JP2014130971A - Method and device for calculating light quantity distribution, recording medium recording program for calculating light quantity distribution, and method and device for exposure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To efficiently and highly accurately calculate light quantity distribution information on a pupil surface of a projection optical system of diffraction light generated from a pattern.SOLUTION: A method for calculating light quantity distribution information on a projection pupil surface of light from a pattern formed on a predetermined surface with a thin film having a plurality of layers with mutually different complex diffraction indexes includes: a step 116 for inputting information on an illumination pupil which illuminates the pattern; steps 124, 126 for sequentially calculating at least one of the transmissivity and the reflectivity when a light flux from portion of the illumination pupil passes through a boundary surface of the plurality of layers in the pattern, and calculating a first complex amplitude distribution on a virtual surface of the light flux after passing through the pattern; and a step 128 for calculating a second complex amplitude distribution on the projection pupil surface by performing Fourier transformation of the first complex amplitude distribution.

Description

  The present invention relates to a calculation technique for calculating information relating to a light quantity distribution of light generated from a pattern, a recording medium on which a program for calculating the light quantity distribution is recorded, an exposure technique using the calculation technique, and a device using the exposure technique It relates to manufacturing technology.

  For example, in an exposure apparatus (projection exposure apparatus) such as a stepper or a scanning stepper used in a lithography process for manufacturing an electronic device (microdevice) such as a semiconductor device or a liquid crystal display element, a pattern of a reticle (mask) is increased. In order to accurately expose a substrate such as a wafer, the optical characteristics (for example, aberration) of the projection optical system must be maintained within a target range. In this regard, when the exposure is continued, the optical characteristics of the projection optical system gradually change depending on the accumulated irradiation energy.

  Therefore, conventionally, an imaging characteristic correction system that predicts the amount of change in the optical characteristics of the projection optical system during exposure, for example, according to the integrated irradiation energy, and corrects the position and angle of a predetermined optical member in the projection optical system, for example. Is used to correct the predicted variation in the optical characteristics (see, for example, Patent Document 1). In this case, as an example, when using the reticle for the first time, before actually exposing the substrate, measure how the optical characteristics of the projection optical system fluctuate according to the integrated irradiation energy, During the exposure, the variation amount of the optical characteristic is predicted based on the measurement result and the integrated irradiation energy.

US Patent Application Publication No. 2006/244940

  As is conventional, each time the first use example reticle and how the optical characteristics in advance before the exposure to perform the method to be measured or to change, possibly productivity of the exposure step (throughput) is reduced is there. Therefore, for example, it is preferable to obtain by calculation how the optical characteristics of the projection optical system fluctuate according to the integrated irradiation energy. For this purpose, the complex amplitude distribution or light quantity distribution of the diffracted light (including zero-order light) generated from the reticle pattern on the pupil plane (or entrance pupil or exit pupil) of the projection optical system is increased. It is necessary to calculate the accuracy.

  Also, since the pattern of recent reticles is becoming increasingly finer, for example, when the pattern is formed on a thin film, in order to accurately calculate the light intensity distribution of the diffracted light, the pattern is used as the structure of the thin film. Must be regarded as a three-dimensional pattern including However, if the actual reticle pattern is regarded as a three-dimensional pattern and the light amount distribution of the diffracted light generated from the pattern is calculated by, for example, strict electromagnetic field analysis (for example, Maxwell equation), the amount of calculation and the calculation time are reduced. It becomes enormous and the practicality decreases. For this reason, it is preferable that the light quantity distribution can be calculated with relatively small accuracy with a smaller calculation amount.

  In view of such circumstances, the aspect of the present invention can calculate light amount distribution information such as complex amplitude distribution on the pupil plane of the projection optical system of diffracted light generated from an exposure pattern efficiently and with high accuracy. The purpose is to do so.

  According to the first aspect of the present invention, the light amount distribution information on the pupil plane of the projection optical system that receives light from the pattern formed on the main surface by the film having a plurality of layers having different complex refractive indexes is calculated. A method for calculating a light amount distribution is provided. This calculation method inputs the information of the illumination pupil of the illumination optical system that illuminates the pattern, and when a part of the illumination pupil passes through the boundary surfaces of the layers in the pattern. Calculating a first complex amplitude distribution on the first surface between the film and the projection optical system of the luminous flux after passing through the pattern by sequentially calculating at least one of the transmittance and the reflectance of And Fourier transforming the first complex amplitude distribution to calculate the second complex amplitude distribution of the diffracted light from the pattern on the pupil plane of the projection optical system.

  According to the second aspect, the exposure method of illuminating a pattern formed by a film having a plurality of layers with light from the illumination optical system and exposing the substrate through the pattern and the projection optical system with the light The light amount distribution of the light from the pattern on the pupil plane of the projection optical system using the light amount distribution calculation method of the aspect of the present invention, and information on the light amount distribution on the pupil plane of the projection optical system. An exposure method is provided that includes determining a variation amount of the optical characteristic of the projection optical system based on the correction amount, and correcting the calculated variation amount of the optical characteristic.

  According to the third aspect, the light amount distribution information on the pupil plane of the projection optical system that receives light from the pattern formed on the main surface by the film having a plurality of layers having different complex refractive indexes is calculated. A light intensity distribution calculation device is provided. The calculation apparatus includes a storage device that stores information on an illumination pupil of an illumination optical system that illuminates the pattern, and a light beam that is a part of the illumination pupil passes through boundary surfaces of the plurality of layers in the pattern. Calculating the first complex amplitude distribution on the first surface between the film and the projection optical system of the luminous flux after passing through the pattern by sequentially calculating at least one of the transmittance and reflectance at the time And an arithmetic unit that calculates the second complex amplitude distribution of the diffracted light from the pattern on the pupil plane of the projection optical system by Fourier-transforming the first complex amplitude distribution.

  According to the fourth aspect, the exposure apparatus illuminates the pattern formed by the film having a plurality of layers with the light from the illumination optical system, and exposes the substrate through the pattern and the projection optical system with the light. And a variation of the optical characteristics of the projection optical system based on information on the light quantity distribution of the light from the pattern on the pupil plane of the projection optical system obtained by the calculation device. An exposure apparatus is provided that includes a control device that obtains the amount and corrects the fluctuation amount of the optical characteristic.

Further, according to the fifth aspect, forming the pattern of the photosensitive layer on the substrate using the exposure method or exposure apparatus of the aspect of the present invention, processing the substrate on which the pattern is formed, A device manufacturing method is provided.
According to the sixth aspect, light amount distribution information on the pupil plane of the projection optical system that receives light from a pattern formed on the main surface by a film having a plurality of layers having different complex refractive indexes is calculated. Therefore, a computer-readable recording medium recording a program for causing a computer to execute the processing of the light amount distribution calculation method according to the aspect of the present invention is provided.

  According to the aspect of the present invention, even when the pattern is a three-dimensional pattern, for example, more efficiently than when performing a strict electromagnetic field analysis, and more than when calculating the pattern as a two-dimensional pattern. The complex amplitude distribution of the diffracted light generated from the pattern on the pupil plane of the projection optical system can be calculated with high accuracy.

It is a figure which shows schematic structure of the exposure apparatus which concerns on an example of embodiment. 2 is a block diagram showing a control system and the like of the exposure apparatus of FIG. It is a flowchart which shows an example of the preparation process of calculation of light quantity distribution information. (A) is an enlarged sectional view showing an example of the structure of a thin film of a glass substrate for a reticle, (B) is an enlarged plan view showing a part of a reticle pattern for actual exposure, and (C) is a pattern of the reticle. It is an expanded sectional view showing an example of a three-dimensional structure. It is a flowchart which shows an example of the calculation process and exposure process of light quantity distribution information. (A) is a figure which shows an example of an illumination pupil, (B) is a figure which shows an example of the division method of an illumination pupil, (C) is a figure which shows a 1st partial illumination pupil, (D) is a 2nd partial illumination. It is a figure which shows a pupil. (A) is an enlarged cross-sectional view showing the optical paths of a plurality of light beams incident perpendicularly to the reticle surface (reticle pattern surface), and (B) is an enlarged cross-sectional view showing the optical paths of a plurality of light beams incident obliquely on the reticle surface. is there. (A) is a diagram showing a Fourier transform pattern of a light beam from the first partial illumination pupil, (B) is a diagram showing a Fourier transform pattern of a light beam from the second partial illumination pupil, and (C) is a diagram from the illumination pupil. The figure which shows an example of the light quantity distribution of all the light beams, (D) is a figure which shows an example of the light quantity distribution formed in a projection pupil plane. It is explanatory drawing of the optical path length of the illumination light which passes the several layer of a glass substrate and a thin film. It is an enlarged plan view which shows a part of pattern of another reticle. It is a flowchart which shows an example of the manufacturing process of an electronic device.

An example of an embodiment of the present invention will be described with reference to FIGS.
FIG. 1 schematically shows the overall configuration of an exposure apparatus EX according to the present embodiment. The exposure apparatus EX is, for example, a scanning exposure type projection exposure apparatus composed of a scanning stepper (scanner). The exposure apparatus EX includes a projection optical system PL. Hereinafter, a reticle R and a semiconductor wafer (hereinafter referred to as a wafer) W are taken in a plane (a plane parallel to a horizontal plane in this embodiment) orthogonal to the Z axis parallel to the optical axis AX of the projection optical system PL. In the following description, the Y axis is taken in the direction in which the and are relatively scanned, and the X axis is taken in the direction perpendicular to the Z axis and the Y axis. In addition, the rotational directions around axes parallel to the X axis, the Y axis, and the Z axis will be described as the θx, θy, and θz directions.

  In FIG. 1, an exposure apparatus EX includes an exposure light source 30 that generates exposure illumination light (exposure light) IL, and an illumination optical system ILS that illuminates a reticle R (mask) using the illumination light IL from the light source 30. , And a reticle stage RST that holds and moves the reticle R. Further, the exposure apparatus EX includes a projection optical system PL that exposes the wafer W (substrate) with illumination light IL emitted from the reticle R, a wafer stage WST that holds and moves the wafer W, and illumination light emitted from the reticle R. The calculation device 10 (see FIG. 2) that calculates information on the light amount distribution on the pupil plane PLP (or the entrance pupil or the exit pupil) of the projection optical system PL of IL (diffracted light), and the overall operation of the device are controlled. The main control device 14 and the like (see FIG. 2) are provided. The exposure main body (illumination optical system ILS, reticle stage RST, projection optical system PL, and wafer stage WST) of the exposure apparatus EX is installed in an environmental chamber (not shown) to which a temperature-controlled clean gas is supplied. Has been.

  As the illumination light IL, for example, ArF excimer laser light (wavelength 193 nm) is used. As illumination light, KrF excimer laser light (wavelength 248 nm), harmonics of a YAG laser or a solid-state laser (semiconductor laser, etc.), or a bright line (i-line etc.) of a mercury lamp can be used. The illumination optical system ILS is linearly polarized or non-polarized in a predetermined direction supplied from the light source 30 as indicated by a dotted line and as disclosed in, for example, US Patent Application Publication No. 2003/0025890. A mirror MR1 that reflects illumination light IL for exposure such as polarized light, a spatial light modulator 32 that reflects the reflected light by an array of multiple tilt angle variable mirror elements, and collects light from the array of mirror elements It has a condensing optical system 33 and a mirror MR2 that reflect, and a fly-eye lens 34 (optical integrator) that forms a surface light source (illumination pupil) on the exit surface from the reflected light. In the present embodiment, the exit surface of the fly-eye lens 34 or a surface in the vicinity thereof can be regarded as the illumination pupil plane IPP.

  By controlling the inclination angle of each mirror element of the spatial light modulator 32, the light amount distribution (light intensity distribution) of the illumination pupil plane IPP is changed to a light amount (light intensity) in a circular region, a multi-pole region, or an annular region. Can be set to a distribution corresponding to various illumination conditions. A region where the amount of light increases on the illumination pupil plane IPP is referred to as an illumination pupil ILP (see FIG. 6A). If necessary, a variable aperture stop 35 is installed on the illumination pupil plane IPP or in the vicinity thereof. The illumination optical system ILS further illuminates the illumination light IL from the surface light source by superimposing an elongated slit-shaped illumination area IAR in the X direction of the pattern surface (hereinafter referred to as the reticle surface) Ra of the reticle R. And a variable field stop (not shown) that defines the shape of the illumination area IAR. Instead of the spatial light modulator 32, a plurality of diffractive optical elements or the like that are replaceably arranged in the illumination optical path can also be used.

  Further, the illumination optical system ILS is provided with a photoelectric sensor (integrator sensor) (not shown) that measures the amount of light branched from the illumination light IL, and the measurement value of the integrator sensor is supplied to the main controller 14. Yes. The main controller 14 can monitor the integrated irradiation energy of the projection optical system PL from the measured value. In addition, it is also possible to use the exposure duration as alternative information for the integrated irradiation energy.

  The reticle R is held on the upper surface of the reticle stage RST by vacuum suction or the like, and a device pattern such as a circuit pattern and an alignment mark (not shown) are formed on the reticle surface Ra. The reticle stage RST can be driven minutely in the XY plane by the reticle stage drive system 41 shown in FIG. 2 including a linear motor, for example, and can be driven at a scanning speed specified in the scanning direction (Y direction).

  Position information within the moving surface of the reticle stage RST (including the position in the X direction, the Y direction, and the rotation angle in the θz direction) is transferred to the moving mirror 22 (or mirror-finished) by the reticle interferometer 24 including a laser interferometer. For example, it is always detected with a resolution of about 0.5 to 0.1 nm via the stage end face. The measurement value of reticle interferometer 24 is sent to main controller 14 in FIG. Main controller 14 controls the position and speed of reticle stage RST by controlling reticle stage drive system 41 based on the measured values.

  In FIG. 1, the projection optical system PL is, for example, both-side telecentric and has a predetermined projection magnification β (for example, a reduction magnification of 1/4 times, 1/5 times, etc.). An aperture stop AS is installed in or near the pupil plane (hereinafter referred to as projection pupil plane) PLP of the projection optical system PL. The projection pupil plane PLP (and the entrance pupil and the exit pupil) is optically conjugate with the illumination pupil plane IPP, and the projection pupil plane PLP is optical Fourier with respect to the reticle plane Ra (the object plane of the projection optical system PL). It is also a conversion surface. The projection optical system PL may be a type that forms an intermediate image. Further, the projection optical system PL may be a refractive system, but may also be a catadioptric system. When the illumination area IAR on the reticle surface Ra is illuminated by the illumination light IL from the illumination optical system ILS, an image of the device pattern in the illumination area IAR is projected via the projection optical system PL by the illumination light IL that has passed through the reticle R. , An exposure area IA (an area conjugate to the illumination area IAR) of one shot area of the wafer W is formed. As an example, the wafer W includes a wafer formed by applying a photoresist (photosensitive material) with a thickness of about several tens to 200 nm to a disk-shaped base made of a semiconductor such as silicon and having a diameter of about 200 to 450 mm.

  Further, in the exposure apparatus EX, in order to perform exposure using the liquid immersion method, local liquid immersion is performed so as to surround the lower end portion of the optical element on the most image plane side (wafer W side) constituting the projection optical system PL. A nozzle unit 18 that constitutes a part of the apparatus and supplies and recovers the exposure liquid Lq (for example, pure water) in the liquid immersion area including the exposure area IA is provided. The nozzle unit 18 is connected to a liquid supply device 43 and a liquid recovery device 44 (see FIG. 2) via a pipe (not shown) for supplying the liquid Lq. If the immersion type exposure apparatus is not used, the above-mentioned local immersion apparatus need not be provided.

  In addition, a pipe (not shown) installed so as to be in contact with the holding mechanism of the plurality of optical elements in the projection optical system PL is provided with a liquid Co whose temperature is controlled from the temperature control unit 28 via the supply pipe 29A. (For example, pure water, fluorine-based liquid, refrigerant, or the like) is supplied, and the liquid Co that has flowed through the piping in the projection optical system PL is recovered by the temperature control unit 28 via the recovery piping 29B. By circulating the liquid Co whose temperature is controlled by the temperature controller 28 in the projection optical system PL, the temperature rise of the plurality of optical elements in the projection optical system PL due to the integrated irradiation energy of the illumination light IL is suppressed. .

Further, the projection optical system PL includes an imaging characteristic correction system 16 that corrects optical characteristics (including imaging characteristics) such as distortion and spherical aberration (wavefront aberration) by controlling the postures of a plurality of predetermined lenses. Is provided. Such an imaging characteristic correction system is disclosed in, for example, US Patent Application Publication No. 2006/244940 (Patent Document 1).
Further, the exposure apparatus EX performs an alignment of the wafer W with an aerial image measurement system (not shown) that measures the position of the image of the alignment mark of the reticle R by the projection optical system PL in order to align the reticle R. For example, an image processing type (FIA type) alignment system AL, an irradiation system 45a and a light receiving system 45b, and an oblique incidence type multi-point autofocus sensor for measuring Z positions at a plurality of locations on the surface of the wafer W ( (Hereinafter referred to as a multi-point AF system) 45 (see FIG. 2).

  Wafer stage WST is supported in a non-contact manner on an upper surface parallel to the XY plane of base board WB via a plurality of air pads (not shown). Wafer stage WST can be driven in the X and Y directions by a stage drive system 42 (see FIG. 2) including, for example, a planar motor or two sets of orthogonal linear motors. Wafer stage WST includes a stage main body that is driven in the X direction and the Y direction, a wafer holder WH that is provided on the stage main body and holds wafer W by vacuum suction, the Z position of wafer W, the θx direction, and the θy direction. And a Z stage mechanism (not shown) for controlling the tilt angle.

  In addition, a wafer interferometer 26 composed of a laser interferometer is arranged for measuring position information of wafer stage WST. Instead of the wafer interferometer 26, an encoder type position measurement system combining a diffraction grating and a detector may be used. Position information within the moving surface of wafer stage WST (including the position in the X direction, the Y direction, and the rotation angle in the θz direction) is always detected by the wafer interferometer 26 with a resolution of about 0.5 to 0.1 nm, for example. The measured value is sent to the main controller 14. Main controller 14 controls the position and speed of wafer stage WST by controlling stage drive system 42 based on the measurement value.

  In addition, measurement unit 20 capable of measuring the light amount distribution (light intensity distribution) of projection pupil plane PLP is incorporated in wafer stage WST. The measurement unit 20 has a surface having the same height as the surface of the wafer W, a flat glass substrate 21A having a pinhole formed on the surface, and light receiving optics that collects illumination light that has passed through the pinhole. It has a system 21B, a CCD or CMOS type two-dimensional image sensor 21C that receives illumination light collected by the light receiving optical system 21B, and a housing 21D that holds these members. With the pinhole of the glass substrate 21A moved into the exposure area IA, the light receiving surface of the image sensor 21C is optically conjugate with respect to the projection pupil plane PLP (or the exit pupil) by the light receiving optical system 21B. By processing the detection signal of the image sensor 21C by an image processing unit (not shown), the light amount distribution on the projection pupil plane PLP can be measured. Information on the measured light quantity distribution is supplied to the main controller 14.

  The main controller 14 composed of a computer includes a plurality of arithmetic processors, a memory, a storage device, and the like. The main control unit 14 includes an input / output unit 48, a recording / reproducing unit 50 that records and reproduces data on a recording medium 51 such as a DVD (digital versatile disk), a CD-ROM, or a flash memory. Data is exchanged between a storage unit 52 such as a semiconductor non-volatile memory, a calculation unit 54 including a calculation processor and a memory, and a host computer 12 that supplies control information to a plurality of exposure apparatuses and a plurality of lithography apparatuses. An interface unit (not shown) is connected. A calculation device 10 (which will be described in detail later) that calculates information on the light amount distribution (for example, including complex amplitude distribution) of the projection pupil plane PLP by the diffracted light from the reticle R is configured including the storage unit 52 and the calculation unit 54. . Note that the arithmetic unit 54 may be one function on software of a computer constituting the main control device 14. The program executed by the main control device 14 and the calculation unit 54 is recorded in, for example, the recording medium 51 and can be read from the recording medium 51 by the recording / reproducing unit 50.

  As a basic operation during exposure of the wafer W, after the alignment of the reticle R and the wafer W is performed, the wafer stage WST is moved in the X direction and the Y direction (step movement), so that the shot of the wafer W to be exposed is shot. The area moves to the front of the exposure area of the projection optical system PL. Then, under the control of the main controller 14, the reticle stage RST and the wafer stage WST are synchronously driven while exposing the shot area of the wafer W with an image of a part of the pattern of the reticle R by the projection optical system PL. By scanning the reticle R and the wafer W with respect to the projection optical system PL in the Y direction, for example, using the projection magnification as the speed ratio, the image of the pattern of the reticle R is scanned and exposed over the entire shot area. By repeating the step movement and the scanning exposure in this way, a pattern image of the reticle R is sequentially exposed to a plurality of shot regions of the wafer W by a step-and-scan method.

  If such exposure is continued, the illumination light IL composed of the diffracted light (including the 0th-order diffracted light) generated from the device pattern of the reticle R passes through the projection optical system PL, and is integrated into the projection optical system PL by the accumulated irradiation energy. The temperature of the plurality of optical elements gradually increases, and the optical characteristics (aberration) of the projection optical system PL vary. In the present embodiment, since the temperature-controlled cooling liquid Co is supplied from the temperature control unit 28 into the projection optical system PL, the temperature distribution of these optical elements gradually saturates from the reticle R. The generated diffracted light converges to a certain temperature distribution according to the light amount distribution on the projection pupil plane PLP. Further, each optical element has a very small coefficient of thermal expansion, so that the amount of deformation is small, but the refractive index distribution slightly changes according to the temperature distribution. Therefore, the fluctuation amount of the temperature distribution from the light amount distribution to the convergence on the projection pupil plane PLP and the temperature distribution at the time of convergence are obtained by calculation, and the optical element (or the optical characteristic variation most greatly contributes from the obtained temperature distribution). By calculating the refractive index distribution of the partial optical elements), it is possible to calculate the fluctuation amount of the optical characteristics of the projection optical system PL at each time point during the exposure.

  The light quantity distribution on the projection pupil plane PLP can be measured by driving the wafer stage WST and moving the measurement unit 20 to the exposure area IA. However, in order to suppress a reduction in the throughput of the exposure process, the measurement unit 20 is It is preferable that the measurement of the used light amount distribution can be omitted. Further, there may be a case where a complex amplitude distribution of the diffracted light from the reticle R on the projection pupil plane PLP is required, but it is difficult for the measurement unit 20 to directly measure the complex amplitude distribution. Therefore, hereinafter, a method for calculating light quantity distribution information on the projection pupil plane PLP of the diffracted light generated from the reticle R using the calculation device 10 and the wafer W are exposed while correcting the optical characteristics using the calculation result. An example of the method will be described.

  First, as shown in the flowchart of FIG. 3, a preparatory process for calculating light quantity distribution information is performed. The calculation of this preparation process is executed in advance by, for example, the host computer 12 of FIG. 2, and the calculation result is supplied to the main controller 14 of the exposure apparatus EX as necessary. This preparation step may also be executed by the main controller 14 of the exposure apparatus EX. First, in step 102 in FIG. 3, for example, the operator inputs the film structure data of the reticle R into the host computer 12.

  As an example, the reticle R pattern of the present embodiment is a reticle that is the lower surface of a glass substrate 56 having a flat plate-like, light-transmitting refractive index n0 and an absorption coefficient (extinction coefficient) k0, as shown in FIG. Assume that the thin film 58 is formed on the surface Ra. In the present embodiment, the thin film 58 includes a first layer 58A having a thickness h1, a refractive index n1, and an absorption coefficient k1 formed on the reticle surface Ra, and a thickness h2 and a refractive index formed on the layer 58A. n2 and a second layer 58B having an absorption coefficient k2. Data of these refractive indexes n0 to n2, absorption coefficients k0 to k3, and thicknesses h1 and h2 are film structure data.

  In the present embodiment, the two layers 58A and 58B have different complex refractive indexes, and the glass substrate 56 and the first layer 58A in contact therewith also have different complex refractive indexes. At this time, considering the boundary surface 60A between the glass substrate 56 and the layer 58A, the boundary surface 60B between the layer 58A and the layer 58B, and the boundary surface 60B between the layer 58B and an external gas layer (for example, an air layer), the glass When the illumination light passes from the substrate 56 side to the layer 58B side, the complex refractive indexes are different from each other before and after the boundary surfaces 60A, 60B, and 60C (when the illumination light is incident and emitted).

When the refractive index of a substance is n and the absorption coefficient is k, the complex refractive index nc of the substance is n + ik. For this reason, the glass substrate 56 and the layer 58A are different in at least one of the refractive indexes n0 and n1 and the absorption coefficients k0 and k1, and the two layers 58A and 58B have the refractive indexes n1 and n2 and the absorption coefficients k1 and k2. At least one of them is different. As an example, the glass substrate 56 is made of quartz (synthetic quartz), the first layer 58A is made of a metal such as chromium (Cr), and the second layer 58B is made of chromium oxide (Cr ₂ O ₃₎ , for example. ) Or the like. As an example, the thickness h1 of the layer 58A is about 80 to 90 nm (for example, 85 nm), the thickness h2 of the layer 58B is about 10 to 20 nm (for example, 15 nm), and the thickness of the thin film 58 is about 100 nm.

  When the wavelength of the illumination light IL is 193 nm, the refractive index n0 when the glass substrate 56 is quartz is approximately 1.55, and the absorption coefficient k0 is approximately 0.00. The refractive index n1 when the layer 58A is chromium is approximately 0.75, the absorption coefficient k1 is approximately 1.45, and the refractive index n2 when the layer 58B is chromium oxide is approximately 1.83. The absorption coefficient k2 is approximately 1.99.

  In step 104, for example, the operator inputs the data of the two-dimensional pattern of the reticle R to the host computer 12. In this embodiment, the pattern formed on the reticle surface Ra is a two-dimensional pattern formed from a plurality of opening patterns in the light shielding region 61 as shown in FIG. 4B when viewed from the + Z direction. The device pattern DP2 is included. The device pattern DP2 is a first line-and-space pattern in which space portions 62Aa made of an opening pattern elongated in the Y direction and line portions 62Ab made of a light-shielding region elongated in the Y direction are arranged at a pitch (period) p1 in the X direction. 62A (hereinafter referred to as an L & S pattern), a second L & S pattern 62B in which space portions 62Ba and line portions 62Bb are arranged at a pitch p2 larger than the pitch p1 in the X direction, and a line width d1 elongated in the Y direction in the X direction. A space pattern (isolated linear pattern) 63.

  As an example, the pitch p1 is a value close to the resolution limit of the projection optical system PL. For example, when the pitch of the image of the projection optical system PL of the L & S pattern 62A is about 120 to 160 nm (during immersion exposure) and the projection magnification β of the projection optical system PL is 1/4, the pitch p1 on the reticle R is 480. The thickness of the thin film 58 (for example, about 100 nm) cannot be ignored. The line width d1 is larger than the pitch p2. In FIG. 4B and the like, for convenience of explanation, the line width d1 is expressed to be approximately the same as the pitch p2. Further, the line width ratio (duty ratio) between the line patterns of the L & S patterns 62A and 62B and the space pattern is approximately 1: 1. Note that the pitches p1 and p2 and the line width d1 are arbitrary, and the duty ratios of the L & S patterns 62A and 62B are also arbitrary. The pitch and duty ratio of the L & S patterns 62A and 62B of the device pattern DP2, the line width of the line portion 63, and a predetermined origin in the XY plane of the L & S patterns 62A and 62B and the line portion 63 (for example, the center of an alignment mark not shown) ) Is a part of the data of the two-dimensional pattern of the reticle R.

  In step 106, the host computer 12 uses the reticle R film structure data input in step 102 and the reticle R two-dimensional pattern data input in step 104, and the three-dimensional structure of the reticle R pattern. To decide. At this time, considering the structure of the layers 58A and 58B of the thin film 58, the two-dimensional device pattern DP2 in FIG. 4A is a device pattern DP3 having a three-dimensional structure as shown in FIG. Become. In FIG. 4C, the space portion 62Aa of the L & S pattern 62A is surrounded by the reticle surface Ra and side surfaces 64A and 64B having a cross section perpendicular to the X axis of the thin film 58 (parallel to the ZY plane), and the line portion. 62Ab is surrounded by the boundary surface 60A, side surfaces 64B and 64C having a cross section perpendicular to the X-axis of the thin film 58, and the boundary surface 60C. A cross section at the end in the + X direction is referred to as a side surface 64D.

  The space portion 62Ba of the L & S pattern 62B is surrounded by the reticle surface Ra and side surfaces 65A and 65B having a cross section perpendicular to the X axis of the thin film 58, and the line portion 62Bb is formed by the boundary surface 60A and the X of the thin film 58. It is surrounded by side surfaces 65B and 65C having a cross section perpendicular to the axis, and a boundary surface 60C. A cross section at the end in the + X direction is referred to as a side surface 65D. The space 63 is surrounded by the reticle surface Ra and side surfaces 66A and 66B having a cross section perpendicular to the X axis of the thin film 58. Further, the line portions 62Ab and 62Bb have a boundary surface 60B therein. In practice, the space portions 62 </ b> Aa, 62 </ b> Ba, and 63 have cross sections perpendicular to the Y axis of the thin film 58 at both ends in the Y direction.

  Positions in the Z direction with respect to the reticle surface Ra of the boundary surfaces 60A-60C defining the L & S patterns 62A, 62B, and predetermined origins in the XY plane of the side surfaces 64A-64D, 65A-65D, 66A, 66B (for example, alignment not shown) Information on coordinates (positional relationship) with respect to the center of the mark is data of the three-dimensional structure of the device pattern DP3 of the reticle R. The data having the three-dimensional structure is stored in a database of a storage device in the host computer 12 (step 108). Note that the illumination condition information of the reticle R is also stored in the database.

  Next, the pattern formed on the reticle R is regarded as a device pattern DP3 having a three-dimensional structure shown in FIG. 4C, and the amount of light distribution of the diffracted light from the device pattern DP3 on the projection pupil plane PLP. Determine if you have information. Note that if the strict electromagnetic field analysis is performed according to the illumination conditions with respect to the device pattern DP3, the calculation amount and the calculation time become enormous and the practicality deteriorates. Therefore, in the present embodiment, the light amount distribution information is calculated with a small amount of calculation while considering the influence of the thin film 58 according to the illumination condition as follows.

  Hereinafter, an example of an operation of performing exposure by calculating information on the light amount distribution of the projection pupil plane PLP (for example, a complex amplitude distribution of an electric field) in the exposure apparatus EX using the data obtained in the above preparation step will be described. This will be described with reference to the flowchart of FIG. This operation is controlled by the main controller 14. Note that the calculation of the light quantity distribution information can be performed by the host computer 12.

  First, in step 112 of FIG. 5, the main controller 14 of FIG. 2 inputs the data TB1 of the three-dimensional structure of the device pattern DP3 of the reticle R determined in step 106 from the host computer 12, and stores the input data TB1. Store in the unit 52. Further, main controller 14 sets a surface 68 (hereinafter referred to as a virtual surface) for calculating information on the light amount distribution in the vicinity of reticle surface Ra, and stores information on the position of virtual surface 68 in storage unit 52. (Step 114). As an example, as shown in FIG. 7A, a virtual surface 68 is set close to the outer surface of the outermost layer 58B of the thin film 58 of the reticle R. The setting of the virtual plane 68 may be performed by the calculation unit 54 described later.

Further, main controller 14 inputs information about the illumination conditions (the shape of illumination pupil ILP and the light amount distribution) of reticle R from host computer 12, and stores the input information about illumination pupil ILP in storage unit 52 (step 116). ). Note that the illumination condition of the reticle R may be recorded in advance in an exposure data file of the storage unit 52, for example.
Then, in response to the operation command of the main controller 14, the calculation unit 54 reads the illumination condition (illumination pupil ILP) of the reticle R from the storage unit 52, and the read illumination pupil ILP has a width equal to the X direction and the Y direction. Divide into a plurality of partial illumination pupils (step 118). The illumination pupil ILP on the illumination pupil plane IPP when illuminating the reticle R is, as an example, shown in FIG. 6A, two fan-shaped regions (hereinafter referred to as pupils) arranged symmetrically in the X direction with respect to the optical axis AX. (Area) 70A, 70B, and a circular pupil area 70C centering on the optical axis AX, the light quantity is assumed to be large. Further, for each of the pupil regions 70A to 70C or regions obtained by further subdividing these pupil regions 70A to 70C, the polarization state of illumination light emitted from these regions (the polarization direction if linearly polarized light) is defined. ing. The distance on the illumination pupil plane IPP is converted to the distance on the projection pupil plane PLP. In this case, the incident angle (tilt angle) of the illumination light from the part with respect to the reticle surface Ra is defined by the distance of the part in the radial direction from the optical axis AX.

  As an example, a region including pupil regions 70A, 70B, and 70C has a distance from the optical axis AX to the X direction xi (i = 0, 1, 2,..., I) (as shown in FIG. 6B). (I is an integer equal to or greater than 2) and is divided into I partial pupil regions 71 (i) whose distance in the Y direction is yi. Although the width Δpx in the X direction and the width Δpy in the Y direction of the partial pupil region 71 (i) are equal as an example, the widths may be different from each other. In addition, the width Δpx (or Δpy) of the partial pupil region 71 (i) can be considered as an example in which illumination lights from the partial pupil region 71 (i) have coherence with each other and have the same polarization state. It is also a size. In the present embodiment, regarding the plurality of partial illumination pupils 71 (i), the illumination light that passes through the partial illumination pupils 71 (i) and enters the reticle surface Ra is detected on the virtual plane 68 in FIG. Whether a complex amplitude distribution of the electric field is formed is calculated.

  Therefore, the computing unit 54 reads the data TB1 of the three-dimensional structure of the pattern of the reticle R and the information on the position of the virtual plane 68. Then, for each partial illumination pupil 71 (i), the calculation unit 54 averages the light flux that passes through the partial illumination pupil 71 (i) and enters the reticle surface Ra in FIG. The incident angle θi and the average intensity ITi are calculated (step 120). The operations from step 120 to step 130 described later are sequentially executed for each partial illumination pupil 71 (i). Hereinafter, for convenience of explanation, the first partial illumination pupil 71A centered on the optical axis AX in FIG. 6C and the first partial illumination pupil located at a position away from the optical axis AX in FIG. 6D in the + X direction. A light beam emitted from the second partial illumination pupil 71B will be described. The same applies to the light beams emitted from the other partial illumination pupils 71 (i).

  That is, the calculation unit 54 determines whether or not the light beam emitted from the partial illumination pupil 71 (i) is perpendicularly incident on the reticle surface Ra (step 122). If the light beam is incident on the reticle surface Ra at an angle, the process proceeds to step 126. Since the first partial illumination pupil 71A in FIG. 6A is on the optical axis AX, the light beam ILA from the partial illumination pupil 71A is perpendicular to the reticle plane Ra as shown in FIG. 7A (Z Incident (parallel to the axis). As described above, the transmittance and reflectance of light perpendicularly incident on the reticle surface Ra are not related to the polarization direction of the light. Therefore, the transmittance and reflectance of the light can be calculated by a single formula as will be described later. . Therefore, when obtaining the light amount distribution information of the light flux from the partial illumination pupil 71A, the routine proceeds to step 124.

  In step 124, the calculation unit 54 determines the reticles of the space portions 62Aa and 62Ba and the space portion 63 of the L & S patterns 62A and 62B and the boundary portions 60A, 60B and 60C of the line portions 62Ab and 62Bb of the L & S patterns 62A and 62B. The transmittance when passing through the surface Ra is calculated, and the complex amplitude distribution of the electric field of the light beam ILA on the virtual surface 68 is calculated from the calculation result. The calculation is executed for a number of light fluxes (including light fluxes ILA1 to ILA7) having a width Δx obtained by dividing the light flux ILA, for example, in the X direction by a center interval Δx. For example, the width Δx is set to about one-fifth or less of the width in the X direction of the line portion 62Aa and the space portion 62Ab of the L & S pattern 62A having the smallest pitch.

For example, for the light flux ILA1 entering the space portion 63, the transmittance t _a when the refractive index of a glass substrate 56 having a refractive index n0 through the reticle surface Ra enters the gas layer of 1 is calculated, the reticle surface Ra When the complex amplitude E _i at the time of incidence is set to 1, for example, the complex amplitude on the virtual plane 68 is calculated using the amplitude E _i and the transmittance t _a . Similarly, the complex amplitude at the virtual plane 68 is calculated for the light beams ILA3, ILA5, ILA6, and ILA8 that pass through the other space portions 62Ba and 62Aa. For the light beam ILA2 that passes through the layers 58A and 58B adjacent to the space portion 63, the transmittance when passing through the boundary surfaces 60A, 60B, and 60C is sequentially calculated, and the complex amplitude when incident on the reticle surface Ra is calculated. The complex amplitude at the virtual plane 68 is calculated using the three transmittances. As an example, the transmittance t _a when incident on the layer 58B having a refractive index n2 through the boundary surface 60B from the layer 58A of the refractive index n1 is the complex of the complex amplitude E _i and the injection time at the time of entering the boundary surface 60B Using the amplitude _Et , it becomes as follows. Here, multiple reflection is ignored. However, the same calculation can be performed when multiple reflection is taken into consideration.

_{E t = E i · t a} = E i · 2n1 / (n1 + n2) ... (1)
The equation (1) and equations relating to the transmittance and reflectance described below are described in, for example, the reference “Max Born & Emil Wolf:“ Principles of Optics ”, Sixth Edition, pp. 36-41 (Pergamon Press, 1980). ) "Is well known. The transmittance when passing through the other boundary surfaces 60A and 60C can also be calculated in the same manner as in equation (1).

The complex amplitude E of the light beam between the reticle surface Ra and the virtual surface 68 and the complex amplitude E of the light beam between the boundary surfaces 60A to 60C are the complex refractive index nc of the optical path, the wavelength λ of the light beam, and the light beam. Using the position z in the Z direction, the angular frequency ω of the luminous flux, and the time t, it can be expressed as follows. E _t is the complex amplitude after passing through the previous interface 60A-60C.
E = E _t exp [−i {(2nc · π / λ) z + ωt}] (2)
Further, the complex refractive index nc in the equation (2) is as follows using the refractive index n and the absorption coefficient k of the optical path.

nc = n + ik (3)
In this case, the absolute value of the complex amplitude of the light beam passing through the layers 58A and 58B decreases according to the absorption coefficient k. The complex amplitude at the virtual plane 68 is similarly calculated for the light beams ILA4 and ILA7 passing through the other line portions 62Bb and 62Ab.
Then, by arranging complex amplitudes calculated for a number of light fluxes having a width Δx arranged at the center interval Δx in the X direction in the X direction, the light flux ILA has a three-dimensional structure of the reticle R in FIG. 7A. A first complex amplitude distribution E1 (X, Y), which is a complex amplitude distribution formed on the virtual surface 68 when entering a pattern having the same, is obtained. Of this first complex amplitude distribution E1 (X, Y), assuming that the distribution along the X axis at the center in the Y direction of the L & S patterns 62A, 62B is E1 (X), this real part ReE1 (X) is As an example, the distribution is as shown in FIG.

  Next, the light beam ILB emitted from the second partial illumination pupil 71B at a position separated in the + X direction with respect to the optical axis AX in FIG. 6D is a direction perpendicular to the reticle surface Ra (Z direction). ) And enter the reticle surface Ra (incident angle θi). For this reason, the operation shifts from step 122 to step 126. As described above, regarding the light beam incident on the reticle surface Ra with an inclination, whether the polarization state is P-polarized light (linearly polarized light whose polarization direction is parallel to the incident surface) or S-polarized light (polarized light whose polarization direction is perpendicular to the incident surface). Since the transmittance and the reflectance differ depending on the response, it is necessary to calculate the transmittance and the reflectance for each polarization component.

In step 126, as shown in FIG. 7B, the computing unit 54 converts the light beam ILB incident on the reticle surface Ra at an incident angle θi into a plurality of light beams (light beams ILB1 to ILB1) having a width Δx at a center interval Δx in the X direction. And the complex amplitude on the virtual plane 68 is calculated for each polarization component as follows for each polarization component.
For example, with respect to the light beam ILB1 incident on the space portion 63, the transmittance t _s when the light beam of the S-polarized component is incident on the gas layer having a refractive index of 1 from the glass substrate 56 having the refractive index n0 via the reticle surface Ra, the reflectance when incident on the side surface 66A of the gas layer r _s and the transmittance t _s is calculated and the further light beam transmitted through the side surface 66A, the boundary surface 60B, the transmittance t _s at 60C is calculated. In this case as well, multiple reflections are ignored. However, the same calculation can be performed when multiple reflection is taken into consideration. For a light beam passing through the boundary surfaces 60A and 60C from the side surface 66A, a complex amplitude whose absolute value gradually decreases from the equation (2) can be calculated according to the absorption coefficients k1 and k2 in the layers 58A and 58B. Using these calculation results, the complex amplitude at the virtual plane 68 of the light beam reflected by the side surface 66A and the light beam transmitted through the side surface 66A can be calculated for the S polarization component of the light beam ILB1.

Regarding the light beam ILB1, the transmittance t _p when the P-polarized component light beam is incident on the gas layer from the glass substrate 56 via the reticle surface Ra, and the reflectance r _p when the light beam is incident on the side surface 66A from the gas layer. and the transmittance t _p is calculated, for further light beam transmitted through the side surface 66A, the boundary surface 60B, the transmittance t _p at 60C is calculated. For the light flux passing through the boundary surfaces 60A and 60C, a complex amplitude whose absolute value gradually decreases can be calculated from the equation (2). Using these calculation results, the complex amplitude at the virtual plane 68 of the light beam reflected by the side surface 66A and the light beam transmitted through the side surface 66A can be calculated for the P-polarized light component of the light beam ILB1. Similarly, for the light beams ILB4, ILB6, ILB7, and ILB9 incident on the other space portions 62Ba and 62Aa, the complex amplitude on the virtual plane 68 is calculated for each polarization component. For the light beam ILB7, the light beam reflected by the side surface 64A is further divided into two by the side surfaces 64A and 64B, so that the complex amplitude of the three light beams is finally calculated.

Here, the reticle surface Ra, the interface 60A-60C, and side 64A, 65A, the reflectance of S-polarized component in the 66A or the like r _s and transmittance t _s, and P-polarized light reflectivity component r _p and the transmittance t _p The calculation formula is shown below. In the following equations, θ _i is the incident angle, θ _t is the refraction angle, n _i is the refractive index of the medium on the incident side, n _t is the refractive index of the medium on the transmission side, E _i ^(s) , E _r ^{( s)} and E _t ^(s) are the complex amplitudes when the S-polarized component is incident, reflected and transmitted, and E _i ^(p) , E _r ^(p) and E _t ^(p) are when the P-polarized component is incident , And complex amplitude at reflection and transmission.

また、図７（Ｂ）において、スペース部６３の中央に斜めに入射する光束ＩＬＢ２に関しては、偏光成分別にレチクル面Ｒａでの透過率を計算することで、仮想面６８での複素振幅が偏光成分別に計算できる。さらに、スペース部６３に近接する領域でレチクル面Ｒａに斜めに入射する光束ＩＬＢ３に関しては、まずＳ偏光成分に関して、ガラス基板５６から境界面６０Ａを介して層５８Ａに入射するときの透過率、層５８Ａの側面６６Ｂで反射するときの反射率、さらに反射光が境界面６０Ｂ，６０Ｃを通過するときの透過率が上記の式を用いて計算される。なお、側面６６Ｂでは、全反射が起こるものとしている。全反射が起こる場合には反射光に位相シフトが発生するため、この位相シフトを考慮する。そして、層５８Ａ，５８Ｂ内での吸収を考慮することで、光束ＩＬＢ３のＳ偏光成分について、側面６６Ｂで反射された光束の仮想面６８における複素振幅が計算できる。同様に、光束ＩＬＢ３のＰ偏光成分についても、仮想面６８における複素振幅が計算できる。

In FIG. 7B, for the light beam ILB2 that is incident obliquely on the center of the space portion 63, the transmittance on the reticle surface Ra is calculated for each polarization component, so that the complex amplitude on the virtual plane 68 becomes the polarization component. It can be calculated separately. Further, regarding the light beam ILB3 obliquely incident on the reticle surface Ra in a region close to the space portion 63, first, regarding the S-polarized light component, the transmittance and the layer when entering the layer 58A from the glass substrate 56 via the boundary surface 60A. The reflectance when reflected by the side surface 66B of 58A and the transmittance when the reflected light passes through the boundary surfaces 60B and 60C are calculated using the above formula. Note that total reflection occurs on the side surface 66B. When total reflection occurs, a phase shift occurs in the reflected light, and this phase shift is taken into consideration. Then, by considering the absorption in the layers 58A and 58B, the complex amplitude on the virtual plane 68 of the light beam reflected by the side surface 66B can be calculated for the S polarization component of the light beam ILB3. Similarly, the complex amplitude on the virtual plane 68 can be calculated for the P-polarized component of the light beam ILB3.

  Similarly, for the light beams ILB5 and ILB8 incident on the other line portions 62Bb and 62Ab, the complex amplitude on the virtual plane 68 is calculated for each polarization component. Then, by arranging, in the X direction, complex amplitudes for each polarization component calculated for a large number of light beams having a width Δx arranged at the center interval Δx in the X direction, the light beam ILB becomes the reticle R of FIG. The first complex amplitude distribution ESi (X, Y) of the S polarization component and the first complex amplitude distribution of the P polarization component which are complex amplitude distributions formed on the virtual surface 68 when obliquely incident on a pattern having a three-dimensional structure EPi (X, Y) is required. Of the first complex amplitude distribution ESi (X, Y), assuming that the distribution along the X axis at the center in the Y direction of the L & S patterns 62A and 62B is Ei (X), the real part ReEi (X) is As an example, the distribution is as shown in FIG.

  Next, in step 128, the computing unit 54 obtains the first complex amplitude distribution (obtained in step 126) obtained in step 124 or 126 with respect to the light beam emitted from the partial illumination pupil 71 (i) (i = 0 to I). There are two distributions for each polarization component), and a second complex amplitude distribution that is a complex amplitude distribution on the projection pupil plane PLP is calculated. As an example, when the first complex amplitude distribution formed on the virtual plane 68 by the light beam emitted from the partial illumination pupil 71A of FIG. 6C is Fourier transformed, as shown in FIG. 8A, the projection pupil plane PLP is obtained. , The first-order diffracted light regions 71AP2 and 71AP3 by the space portion 63, the ± first-order diffracted light regions 71AP4 and 71AP5 by the L & S pattern 62B, and the ± 1 by the L & S pattern 62A. A complex amplitude distribution 73A having a large absolute value in a region including the regions 71AP6 and 71AP7 of the first-order diffracted light is obtained. In FIG. 8A and the like, the dotted curve is the aperture 72 limited by the aperture stop AS of the projection optical system PL.

  Similarly, when the first complex amplitude distribution formed on the virtual plane 68 by the light beam emitted from the partial illumination pupil 71B of FIG. 6D is Fourier transformed, as shown in FIG. 8B, the projection pupil plane PLP is obtained. , A complex amplitude distribution 73B having a large absolute value in a region including a zero-order light region 71BP1 separated from the optical axis AX in the X direction and a plurality of diffracted light regions arranged symmetrically in the X direction with respect to this region. can get.

In the next step 130, the calculation unit 54 individually rotates the wavefront aberration to the second complex amplitude distribution obtained in step 128 with respect to the light beam emitted from the partial illumination pupil 71 (i) (i = 0 to I). Add symmetrical aberrations. This is because the aberration caused by the difference in the optical path length to the virtual surface 68 according to the incident angle of the individual light flux with respect to the reticle surface Ra, and the Z position between the virtual surface 68 and the object surface of the projection optical system PL. It means to consider the case where there is a deviation. In this case, as shown in FIG. 9, when the light beam ILB emitted from the partial illumination pupil 71 (i) is incident on the layer 58A from the glass substrate 56, the refraction angle is θ1, and the layer 58A (refractive index n1, thickness) The angle of refraction when incident on the layer 58B (refractive index n2, thickness h2) from the height h1) is θ2. At this time, the optical path length L _effe when the light beam ILB passes through the layers 58A and 58B is as follows. In FIG. 9, the range of integration of the following expression is the case where the subscript i is 1 or 2.

そして、波面収差をｊ次（ｊ＝１，２，３，…）のツェルニケ(Zernike) 多項式の係数（ツェルニケ係数）Ｚｊで表すものとして、回転対称収差中の球面収差に関するツェルニケ係数Ｚ４，Ｚ９（さらにＺ１６を含めてもよい）を計算する。このとき、投影光学系ＰＬのツェルニケ係数Ｚ４，Ｚ９に関する感度を∂Ｚ４／∂Ｌ、∂Ｚ９／∂Ｌとして、ツェルニケ係数Ｚ４，Ｚ９で表される波面収差を計算結果に合わせるための既知の係数をｃｚ４，ｃｚ９とすると、光路長Ｌ_effeを用いてツェルニケ係数Ｚ４，Ｚ９は次のように計算できる。

Assuming that the wavefront aberration is expressed by a coefficient (Zernike coefficient) Zj of a j-th order (j = 1, 2, 3,...) Zernike polynomial (Zernike coefficient) Zj, Zernike coefficients Z4, Z9 (for spherical aberration in rotationally symmetric aberration) Further, Z16 may be included). At this time, the sensitivity regarding the Zernike coefficients Z4 and Z9 of the projection optical system PL is set to ∂Z4 / ∂L and ∂Z9 / ∂L, and the known coefficients for adjusting the wavefront aberration represented by the Zernike coefficients Z4 and Z9 to the calculation result the When CZ4, CZ9, Zernike coefficients Z4, Z9 with optical path length L _effe can be calculated as follows.

Z4 = cz4 (∂Z4 / ∂L) L _effe (7A)
Z9 = cz9 (∂Z9 / ∂L) L _effe (7B)
The coefficients cz4 and cz9 are, for example, the result of calculating the complex amplitude distribution on the projection pupil plane PLP by the calculation method of the present embodiment for the light beam passing through a part of the L & S pattern 62A, and the wavefront of the projection optical system PL. It can be obtained by comparing the measured value of aberration.
Note that when obtaining the Zernike coefficient, the pitch of the L & S pattern, the width of the line portion, the width of the space portion, the duty ratio, and the like may be taken into consideration.

  Then, the complex amplitude distribution corresponding to the Zernike coefficients Z4 and Z9 is added to the second complex amplitude distribution of the light beam emitted from the corresponding partial illumination pupil 71 (i) (i = 0 to I). As a result, the second complex amplitude distribution on the projection pupil plane PLP of the light beam emitted from each partial illumination pupil 71 (i) (i = 0 to I) is obtained for each polarization component. If the rotationally symmetric aberration is small, step 130 may be omitted.

  Thereafter, the calculation unit 54 calculates, for example, the square of the absolute value of the second complex amplitude distribution for each light beam emitted from the partial illumination pupil 71 (i), and calculates the light amount distribution on the projection pupil plane PLP (hereinafter referred to as the partial light amount). Distribution)) (step 132). Further, the computing unit 54 integrates the I partial light quantity distributions obtained for each partial pupil region 70 (i) to obtain a light quantity distribution 74 on the projection pupil plane PLP shown in FIG. 8C (step 134). ). Actually, in the light quantity distribution 74, as shown in FIG. 8D, the light quantity distribution 75 in which the light quantity increases in the hatched area in the opening 72 becomes the light quantity distribution on the projection pupil plane PLP. Information on the light quantity distribution 75 is supplied to the main controller 14.

  In the next step 136, the reticle R is loaded onto the reticle stage RST of FIG. 1 by a reticle loader system (not shown), and alignment is performed. Then, alignment is performed by loading an unexposed wafer W coated with a photoresist onto wafer stage WST (step 138). In main controller 14, the projection pupil plane PLP supplied from operation unit 54 in step 134 is displayed. A variation amount of the optical characteristic (for example, aberration) of the projection optical system PL is calculated from the light amount distribution and the integrated irradiation energy measured by, for example, an integrator sensor (not shown) (step 140), and this variation amount is calculated as the imaging characteristic correction system 16. (Step 142). In this state, the wafer W is scanned and exposed with an image of the pattern of the reticle R by the projection optical system PL (step 144). Thereafter, when the next wafer is exposed in step 146, the operation returns to step 138, and the next wafer loading, calculation and correction of the variation amount of the optical characteristics of the projection optical system PL, and wafer exposure are repeated.

  As described above, according to the present embodiment, the complex amplitude distribution on the projection pupil plane PLP of the diffracted light from the reticle R is calculated in consideration of the three-dimensional structure of the reticle R, and the light amount on the projection pupil plane PLP is calculated from this complex amplitude distribution. Since the distribution is calculated and the fluctuation amount of the optical characteristics of the projection optical system PL is corrected based on the calculation result, even if the reticle R has a three-dimensional structure, the pattern image of the reticle R is always highly accurate on the wafer. Can be exposed to W.

  As described above, the exposure apparatus EX of the present embodiment uses the thin film 58 (film) having a plurality of layers 58A and 58B having different complex refractive indexes on the reticle surface Ra (main surface) as the pattern surface of the reticle R. Is provided with a calculation device 10 for calculating light quantity distribution information on the pupil plane (projection pupil plane PLP) of the projection optical system PL that receives light from the device pattern DP3 formed in the above. The calculation apparatus 10 includes a storage unit 52 that stores information on the illumination pupil ILP of the illumination optical system ILS that illuminates the device pattern DP3, and a calculation unit 54. Then, the calculation unit 54 inputs information on the light amount distribution of the illumination pupil ILP from the storage unit 52 (step 116), and the light beams ILA and ILB from the partial illumination pupils 71A and 71B of the illumination pupil ILP are converted into the device pattern DP3. By sequentially calculating at least one of the transmittance and the reflectance when passing through the boundary surfaces 60A to 60C of the plurality of layers 58A and 58B, the thin film 58 of the light beams ILA and ILB after passing through the device pattern DP3, A first complex amplitude distribution on the virtual plane 68 (first surface) between the projection optical system PL and the projection optical system PL is calculated (steps 124 and 126), and the first complex amplitude distribution is Fourier transformed to obtain a device pattern on the projection pupil plane PLP. A second complex amplitude distribution of the diffracted light from DP3 is calculated (step 128).

  According to the calculation device 10 of this embodiment or the light amount distribution information calculation method using the calculation device 10, when the device pattern DP3 is a three-dimensional pattern formed on the thin film 58 having a plurality of layers, The first complex amplitude distribution on the virtual plane 68 is calculated by calculating the reflectance and / or transmittance of the light beam at the boundary surfaces 60A to 60C and the like, and the two-dimensional first complex amplitude distribution is Fourier transformed. The second complex amplitude distribution on the projection pupil plane PLP is calculated. Therefore, for example, the projection pupil plane PLP of the diffracted light generated from the device pattern DP3 is more efficient than when performing strict electromagnetic field analysis and with higher accuracy than when the device pattern DP3 is calculated as a two-dimensional pattern. The complex amplitude distribution at can be calculated. Further, the light quantity distribution can be calculated using this complex amplitude distribution.

  The recording medium 51 stores a program that causes the computer including the storage unit 52 and the calculation unit 54 to execute the operations of steps 112 to 128. The main control device 14 reads out the program from the recording medium 51 and the computer. By executing this, the calculation of the light amount distribution information of the present embodiment can be executed efficiently. The program causes the computer to input information on the light amount distribution of the illumination pupil ILP of the illumination optical system ILS that illuminates the device pattern DP3, the luminous flux ILA from the partial illumination pupils 71A, 71B, etc. of the illumination pupil ILP, The light flux after passing through the device pattern DP3 by sequentially calculating at least one of transmittance and reflectance when the ILB passes through the boundary surfaces 60A to 60C of the plurality of layers 58A and 58B in the device pattern DP3. First calculation means for calculating the first complex amplitude distribution on the virtual plane 68 between the thin film 58 such as ILA and ILB and the projection optical system PL, and the first complex amplitude distribution on the projection pupil plane PLP by Fourier transforming the first complex amplitude distribution It functions as a second calculation means for calculating the second complex amplitude distribution of the diffracted light from the device pattern DP3. With this program, the complex amplitude distribution (light quantity distribution information) on the projection pupil plane PLP can be calculated efficiently.

  The exposure apparatus EX also includes a wafer W (substrate) via the device pattern DP3 of the reticle R formed by the thin film 58 having the plurality of layers 58A and 58B with the illumination light IL from the illumination optical system ILS and the projection optical system PL. The light amount distribution information calculation device 10 of the present embodiment and the projection optical system based on the light amount distribution information of the light from the device pattern DP3 on the projection pupil plane PLP obtained by the calculation device 10 The main controller 14 is provided with a fluctuation amount of the PL aberration (optical characteristic) (step 140) and the fluctuation amount of the optical characteristic is corrected through the imaging characteristic correction system 16 (step 142).

  According to the exposure apparatus EX or the exposure method by the exposure apparatus EX, without actually measuring the light quantity distribution on the projection pupil plane PLP of the light from the pattern of the reticle R or the aberration fluctuation state of the projection optical system PL, It is possible to predict with high accuracy the aberration fluctuation amount of the projection optical system PL when the exposure using the reticle R is continued. Accordingly, by correcting the predicted aberration fluctuation amount, even when the pattern of the reticle R is substantially a three-dimensional pattern, the pattern of the reticle R can be accurately applied to the wafer W without reducing the throughput. Can be exposed.

The calculation of the above embodiment is also performed when the pattern of the reticle R is formed in a thin film of three or more layers, or when the device pattern is a phase shift pattern (for example, a pattern in which a phase shifter is embedded in a space portion). Devices and calculation methods can be applied.
Further, in the calculation method of the present embodiment, the two-dimensional contact hole patterns 62CA, 6CBB having the pitches p3, p4, etc., as shown by the device pattern DP2A of the reticle R1 in FIG. It can also be applied when including.
In the above embodiment, the complex amplitude distribution corresponding to the Zernike coefficients Z4, Z9 (Z16) is added to the second complex amplitude distribution. However, a higher-order 0θ term (Zernike coefficient Z25, A complex amplitude distribution corresponding to Z36, Z49, Z64, Z81,...) May be added to the second complex amplitude distribution.

  In addition, when the exposure apparatus EX of the above embodiment manufactures an electronic device (microdevice) such as a semiconductor device by using an exposure method, the electronic device performs device function / performance design as shown in FIG. Step 221 to be performed, Step 222 to manufacture a mask (reticle) based on this design step, Step 223 to manufacture a substrate (wafer) that is a base material of the device, the exposure apparatus EX, EXA or the exposure method of the above-described embodiment A process of exposing the mask pattern onto the substrate, a process of developing the exposed substrate, a substrate processing step 224 including heating (curing) and etching process of the developed substrate, a device assembly step (dicing process, bonding process, packaging process, etc.) 225) as well as the inspection step 22 It is manufactured through the like.

  In other words, the device manufacturing method includes the steps of exposing the substrate (wafer W) through the mask pattern using the exposure apparatus EX or the exposure method of the above embodiment, and processing the exposed substrate. (I.e., developing the resist on the substrate and forming a mask layer corresponding to the mask pattern on the surface of the substrate; and processing the surface of the substrate through the mask layer (heating, etching, etc.) ) Processing step).

According to this device manufacturing method, the reticle pattern image can be exposed onto the wafer with high accuracy in the exposure apparatus or the exposure method, so that the electronic device can be efficiently manufactured with high accuracy.
Note that the light amount distribution calculation method and apparatus of the above embodiment can be applied to a stepper type exposure apparatus or the like. The light amount distribution calculation method and apparatus of the above embodiment can be applied to an exposure apparatus (EUV exposure apparatus) that uses extreme ultraviolet light (Extreme Ultraviolet Light: hereinafter referred to as EUV light) having a wavelength of 100 nm or less as exposure light.
In addition, the light amount distribution calculation apparatus of the above embodiment may not be built in or connected to the exposure apparatus, and may be used independently of the exposure apparatus. The light quantity distribution calculation method of the above embodiment may also be used independently of the exposure apparatus.

In addition, the light quantity distribution calculation method and apparatus of the above-described embodiment can be applied to the SMO (Source and Mask) which simultaneously optimizes the optical proximity effect correction (OPC) modeling process and the mask (reticle) pattern and the illumination light source. Optimization) or SO (Source Optimization) for optimizing the illumination light source.
When calculating the BFD (Best Focus Debiations) using the light quantity distribution calculation method and apparatus of the above embodiment, the BFD remaining in the projection optical system and the BFD resulting from the phase shift caused by the resist thickness are calculated. You may consider it.

In the device manufacturing method of the present embodiment, the method of manufacturing a semiconductor device has been particularly described. However, the device manufacturing method of the present embodiment can be applied to a semiconductor material such as a liquid crystal panel or a magnetic disk in addition to a device using a semiconductor material. The present invention can also be applied to the manufacture of devices using other materials.
In addition, this invention is not limited to the above-mentioned embodiment, A various structure can be taken in the range which does not deviate from the summary of this invention.

  EX ... exposure apparatus, ILS ... illumination optical system, R ... reticle, PL ... projection optical system, W ... wafer, DP3 ... device pattern, ILP ... illumination pupil, PLP ... projection pupil plane, 10 ... light quantity distribution information calculation device, DESCRIPTION OF SYMBOLS 14 ... Main control apparatus, 20 ... Measurement part of light quantity distribution, 51 ... Recording medium, 52 ... Memory | storage part, 54 ... Calculation part, 58 ... Thin film, 58A, 58B ... Layer, 60A-60C ... Boundary surface, 64A, 65A, 66A ... Side surface (cross section)

Claims (15)

A light amount distribution calculation method for calculating light amount distribution information on a pupil plane of a projection optical system that receives light from a pattern formed on a main surface by a film having a plurality of layers having different complex refractive indexes,
Inputting information of an illumination pupil of an illumination optical system that illuminates the pattern;
By sequentially calculating at least one of transmittance and reflectance when a part of the illumination pupil passes through the boundary surface of the plurality of layers in the pattern, the light after passing through the pattern Calculating a first complex amplitude distribution on a first surface between the film and the projection optical system of a light beam;
Calculating a second complex amplitude distribution of diffracted light from the pattern on the pupil plane of the projection optical system by performing Fourier transform on the first complex amplitude distribution;
Calculation method including When the part of the light flux is incident obliquely with respect to an axis perpendicular to the main surface,
The calculation of the first complex amplitude distribution is to calculate at least one of transmittance and reflectance when passing through the boundary surface of the plurality of layers in the pattern for each of two orthogonal polarization components of the partial light flux. The calculation method according to claim 1, comprising calculating sequentially. When the part of the light beam passes through the cross section of the film,
The calculation method according to claim 1, wherein calculating the first complex amplitude distribution includes calculating at least one of transmittance and reflectance when the light flux passes through the cross section. Calculating an optical path length when the luminous flux passes through the film according to an incident angle when the partial luminous flux is incident on the main surface;
Adding a wavefront aberration component calculated using the calculated optical path length to the second complex amplitude distribution;
The calculation method as described in any one of Claims 1 thru | or 3 containing these.   The calculation method according to claim 1, wherein the film has at least two layers. In an exposure method of illuminating a pattern formed by a film having a plurality of layers with light from an illumination optical system, and exposing the substrate with the light through the pattern and the projection optical system,
Obtaining a light amount distribution of light from the pattern on the pupil plane of the projection optical system using the light amount distribution calculation method according to claim 1;
Obtaining a fluctuation amount of the optical characteristics of the projection optical system based on information on the light amount distribution on the pupil plane of the projection optical system;
Correcting the obtained variation amount of the optical characteristics;
An exposure method comprising: A light amount distribution calculating device for calculating light amount distribution information on a pupil plane of a projection optical system that receives light from a pattern formed on a main surface by a film having a plurality of layers having different complex refractive indexes,
A storage device for storing information on an illumination pupil of an illumination optical system that illuminates the pattern;
By sequentially calculating at least one of transmittance and reflectance when a part of the illumination pupil passes through the boundary surface of the plurality of layers in the pattern, the light after passing through the pattern Diffraction from the pattern on the pupil plane of the projection optical system by calculating a first complex amplitude distribution on the first surface between the film and the projection optical system of the light beam, and Fourier transforming the first complex amplitude distribution An arithmetic unit for calculating the second complex amplitude distribution of light;
A computing device comprising: When the part of the light flux is incident obliquely with respect to an axis perpendicular to the main surface,
The arithmetic unit is:
In order to calculate the first complex amplitude distribution, at least one of the transmittance and the reflectance when passing through the boundary surface of the plurality of layers in the pattern is determined for each of two orthogonal polarization components of the partial luminous flux. The calculation device according to claim 7 which calculates sequentially. When the part of the light beam passes through the cross section of the film,
The arithmetic unit is:
The calculation apparatus according to claim 7 or 8, wherein at least one of transmittance and reflectance when the light beam passes through the cross section is calculated in order to calculate the first complex amplitude distribution. The arithmetic unit is:
A wavefront aberration component calculated using the calculated optical path length by calculating an optical path length when the light beam passes through the film according to an incident angle when the partial light beam is incident on the main surface. 10 is added to the second complex amplitude distribution. The calculation device according to claim 7.   The computing device according to claim 7, wherein the film has at least two of the layers. In an exposure apparatus that illuminates a pattern formed by a film having a plurality of layers with light from an illumination optical system and exposes a substrate through the pattern and the projection optical system with the light,
The light quantity distribution calculating device according to any one of claims 7 to 11,
Control for obtaining a variation amount of the optical characteristic of the projection optical system based on information on a light amount distribution of the light from the pattern on the pupil plane of the projection optical system obtained by the calculation device, and correcting the variation amount of the optical characteristic. Equipment,
An exposure apparatus comprising: Forming a pattern of a photosensitive layer on a substrate using the exposure method according to claim 6;
Processing the substrate on which the pattern is formed;
A device manufacturing method including: Forming a pattern of a photosensitive layer on a substrate using the exposure apparatus according to claim 12;
Processing the substrate on which the pattern is formed;
A device manufacturing method including: 6. The light amount distribution information on a pupil plane of a projection optical system that receives light from a pattern formed on a main surface by a film having a plurality of layers having different complex refractive indexes from each other. A computer-readable recording medium on which a program for causing a computer to execute the processing of the light quantity distribution calculation method according to claim 1 is recorded.

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