist layer formed on the transferred substrate by a 1/4 reduction projection exposure optical system with a numerical aperture of 0.5 using a (248 nm) illumination system, and this is exposed to 0.25 μm.
m line & space pattern could be formed. The depth of focus of this pattern was about 1.8 μm.

In this example, a material having a composition of SiN was used as the semitransparent film, but the material is not limited to this, and S
iO, SiON, CrO, CrN, CrON, MoSi
O, MoSiN, MoSiON, TiO, TiN, Ti
ON, AlO, AlN, AlON, GaAsO, WSi
It may have O, WSiN, WSiON, or the like in the composition or a part of the composition.

Further, the applied pattern is not limited to the hole pattern and the line & space pattern, but can be applied to an isolated remaining pattern, an isolated pattern, and a combination of these patterns. Further, the applicable size may be any size.

Also, the illumination system at the time of exposure is not limited to these, and an illumination system in which an aperture is provided at a position symmetrical at least four times with respect to the optical axis, or at a position symmetrical at least twice with respect to the optical axis. An illumination system provided with a hole may be used.

Example 6 In this example, the KrF semi-transparent phase shift film has an intensity transmittance of 6% and a phase difference of 180 ±.
The relationship among the refractive index n, the extinction coefficient k, and the film thickness d satisfying 5 ° is
It is obtained by the invention of claim 2. Here, the form of calculation is performed by the method shown in FIG. 2, and the extinction coefficient is k
= 0.5 to 1.2 for each value. The results obtained in this example are shown in FIG. In the figure, the left vertical axis shows the refractive index n, and the right vertical axis shows the film thickness d. As shown in FIG. 7, the refractive index n, the extinction coefficient k, and the film thickness d could be uniquely determined. The range of the refractive index n with respect to the extinction coefficient k is shown with a halftone dot, and the range of the film thickness d with respect to the refractive index n is shown with a black region.
As described above, according to this embodiment, the allowable ranges of the refractive index n, the extinction coefficient k, and the film thickness d can be accurately obtained even when the transmittance has a range.

In the present embodiment, the extinction coefficient k is intermittently changed to obtain the refractive index n and the film thickness d, but it is more preferable to continuously change k to obtain the refractive index n and the film thickness d.

Also, when the analysis is performed using the inventions of claim 1 and claim 3, the same range of the refractive index n, the extinction coefficient k, and the film thickness d as in the present embodiment is obtained. I was able to.

In this embodiment, the exposure wavelength is set to KrF (248n
m), but the g-line (436
nm), i-line (365 nm), ArF (193 nm) and other wavelengths.

In this embodiment, the desired intensity transmittance is set to 6
%, The phase difference is set to 180 ± 5 °, but the invention is not limited to this, and it can be sufficiently applied even in the range of intensity transmittance of 1% to 20% or phase difference of 90 to 270 ° depending on the performance at the time of exposure. is there.

Furthermore, although the extinction coefficient of 0.5 is set as the lower limit,
The value is not limited to this, and any value larger than 0 can be used.

(Embodiment 7) In this embodiment, regarding the g-line semitransparent phase shift film, the relationship between the intensity transmittance 3%, the refractive index n satisfying the phase difference 180 °, the extinction coefficient k, and the film thickness d is as follows. It is obtained by the invention of claim 2. Here, the calculation mode is the method shown in FIG. 3, and the film thickness is d = 40 nm.
It was calculated for each value from to 400 nm.

The results obtained in this example are shown in FIG. In the figure, the left vertical axis shows the refractive index k, and the right vertical axis shows the extinction coefficient k. As shown in FIG. 8, the refractive index n and the extinction coefficient k could be uniquely determined for each film thickness d.

In this embodiment, the film thickness d is intermittently changed to obtain the refractive index n and the extinction coefficient k, but it is more preferable to continuously change d.

Also, when the analysis is performed using the invention of claim 1 and the invention of claim 3, the same combination of the refractive index n, the extinction coefficient k, and the film thickness d as in the present embodiment is obtained. I was able to.

In this embodiment, the exposure wavelength is set to the g-line (436n).
m), but not limited to this, i line (365
nm), KrF (248 nm), ArF (193 nm)
There is no problem even if applied to such wavelengths.

In this embodiment, the desired intensity transmittance is set to 3
%, The phase difference is 180 °, but the invention is not limited to this, and it can be sufficiently applied in the range of intensity transmittance of 1% to 20% or phase difference of 120 to 240 ° depending on the performance at the time of exposure. .

Further, although the extinction coefficient of 40 nm is set as the lower limit, the present invention is not limited to this and any value larger than 0 can be used.

(Embodiment 8) The intensity transmittance is adjusted by adjusting the power during film formation with Si as the target so that the relationship among the refractive index n, the extinction coefficient k, and the film thickness d obtained in Embodiment 7 can be obtained. Three
%, A Si single-layer semitransparent phase shift film having a phase difference of 180 ° was formed. At this time, (refractive index, extinction coefficient, film thickness) = (4.65, 1.44
8, 62.9 nm).

By processing the translucent substrate on which the semitransparent phase shift film is formed, a region of the translucent substrate from which the semitransparent phase shift film of 3 μm square is removed and a translucent substrate of 2.5 μm are processed. A line & space pattern was formed in which translucent phase shift parts and translucent substrate exposed parts were alternately arranged.

Using this translucent substrate, a g-line (436 nm) illumination system with a coherent factor σ = 0.3 is used, and a 1/5 reduction projection exposure optical system with a numerical aperture of 0.55 is used to form it on the substrate to be transferred. An image was formed on the resist layer and exposed to light, whereby a hole pattern of 0.6 μm could be formed. The depth of focus of this pattern was about 2.1 μm.

Similarly, using this translucent substrate, an illumination system having a coherent factor σ = 0.6 and an obstruction area of 0.5σ is used, and transferred by a ⅕ reduction projection exposure optical system with a numerical aperture of 0.55. Form an image on the resist layer formed on the substrate,
By exposing this, a line & space pattern of 0.5 μm could be formed. The depth of focus of this pattern was about 2.8 μm.

In this embodiment, a material having a composition of Si is used as the semi-transparent film, but the material is not limited to this.
O, SiON, CrO, CrN, CrON, MoSi
O, MoSiN, MoSiON, TiO, TiN, Ti
ON, AlO, AlN, AlON, GaAsO, WSi
It may have O, WSiN, WSiON, or the like in the composition or a part of the composition.

Further, the applied pattern is not limited to the hole pattern and the line & space pattern, but can be applied to an isolated remaining pattern, an isolated pattern, and a combination of these patterns. Further, the applicable size may be any size.

Also, the illumination system at the time of exposure is not limited to these, and an illumination system in which an aperture is provided at a position symmetrical at least four times with respect to the optical axis, or at a position symmetrical at least twice with respect to the optical axis. An illumination system provided with a hole may be used.

Example 9 In this example, the g-line translucent phase shift film has an intensity transmittance of 3 ± 1% and a phase difference of 180.
The relationship among the refractive index n, the extinction coefficient k, and the film thickness d satisfying ± 10 ° is obtained by the invention of claim 2. here,
The calculation is performed by the method shown in FIG.
= 40 nm to 400 nm for each value.

The results obtained in this example are shown in FIG. In the figure, the left vertical axis shows the refractive index k, and the right vertical axis shows the extinction coefficient k. As shown in FIG. 9, the refractive index n and the extinction coefficient k could be uniquely determined for each film thickness d. The range of the refractive index n with respect to the film thickness d is shown by a halftone dot, and the range of the extinction coefficient k with respect to the film thickness d is shown by a shaded area. As described above, according to this method, the allowable ranges of the refractive index n, the extinction coefficient k, and the film thickness d can be accurately obtained even when the transmittance and the phase difference have ranges.

In this embodiment, the refractive index n and the extinction coefficient k are obtained by intermittently changing the film thickness d, but it is more preferable that the refractive index n and the extinction coefficient k are continuously changed.

Further, even when the analysis is performed using the invention of claim 2 and the invention of claim 3, the same combination of the refractive index n, the extinction coefficient k, and the film thickness d as in the present embodiment is obtained. I was able to.

In this embodiment, the exposure wavelength is set to the g-line (436n).
m), but not limited to this, i-line (365n
m), KrF (248 nm), ArF (193 nm), etc.

In this embodiment, the desired intensity transmittance is set to 3
± 1% and a phase difference of 180 ± 10 ° are set, but not limited to this, but the intensity transmittance is 1% or more depending on the performance during exposure.
It is sufficiently applicable even in the range of 20% or the phase difference of 90 to 270 °.

Further, although the extinction coefficient of 40 nm is set as the lower limit, it is not limited to this and any value larger than 0 can be used.

(Embodiment 10) In this embodiment, an i-line semitransparent phase shift film has an intensity transmittance of 5 ± 1% and a phase difference of 18%.
The relationship between the extinction coefficient k and the film thickness d when satisfying 0 ± 5 ° and fixing the refractive index n = 4 is obtained by the application method of the invention of claim 1. Here, the form of calculation was performed by the method shown in FIG.

The results obtained in this example are shown in FIG. In the figure, the extinction coefficient k is shown on the horizontal axis and the film thickness d is shown on the vertical axis. When the refractive index n is fixed, the combination of the extinction coefficient k and the film thickness d can be represented by a region surrounded by four curves as shown in FIG. Thus, as shown in FIG. 10, the range of the extinction coefficient k and the film thickness d could be determined under a constant refractive index n = 4. That is, the area obtained here is (transmittance, phase difference) =
With the coordinates given by the combination of the extinction coefficient and the film thickness satisfying (upper limit transmittance, no question) and (lower limit transmittance, no question) and (no question, upper limit phase difference) and (no question, lower limit phase difference) as a boundary, Given as a closed area at these coordinates.

In this embodiment, the exposure wavelength is i-line (365n).
m), but it is not limited to this and g line (436n
m), KrF (248 nm), ArF (193 nm), etc.

In this embodiment, the desired intensity transmittance is 5
± 1% and the phase difference was 180 ± 10 °, but not limited to this, but the one including the desired value and the desired range depends on the performance at the time of exposure, and the intensity transmittance is 1% to 20% or Phase difference 90
It is sufficiently applicable within the range of ˜270 °.

Further, the refractive index n = 4 is defined, but the invention is not limited to this, and any value larger than 1 can be used.

(Embodiment 11) In this embodiment, the KrF semitransparent phase shift film has an intensity transmittance of 6 ± 1% and a phase difference of 1.
The relationship between the refractive index n and the film thickness d when 80 ± 5 ° is satisfied and the refractive index n is fixed to 4 is obtained by the application method of the invention of claim 2. Here, the form of calculation was performed by the method shown in FIG.

The results obtained in this example are shown in FIG. In the figure, the horizontal axis represents the refractive index n and the vertical axis represents the film thickness d. When the extinction coefficient k is fixed, the combination of the refractive index n and the film thickness d can be represented by a region surrounded by four solid curves as shown in FIG. In this way, as shown in FIG. 11, the range of the refractive index n and the film thickness d could be determined under the constant extinction coefficient k = 0.4. That is, the area obtained here is (transmittance, phase difference)
= (Upper limit transmittance, no question) and (lower limit transmittance, no question) and (no question, upper limit phase difference) and (no question, lower limit phase difference) with coordinates given by a combination of refractive index and film thickness as boundaries, Given as a closed area at these coordinates.

In this embodiment, the exposure wavelength is set to KrF (248n
m), but it is not limited to this and g line (436n
m), i-line (365 nm), ArF (193 nm) and other wavelengths do not pose any problem.

In this embodiment, the desired intensity transmittance is 5
± 1% and the phase difference was 180 ± 10 °, but not limited to this, but the one including the desired value and the desired range depends on the performance at the time of exposure, and the intensity transmittance is 1% to 20% or Phase difference 90
It is sufficiently applicable within the range of ˜270 °.

Furthermore, although the extinction coefficient k is set to 0.4, it is not limited to this and any value larger than 0 can be used.

Example 12 In this example, the g-line translucent phase shift film has an intensity transmittance of 3 ± 1% and a phase difference of 180.
The relationship between the refractive index n and the extinction coefficient k when satisfying ± 10 ° and fixing the film thickness d = 80 nm is obtained by the application method of the invention of claim 3. Here, the form of calculation was performed by the method shown in FIG.

The results obtained in this example are shown in FIG. In the figure, the horizontal axis shows the refractive index n and the vertical axis shows the extinction coefficient k. When the film thickness d is fixed and considered, the combination of the refractive index n and the extinction coefficient k can be represented by a region surrounded by four solid curves as shown in FIG. Thus, as shown in FIG. 12, the film thickness d = 80 nm
It was possible to define the range of the refractive index n and the extinction coefficient k under a constant condition. That is, the region obtained here satisfies (transmittance, phase difference) = (upper limit transmittance, no question) and (lower limit transmittance, no question) and (no question, upper limit phase difference) and (no question, lower limit phase difference). The coordinates given by the combination of the refractive index and the extinction coefficient are taken as boundaries, and these coordinates are given as a closed region.

In this embodiment, the exposure wavelength is set to the g-line (436n).
m), but not limited to this, i-line (365n
m), KrF (248 nm), ArF (193 nm), etc.

In this embodiment, the desired intensity transmittance is set to 3
± 1% and the phase difference was 180 ± 10 °, but not limited to this, but the one including the desired value and the desired range depends on the performance at the time of exposure, and the intensity transmittance is 1% to 20% or Phase difference 12
It is sufficiently applicable in the range of 0 to 240 °.

Further, although the film thickness d is set to 80 nm, the invention is not limited to this, and any value larger than 0 can be used.

Example 13 In this example, the i-line translucent phase shift film satisfies the intensity transmittance of 4.9 ± 0.5%, the phase difference of 180 ± 5 ° and the film thickness d = 99.8. ± 1n
The range of the refractive index n, the extinction coefficient k, and the film thickness d when the range of m is determined by the application method of the invention of claim 3. Here, the form of calculation was performed by the method shown in FIG.

Here, the film thickness was set to 99.8 nm. 9
The film thickness value of 9.8 nm is a combination of the extinction coefficient k and the film thickness d when the intensity transmittance is 4.9%, the phase difference φ is 180 °, and the refractive index n is 2.9. It was obtained from the invention of.

Furthermore, the refractive index n,
The relationship of the extinction coefficient k may be defined as follows. First,
Appropriate film thickness range is ± 1 nm for 99.8 nm
And The appropriate film thickness range referred to here is the performance of the apparatus used for film formation (the film thickness range obtained in-plane for the film formation target substrate, film formation target substrates were formed on a plurality of substrates under the same conditions). It is determined by the film thickness range that sometimes occurs).
Considering that the refractive index n and the extinction coefficient k monotonously increase when the film thickness d monotonously decreases with respect to this film thickness range, the calculation procedure was determined as follows.

(1) The combination of the refractive index n and the extinction coefficient k when the film thickness is maximum is determined.

(2) The combination of the refractive index n and the extinction coefficient k when the film thickness is the minimum value is determined.

(3) The intersection of the refractive index n and the extinction coefficient k obtained in (1) and (2) is obtained.

By the above steps, the desired transmittance t,
FIG. 14 shows the ranges of the refractive index n and the extinction coefficient k that are satisfied when the range of the phase difference φ is obtained and an appropriate range of the film thickness is given.
It can be easily and quickly set as indicated by the diagonal lines.

In this embodiment, the exposure wavelength is i-line (365n).
m), but the g-line (436
nm), KrF (248 nm), ArF (193 nm)
There is no problem even if applied to such wavelengths.

In this embodiment, the desired intensity transmittance is 4.9 ± 0.5% and the phase difference is 180 ± 5 °. However, the present invention is not limited to this, and it depends on the performance during exposure. A material including a desired value and a desired range is sufficiently applicable as long as the intensity transmittance is 1 to 20% or the phase difference is 120 to 240 °.

Further, although the film thickness d is set to be 99.8 nm,
The value is not limited to this, and any value larger than 0 can be used.

Similar to the present embodiment, by using the application example of the invention of claim 1, the extinction coefficient k and the film thickness d are set so as to satisfy an appropriate refractive index range for a desired phase difference and transmittance range. You can ask for combinations.

Further, as in the case of this embodiment, by using the application example of the invention of claim 2, the refractive index n and the film thickness satisfying the appropriate extinction coefficient range for the desired phase difference and transmittance range. The combination of d can be obtained.

Here, the appropriate refractive index range or the appropriate extinction coefficient range is the performance of the apparatus used for film formation (the range of the refractive index or extinction coefficient obtained in the plane of the film formation target substrate, the film formation target substrate). Is preferably determined by the range of the refractive index or extinction coefficient generated when the film is formed on a plurality of substrates under the same conditions.

(Embodiment 14) In this embodiment, Embodiment 13 will be described.
The permissible ranges of the refractive index n and the extinction coefficient k obtained by the above method were examined in more detail.

First, let the ranges of the desired refractive index n and the extinction coefficient k in FIG. 13 be the allowable ranges of the refractive index at arbitrary extinction coefficients, and let the extinction coefficient be allowable for Δn and the arbitrary refractive index n. The range is represented by Δk. Furthermore, Δn and Δk
Was divided by the exposure wavelength / exposure wavelength to set values dn and dk.

In FIG. 14, exposure wavelength = 365 nm (i line)
And allowable phase difference 180 at 248 nm (KrF)
Satisfies ± 5 degrees and allowable intensity transmittance of 5 ± 0.5% d
The refractive index dependence of n and dk is shown. Here, the one for the i line is shown by a solid line, and the one for KrF is shown by a broken line. d
It was found that both n and dk show almost constant values independent of the refractive index. Further, dn and dk at the KrF wavelength are i
It was found that the same value as the line was not dependent on the wavelength.

FIG. 15 shows dn and dk with respect to the allowable phase difference amount Pe when the reference phase difference is 180 degrees. Here, the reference transmittance T is 5%, and the film thickness variation De is 0.0
It was set to 1. The solid line is the ratio of the variation of the transmittance to the desired transmittance Te = ± 0.1 (intensity transmittance 5 ± 0.5%), and the broken line is Te = ± 0.2 (intensity transmittance 5 ± 1%). It is a value. Both dn and dk could be expressed as a linear function with respect to Pe.

FIG. 16 shows dn and dk with respect to the allowable transmittance Te for the standard transmittance of 5% with the phase difference of 180 ± 5 degrees. The film thickness variation De was set to 0.01. Te
The dn and dk values with respect to were both able to be expressed by a linear function with respect to Te, similarly to the change with respect to Pe.

FIG. 17 shows that dn, d with respect to the reference transmittance T.
I asked for k. Here, the allowable phase difference Pe is set to ± 5 degrees with respect to 180. The film thickness variation De was set to 0.01. The solid line for the allowable transmittance Te = 0.1 is Te =
0.2 is shown by a broken line. The change of dn and dk with respect to T could be expressed by a linear function.

FIG. 18 shows dn and dk with respect to the HT film thickness variation rate W when the phase difference allowable amount Pe and the intensity transmittance allowable amount Te are arbitrarily selected. Each of dn and dk shown in FIG. 18 can be expressed by a linear function with respect to the film thickness variation rate w. Further, those slopes do not depend on the phase difference allowable amount Pe and the intensity transmittance allowable amount Te, and show a constant slope at each dn and dk.

From the results shown in FIGS. 14 to 18, Δn and Δk are first-order polynomials of the phase difference allowable amount Pe, the reference transmittance T, the transmittance allowable amount Te, the optimum film thickness D and the film thickness variation ratio De. Can be expressed as in (Equation 9) and (Equation 10).

Δn = ± λ (5.58Pe + 0.167T-12.7Te-982De-0.68) / 2000D (Equation 9) Δk = ± λ (-0.413Pe + 0.417T + 163Te-312De-2.41) / 2000D (Equation 10) ) Further, with respect to (Equation 9) and (Equation 10), the phase fluctuation amount Pe = 1
0 degree, ratio of intensity transmittance variation to desired transmittance Te =
0.2 and a ratio of the variation of the semitransparent phase shift film thickness to the desired film thickness De = 0.01, (Equation 9) and (Equation 10) are changed to (Equation 11) and (Equation 12), respectively. Can be represented. Here, the influence of the desired transmittance T on Δn and Δk is very small, and there is almost no difference between Δn and Δk in the range of the intensity transmittance T = 1 to 20%. That is,
(Equation 11) and (Equation 12) are given regardless of the desired transmittance.

Δn = ± 0.214λ / D (Equation 11) Δk = ± 0.115λ / D (Equation 12)

[0192]

As described above in detail, according to the present invention, the conventional semitransparent phase shift film is not grasped by the indirect information such as the phase difference and the transmittance but the refractive index, the extinction coefficient and the film thickness. It becomes possible to capture more specific information and personality. Furthermore, it becomes possible to clarify the allowable ranges of the refractive index, the extinction coefficient, and the film thickness.

[Brief description of drawings]

FIG. 1 is a diagram showing a calculation algorithm according to the invention of claim 1;

FIG. 2 is a diagram showing a calculation algorithm according to the invention of claim 2;

FIG. 3 is a diagram showing a calculation algorithm according to the invention of claim 3;

FIG. 4 is a diagram for explaining the first embodiment and showing the relationship between the extinction coefficient and the film thickness with respect to the refractive index calculated using the invention of claim 1.

FIG. 5 is a view for explaining the third embodiment and showing the extinction coefficient and the allowable range of the film thickness with respect to the refractive index calculated using the invention of claim 1.

FIG. 6 is a graph for explaining the fourth embodiment and showing the relationship between the extinction coefficient calculated using the invention of claim 2 and the refractive index and film thickness.

FIG. 7 is a diagram for explaining the sixth embodiment and showing the allowable ranges of the refractive index and the film thickness with respect to the extinction coefficient calculated using the invention of claim 2;

FIG. 8 is a graph for explaining the seventh embodiment and showing the relationship between the refractive index and the extinction coefficient with respect to the film thickness calculated using the invention of claim 3;

FIG. 9 is a diagram for explaining the ninth embodiment and showing the allowable ranges of the refractive index and the extinction coefficient with respect to the film thickness calculated using the invention of claim 3;

FIG. 10 is a view for explaining the tenth embodiment and showing the extinction coefficient and the allowable range of the film thickness when the refractive index is fixed according to the application of the invention of claim 1.

FIG. 11 is a diagram for explaining the eleventh embodiment and showing the allowable range of the refractive index and the film thickness when the extinction coefficient according to the application of the invention of claim 2 is fixed.

FIG. 12 is a view for explaining the twelfth embodiment and showing the allowable range of the refractive index and the extinction coefficient when the film thickness is fixed according to the application of the invention of claim 3;

FIG. 13 is a view for explaining the fourteenth embodiment and showing the permissible ranges of the refractive index and the extinction coefficient when an appropriate range is set for the film thickness according to the application of the invention of claim 3;

FIG. 14 is a graph showing the dependence of the refractive index n of dn and dk on the exposure wavelength λ in the fourteenth embodiment.

FIG. 15 is a diagram for explaining the dependence of the phase difference variation amount Pe on dn and dk in the fourteenth embodiment.

FIG. 16 is a diagram for explaining the dependence of the ratio Te on the reference transmittance of the transmittance fluctuation amounts of dn and dk in the fourteenth embodiment.

FIG. 17 is a diagram for explaining the dependency of dn and dk on the reference transmittance T in the fourteenth embodiment.

FIG. 18 is a diagram for explaining the dependence of the ratio Pe of the variation in film thickness of dn and dk on the reference film thickness in the fourteenth embodiment.

[Explanation of symbols]

 11, 12, 13 ... Initial setting means 20 ... Means for calculating transmittance tc and phase difference φc 30 ... Means for comparing calculated values tc, φc with ideal values t, φ 41, 42, 43 ... Resetting means

Claims (3)

[Claims] 1. A step of giving an initial value of an extinction coefficient k and a film thickness d of the semitransparent film at the exposure wavelength λ to an arbitrary refractive index n of the semitransparent film at the exposure wavelength λ, and the semitransparent film. The refractive index n, extinction coefficient k, film thickness d, and the refractive index, extinction coefficient, and film thickness of the substrate on which the semitransparent film is formed, and multiple reflection are taken into consideration from the transmissivity tc of the semitransparent film, Comparing the steps of calculating the phase difference φc of light transmitted through the transparent portion and the semitransparent film, and the step of comparing the calculated transmittance tc and phase difference φc with the desired transmittance t and phase difference φ. Resetting the extinction coefficient k and the film thickness d from the obtained phase error and transmittance error, respectively, based on the reset film thickness d and extinction coefficient k, the transmittance tc, The calculation process and the comparison process of the phase difference φc are performed, and both the transmittance tc and the phase difference φc match the desired values φ, t. Design method translucent film and repeating the re-setting step of the steps of calculating and comparing steps. 2. A step of giving initial values of a refractive index n and a film thickness d of the semitransparent film at the exposure wavelength λ to an arbitrary extinction coefficient k of the semitransparent film at the exposure wavelength λ, and the semitransparent film. The refractive index n, extinction coefficient k, film thickness d, and the refractive index, extinction coefficient, and film thickness of the substrate on which the semitransparent film is formed, and multiple reflection are taken into consideration from the transmissivity tc of the semitransparent film, Comparing the steps of calculating the phase difference φc of light transmitted through the transparent portion and the semitransparent film, and the step of comparing the calculated transmittance tc and phase difference φc with the desired transmittance t and phase difference φ. Resetting the refractive index n and the film thickness d from the obtained phase error and the transmittance error, respectively, based on the reset refractive index n and the film thickness d, the transmittance tc and the phase difference. φc calculation step and comparison step are performed, and both the transmittance tc and the phase difference φc match the desired values φ and t. Design method translucent film and repeating the re-setting step of the steps of calculating and comparing steps. 3. A step of giving initial values of a refractive index n and an extinction coefficient k of the semitransparent film at the exposure wavelength λ to an arbitrary film thickness d of the semitransparent film at the exposure wavelength λ, and the semitransparent film. The refractive index n, extinction coefficient k, film thickness d, and the refractive index, extinction coefficient, and film thickness of the substrate on which the semitransparent film is formed, and multiple reflection are taken into consideration from the transmissivity tc of the semitransparent film, Comparing the step of calculating the phase difference φc of light transmitted through the transparent portion and the semi-transparent film and the step of comparing the calculated transmittance tc and phase difference φc with the desired transmittance t and phase difference φ Resetting the refractive index n and the extinction coefficient k from the obtained phase error and transmittance error, respectively, based on the reset refractive index n and extinction coefficient k, the transmittance tc, Perform the phase difference φc calculation step and comparison step,
A method for designing a semitransparent film, characterized in that the step of resetting, the step of calculating, and the step of comparing are repeated until both the transmittance tc and the phase difference φc match the desired values φ, t.