KR20090030216A - Mask data generation method, mask fabrication method, exposure method, device fabrication method, and storage medium - Google Patents

Abstract

A mask data generation method, a mask fabrication method, an exposure method, a device fabrication method, and a storage medium is provided to increase coherency by inserting an auxiliary pattern into a place having lower coherency. A controller(20), a display unit(30), a memory unit(40), an input unit(50) and a media interface(60) are connected to a bus wire(10). The Controller is composed of CPU, GPU, and DSP or a microcomputer and includes a cache memory for a temporary memory. The controller uses data stored in a memory unit and calculates processing, and the display unit indicates the information relating to execution of a mask data generating program. The memory unit stores the mask data generating program provided from a storage medium(70) connected to the media interface. The memory unit stores the mask data(408) as the output information.

Description

Mask data generation method, mask manufacturing method, exposure method, device manufacturing method and storage medium {MASK DATA GENERATION METHOD, MASK FABRICATION METHOD, EXPOSURE METHOD, DEVICE FABRICATION METHOD, AND STORAGE MEDIUM}

The present invention relates to a method of generating mask data, a method of making a mask, an exposure method, a device manufacturing method and a storage medium.

The exposure apparatus is used when manufacturing fine semiconductor devices, such as a semiconductor memory and a logic circuit, using photolithography technique. The exposure apparatus projects and transfers the circuit pattern formed on the mask (reticle) onto a substrate such as a wafer by a projection optical system. In recent years, as miniaturization of a semiconductor device advances, in an exposure apparatus, it is necessary to form the pattern which has a line width smaller than an exposure wavelength (wavelength of exposure light). However, in such a fine pattern, since the influence of light diffraction is remarkable, the outline (pattern shape) of the pattern is not formed in the wafer as it is. For example, the corners of the pattern are rounded or the length of the pattern is shortened.

In recent years, in order to reduce the deterioration of the shape precision of the pattern formed in the wafer, a mask pattern is designed by performing a pattern shape correction process (so-called OPC (Optical Proximity Correction)). The OPC corrects the pattern shape in accordance with a rule-based system or a model base system using light simulation in consideration of the shape of each mask pattern element and the influence of surrounding elements.

The model base system using the optical simulation deforms the mask pattern until a desired optical image is obtained. A method of inserting an auxiliary pattern small enough to not be resolved is also proposed.

Japanese Patent Application Laid-Open No. 2004-221594 (Patent Document 1) and Robert Socha, Douglas Van Den Broeke, Stephen Hsu, J. Fung Chen, Tom Laidig, Noel Corcoran, Uwe Hollerbach, Kurt E. Wampler, Xuelong shi, and Will Conley, "Contact Hole Reticle Optimization by Using Interference Mapping Lithography (IML (TM))", Proceedings of SPIE, USA, SPIE press, 2005, Vol.5853, pp.180-193 " A technique for deriving whether or not to be calculated by numerical calculation is disclosed, which obtains an interference map by numerical calculation, and derives a position that interferes with each other on the mask and a position that cancels the interference with each other. The auxiliary pattern is inserted so that the phase of the exposure light passing through the main pattern to be transferred and the phase of the exposure light passing through the auxiliary pattern are equal to each other. One The auxiliary pattern is inserted so that the phase of the exposure light and the phase of the exposure light passing through the auxiliary pattern have a difference of 180 degrees. As a result, the main pattern to be transferred and the auxiliary pattern strongly interfere with each other, so that the main pattern can be successfully exposed. The above-described interference map shows the light amplitude on the upper surface which is in an image-relative relationship with respect to the mask surface The main pattern is an element existing on the mask and an element transferred onto the wafer.

Circuit patterns may be broadly classified into line patterns and contact hole patterns.

The technique disclosed in Patent Literature 1 calculates an auxiliary pattern assuming that the line pattern is the same as the one-dimensional line and the contact hole pattern is the same as the point where there is no size. Thus, the shape of the main pattern cannot be calculated. In order to cope with this situation, it is necessary to calculate the position, shape and size of the auxiliary pattern and then newly calculate the main pattern. It is common to perform optical proximity effect correction of the main pattern to calculate its specifications according to the model base system from the non-approximated aerial image rather than the approximate aerial image. Therefore, in patent document 1, in order to obtain the mask pattern containing a main pattern and an auxiliary pattern, calculation of the aerial image which is not approximate is requested many times, and a long calculation time is needed.

Moreover, in patent document 1, since the main pattern is approximated by a line or a point when calculating an auxiliary pattern, the interaction of the optical proximity effect of a main pattern and an auxiliary pattern is not considered. Therefore, the corrected main pattern acquired later causes an optical proximity effect to the auxiliary pattern acquired first. As a result, the effect of the anticipated auxiliary pattern may not be acquired, or it may adversely affect the mask pattern acquired by the auxiliary pattern. In particular, when the line pattern is used as the main pattern, the insertion of the auxiliary pattern is very difficult because the shape change by the optical proximity effect correction is large in the line leading part and the bent part.

The present invention provides a generation method for generating data on a mask which forms a fine pattern with high precision.

According to one aspect of the invention, the computer generates data of a mask used in an exposure apparatus having an illumination optical system for illuminating the mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate. A generating method is provided, wherein the generating method comprises information on the light intensity distribution formed by the illumination optical system on the pupil plane of the projection optical system, information on the wavelength of light from the light source, and an image plane side of the projection optical system. From an aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system based on the information on the numerical aperture of the and the target pattern to be formed on the substrate, and from the aerial image calculated by the aerial image calculation step. The two-dimensional image extraction step of extracting the two-dimensional image and the two-dimensional image extracted in the two-dimensional image extraction step Extracting a peak portion at which the light intensity becomes a peak value in a region excluding a region in which the main pattern is projected onto the upper surface, from a main pattern determination step for determining a main pattern and an aerial image calculated in the aerial image calculation step; The peak portion extraction step, an auxiliary pattern determination step for determining an auxiliary pattern based on the light intensity of the peak portion extracted in the peak portion extraction step, and an auxiliary pattern determined in the auxiliary pattern determination step, are extracted in the peak part extraction step. And a generating step of inserting into the portion of the mask corresponding to the peak portion and generating pattern data including the main pattern and the auxiliary pattern determined in the main pattern determination step as data of the mask.

According to a second aspect of the present invention, data of a mask used in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate is generated by a computer. A generating method is provided, wherein the generating method includes information on a light intensity distribution formed by the illumination optical system on the pupil plane of the projection optical system, information on a wavelength of light from the light source, and the projection optical system. A first aerial image calculation step of calculating an aerial image formed on the upper surface of the projection optical system based on information on the numerical aperture on the image surface side, a target pattern to be formed on the substrate, and the first aerial image calculation; A first two-dimensional image extraction step for extracting a two-dimensional image from the aerial image calculated in the step; and a two-dimensional image extracted in the first two-dimensional image extraction step In the area | region except the area | region where the said main pattern is projected on the said upper surface from the 1st main pattern determination step which determines the main pattern of the said mask based on, and the aerial image computed by the said 1st aerial image calculation step, A first peak portion extraction step for extracting a peak portion at which the light intensity becomes a peak value, and a first auxiliary pattern for determining an auxiliary pattern based on the light intensity of the peak portion extracted in the first peak portion extraction step In the auxiliary pattern and the first main pattern determination step, which are inserted in the portion of the mask corresponding to the peak portion extracted in the first peak portion extraction step and determined in the first auxiliary pattern determination step, A pattern including the determined main pattern, information on the light intensity distribution formed by the illumination optical system on the pupil plane of the projection optical system, and the light source A second aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system based on the information on the wavelength of light and the numerical aperture on the image surface side of the projection optical system; Based on the second two-dimensional image extraction step of extracting the two-dimensional image from the aerial image calculated in the aerial image calculation step and the two-dimensional image extracted in the second two-dimensional image extraction step, the main pattern of the mask is applied. A peak portion at which the light intensity becomes a peak value in a region excluding the region where the main pattern is projected on the image surface from the second main pattern determination step to be determined and the aerial image calculated in the second aerial image calculation step. A second peak portion extraction step of extracting a second step, a second auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the second peak portion extraction step, A main pattern determined in the second main pattern determination step by inserting the auxiliary pattern determined in the second auxiliary pattern determination step into a portion of the mask corresponding to the peak portion extracted in the second peak portion extraction step; And a generation step of generating pattern data including an auxiliary pattern as data of the mask.

According to a third aspect of the present invention, there is provided a mask fabrication method comprising fabricating a mask based on data generated by the generation method.

According to the fourth aspect of the present invention, there is provided a step of manufacturing a mask by the mask manufacturing method, illuminating the manufactured mask, and projecting the pattern image of the mask onto a substrate through a projection optical system. A method is provided.

According to a fifth aspect of the present invention, there is provided a device manufacturing method comprising a step of exposing a substrate using the above exposure method and a step of performing a developing step on the exposed substrate.

According to a sixth aspect of the present invention, data of a mask used in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate is generated by a computer. A storage medium storing a program to be generated is provided, the storage medium comprising: information on the light intensity distribution that the illumination optical system forms on the pupil plane of the projection optical system, information on the wavelength of light from the light source, An aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system based on information on the numerical aperture on the image surface side of the projection optical system, a target pattern to be formed on the substrate, and the aerial image calculation step A two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated at < RTI ID = 0.0 > and < / RTI > On the other hand, the light intensity becomes a peak value in a region excluding a region in which the main pattern is projected onto the upper surface from the main pattern determination step of determining the main pattern of the mask and the aerial image calculated in the aerial image calculation step. A peak portion extraction step for extracting a peak portion, an auxiliary pattern determination step for determining an auxiliary pattern based on light intensity of the peak portion extracted in the peak portion extraction step, and an auxiliary pattern determined in the auxiliary pattern determination step; A generation step of inserting into the portion of the mask corresponding to the peak portion extracted in the partial extraction step and generating pattern data including the main pattern and the auxiliary pattern determined in the main pattern determination step as the data of the mask is executed by the computer. .

According to a seventh aspect of the present invention, data of a mask used in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate is provided to the computer. A storage medium storing a program to be generated is provided, the storage medium comprising information on the light intensity distribution formed by the illumination optical system on the pupil plane of the projection optical system, information on the wavelength of light from the light source, A first aerial image calculation step of calculating an aerial image formed on the upper surface of the projection optical system based on information on the numerical aperture on the image surface side of the projection optical system and a target pattern to be formed on the substrate; A first two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the first aerial image calculation step, and the first two-dimensional image extraction step The main pattern is projected onto the upper surface from a first main pattern determination step of determining a main pattern of the mask based on a two-dimensional image extracted from the first image and an aerial image calculated in the first aerial image calculating step. In the regions other than the region, the auxiliary pattern is extracted based on the first peak portion extraction step for extracting the peak portion where the light intensity becomes the peak value and the light intensity of the peak portion extracted in the first peak portion extraction step. A first auxiliary pattern determination step for determining and an auxiliary pattern and a first insertion pattern determined in the first auxiliary pattern determination step and inserted into a portion of a mask corresponding to the peak part extracted in the first peak portion extraction step; A pattern comprising the main pattern determined in the main pattern determination step of the information, information on the light intensity distribution formed by the illumination optical system on the pupil plane of the projection optical system, and an image A second aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system based on the information on the wavelength of light from the light source and the numerical aperture on the image surface side of the projection optical system; On the basis of the second two-dimensional image extraction step of extracting the two-dimensional image from the aerial image calculated in the second aerial image calculation step and the two-dimensional image extracted in the second two-dimensional image extraction step The light intensity peaks in a region excluding the region where the main pattern is projected on the upper surface from the second main pattern determination step for determining the main pattern of the mask and the aerial image calculated in the second aerial image calculation step. A second auxiliary part for determining an auxiliary pattern based on a second peak part extraction step for extracting a peak part that becomes a value and a light intensity of the peak part extracted in the second peak part extraction step; The pattern determination step and the auxiliary pattern determined in the second auxiliary pattern determination step are inserted into a portion of the mask corresponding to the peak portion extracted in the second peak portion extraction step, and in the second main pattern determination step. A generation step of generating pattern data including the determined main pattern and the auxiliary pattern as data of the mask is executed by a computer.

Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the accompanying drawings.

Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings. In addition, in each figure, the same code | symbol is attached | subjected to the same member, and the overlapping description is abbreviate | omitted.

BACKGROUND OF THE INVENTION Field of the Invention The present invention provides manufacturing of various devices such as semiconductor chips such as ICs and LSIs, display elements such as liquid crystal panels, detection elements such as magnetic heads, and imaging elements such as CCDs, and data for masks used in micromechanics. Applicable when generating (mask pattern). Here, micromechanics refers to a technique for manufacturing a fine mechanical system in micrometer units by applying a semiconductor integrated circuit manufacturing technology to the production of microstructures, or such a mechanical system itself. According to the present invention, for example, an exposure apparatus including a projection optical system having a large numerical aperture NA and a data (mask pattern) of a mask used in a liquid immersion exposure apparatus that fills a space between the projection optical system and the wafer with a liquid. Suitable for production.

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

The software function of the computer system includes programming with executable software code and can generate data of a mask that accurately forms fine patterns. The software code is executed by the processor of the computer system. During a software code operation, code or related data records are stored in a computer platform. However, software code is often stored elsewhere or loaded into a suitable computer system. Thus, the software code may be held on at least one computer readable recording medium as one or a plurality of modules. The contents of the present invention are described in the form of the above-described code, and can function as one or more software products.

1 is a schematic block diagram showing the configuration of a processing apparatus 1 for executing a generating method according to an aspect of the present invention. Mask data is generated using this generation method.

The processing apparatus 1 is configured of, for example, a general-purpose computer, and as shown in FIG. 1, the bus wiring 10, the control unit 20, the display unit 30, the storage unit 40, And an input unit 50 and a media interface 60.

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

The control unit 20 is composed of a CPU, a GPU, a DSP, or a microcomputer, and includes a cache memory for temporary storage. The control unit 20 starts and executes the mask data generation program 401 stored in the storage unit 40 based on the start command of the mask data generation program 401 inputted by the user via the input unit 50. . The control unit 20 executes arithmetic processing included in the method for creating mask data (to be described later) using the data stored in the storage unit 40.

The display part 30 is comprised with display devices, such as a CRT display and a liquid crystal display, for example. For example, the display unit 30 stores information related to the execution of the mask data generation program 401 (for example, the two-dimensional image 410 of the approximate aerial image (described later), the mask data 408, and the like). Display.

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

The storage unit 40 is input information when executing the mask data generation program 401, and includes pattern data 402, effective light source information 403, NA information 404, lambda information 405, and the like. The aberration information 406 and the resist information 407 are stored. The storage unit 40 also stores the mask data 408 as output information after executing the mask data generation program 401. The storage unit 40 is information stored temporarily during the execution of the mask data generation program 401, and includes 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 is stored.

The mask data generation program 401 is used to generate mask data 408 representing data such as a pattern of a mask used in the exposure apparatus and a pattern formed by the pattern forming portion of the spatial light modulator SLM. In this case, the pattern elements are formed into polygons, and their aggregates constitute the pattern of the entire mask.

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

The effective light source information 403 is information on 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 about the numerical aperture NA on the image surface side of the projection optical system of the exposure apparatus.

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

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

The resist information 407 is information about a resist applied to the wafer.

The mask data 408 is data representing an actual mask pattern generated by executing the mask data generation program 401.

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

The two-dimensional image 410 is generated during the execution of the mask data generation program 401 and is obtained when the approximate aerial image 409 is cut according to the reference slice value.

The modified pattern data 411 includes a main pattern deformed by executing the mask data generation program 401 and an auxiliary pattern inserted by executing the mask data generation program 401.

The pattern data 402, the mask data 408, and the deformation pattern data 411 include information such as the position, size, shape, transmittance, and phase of the main pattern and the auxiliary pattern. The pattern data 402, the mask data 408, and the modified pattern data 411 also include information such as transmittance and phase of a region (background) in which the main pattern and the auxiliary pattern do not exist.

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

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

Hereinafter, with reference to FIG. 2, the process which the control part 20 of the processing apparatus 1 executes a mask data generation program and produces | generates mask data is demonstrated.

In step S102, the control unit 20 generates 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, lambda information, aberration information, and resist information). Calculate. Note that the input information (pattern data, effective light source information, NA information, lambda information, aberration information, resist 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 taken to produce an approximate aerial image is overwhelmingly shorter than the time taken to produce a rigorous aerial image. The second reason is that the approximate aerial image improves the coherency of the pattern, thereby clearly showing the optical proximity effect.

Various methods of calculating the approximate aerial image have been disclosed conventionally. For example, the approximate aerial image can be calculated by modifying the interference map disclosed in Patent Document 1. In this case, singular value decomposition is performed on the Transmission Cross Coefficient (TCC). The i-th eigenvalue is lambda _i , and the i-th eigenfunction is? _I (f, g). However, (f, g) is a coordinate of the pupil plane of a projection optical system. Moreover, TCC shows the coherence (the degree of interference according to the distance on a mask surface) of an effective light source. According to Patent Literature 1, the interference map e (x, y) is the sum of a plurality of eigenfunctions, and can be represented by the following formula (1).

···(1)

···(One)

In this equation, FT represents a Fourier transform, and normally N 'is 1.

In patent document 1, the interference map of the whole mask is derived by substituting each mask pattern element with a dot or a line, and performing an interference map and convolution. Thus, the interference map e (x, y) represents simple coherence.

However, the interference map e (x, y) does not consider the pattern of the mask (outer shape, etc.). When such an interference map is used for calculating the approximate aerial image, it is necessary to derive the interference map e '(x, y) in consideration of the mask pattern.

For this purpose, singular value decomposition is performed on the TCC. Lambda _i for the i-th eigenvalue,? _I (f, g) for the i-th eigenfunction, and a (f, g) for diffraction light distribution of the pattern of the mask. In this case, the interference map e '(x, y) in consideration of the pattern of the mask is derived from Equation 2 below.

···(2)

···(2)

The approximate aerial image is calculated by using the interference map e '(x, y) represented by the expression (2).

A method for calculating approximate aerial images without decomposition of singular values (unique values) of TCC is described. The mask pattern and the wafer pattern in the semiconductor exposure apparatus have a partial coherent imaging relationship. The partial coherent imaging requires information of the effective light source in order to determine coherence on the mask surface. Here, the coherency means the degree of coherence according to the distance on the mask surface.

The coherency of the effective light source is included in the TCC described above. Generally, TCC is defined as the pupil plane of a projection optical system, and represents the area | region where the effective light source, the pupil function of a projection optical system, and the complex conjugate of the pupil function of a projection optical system overlap each other. TCC can be represented by a four-dimensional function, as shown in Equation 3 below.

···(3)

(3)

In this equation, the coordinate of the pupil plane is (f, g), the function representing the effective light source is called S (f, g), and the pupil function is called P (f, g). Where * denotes complex conjugate and the integral ranges from -∞ to ∞. The aberration of the projection optical system, the polarization of the illumination light, the resist information, and the like can be included in the pupil function P (f, g). In this specification, a "pupillary function" often includes information of polarization, aberration, and resist as needed.

The function I (x, y) expressing the aerial image using the TCC is calculated as a quadratic integration of the TCC as shown in Equation 4 below.

···（4)

···(4)

In this expression, a function that represents a Fourier transform of a function representing a mask, that is, a function representing a spectral distribution (diffraction light distribution) of the mask is a (f, g). Where * denotes complex conjugate and the integral ranges from -∞ to ∞. M. Born and E. Wolf, "Principles of Optics", England, Cambridge University Press, 1999, 7th (extended) edition, pp. 554-632 has a detailed description of Equation 4.

Assume that Equation 4 is calculated directly using a computer. In this case, using Discretized Variable, Equation 4 can be modified as follows.

···（5)

(5)

However, F ^-1 means an inverse Fourier transform. W _{f ' , g'} (f ", g") is defined by the following formula 6 with respect to certain fixed coordinates (f ', g').

W _{f ' , g'} (f ", g") = TCC (f ', g', f ", g") ... (6)

Since (f ', g') is fixed here, W _{f ' , g'} (f ", g") are two-dimensional functions, and are referred to herein as two-dimensional mutual transmission coefficients (TCC). The two-dimensional TCC W _{f ' , g'} (f ", g") is recalculated each time the value of (f ', g') changes when executing an addition loop in computer calculation. In Equation 5, the TCC described by the four-dimensional function of Equation 3 is not necessary, and only the double loop needs to be calculated. Therefore, by using the two-dimensional mutual transmission coefficient, it is possible to shorten the calculation time and to reduce the calculation amount (prevention of increase in data volume of the computer memory).

Equation 5 can be changed as in Equation 7 below.

···(7)

(7)

Y _{f ' , g'} (x, y) are defined as in Equation 8 below.

···(8)

···(8)

The aerial image calculation method using Formula 7 is called an aerial phase decomposition method in this specification, and Y _{f ' and g'} (x, y) defined for every coordinate (f ', g') express a component of the aerial phase ( Aerial phase components).

Hereinafter, the difference between Formula 3 and Formula 6 will be described in detail. It is assumed that the center of the effective light source is the origin of the pupil coordinate system. The function obtained by shifting the pupil function P (f, g) of the projection optical system by the coordinate (f ', g') and the complex conjugate function P ^* (f, g) of the function P (f, g) are coordinates (f " , g "), and TCC is defined as the sum of the overlapping function and the function representing the effective light source. P ^* (f, g) is the complex conjugate function of the pupil function of the projection optical system. It may be called.

W _{f ' , g'} (f ", g") in Formula 6 is defined when P (f, g) is shifted by a fixed amount (f ', g'). W _{f ' and g'} (f ", g") are overlapped portions of the effective light source and the pupil function, and a function obtained by shifting P ^* (f, g) by (f ", g") overlaps the effective light source. It is defined as the sum of the parts that are present.

Y _{f ' , g'} (x, y) are also defined when P (f, g) is shifted by a certain amount (f ', g'). The inverse Fourier transform is performed by multiplying a function a ^* (f ", g") as a complex conjugate by a function representing W _{f ', g'} (f ", g") and the spectral amplitude (diffraction light amplitude) of the mask. In addition, a function exp [-i2π (f'x + g'y)] and a coordinate (f ', g') representing an incidence effect corresponding to the shift of the pupil function is obtained from the function obtained by inverse Fourier transform. Y _{f ' and g'} (x, y) are calculated by multiplying the amplitude a (f ', g') of the diffracted light in. Is called the complex conjugate function of the diffracted light distribution.

Hereinafter, the function exp [-i2π (f'x + g'y)], which means the injective effect, will be described. The angle formed by the traveling direction of the plane wave represented by exp [-i2π (f'x + g'y)] and the optical axis is called θ. sin ² θ = (NA / λ) (f ' ² + g ' ² ), the traveling direction of the plane wave is inclined with respect to the optical axis. As such, this function implies an injective effect. exp [-i2π (f'x + g'y)] is a plane wave traveling in the direction of a line connecting the coordinates (f ', g') on the pupil plane and the point where the optical axis intersects the image plane. Can also be regarded as a function representing. Since the diffracted light amplitude a (f ', g') at the coordinates (f ', g') on the pupil plane is an integer, multiplying the amplitude of the diffracted light at the coordinates (f ', g') is an integer. You can also say that you are hungry.

Next, the aerial image approximation will be described. As in Equation 9, we define a function I _app (x, y) that represents an approximate aerial image.

·‥ (9)

‥ (9)

At this time, there are M combinations of coordinates f 'and g', and M 'is an integer of M or less. When M '= M, the approximate aerial image corresponds to Equation 7, and a complete hollow phase can be obtained. In the case of M '= 1, the approximate hollow phase is Y _{0 , 0} (x, y) as in Equation 10.

·‥ (식10)

(10)

In this equation, a (0, 0) is an integer, and W _{0 , 0} (f ", g") is a convolutional integration of a function representing an effective light source and a complex conjugate function of the pupil plane. In addition, the Fourier transform and the inverse Fourier transform may be used interchangeably. Therefore, Y _{0 , 0} (x, y) is a Fourier by multiplying the convolutional integration of a function representing an effective light source with a pupil function or a complex conjugate function of the pupil function by multiplying the diffracted light distribution or the complex conjugate function of the diffracted light distribution. Transformed or inverse Fourier transformed.

Thus, the approximate aerial image is defined by a function obtained by adding one or more aerial phase components Y _{f ' , g'} (x, y) assuming that the integer M 'is less than or equal to M using equations 9 or 10: . In the following examples, the approximate aerial image is calculated by using one aerial image component Y _{f ' , g'} (x, y) assuming M '= 1 in Equation 9. Equation 2 can also be used to calculate an approximate aerial image.

Next, the physical meaning of the approximate aerial image will be described in detail. In coherent imaging, a point image distribution function (a function meaning intensity distribution of a point phase) can be determined. A Fresnel lens can be manufactured by setting the positive (+) position of the point distribution function as the opening portion and the negative (-) position of the point distribution function as the light shielding portion (or an opening having a phase of 180 degrees). Can be. When coherent illumination is performed using the produced Fresnel lens as a mask, an isolated contact hole can be formed by exposure.

Fresnel lenses can be defined in coherent illumination based on a point distribution function. However, in partial coherent illumination, the point distribution function cannot be calculated. This is because the amplitude of the upper surface cannot be calculated in the partial coherent imaging. Therefore, the eigenvalue decomposition method approximates the amplitude of the upper surface.

However, the physical meaning of the calculation method using the two-dimensional mutual permeability coefficient is different from the eigenvalue decomposition method. First, the point distribution 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 convolutional integration between the pupil function and the effective light source, and becomes the pupil function itself. It is well known that the frequency response of incoherent illumination is given by the autocorrelation of the pupil function. If the exposure apparatus assumes incoherent illumination with coherency σ = 1, the frequency response characteristic of the incoherent illumination is given by the effective light source of the pupil function.

In this respect, the frequency response characteristic in the partial coherent illumination is approximated by the convolution integration between the pupil function and the effective light source. That is, the frequency response characteristic is approximated by W _{0 , 0} (f ", g"). Therefore, W _0,0 (f ", g") may be Fourier transformed to obtain a point distribution function in partial coherent illumination. If the opening and the light shield of the mask are determined according to the point distribution function calculated in this way, the isolated contact hole can be formed by exposure under the same effect as the Fresnel lens.

In order to improve the imaging characteristic with respect to an arbitrary mask pattern, the convolution integration of a point distribution function and a mask function may be calculated, and a mask pattern may be determined based on the acquired result. According to equation 10, Y _{0 , 0} (x, y) is obtained by Fourier transforming the diffraction light distribution and the product of W _{0 , 0} (f ", g"). The diffracted light distribution is the Fourier transform of the mask function, and W _{0 , 0} (f ", g") is the Fourier transform of the point distribution function. As a result, according to the formula, Y _{0 , 0} (x, y) is the convolutional integral of the mask function and the point distribution function.

According to the above description, deriving Y _{0 , 0} (x, y) is synonymous with calculating the convolutional integration between the point distribution function and the mask function in partial coherent imaging.

As described above, W _{0 , 0} (f ", g") approximates the frequency response characteristic during partial coherent illumination. W _{f ' and g'} (f ", g") other than W _{0 , 0} (f ", g") may be regarded as frequency response characteristics omitted when approximating the frequency response characteristics in partial coherent illumination. . Y _{f ' and g'} (x, y) other than Y _{0 , 0} (x, y) are components that are omitted when calculating the convolutional integration between the point distribution function and the mask pattern function in partial coherent illumination. can do. Therefore, when M 'is set to 1 or more in Equation 9, the accuracy of the approximation is improved.

Since conventional interference maps are obtained by eigenvalue decomposition of a four-dimensional TCC, aerial image calculation requires square the absolute value of the eigenfunction and add the resulting value. However, in order to calculate an aerial image by the aerial phase decomposition method like Formula 7, it is only necessary to add the aerial phase component without raising the absolute value of the aerial phase component. Aerial phase decomposition and singular value (intrinsic value) decomposition have different properties because they use different physical quantities.

In step S104, a two-dimensional image is extracted from the approximate aerial image calculated in step S102. Specifically, the reference slice value Io is set to extract the two-dimensional image in the cross section of the approximate aerial image. For example, when the pattern data is a transmission pattern, a portion whose intensity value is equal to or greater than a predetermined value (threshold that can be arbitrarily set) is extracted from the approximate hollow image as a two-dimensional image. When the pattern data is a light shielding pattern, a portion whose intensity value is equal to or less than a predetermined value (threshold that can be arbitrarily set) is extracted from the approximate aerial image 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 to determine whether or not the difference between the two-dimensional image and the target pattern is within a preset allowable range. The parameter (evaluation value) used when comparing the two-dimensional image and the target pattern may be a line width or a pattern length, or may be a normalized image log slope (NILS) or an intensity peak value.

When the control unit 20 determines that the difference between the two-dimensional image and the target pattern is outside the allowable range in step S106, 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. Determine the main pattern. Specifically, in step S108, the control unit 20 deforms the shape of the main pattern based on the two-dimensional image to determine the new main pattern. In addition, the detailed process in the determination of the main pattern of step S108 is demonstrated in 1st thru | or 4th Example mentioned later.

In step S110, the control unit 20 calculates an approximate aerial image from the effective light source information, NA information, lambda information, aberration information, and resist information input from the user, using the main pattern modified in step S108 as pattern data. This process returns to step S104. The processing operation of steps S104 to S110 is repeated until the difference between the two-dimensional image and the target pattern is within the allowable range.

In step S106, when the control unit 20 determines 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 the auxiliary pattern. First, a position (secondary pattern insertion position) at which an auxiliary pattern is inserted is extracted from the approximate aerial image (that is, the approximate aerial image of the modified main pattern) calculated in step S110. The auxiliary pattern insertion position does not exceed the reference slice value Io and also has a light intensity peak value (local maxima or local minima) in an area that does not overlap the main pattern (i.e., an area except the area where the target pattern is projected). ) Is the peak portion. Note that in practice, the auxiliary pattern insertion position is a portion on the mask corresponding to the peak portion. The size of the auxiliary pattern is determined based on the light intensity of this peak portion, and this auxiliary pattern is inserted at the peak position. Detailed processing in the determination of the auxiliary pattern in step S112 will be described in the first to fourth embodiments described later.

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

Thus, the mask data generation program (mask data generation method) executes 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. do.

Note that the insertion of the auxiliary pattern changes the optical proximity effect to the main pattern. When this occurs, as shown in Fig. 3, the mask data may be generated in consideration of the optical proximity effect between the main pattern and the auxiliary pattern.

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, input information other than the pattern data is effective light source information, NA information, lambda information, aberration information, and resist information input from the user.

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 and the target pattern extracted in step S118 to determine whether or not the difference between the two-dimensional image and the target pattern is within a preset allowable range.

In step S120, when the control unit 20 determines that the difference between the two-dimensional image and the target pattern is outside the allowable range, the process returns to step S108. The control unit 20 determines the main pattern so that the difference between the two-dimensional image and the target pattern is within the allowable range.

If the control unit 20 determines 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 as a mask data a pattern obtained by adding a main pattern determined in step S108 and an auxiliary pattern as determined in step S112.

In the processing 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 Is executed. 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 image extraction step corresponding to step S118 Is executed. Then, the second main pattern determination step corresponding to step S108, the second peak partial extraction step and the second auxiliary pattern determination step corresponding to step S112, and the generation step corresponding to step S114 are executed.

By generating the mask data by the processing shown in Figs. 2 and 3 and exposing the mask data by inputting the created data into the EB drawing device, a fine pattern can be formed on the substrate with high precision. That is, it becomes possible to generate data of the mask which can form a fine pattern with high precision. In addition, the created mask pattern may contain patterns other than the pattern created by said mask data creation program.

Hereinafter, in the first to fourth embodiments, a process of generating mask data by executing a mask data generation program will be described in detail, and the mask data generated by such a process will be described. The wavelength of the exposure light is λ, the numerical aperture on the image plane side of the projection optical system is NA, and the ratio between the numerical aperture of the illumination light incident on the mask surface from the illumination optical system and the numerical aperture on the object surface side of the projection optical system is sigma. It is called.

In the exposure apparatus, various values can be set for the wavelength? Of the exposure light and the numerical aperture NA of the projection optical system, and therefore, it is preferable to normalize the pattern size of the mask to (? / NA). For example, when λ = 248 nm and NA = 0.73, a pattern having a size of 100 nm is normalized to 0.29 by the above-described method. This standardization is hereinafter referred to as k1 conversion.

The size of the pattern on the mask surface and the size of the pattern on the wafer surface differ only by the magnification of the projection optical system. However, in the following embodiments, for simplicity, the size of the pattern on the mask surface is multiplied by the magnification of the projection optical system, and the size of the pattern on the mask surface and the size of the pattern on the wafer surface are 1: 1. Set According to this setting, the ratio between the coordinate system on the mask surface and the coordinate system on the wafer surface is also 1: 1.

<First Embodiment>

In the first embodiment, a case is considered in which the exposure apparatus uses a projection optical system having NA (corresponding to NA information) of 0.73 and exposure light having a wavelength of 248 nm (corresponding to λ information). In addition, it is assumed that the projection optical system has aberration (corresponding to aberration information), and does not consider the resist applied to the wafer (corresponding to the resist information). In addition, illumination light shall be unpolarized 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, the isolated line pattern is called a light shielding pattern (i.e., the transmittance is zero), and the transmittance | permeability of the area | region (background) in which such an isolated line pattern does not exist is called 1. In addition, the phase was said to be zero over the whole area | region. 4 is a chart showing a target pattern (pattern data) in the first embodiment.

As the effective light source, quadrupole illumination (corresponding to the effective light source information) as shown in Fig. 5 is used. In Fig. 5, the white circular line means sigma = 1, and the four white regions mean light irradiation units. 5 is a chart which shows the effective light source in 1st Example. 5 exemplarily shows an effective light source, and the present invention is not limited thereto.

First, using Equation 10, an approximate aerial image shown in FIG. 6A is calculated from the target pattern and the above-described input information (effective light source information, NA information, lambda information, aberration information, and resist information). In FIG. 6A, the target pattern is represented by a solid line superimposed on the approximate air.

In the approximate aerial image shown in FIG. 6A, the isolated line pattern has a rounded tip, and the dimension of the light shielding portion of the target pattern is shorter than that of the target pattern.

After the mask data generation program 401 described above is executed, the approximate aerial image shown in FIG. 6B after the main pattern is modified is calculated. In the approximate aerial image shown in FIG. 6B, the intensity distribution inside the target pattern shown by the solid line superimposed on it is substantially the same.

FIG. 7A shows a two-dimensional image (cross section image) obtained by cutting the approximate aerial image shown in FIG. 6A along the reference slice values Io 0.95Io and 1.05Io. Similarly, the two-dimensional image (cross section image) obtained by cutting the approximate aerial image shown in FIG. 6B along the reference slice values 0.95Io and 1.05Io is shown in FIG. 7B. 7A and 7B, the target pattern is shown by the solid line superimposed on two dimensions. In addition, the reference slice value Io is also called a threshold below.

The difference with the target pattern (for example, shape change, degree of inclination, intensity value or intensity peak, and log-slope) can be calculated from the two-dimensional image of the approximate aerial image shown in FIGS. 7A and 7B. Based on this difference, the main pattern is determined (deformed).

The determination (deformation) of a main pattern is demonstrated concretely. First, as shown in Fig. 8A, the target pattern and the pattern data (the initial pattern data are the same as the target pattern) are divided, and the two-dimensional image is divided into the same division number. Then, the target pattern and the divided elements of the two-dimensional image are compared with each other, and the pattern data is modified (corrected) based on this difference. However, the target pattern is not deformed. The division of the pattern data may be performed by removing unnecessary elements or adding new elements.

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

Next, an auxiliary pattern is inserted. From the approximate aerial image shown in Fig. 6B, the peak portion where the light intensity becomes a peak value is extracted in a region that does not overlap the target pattern (i.e., the region except the region where the main pattern is projected). When the target pattern is a light shielding pattern, the light intensity is greater than or equal to the threshold and a peak portion of a region darker than the background is calculated, and a square auxiliary pattern is inserted into the peak portion. In the case of using the line pattern, the peak portion may be detected one-dimensionally and the peak portion may be extracted. In this case, the peak portion may be detected at least in a direction perpendicular to the longitudinal direction of the line pattern and in a direction parallel to the longitudinal direction of the line pattern. In addition, the position where the auxiliary pattern is inserted may be the center position of the peak portion in a region darker than the background. However, in the case of using a line pattern having a certain size, the strength of the main pattern in the approximate air influences the position far from the main pattern. Therefore, even in the region not overlapping with the main pattern, the peak portion overlaps the intensity peak due to the interference, making it difficult to detect the peak portion. Under these circumstances, the value (positive value and negative value) of the second derivative (e.g., the second derivative of each of the orthogonal biaxial directions, summed up (Laplacians)) is obtained. The method of calculating and calculating a peak position (part) can also be used. 38 shows a map of the second derivatives of the intensity distribution (Laplacians). The first derivative of the intensity distribution along each direction is vulnerable to noise and difficult to handle. Therefore, the method of calculating the peak position by calculating the value of the second derivative of the intensity distribution in a line pattern having a specific size and complex shape is effective.

The dimensions of one side of the auxiliary pattern shall be small enough to be unresolved. Specifically, in the case of using a light shielding pattern, the dimension of this one side is the difference between the light intensity of the background and the minimum value of the light intensity of the main pattern, and the minimum value of the light intensity of the region that does not overlap the light intensity of the background and the target pattern. Calculated based on the ratio between When using a line pattern, depending on the exposure process and the magnitude | size of a main pattern, the dimension of one side of an auxiliary pattern is a dimension about 1/3 to 1/2 of the width direction of a line pattern. When using a light transmissive pattern, the dimension of one side may be larger than the value. In the first embodiment, the dimension of one side in the width direction of the auxiliary pattern is 40 nm.

When the above-described auxiliary pattern is inserted into the modified main pattern, pattern data as shown in Fig. 9 is obtained. Thus, the pattern data shown in FIG. 9 is generated as mask data. It is checked (evaluated) whether a mask produced from such mask data forms a desired aerial image on the wafer surface.

Instead of calculating the approximate aerial image and evaluating the mask data, the aerial image is rigorously calculated to evaluate the mask data. The two-dimensional image of the aerial image calculated strictly from the pattern data (mask data) shown in FIG. 9 is shown in FIG. Referring to Fig. 10, the two-dimensional image is uniform and its length is not shortened, i.e., close to the target pattern.

For comparison, the aerial image is calculated for the target pattern itself and for the pattern obtained by inserting a typical auxiliary pattern (scattering bars) into the target pattern itself. About the target pattern itself as shown in FIG. 11A and the pattern obtained by inserting the auxiliary pattern (scattering bar) of 40 nm in width at the interval of half pitch (120 nm) to the target pattern as shown in FIG. 12A. Calculate the aerial image. A two-dimensional image of the aerial image calculated from the target pattern itself as shown in FIG. 11A is shown in FIG. 11B. 12B shows a two-dimensional image of an aerial image calculated from a pattern obtained by inserting a scattering bar into a target pattern as shown in FIG. 12A.

The two-dimensional image of the aerial image calculated from the pattern data shown in Figs. 8B, 9, 11A, and 12A is quantitatively evaluated. Specifically, the aerial image was calculated by changing the defocus from the pattern data, thereby calculating the line width. In this embodiment, when the horizontal axis is the x-axis and the vertical axis is the y-axis in each drawing, the center of the two-dimensional image (x = 0, y = 0) and the position of 70% of y = 1200 from the center (x = 0, y = 840), and the line width was calculated at the 90% position (x = 0, y = 1080) of y = 1200 from the center.

The line width computed from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 8B is shown in FIG. The line width computed from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 9 is shown in FIG. The line width computed from the two-dimensional image of the aerial image based on the pattern data shown to FIG. 11A is shown in FIG. The line width computed from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 12A is 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 dimension was nm.

Referring to FIG. 15, in the two-dimensional image in the air based on the target pattern as shown in FIG. 11A, the line width at the position of 90% from the center is small, and the line width change with respect to the focus is large.

Referring to FIG. 16, in the two-dimensional image in the air based on the pattern obtained by inserting the scattering bar into the target pattern as shown in FIG. 12A, the line width change with respect to the focus is gentle, but 70% and 90% Variations in line width at locations are large.

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

Referring to Fig. 14, in the two-dimensional image in the air based on the pattern obtained by inserting the auxiliary pattern into the modified main pattern as shown in Fig. 9, the deviation of the line width at the position of 70% and 90% from the center is It is the smallest, and changes in line width to focus are more gentle.

Thus, the image performance of the mask data (pattern data) generated by the mask data generation program 401 described above is further improved than the mask data obtained by adding scattering bars generated according to the prior art. Thereby, an isolated line pattern can be formed with high precision.

In addition, instead of making the size of the auxiliary pattern constant, the size of the auxiliary pattern may be changed according to the light intensity (size of the peak value) of the peak portion. Specifically, as shown in FIG. 17, when the length of one side of the i-th auxiliary pattern is a _i and the reference dimension is a _o , the length a _i of one side of the i-th auxiliary pattern is changed. Two ways to do this are available. 17 is a diagram for explaining a method of changing the size of the auxiliary pattern.

In the first method, the length a _i of one side of the i-th auxiliary pattern is changed in proportion to the light intensity of the peak portion, as shown in Equation 11 below.

: 투과 패턴의 경우

: For transmission pattern

:차광 패턴의 경우 ·‥ (11)

: In the case of shading pattern · ‥ (11)

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

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 a _i of one side of the i-th auxiliary pattern in inverse proportion to the light intensity of the peak portion, as shown by the following Expression (12).

: 투과 패턴의 경우

: For transmission pattern

:차광 패턴의 경우 ···(12)

: For shading pattern ... (12)

In the case of the second method, the length a_1imit as the upper limit is determined in advance, and a _i For a_1imit, set a _i = a_1imit.

FIG. 18B shows the 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, the distribution of the approximate aerial image after the insertion of the auxiliary pattern is not significantly changed as before the insertion of the auxiliary pattern. Therefore, the pattern shape reproducibility at the time of insertion of an auxiliary pattern does not change much as the case where an auxiliary pattern is not inserted, but there is little change of image performance, such as focus depth enlargement.

On the other hand, in the second method, the distribution of the approximate aerial image after the insertion of the auxiliary pattern changes significantly compared with before the insertion of the auxiliary pattern. Therefore, since the second method functions to change the distribution of the approximate aerial image, it is suitable for active utilization such as arbitrarily manipulating 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 location where the coherency is small. That is, coherency can be emphasized by inserting a relatively large auxiliary pattern at a position where coherency is small. It is also possible to maximize changes in image performance, such as expanding the depth of focus.

In addition, even when a large auxiliary pattern is inserted at a position where the coherency is small, the auxiliary pattern is not unnecessarily resolved if the upper limit size at which the auxiliary pattern is not resolved beyond the threshold is determined. The size of the upper limit at which the auxiliary pattern is not resolved actually depends on the strength of the approximate aerial image at the position where the auxiliary pattern is inserted. Therefore, you may calculate each magnitude | size of an auxiliary pattern based on the intensity | strength of the position into which an auxiliary pattern is inserted. However, since the pattern shape reproduction type changes significantly compared with the case where the auxiliary pattern is not inserted, care should be taken. In the case where the pattern shape or the like is overcorrected, it is possible to correct this overcorrection again, as described later in the third embodiment.

Second Embodiment

In the second embodiment, a case is considered in which the exposure apparatus uses a projection optical system having an NA of 0.75 (corresponding to NA information) and an exposure apparatus having a wavelength of 193 nm (corresponding to λ information). In addition, it is assumed that the projection optical system has aberration (corresponding to aberration information), and does not consider the resist applied to the wafer (corresponding to resist information). In addition, illumination light shall be unpolarized light.

The target pattern (pattern data) is a contact hole pattern as shown in FIG. 19, and it is assumed that the width is 120 nm and the half pitch is 100 nm (k1 conversion value = 0.39). In Fig. 19, the contact hole pattern is a transmission pattern (i.e., transmittance is 1), and the transmittance of the region (background) where such a contact hole pattern does not exist is zero. In addition, the phase is zero over all regions. 19 is a chart showing a target pattern (pattern data) in the second embodiment.

The effective light source uses quadrupole illumination (corresponding to the effective light source information) as shown in FIG. 20. In FIG. 20, the white circular line represents sigma = 1 and four white regions represent light irradiation portions. 20 is a chart which shows the effective light source in 2nd Example.

First, using Equation 10, an approximate aerial image shown in FIG. 21A is calculated from the target pattern and the above-described input information (effective light source information, NA information, lambda information, aberration information, and resist information). In addition, in FIG. 21A, the target pattern is shown by the solid line superimposed on the approximate air.

On the approximate aerial image shown in FIG. 21A, the light intensity peak value varies with each contact hole pattern.

After the mask data generation program 401 described above is executed to deform the main pattern, the approximate aerial image shown in FIG. 21B is calculated. On the approximate aerial image shown in FIG. 21B, the intensity peak value is almost uniform for each contact hole pattern.

The determination (deformation) of a main pattern is demonstrated concretely. Since the shape of the contact hole pattern is not complicated, only the size and position of the target pattern is changed without dividing the target pattern. However, similarly to the first embodiment, the target pattern can be divided to determine (deform) the main pattern.

The pattern data is modified (corrected) based on the difference between the target pattern and the two-dimensional image on the approximate aerial image. However, the target pattern is not deformed. Then, the approximate aerial image is calculated using the modified pattern data as new pattern data. The same process is repeated until the difference between the target pattern and the two-dimensional image is within the allowable range. From the pattern data thus obtained, an approximate aerial image shown in FIG. 21B is calculated.

In addition, a peak portion at which the light intensity becomes a peak value is extracted from the approximate aerial image shown in FIG. 21B 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 each target pattern is a transmission pattern, the peak part of the area | region where light intensity is below a threshold and is brighter than a background is computed, and a square auxiliary pattern is inserted in the peak part. In the case of using the contact hole pattern, the peak portion may be extracted two-dimensionally and the peak portion may be extracted. The position where the auxiliary pattern is inserted may be the center position of the peak portion in the region brighter than the background. In addition, even when using a contact hole pattern, the peak position (part) can be easily calculated by calculating the value of the second derivative (for example, Laplacians) of the light intensity distribution on the approximate aerial. 39 shows a map of the second derivative of the intensity distribution (Laplacians). Even in the case of using a contact hole pattern having a certain size, the strength of the main pattern in the approximate air affects a position far from the main pattern. Therefore, also in the region which does not overlap with a main pattern, a peak part overlaps with the intensity peak by interference, and it becomes difficult to detect a peak part.

The dimension of one side of the auxiliary pattern should be small enough not to be resolved. Specifically, in the case of using the transmission pattern, the dimension of one side is calculated according to 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 that does not overlap with the target pattern. Depending on the exposure process and the size of the main pattern, when the contact hole pattern is used, the dimension of one side of the auxiliary pattern is about 60% to 80% of the line width of the contact hole pattern. In the second embodiment, the dimension of one side of the auxiliary pattern is 75 nm.

When the above-described auxiliary pattern is inserted into the modified 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 checked (evaluated) whether or not a mask produced from such mask data forms a desired aerial image on the wafer surface.

The two-dimensional image of the aerial image calculated strictly from the pattern data (mask data) shown in FIG. 22 is shown in FIG. In addition, the two-dimensional image of the aerial image calculated strictly from the target pattern itself as shown in FIG. 24A is shown in FIG. 24B. When comparing FIG. 23 and FIG. 24B, it turns out that the two-dimensional image shown in FIG. 23 is more uniform in contact hole than the two-dimensional image shown in FIG. 24B, and the elliptic distortion is reduced.

The 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 by changing the defocus from the pattern data, thereby calculating the line width (hole diameter). In this embodiment, the isolation contact hole pattern CH ₁ present at the center of the two-dimensional image, the contact hole pattern CH ₂ present at the edge of the hole array where the holes are concentrated, and the contact hole pattern CH ₃ present at the center of the hole array are provided. The line width CD was calculated (see FIG. 24A).

The line width computed from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 22 is shown in FIG. The line width computed from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 24A is shown in FIG. 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 in the air based on the target patterns themselves as shown in FIG. 24A, the variation in the line width of the isolated contact hole pattern and the contact hole pattern of the hole array in which the holes are concentrated is large. The change in line width with respect to the focus is also large.

Referring to Fig. 25, in the two-dimensional image in the air based on the pattern obtained by inserting the auxiliary pattern into the deformed main pattern as shown in Fig. 22, the variation in the line width is small and the line width change with respect to the focus is also small.

Thus, the image performance of the mask data (pattern data) generated from the mask data generation program 401 described above is better than the mask data generated according to the prior art. As a result, the contact hole pattern can be formed with high precision.

In addition, as in the first embodiment, instead of making the size of the auxiliary pattern constant, the size of the auxiliary pattern may be changed according to the light intensity (size of the peak value) of the peak portion. 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 the isolated contact hole pattern or the contact hole pattern present at the edge of the hole array in which the holes are dense.

The line width computed from the isolated contact hole pattern which exists in the center of the two-dimensional image of the aerial image based on the pattern data shown to FIG. 22 and FIG. 27 is shown in FIG. As described above, the pattern data shown in FIG. 22 is obtained by making the size of the auxiliary pattern constant, and the pattern data shown in FIG. 27 is obtained by changing the size of the auxiliary pattern. In Fig. 28, the horizontal axis represents defocus (µm) and the vertical axis represents line width CD (nm).

Referring to FIG. 28, the line width change with respect to the focus when the size of the auxiliary pattern is changed (FIG. 27) is smaller than that when the size of the auxiliary pattern is kept constant (FIG. 22) (that is, the focus characteristic is excellent. ).

Third Embodiment

As described above, a new optical proximity effect is generated between the auxiliary pattern and the main pattern by inserting the auxiliary pattern. In particular, when the size of the auxiliary pattern is changed in inverse proportion to the light intensity of the peak portion, the coherency changes significantly. For this reason, a deviation may occur in pattern shape reproducibility and individual pattern shapes. In such a case, it is effective to recalculate the approximate aerial image after inserting the auxiliary pattern into the deformed main pattern as shown in the flowchart shown in Fig. 3, and to further deform (correct) these pattern data.

In the third embodiment, the description is made using the example of the first embodiment. 29A shows an approximate aerial image calculated before the auxiliary pattern is inserted into the modified main pattern in the first embodiment. 29B shows an approximate aerial image calculated after inserting the auxiliary pattern of a constant size into the modified main pattern in the first embodiment. Comparing the approximate aerial image shown in Fig. 29A with the approximate aerial image shown in Fig. 29B, it can be seen that the distribution is greatly changed. A two-dimensional image is extracted from the approximate aerial image shown in Fig. 29B, and the main pattern is modified based on this two-dimensional image as in the first embodiment. Also, an auxiliary pattern is inserted into the main pattern. It is okay to use or not use the same auxiliary pattern without extracting a new one. In this case, the optical proximity effect changed by inserting the auxiliary pattern can be corrected as a change in the shape of the main pattern. Then, the approximate aerial image is calculated using the modified pattern data as new pattern data. The same process is repeated until the difference between the target pattern and the two-dimensional image is within the allowable range. The pattern data (mask data) obtained in this way is shown in FIG.

The 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. In this embodiment, when the horizontal axis in each drawing is x and the vertical axis is y, the center of the two-dimensional image (x = 0, y = 0), the position of 70% of y = 1200 from the center (x = 0, y = 840) and the line width was calculated at the 90% position (x = 0, y = 1080) of y = 1200 from the center.

The line width computed from the two-dimensional image of the aerial image of the pattern data shown in FIG. 30 is shown in FIG. Comparing FIG. 15 with FIG. 31, it can be seen that, in the two-dimensional image in the air based on the pattern data shown in FIG. 30, the variation in the line width is small, and the change in the line width with respect to the focus is more gentle than that shown in FIG. 11A. In addition, the calculation result of the line width shown in FIG. 31 is substantially the same as the calculation result of the line width shown in FIG.

In the case of using a line pattern, shortening of the length of the line pattern is a big problem. In order to solve this problem, the tip of a line pattern is evaluated. In the best focus state, 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 according to the defocus, it is preferable that the length of the line pattern does not change with focus. Moreover, it is preferable that the contrast of the tip of a line pattern is good. The contrast at the tip of the line pattern is evaluated based on NILS.

FIG. 32 shows the result of investigating the change caused by the focus by dividing the length of the line pattern before focus by the length in the best focus state. 33 shows the result of investigating the change by focus by calculating the NILS of the tip of the line pattern. 32 and 33, Pattern_before shows the case where the pattern data is the target pattern itself (i.e., initial pattern data) (FIG. 11A). SB shows the case where the pattern data is a pattern obtained by inserting a scattering bar into the target pattern (FIG. 12A). The OPC shows the case where the pattern data is a pattern obtained by deforming the main pattern based on the approximate aerial image (FIG. 8B). OPC1 + assist1 shows a case where the pattern data is a pattern obtained by modifying the main pattern of the first embodiment based on the approximate aerial image and inserting an auxiliary pattern having a constant size into the main pattern (FIG. 9). OPC2 + assist2 shows a case where the pattern data is a pattern obtained by modifying the main pattern of the third embodiment based on the approximate aerial image and inserting an auxiliary pattern having a constant size into the main pattern (Fig. 30).

Referring to Fig. 32, in each of OPC1 + assist1 (Fig. 9) and OPC2 + assist2 (Fig. 30), the change in the length of the line pattern due to the deviation in focus is the smallest.

Referring to Fig. 33, in OPC2 + assist2 (Fig. 30), the NILS at the tip of the line pattern is the largest in the best focus. In OPC1 + assist1 (FIG. 9), the NILS at the tip of the line pattern is slightly weaker than OPC2 + assist2, but hardly changes in focus.

Fourth Embodiment

Next, an embodiment in which the target pattern is a line pattern of another shape will be described. The fourth embodiment considers a case where the exposure apparatus uses a projection optical system having an NA of NA (corresponding to NA information) and exposure light having a wavelength of 193 nm (corresponding to λ information). In addition, the projection optical system adds the shift (defocus) of the focus position as the aberration of the projection optical system, but does not consider the resist applied to the wafer (corresponding to the resist information). In addition, illumination light shall be unpolarized light.

The target pattern (pattern data) is an L-shaped pattern as shown in FIG. 35, and the length and width dimensions are 1200 nm. In FIG. 35, the isolated line pattern is a light shielding pattern (i.e., the transmittance is zero), and the transmittance of the region (background) where such isolated line pattern does not exist is 1. In addition, the phase is zero over all regions. 35 is a chart showing a target pattern (pattern data) in the fourth embodiment. The effective light source uses quadrupole illumination (corresponding to the effective light source information) as shown in FIG. 5.

First, using Equation 10, an approximate aerial image is calculated from the target pattern and the above-described input information (effective light source information, NA information, lambda information, aberration information, and resist information). Next, a two-dimensional image is extracted from the calculated approximate aerial image. The pattern data is calculated based on the difference between the target pattern and the two-dimensional image of the approximate aerial image. Furthermore, in the area | region which does not overlap with a target pattern from the approximate aerial image computed from pattern data, the peak part which light intensity becomes a peak value is extracted, and an auxiliary pattern is inserted by it.

In this way, the pattern data shown in FIG. 36 is generated as mask data. The aerial images strictly calculated from such mask data are shown in Figs. 37A and 37B. 37A shows an aerial image formed in the best focus state. The aerial image formed by defocusing by 0.2 µm is shown in Fig. 37B. Referring to Figs. 37A and 37B, deterioration of the image performance projected onto the wafer when defocused is obtained by obtaining an aerial image having uniform and small distortion at the corners. That is, the depth of focus is increased, and the image performance is improved.

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

The exposure apparatus 100 is a liquid immersion exposure apparatus that transfers the pattern of the mask 130 to the wafer 150 by exposure via a liquid LW supplied between the projection optical system 140 and the wafer 150. Although the exposure apparatus 100 adopts a step-and-scan method in this embodiment, a step-and-repeat method and other exposure methods can also be adopted.

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 the mask 130 is mounted, a projection optical system 140, and a wafer. A wafer stage 155 on which 150 is mounted, a liquid supply / recovery unit 160, and a main control system 170 are provided. Moreover, the light source 110 and the illumination optical system 120 comprise the illumination device which illuminates the mask 130 in which the circuit pattern for transcription | transfer was 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 may be used as the light source 110.

The illumination optical system 120 illuminates the mask 130 using the 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 the present embodiment, the illumination optical system 120 includes the beam shaping optical system 121, the condensing optical system 122, the polarization control unit 123, the optical integrator 124, and the aperture stop 125. ). In addition, 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 is, for example, a beam expander or the like 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 to a predetermined value (for example, converts the cross-sectional shape from rectangular to square). In the present 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 shape and angle of light incident on the optical integrator 124.

The polarization control unit 123 includes a polarizing element, for example, and is disposed at a position substantially conjugate with the pupil plane 142 of the projection optical system 140. The polarization control unit 123 controls the polarization state of the predetermined region 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 equalizing the illumination light illuminating the mask 130, converting the angular distribution of incident light into a position distribution, and outputting the acquired light. The optical integrator 124 is, for example, a fly-eye lens in which the incident surface and the exit surface maintain a Fourier transform relationship. In addition, a fly's eye lens is comprised by combining several rod lens (namely, a micro lens element). However, the optical integrator 124 is not limited to a fly's eye lens, and may be an optical rod, a diffraction grating, a cylindrical lens array plate, or the like.

The aperture stop 125 is immediately after the exit surface of the optical integrator 124 and is disposed 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 can be switched in accordance with the illumination mode. In addition, the aperture stop may or may not be used, and the shape of the effective light source may be adjusted by arranging the diffractive optical element CGH or the prism on the light source side with respect to the optical integrator 124.

The condenser lens 126 condenses the light passing from the secondary light source formed near the exit surface of the optical integrator 124 and passed through the aperture stop 125, and through the bending mirror 127, through a masking blade ( Evenly illuminate 128).

The masking blade 128 is arrange | positioned in the position substantially conjugated with the mask 130, and is comprised by several movable light shielding plate. The masking blade 128 forms an approximately rectangular opening corresponding to the effective area of the projection optical system 140. The light passing through the masking blade 128 is used as illumination light for illuminating the mask 130.

The imaging lens 129 forms an image of the light passing through the opening of the masking blade 128 in the mask 130.

The mask 130 is produced based on the mask data generated by the processing apparatus 1 described above, and has a circuit pattern (main pattern) and an auxiliary pattern to be transferred. The mask 130 is supported and driven by the mask stage 135. The diffracted light generated 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 to have an optically conjugate relationship. Since the exposure apparatus 100 is a step-and-scan exposure apparatus, the circuit pattern to be transferred of the mask 130 is transferred to the wafer 150 by synchronously scanning the mask 130 and the wafer 150. In addition, if the exposure apparatus 100 is an exposure apparatus of a step and repeat method, it exposes in the state which stopped the mask 130 and the wafer 150. FIG.

The mask stage 135 supports the mask 130 via a mask chuck and is connected to a drive mechanism (not shown). The drive mechanism (not shown in the figure) is composed of, for example, a linear motor, and drives the mask stage 135 in the X-axis direction, the Y-axis direction, the Z-axis direction, and the rotation direction of each axis. In addition, the scanning direction in the surface of the mask 130 or the wafer 150 is the Y-axis direction, the direction perpendicular to the X-axis direction, and the direction perpendicular to the surface of the mask 130 or the wafer 150 is the Z-axis direction. It is done.

The projection optical system 140 projects the circuit pattern of the mask 130 onto the wafer 150. The projection optical system 140 may be a refractometer, a reflective refractometer, or a reflectometer. The final lens (final surface) of the projection optical system 140 is coated with a coating for reducing the influence of the liquid LW supplied from the liquid supply / recovery unit 160.

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

The wafer stage 155 supports the wafer 150 and, like the mask stage 135, uses the linear motor to operate the wafer 150 in the X-axis direction, the Y-axis direction, the Z-axis direction, and the rotation direction of each axis. Move it.

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 also 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. As the liquid LW, a material having a high transmittance with respect to the exposure light, preventing dirt from adhering to the projection optical system 140 (the final lens thereof), and selecting a material having good matching with the resist process is selected.

The main control system 170 includes 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 synchronizes the mask stage 135 with the wafer stage 155. Control the injection. The main control system 170 also controls the supply, recovery, and switching of the supply / recovery stoppage of the liquid LW based on the scanning direction and the speed of the wafer stage 155 at the time of exposure. In particular, the main control system 170 performs lighting control based on the information input from the monitor and the input device and the information from the lighting device. For example, the main control system 170 controls the drive of the aperture stop 125 through the drive mechanism. Control information and other information by the main control system 170 are displayed on the monitor and the monitor of the input device. The main control system 170 receives the information of the effective light source according to one of the above embodiments, and controls the aperture stop, the diffractive optical element, the prism, and the like to form the effective light source.

In exposure, the light beam generated from the light source 110 illuminates the mask 130 by the illumination optical system 120. The light beam passing through the mask 130 and reflecting the circuit pattern of the mask 130 is imaged on the wafer 150 by the projection optical system 140 via the liquid LW. The exposure apparatus 100 can provide devices (eg, semiconductor elements, LCD elements, imaging elements (CCDs, etc.), thin film magnetic heads, etc.) having excellent imaging performance and high throughput and good economical efficiency. Such a device includes a process of exposing a substrate (for example, a wafer or a glass plate) to which a resist (photosensitive agent) is applied using the exposure apparatus 100, a process of developing the exposed substrate, and other well-known methods. It is manufactured by a process.

While the invention has been described with reference to exemplary embodiments, it will be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.

1 is a schematic block diagram showing the configuration of a processing apparatus for executing a generating method according to an aspect of the present invention.

FIG. 2 is a flowchart for explaining a process in which a control unit of the processing apparatus shown in FIG. 1 executes a mask data generation program to generate mask data.

FIG. 3 is a flowchart for explaining another processing in which the control unit of the processing apparatus shown in FIG. 1 executes the mask data generation program to generate mask data.

4 is a chart showing a target pattern (pattern data) according to the first embodiment.

5 is a chart illustrating an effective light source according to the first embodiment.

6A and 6B are charts showing approximate aerial images calculated in the first embodiment.

7A and 7B are diagrams showing two-dimensional images extracted from the approximate aerial image shown in FIGS. 6A and 6B.

8A and 8B are charts for explaining the deformation of the pattern data (main pattern).

FIG. 9 is a chart showing pattern data obtained by inserting an auxiliary pattern into a main pattern in the first embodiment.

FIG. 10 is a view showing a two-dimensional image of the rigid aerial image acquired from the pattern data shown in FIG. 9.

11A is a chart illustrating a target pattern according to the first embodiment.

FIG. 11B is a diagram showing a two-dimensional image of an aerial image calculated from the target pattern shown in FIG. 11A.

12A is a chart showing a pattern obtained by inserting a scattering bar into a target pattern according to the first embodiment.

FIG. 12B is a view showing a two-dimensional image of the aerial image calculated from the pattern shown in FIG. 12A.

FIG. 13 is a graph showing the line width calculated from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 8B.

FIG. 14 is a graph showing the line widths calculated from the two-dimensional images of the aerial image based on the pattern data shown in FIG. 9.

FIG. 15 is a graph showing the line widths calculated from the two-dimensional images of the aerial image based on the pattern data shown in FIG. 11A.

FIG. 16 is a graph showing the line width calculated from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 12A.

17 is a diagram for explaining a method of changing the size of an auxiliary pattern.

18A and 18B are charts showing the pattern data when the size of the auxiliary pattern in the pattern data shown in FIG. 9 is changed.

19 is a chart showing a target pattern (pattern data) according to the second embodiment.

20 is a chart illustrating an effective light source according to a second embodiment.

21A and 21B are charts showing the approximate aerial image calculated in the second embodiment.

FIG. 22 is a chart showing pattern data obtained by inserting an auxiliary pattern into a main pattern in the second embodiment. FIG.

FIG. 23 is a diagram showing a two-dimensional image of the rigid aerial image acquired from the pattern data shown in FIG. 22.

24A is a chart illustrating a target pattern according to a second embodiment.

24B is a diagram showing a two-dimensional image of the aerial image calculated from the target pattern shown in FIG. 24A.

FIG. 25 is a graph showing the line widths calculated from the two-dimensional images of the aerial image based on the pattern data shown in FIG. 22.

FIG. 26 is a graph showing the line width calculated from the two-dimensional image of the aerial image based on the pattern data shown in FIG. 24A.

FIG. 27 is a chart showing pattern data when the size of the auxiliary pattern in the pattern data shown in FIG. 22 is changed.

FIG. 28 is a graph showing the line width calculated from the isolated contact hole pattern existing in the center of the two-dimensional image in the air based on the pattern data shown in FIGS. 22 and 27.

FIG. 29A is a chart showing an approximate aerial image calculated before inserting an auxiliary pattern into a modified main pattern in the first embodiment.

FIG. 29B is a chart showing an approximate aerial image calculated after the auxiliary pattern having a constant size is inserted into the modified main pattern in the first embodiment.

FIG. 30 is a chart showing pattern data obtained by inserting an auxiliary pattern into a main pattern in the third embodiment. FIG.

FIG. 31 is a graph showing the line widths calculated from the two-dimensional images of the aerial image based on the pattern data shown in FIG. 30.

Fig. 32 is a graph showing the results of investigating changes caused by focus by dividing the length of the line pattern before focus by the length of the best focus state.

Fig. 33 is a graph showing the results of investigating changes caused by focus by calculating NILS at the tip of the line pattern.

34 is a schematic block diagram showing the configuration of an exposure apparatus according to an aspect of the present invention.

35 is a chart showing a target pattern (pattern data) according to the fourth embodiment.

36 is a diagram showing pattern data obtained by inserting an auxiliary pattern into a target pattern in the fourth embodiment.

FIG. 37A is a view showing the rigid aerial image acquired from the mask pattern shown in FIG. 36.

FIG. 37B is a view showing the exact aerial image at the time of defocus. FIG.

FIG. 38 is a chart showing the second derivative of the approximate aerial image shown in FIG. 6B.

FIG. 39 is a chart showing the second derivative of the approximate aerial image shown in FIG. 21B.

Claims (12)

A generation method of generating data of a mask used by a computer in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate, The illumination optical system is formed on the substrate, the information on the light intensity distribution formed on the pupil plane of the projection optical system, the information on the wavelength of light from the light source, the information on the numerical aperture on the image plane side of the projection optical system, and the substrate An aerial image calculation step of calculating an aerial image formed on an upper surface of the transparent optical system based on a target pattern to be performed; A two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the aerial image calculation step; A main pattern determination step of determining a main pattern of the mask based on the two-dimensional image extracted in the two-dimensional image extraction step; A peak portion extraction step of extracting a peak portion at which the light intensity becomes a peak value in a region excluding the region in which the main pattern is projected on the image surface from the aerial image calculated in the aerial image calculation step; An auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the peak portion extraction step; Inserting the auxiliary pattern determined in the auxiliary pattern determination step into the portion of the mask corresponding to the peak portion extracted in the peak portion extraction step, the pattern data including the main pattern and the auxiliary pattern determined in the main pattern determination step, the mask And a generating step of generating as data of the present invention. The method of claim 1, In the two-dimensional image extraction step, When the target pattern is a transmission pattern, a region in which the light intensity on the air is greater than or equal to a threshold is extracted, And generating a region in which the light intensity on the air is less than or equal to a threshold when the target pattern is a light shielding pattern. The method of claim 1, In the main pattern determination step, the main pattern is deformed until the difference between the two-dimensional image and the target pattern is within an allowable range. The method of claim 3, wherein And one of light intensity, NILS, and line width of the aerial image as an evaluation value of the difference between the two-dimensional image and the target pattern. The method of claim 1, In the auxiliary pattern determination step, In the case where the target pattern is a transmission pattern, the size of the auxiliary pattern is based on a ratio between the maximum value of the light intensity of the main pattern and the maximum value of the light intensity of an area excluding the area where the main pattern is projected onto the substrate. To determine, In the case where 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 light intensity of an area except the area where the light intensity of the background and the main pattern are projected onto the substrate. And determining the size of the auxiliary pattern based on a ratio between the difference between the minimum value and the minimum value. The method of claim 1, In the peak portion extraction step, a second derivative of the aerial phase calculated in the aerial phase calculation step is extracted, and the peak portion is extracted based on the obtained second derivative. A generation method of generating, by a computer, data of a mask used in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate. The illumination optical system is formed on the substrate, the information on the light intensity distribution formed on the pupil plane of the projection optical system, the information on the wavelength of light from the light source, the information on the numerical aperture on the image plane side of the projection optical system, and the substrate A first aerial image calculation step of calculating an aerial image formed on an image plane of the projection optical system based on a target pattern to be performed; A first two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the first aerial image calculation step, A first main pattern determination step of determining a main pattern of the mask based on the two-dimensional image extracted in the first two-dimensional image extraction step, A first peak portion extraction step for extracting a peak portion at which light intensity becomes a peak value in a region excluding the region where the main pattern is projected on the image surface from the aerial image calculated in the first aerial image calculation step; and, A first auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the first peak portion extraction step; The auxiliary pattern determined in the first auxiliary pattern determination step and inserted into the portion of the mask corresponding to the peak portion extracted in the first peak portion extraction step and the main pattern determined in the first main pattern determination step A pattern to be included, information about a light intensity distribution in which the illumination optical system is formed on the pupil plane of the projection optical system, information about a wavelength of light from the light source, and information about a numerical aperture on the image plane side of the projection optical system. A second aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system, A second two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the second aerial image calculation step, A second main pattern determination step of determining a main pattern of the mask on the basis of the two-dimensional image extracted in the second two-dimensional image extraction step; A second peak portion extraction step for extracting a peak portion at which the light intensity becomes a peak value in an area excluding the region in which the main pattern is projected on the image surface from the aerial image calculated in the second aerial image calculation step; , A second auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the second peak portion extraction step; A main pattern determined in the second main pattern determination step by inserting the auxiliary pattern determined in the second auxiliary pattern determination step into a portion of the mask corresponding to the peak portion extracted in the second peak portion extraction step; And a generating step of generating pattern data including an auxiliary pattern as data of said mask. A mask fabrication method comprising fabricating a mask based on data generated by the generation method according to any one of claims 1 to 7. A step of producing a mask by the mask manufacturing method according to claim 8, A step of illuminating the made mask, And projecting the pattern image of the mask onto a substrate through a projection optical system. Exposing the substrate using the exposure method according to claim 9, A device manufacturing method comprising the step of performing a developing process on an exposed substrate. As a storage medium storing a program for generating, by a computer, data of a mask used in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate. , The illumination optical system is formed on the substrate, the information on the light intensity distribution formed on the pupil plane of the projection optical system, the information on the wavelength of light from the light source, the information on the numerical aperture on the image plane side of the projection optical system, and the substrate An aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system based on a target pattern to be performed; A two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the aerial image calculation step; A main pattern determination step of determining a main pattern of the mask based on the two-dimensional image extracted in the two-dimensional image extraction step; A peak portion extraction step of extracting a peak portion at which the light intensity becomes a peak value in an area excluding the region where the main pattern is projected on the image surface from the aerial image calculated in the aerial image calculation step; An auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the peak portion extraction step; The auxiliary pattern determined in the auxiliary pattern determination step is inserted into a portion of the mask corresponding to the peak portion extracted in the peak portion extraction step, and pattern data including the main pattern and the auxiliary pattern determined in the main pattern determination step is included in the mask. A storage medium characterized by executing a generation step to be generated as data by a computer. A storage medium storing a program for generating, by a computer, data of a mask used in an exposure apparatus having an illumination optical system for illuminating a mask using light from a light source and a projection optical system for projecting the pattern of the mask onto a substrate. , The information on the light intensity distribution formed in the pupil plane of the projection optical system by the illumination optical system, information on the wavelength of light from the light source, information on the numerical aperture on the image plane side of the projection optical system, and the substrate A first aerial image calculation step of calculating an aerial image formed on an image plane of the projection optical system based on a target pattern to be formed; A first two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the first aerial image calculation step, A first main pattern determination step of determining a main pattern of the mask based on the two-dimensional image extracted in the first two-dimensional image extraction step, A first peak portion extraction step for extracting a peak portion at which light intensity becomes a peak value in a region excluding the region where the main pattern is projected on the image surface from the aerial image calculated in the first aerial image calculation step; and, A first auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the first peak portion extraction step; An auxiliary pattern inserted in a portion of a mask corresponding to the peak portion extracted in the first peak portion extraction step and determined in the first auxiliary pattern determination step and a main pattern determined in the first main pattern determination step A pattern to be formed, the illumination optical system based on information on the light intensity distribution formed on the pupil plane of the projection optical system, information on the wavelength of light from the light source, and information on the numerical aperture on the image plane side of the projection optical system. A second aerial image calculation step of calculating an aerial image formed on the upper surface of the transparent optical system, A second two-dimensional image extraction step of extracting a two-dimensional image from the aerial image calculated in the second aerial image calculating step, A second main pattern determination step of determining a main pattern of the mask on the basis of the two-dimensional image extracted in the second two-dimensional image extraction step; A second peak portion extraction step for extracting a peak portion at which the light intensity becomes a peak value in an area excluding the region in which the main pattern is projected on the image surface from the aerial image calculated in the second aerial image calculation step; , A second auxiliary pattern determination step of determining an auxiliary pattern based on the light intensity of the peak portion extracted in the second peak portion extraction step; The auxiliary pattern determined in the second auxiliary pattern determination step is inserted into a portion of the mask corresponding to the peak portion extracted in the second peak portion extraction step, and the main pattern and the auxiliary pattern determined in the second main pattern determination step A storage medium characterized in that a computer generates a generation step of generating pattern data including a pattern as data of the mask.

Images