JP2015176957A - Method and device for measuring focus characteristic of projection optical system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide method and device for measuring the focus characteristic of a projection optical system that can perform high-precision function approximation of a tendency that the length of a projection image of a wedge-shaped projection image varies according to a focus position, and measure the focus characteristic of a projection optical system with high precision.SOLUTION: A wedge-shaped pattern is projected by a projection optical system to form a projection image of the wedge-shaped pattern, and the length in a long-axis direction of the wedge of the projection image or a transfer image of the projection image is measured at each of focus positions Zn of n which are changed in the focal depth direction of the projection optical system by every predetermined amount. When the length in the wedge long-axis direction measured at each of the focus positions Zn of n is represented by Lpn, the length Lpn is defined as a model function f(Zn) containing a trigonometric function having the focus position Zn as a variable. Plural coefficients of the model function f(Zn) are approximately calculated, and a variation characteristic represented by the model function f(Zn) is determined, whereby the best focus position is specified with high precision.

Description

  The present invention relates to a method for measuring a focus characteristic of a projection optical system from a measurement result of a dimensional change of a fine pattern projected by a projection optical system such as a projection exposure apparatus, and a measurement apparatus.

  In the manufacturing process of a semiconductor device such as a CPU, a memory, a gate array, and a logic IC, a laminated structure using various materials is formed on the surface of a substrate such as a semiconductor wafer. Most layers of the laminated structure have a light exposure pattern by ultraviolet rays corresponding to the pattern of each layer (transistor electrodes, wiring, contact holes, etc.) on the photoresist film applied to the surface of the substrate, and a projection exposure apparatus. It is formed by using and exposing. At that time, it is required that the projected image of the light pattern generated via the projection optical system of the projection exposure apparatus is accurately focused (focused) on the surface of the photoresist film, for example.

In recent state-of-the-art projection exposure apparatuses, ultraviolet rays (center wavelength λ is 193 nm) from an ArF excimer laser light source are used as exposure illumination light, and the front lens on the image plane side of the projection optical system and the photoresist film on the substrate The minimum dimension of the resolvable pattern (line width, etc.) by using an immersion method in which a liquid such as ultrapure water is interposed between the projection optical system and the numerical aperture (NA) on the image side of the projection optical system is 1.0 or more. ) Is set to several tens of nm or less. As described above, in the projection exposure apparatus having a high resolution, the wavelength λ of the illumination light for exposure is short and the numerical aperture (NA) is extremely large, so that the range of the depth of focus (DOF) is extremely narrow. The depth of focus (DOF) is expressed by DOF = k · (λ / NA ² ) where k is a process constant (0 <k <1).

  In such a projection exposure apparatus, in order to match the best focus position (best image plane) of the projection image generated by the projection optical system with the surface of the substrate (surface of the photoresist film), the best focus position and the substrate A focus sensor that detects a focus deviation with respect to the surface with high accuracy, and a focus adjustment mechanism that moves the substrate in a direction (Z direction) perpendicular to the best image plane based on the focus deviation detected by the focus sensor (so-called Z stage for Z position adjustment). As a result, the surface of the substrate is positioned within the range of the depth of focus (DOF), and pattern exposure is performed in a good focus state.

  However, in a state-of-the-art projection exposure apparatus, the range of the depth of focus (DOF) including the best image plane is extremely narrow, and the position in the Z direction on the substrate surface that the focus sensor determines to be the best image plane and the projection optical system are true. It is necessary to always match the generated best image plane with high accuracy. For this purpose, it is important to accurately determine the Z position (focus position) of the best image plane that is truly generated by the projection optical system.

  Therefore, for example, as disclosed in Patent Document 1, a reticle (mask) provided with a wedge-shaped pattern is mounted on a projection exposure apparatus, and the wedge-shaped pattern is focused on a photoresist film on a substrate by a certain amount (ΔZ). The exposure is performed while changing, the developed substrate is developed, and the change in the length of the wedge-shaped pattern (resist image) exposed at each focus position is obtained by a measuring device (or alignment system), and the best focus position (best image plane) Is known to seek. The wedge-shaped pattern on the reticle is a long and narrow line with the apex angle of the wedge set at an acute angle, so that the apex angle portion is sensitively dulled by a slight change in the focus position during exposure, and the wedge shape becomes a resist image. The total length of the pattern changes with high sensitivity according to the change of the focus position.

Patent Document 2 discloses a wedge-shaped pattern (resist image) obtained by performing exposure while changing the Z position of a substrate by a certain amount (ΔZ) in a focus position detection method using a similar wedge-shaped pattern. It is disclosed that each length is approximated with a function using the Z position as a variable, and the Z position where the approximate curve has the maximum value is set as the best focus position. In Patent Document 2, an nth power is used as a model function for approximating (fitting) the length of a wedge-shaped pattern obtained as a resist image with a function having a Z position (focus position) at the time of exposure as a variable. It is shown that the function (Z ⁿ ) is used.

U.S. Pat. No. 4,908,656 JP 09-082620 A

  However, in a state-of-the-art projection exposure apparatus, since the depth of focus (DOF) is extremely narrow and the resolution is extremely high (having a resolution of several tens of nanometers), the wedge-shaped pattern is also miniaturized, and the reticle (mask) ) With the Koehler illumination method, the shape and distribution of the light source image can be changed not only to a general circular shape but also to a shape and distribution corresponding to a modified illumination method such as an annular, dipole, quadrupole, etc. Therefore, it has been found that an error remains in the fitting using an n-order function as a model as in Patent Document 2.

  Therefore, the present invention uses a wedge-shaped pattern to expose the substrate when determining the best focus position of the projection optical system (the position of the best image plane along the optical axis or principal ray). To provide a method and a measuring apparatus for measuring the focus characteristic of a projection optical system with high accuracy by approximating the change tendency of the length of the wedge-shaped pattern image for each focus position with a function approximation (fitting) with high accuracy With the goal. It is another object of the present invention to provide a method and a measuring apparatus for measuring a focus characteristic with high accuracy corresponding to a difference in illumination conditions (shape and distribution of a light source image) of a projection exposure apparatus.

In the first aspect of the present invention, in measuring the focus characteristic of the projection optical system, a step of projecting a wedge-shaped pattern image onto the image plane side of the projection optical system and the direction of the focal depth of the projection optical system (optical axis or A step of acquiring an image profile of a projected wedge-shaped pattern at each of a plurality of focus positions changed by a predetermined amount in the Z direction along the principal ray), and a step of acquiring the acquired image profile for each of the plurality of focus positions. Measuring the length in the direction in which the acute angle of the wedge-shaped pattern extends;
Determining a change characteristic of the length of the measured image profile with respect to the focus position using a model function including a trigonometric function with the focus position as a variable. Here, a model function including a trigonometric function means a function that can be defined using a sine function [sin (Z)] or a cosine function [cos (Z)], and the sine function is divided by the variable (Z). The sync function [sinc (Z)] is also included.

  According to a second aspect of the present invention, there is provided an apparatus for measuring a focus characteristic of a projection optical system, which is a projection image of a wedge-shaped pattern formed by projection of a wedge-shaped pattern by the projection optical system, or a wedge major axis direction of the transferred image. Is measured at each of the n focus positions changed by a predetermined amount in the direction of the depth of focus of the projection optical system, and the wedge long axis is measured by the measurement apparatus at each of the n focus positions. When the length in the direction is Lpn and the plurality of focus positions are Zn, the length Lpn is defined as a model function f (Zn) including a trigonometric function that changes the focus position Zn, and a plurality of the model functions f (Z) are defined. And a calculator for determining a change characteristic represented by the model function f (Z) by approximating the coefficients of the above, and a focus characteristic measuring device.

  In the embodiment, since the change characteristic for each focus position of the length of the wedge-shaped pattern image projected by the projection optical system is approximated (fitted) by a model function represented by a trigonometric function, a narrow depth of focus (DOF) ) Can measure the focus characteristic with high accuracy and determine the best focus position more accurately. In addition, by using approximation (fitting) using a model function represented by a trigonometric function, the focus characteristics can be measured with high accuracy even if there is a difference in illumination conditions (particularly the shape and distribution of the light source image). .

FIG. 3 is a diagram for explaining an outline of a focus characteristic measurement method according to the first embodiment. The figure which shows the structure of the projection exposure apparatus suitable for applying the measuring method by 1st Embodiment. The figure which shows arrangement | positioning of the optical filter for modified illumination installed in the illumination optical system of the projection exposure apparatus of FIG. FIG. 3 is an optical path diagram schematically showing an imaging relationship between the illumination optical system and the projection optical system and a pupil conjugate relationship in the projection exposure apparatus of FIG. 2. The figure which shows an example of the shape of the wedge-shaped pattern (FWM) in 1st Embodiment. The figure which shows the difference in the amplitude intensity | strength in two different positions of the major axis direction (y direction) of the wedge-shaped pattern (FWM) of FIG. The graph which compares the defocus dependence of the length of the major axis direction of the wedge-shaped pattern (FWM) image based on the model analysis formula in 1st Embodiment, and the calculation result by commercially available simulation software. The figure which shows an example of the light source arrangement | positioning set in the pupil in an illumination optical system at the time of inclination illumination (deformation illumination). The figure which shows an example of the setting of light source distribution at the time of assuming that the illumination pupil (circle) in an illumination optical system is a square (rectangle). The figure which shows the 1st example of the light source distribution set to the square illumination pupil of FIG. FIG. 11 is a diagram for explaining a distribution of imaging light flux (diffracted light) generated on the pupil plane in the projection optical system corresponding to the light source distribution in the square illumination pupil of FIG. 10. The figure which shows the 2nd example of the light source distribution set to the square illumination pupil of FIG. FIG. 13 is a view for explaining a distribution of imaging light flux (diffracted light) generated on a pupil plane in the projection optical system corresponding to the light source distribution in the square illumination pupil of FIG. 12. The graph which compares the change characteristic according to the focus position of the length of the projection image of the wedge-shaped pattern fitted with the model function containing a Sinc function, and the calculation result by commercially available simulation software. The figure which shows an example of the whole pattern arrangement | positioning of the reticle prepared for verification experiment, and the arrangement | sequence of a wedge-shaped pattern. Based on the measured value of the size of the wedge pattern image at each of the seven focus positions obtained by the test exposure using the reticle shown in FIG. 15, the wedge axis length change characteristic is approximated by a Sinc function and a quadratic function. A graph contrasting the case of approximation. Based on the measured value of the size of the wedge pattern image at each of the nine focus positions obtained by the test exposure using the reticle shown in FIG. 15, the wedge axis length change characteristic is approximated by a Sinc function and a quadratic function. A graph contrasting the case of approximation. Based on the measured value of the size of the wedge pattern image at each of the 11 focus positions obtained by the test exposure using the reticle shown in FIG. 15, the wedge axis length change characteristic is approximated by a Sinc function and a quadratic function. A graph contrasting the case of approximation. Based on the measured value of the size of the wedge pattern image for each of the 13 focus positions obtained by the test exposure using the reticle of FIG. 15, the wedge axis length change characteristic is approximated by a Sinc function and a quadratic function. A graph contrasting the case of approximation. Based on the actually measured value of the size of the wedge pattern image at each of the 15 focus positions obtained by the test exposure using the reticle of FIG. 15, the change characteristic of the wedge axis length is approximated by a Sinc function and a quadratic function. A graph contrasting the case of approximation. The graph which shows about the case where the change tendency of the specific precision of the best focus position according to the score of the measured value of the wedge axis length for every focus position used for approximation (fitting) is approximated by each of the quadratic function, the Sinc function and the Cos function . The figure which shows schematic structure of the photolithography system with which the exposure apparatus EXP and the coater developer C / D to which the measuring method or measuring device by 2nd Embodiment is applied were connected in-line. The figure explaining the structure of the alignment system ALG mounted in the exposure apparatus EXP of FIG. 22 as a measuring apparatus by 2nd Embodiment. The figure explaining the structure of the image processing unit which processes the image signal from the image pick-up element of the alignment system ALG of FIG. The figure explaining the structure of the aerial image measurement sensor POD mounted in the exposure apparatus EXP of FIG. 22 as a measuring apparatus by 3rd Embodiment. FIG. 10 is a diagram for explaining a method of measuring an intensity distribution (gradation) of zero-order light from a fine wedge structure pattern as an optical property evaluation method according to the fourth embodiment. FIG. 27 is a diagram for explaining an example in which a pair of test patterns DM1 and DM2 in FIG. 26 is repeatedly arranged in the X direction and used as a dose monitor (or focus monitor).

Hereinafter, the present embodiment will be described with reference to the drawings.
[First Embodiment]
The outline of the first embodiment of the focus characteristic measuring method according to the present invention will be described below with reference to FIG. In FIG. 1, the wedge-shaped pattern WM is formed in measurement pattern regions PG arranged at a plurality of locations in the pattern formation region PA of the test reticle TR. Here, the projection exposure apparatus EXP is a step-and-repeat stepper, and the test reticle TR is such that the entire rectangular pattern formation area PA is included in the projection field (circular) on the object plane side of the projection optical system PL. Is positioned. The plurality of measurement pattern areas PG includes a measurement pattern area PG located at the center of the pattern formation area PA, that is, the center of the projection field of the projection optical system PL, and from there, for example, an image height of 20%, 40%, 60%, It is composed of a plurality of measurement pattern regions PG arranged at 80% positions.

As an example, the wedge-shaped pattern WM formed in each measurement pattern region PG is formed by pitching long diamond-shaped (parallelogram) wedge patterns M1, M2, M3, and M4 having a length L and a width W in the direction of the width W. It is arranged with P. Although not shown, in each measurement pattern region PG, in addition to the wedge-shaped pattern WM shown in FIG. 1, a wedge-shaped pattern WM ′ obtained by rotating it by 90 ° is also provided. As an example, the wedge patterns M1 to M4 constituting the wedge-shaped pattern WM are created such that the dimensions on the projection image side are length L = 10 μm, width W = 0.5 μm, and pitch P = 1.0 μm. Therefore, in this case, the apex angle θmc extending in the length direction of each wedge pattern M1 to M4 is approximately an acute angle of θmc = tan ⁻¹ (0.5 / 5) ≈5.7 °.

  When the test reticle TR having such a wedge-shaped pattern WM (WM ′) is positioned at a predetermined position on the object surface side of the projection optical system PL, the projection exposure apparatus EXP passes through the illumination optical system and the test reticle TR Illumination light having a uniform (uniform) illuminance distribution is applied to the entire pattern formation area PA. As a result, light from the entire pattern formation area PA enters the projection optical system PL, and a projection image of the pattern formation area PA including the wedge-shaped pattern WM (WM ′) is generated on the image plane side of the projection optical system PL. .

  A test exposure wafer TW having a photoresist layer (photosensitive layer) formed on the surface thereof is disposed on the image plane side of the projection optical system PL. Wafer TW is sucked and held on a wafer holder in exposure apparatus EXP. The wafer holder is provided on a Z stage that can be finely moved in the optical axis direction (Z direction) of the projection optical system PL, and the Z stage is 2 in the XY direction parallel to the image plane orthogonal to the optical axis of the projection optical system PL. It is provided on an XY stage that can move dimensionally. The stage mechanism for holding the wafer TW is not only a stack structure in which the Z stage is placed on the XY stage, but also a monolithic structure that can hold the wafer and move in three dimensions in the XY direction and the Z direction. May be.

  In the case of a stepper, when a projected image of a pattern formation area PA including a wedge-shaped pattern WM (WM ′) is exposed to one shot area SA of the photoresist layer of the wafer TW with a predetermined exposure amount (DOSE amount), the wafer The TW is stepped by a distance equal to or larger than the size of the shot area SA in the X direction or the Y direction by the stage mechanism, and the projection image of the pattern formation area PA is exposed again to the adjacent shot area on the wafer TW. At this time, the exposure amount (illuminance × time) for each shot area is controlled to be constant, and the focus position of the wafer TW (position in the depth of focus direction of the projection optical system PL) is set by ΔZ for each shot area. In other words, the stage mechanism is controlled such that the wafer TW is exposed at each of the plurality of focus positions Z1, Z2, Z3.

  In order to adjust the focus position, the exposure apparatus EXP includes a focus sensor that measures the position in the Z direction of the surface (photoresist layer) of the wafer TW with high accuracy. A typical focus sensor projects obliquely incident measurement light onto the wafer surface, photoelectrically detects changes in the light receiving position of the reflected light, and measures the position in the Z direction on the wafer surface. It is a sensor. In general, the focus sensor provided in the projection exposure apparatus EXP outputs position information in the Z direction (direction of the focal depth of the projection optical system PL) on the surface of the wafer as a displacement amount from the reference position (origin).

  Therefore, when the measurement light from the focus sensor is projected onto the measurement area on the wafer surface, the displacement output from the focus sensor is the displacement from the reference position (origin) of the focus sensor itself. The amount of displacement of the wafer surface in the Z direction with respect to the best image plane (best focus plane) of the projected image of the pattern formation area PA (wedge pattern WM) projected by the projection optical system PL is not directly measured. Therefore, the projection exposure apparatus EXP sets the deviation (error) amount between the Z position of the reference position (origin) held by the focus sensor itself and the Z position of the best image plane of the projection optical system PL as an offset value. And a function (focus calibration function) for adjusting the deviation (error) amount to be equal to or less than an allowable value.

Thus, the wafer TW exposed by the exposure apparatus EXP is sent to the developing apparatus, and the photoresist layer is developed under predetermined conditions. The developed wafer TW has resist patterns WMp (patterns P1, P2, P3, P3, P3, P3, P3, P3, P3, P3, P3) corresponding to the optical profile of the projection image of the wedge-shaped pattern WM (wedge patterns M1 to M4), P4) is generated. Since the focus position at the time of exposure is changed by ΔZ for each shot area on the wafer TW, as the deviation from the best focus position increases, the apex angle portions of the patterns P1, P2, P3, and P4 constituting the resist pattern WMp are As a result, the length Lp of the resist pattern WMp becomes smaller.

  In this embodiment, by developing the exposed wafer TW, the profile of the projection image of the wedge-shaped pattern WM (wedge patterns M1 to M4) is obtained as the resist pattern WMp. However, depending on the photoresist, the image may not be developed. Also, it is possible to obtain a profile of the projection image of the wedge-shaped pattern WM (wedge patterns M1 to M4). For example, when a projection image of a wedge-shaped pattern WM (wedge patterns M1 to M4) due to ultraviolet rays is projected in a dye-containing resist or the like, an optical contrast difference is generated between a photosensitive portion and an unexposed portion, and a so-called latent image has a wedge shape The image profile of the pattern WM (wedge patterns M1 to M4) can be observed (measured).

The wafer TW on which the resist pattern WMp (hereinafter also including a latent image) has been generated in this way is under an alignment system (such as an optical microscope with an image sensor) mounted on the exposure apparatus EXP or an independent wafer inspection apparatus. The length Lp of the resist pattern WMp is measured for each of a plurality of focus positions during exposure. The plurality of focus positions Z are, for example, positions that are changed by ΔZ = 0.2 μm in each of the positive direction and the negative direction with respect to the zero position set as the reference position (origin) by the focus sensor of the exposure apparatus EXP. it can. The value of the change amount ΔZ of the focus position is preferably determined according to the focal depth (DOF) range of the projection optical system PL to be measured. For example, the change amount ΔZ is set such that at least three different focus positions fall within the theoretical depth of focus range.

  Here, the graph in FIG. 1 is a graph showing change characteristics in which the horizontal axis is the focus position Z of the surface of the wafer TW during exposure and the vertical axis is the length Lp of the measured resist pattern WMp. Are plot points of measured values of the length Lp of the resist pattern WMp exposed at each focus position Z that changes by 0.2 μm. In the graph in FIG. 1, the resist pattern WMp is generated by changing the focus position Z for obtaining the actual measurement value by 0.2 μm in a range of −0.8 μm to +0.8 μm so as to be 9 points including the zero position. doing.

  The actually measured values of the lengths Lp of the nine measured resist patterns WMp are the measured values of the nine points using the sink function Sinc (Z) in the model function f (Z) with the focus position Z as a variable. The curve of the change characteristic approximated (fitted) so that the deviation from the average is the smallest is determined. That is, a change characteristic approximated by the sink function Sinc (Z) is calculated. The reason why the sink function Sinc (Z) is used as the model function and the fact that the fitting accuracy is improved as compared with the case of approximation by a conventional n-order function, for example, a quadratic function will be described later.

  Although the details will be described later, the model function f (Z) used here represents the length Lp of the resist pattern WMp (projected image profile) and is defined by Lp = f (Z). Further, the model function f (Z) is a sink function Sinc (Z) [= sin (Z) / Z] obtained by dividing the sine function sin (Z) with the focus position Z as a variable by the focus position Z. In the present embodiment, the sink function Sinc (Z) is treated as a function that can be expressed by a sine function, a function that is defined based on the sine function, or a function that has an inherent sine function.

The model function f (Z) of this embodiment is defined by the following sink function Sinc (Z) including four unknowns b ₀ , b ₁ , b ₂ , and b ₃ .
... (1)
Since nine actual measurement values Lp are obtained for each of nine different focus positions Z, the nine focus positions Z1, Z2,..., Z9 at the time of exposure and the resist obtained at each focus position Z are obtained. Based on the measured values Lp1, Lp2,..., Lp9 of the pattern WMp, the four unknowns b ₀ , b ₁ , b ₂ , b ₃ can be calculated using the least square approximation method or the like. A change characteristic (curve) approximated by the function Sinc (Z) can be determined.

Next, on the change characteristic [Equation (1)] approximated by the sync function Sinc (Z), the focus position at which the length Lp is the maximum value and the focus position at which the focus sensor of the exposure apparatus EXP is set to the zero position. A deviation amount in the Z direction, that is, an error ΔFe is calculated. The obtained error ΔFe is the offset between the true best image plane (best focus plane) of the projection optical system PL and the reference position (zero position) in the Z direction of the focus sensor itself. The error ΔFe is incorporated as a correction value during focus calibration of the exposure apparatus EXP. As a result, when the wafer for an actual device is exposed, the wafer is positioned at the Z position shifted by the error ΔFe with respect to the Z position of the wafer surface measured by the focus sensor as the zero position. Is precisely matched to the best focus plane of the projection optical system PL. Note that the actual error ΔFe includes not only the offset of the focus sensor itself but also the error of the stage mechanism that finely moves the wafer TW in the Z direction.

(Configuration of Projection Exposure Apparatus Suitable for First Embodiment)
FIG. 2 is a perspective view showing a configuration of a projection exposure apparatus suitable for applying the measurement method according to the first embodiment. The projection exposure apparatus EXP in FIG. 2 is a stepper that sequentially exposes a pattern image in the pattern formation area PA of the reticle TR to each of a plurality of shot areas on the wafer TW as a photosensitive substrate by a step-and-repeat method. .

  The illumination beam EB from the mercury lamp or excimer laser light source is reflected by the mirror 10 and then enters the fly-eye lens 18 through the beam shaping optical system 12, the beam intensity adjustment system 14, and the input lens system 16. The fly-eye lens 18 is a two-dimensional array of a large number of microlenses, and a point light source image of the illumination beam EB is generated on the exit surface of each microlens. Accordingly, a surface light source in which a large number of point light source images are two-dimensionally gathered is formed on the exit side of the fly-eye lens 18. On the exit side of the fly-eye lens 18, a rotating turret 20 equipped with several optical filters for switching illumination conditions is provided.

  For example, as shown in FIG. 3, the rotating turret 20 is provided with different optical filters 20A, 20B, 20C, and 20D every 90 degrees in the circumferential direction of the disk that can rotate around the rotation axis 20X. Each of the optical filters 20A to 20D is disposed in a plane (parallel to the XY plane) orthogonal to the central optical axis (parallel to the Z axis) of the fly-eye lens 18, and is switched by rotation around the rotation axis 20X. The surface light source formed on the exit side of the eye lens 18 is limited to a predetermined shape (distribution). The optical filter 20A limits the surface light source on the emission side of the fly-eye lens 18 to a circle with a predetermined diameter. The optical filter 20B has two openings for limiting the surface light source to two spaced poles, the optical filter 20C has four openings for limiting the surface light source to four spaced poles, and the optical filter 20D. Has an opening for limiting the surface light source to an annular shape. Note that the diameter of the circular aperture of the optical filter 20A is determined according to an illumination sigma value (0 <σ ≦ 1) which is one of illumination conditions. The optical filters 20B, 20C, and 20D are used when pattern exposure is performed by a so-called modified illumination method.

  Illumination light from the fly-eye lens 18 (surface light source) whose shape and distribution is limited by any one of the optical filters 20A to 20D is reflected by the mirror 22 and is incident on the lens system 24. A diaphragm plate 26 is irradiated. The lens system 24 is arranged so as to be a Koehler illumination method in order to irradiate the illumination blind 26 with illumination light having a uniform illuminance distribution. That is, the exit surface of the fly eye lens 18 (the surface light source or the position of the optical filters 20A to 20D) is set to be the front focal position of the lens system 24, and the illumination blind 26 is illuminated in a telecentric state. The optical systems (16 to 24) arranged in front of the illumination blind 26 constitute a blind illumination system, and the exit surface of the fly-eye lens 18 (the position of the surface light source or the optical filters 20A to 20D) is the position of the illumination blind 26. Are arranged on the pupil plane having a Fourier transform relationship.

  In the illumination blind 26, a rectangular opening 26A is formed in accordance with the pattern formation area PA (see FIG. 1) of the reticle TR, and the illumination light passing through the opening 26A is transmitted through the lens system 28, the mirror 30, The reticle TR is irradiated through the condenser lens 32. The lens system 28, the mirror 30, and the condenser lens 32 constitute a blind imaging system that images the aperture 26A of the illumination blind 26 on the reticle TR, and an illumination area IA similar to the aperture 26A is formed on the reticle TR. Is done. The illumination area IA is set to a size that covers the pattern formation area PA of the reticle TR. Since the illumination area IA is optically conjugate with the opening 26A of the illumination blind 26, the illuminance distribution in the illumination area IA is also uniform (uniform).

  When the pattern formation area PA (see FIG. 1) of the reticle TR is irradiated by the illumination area IA on the reticle TR, the imaging light beam generated from the pattern in the pattern formation area PA is applied to the bilateral telecentric projection optical system PL. Incident. The imaging light beam reaches the shot area SA on the wafer TW through the aperture stop Ap disposed on the pupil plane ep of the projection optical system PL. As a result, a projection area similar to the pattern formation area PA reduced by a projection magnification of the projection optical system PL, for example, 1/4, is set in the shot area SA, and a projection image of the pattern is set in the projection area. Is generated.

The reticle TR is supported on the object plane side of the projection optical system PL by a reticle stage (not shown), and the wafer TW is moved to the image plane side of the projection optical system PL by a Z stage 34 on an XY stage capable of two-dimensional movement. Supported. The focus position (Z-direction position) of the shot area SA of the wafer TW is such that the measurement light that does not expose the photosensitive layer is projected from the oblique direction onto the surface of the wafer TW, and the measurement light on the surface of the wafer TW. Sequential measurement is performed by an oblique-incidence AF sensor having a light receiving unit 38B that receives reflected light.

  The light receiving unit 38B sequentially measures the deviation in the Z direction between the reference position (zero position) in the Z direction itself and the surface of the wafer TW (the upper surface of the photosensitive layer), and the Z stage has a predetermined deviation. Servo-controlled so as to be a value (zero or a specified constant value). Thus, the surface of the wafer TW (projection area portion) is exposed in a state in which the projection image from the projection optical system PL is in focus (a state in which focus adjustment is performed). As shown in FIG. 2, when the projection optical system PL is an all-refractive type composed only of refractive elements (lenses), the best focus plane of the projected image is a plane perpendicular to the optical axis AX (parallel to the Z axis) ( Therefore, the focus (focus) adjustment can be said to be a relative position adjustment in the direction of the optical axis AX between the best focus surface and the photosensitive substrate (wafer TW).

  On the other hand, in a catadioptric projection optical system composed of a plurality of refractive elements and reflective mirrors, or a total reflection type projection optical system composed of only reflective mirrors, the optical axis AX is not perpendicular to the best focus plane of the projected image There is also. In that case, in the case of a telecentric projection optical system on the image side, the principal ray of the imaging light beam for generating the projection image is perpendicular to the best focus plane. Therefore, in this case, the focus (focus) adjustment can be said to be a relative position adjustment in the principal ray direction between the best focus surface and the photosensitive substrate. Further, a depth of focus (DOF) of a predetermined width exists on the image side of the projection optical system with the best focus surface interposed therebetween. Since the direction of the depth of focus (DOF) is defined by the optical axis direction of the projection optical system or the principal ray direction of the imaging light beam, the focus (focus) adjustment is performed in the direction of the focal depth of the best focus surface and the photosensitive substrate. It can also be said that the relative position is adjusted.

  As described above, in the projection exposure apparatus EXP of FIG. 2, the pupil plane ep of the projection optical system PL is a surface light source formed on the exit side of the fly-eye lens 18 constituting the blind illumination system, or the openings of the optical filters 20A to 20D. And optically conjugate. Accordingly, the image of the surface light source (0th-order light) is distributed on the pupil plane ep of the projection optical system PL in a shape limited by any one of the optical filters 20A to 20D. Furthermore, since the imaging light beam includes diffracted light (primary light, secondary light, tertiary light, etc.) generated in the pattern of the reticle TR, the primary light, on the pupil plane ep of the projection optical system PL, Diffracted light such as secondary light and tertiary light is distributed according to the distribution shape of the image of the surface light source (0th-order light) and the pattern shape of the reticle TR.

  Although omitted in FIG. 2, an image detection type alignment system ALG for observing an alignment mark formed on the wafer TW with an image sensor is provided near the projection optical system PL. This alignment system ALG has an image processing function (waveform analysis software) that analyzes the image waveform of the captured alignment mark and obtains the edge position, mark width (dimension), interval, etc. of the alignment mark within the imaging field of view. It has been. Therefore, if the wafer TW on which the resist pattern WMp corresponding to the wedge-shaped pattern WM is generated is placed on the Z stage 34, the resist pattern WMp is captured within the imaging field of the alignment system ALG, and the resist pattern WMp is captured by the waveform analysis software. Can be actually measured.

(1. Analysis of defocus dependence of wedge pattern length)
In the conventional patent documents 1 and 2, etc., physical clarification about the relationship between the focus change and the length change of the projection image (resist image) of the wedge-shaped pattern (hereinafter also referred to as the wedge pattern image length change) is insufficient. Met. Therefore, as in Patent Document 2, it is physically significant to obtain the optimum focus position (best focus position) by approximating the change characteristic of the wedge length with a model function created by an nth power function. I was wondering. Therefore, in the following, the characteristics (defocus dependence) of the change in the length of the wedge pattern image due to the change in the focus position Z are analyzed based on the optical theory. In the following description, the wedge-shaped pattern is also called a focus wedge mark (Focus Wedge Mark), and may be abbreviated as FWM. Further, the change in the length of the projection image (resist image WMp) of the wedge pattern (the change in the length of the wedge pattern image) may be referred to as the change in the length of the FWM image.

In the analysis, the geometric optical arrangement of the illumination optical system (including the blind imaging system) and the projection optical system PL of the projection exposure apparatus EXP shown in FIG. 2 is determined as schematically shown in FIG. Since the illumination blind 26 and the reticle TR are in a conjugate relationship with each other by the blind imaging system, an illumination pupil ip exists inside the blind imaging system. The illumination pupil ip is conjugate with the light source surface generated on the exit side of the fly-eye lens 18 or the surface of the opening of the optical filter 20A (or 20B, 20C, 20D). Further, the illumination pupil ip is also conjugate with the pupil ep of the projection optical system PL, and a light source image is distributed on the illumination pupil ip in a shape limited by the openings of the optical filters 20A to 20D. The amplitude intensity of the light source image generated at the illumination pupil ip is S (ξ _s , η _s ).

The reticle TR arranged on the object surface is a transmission type mask in which a pattern is formed by a light shielding layer such as chromium on the surface of a transparent quartz substrate, and the amplitude intensity of the pattern corresponding to the transmission / light shielding is expressed as T (x, y ). The amplitude intensity U (x, y) of the projection image on the image plane of the projection optical system PL on which the wafer TW is arranged is the amplitude intensity T (x, y) of the pattern of the reticle TR, and the amplitude of the light source image at the illumination pupil ip. It is defined by the intensity S (ξ _s , η _s ) and various aberrations of the projection optical system PL.

  Here, the wedge-shaped pattern WM formed on the reticle TR is a plurality of wedge patterns (diamonds) M1, M2,... Formed by depositing a chromium light-shielding layer on the quartz reticle TR, as in FIG. Composed. In order to simplify the theoretical handling, a plurality of wedge patterns (diamonds) M1, M2,... (FWM) are innumerable at a pitch P along the X direction on the reticle TR as shown in FIG. Shall be placed. In FIG. 5, the X-axis direction of the orthogonal coordinates is the wedge pattern M1, M2,... (FWM) repetition direction (pitch direction), and the Y-axis direction is the top of the wedge patterns M1, M2,. The direction in which the corner extends. Each wedge pattern M1, M2,... Is a rhombus having the major axis in the Y direction and the minor axis in the X direction, the maximum width in the minor axis direction is W, and the length in the major axis direction is L. In FIG. 5, for the sake of explanation, the center point of one wedge pattern M3 (light shielding layer) is the origin of the XY coordinates.

  When the geometric magnification of the length in the major axis direction with respect to the length in the minor axis direction of the wedge patterns M1, M2,... Is sufficiently large, the light intensity on the Y axis (X = 0) in FIG. The influence of the diffraction effect in the axial direction can be ignored. This is supported by a high-precision agreement between an analysis calculation described later and a numerical simulation. Therefore, the light intensity of the wedge patterns M1, M2,... (FWM) in the region of Y> 0 (or Y <0) in FIG. 5 is determined by the diffraction effect in the pitch direction (X-axis direction). Assuming various lines parallel to the X axis on the wedge patterns M1, M2... (FWM), the wedge patterns M1, M2. It can be regarded as a line & space (L & S) pattern having a different pitch line width ratio (Duty Ratio) for each position.

  For example, in FIG. 5, the width W and the pitch P of each wedge pattern M1, M2,... Are in a relationship of 2W = P, and the light transmission portion between the wedge patterns M1, M2,. When the interval in the X direction of the bright line) is D, the pitch line width ratio D / P (duty ratio D / P) on the line parallel to the X axis with the Y coordinate Y = + L / 4 is shown in FIG. ) As shown in FIG. Further, the duty ratio D / P on the X axis where the Y coordinate is Y = 0 is 0.5 as shown in FIG. In addition, the vertical axis | shaft of Fig.6 (a), (b) represents the amplitude intensity | strength T normalized by 1.0.

Therefore, if the wedge patterns M1, M2,... (FWM) are regarded as a one-dimensional L & S pattern in which bright lines of width D are infinitely arranged at a pitch P, the amplitude intensity T of the L & S pattern is expressed by the following equation (2). It is expressed as follows.
... (2)
In the formula (2), m represents a diffraction order (1, 2,...) Of 1 or more, and λ represents the wavelength of illumination light.

(A. In the case of imaging with coherent illumination)
For the analysis, when the wedge pattern M1, M2,... (L & S pattern) is imaged under the coherent illumination by the projection optical system PL, that is, the light source in the Koehler illumination method is not a plane but a point, and the reticle TR. Assume that the illumination light is a parallel light beam having no numerical aperture. In this case, the amplitude intensity U (x, y) of the projected image of the wedge patterns M1, M2,... (L & S pattern) projected on the image plane side of the projection optical system PL is expressed by the following equation (3). .
... (3)
In Equation (3), k is a wave number defined by 2π / λ, and φ is a wavefront aberration accompanying defocus. Further, NA in Expression (3) is the numerical aperture on the image side of the projection optical system PL shown in FIG. 2, which is an imaging light beam that can pass through a circular aperture stop Ap arranged in the pupil ep ( Corresponds to the maximum diameter (including zero-order light and first-order or higher-order diffracted light).

Here, the amplitude intensity of 0-order light generated from the wedge pattern M1, M2 ··· (L & S pattern) and a _0, when the amplitude intensity of the primary or more m-order diffracted light and a _m, the following formula (4) (5).
... (4)
... (5)
If m order diffracted light generated from the wedge patterns M1, M2,... (L & S pattern) passes up to ± 1st order diffracted light through the numerical aperture NA of the projection optical system PL, the integration range in Expression (3) is The determined numerical aperture NA is defined as the following equation (6).
... (6)
The wedge patterns M1, M2,... (L & S pattern) are imaged with diffracted light up to ± 1st order in the range of equation (6), but second-order or higher-order diffracted light is incident. Even in the case, it can be similarly analyzed based on the equation (5) or the like.

Now, in the case of coherent illumination in which a parallel light beam is perpendicularly incident on the reticle TR, the phase difference between the 0th order light and the ± 1st order light is expressed by Expression (7) using the defocus amount Z on the image plane.
... (7)
However, C is a constant, and θ is the incident angle of the first-order diffracted light on the image plane defined by the following formula (8).
... (8)

Substituting Equations (2), (4), (5), (7), and (8) into Equation (3) for the previous imaging defined assuming coherent imaging, the absolute value is (9), the intensity distribution (image profile) of the projected image in consideration of the defocus aberration can be obtained.
... (9)
The length Lp of the FWM image along the Y axis transferred to the resist layer is determined by the relationship between the exposure threshold (threshold) inherent to the resist and the exposure amount. For example, the light intensity distribution I (y) in the long axis (Y axis) direction at the center in the X axis (short axis) direction of the wedge pattern M3 shown in FIG. 5 is substituted with 0 in x in the equation (9). Thus, the following equation (10) is obtained.
(10)

Further, when the equations (4) and (5) are substituted into the equation (10), the change in the light intensity distribution on the Y-axis is represented by the width D and the pitch P of the FWM bright line as in the following equation (11). Is obtained.
(11)
However, k is a wave number defined by 2π / λ, and the y coordinate is valid in the range where the duty ratio D / P exists, and therefore 0 ≦ y <L / 2 is defined as the domain. From the above, the defocus dependence of the length Lp in the long axis direction of the projection image of the wedge pattern (FWM) is calculated as a nonlinear equation related to the duty ratio D / P (changes according to the y position). Is required. Since this equation (11) includes a cos function with the focus position Z as a variable, it is called a model analysis equation represented by a cosine function. Note that the duty ratio D / P is determined based on the design length L of the FWM on the image side, the design width W of one wedge pattern (light shielding), and the design pitch P of the FWM. Within the domain of direction, D / P = (1−W / P) + (2W / L · P) y, and when the pitch P and width W are P = 2W, D / P = 1/2 + (1 / L) y.

  7 assumes a wedge-shaped pattern having a pitch P = 1 μm, a design length L = 10 μm, and a width W = 0.5 μm on the projection image side as an FWM as shown in FIG. It is the graph which represented the change characteristic (defocus dependence) of the length Lp of the major axis direction of the FWM image using the model analysis formula represented by a function for every different exposure amount (Dose amount). The horizontal axis in FIG. 7 represents the defocus amount Z (μm) with 0 as the best focus position, and the vertical axis represents the length Lp (μm) in the major axis direction of the FWM projection image. The plot points indicated by ◆, ■, ▲, and ● are changed by 0.1 μm by using the imaging calculation software “Dr. Litho” provided by the Francofafa Institute in Germany. Represents the result of numerical simulation.

  Further, the exposure conditions premised on FIG. 7 were i-line with an exposure wavelength λ of 365 nm, a numerical aperture NA on the image side of the projection optical system of 0.5, and an illumination sigma value σ = 0 (coherent illumination). Since the domain of the expression (11) is 0 ≦ y <L / 2, the change characteristic of the length Lp in FIG. 7 is based on the model analysis expression represented by the cosine function of the expression (11). The length of the FWM image to be obtained is doubled. As shown in FIG. 7, the imaging calculation software “Dr. Litho” was used as the change characteristic of the length Lp of the FWM image based on the model analysis expression (approximate expression) represented by the cosine function of Expression (11). It turns out that it corresponds well with the simulation result.

  From the above, the length (Lp) in the major axis direction of the FWM image is the duty ratio D / P (which is a constant component in the cosine function with the focus position Z in the model analysis expression of Expression (11) as a variable. It depends on the y position). That is, the length change characteristic in the major axis direction of the FWM image is determined by the one-dimensional structure in the minor axis direction of the FWM.

(B. In the case of imaging with tilted illumination)
Next, based on the analysis of the imaging state by the three-beam interference in the above-mentioned coherent illumination (interference between the 0th-order light and the ± 1st-order diffracted light), the two-beam interference in the tilt illumination method (modified illumination method) ( In a typical example, analysis of an imaging state by interference between one of ± first-order diffracted light and zero-order light will be described. Here, the positional relationship of the 0th-order light and the 1st-order diffracted light within the pupil plane ep of the projection optical system PL is set as the range of the following formula (12).
(12)
Further, as the simplest model for evaluating the influence of illumination coherence on image formation, as shown in FIG. 8, in the pupil ip of the illumination system, two points that are point-symmetric with respect to the pupil center (the point through which the optical axis AX passes) Assume an illumination condition consisting of a light source A (ξ _s , η _s ) and a point light source B (−ξ _s , −η _s ). In FIG. 8, the orthogonal coordinate system ξ _s η _s whose origin is the center of the pupil ip is not in a one-to-one relationship with the XY coordinate system of the object plane or the image plane, but the directions of the coordinate axes are aligned, so that it is convenient. The vertical axis η _s is the Y direction, and the horizontal axis ξ _s is the X direction.

The illumination light ILa from the point light source A becomes a parallel light beam inclined with respect to the optical axis AX and irradiates the reticle TR, and the illumination light ILb from the point light source B is in a direction symmetrical to the illumination light ILa with respect to the optical axis AX. The reticle TR is irradiated with an inclined parallel light beam. The amplitude intensity U _A (x, y) of the image projected onto the image plane via the projection optical system PL by the illumination light ILa and the amplitude of the image projected onto the image plane via the projection optical system PL by the illumination light ILb The intensity U _B (x, y) is expressed by the following equations (13) and (14), respectively.
... (13)
(14)
However, φ ₋₁ , φ ₀ , and φ ₁ mean wavefront aberration due to defocusing, and are expressed as the following equations (15) and (16) when the defocus amount Z is used.
... (15)
... (16)

Furthermore, the phase components θ ₀ and θ ₁ in the equations (15) and (16) correspond to the positions of the point light sources A and B in the illumination pupil ip shown in FIG. 8, and the following equations (17), It is expressed as (18).
... (17)
... (18)

Thereby, the light intensity distribution I _A (x, y) of the projection image formed on the image plane by the illumination light from the point light source A and the light of the projection image formed on the image plane by the illumination light from the point light source B The intensity distribution I _B (x, y) is defined by the following equations (19) and (20).
... (19)
... (20)
Furthermore, assuming that the illumination light from the point light source A and the illumination light from the point light source B are incoherent in a spatially and temporally incoherent state (or extremely low), the point light sources A and B The light intensity distribution I (x, y) of the projected image generated on the image plane by both of these is defined by the following expression (21) obtained by simply adding the light intensity distributions of expressions (19) and (20). .
(21)

When the x-coordinate value of this equation (21) is 0, the light intensity distribution I (y) along the Y axis (long axis) of the FWM image is represented by equation (22) as in the previous equation (10). Is obtained.
(22)
This expression (22) is physically the same expression except for the difference in coefficient from the expression (11) derived in the image formation by the three-beam interference. From this equation (22), when the position ξ _s has a relationship of ξ _s = λ / 2P in the η _s axis (X axis) direction within the plane of the illumination pupil ip shown in FIG. , (16), the phase components θ ₀ and θ ₁ become θ ₁ = θ ₀ . Therefore, the cos function with the focus position Z as a variable in the equation (22) does not depend on the defocus amount (Z position change amount). Therefore, the light intensity distribution I (y) is substantially constant within a certain range in the Z direction, and a large depth of focus (DOF) is obtained. This means imaging by pure two-beam interference.

(C. Imaging with partial coherent illumination)
However, in the actual projection exposure apparatus, the reticle TR is not irradiated only with illumination light from the point light source A (or B) as shown in FIG. It is irradiated with illumination light. Such an illumination form is called partial coherent illumination. From the above equation (22), the light intensity distribution in the Y-axis direction of the FWM image generated on the image plane by the illumination light from the point light source that does not satisfy the relationship of ξ _s = λ / 2P (that is, θ ₁ = θ ₀ ). It can be seen that I (y) exhibits defocus characteristics (length change characteristics in the long axis direction of the FWM image) in accordance with the cos function centered on the best focus position (Z = 0).

  The light intensity distribution I (y) of the projection image under partial coherent illumination is theoretically based on the distribution shape of the light sources (multiple points or planes) in the circular illumination pupil ip. Is obtained by integrating (linear addition). However, it is difficult to analytically perform image formation calculation (calculation of the light intensity distribution of the projection image) when an arbitrary light source shape is set within the circular illumination pupil ip (or within the projection pupil ep). Therefore, when imaging under partial coherent illumination is considered, a square pupil aperture having a side length of 2 NA is assumed based on the numerical aperture NA on the image side of the projection optical system PL.

As apparent from the equation (22), the amount of change of the light intensity distribution I (y) with respect to the defocus amount, so-called defocus sensitivity, is determined by the difference between the phase components θ ₀ and θ ₁ of the 0th order light and the 1st order diffracted light. If the difference is large, the value of (cos θ ₁ −cos θ ₀ ) increases and the defocus sensitivity increases. The difference between the phase components θ ₀ and θ ₁ that determine the sensitivity is expressed by the following equation (23).
... (23)

As an example, a square pupil opening assumed for analytical consideration is set as shown in FIG.
FIG. 9 schematically shows a square illumination pupil ip ′ included in a circular illumination pupil ip around the optical axis AX, and the coordinate systems ξ _s and η _s are set to be the same as those in FIG. The square illumination pupil ip ′ has a central rectangular area a (II) through which the optical axis AX passes in the ξ _s- axis (X-axis) direction (the direction of the pitch P of the FWM), and two rectangular areas a ( It shall be composed of the three areas of I).
The length from the center of the square illumination pupil ip ′ (optical axis AX) to the side in the ξ _s axis (X axis) direction (parallel to the η _s axis) and the center of the square illumination pupil ip ′ (light It is assumed that the length from the axis AX) to the side in the η _s axis (Y axis) direction (parallel to the ξ _s axis) corresponds to the numerical aperture NA. Therefore, if the length of the square illumination pupil ip ′ in the η _s- axis (Y-axis) direction is Lη, the length in the ξ _s- axis (X-axis) direction is also Lη.

Here, the arrangement range of the point light sources A and B for image formation by two-beam interference is expressed as the following formulas (24) and (25).
... (24)
... (25)
Furthermore, when the position of the point light source that can form an image with pure two-beam interference by tilt illumination is the points C1 and C2 that are the optical centers of the rectangular regions a (I) on both sides in FIG. coordinates and (-λ / 2P, 0), the coordinates of the point C2 (λ / 2P, 0) becomes, xi] _s axis of each rectangular region a (I) (X-axis) direction of the length Lξ, η _s axis The length Lη in the (Y axis) direction is expressed by equations (26) and (27).
... (26)
... (27)
Of the square illumination pupil ip ′ configured under the above conditions, as shown in FIG. 10, in the ξ _s- axis (X-axis) direction across the central rectangular area a (II) where no illumination light exists. Illumination light from each of the two rectangular regions a (I) arranged symmetrically contributes to effective projection exposure.

In FIG. 10, an arbitrary point (point light source) in the rectangular area a (I) on the right side in the square illumination pupil ip ′ and positioned on the ξ _s axis (X axis) is defined as C2 ′. C2 ′ is located at a distance ξ _s ′ from the optical axis AX. In this case, the imaging light beam generated from the FWM on the reticle TR irradiated by the illumination light from the point (point light source) C2 ′ is along the ξ _s axis (X axis) direction in the pupil ep of the projection optical system PL. Thus, for example, as shown in FIG. 11, the zero-order light and the ± first-order light are arranged separately.

FIG. 11 shows a projection pupil ep ′ which is set so as to be inscribed in the circular projection pupil ep of the projection optical system PL and set to a square in correspondence with the square illumination pupil ip ′. Each size of the square projection pupil ep ′ in the ξ _s- axis (X-axis) direction and the η _s- axis (Y-axis) direction is 2NA corresponding to the square illumination pupil ip ′. The zero-order light generated from the FWM on the reticle TR by the illumination light from the point C2 ′ in FIG. 10 is within the square projection pupil ep ′ as shown in FIG. 11, and the ξ _s axis at a distance ξ _s ′ from the optical axis AX. Located in the positive range on the (X axis). Further, of the ± first-order light generated from the FWM on the reticle TR, for example, the −1st-order light is a distance (ξ _s ′ −λ /) from the optical axis AX in the square projection pupil ep ′ as shown in FIG. P) is located in the negative region on the ξ _s- axis (X-axis).
Accordingly, the coordinate position of the zero-order light within the square projection pupil ep ′ is [+ ξ _s ′, 0], and the coordinate position of the −1st-order light is [− (ξ _s ′ −λ / P), 0]. In this case, the FWM image is formed by two-beam interference between the 0th order light and the −1st order light. Note that + 1st order light is also generated from the FWM, but it does not contribute to the formation of the FWM image because it goes to a position outside the square projection pupil ep ′ (on the right side of the 0th order light in FIG. 11).

Next, the case where the same FWM as in the case of FIGS. 10 and 11 is illuminated by the illumination light from the point light source located in the central rectangular area a (II) shown in FIG. 9 will be described with reference to FIGS. To do. As shown in FIG. 12, it is assumed that the point light source is located as a point C2 ′ at a distance ξ _s ′ from the optical axis AX in a positive area on the ξ _s axis (X axis) in the rectangular area a (II). As shown in FIG. 13, the zero-order light is located at a distance ξ _s ′ from the optical axis AX on the ξ _s axis (X axis) in the square projection pupil ep ′, but the pitch P of the FWM is 10 and 11, the distance on the ξ _s axis (X axis) from the 0th order light to the −1st order light is the same as in FIG. 11, and the −1st order light is square. Is located outside the projection pupil ep ′. Therefore, in the case of illumination light from a point light source located at a point C2 ′ in the rectangular area a (II) in the illumination pupil ip ′, only the 0th order light from the FWM on the reticle TR passes through the projection optical system PL. Therefore, it becomes bias light (DC component) that does not generate the intensity distribution of the FWM image.

From the above, for each of the rectangular area a (I) and rectangular area a (II), adding the light intensity distribution obtained by integrating the previous equation (22) in the range of the equations (24) and (25), The light intensity distribution I (y) of the FWM image can be obtained. Here, the integrated light intensity distribution of the FWM image when the illumination light is distributed in the rectangular area a (I) is I _I (y), and the FWM when the illumination light is distributed in the rectangular area a (II). When the integrated light intensity distribution of the image is I _II (y), the total light intensity distribution I (y) of the FWM image is expressed by the following equation (28).
... (28)
However, as shown in FIGS. 12 and 13, when the light source is located in the rectangular area a (II), only the 0th-order light has a bias intensity, so that the light intensity distribution I _II (y) does not need to be integrated. It becomes a constant value and is expressed by the following equation (29).
... (29)
Since the focus position Z is not included as a variable in the equation (29), the light intensity distribution I _II in the equation (28) is obtained when obtaining the defocus dependency of the length of the FWM image in the long axis direction. (Y) may be ignored.

On the other hand, the light intensity distribution I _I (y) of the FWM image when the illumination light is distributed in the rectangular area a (I) is expressed by the following equation (30).

... (30)

  As described above, assuming that the illumination pupil ip ′ and the projection pupil ep ′ are square (rectangular), unlike the case of imaging by three-beam interference under coherent illumination in which a parallel light beam is perpendicularly incident on the reticle TR, partial coherent illumination. In the image formation by the two-beam interference under, the length change in the major axis direction of the FWM image with respect to the defocus aberration (focus position Z) can behave as a single sinc function as shown in Expression (30). I understand. Therefore, under a certain condition, the change characteristic of the length of the FWM image approximated by the sinc function (model function) of Expression (30) is compared with the simulation result by the imaging calculation software “Dr. Litho”. View.

  FIG. 14 shows normal illumination (circular surface light source) when the numerical aperture NA of the projection optical system PL (1/4 reduction) is 0.62, the wavelength λ is 365 nm (i-line), and the illumination sigma value σ is 0.7. 6 is a graph showing the length change characteristic in the major axis direction of the FWM image in the case of (1) when the exposure amount (Dose) is 0.4 times, 0.5 times, and 0.6 times the specified value. The prescribed value means the light intensity (1.0) that reaches the image plane side through the transmission part of the reticle TR. The vertical axis in FIG. 14 represents the length Lp (μm) of the FWM image, and the horizontal axis represents the focus position Z (the height position of the Z stage). The dimensions of the FWM (image side) were a length L of 12.0 μm, a width W of 0.28 μm, and a pitch P of 0.56 μm. Further, the simulation result of the wedge length Lp of the FWM image obtained by the imaging calculation software “Dr. Litho” is represented by plot points of ◆, ●, and ▲.

In FIG. 14, the defocus dependence of the wedge length Lp of the FWM image by the model function using the sinc function derived as in Expression (30) is in good agreement with the simulation results over a wide focus range. It can also be seen that as the defocus amount increases, the wedge length Lp of the FWM image does not decrease monotonously but tends to converge to a certain range of values. For this reason, in the conventional approximation by a power function (Z ⁿ ) such as square, it is possible to fit the trend of the length change of the FWM image near the best focus position (Z = 0) with good accuracy. It can be seen that the fitting accuracy deteriorates as the defocus amount increases.

  As described above, the model function [Equation (30)] including the sinc function derived on the assumption that the illumination pupil ip ′ and the projection pupil ep ′ are square is the focus position where the defocus amount is large. It can be seen that the FWM image (resist image) obtained actually fits well with the tendency of the length change in the major axis direction. Incidentally, compared to the theoretical depth of focus DOF derived from the NA of the projection optical system PL and the wavelength λ of the illumination light, the fitting by the model function including the sinc function is about twice as wide as the depth of focus DOF. Maintains accuracy over a range.

(Approximate experiment using model function including sinc function)
Next, a method of estimating the best focus position based on the dimension data in the major axis direction of the actually measured FWM image by using the model function expression composed of the sinc function obtained as described above. explain. First, the best focus position Z _best determined based on the length change characteristic of the FWM image is defined by the following equation (31).
... (31)
Here, Zo is the theoretical best focus position of the FWM image, ΔZ is the accuracy (Accuracy) of the focus position, and 3σz is the measurement reproducibility (Precision) of the dimensions of the FWM image (resist image).

  In the exposure process of an actual device pattern, the best focus position suitable for the projected image of the device pattern may be slightly different from the theoretical best focus position Zo of the FWM image. This error is the focus of the exposure apparatus as a process offset that can change depending on the shape of the device pattern, the structure of the wafer surface, and the like, in addition to the error on the exposure apparatus system such as the error ΔFe described in FIG. It is set as a correction value in the adjustment mechanism.

  Using the reduction projection type exposure apparatus NSR-SF155 manufactured and sold by Nikon Corporation as an actual exposure apparatus, the FWM image is exposed on the resist layer of the wafer TW, the developed resist image is measured, and the sinc function is calculated. An experiment was conducted to confirm the fitting accuracy of the model function. In the reduction projection type exposure apparatus used for exposure, the illumination light is i-line (wavelength 365 nm), the numerical aperture of the projection optical system PL is 0.62, the illumination sigma value σ is 0.7 (normal circular surface light source), A stepper with a reduction ratio of 1/4. In this case, if the process constant k related to focus is about 0.5, the depth of focus DOF is in the range of about ± 0.5 μm in width. Using this stepper, as described with reference to FIG. 1, the focus area Z (position of the Z stage) is changed by 0.2 μm at a time so that the pattern area PA of the reticle TR including the FWM is changed on the wafer TW. Different shot areas were sequentially exposed, and the exposed wafer TW was developed to obtain an FWM resist image.

Conventionally, a quadratic function has been used for fitting the change characteristics based on the measurement data of the length Lp in the long axis direction of the wedge pattern formed on the wafer. Therefore, in the following experimental results, for comparison A fitting curve based on a quadratic function (power function) will be shown. The approximation by the quadratic function reflects the effect of defocus, which is an even function aberration, on the primitive, but the approximation by the sinc function is more robust to the defocus area expansion of the measurement data.
The model function based on the quadratic function is represented by the following equation (32).
... (32)
However, Lp ′ is the length (or measured length) of the FWM image in the long axis direction, and Z is the focus position of the wafer TW (Z-axis direction position of the Z stage). There are three unknowns a ₀ , a ₁ , and a ₂ determined by the fitting. The three unknowns are the lengths Lp1 ′, Lp2 ′, Lp3 ′,... (Actually measured values) of the FWM image exposed at each of three or more different focus positions Z1, Z2, Z3,. ) Using the least square approximation method.

On the other hand, the model function including the sinc function employed in the present embodiment is derived on the assumption of incoherent illumination, and is the same as Equation (1) above, but the four unknowns are b ₀ , b _It shall be represented by the following formula (33) including ₁ , b ₂ , and b ₃ .
... (33)
The four unknowns are the lengths Lp1, Lp2, Lp3, Lp4,... (Measured in the long axis direction of the FWM image exposed at each of four or more different focus positions Z1, Z2, Z3, Z4,. Value), and is obtained by the least square approximation method. Note that the sinc function sinc [b1 (z−b2)] in the equation (33) has a single period, and sin [b1 (z−b2)] / [b1 (z−b2)] when using a sine function. ] Is equivalent.

  An example of the pattern arrangement of the test reticle TR used in the experiment is shown in FIG. In FIG. 15, reticle marks Am for precise positioning are formed at three positions around the test reticle TR after the test reticle TR is mounted at a predetermined position in the reduction projection exposure apparatus. The rectangular frame-shaped light shielding band SB is formed in a size included in a circular projection field on the object surface side of the projection optical system PL, and the inside of the light shielding band SB is a pattern formation region PA. In this pattern formation area PA, a total of nine pattern blocks PG1 to PG9, three in the X direction and three in the Y direction, are arranged in a 3 × 3 matrix, and one of these pattern blocks PG5 has a projection field of view. , In this case, at a position where the optical axis AX of the projection optical system PL passes.

  Each of the nine pattern blocks PG1 to PG9 includes, for example, two wedge-shaped patterns FWMx1 and FWMx2 whose pitch direction is the Y direction and two wedge-shaped patterns whose pitch direction is the X direction, as representatively, for example, the pattern block PG8. FWMy1 and FWMy2 are formed. The wedge-shaped patterns FWMx1 and FWMy1 or the wedge-shaped patterns FWMx2 and FWMy2 that make a pair in the XY direction have a total length L of 12 μm and a width corresponding to the characteristics of the projection optical system PL of the reduction projection exposure apparatus used in the experiment. W was 0.28 μm and pitch P was 0.56 μm (see FIG. 5).

  Using the test reticle TR as shown in FIG. 15, the focus position Z is changed by 0.2 μm for each shot exposure by the method described in FIG. 1, and the pattern formation area PA (9) is formed on the test wafer TW. The projection image of (including two pattern blocks PG1 to PG9) is exposed by the step & repeat method. The change width of the focus position Z was set to −1.4 μm to +1.4 μm, which is about three times the width of the focal depth DOF ± 0.5 μm, and 15 focus positions were set every 0.2 μm. Therefore, fifteen shot areas (images of the pattern formation area PA) exposed with different focus positions by 0.2 μm are arranged on the test wafer TW.

  After the development of the exposed test wafer TW, the dimension Lp in the wedge major axis direction of each of the wedge-shaped patterns FWMx1, FWMx2, FWMy1, and FWMy2 included in the pattern blocks PG1 to PG9 for each shot area generated as a resist image is measured. To do. Then, an average value of the actually measured lengths Lp of a plurality of wedge patterns included in one pattern block PGn is obtained as the length Lp of the FWM image. At that time, the average value may be obtained by dividing into wedge-shaped patterns FWMx1 and FWMx2 whose wedge length changes in the X direction and wedge-shaped patterns FWMy1 and FWMy2 whose wedge length changes in the Y direction.

  Next, paying attention to, for example, the pattern block PG5 located at the center of each of the 15 shot regions, the length Lp of the FWM image obtained for each of the 15 pattern blocks PG5 is set to the maximum number of samples 15. Assess the closeness. For comparison, the lengths of seven FWM images obtained corresponding to each of the seven points in the range of −0.6 μm to +0.6 μm among the lengths Lp of the 15 FWM images. Approximate example using Lp (7 measurement points), Approximate example using length Lp of 9 FWM images obtained corresponding to each of 9 points in the focus range of -0.8 μm to +0.8 μm (9 measurement points), an approximation example (11 measurement points) using the length Lp of 11 FWM images obtained corresponding to each of 11 points in the range of the focus position from −1.0 μm to +1.0 μm, An example of approximation (13 measurement points) using the length Lp of 13 FWM images obtained corresponding to each of 13 points in the range of the focus position in the range of −1.2 μm to +1.2 μm is also illustrated.

  FIG. 16 shows a change characteristic obtained by fitting the length Lp of seven actually measured FWM images with a quadratic function defined by the equation (32) in the case of seven measurement points, and is defined by the equation (33). It is a graph which shows the change characteristic fitted with the sinc function. In the case of seven measurement points, the length Lp of the seven FWM images used for approximation is obtained at the focus position Z within the range of the focal depth DOF (± 0.5 μm). Both the approximate change characteristic and the change characteristic approximated by the sinc function are in good agreement with the measured value Lp.

  FIG. 17 shows a change characteristic obtained by fitting the length Lp of nine actually measured FWM images with a quadratic function defined by the equation (32) in the case of nine measurement points, and is defined by the equation (33). It is a graph which shows the change characteristic fitted with the sinc function. In the case of 9 measurement points, since the length Lp of the 9 FWM images used for approximation includes those obtained at the focus position Z slightly outside the range of the focal depth DOF (± 0.5 μm), a quadratic function The change characteristic approximated by (3) brings a slight error with respect to the actual measurement value Lp. On the other hand, the change characteristic approximated by the sinc function matches well with the actual measurement value Lp.

  FIG. 18 shows a change characteristic obtained by fitting the length Lp of 11 actually measured FWM images with a quadratic function defined by Expression (32) in the case of 11 measurement points, and is defined by Expression (33). It is a graph which shows the change characteristic fitted with the sinc function. In the case of 11 measurement points, the length Lp of 11 FWM images used for approximation includes those obtained at a focus position Z that is about twice out of the range of the depth of focus DOF (± 0.5 μm). The change characteristic approximated by the next function brings a large error with respect to the actual measurement value Lp. On the other hand, the change characteristic approximated by the sinc function matches well with the actual measurement value Lp.

  FIG. 19 shows the characteristics in the case of 13 measurement points, and the characteristics obtained by fitting the length Lp of 13 actually measured FWM images with a quadratic function of Expression (32) and the fitting with the sinc function of Expression (33). It is a graph which shows the changed characteristic. In the case of 13 measurement points, the length Lp of the 13 FWM images used for approximation includes those obtained at the focus position Z far outside the range of the depth of focus DOF (± 0.5 μm). The change characteristic approximated by (3) brings a large error with respect to the actual measurement value Lp. On the other hand, the change characteristic approximated by the sinc function matches well with the actual measurement value Lp.

  FIG. 20 shows the characteristics in the case of 15 measurement points, and the variation characteristics obtained by fitting the length Lp of 15 actually measured FWM images with a quadratic function of Expression (32) and the fitting with the sinc function of Expression (33). It is a graph which shows the changed characteristic. In the case of 15 measurement points, the length Lp of 15 FWM images used for approximation includes those obtained at a focus position Z that is about 3 times out of the range of the depth of focus DOF (± 0.5 μm). Although the change characteristic approximated by the quadratic function has a large error with respect to the actual measurement value Lp, the change characteristic approximated by the sinc function matches well with the actual measurement value Lp even at a large defocus position.

  As described above, it can be seen that the fitting of the focus change characteristic using the sinc function of Expression (33) matches well with the actually measured value under the incoherent illumination condition. Therefore, if the four coefficients b0 to b3 of the sinc function of the equation (33) are specified by the least square approximation method or the like using many actually measured values Lp with different focus positions, the wedge length on the change characteristic from the function is determined. If the focus position Z at which is the longest is obtained, it becomes the best focus position at the center in the projection field of the projection optical system PL.

The exact best focus position Z _best is defined by the previous equation (31), but from the change characteristic by the sinc function obtained as shown in FIGS. 16 to 20, the theoretical best focus position in the equation (31). Let us calculate Zo and the accuracy ΔZ of the focus position. Therefore, here, the actual measurement of the wedge length of the resist image of all the wedge patterns of the nine pattern blocks PG1 to PG9 included in each of the 15 shot areas exposed by changing the focus position Z by 0.2 μm. A value obtained by averaging the values Lp is set as an actual measurement value corresponding to one focus position Z.

  In FIG. 21, the horizontal axis represents the number of measurement points (the number of changes in the focus position Z during exposure), and the vertical axis represents the deviation of the best focus position determined by fitting with approximation functions (secondary function, sinc function, cos function). It is a graph representing (error) and represents the dependence of the specific accuracy of the best focus position on the number of measurement points. The plot point ▲ in FIG. 21 represents the best focus position determined from the change characteristic fitted by the quadratic function of Expression (32), and the plot point ■ is from the change characteristic fitted by the sinc function of Expression (33). The determined best focus position is represented, and the plot point ● represents the best focus position when the sinc function of Equation (33) is changed to a cos function for comparison. An error range bar extending vertically above and below each plot point represents the standard deviation of the actually measured value Lp of the wedge length of the wedge pattern image obtained in each of the nine pattern blocks PG1 to PG9.

  FIG. 21 also shows data when the number of measurement points is 5, that is, when the exposure is performed by changing the focus position Z by 0.2 μm in five places in the range of −0.4 μm to +0.4 μm. However, the accuracy of specifying the best focus position was low regardless of which function was used. From the graph of FIG. 21, in the projection exposure apparatus used as an experiment target, the number of measurement points is preferably 7 or more in order to specify the best focus position. Therefore, when the best focus position (plot point ■) determined by the sinc function is viewed at five measurement points 7 to 15, the average value is about −30.9 nm. Therefore, this value is the best focus position Zo in the previous equation (31). Furthermore, the deviation (variation) from the average value −30.9 nm of the best focus positions (plot points approximated by the sinc function) of the measurement points 7 to 15 is the focus position in the above equation (31). Corresponding to the accuracy ΔZ of ΔZ = −3 nm to +2 nm.

  On the other hand, when the best focus position (plot point ▲) obtained by fitting using a quadratic function is viewed at five measurement points 7 to 15, the average value is obtained, but it is not always accurate. Not a value. Therefore, the average value of the best focus position Zo is set to the average value −30.9 nm obtained from the fitting of the sinc function, and the accuracy (Accuracy) ΔZ of the focus position in the above equation (31) is measured from 7 to 7 points. Assuming a deviation (variation) from the average value −30.9 nm of each of the 15 best focus positions (plot points ▲ approximated by a quadratic function), the range was ΔZ = + 2 nm to +10 nm.

  Also, the best focus position (plot point ●) Zo obtained by fitting using the cos function is the best focus position (plot point ■) Zo obtained by fitting using the sinc function while the number of measurement points is small. However, as the number of measurement points increases, that is, as the defocus range increases, the accuracy of specifying the best focus position Zo and the accuracy (Accuracy) ΔZ of the focus position become worse.

  As described above, the accuracy (Accuracy) ΔZ of the focus position obtained by the fitting using the sinc function is approximately equal to the accuracy (Accuracy) ΔZ of the focus position obtained by the fitting using the conventional quadratic function. It is improved to 1/3. Further, the best focus position Zo obtained by fitting using a quadratic function varies depending on the number of points at which the focus position Z is shaken at the time of exposure, that is, the number of measurement points, while the sinc function (or cos function). The best focus position Zo determined by fitting using () is relatively stable without being affected by the number of measurement points.

  As described above, when obtaining the focus change characteristic using the wedge-shaped pattern FWM, it is beneficial from the following two viewpoints to adopt the sinc function (or cos function) as an approximate function for fitting the actual measurement value Lp. The first aspect is that the robustness can be ensured even when the data set used for fitting (a set of measured values Lp of the wedge length of the wedge pattern image acquired for each number of measurement points) is extended to the defocus area. Is a point. In the experiment results shown in FIGS. 16 to 20, the best focus position can be specified with high accuracy and high accuracy even when the exposure is performed with the focus position shifted over a range close to three times the width of the depth of focus DOF.

  In a field where a projection exposure apparatus is actually used, a change in a defocus area wider than a quadratic function capable of performing an effective estimation only within the focal depth DOF range, particularly in a defocus area outside the focal depth DOF range. The sinc function that can use the actual measurement value Lp in the slope portion on the characteristic has an advantage that the measurement environment can be given flexibility. The second aspect is that the influence of defocusing of a projection image under two-beam interference in the tilt illumination method or a projection image under incoherent illumination is essentially expressed as a light intensity distribution by a sinc function. Making the function (trigonometric function) a fitting function is a point that directly reflects a physical phenomenon.

(Setting the sinc function cycle)
Even if the same projection exposure apparatus is used, the periodic component of the sinc function defined by Expression (33) changes because the DOF changes depending on the illumination conditions, the physical properties (material, thickness, etc.) of the resist layer, and the process. Come. Accordingly, the coefficients b1 and b2 in the equation (33), which are the periodic components of the sinc function, may be individually determined as optimum values from the actual wedge length measurement data (Lp).

(Application to different exposure equipment)
In the above experiment, the projection optical system PL using i-line having a wavelength of 365 nm as illumination light is used. However, even with other exposure apparatuses having different wavelengths λ and numerical aperture NA of illumination light, the sinc function is determined by the scaling law. A focus change characteristic (best focus position Zo, focus position accuracy ΔZ) using fitting by (or cos function) can be estimated. In that case, it can be assumed that the periodic component of the sinc function changes with the square of the ratio of the numerical aperture NA between different projection optical systems and changes with the ratio of different wavelengths λ. If the cycle of the sinc function is smaller than that in the previous experiment, the amount of change in the focus position Z during exposure of the test wafer TW is reduced, and the number of measurement points is 7 within the range of the focal depth DOF. It is desirable to set so that exists.

Therefore, the numerical aperture of the projection optical system PL used in the previous experiment is NA _i , and the wavelength of the illumination light is λ _i , whereas the state-of-the-art immersion exposure apparatus using an ArF excimer laser (wavelength 193 nm) is used. When the numerical aperture of the projection optical system is NA _Arf , the wavelength of illumination light is λ _Arf, and the focus position accuracy ΔZ obtained in the previous experiment is ΔZ _i , the focus position by the projection optical system of the ArF immersion exposure apparatus The accuracy ΔZ _Arf is expressed by a relationship such as the following equation (34). The focus position accuracy ΔZ _i obtained in the previous experiment is set to −2 nm to +3 nm (about 5 nm in width) from the graph shown in FIG.

... (34)
Here, when the wavelength λ _Arf of the ArF immersion exposure apparatus is 193 nm and the numerical aperture NA _Arf is 1.35, the accuracy ΔZ _Arf of the focus position of the ArF immersion exposure apparatus is −0.34 nm to +0.22 ( It is estimated that the width is about 0.56 nm.

  When the focus change characteristic is actually measured by projecting and exposing the wedge pattern FWM by the ArF immersion exposure apparatus, the length L, width W, and pitch P of the wedge pattern FWM drawn on the test reticle TR are set to It is proportionally reduced to about 1/5 to 1/10 with respect to the conditions (L = 12 μm, W = 0.28 μm, P = 0.56 μm as dimensions on the image plane side).

  As described above, in the case of coherent illumination in which illumination light is distributed as a point light source at the illumination pupil ip, the change in the light intensity distribution accompanying the defocus of the projection image of the wedge-shaped pattern FWM is a trigonometric function, particularly a cosine function. Can be approximated. Further, when a sinc function derived by assuming that the illumination pupil ip or the projection pupil ep is a square aperture is used for fitting, coherent illumination, tilt illumination for projection exposure by two-beam interference, and general incoherent illumination Even in this case, the best focus position can be obtained with high accuracy and high accuracy by using the wedge length actual measurement value Lp of the projection image of the wedge-shaped pattern FWM acquired over a wide defocus range. In other words, including the effects of illumination conditions (illumination light wavelength, light source distribution and shape, illumination σ value, etc.) and exposure conditions (projection optical system numerical aperture NA, exposure amount, resist layer thickness, material, etc.) Thus, the focus change characteristic and the best focus position can be obtained precisely.

[Second Embodiment]
Next, an example of an apparatus configuration when the above-described best focus position measurement method is performed on an exposure apparatus will be described with reference to FIGS. FIG. 22 shows inline an exposure apparatus EXP for projecting and exposing a device pattern such as a semiconductor element or an IC chip on a wafer, and a coater developer C / D for applying a photoresist to the wafer or developing an exposed wafer. 1 shows a schematic configuration of a connected photolithography system.

  The coater / developer C / D temporarily stores a coater CTR for applying a photoresist layer to the surface of the wafer stocked in the supply port FP1 and drying it, and the wafer on which the resist layer is formed. At the same time, the wafer B is carried out to the exposure apparatus EXP and the buffer BFP for receiving the exposed wafer from the exposure apparatus EXP, and the wafer exposed by the exposure apparatus EXP is carried in, developed and dried, and developed. And a developer unit DVR for sending the subsequent wafer to the recovery port unit FP2.

  The exposure apparatus EXP receives a wafer on which a resist layer is formed from the buffer unit BFP of the coater developer C / D, performs pre-alignment, and exposes the exposed wafer to the buffer unit BFP and the wafer transfer unit WTP. Wafer stage WST (34 and 36 in FIG. 2) that can move the wafer to be moved in the XY and Z directions, reticle storage unit RC that stocks device reticles and test reticles TR, and on the wafer Alignment system ALG that captures the alignment mark and reference mark on the wafer stage and measures the mark position (wafer position relative to projection optical system PL) by image analysis of the mark image, and above projection optical system PL (object surface) A reticle stage RST that supports the reticle on the side) and can be moved finely on the XY plane, and a reticle And a lighting system ILU which irradiates illumination light for exposure to Le.

  The alignment system ALG is configured similarly to the optical microscope, for example, as shown in FIG. In FIG. 23, an alignment system ALG includes an illumination system (here, only the final lens is shown) 200 that emits alignment illumination light ILa, an illumination field stop 202 that defines an illumination area on the wafer, a lens system 204, and illumination light ILa. And a beam splitter 206 that separates the observation light, and an objective lens 208 that projects the illumination light ILa onto the wafer and enters the observation light from the wafer. These illumination system 200, illumination field stop 202, lens system 204, and beam splitter 206 are arranged along the optical axis AXa of the objective lens 208.

  Observation light from the wafer incident on the objective lens 208 is reflected by the beam splitter 206, and passes through the lens system 210, the optical index plate 212, and the imaging lens system 214, and a two-dimensional image sensor 216 such as a CCD or CMOS. Reach the imaging surface. Thereby, the image sensor 216 outputs an image signal corresponding to the contrast of the enlarged image of the mark formed on the wafer surface or the enlarged image of the wedge-shaped resist pattern (WMp in FIG. 1) on the test wafer TW.

  The optical index plate 212 is obtained by forming a light-shielding index pattern (light-shielding line) on a transparent quartz parallel plate, and an imaging system including an objective lens 208, a beam splitter 206, and a lens system 210. Is arranged so as to be optically conjugate with the wafer surface. Therefore, an enlarged aerial image (intermediate image) of the wafer surface mark and wedge-shaped resist pattern (WMp) is formed on the transparent portion of the optical index plate 212. Further, the imaging surface of the imaging element 216 is arranged at a position optically conjugate with the optical index plate 212 by the imaging lens system 214. Therefore, an enlarged image of the mark on the wafer and the wedge-shaped resist pattern (WMp) is generated on the imaging surface of the imaging element 216 along with the index pattern image of the optical index plate 212.

  In such an in-line photolithography system, in the case of normal wafer processing, one wafer in the supply port unit FP1 is transferred in the order of the coater unit CTR, the buffer unit BFP, and the wafer transfer unit WTP. Finally, it is placed on wafer stage WST and exposed after alignment. After the exposure, the wafer is sent from wafer stage WST to wafer transport unit WTP, buffer unit BFP, developer unit DVR in this order, and finally stored in recovery port unit FP2.

  However, when the test reticle TR is placed on the reticle stage RST and the wedge-shaped pattern FWM is exposed on the test wafer TW, the test wafer TW developed by the developer unit DVR is returned to the recovery port unit via the return transport system TP. It is sent to the buffer unit BFP, not to FP2. The return transport system TP may be configured by a transport mechanism (robot arm and rail, etc.) provided individually, or configured to send each unit unit in the coater unit CTR in a non-processed state (skip mode). There may be.

  The developed test wafer TW sent to the buffer unit BFP is sent to the wafer transport unit WTP of the exposure apparatus EXP, pre-aligned, and then placed on the wafer stage WST. Although not shown, a wafer mark to be exposed on the test wafer TW is formed in the peripheral portion in the pattern formation area PA of the test reticle TR. Therefore, in each shot area of the developed test wafer TW placed on the wafer stage WST, a resist image of the wafer mark (hereinafter simply referred to as a wafer mark) is formed along with the wedge-shaped pattern image (resist image) WMp. Has been.

  The exposure apparatus EXP detects the wafer mark of the test wafer TW on the wafer stage WST by the alignment system ALG in FIG. 23, and the position of the shot region (or wedge pattern WMp) on the test wafer TW with respect to the observation field of the objective lens 208 Is set as a position coordinate by the Westage WST. Thereby, the wedge pattern WMp desired to be measured on the test wafer TW can be brought into the observation field of the objective lens 208 only by changing the position coordinates of the wafer stage WST.

  In the present embodiment, the profile (such as the dimension in the wedge major axis direction) of the wedge-shaped pattern image WMp on the test wafer TW is measured by the imaging device 216 of the alignment system ALG shown in FIG. Therefore, the exposure apparatus EXP is provided with an image processing unit (a board including a CPU) as shown in FIG. The image processing unit includes an adjustment amplifier GCA that corrects the amplitude and offset of the image signal from the image sensor 216, and an A / D converter ADC that converts the luminance value of the adjusted image signal into a digital value at least in pixel units. A memory VRAM that temporarily stores digital data (digital image data) of the image signal, and a sub processor that executes various arithmetic processes according to a predetermined program using the digital image data stored in the memory VRAM. Computer) SPC is provided.

This sub-processor SPC is connected to the main computer of the exposure apparatus EXP and the host computer of the lithography system by wire or wirelessly, and exchanges various types of information, and an error ΔFe (see FIG. 1) with respect to the best focus position, or The best focus position Z _best defined by the equation (31) is obtained based on the fitting by the Sinc function. In the case of the present embodiment, shot map information when the test wafer TW is exposed, and focus position information at the time of exposure corresponding to the shot map (the swing width in the Z direction when changing the focus position, the test wafer TW at the time of exposure) The Z position, the number of points for changing the focus position, etc.) are sent from the main computer to the sub processor SPC, and the determined focus error ΔFe or the best focus position Z _best is sent to the main computer.

The sub-processor SPC generally obtains the focus error ΔFe or the best focus position Z _best by a calculation process according to a predetermined program according to the procedure shown in FIG. 1, and the processing procedure by the program is shown in FIG. These are shown as steps 250-255. In step 250, preprocessing is performed to suppress or remove noise components or improve image contrast from the digital image data of the wedge pattern image WMp stored in the memory VRAM.

  In step 251, based on the digital image data of the wedge pattern image WMp, the image positions (pixel positions) of the two end portions in the long axis direction of the wedge pattern image WMp are detected. In step 252, the image of the end portion is detected. The length Lp of the wedge pattern image WMp is calculated from the position. In general, since digital image data samples the waveform of an image signal in units of pixels of the image sensor 216, a conversion value indicating how much one pixel or pixel pitch of the image sensor 216 is on the test wafer TW. Using (μm / pixel), the length Lp of the wedge pattern image WMp is obtained.

  In the next step 253, the obtained length Lp of the wedge pattern image WMp is collected and stored in association with shot map information and focus position information from the main computer. At that time, for each of the nine pattern blocks PG1 to PG9 (see FIG. 15), all the lengths Lp of the wedge pattern image WMp included in one pattern block PGn are measured and averaged, or the wedge length The wedge direction image WMp whose axial direction is the X direction and the wedge pattern image WMp whose Y direction is the Y direction are divided and averaged. Alternatively, only the length Lp of the wedge pattern image WMp included in only the pattern block PG5 located at the center in each shot may be measured to obtain the average value.

  Next, in step 254, the length Lp (average value) of the wedge pattern image WMp measured for each focus position (ie, shot position) of the test wafer TW at the time of exposure is defined by the above equation (33). Based on such a SINC function, the four coefficients b0, b1, b2, b3 in the equation (33) are calculated by the least square approximation method, and the length of the wedge pattern image WMp with the focus position (Z position) as a variable is calculated. The change characteristic of Lp, that is, the focus change characteristic is determined. At that time, as described above with reference to FIG. 21, the number of measurement points corresponding to a plurality of focus positions different in the Z direction is about 7 to 15 over a defocus range that is 1 to 3 times the width of the focal depth DOF. It is preferable to set the measurement points (Z positions) to be distributed.

In the next step 255, a focus position (Z position) at which the length Lp of the wedge pattern image WMp is maximized is obtained from the focus change characteristic determined based on the equation (33), and the best focus position [ Zo] in the formula (31). Further, if there is a deviation between the focus position detected by the incident-incidence AF sensor (38A, 38B in FIG. 2) of the exposure apparatus EXP as the zero point and the obtained best focus position (Zo), the deviation is focused. The error ΔFe is sent to the main computer. Further, the sub processor SPC obtains the accuracy (Accuracy) ΔZ of the focus position in Expression (31) or the measurement reproducibility (Precision) from the actual measurement data of the length Lp of the multiple wedge pattern images WMp on the test wafer TW. ) 3σz is also obtained, and therefore data relating to the best focus position Z _best defined by the equation (31) can be sent to the main computer.

(Application to image plane deformation measurement)
As described above, the best focus position can be specified precisely. However, as shown in FIG. 15, for example, a plurality of patterns are provided at different positions in the projection area (pattern area PA) in the test reticle TR. Since there are blocks PG1 to PG9, the best focus position can be obtained for each location of each pattern block PGn using the SINC function fitting of Expression (33).

  As shown in step 256 in FIG. 24, the sub processor SPC also includes an additional program for obtaining the best focus position at each position of, for example, nine pattern blocks PG1 to PG9. According to such a program, it is possible to obtain deformations such as curvature and distortion of the projected image plane by approximating the best focus position (Z position) at each of the nine positions in the projection area (shot area) with a surface. it can. However, in this case, the pattern surface of the test reticle TR held on the reticle stage RST may be bent from an ideal plane. Therefore, depending on the amount of the bending error (curving error), the error is corrected. There is also a need. The deformation information of the projection image plane obtained in this way is sent from the sub processor SPC to the main computer and used as one of the correction factors in the exposure process of the device pattern.

(Third embodiment)
In the above description, the projection image of the wedge-shaped pattern FWM is exposed on the resist layer, and the profile of the wedge pattern WMp (length Lp in the wedge major axis direction) formed as the resist image is measured. In the exposure apparatus incorporating the aerial image measurement sensor POD as shown in FIG. 25, it is possible to measure the light intensity distribution (profile) of the projection image of the wedge-shaped pattern FWM using the aerial image measurement sensor POD. .

  In FIG. 25, the telecentric imaging light beam Le1 from the wedge-shaped pattern FWM exiting the lens GL closest to the image plane of the projection optical system PL has the sharpest light intensity distribution Uwm (into the wedge pattern image WMp at the best focus position Zo). Equivalent). The aerial image measurement sensor POD transmits through the slit plate Gp1 disposed on the wafer stage WST in parallel with the best focus surface, the condensing lens Gp2 disposed below the slit plate Gp1, and the slit SS of the slit plate Gp1. A photodetector PD that receives a part of the imaging light beam Le1 collected by the condenser lens Gp2. The slit SS of the slit plate Gp1 is elongated in a direction parallel to the pitch direction of the wedge-shaped pattern FWM, and is provided so as to cross the light intensity distribution Uwm of the imaging light beam Le1 by the movement of the wafer stage WST in the X direction or the Y direction. It is done.

  For example, as shown in FIG. 25, when the pitch direction of the wedge-shaped pattern FWM (each wedge pattern is a light-shielding portion on the reticle) is the Y direction, the slit SS of the slit plate Gp1 is also arranged so as to be elongated in the Y direction. Wafer stage WST is moved (scanned) so that slit SS of slit plate Gp1 moves in the X direction with respect to the projected image of pattern FWM. Along with this scanning, the photoelectric signal Iss output from the photodetector PD has a waveform that drops to about ½ in the vicinity of the center in the X direction corresponding to the light intensity distribution Uwm of the projection image of the wedge-shaped pattern FWM. Is output. The intensity change (waveform) of the photoelectric signal Iss is digitally sampled in association with the position measurement information from the length measuring laser interferometer that measures the position of the wafer stage WST with high accuracy, and is output from the image sensor 216 in FIG. Similar to the image signal, it is stored as digital waveform data in a memory VRAM or the like. Note that the wedge-shaped pattern FWM may be a pattern in which each wedge pattern is a transmission portion and the periphery thereof is a light-shielding portion.

  In order to measure the light intensity distribution Uwm of the projection image of the wedge-shaped pattern FWM at a plurality of focus positions (Z positions) different from the best focus position Zo, the slit surface (front surface) of the slit plate Gp1 is Z by 0.2 μm, for example. The wafer stage WST is controlled so that the slit SS of the slit plate Gp1 scans the imaging light beam Le1 in the X direction. The waveform data of the photoelectric signal Iss output each time the slit SS of the slit plate Gp1 scans the imaging light beam Le1 is stored. The stored waveform data has a profile (intensity distribution) in the major axis direction of the projection image of the wedge-shaped pattern FWM, and the wedge-shaped pattern FWM is obtained for each of a plurality of focus positions (Z positions) by a process similar to the image analysis process. The length Lp of the projected image in the wedge long axis direction is obtained. Subsequent processing is executed in the same manner as Steps 253 to 255 or Step 256 shown in FIG.

(Other measuring devices)
As an apparatus for observing and measuring the profile (length Lp in the wedge long axis direction) of the wedge pattern image WMp formed as a resist layer on the test wafer TW, an apparatus other than an optical microscope mounted on the exposure apparatus EXP is used. In addition, a confocal microscope, a scatterometer, a scanning electron microscope (SEM), a He ion microscope, a scanning probe microscope (SPM), an atomic force microscope (AFM), and the like can be used. These observation / measurement apparatuses are generally not used in an exposure apparatus but are used offline as a stand-alone measurement apparatus.

(Fourth embodiment)
In each of the above embodiments, the method of transferring the profile of the projection image of the wedge pattern to the resist layer requires a plurality of shot exposures with the focus position Z being changed by a certain amount. Therefore, the exposure energy given to the resist layer in each shot exposure, so-called dose (DOSE) amount, is set to be constant. This is because the length Lp of the major axis dimension of the wedge image (resist image) also changes when the DOSE amount varies for each shot exposure.

  Therefore, a dose monitor that obtains a change in the DOSE amount by using a profile change of the projection image of the wedge-shaped pattern as shown in FIG. 1 or FIG. 5 can be configured. In this case, the focus position Z is fixed at, for example, the best focus position, the test exposure is performed while changing the DOSE amount by a certain amount for each shot exposure, and the profile of the wedge image generated in each shot exposure (in the wedge long axis direction). The change characteristics (correlation equation, map, etc.) of the length Lp) are stored as a database. When monitoring whether the exposure amount is accurately obtained according to the command value set in the exposure apparatus during actual device exposure work, corners in the reticle for the actual device (street line section and TEG pattern area) Etc.), a wedge pattern is put in, the length Lp of the resist image of the wedge pattern after development is measured, and the correlation formula between the DOSE amount (exposure amount) stored in advance as a database and the length Lp of the wedge image It is possible to check whether the exposure apparatus gives an accurate exposure amount according to the command value to the resist layer with reference to the map and the like.

  However, the wedge-shaped patterns (WM, FWM) shown in FIG. 1 or FIG. 5 are optimized for the purpose of obtaining the best focus position (for focus / monitor). Therefore, an example of a wedge-shaped pattern optimized for dose monitoring will be described as a fourth embodiment with reference to FIG.

  FIG. 26 is a diagram for explaining the shape of a pair of test patterns DM1 and DM2 optimized for a dose monitor and a measuring method as a dose monitor. In FIG. 26, the test pattern DM1 has an edge Es linearly extending in the Y direction, and a line pattern portion PDa extending from the edge Es in the Y direction with a constant width in the + X direction, and the line pattern portion PDa. And a wedge-shaped pattern portion PDb in which a plurality of acute-angled triangular patterns protruding with a fixed dimension in the + X direction are continuously arranged in the Y direction. The test pattern DM2 is arranged at a distance SD from the test pattern DM1 in the + X direction, and has a shape in which the test pattern DM1 is bent symmetrically with respect to a center line passing through the center in the X direction of the distance SD in the Y direction.

  One triangular pattern of the wedge-shaped pattern portion PDb of the test patterns DM1 and DM2 is, for example, about 3 μmm at the tip of a linear pattern having a Y-direction line width of 0.12 μm and an X-direction length of 4.5 μm. It is formed. The remaining portion of the linear pattern in the X direction (1.5 μm in the X direction) forms a line pattern portion PDa. The reticle TR on which such test patterns DM1 and DM2 are formed is disposed on the object surface side of the projection optical system PL, the wafer TW on which a resist layer is formed is disposed on the image surface side, and a certain amount is dosed for each shot exposure. Multiple shot exposures are performed with varying amounts. The exposed wafer TW is developed, and the resist images of the test patterns DM1 and DM2 in each shot transferred to the resist layer are transferred via an alignment system ALG as shown in FIG. 23 or a similar observation optical system. Take an image.

  At that time, the horizontal scanning line Sv by the imaging device of the alignment system ALG (observation optical system) is set to be in the X direction as shown in FIG. That is, the direction in which the individual triangular patterns constituting the wedge-shaped pattern portions PDb of the test patterns DM1 and DM2 extend (the wedge major axis direction) and the direction of the horizontal scanning line Sv of the image sensor are made to coincide. Then, the image signals obtained for each horizontal scanning line Sv are accumulated (synchronously added) in the vertical scanning direction in units of pixels over a plurality of horizontal scanning lines.

  As a result, the integrated image signal has a signal waveform Fua or Fab as shown in the lower part of FIG. The signal waveform Fua is a state in which a dose amount (exposure amount) most suitable for the resist layer on the wafer TW is given, and a resist image having a triangular pattern is obtained near the tip of the wedge-shaped pattern portion PDb. On the other hand, in the signal waveform Fab, a slightly larger dose amount (exposure amount) is given to the resist layer on the wafer TW, and the triangular pattern resist image disappears near the tip of the wedge-shaped pattern portion PDb. . Note that the signal waveforms Fua and Fub are expressed as the reflectance of the resist image (or the ground) corresponding to the test patterns DM1 and DM2 is lower than the reflectance of the surrounding ground (or resist layer).

  In the case of the signal waveform Fab, the tip of the wedge-shaped pattern portion PDb of the test pattern DM1 that has become the resist image disappears by ΔXk in the −X direction and becomes short, and the tip of the wedge-shaped pattern portion PDb of the test pattern DM2 that has become the resist image. Disappears by ΔXk in the + X direction and becomes shorter. In addition, the position in the resist image of the edge Es of the line pattern portion PDa of the test pattern DM1 is shifted by ΔXL in the + X direction, and the position in the resist image of the edge Es of the line pattern portion PDa of the test pattern DM2 is −X. The direction is shifted by ΔXL.

  Therefore, the center-of-gravity position Ga1 in the X direction of the bottom waveform portion corresponding to the resist image of the test pattern DM1 in the signal waveform Fua obtained with an appropriate exposure amount and the bottom waveform portion corresponding to the resist image of the test pattern DM2. The distance Lga from the center of gravity position Ga2 in the X direction is measured. Similarly, the center-of-gravity position Gb1 in the X direction of the bottom waveform portion corresponding to the resist image of the test pattern DM1 in the signal waveform Fab obtained with the overexposure exposure amount, and the bottom shape corresponding to the resist image of the test pattern DM2 The distance Lgb between the waveform portion and the center of gravity position Gb2 in the X direction is measured. The resist image of each triangular pattern at the tip of the wedge-shaped pattern portion PDb is sensitive to a change in exposure amount, and the position in the X direction of the tip of the triangle pattern changes greatly with a slight change in exposure amount. On the other hand, the position change in the X direction in the resist image of the edge Es of the line pattern portion PDa is insensitive to a slight change in the exposure amount. Therefore, the position change | ΔXk | in the X direction in the resist image at the tip of the wedge-shaped pattern portion PDb and the position change | ΔXL | in the X direction in the resist image at the edge Es are | ΔXk |> | ΔXL |

  Therefore, as shown in FIG. 26, when a pair of test patterns DM1 and DM2 in which the wedge-shaped pattern portions PDb are opposed to each other are provided, a slight change in the exposure amount can be measured as a change in the interval distances Lga and Lgb. As described above, since the position of the resist image corresponding to the edge Es of the line pattern portion PDa is insensitive to the change in exposure amount, it has a bottom waveform corresponding to only one of the test patterns DM1 and DM2. A change in exposure amount may be obtained from the distance in the X direction between the center of gravity position and the edge Es. Note that the pair of test patterns DM1 and DM2 may be arranged such that the edges Es of the line pattern portion PDa face each other, or a pair of test patterns DM1 and DM2 may be repeatedly arranged in the X direction. Such an arrangement example will be described later.

  By the way, as shown in FIG. 26, the dimensions of a single triangular pattern are about 3 μm in the longitudinal direction (X direction) of the wedge and about 0.12 μm as the maximum width (Y direction) of the wedge. In the case of a wedge-shaped pattern portion PDb in which a plurality of dots are densely packed in the Y direction at a pitch of 0.12 μm (period), the wedge-shaped pattern portion PDb is limited by the numerical aperture (NA) of the objective lens of the alignment system ALG and other observation optical systems. ± 1st-order diffracted light and other high-order diffracted light generated from the corresponding resist image may be scattered by the pupil of the observation optical system and do not reach the image sensor. For this reason, even if each triangular pattern of the wedge-shaped pattern portion PDb is generated as a resist image substantially retaining its shape by an immersion exposure apparatus having a resolution of 20 nm line width, the observation optical system (objective lens) Most of the light that reaches the image sensor via () becomes zero-order light (regular reflected light) from the resist image corresponding to the wedge-shaped pattern portion PDb, and cannot be observed as the image shape of each triangular pattern.

However, since the 0th-order light intensity generated from the entire resist image corresponding to the wedge-shaped pattern portion PDb changes in the longitudinal direction of the wedge of the triangular pattern, it is observed as a gradation image in which the luminance (lightness / darkness) changes in the X direction. In addition, a portion corresponding to the gradation image (wedge pattern portion PDb) also appears in the image signal from the image pickup device in a slope shape in which the intensity gradually changes in the signal waveform Fua in FIG. The fact that the intensity of the 0th-order light generated from the entire resist image corresponding to the wedge-shaped pattern portion PDb changes in the longitudinal direction of the wedge as shown in the equation (4) using FIG. Is clear from the amplitude intensity a ₀ = D / P (pitch line width ratio).

  As described above, in the present embodiment, the test pattern is elongated along the first direction (X direction in FIG. 26), and the width in the second direction (Y direction in FIG. 26) orthogonal to the first direction is the first. Using a reticle configured by arranging a plurality of wedge-shaped patterns decreasing along one direction at a predetermined period in the second direction, a test pattern on the reticle is used as an image plane of a projection optical system (imaging optical system). And projecting the optical profile of the projected image of the test pattern to the photosensitive layer, and in the first direction of the zero-order light generated from the entire optical profile transferred to the photosensitive layer via the observation optical system Detecting an intensity distribution along the line and determining an image fidelity with respect to the first direction of the test pattern transferred to the photosensitive layer based on the detected intensity distribution, Projection optics Evaluation method for evaluating the optical characteristics and exposure performance (imaging optical system) can be obtained.

  Thereby, even when the line width orthogonal to the major axis direction of one wedge pattern formed as a resist image (corresponding to W in FIGS. 1 and 5) is so small that it cannot be resolved by the observation optical system, By measuring the dimensional change of the gradation image (grayscale image due to the intensity of light) generated by the 0th-order light generated from the entire pattern in which multiple wedge patterns are arranged in the line width direction, not only the change in dose but also the focus Changes in position can also be monitored. That is, it is possible to easily measure how much the projection image of the pattern by the projection optical system (imaging optical system) is projected (transferred) on the projection surface.

(Fifth embodiment)
Next, an example in which a pair of test patterns DM1 and DM2 in FIG. 26 is repeatedly arranged in the X direction and used as a dose monitor (or focus monitor) will be described with reference to FIG. FIG. 27A shows the shapes of the test patterns DM1 and DM2 formed on the reticle TR. By repeatedly arranging the pairs of test patterns DM1 and DM2 at a constant interval in the X direction, the line pattern portion PDa The portions La where the edges Es (extending in the Y direction) face each other and the portions Lb where the wedge-shaped pattern portions PDb face each other are alternately formed in the X direction. Here, the portion La is configured as a thin line extending in the Y direction with a line width of about several μm (on-wafer dimension) in the X direction, and the portion Lb is about several μm in the X direction between the tips of the wedge triangles ( It is configured as a thin line extending in the Y direction with a line width of (on-wafer dimension).

  FIG. 27B shows a test imaged by the alignment system ALG or a similar observation optical system after exposing and developing the test patterns DM1 and DM2 formed on the reticle TR of FIG. 27A on the resist layer. An example of display images of resist images DM1 ′ and DM2 ′ of patterns DM1 and DM2 is shown. Of the resist images DM1 ′ and DM2 ′ picked up by an image pickup device such as a CCD, the resist image PDb ′ corresponding to the wedge-shaped pattern portion PDb appears as a gradation in the X direction and corresponds to the edge Es of the line pattern portion PDa. The resist image Es ′ appears with a steep contrast in the X direction. 27A and 27B, the dimensions and arrangement of the test patterns DM1 and DM2 are, for example, the line widths of the thin line portion La and the thin line portion Lb are about 2 μm on the wafer, and the test patterns DM1 and DM2 The repeat pitch in the X direction is set to be about 6 μm on the wafer. In this case, the entire width of the test patterns DM1 and DM2 in the X direction is set to about 4 μm on the wafer.

  FIG. 27C shows an example of the waveform of the image signal Fu obtained by synchronous addition by scanning such resist images DM1 'and DM2' with a plurality of horizontal scanning lines Sv of the image sensor. As described above, the line width Lgc of the thin line portion La sandwiched between the two resist images Es ′ facing each other is insensitive to a slight change in the dose amount (or a change in the focus position). , Not much change. On the other hand, the line width Lga of the thin line portion Lb sandwiched between the resist images PDb ′ is sensitive to a change in dose (or a change in focus position), and changes according to the dose during exposure. . Therefore, based on the image signal Fu as shown in FIG. 27C, each line width Lgc of the resist image corresponding to the plurality of thin line portions La and each line width Lga of the resist image corresponding to the plurality of thin line portions Lb are measured. The average value Avc of the line width Lgc and the average value Ava of the line width Lga are obtained. Then, when the change characteristic of the average value Ava of the line width Lga is obtained on the basis of the average value Avc of the line width Lgc, the optimum value of the dose amount can be found.

  Specifically, the test patterns DM1 and DM2 in FIG. 27A are sequentially exposed to a plurality of shot areas on the wafer TW while changing the dose amount by a certain amount, and then the resist layer is developed. The resist images of the test patterns DM1 and DM2 formed on the wafer TW for each of a plurality of doses (shot regions) are sequentially observed to obtain an image signal Fu as shown in FIG. The image signal Fu obtained for each dose amount is analyzed to obtain an average value Avc of the line width Lgc and an average value Ava of the line width Lga. As the dose changes, the average value Avc of the line width Lgc changes gradually, and the average value Ava of the line width Lga changes greatly. That is, assuming a relationship graph with the line width value of the resist image corresponding to the thin line portions La and Lb as the vertical axis and the dose amount as the horizontal axis, a graph line representing a change in the average value Avc of the line width Lgc due to the dose amount The slope of the graph line is small, and the slope of the graph line representing the change due to the dose amount of the average value Ava of the line width Lga is large.

  As described above, in the present embodiment, using the wedge-shaped pattern, the first resist image having a high sensitivity of the line width change with respect to the dose (or focus position) change and the line width with respect to the dose (or focus position) change. A second resist image having a low change sensitivity can be obtained, and the line width change of the first resist image can be obtained with reference to the line width change of the second resist image. A monitor (or focus monitor) is obtained.

EXP ... exposure apparatus, PL ... projection optical system, TR ... test reticle, TW ... test wafer, WM, FW, FWM ... wedge pattern, WMp ... wedge pattern image (resist image), ip ... illumination pupil, ip '... square Specified illumination pupil, ep ... projection pupil, ep '... projection pupil defined by a square, Lp ... length in the long axis direction of the wedge pattern image, ALG ... alignment system, PG1 to PG9 ... pattern block, C / D ... coater Developer, Coater part ... CTR, Developer part ... DVR, ILU ... Illumination system, RST ... Reticle stage, WST ... Wafer stage, SPC ... Sub processor, POD ... Aerial image measurement sensor

Claims (16)

A method for measuring a focus characteristic of a projection optical system,
Projecting an image of a wedge-shaped pattern on the image plane side of the projection optical system;
Obtaining an image profile of the projected wedge-shaped pattern at each of a plurality of focus positions changed by a predetermined amount in the direction of the depth of focus of the projection optical system;
Measuring a length in a direction in which an acute angle of the wedge-shaped pattern of the acquired image profile extends for each of the plurality of focus positions;
Determining a change characteristic of the length of the measured image profile with respect to the focus position using a model function including a trigonometric function having the focus position as a variable;
Measurement method of focus characteristics including In the step of acquiring the image profile, a photosensitive layer of a photosensitive substrate is set at each of the plurality of focus positions, and the image of the wedge-shaped pattern is made identical at a different position of the photosensitive layer for each set focus position. A step of performing projection exposure with an exposure amount of
Generating an image profile of the wedge-shaped pattern in the photosensitive layer;
The focus characteristic measuring method according to claim 1. The model function is defined as Lp = f (Z) where Z is the focus position and Lp is the length of the image profile. The model function f (Z) is a sine function including a plurality of unknowns. Or defined based on cosine function,
The focus characteristic measuring method according to claim 1. The model function f (Z) is defined by a sink function Sinc (Z) obtained by dividing a sine function sin (Z) with the focus position Z as a variable by the focus position Z.
The focus characteristic measuring method according to claim 3. The model function f (Z) is a sink function including four unknowns b ₀ , b ₁ , b ₂ , b ₃ ,
f (Z) = b ₀ · Sinc [b ₁ · (Z−b ₂ )] + b ₃
The focus characteristic measuring method according to claim 4. In the step of determining the change characteristic, the plurality of focus positions are set to four or more focus positions Zj (j = 1 to 2) different from each other, and the image profile at each focus position Zj measured in the measurement step. Is Lpj (j = 1, 2˜), the four unknowns b ₀ , b ₁ , b ₂ , b of the model function f (Z) using the focus position Zj and the length Lpj. Including the step of calculating ₃ .
The focus characteristic measuring method according to claim 5. The focus position at which the value of the change characteristic of the sink function Sinc (Z) defined by the calculated four unknowns b ₀ , b ₁ , b ₂ , b ₃ is the largest is the best focus of the projection optical system. To determine the position,
The focus characteristic measuring method according to claim 6. The model function f (Z) is defined by a cosine function cos (Z) with the focus position Z as a variable.
The focus characteristic measuring method according to claim 3. The projecting step includes a step of arranging a mask having the wedge-shaped pattern on the object surface side of the projection optical system, irradiating the mask with illumination light having a uniform illuminance distribution projected from the illumination optical system, Allowing light from a wedge-shaped pattern to enter the projection optical system,
The illumination optical system forms a light source distribution of a predetermined shape on a surface optically conjugate with the pupil plane of the projection optical system or a surface in the vicinity thereof.
The focus characteristic measuring method according to claim 3. The model function f (Z) is a sine function Sinc (Z) obtained by dividing a sine function sin (Z) with the focus position Z as a variable by the focus position Z, or a cosine function cos with the focus position Z as a variable. Defined in (Z),
The focus characteristic measuring method according to claim 9. In the step of determining the change characteristic, one of the model functions of the sinc function Sinc (Z) and the cosine function cos (Z) is determined according to the shape of the light source distribution set in the projecting step. To determine the change characteristic,
The focus characteristic measuring method according to claim 10. In the step of acquiring the image profile, a range in which the focus position is changed by the predetermined amount in the direction of the depth of focus, a wavelength λ of illumination light for projecting the wedge-shaped image, and an aperture of the projection optical system It is set to 1 to 3 times the width of the focal depth determined according to the number NA.
The focus characteristic measuring method according to any one of claims 1 to 11. In the step of acquiring the image profile, the predetermined amount when the focus position is changed in the direction of the depth of focus is set so that at least five different focus positions are allocated within the range of the depth of focus. ,
The focus characteristic measuring method according to claim 12. An apparatus for measuring a focus characteristic of a projection optical system,
The wedge-shaped pattern projection image formed by projection of the wedge-shaped pattern by the projection optical system, or the length of the transferred image in the wedge major axis direction is changed by a predetermined amount in the direction of the focal depth of the projection optical system. a measuring device for measuring at each of the n focus positions Zn;
When the length in the wedge long axis direction measured by the measuring device for each of the n focus positions Zn is Lpn, the length Lpn includes a model function f (Zn) including a trigonometric function that changes the focus position Zn. A calculator that approximates a plurality of coefficients of the model function f (Zn) and determines a change characteristic represented by the model function f (Zn);
Focus characteristic measuring device including The model function f (Zn) is a sinc function Sinc (Zn) obtained by dividing a sine function sin (Zn) having the focus position Zn as a variable by the focus position Zn, or a cosine function cos having the focus position Zn as a variable. Defined by (Zn),
The focus characteristic measuring apparatus according to claim 14. The model function f (Zn) includes four coefficients b ₀ , b ₁ , b ₂ , b ₃ ,
Lpn = f (Zn) = b ₀ · Sinc [b ₁ · (Zn−b ₂ )] + b ₃ ,
The calculator uses a _first calculation for determining the values of the four coefficients b ₀ , b ₁ , b ₂ , and b ₃ by an approximate calculation using the n lengths Lpn measured by the measuring device. The best focus position at which the length Lpn is maximized is specified from the change characteristics of the model function f (Zn) defined by the determined values of the coefficients b ₀ , b ₁ , b ₂ , and b ₃ . A program for executing the operation of 2;
The focus characteristic measuring apparatus according to claim 15.