JP2013011898A - Original data generation method, original generation method, program for generating original data, and processor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a generation method of generating original data for forming a fine pattern with high precision.SOLUTION: Provided is a generation method for generating, by a computer, original data to be used in an exposure device comprising: an illumination optical system for illuminating an original by using light from a light source; and a projection optical system for projecting a pattern of the original onto a substrate. The generation method determines a main pattern on the basis of an approximated aerial image and inserts an auxiliary pattern, thereby, generates the original data.

Description

  The present invention relates to a method for generating original data, an original creating method, a program for creating original data, and a processing apparatus.

  An exposure apparatus is used when a fine semiconductor device such as a semiconductor memory or a logic circuit is manufactured by using a photolithography technique. The exposure apparatus projects a circuit pattern drawn on a mask (reticle) that is an original plate onto a substrate such as a wafer by a projection optical system to transfer the circuit pattern. In recent years, miniaturization of semiconductor devices has progressed, and in an exposure apparatus, it is necessary to form a pattern having a dimension smaller than the exposure wavelength (exposure light wavelength). However, for such a fine pattern, the influence of light diffraction will appear remarkably, so the outline of the pattern (pattern shape) is not formed on the wafer as it is, the corners of the pattern are rounded, The shape accuracy is greatly deteriorated, for example, the length of the pattern is shortened.

  Therefore, in recent years, in order to reduce the deterioration of the shape accuracy of the pattern formed on the wafer, the mask pattern is designed by performing a process for correcting the pattern shape (so-called optical proximity correction (OPC)). Has been. OPC corrects the pattern shape for each element of the mask pattern in consideration of the shape and the influence of surrounding elements on the basis of a model using a rule base or optical simulation.

  In the model base using the optical simulation, the mask pattern is deformed until a desired transfer pattern is obtained. For example, if the optical image is partially inflated, the mask pattern is thinned accordingly, and if the optical image is partially thinned, the mask pattern is inflated accordingly and the optical image is recalculated, and the mask pattern is A method of gradually pursuing, a so-called sequential improvement method has been proposed. A method for driving a mask pattern using a genetic algorithm is also proposed. Furthermore, a method of inserting an auxiliary pattern having a size that is not resolved has been proposed.

  Patent Document 1 and Non-Patent Document 1 disclose a technique for deriving how to insert an auxiliary pattern by numerical calculation. In such a technique, an interference map (hereinafter referred to as “interference map”) is obtained by numerical calculation, and a position (region) that interferes with each other on the mask and a position (region) that cancels interference are derived. . Then, an auxiliary pattern is inserted at the position where interference occurs in the interference map so that the phase of light passing through the desired pattern is equal to the phase of light passing through the auxiliary pattern. In addition, an auxiliary pattern is inserted at a position where the interference is canceled in the interference map so that the difference between the phase of the light passing through the desired pattern and the phase of the light passing through the auxiliary pattern becomes 180 degrees. As a result, the light that has passed through the desired pattern and the light that has passed through the auxiliary pattern interfere strongly, and the desired pattern can be accurately exposed. Since the mask surface and the wafer surface are in an imaging relationship, the interference map can be regarded as obtaining the amplitude on the image surface. The desired pattern is an element present on the mask and is an element (main pattern) transferred to the wafer.

JP 2004-221594 A

Robert Socha, Douglas Van Den Broeke, Stephen Hsu, J. et al. Fung Chen, Tom Laidig, Noel Cororan, Uwe Hollerbach, Kurt E. et al. Wampler, Xuelong Shi, Will Conley, "Contact Hole Repetition by Using Interference Mapping Lithography (IML (TM)), United States, SPIE, USA, SPIE. 5853, p. 180-193

  Circuit patterns can be broadly divided into line patterns (wiring patterns) and contact hole patterns.

  Since the technique disclosed in Patent Document 1 is a technique for obtaining only an auxiliary pattern by approximating a contact hole pattern with a line having an unsized size and a contact hole pattern having no size, the shape of the main pattern is obtained. I can't. Therefore, after obtaining the position, shape, size, etc. of the auxiliary pattern, the main pattern must be newly obtained. In the optical proximity effect correction of the main pattern, a method of obtaining a model base from a non-approximate aerial image instead of an approximate aerial image is common. Therefore, in patent document 1, in order to obtain the mask pattern containing a main pattern and an auxiliary pattern, the aerial image calculation which is not approximated must be calculated many times, and there is a problem that much calculation time is required. is there.

  Further, in Patent Document 1, since the main pattern is approximated by a line or a point when the auxiliary pattern is obtained, the interaction of the optical proximity effect between the main pattern and the auxiliary pattern is not considered. Therefore, the main pattern subjected to the optical proximity effect correction obtained later exerts the optical proximity effect on the previously obtained auxiliary pattern. As a result, the expected effect of the auxiliary pattern may not be obtained, or the auxiliary pattern may have an adverse effect. In particular, in the line pattern, the shape change due to the optical proximity effect correction is large at the line tip portion or the bent portion of the main pattern, and it is very difficult to insert the auxiliary pattern.

  Accordingly, an object of the present invention is to provide a generation method for generating original data for accurately forming a fine pattern.

  In order to achieve the above object, a generation method as one aspect of the present invention includes an illumination optical system that illuminates an original using light from a light source, and a projection optical system that projects an image of the pattern on the original onto a substrate. A generation method for generating data of the original used in an exposure apparatus including a computer based on a function representing a light intensity distribution on a pupil plane of the projection optical system and a pupil function of the projection optical system A first calculation step of calculating an approximate aerial image formed on the image plane of the projection optical system based on the two-dimensional mutual transmission coefficient and the pattern on the object plane of the projection optical system; A two-dimensional image extraction step for extracting a two-dimensional image from the approximate aerial image calculated in the first calculation step, and the two-dimensional image extracted in the two-dimensional image extraction step. A main pattern determining step of determining the main pattern by changing the shape of the main pattern of the plate; a second calculating step of calculating an approximate aerial image formed on the image plane for the determined main pattern; A peak portion extraction step for extracting a peak portion where the light intensity reaches a peak in a region excluding the region where the main pattern is projected onto the image plane from the approximate aerial image calculated in the second calculation step; An auxiliary pattern determining step for determining an auxiliary pattern based on the light intensity of the peak portion, and inserting the determined auxiliary pattern into the portion of the original plate corresponding to the extracted peak portion. And generating a pattern data including a pattern and an auxiliary pattern as the original data.

  A program according to another aspect of the present invention causes a computer to execute the above-described generation method.

  According to still another aspect of the present invention, there is provided a method for creating an original based on the data generated by the above-described generation method.

  A processing apparatus according to another aspect of the present invention is characterized by executing the above-described generation method.

  Further objects and other features of the present invention will become apparent from the preferred embodiments described below with reference to the accompanying drawings.

  ADVANTAGE OF THE INVENTION According to this invention, the production | generation method which produces | generates the data of the original plate which forms a fine pattern accurately can be provided, for example.

It is a schematic block diagram which shows the structure of the processing apparatus which performs the production | generation method as 1 side of this invention. It is a flowchart for demonstrating the process in which the control part of the processing apparatus shown in FIG. 1 performs a mask data generation program, and produces | generates mask data. It is a flowchart for demonstrating the process in which the control part of the processing apparatus shown in FIG. 1 performs a mask data generation program, and produces | generates mask data. It is a figure which shows the target pattern (pattern data) in Example 1. FIG. It is a figure which shows the effective light source in Example 1. FIG. FIG. 5 is a diagram illustrating an approximate aerial image calculated in the first embodiment. It is a figure which shows the two-dimensional image extracted from the approximate aerial image shown in FIG. It is a figure for demonstrating the deformation | transformation of pattern data (main pattern). It is a figure which shows the pattern data in which the auxiliary pattern was inserted in Example 1. FIG. It is a figure which shows the two-dimensional image of the exact aerial image obtained from the pattern data shown in FIG. FIG. 11A is a diagram showing a target pattern in the first embodiment, and FIG. 11B shows a two-dimensional image of an aerial image calculated from FIG. 11A. FIG. 12A is a diagram showing a pattern obtained by inserting a scattering bar into the target pattern in the first embodiment, and FIG. 12B is a two-dimensional image of an aerial image calculated from the pattern shown in FIG. FIG. It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG.8 (b). It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown to Fig.11 (a). It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown to Fig.12 (a). It is a figure for demonstrating the method to change the magnitude | size of an auxiliary pattern. It is a figure which shows the pattern data at the time of changing the magnitude | size of the auxiliary pattern in the pattern data shown in FIG. It is a figure which shows the target pattern (pattern data) in Example 2. FIG. It is a figure which shows the effective light source in Example 2. FIG. FIG. 10 is a diagram illustrating an approximate aerial image calculated in the second embodiment. It is a figure which shows the pattern data in which the auxiliary pattern was inserted in Example 2. FIG. It is a figure which shows the two-dimensional image of the exact aerial image obtained from the pattern data shown in FIG. FIG. 24A shows a target pattern in the second embodiment, and FIG. 24B shows a two-dimensional image of an aerial image calculated from FIG. It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown to Fig.24 (a). It is a figure which shows the pattern data at the time of changing the magnitude | size of the auxiliary pattern in the pattern data shown in FIG. It is a figure which shows the line | wire width calculated from the isolated contact hole pattern which exists in the center among the two-dimensional images of the aerial image of the pattern data shown in FIG.22 and FIG.27. FIG. 29A is a diagram showing an approximate aerial image calculated before the auxiliary pattern is inserted into the main pattern deformed in the first embodiment, and FIG. 29B is a diagram showing a constant main pattern deformed in the first embodiment. It is a figure which shows the approximate aerial image calculated after inserting the auxiliary | assistant pattern of a magnitude | size. It is a figure which shows the pattern data in which the auxiliary pattern was inserted in Example 3. FIG. It is a figure which shows the line | wire width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. It is a figure which shows the result of having investigated the change by a focus by dividing the length of a line pattern by the length at the time of the best focus. It is a figure which shows the result of having calculated the NILS of the front-end | tip of a line pattern, and investigated the change by a focus. It is a schematic block diagram which shows the structure of the exposure apparatus as 1 side surface of this invention. It is a flowchart for demonstrating manufacture of a device. FIG. 36 is a detailed flowchart of the wafer process in Step 4 shown in FIG. 35. FIG. It is a figure which shows the target pattern (pattern data) in Example 4. FIG. It is a figure which shows the pattern data in which the auxiliary pattern was inserted in Example 4. FIG. FIG. 39A shows a strict aerial image obtained from the mask pattern shown in FIG. FIG. 39B shows a strict aerial image at the time of defocusing. FIG. 7 is a diagram showing a second-order derivative of the approximate aerial image shown in FIG. FIG. 22 is a diagram showing a second-order derivative of the approximate aerial image shown in FIG.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of the invention will be described with reference to the accompanying drawings. In each figure, the same reference numerals are assigned to the same members, and duplicate descriptions are omitted.

  The present invention provides original data (mask pattern) used in the manufacture of various devices such as semiconductor chips such as IC and LSI, display elements such as liquid crystal panels, detection elements such as magnetic heads, and imaging elements such as CCDs, and micromechanics. It can be applied when generating. Here, the micromechanics refers to a technique for creating a micron-scale mechanical system having advanced functions by applying a semiconductor integrated circuit manufacturing technique to the manufacture of a fine structure, or the mechanical system itself. The present invention is, for example, for generating original data (mask pattern) used in an exposure apparatus having a projection optical system having a large numerical aperture (NA) or an immersion exposure apparatus that fills a space between the projection optical system and the wafer with a liquid. Is preferred.

  The concepts disclosed in the present invention can be modeled mathematically. Accordingly, the present invention can be implemented as a software function of a computer system.

  The software function of the computer system includes programming having executable software code, and in this embodiment, original data (mask data) that forms a fine pattern with high accuracy can be generated. The software code is executed by the processor of the computer system. During software code operation, the code or associated data record is stored within the computer platform. However, the software code may be stored elsewhere or loaded into a suitable computer system. Thus, the software code can be held on at least one computer readable recording medium as one or more modules. The present invention is described in the form of the code described above and can function as one or more software products.

  FIG. 1 is a schematic block diagram illustrating a configuration of a processing apparatus 1 that executes a generation method according to one aspect of the present invention. This generation method generates original (mask) data.

  The processing device 1 is configured by, for example, a general-purpose computer, and as illustrated in FIG. 1, a bus wiring 10, a control unit 20, a display unit 30, a storage unit 40, an input unit 50, a medium interface 60, and the like. Have

  The bus wiring 10 connects the control unit 20, the display unit 30, the storage unit 40, the input unit 50, and the medium interface 60 to each other.

  The control unit 20 includes a CPU, GPU, DSP, or microcomputer, and includes a cache memory for temporary storage. The control unit 20 activates and executes the mask data generation program 401 stored in the storage unit 40 based on the activation command of the mask data generation program 401 input from the user via the input unit 50. The control unit 20 uses the data stored in the storage unit 40 to perform operations associated with a mask data creation method described later.

  The display unit 30 is configured by a display device such as a CRT display or a liquid crystal display, for example. The display unit 30 displays, for example, information related to the execution of the mask data generation program 401 (for example, a two-dimensional image 410 of an approximate aerial image and mask data 408 described later).

  The storage unit 40 is configured by, for example, a memory or a hard disk. The storage unit 40 stores a mask data generation program 401 provided from the storage medium 70 connected to the medium interface 60.

  The storage unit 40 stores pattern data 402, effective light source information 403, NA information 404, λ information 405, aberration information 406, and resist information 407 as input information when executing the mask data generation program 401. To do. Further, the storage unit 40 stores mask data (original data) 408 as output information after the mask data generation program 401 is executed. Further, the storage unit 40 stores an approximate aerial image 409, a two-dimensional image 410 of the approximate aerial image, and deformation pattern data (main pattern and auxiliary pattern) 411 as temporary storage information during execution of the mask data generation program 401.

  The mask data generation program 401 is a program for generating mask data 408 indicating data such as a mask pattern used in an exposure apparatus and a pattern formed by a pattern forming unit of a spatial light modulator (SLM). Here, the pattern is formed by a closed figure, and the pattern of the entire mask is composed of the aggregate.

  The pattern data 402 is data of a layout-designed pattern (a desired pattern to be formed on a wafer, called a layout pattern or a target pattern) in designing an integrated circuit or the like.

  The effective light source information 403 is information regarding the light intensity distribution (effective light source) and polarization formed on the pupil plane of the projection optical system of the exposure apparatus.

  The NA information 404 is information regarding the numerical aperture (NA) on the image plane side of the projection optical system of the exposure apparatus.

  The λ information 405 is information regarding the wavelength of light (exposure light) emitted from the light source of the exposure apparatus.

  The aberration information 406 is information related to the aberration of the projection optical system of the exposure apparatus.

  The resist information 407 is information regarding the resist applied to the wafer.

  The mask data 408 is data indicating a mask pattern which is an actual original generated by executing the mask data generation program 401.

  The approximate aerial image 409 is generated during execution of the mask data generation program 401, and shows an approximate aerial image distribution formed by interference with main diffracted light on the wafer surface.

  The two-dimensional image 410 is a two-dimensional image that is generated during execution of the mask data generation program 401 and is obtained by cutting the approximate aerial image 409 with a reference slice value.

  The deformation pattern data 411 is data including a main pattern that is deformed by executing the mask data generation program 401 and an auxiliary pattern that is inserted by executing the mask data generation program 401.

  Note that the pattern data 402, the mask data 408, and the deformation pattern data 411 include the position, size, shape, transmittance, phase information, and the like of the main pattern and the auxiliary pattern. Further, the pattern data 402, the mask data 408, and the deformation pattern data 411 include the transmittance and phase information of an area (background) where the main pattern and the auxiliary pattern do not exist.

  The input unit 50 includes, for example, a keyboard and a mouse. The user can input input information of the mask data generation program 401 through the input unit 50.

  The medium interface 60 includes, for example, a floppy (registered trademark) disk drive, a CD-ROM drive, a USB interface, and the like, and is configured to be connectable to the storage medium 70. The storage medium 70 is a floppy (registered trademark) disk, CD-ROM, USB memory, or the like, and provides a mask data generation program 401 and other programs executed by the processing device 1.

  Hereinafter, a process in which the control unit 20 of the processing apparatus 1 executes the mask data generation program to generate mask data will be described with reference to FIG.

  In step S102, the control unit 20 calculates an approximate aerial image (that is, an approximate aerial image of the target pattern) based on the input information (pattern data, effective light source information, NA information, λ information, aberration information, and resist information). . The input information (pattern data, effective light source information, NA information, λ information, aberration information, registration information) is input from the user via the input unit 50 and stored in the storage unit 40.

  In step S102, there are two reasons for calculating the approximate aerial image without strictly calculating the aerial image. The first reason is that the time for calculating the approximate aerial image can be much less than the time for calculating the exact aerial image. The second reason is that in the approximate aerial image, the coherence of the pattern is emphasized, and the state of the optical proximity effect is easy to understand.

Various methods for calculating an approximate aerial image have been disclosed in the past. For example, an approximate aerial image can be calculated by modifying the interference map in Patent Document 1. A singular value decomposition is performed on a transmission cross coefficient (TCC), and the i-th eigenvalue is set to λ _i and the i-th eigenfunction is set to Φ _i (f, g). However, (f, g) are the coordinates of the pupil plane of the projection optical system. TCC indicates the coherence of the effective light source (the degree of interference according to the distance on the mask surface). According to Patent Document 1, the interference map e (x, y) is assumed to be a sum of a plurality of eigenfunctions, and can be expressed by the following Equation 1.

  In Equation 1, FT represents a Fourier transform. In general, N ′ is 1.

  In Patent Literature 1, an interference map of the entire mask is derived by replacing the pattern with dots and lines and taking the convolution with the interference map. Therefore, the interference map e (x, y) shows simple coherence.

  However, since the interference map e (x, y) does not consider the mask pattern (outer shape, etc.), when used for calculating the approximate aerial image, the interference map e ′ (x, y taking into account the mask pattern). y) must be derived.

Therefore, TCC is subjected to singular value decomposition, the i-th eigenvalue is λ _i , the i-th eigenfunction is Φ _i (f, g), and the diffracted light distribution of the mask pattern is a (f, g). In this case, an interference map e ′ (x, y) in consideration of the mask pattern can be derived from Equation 2 below.

  By using the interference map e ′ (x, y) shown in Expression 2, an approximate aerial image can be calculated.

  A method for calculating an approximate aerial image without decomposing TCC into singular values (eigenvalues) will be described. The relationship between the mask pattern and the wafer pattern in the semiconductor exposure apparatus is a partial coherent imaging relationship. In partial coherent imaging, information on the effective light source is required to know the coherence on the mask surface. Here, coherency represents the degree of interference according to the distance on the mask surface.

  The coherency of the effective light source is built into the TCC described above. Generally, TCC is defined by the pupil plane of the projection optical system, and is an overlapping portion of an effective light source, a pupil function of the projection optical system, and a complex conjugate of the pupil function of the projection optical system. The coordinates of the pupil plane are (f, g). If the function representing the effective light source is S (f, g) and the pupil function is P (f, g), TCC is

And a four-dimensional function. However, * represents a complex conjugate and the integration range is from −∞ to ∞. Since the aberration of the projection optical system, the polarization of the illumination light, the resist information, and the like can be incorporated into the pupil function P (f, g), in this specification, the polarization, aberration, and , May contain resist information.

  In order to obtain a function I (x, y) that expresses an aerial image using TCC, a function that expresses a mask spectral distribution (diffracted light distribution) by a Fourier transform of a function that expresses a mask, that is, a (f , G)

The quadruple integration may be performed as follows. However, * represents a complex conjugate and the integration range is from −∞ to ∞. M.M. Born and E.M. Wolf, “Principles of Optics”, Cambridge University Press, 1999, 7th (extended) edition, p. 554-632 has a more detailed explanation of Equation 4.

  In the case of directly calculating Formula 4 using a computer, it can be transformed as follows using discretized variables.

However, F- ¹ represents an inverse Fourier transform. W _{f ′, g ′} (f ″, g ″) is fixed (f ′, g ′),

Defined by Here, since (f ′, g ′) is fixed, W _{f ′, g ′} (f ″, g ″) is a two-dimensional function, and is referred to as a two-dimensional mutual transmission coefficient in this specification. The two-dimensional mutual transmission coefficient W _{f ′, g ′} (f ″, g ″) is recalculated every time the value of (f ′, g ′) changes during the addition loop in the computer calculation. In Equation 5, the TCC which is a four-dimensional function is not necessary, and only a double loop calculation is required. Therefore, by using the two-dimensional mutual transmission coefficient, the calculation time can be shortened and the calculation amount can be reduced (the increase in computer memory can be prevented).

  If we rewrite Equation 5,

However,

It is. The aerial image calculation method using Equation 7 is referred to as an aerial image decomposition method in this specification, and Y _{f ′, g ′} (x, y) defined for each coordinate (f ′, g ′) is defined as an aerial image. It is called a function (aerial image component) that expresses the component.

Hereinafter, the difference between Formula 3 and Formula 6 will be described in detail. The center of the effective light source is assumed to be at the origin of the pupil coordinate system. A function obtained by shifting the pupil function P (f, g) of the projection optical system by coordinates (f ′, g ′) and a complex conjugate function P ^* (f, g) of P (f, g) are represented by coordinates (f ″). , G '') and the sum of the portions where the function representing the effective light source overlaps is defined as TCC. Note that P ^* (f, g) may be called a complex conjugate function of the pupil function of the projection optical system.

On the other hand, W _{f ′, g ′} (f ″, g ″) in Expression 6 is defined when the deviation of P (f, g) is a constant amount (f ′, g ′). The sum of the portion where the effective light source overlaps with the pupil function and the portion where P ^* (f, g) overlaps with the function shifted by (f ″, g ″) is W _{f ′, g ′} (f ′ ', G'').

Y _{f ′, g ′} (x, y) is also defined when the deviation of P (f, g) is a constant amount (f ′, g ′). Multiplying W _{f ′, g ′} (f ″, g ″) by a function a ^* (f ″, g ″) that is a complex conjugate of the function expressing the spectral amplitude (diffracted light amplitude) of the mask. And inverse Fourier transform. Then, the inverse Fourier transform function is added to the functions exp [−i2π (f′x + g′y)] and (f ′, g ′) representing the oblique incidence effect corresponding to the pupil function deviation, and the amplitude a ( Multiplying _{f ′, g ′} ) yields Y _{f ′, g ′} (x, y). A function obtained by making the function expressing the diffracted light amplitude of the mask a complex conjugate is called a complex conjugate function of the diffracted light distribution of the mask.

The function exp [−i2π (f′x + g′y)] representing the oblique incidence effect will be described below. Let θ be the angle between the traveling direction of the plane wave represented by exp [−i2π (f′x + g′y)] and the optical axis. Since there is a relationship of sin ² θ = (NA / λ) (f ′ ² + g ′ ² ), the traveling direction of the plane wave is inclined with respect to the optical axis. Therefore, it represents an oblique incidence effect. exp [−i2π (f′x + g′y)] can also be regarded as a function representing a plane wave that travels in a direction connecting (f ′, g ′) on the pupil plane and a point where the optical axis intersects the image plane. . Since the diffracted light amplitude a (f ′, g ′) at the pupil plane coordinates (f ′, g ′) is a constant, multiplying the amplitude of the diffracted light at (f ′, g ′) is multiplied by a constant. In other words,

Next, approximation of an aerial image will be described. As shown in Equation 9, a function I _app (x, y) that represents an approximate aerial image (hereinafter, approximate aerial image) is defined.

At this time, there are M combinations of (f ′, g ′), and M ′ is an integer equal to or less than M. When M ′ = 1, the approximate aerial image represents Y _0,0 (x, y) as in Expression 10. When M ′ = M, this corresponds to Equation 7, and a complete aerial image can be obtained.

Note that a (0, 0) is a constant, and W _0,0 (f ″, g ″) is a convolution integral of a function representing an effective light source and a complex conjugate function of a pupil function. Note that the Fourier transform and the inverse Fourier transform may be used interchangeably. Therefore, Y _0,0 (x, y) is Fourier obtained by multiplying the convolution integral of the function representing the effective light source and the pupil function or the complex conjugate function of the pupil function by the diffracted light distribution or the complex conjugate function of the diffracted light distribution. It has been transformed or inverse Fourier transformed.

As described above, the approximate aerial image is a function obtained by adding one or two or more of the aerial image components Y _{f ′, g ′} (x, y) whose M ′ is less than or equal to M using Equation 9 or 10. And In the following embodiment, an approximate aerial image is calculated by using one of the aerial image components Y _{f ′, g ′} (x, y) (Equation 10) with M ′ = 1 in Equation 9. However, an approximate aerial image can also be calculated using Equation 2.

  Next, the physical meaning of the approximate aerial image will be described in detail. In coherent imaging, a point spread function (a function representing the intensity distribution of a point image) can be determined. If the point spread function has a positive position as an opening and a negative position as a light shielding part (or an opening having a phase of 180 degrees), a Fresnel lens can be created. An isolated contact hole can be exposed by coherent illumination using the Fresnel lens thus created as a mask.

  A Fresnel lens can be defined during coherent illumination based on a point spread function. However, the point spread function cannot be obtained when partially coherent. This is because the image plane amplitude cannot be obtained by partial coherent imaging. Therefore, the eigenvalue decomposition method approximates the amplitude of the image plane.

  However, the physical meaning of the calculation method using the above-described two-dimensional mutual transmission coefficient is different from the eigenvalue decomposition method. First, the point spread function is given by Fourier transform of a frequency transfer characteristic (Modulation Transfer Function). The frequency response characteristic at the time of coherent illumination is given by the convolution integral of the pupil function and the effective light source, and becomes the pupil function itself. It is a well-known fact that the frequency response characteristic during incoherent illumination is given by the autocorrelation of the pupil function. Assuming that incoherent illumination is illumination with σ = 1 in the exposure apparatus, the frequency response characteristic is given by an effective light source of the pupil function even during incoherent illumination.

Therefore, the frequency response characteristic at the time of partial coherent illumination is approximated by a convolution integral of a pupil function and an effective light source. That is, it is approximated that W _0,0 (f ″, g ″) is a frequency response characteristic. Therefore, in order to obtain a point spread function at the time of partial coherent illumination, W _0,0 (f ″, g ″) may be Fourier-transformed. If the mask opening and the light shielding portion are determined according to the point spread function thus obtained, the isolated contact hole can be exposed with the same effect as the Fresnel lens.

In order to improve imaging characteristics for an arbitrary mask pattern, a point pattern distribution function and a mask function may be convolved and integrated, and a mass pattern may be determined based on the obtained result. Here, according to Equation 10, it can be seen that Y _0,0 (x, y) is the product of Fourier transform of the product of the diffracted light and W _0,0 (f ″, g ″). The diffracted light is the Fourier transform of the mask function, and W _0,0 (f ″, g ″) is the Fourier transform of the point spread function. As a result, according to the formula, Y _0,0 (x, y) is a convolution integral of the mask function and the point spread function.

From the above, deriving Y _0,0 (x, y) is equivalent to obtaining the convolution integral of the point spread function and the mask function at the time of partial coherent imaging.

It has been described that W _0,0 (f ″, g ″) approximates the frequency response characteristic during partial coherent illumination. _{W 0,0 (f '', g} '') other than _{W f ', g' (f} '', g '') , the frequency response characteristics omitted in approximating the frequency response characteristic in partial coherent illumination You can say that. Therefore, Y _{f ′, g ′} (x, y) other than Y _0,0 (x, y) is a component omitted when performing convolution integration of the point spread function and the mask pattern during partial coherent illumination. It can be said that there is. Therefore, when M ′ is set to 1 or more in Equation 9, the accuracy of approximation is improved.

  A conventional interference map is obtained as a result of eigenvalue decomposition of a four-dimensional TCC, and in order to obtain an aerial image, the absolute value of the eigenfunction must be squared and added. However, in order to obtain an aerial image by the aerial image decomposition method as shown in Equation 7, it is not necessary to take the square of the absolute value of the aerial image component, and it is sufficient to simply add the aerial image components. Therefore, the aerial image decomposition method and the singular value (eigenvalue) decomposition method handle physical quantities having different units, and their properties are completely different.

  In step S104, a two-dimensional image is extracted from the approximate aerial image calculated in step S102. Specifically, a reference slice value (Io) is set, and a two-dimensional image at the cross section of the approximate aerial image is extracted. For example, when the pattern data is a transmission pattern, a portion where the intensity value of the approximate aerial image is equal to or greater than a predetermined value (a threshold value that can be arbitrarily set) is extracted as a two-dimensional image. When the pattern data is a light shielding pattern, a portion where the intensity value of the approximate aerial image is equal to or less than a predetermined value (a threshold value that can be arbitrarily set) is extracted as a two-dimensional image.

  In step S106, the control unit 20 compares the two-dimensional image extracted in step S104 with the target pattern and determines whether or not the difference between the two-dimensional image and the target pattern is within a preset allowable range. . The parameter (evaluation value) for comparing the two-dimensional image with the target pattern may be a line width, a pattern length, or the like, or a NILS (Normalized Image Log Slope) or an intensity peak value. .

  If it is determined in step S106 that the difference between the two-dimensional image and the target pattern is not within the allowable range, the control unit 20 determines that the difference between the two-dimensional image and the target pattern is within the allowable range in step S108. The main pattern is determined as follows. Specifically, in step S106, the main pattern is determined by deforming the shape of the main pattern based on the two-dimensional image. Detailed processing in determining the main pattern in step S106 will be described in Examples 1 to 4 described later.

  In step S110, the control unit 20 uses the main pattern deformed in step S108 as pattern data, calculates an approximate aerial image from effective light source information, NA information, λ information, aberration information, and resist information input by the user, The process returns to step S104. Steps S104 to S110 are repeated until the difference between the two-dimensional image and the target pattern falls within an allowable range.

  When it is determined in step S106 that the difference between the two-dimensional image and the target pattern is within the allowable range, in step S112, the control unit 20 determines an auxiliary pattern. First, a position (auxiliary pattern insertion position) for inserting an auxiliary pattern is extracted from the approximate aerial image calculated in step S110 (that is, the approximate aerial image of the deformed main pattern). The auxiliary pattern insertion position has a light intensity peak (maximum value or minimum value) in a region that does not exceed the reference slice value (Io) and does not overlap the main pattern (that is, a region other than the region where the target pattern is projected). This is the peak part. It should be noted that the auxiliary pattern insertion position is actually a portion on the mask corresponding to the peak portion. Then, the size of the auxiliary pattern is determined based on the light intensity of the peak portion, and the auxiliary pattern having such a size is inserted at the auxiliary pattern insertion position. Detailed processing in the determination of the auxiliary pattern in step S112 will be described in Examples 1 to 4 described later.

  In step S114, the control unit 20 generates, as mask data, data including the main pattern determined in step S108 and the auxiliary pattern determined (inserted) in step S112.

  Thus, the mask data generation program (mask data generation method) includes an aerial image calculation step, a two-dimensional image extraction step, a main pattern determination step, a peak portion extraction step, an auxiliary pattern determination step, and a generation step. And execute.

  However, the insertion of the auxiliary pattern may cause a change in the optical proximity effect with the main pattern. In such a case, mask data may be generated in consideration of the optical proximity effect between the main pattern and the auxiliary pattern, as shown in FIG.

  Referring to FIG. 3, in step S116, the control unit 20 calculates an approximate aerial image using the pattern obtained by adding the main pattern determined in step S108 and the auxiliary pattern determined in step S112 as pattern data. However, as input information other than pattern data, effective light source information, NA information, λ information, aberration information, and resist information input from the user are used.

  In step S118, the control unit 20 extracts a two-dimensional image from the approximate aerial image calculated in step S116.

  In step S120, the control unit 20 compares the two-dimensional image extracted in step S118 with the target pattern, and determines whether or not the difference between the two-dimensional image and the target pattern is within a preset allowable range. .

  If it is determined in step S120 that the difference between the two-dimensional image and the target pattern is not within the allowable range, the process returns to step S108, and the control unit 20 determines that the difference between the two-dimensional image and the target pattern is within the allowable range. The main pattern is determined so that

  If it is determined in step S120 that the difference between the two-dimensional image and the target pattern is within the allowable range, the process proceeds to step S114. In step S114, the control unit 20 generates a pattern obtained by adding the main pattern determined in step S108 and the auxiliary pattern determined in step S112 as mask data.

  In the process shown in FIG. 3, first, a first aerial image calculation step corresponding to step S102, a first two-dimensional image extraction step corresponding to step S104, and a first main pattern determination step corresponding to step S108. Are executed. Next, a first peak portion extraction step corresponding to step S112, a first auxiliary pattern determination step, a second aerial image calculation step corresponding to step S116, and a second two-dimensional corresponding to step S118 An image extraction step is performed. Then, a second main pattern determination step corresponding to step S108, a second peak portion extraction step corresponding to step S112, a second auxiliary pattern determination step, and a generation step corresponding to step S114 are executed. Is done.

  The original data is created by the process shown in FIGS. 2 and 3 and the exposure process is performed using the original created by inputting the data to the EB drawing apparatus. A pattern can be formed with high accuracy. That is, it is possible to generate original data that can form a fine pattern with high accuracy. The original pattern to be created may include a pattern other than the pattern created by the above-described mask data creation program.

  Hereinafter, in the first to fourth embodiments, a process for executing the mask data generation program to generate the mask data will be specifically described, and mask data generated by the process will be described. Note that the wavelength of the exposure light is λ, and the numerical aperture on the image side of the projection optical system is NA. Also, let σ be the ratio of the numerical aperture of the illumination light incident on the mask surface from the illumination optical system and the numerical aperture on the object side of the projection optical system.

  In the exposure apparatus, since various values can be set for the wavelength λ of the exposure light and the numerical aperture NA of the projection optical system, it is preferable to normalize the mask pattern size by (λ / NA). For example, when λ is 248 nm and NA is 0.73, the 100 nm pattern is 0.29 due to the above-described normalization. Such normalization is referred to as k1 conversion.

  The pattern size on the mask surface and the pattern size on the wafer surface differ by the magnification of the projection optical system. However, in the following, in order to simplify the explanation, the pattern size on the mask surface and the pattern size on the wafer surface are 1: 1 corresponds. Thereby, the coordinate system of the mask surface and the coordinate system of the wafer surface correspond 1: 1.

  In the first embodiment, a case where the NA of the projection optical system is 0.73 (corresponding to NA information) and the wavelength of exposure light is 248 nm (corresponding to λ information) is considered as the exposure apparatus. The projection optical system has no aberration (corresponding to aberration information) and does not consider the resist applied to the wafer (corresponding to resist information). The illumination light is assumed to be non-polarized light.

  The target pattern (pattern data) is an isolated line pattern as shown in FIG. 4 and has a line width of 120 nm and a length of 2400 nm. In FIG. 4, it is assumed that the isolated line pattern is a light-shielding pattern (that is, the transmittance is zero), and the transmittance of a region (background) where such an isolated line pattern does not exist is 1. All phases were zero. FIG. 4 is a diagram illustrating a target pattern (pattern data) in the first embodiment.

  As the effective light source, quadrupole illumination (corresponding to effective light source information) as shown in FIG. 5 is used. In FIG. 5, the white circle represents σ = 1, and the four white areas represent the light irradiation unit. Here, FIG. 5 is a diagram illustrating an effective light source in the first embodiment. The effective light source is shown as an example and is not limited to this.

  First, when an approximate aerial image is calculated from the target pattern and the above-described input information (effective light source information, NA information, λ information, aberration information, and resist information) using Expression 10, the approximate aerial image shown in FIG. Is obtained. In FIG. 6A, the target pattern is shown by being overlapped with a black line.

  In the approximate aerial image shown in FIG. 6A, it can be seen that the tip of the isolated line pattern is wavy and the light shielding portion in the longitudinal direction of the target pattern is shorter than the target pattern.

  If the approximate aerial image after deforming the main pattern by executing the mask data generation program 401 described above is calculated, an approximate aerial image shown in FIG. 6B is obtained. In the approximate aerial image shown in FIG. 6B, the intensity distribution inside the overlaid target pattern is substantially uniform.

  FIG. 7A shows a two-dimensional image (cross-sectional image) obtained by cutting the approximate aerial image shown in FIG. 6A with reference slice values (Io), 0.95 Io, and 1.05 Io. Similarly, FIG. 7B shows a two-dimensional image (cross-sectional image) obtained by cutting the approximate aerial image shown in FIG. 6B with reference slice values (Io), 0.95 Io, and 1.05 Io. In FIG. 7A and FIG. 7B, the target pattern is shown superimposed with a black line. The reference slice value (Io) is also referred to as a threshold value below.

  It is possible to obtain a difference (for example, shape change, degree of inclination, intensity value or intensity peak, Log-slope) from the target pattern from the two-dimensional image of the approximate aerial image shown in FIGS. 7A and 7B. The main pattern is determined (deformed) based on this.

  The determination (deformation) of the main pattern will be specifically described. First, as shown in FIG. 8A, the target pattern and pattern data (the initial pattern data is the same as the target pattern) are divided, and the two-dimensional image is divided by the same number of divisions. Then, the target pattern is compared with the divided elements of the two-dimensional image, and the pattern data is deformed (corrected) based on the difference. However, the target pattern is not deformed. The pattern data may be divided by removing unnecessary elements or adding new elements.

  When the divided elements of the pattern data are transformed based on the difference between the target pattern and the two-dimensional image, the pattern data shown in FIG. 8B is obtained. Then, an approximate aerial image is calculated using the modified pattern data as new pattern data, and the same processing is repeated until the difference between the target pattern and the two-dimensional image falls within an allowable range. As described above, the approximate aerial image shown in FIG. 6B is calculated from the pattern data shown in FIG.

  Next, an auxiliary pattern is inserted. From the approximate aerial image shown in FIG. 6B, a peak portion where the light intensity reaches a peak is extracted in a region that does not overlap the target pattern (that is, a region other than the region where the main pattern is projected). When the target pattern is a light-shielding pattern, a peak in an area that is equal to or greater than the threshold and darker than the background is obtained, and a rectangular auxiliary pattern is inserted into the peak portion. In the line pattern, it is only necessary to detect the peak part in a one-dimensional manner and extract the peak part. At least the peak part is detected along the direction perpendicular to the longitudinal direction of the line pattern and the direction parallel to the longitudinal direction of the line pattern. do it. Note that the position at which the auxiliary pattern is inserted may be the barycentric position of the peak portion in a darker area than the background. In addition, the peak position (partial) is obtained by calculating the value (positive / negative) of the second derivative of the light intensity distribution of the approximate aerial image (for example, the second derivative with respect to each of the orthogonal two-axis directions and taking the sum (Laplace)). ) Can also be calculated. A map of the second derivative (Laplacian) of the intensity distribution is shown in FIG. The line pattern having the size affects the position where the intensity of the main pattern is far from the main pattern in the approximate aerial image. Therefore, even in a region that does not overlap with the main pattern, it overlaps with the intensity peak due to interference, making it difficult to detect the peak portion. The first-order gradient in each direction is easy to carry noise and difficult to handle. Therefore, it is effective to calculate the peak position by obtaining the value of the second derivative of the intensity distribution in a line pattern having a size and a complicated shape.

  The size of one side of the auxiliary pattern needs to be a line width that does not resolve. Specifically, in the light shielding pattern, the difference between the light intensity of the background and the minimum value of the light intensity of the main pattern, and the difference between the light intensity of the background and the minimum value of the light intensity of the region that does not overlap the target pattern. It is determined by the ratio. Although it depends on the exposure process, in the case of a line pattern, the size of one side of the auxiliary pattern is about 1/3 to 1/2 of the short direction of the line pattern. In Example 1, the size of one side of the square auxiliary pattern was 40 nm.

  When the auxiliary pattern described above is inserted into the deformed main pattern, pattern data as shown in FIG. 9 is obtained. In this way, the pattern data shown in FIG. 9 is generated as mask data. It is confirmed (evaluated) whether the mask manufactured from the mask data forms a desired aerial image on the wafer surface.

  When evaluating the mask data, the aerial image, not the approximate aerial image, is strictly calculated and evaluated. FIG. 10 shows a two-dimensional image of the aerial image calculated strictly from the pattern data (mask data) shown in FIG. Referring to FIG. 10, it can be seen that the image is uniform and the length is not shortened, and is closer to the target pattern.

  Here, for comparison, an aerial image is calculated for the target pattern itself and a pattern in which a typical auxiliary pattern (scattering bar) is inserted into the target pattern itself. Calculation is performed for a target pattern itself as shown in FIG. 11A and a pattern in which an auxiliary pattern (scattering bar) having a width of 40 nm is inserted at a half pitch (120 nm) into the target pattern as shown in FIG. To do. A two-dimensional image of an aerial image calculated from the target pattern itself as shown in FIG. 11A is shown in FIG. 11B, and a pattern in which a scattering bar is inserted into the target pattern as shown in FIG. A two-dimensional image of the aerial image calculated from the above is shown in FIG.

  A two-dimensional image of the aerial image calculated from the pattern data shown in FIGS. 8B, 9, 11 A and 12 A is quantitatively evaluated. Specifically, the aerial image was calculated by changing the defocus from the pattern data, and the line width was calculated. Here, when the horizontal axis of each figure is x and the vertical axis is y, the center of the two-dimensional image (x = 0, y = 0) and 70% of the position from the center to y = 1200 (x = 0) , Y = 840) and 90% of the line width (x = 0, y = 1080) with respect to y = 1200 from the center.

  FIG. 13 shows the line width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. The line width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. 9 is shown in FIG. FIG. 15 shows the line width calculated from the two-dimensional aerial image of the pattern data shown in FIG. FIG. 16 shows the line width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. 13 to 16, the horizontal axis represents defocus (μm), and the vertical axis represents line width CD (nm). Here, the unit of length was nm.

  Referring to FIG. 15, in the two-dimensional image of the aerial image of the target pattern itself as shown in FIG. 11A, the line width at 90% of the position is narrower, and the line width change with respect to the focus changes. large.

  Referring to FIG. 16, in the two-dimensional image of the aerial image of the pattern in which the scattering bar is inserted into the target pattern as shown in FIG. 12 (a), the line width change with respect to the focus is moderate, but from the center. The variation in line width at 70% and 90% positions is large.

  Referring to FIG. 13, in the two-dimensional image of the aerial image of the deformed main pattern as shown in FIG. 8B, the line width variation at the positions of 70% and 90% is small.

  Referring to FIG. 14, in the two-dimensional aerial image of the pattern in which the auxiliary pattern is inserted into the deformed main pattern as shown in FIG. 9, there is a variation in the line width at 70% and 90% positions from the center. It becomes the smallest and the line width change with respect to the focus is moderate.

  As described above, the mask data (pattern data) generated from the mask data generation program 401 described above has improved image performance over the mask data to which the scattering bar generated by the conventional technique is added, and the isolated line pattern. Can be formed with high accuracy.

  Note that the size of the auxiliary pattern may be changed according to the light intensity (peak value size) of the peak portion instead of making the size of the auxiliary pattern constant. Specifically, as shown in FIG. 17, when the length of one side of the i-th auxiliary pattern is ai and the reference size is ao, the length of one side ai of the i-th auxiliary pattern is Two methods are conceivable as changing methods. Here, FIG. 17 is a diagram for explaining a method of changing the size of the auxiliary pattern.

  The first method is a method of changing the length ai of one side of the i-th auxiliary pattern in proportion to the light intensity of the peak portion, as expressed by the following formula 11.

  In Equation 11, Ii is the light intensity value at the position of the i-th auxiliary pattern, and Iback is the background transmittance.

  FIG. 18A shows pattern data when the size of the auxiliary pattern in the pattern data (mask data) shown in FIG. 9 is changed by the first method.

  The second method is a method of changing the length ai of one side of the i-th auxiliary pattern in inverse proportion to the light intensity of the peak portion, as expressed by the following Expression 12.

  In the case of the second method, an upper limit length a_limit is determined in advance, and if ai> a_limit, ai = a_limit.

  FIG. 18B shows pattern data when the size of the auxiliary pattern in the pattern data (mask data) shown in FIG. 9 is changed by the second method.

  In the case of the first method, when an approximate aerial image is calculated by inserting an auxiliary pattern, the distribution of the approximate aerial image is not significantly different from that before the auxiliary pattern is inserted. Therefore, the pattern shape reproducibility is not significantly different from that in the case where the auxiliary pattern is not inserted, but there is little change in image performance such as focus depth expansion.

  On the other hand, in the case of the second method, when the approximate aerial image is calculated by inserting the auxiliary pattern, the distribution of the approximate aerial image is significantly different from that before the auxiliary pattern is inserted. Therefore, the second method is a method of changing the distribution of the approximate aerial image, and is suitable for active use such as arbitrarily operating the approximate aerial image.

  For example, the second method can increase the influence on the main pattern by inserting a relatively large auxiliary pattern at a position having low coherence. In other words, the coherence can be enhanced by inserting a relatively large auxiliary pattern at a position having a small coherence. In addition, changes in image performance such as focus depth expansion can be maximized.

  Also, even if a relatively large auxiliary pattern is inserted at a position with low coherence, if the upper limit size is determined so that the resolution does not exceed the threshold, the auxiliary pattern may be unnecessarily resolved. Absent. The size of the upper limit at which the auxiliary pattern is not resolved actually depends on the intensity of the approximate aerial image at the position where the auxiliary pattern is arranged, so that each of the auxiliary patterns is based on the intensity at the position where the auxiliary pattern is arranged. You may ask for the size of. However, it should be noted that the pattern shape reproducibility changes greatly from the case where no auxiliary pattern is inserted. When the pattern shape is overcorrected, it is possible to correct the overcorrection as will be described later in the third embodiment.

  In the second embodiment, the case where the NA of the projection optical system is 0.75 (corresponding to NA information) and the wavelength of the exposure light is 193 nm (corresponding to λ information) is considered as the exposure apparatus. The projection optical system has no aberration (corresponding to aberration information) and does not consider the resist applied to the wafer (corresponding to resist information). Note that the illumination light is non-polarized light.

  The target pattern (pattern data) is a contact hole pattern as shown in FIG. 19 and has a width of 120 nm and a half pitch of 100 nm (k1 conversion = 0.39). In FIG. 19, it is assumed that the contact hole pattern is a transmission pattern (that is, the transmittance is 1), and the transmittance of a region (background) where such a contact hole pattern does not exist is zero. All phases were zero. FIG. 19 is a diagram illustrating a target pattern (pattern data) according to the second embodiment.

  As an effective light source, quadrupole illumination (corresponding to effective light source information) as shown in FIG. 20 is used. In FIG. 20, a white circle represents σ = 1, and four white areas represent light irradiation portions. Here, FIG. 20 is a diagram illustrating an effective light source in the second embodiment.

  First, when an approximate aerial image is calculated from the target pattern and the above-described input information (effective light source information, NA information, λ information, aberration information, and resist information) using Expression 10, the approximate aerial image shown in FIG. Is obtained. In FIG. 21 (a), the target pattern is shown superimposed with a black line.

  The approximate aerial image shown in FIG. 21A shows that the light intensity peak value varies depending on the contact hole patterns.

  When the approximate aerial image after deforming the main pattern by executing the mask data generation program 401 described above is calculated, an approximate aerial image shown in FIG. 21B is obtained. In the approximate aerial image shown in FIG. 21 (b), the intensity peak value is almost uniform in each contact hole pattern.

  The determination (deformation) of the main pattern will be specifically described. Since the contact hole pattern is not a complicated shape, only the size and the position are changed without dividing the target pattern, but the main pattern can be determined (deformed) by dividing the target pattern as in the first embodiment. Is possible.

  Based on the difference obtained by comparing the target pattern and the two-dimensional image of the approximate aerial image, the pattern data is transformed (corrected). However, the target pattern is not deformed. Then, an approximate aerial image is calculated using the modified pattern data as new pattern data, and the same processing is repeated until the difference between the target pattern and the two-dimensional image falls within an allowable range. From the pattern data obtained in this way, an approximate aerial image shown in FIG. 21B is calculated.

  Further, from the approximate aerial image shown in FIG. 21B, a peak portion where the light intensity reaches a peak is extracted in a region that does not overlap with the target pattern (that is, a region excluding the region where the main pattern is projected). When the target pattern is a transmission pattern, a peak in an area that is equal to or smaller than the threshold and brighter than the background is obtained, and a rectangular auxiliary pattern is inserted into the peak portion. In the contact hole pattern, the peak portion may be extracted by detecting the peak portion two-dimensionally. Note that the position where the auxiliary pattern is inserted may be the position of the center of gravity of the peak portion in an area brighter than the background. For the contact hole pattern, the peak position (part) can be easily calculated by obtaining the value of the second derivative (for example, Laplacian) of the light intensity distribution of the approximate aerial image. FIG. 41 shows a map of the second derivative (Laplacian) of the intensity distribution. If the contact hole pattern has a certain size, the strength of the main pattern affects the position away from the main pattern in the approximate aerial image. Therefore, even in a region that does not overlap with the main pattern, it overlaps with the intensity peak due to interference, making detection difficult.

  The size of one side of the auxiliary pattern needs to be a line width that does not resolve. Specifically, in the transmission pattern, it is obtained by a ratio between the maximum value of the light intensity of the main pattern and the maximum value of the light intensity of the region not overlapping with the target pattern. Although it depends on the exposure process, in the case of a contact hole pattern, the size of one side of the auxiliary pattern is about 60% to 80% of the line width of the contact hole pattern. In Example 2, the size of one side of the auxiliary pattern was 75 nm.

  When the auxiliary pattern described above is inserted into the deformed main pattern, pattern data as shown in FIG. 22 is obtained. Thus, the pattern data shown in FIG. 22 is generated as mask data. It is confirmed (evaluated) whether the mask manufactured from the mask data forms a desired aerial image on the wafer surface.

  FIG. 23 shows a two-dimensional image of the aerial image calculated strictly from the pattern data (mask data) shown in FIG. FIG. 24B shows a two-dimensional image of an aerial image calculated strictly from the target pattern itself as shown in FIG. Comparing FIG. 23 and FIG. 24B, the two-dimensional image shown in FIG. 23 has better uniformity of each contact hole than the two-dimensional image shown in FIG. 24B, and the elliptical distortion is reduced. You can see that

A two-dimensional image of the aerial image calculated from the pattern data shown in FIGS. 22 and 24A is quantitatively evaluated. Specifically, the aerial image was calculated from the pattern data by changing the defocus, and the line width (hole diameter) was calculated. Here, the line widths of the isolated contact hole pattern CH ₁ existing at the center of the two-dimensional image, the contact hole pattern CH ₂ existing at the end of the dense hole array, and the contact hole pattern CH ₃ existing at the center of the hole array CD was calculated (see FIG. 24A).

  The line width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. 22 is shown in FIG. FIG. 26 shows the line width calculated from the two-dimensional aerial image of the pattern data shown in FIG. In FIGS. 25 and 26, the horizontal axis represents defocus (μm), and the vertical axis represents line width CD (nm).

  Referring to FIG. 26, in the two-dimensional image of the aerial image of the target pattern itself as shown in FIG. 24A, there is a variation in line width in the isolated contact hole pattern and the contact hole pattern of the dense hole array. Large, line width change with respect to focus is also large.

  Referring to FIG. 25, in the two-dimensional image of the aerial image of the pattern in which the auxiliary pattern is inserted into the deformed main pattern as shown in FIG. 22, the variation in the line width is small, and the change in the line width with respect to the focus is moderate. It has become.

  As described above, the mask data (pattern data) generated from the above-described mask data generation program 401 has improved image performance over the mask data generated by the prior art, and forms the contact hole pattern with high accuracy. Can do.

  Further, as in the first embodiment, the size of the auxiliary pattern may be changed in accordance with the light intensity (peak value size) of the peak portion instead of making the size of the auxiliary pattern constant. FIG. 27 shows pattern data when the size of the auxiliary pattern in the pattern data (mask data) shown in FIG. 22 is changed by the second method.

  By changing the size of the auxiliary pattern, it is possible to improve the effect of the auxiliary pattern on an isolated contact hole pattern or a contact hole pattern that exists at the end of a dense hole array.

  FIG. 28 shows the line width calculated from the isolated contact hole pattern existing at the center of the two-dimensional aerial image of the pattern data shown in FIGS. As described above, the pattern data shown in FIG. 22 is a case where the size of the auxiliary pattern is constant, and the pattern data shown in FIG. 27 is a case where the size of the auxiliary pattern is changed. In FIG. 28, the horizontal axis represents defocus (μm), and the vertical axis represents line width CD (nm).

  Referring to FIG. 28, when the size of the auxiliary pattern is changed (FIG. 27), the line width change with respect to the focus is small compared to the case where the size of the auxiliary pattern is constant (FIG. 22) (that is, It can be seen that the focus characteristics are excellent.

  As described above, the insertion of the auxiliary pattern causes a new optical proximity effect between the auxiliary pattern and the main pattern. In particular, when the size of the auxiliary pattern is changed in inverse proportion to the light intensity at the peak portion, the coherence changes greatly, so that there is a possibility that the pattern shape reproducibility and individual pattern shapes may vary. In such a case, as shown in the flowchart of FIG. 3, after inserting the auxiliary pattern into the deformed main pattern, the approximate aerial image is calculated again, and these pattern data can be further deformed (corrected). It is effective.

  The third embodiment will be described using the example of the first embodiment. FIG. 29A shows an approximate aerial image calculated before the auxiliary pattern is inserted into the deformed main pattern in the first embodiment, and after the auxiliary pattern having a certain size is inserted into the deformed main pattern in the first embodiment. The approximate aerial image calculated in step (b) is shown in FIG. When comparing the approximate aerial image shown in FIG. 29A and the approximate aerial image shown in FIG. 29B, the distribution changes greatly.

  A two-dimensional image is extracted from the approximate aerial image shown in FIG. 29B, and the main pattern is deformed based on the two-dimensional image, as in the first embodiment. Further, an auxiliary pattern is inserted. The auxiliary pattern may or may not be newly extracted as it is. In this case, the optical proximity effect that is changed by inserting the auxiliary pattern can be corrected as a change in the shape of the main pattern. Then, an approximate aerial image is calculated using the modified pattern data as new pattern data, and the same processing is repeated until the difference between the target pattern and the two-dimensional image falls within an allowable range. The pattern data (mask data) thus obtained is shown in FIG.

  A two-dimensional image of the aerial image calculated from the pattern data shown in FIG. 30 is quantitatively evaluated. Specifically, the aerial image was calculated by changing the defocus from the pattern data, and the line width was calculated. Here, when the horizontal axis of each figure is x and the vertical axis is y, the center of the two-dimensional image (x = 0, y = 0) and 70% of the position from the center to y = 1200 (x = 0) , Y = 840) and 90% of the line width (x = 0, y = 1080) with respect to y = 1200 from the center.

  The line width calculated from the two-dimensional image of the aerial image of the pattern data shown in FIG. 30 is shown in FIG. When comparing FIG. 15 and FIG. 31, the two-dimensional image of the aerial image of the pattern data shown in FIG. 30 has a small variation in line width, and the change in line width with respect to the focus is gentle. Further, the calculation result of the line width shown in FIG. 31 is almost the same as the calculation result of the line width shown in FIG.

  In the line pattern, shortening the length of the line pattern is a big problem. Therefore, the tip of the line pattern is evaluated. In the best focus, the length of the line pattern may be increased in anticipation of the shortening of the line pattern. However, since the line pattern is shortened as defocusing is performed, it is preferable that the length of the line pattern does not change due to the focus. Moreover, it is preferable that the contrast of the tip of the line pattern is good. The contrast of the tip of the line pattern is evaluated by NILS.

  FIG. 32 shows the result of examining the change due to the focus by dividing the length of the line pattern by the length at the time of the best focus. FIG. 33 shows the result of calculating the NILS at the tip of the line pattern and examining the change due to the focus. 32 and 33, pattern_before indicates that the pattern data is the target pattern itself (that is, initial pattern data) (FIG. 11A). SB shows a case where a scattering bar is inserted into the target pattern (FIG. 12A). OPC shows a case where the main pattern is deformed based on the approximate aerial image (FIG. 8B). OPC1 + assist1 shows a case where the main pattern of the first embodiment is deformed based on the approximate aerial image and an auxiliary pattern having a constant size is inserted (FIG. 9). OPC2 + assist2 shows a case (FIG. 30) of a pattern in which an auxiliary pattern having a constant size is inserted by deforming the main pattern of the third embodiment based on the approximate aerial image.

  Referring to FIG. 32, it can be seen that in OPC1 + assist1 (FIG. 9) and OPC2 + assist2 (FIG. 30), the change in the length of the line pattern is the smallest with respect to the variation in focus.

  33, OPC2 + assist2 (FIG. 30) has the largest NILS at the tip of the line pattern at the best focus. Further, OPC1 + assist1 (FIG. 9) shows that NILS at the end of the line pattern is slightly inferior to OPC2 + assist2 at best focus, but hardly changes with respect to focus.

  Next, an example in which the target pattern is a pattern different from the line pattern will be described. As an exposure apparatus, consider a case where the NA of the projection optical system is 0.73 (corresponding to NA information) and the wavelength of exposure light is 193 nm (corresponding to λ information). A shift of the focal position (defocus) is added as an aberration of the projection optical system. The resist applied to the wafer is not considered (corresponding to resist information). The illumination light is assumed to be non-polarized light.

  The target pattern (pattern data) is an L-shaped (Elbow) pattern as shown in FIG. 37, and the vertical and horizontal lengths are 1200 nm. In FIG. 37, it is assumed that the isolated line pattern is a light shielding pattern (that is, the transmittance is zero), and the transmittance of a region (background) where such an isolated line pattern does not exist is 1. All phases were zero. FIG. 37 is a diagram illustrating a target pattern (pattern data) according to the fourth embodiment. The effective light source is quadrupole illumination (corresponding to effective light source information) as shown in FIG.

  First, using Formula 10, an approximate aerial image is calculated from the target pattern and the above-described input information (effective light source information, NA information, λ information, aberration information, and resist information). Next, a two-dimensional image is extracted from the calculated approximate aerial image. Then, pattern data is calculated based on the difference obtained by comparing the target pattern with the two-dimensional image of the approximate aerial image. Further, from the approximate aerial image obtained from the pattern data, a peak portion where the light intensity reaches a peak is extracted in a region that does not overlap the target pattern, and an auxiliary pattern is inserted.

  In this way, the pattern data shown in FIG. 38 is generated as mask data. FIG. 39 shows a strictly calculated aerial image from such mask data. In FIG. 44, an image formed with the best focus is shown in FIG. 44 (a), and an image formed with 0.2 μm defocusing is shown in FIG. 44 (b). Referring to FIG. 44, the image is uniform and has little distortion at the corners, and deterioration in image performance projected onto the wafer when defocused is suppressed. That is, the depth of focus is increased and the imaging performance is improved.

  Next, the exposure apparatus 100 will be described with reference to FIG. FIG. 34 is a schematic block diagram showing the configuration of the exposure apparatus 100. Here, as the mask, the mask 130 manufactured based on the mask data generated by executing the above-described mask data generation program is used.

  The exposure apparatus 100 is an immersion exposure apparatus that exposes the pattern of the mask 130 onto the wafer 150 via the liquid LW supplied between the projection optical system 140 and the wafer 150. In this embodiment, the exposure apparatus 100 applies the step-and-scan method, but a step-and-repeat method and other exposure methods can also be applied.

  As shown in FIG. 34, the exposure apparatus 100 includes a light source 110, an illumination optical system 120, a mask stage 135 on which a mask 130 is placed, a projection optical system 140, a wafer stage 155 on which a wafer 150 is placed, A liquid supply / recovery unit 160 and a main control system 170 are provided. The light source 110 and the illumination optical system 120 constitute an illumination device that illuminates the mask 130 on which a transfer circuit pattern is formed.

The light source 110 uses an excimer laser such as a KrF excimer laser having a wavelength of about 248 nm or an ArF excimer laser having a wavelength of about 193 nm. However, the type and number of the light sources 110 are not limited. For example, an F ₂ laser having a wavelength of about 157 nm can be used as the light source 110.

  The illumination optical system 120 is an optical system that illuminates the mask 130 using light from the light source 110. The illumination optical system 120 can realize various illumination modes such as conventional illumination and modified illumination (for example, quadrupole illumination). In this embodiment, the illumination optical system 120 includes a beam shaping optical system 121, a condensing optical system 122, a polarization controller 123, an optical integrator 124, and an aperture stop 125. Furthermore, the illumination optical system 120 includes a condenser lens 126, a bending mirror 127, a masking blade 128, and an imaging lens 129.

  The beam shaping optical system 121 uses, for example, a beam expander including a plurality of cylindrical lenses. The beam shaping optical system 121 converts the aspect ratio of the cross-sectional shape of the parallel light from the light source 110 into a predetermined value (for example, the cross-sectional shape is changed from a rectangle to a square). In this embodiment, the beam shaping optical system 121 shapes the light from the light source 110 into light having a size and a divergence angle necessary for illuminating the optical integrator 124.

  The condensing optical system 122 includes a plurality of optical elements, and efficiently guides the light shaped by the beam shaping optical system 121 to the optical integrator 124. The condensing optical system 122 includes, for example, a zoom lens system, and adjusts the distribution of the shape and angle of light incident on the optical integrator 124.

  The polarization controller 123 includes, for example, a polarizing element, and is disposed at a position substantially conjugate with the pupil plane 142 of the projection optical system 140. The polarization controller 123 controls the polarization state of a predetermined area of the effective light source formed on the pupil plane 142 of the projection optical system 140.

  The optical integrator 124 has a function of making the illumination light that illuminates the mask 130 uniform, converting the angle distribution of the incident light into a position distribution, and emitting it. The optical integrator 124 uses, for example, a fly-eye lens in which the entrance surface and the exit surface are maintained in a Fourier transform relationship. The fly-eye lens is configured by combining a plurality of rod lenses (that is, micro lens elements). However, the optical integrator 124 is not limited to the fly-eye lens, and may use an optical rod, a diffraction grating, a cylindrical lens array plate arranged so that each set is orthogonal, or the like.

  The aperture stop 125 is disposed at a position immediately after the exit surface of the optical integrator 124 and at a position substantially conjugate with an effective light source formed on the pupil plane 142 of the projection optical system 140. The aperture shape of the aperture stop 125 corresponds to the light intensity distribution (that is, the effective light source shape) of the effective light source formed on the pupil plane 142 of the projection optical system 140. In other words, the aperture stop 125 controls the light intensity distribution of the effective light source. The aperture stop 125 is configured to be switchable according to the illumination mode. The shape of the effective light source may be adjusted by arranging a diffractive optical element (CGH) or a prism on the light source side of the optical integrator 124 without using the aperture stop or in combination.

  The condensing lens 126 condenses the light emitted from the secondary light source formed near the exit surface of the optical integrator 124 and passed through the aperture stop 125, and uniformly illuminates the masking blade 128 via the bending mirror 127. To do.

  The masking blade 128 is disposed at a position substantially conjugate with the mask 130, and includes a plurality of movable light shielding plates. The masking blade 128 forms a substantially rectangular opening corresponding to the effective area of the projection optical system 140. The light that has passed through the masking blade 128 is used as illumination light that illuminates the mask 130.

  The imaging lens 129 images the light that has passed through the opening of the masking blade 128 on the mask 130.

  The mask 130 is manufactured based on the mask data generated by the processing apparatus 1 described above, and has a circuit pattern (main pattern) to be transferred and an auxiliary pattern. The mask 130 is supported and driven by the mask stage 135. The diffracted light emitted from the mask 130 is projected onto the wafer 150 via the projection optical system 140. The mask 130 and the wafer 150 are arranged in an optically conjugate relationship. Since the exposure apparatus 100 is a step-and-scan exposure apparatus, the circuit pattern to be transferred from the mask 130 is transferred to the wafer 150 by synchronously scanning the mask 130 and the wafer 150. If exposure apparatus 100 is a step-and-repeat exposure apparatus, exposure is performed with mask 130 and wafer 150 being stationary.

  The mask stage 135 supports the mask 130 via a mask chuck and is connected to a driving mechanism (not shown). A drive mechanism (not shown) is configured by, for example, a linear motor, and drives the mask stage 135 in the X-axis direction, the Y-axis direction, the X-axis direction, and the rotation direction of each axis. In the plane of the mask 130 or the wafer 150, the scanning direction is the Y axis, the direction perpendicular to the Y axis is the X axis, and the direction perpendicular to the mask 130 or the wafer 150 is the Z axis.

  The projection optical system 140 is an optical system that projects the circuit pattern of the mask 130 onto the wafer 150. The projection optical system 140 can use a refractive system, a catadioptric system, or a reflective system. The final lens (final surface) of the projection optical system 140 is coated to reduce (protect) the influence of the liquid LW supplied from the liquid supply / recovery unit 160.

  The wafer 150 is a substrate onto which the circuit pattern of the mask 130 is projected (transferred). However, the wafer 150 can be replaced with a glass plate or other substrate. A resist is applied to the wafer 150.

  The wafer stage 155 supports the wafer 150 and moves the wafer 150 in the X-axis direction, the Y-axis direction, the Z-axis direction, and the rotation directions of the respective axes using a linear motor, similarly to the mask stage 135.

  The liquid supply / recovery unit 160 has a function of supplying the liquid LW to the space between the final lens (final surface) of the projection optical system 140 and the wafer 150. The liquid supply / recovery unit 160 has a function of recovering the liquid LW supplied to the space between the final lens of the projection optical system 140 and the wafer 150. For the liquid LW, a substance that has a high transmittance with respect to the exposure light, does not attach dirt to the projection optical system 140 (the final lens), and has a good matching with the resist process is selected.

  The main control system 170 has a CPU and a memory, and controls the operation of the exposure apparatus 100. For example, the main control system 170 is electrically connected to the mask stage 135, the wafer stage 155, and the liquid supply / recovery unit 160, and controls synchronous scanning of the mask stage 135 and the wafer stage 155. In addition, the main control system 170 controls supply and recovery of the liquid LW or switching of the stop based on the scanning direction and speed of the wafer stage 155 at the time of exposure. In particular, the main control system 170 performs illumination control based on information input from the monitor and the input device and information from the illumination device. For example, the main control system 170 drives and controls the aperture stop 125 via a driving mechanism. Control information by the main control system 170 and other information are displayed on the monitor and the monitor of the input device. The main control system 170 receives information on the effective light source in the above-described embodiment, and forms an effective light source by controlling the aperture stop, the diffractive optical element, the prism, and the like.

  In the exposure, the light beam emitted from the light source 110 illuminates the mask 130 by the illumination optical system 120. The light flux that passes through the mask 130 and reflects the circuit pattern is imaged on the wafer 150 by the projection optical system 140 via the liquid LW. The exposure apparatus 100 can provide a device (semiconductor element, LCD element, imaging element (CCD, etc.), thin film magnetic head, etc.) with excellent imaging performance, high throughput and good economic efficiency.

  With reference to FIGS. 35 and 36, an embodiment of a device manufacturing method using the exposure apparatus 100 will be described. FIG. 35 is a flowchart for explaining how to fabricate devices (ie, semiconductor chips such as IC and LSI, LCDs, CCDs, and the like). Here, the manufacture of a semiconductor chip will be described as an example. In step 1 (circuit design), a device circuit is designed. In step 2 (mask production), a mask on which the designed circuit pattern is formed is produced. Specifically, by executing the above-described original (mask) data creation method by the processing device 1, mask data is created, the mask data is given to the EB drawing device as input, and Cr corresponding to the mask data is created. Or the like is drawn on the mask 130. Thereby, the mask 130 is created. In step 3 (wafer manufacture), a wafer is manufactured using a material such as silicon. Step 4 (wafer process) is called a pre-process, and an actual circuit is formed on the wafer by lithography using the reticle and wafer. Step 5 (assembly) is called a post-process, and is a process for forming a semiconductor chip using the wafer created in step 4. Including. In step 6 (inspection), inspections such as an operation confirmation test and a durability test of the semiconductor device created in step 5 are performed. Through these steps, the semiconductor device is completed and shipped (step 7).

  FIG. 36 is a detailed flowchart of the wafer process in Step 4. In step 11 (oxidation), the surface of the wafer is oxidized. In step 12 (CVD), an insulating film is formed on the surface of the wafer. In step 13 (electrode formation), an electrode is formed on the wafer by vapor deposition or the like. In step 14 (ion implantation), ions are implanted into the wafer. In step 15 (resist process), a photosensitive agent is applied to the wafer. Step 16 (exposure) uses the exposure apparatus 100 to expose a reticle circuit pattern onto the wafer. In step 17 (development), the exposed wafer is developed. In step 18 (etching), portions other than the developed resist image are removed. In step 19 (resist stripping), the resist that has become unnecessary after etching is removed. By repeating these steps, multiple circuit patterns are formed on the wafer. According to such a device manufacturing method, a high-quality device can be manufactured with high throughput. Thus, the device manufacturing method using the exposure apparatus 100 and the resulting device also constitute one aspect of the present invention.

  The preferred embodiments of the present invention have been described above, but the present invention is not limited to these embodiments, and various modifications and changes can be made within the scope of the gist.

DESCRIPTION OF SYMBOLS 1 Processing apparatus 20 Control part 40 Memory | storage part 401 Mask data generation program 402 Pattern data 403 Effective light source information 404 NA information 405 lambda information 406 Aberration information 407 Registration information 408 Mask data 409 Approximate aerial image 410 Two-dimensional image 411 Deformation pattern data 50 Input Unit 60 Medium interface 70 Storage medium 100 Exposure apparatus 110 Light source 120 Illumination optical system 121 Beam shaping optical system 122 Condensing optical system 123 Polarization control unit 124 Optical integrator 125 Aperture stop 130 Mask 140 Projection optical system 150 Wafer 170 Main control system

Claims (6)

A generation method for generating data of the original by a computer used in an exposure apparatus including an illumination optical system that illuminates the original using light from a light source and a projection optical system that projects a pattern image of the original on a substrate. There,
Obtaining a two-dimensional mutual transmission coefficient based on a function representing a light intensity distribution on the pupil plane of the projection optical system and a pupil function of the projection optical system;
A first calculation step of calculating an approximate aerial image formed on the image plane of the projection optical system based on the two-dimensional mutual transmission coefficient and a pattern on the object plane of the projection optical system;
A two-dimensional image extraction step of extracting a two-dimensional image from the approximate aerial image calculated in the first calculation step;
A main pattern determining step of determining the main pattern by changing the shape of the main pattern of the original based on the two-dimensional image extracted in the two-dimensional image extraction step;
A second calculation step of calculating an approximate aerial image formed on the image plane for the determined main pattern;
A peak portion extraction step for extracting a peak portion where the light intensity reaches a peak in a region excluding a region where the main pattern is projected onto the image plane from the approximate aerial image calculated in the second calculation step;
An auxiliary pattern determining step for determining an auxiliary pattern based on the light intensity of the extracted peak portion;
A generation step of inserting the determined auxiliary pattern into the portion of the original corresponding to the extracted peak portion, and generating pattern data including the determined main pattern and auxiliary pattern as the original data A generation method characterized by comprising: In the auxiliary pattern determination step,
When the target pattern is a transmissive pattern, the auxiliary pattern is based on the ratio between the maximum value of the light intensity of the main pattern and the maximum value of the light intensity of the region excluding the region where the main pattern is projected onto the substrate. Determine the size of the pattern,
When the target pattern is a light shielding pattern, the difference between the light intensity of the background and the minimum value of the light intensity of the main pattern, and the area where the light intensity of the background and the main pattern are projected onto the substrate are excluded. The generation method according to claim 1, wherein the size of the auxiliary pattern is determined based on a ratio with a difference from the minimum value of the light intensity of the region.   2. The peak portion extraction step, wherein the aerial image calculated in the second calculation step is second-order differentiated, and the peak portion is extracted based on a value obtained by the second-order differentiation. Or the production | generation method of 2.   4. An original plate creation method, comprising: creating an original plate based on data generated by the generation method according to any one of claims 1 to 3.   A program for causing a computer to execute the generation method according to any one of claims 1 to 3.   The processing apparatus which performs the production | generation method of any one of Claims 1 thru | or 3.