JP7128756B2 - Model data generation method, pattern measurement method, correction pattern data generation method, and model data generation device - Google Patents

Description

The present invention relates to a model data generation method, a pattern measurement method, a correction pattern data generation method, and a model data generation device.

2. Description of the Related Art Conventionally, photomasks have been widely used to transfer patterns onto substrates such as semiconductor substrates or display substrates. In order to properly transfer the pattern to this substrate, the pattern on the photomask must be formed in a desired shape. Therefore, an inspection apparatus for inspecting the pattern of the photomask is widely used (for example, Patent Document 1).

The pattern inspection apparatus of Patent Document 1 includes an electron microscope and a work station. An electron microscope acquires an image of the pattern formed on the photomask. The workstation converts the image into pattern data, and applies light intensity distribution simulation to this pattern data to determine the intensity distribution of the light exposed on the substrate. The workstation inspects the pattern for defects based on the difference between this light intensity distribution and the reference light intensity distribution.

Japanese Patent No. 4091605

However, in the technique described in Patent Document 1, binary data is used as pattern data. Specifically, the light-transmitting portion of the photomask is set to "1", and the light-shielding portion is set to "0". According to this, the calculation accuracy of the light intensity distribution calculated by the light intensity distribution simulation becomes low. In other words, this pattern data does not contribute to the improvement of the calculation accuracy of the light intensity distribution.

SUMMARY OF THE INVENTION Accordingly, it is an object of the present invention to provide a model data generating method and a model data generating apparatus for generating model data that contributes to improving the accuracy of light intensity distribution calculation.

A first aspect of the model data generation method is model data input to an image simulator that calculates the intensity distribution of light that has passed through a predetermined optical system using a fast Fourier transform and an inverse fast Fourier transform. A method for generating model data representing the distribution of light transmitted through a pattern of a mask with discrete values, wherein the cutoff frequency of a predetermined function is set to be less than or equal to 1/4 of the reciprocal of the spatial resolution of the discrete values. Secondly, the model data is generated, and the predetermined function is a function obtained by connecting together waveforms along which the intensity change portion of the light intensity distribution included in the model data is followed.

A first aspect of the pattern measurement method is a method for measuring the shape of a pattern of a photomask, wherein light from the photomask passes through a predetermined optical system and forms an image on an imaging surface to obtain a captured image. a first step; a second step of generating model data representing the distribution of light transmitted through a pattern having a certain pattern shape by using the model data generation method according to the first aspect; Fast Fourier transform and inverse fast Fourier transform are performed on the model data to simulate a light intensity distribution on the imaging plane when light is imaged on the imaging plane through the optical system. a fourth step of determining whether the difference between the simulated intensity distribution and the light intensity distribution in the captured image is greater than a reference value; and the difference is greater than the reference value. a fifth step of correcting the pattern shape of the model data and repeating the second to fourth steps; and measuring the pattern shape of the model data when the difference is equal to or less than the reference value. and a sixth step.

A second aspect of the pattern measuring method is the pattern measuring method according to the first aspect, wherein the correction width of the pattern shape in the fifth step is narrower than the spatial resolution of the discrete values.

A third aspect of the pattern measuring method is the pattern measuring method according to the first or second aspect, wherein the captured image includes a line pattern extending in one direction from end to end of the captured image. and the third step includes a step of performing a fast Fourier transform on the model data to calculate a diffraction pattern, and a step of two-dimensionally arranging the diffraction pattern on each region of the Fourier transform plane. and performing an inverse Fourier transform on the diffraction pattern of each region of the Fourier transform surface.

A fourth aspect of the pattern measurement method is the pattern measurement method according to any one of the first to third aspects, wherein the simulated intensity distribution calculated in the third step and adopted in the second step The method further comprises a seventh step of associating the pattern shapes of the model data thus obtained with each other and storing them in a storage medium as a database, wherein the patterns of the model data adopted in the second step subsequent to the seventh step. When the simulation intensity distribution corresponding to the shape is stored in the database, the third step is not performed, and in the fourth step, the simulation intensity distribution read from the database and the intensity distribution in the captured image are combined. It is determined whether the difference is greater than the reference value.

A first aspect of the correction pattern data generation method is a method of generating correction pattern data indicating a correction pattern for repairing a defective photomask, wherein the correction pattern data is generated from the photomask via a predetermined first optical system. A first step of acquiring a captured image based on light, and a first step of generating model data representing the distribution of light transmitted through a mask on which correction pattern candidates are formed, by the method of generating model data according to the first aspect. a third step of synthesizing the captured image and the model data to generate input data; and a second optical system in which the light indicated by the input data has a numerical aperture smaller than that of the first optical system. a fourth step of calculating a simulated intensity distribution, which is the intensity distribution of light on the substrate when the substrate is irradiated via the light source, by performing a fast Fourier transform and an inverse fast Fourier transform on the input data; a difference between a reference intensity distribution indicating an intensity distribution of light on the substrate when light transmitted through a regular photomask is irradiated onto the substrate via the second optical system, and the simulation intensity distribution; a fifth step of determining whether or not the difference is greater than the reference value; and when the difference is greater than the reference value, modifying the shape of the correction pattern candidate and repeating the second to fifth steps. A sixth step; and a seventh step of adopting the correction pattern candidate as the correction pattern data when the difference is equal to or less than the reference value.

A second aspect of the correction pattern data generation method is the correction pattern data generation method according to the first aspect, wherein the correction width for the shape of the candidate for the correction pattern in the sixth step is the space of the discrete values. Narrower than resolution.

A first aspect of the model data generation device is model data input to an image simulator that calculates the intensity distribution of light that has passed through a predetermined optical system using a fast Fourier transform and an inverse fast Fourier transform. An apparatus for generating model data representing the distribution of light transmitted through a pattern of a mask with discrete values, wherein the cutoff frequency of a predetermined function is set to be less than or equal to 1/4 of the reciprocal of the spatial resolution of the discrete values. (2) a model generation unit for generating the model data, wherein the predetermined function is a function obtained by connecting waveforms along which intensity change portions of the light intensity distribution included in the model data are connected to each other;

According to the first aspect of the model data generation method and the first aspect of the model data generation device, it contributes to the improvement of the calculation accuracy of the intensity distribution by the image simulator.

According to the first aspect of the pattern measurement method, the simulation intensity distribution can be calculated with high accuracy, so the pattern shape can be obtained with high accuracy.

According to the second aspect of the pattern measuring method, the pattern shape can be determined with even higher accuracy.

According to the third aspect of the pattern measurement method, since the diffraction pattern is arranged in each region of the Fourier transform plane, it is not necessary to calculate the diffraction pattern for each region. Therefore, the number of calculations can be reduced.

According to the fourth aspect of the pattern measurement method, when the simulation intensity distribution is stored in the database, the simulation intensity distribution is utilized, so there is no need to calculate the simulation intensity distribution again. According to this, the number of calculations can be reduced.

According to the first aspect of the correction pattern data generation method, a more appropriate correction pattern can be determined in advance.

According to the second aspect of the correction pattern data generation method, more appropriate correction pattern data can be generated.

It is a perspective view which shows an example of the external appearance of a pattern measuring apparatus roughly. It is a figure which shows roughly an example of a structure of a pattern measuring apparatus. It is a figure which shows an example of a captured image roughly. It is a figure which shows the example of light intensity distribution roughly. 3 is a functional block diagram schematically showing an example of the internal configuration of a control unit; FIG. FIG. 4 is a diagram schematically showing an example of a model intensity distribution; 4 is a graph showing a Hann function; FIG. 4 is a diagram schematically showing an example of model intensity distributions before and after updating; FIG. 4 is a diagram schematically showing an example of a model intensity distribution; FIG. 10 is a graph showing the relationship between the line width of the pattern in FIG. 9 and the calculated line width; FIG. 9 is a graph showing the relationship between the line width of the pattern in FIG. 8 and the calculated line width; 4 is a graph showing the relationship between the ratio of spatial frequency to cutoff frequency and the deviation that is an index of calculation accuracy. It is a figure for demonstrating a simulation process. 4 is a flow chart showing an example of the operation of the image simulator; It is a figure which shows roughly another example of a captured image. FIG. 4 is a diagram schematically showing an example of a model intensity distribution; FIG. 5 is a functional block diagram schematically showing another example of the configuration of the control section; It is a figure which shows roughly another example of a captured image. FIG. 4 is a plan view schematically showing an example of a configuration of a photomask on which correction patterns are formed; FIG. 5 is a functional block diagram schematically showing another example of the configuration of the control section; It is a graph which shows roughly an example of the light intensity distribution in a captured image. 4 is a graph schematically showing an example of light intensity distribution in input data; It is a graph which shows an example of a simulation result.

Hereinafter, embodiments will be described in detail with reference to the drawings. In the drawings, for the purpose of facilitating understanding, the dimensions and numbers of each part are exaggerated or simplified as necessary. Parts having similar configurations and functions are denoted by the same reference numerals, and duplicate descriptions will be omitted in the following description. In addition, in the drawings, XYZ orthogonal coordinates are appropriately shown for explanation of the positional relationship of each component. For example, the Z axis is arranged along the vertical direction, and the X and Y axes are arranged along the horizontal direction. In the following description, one side in the Z-axis direction is also called the +Z side, and the other side is also called the -Z side. The same is true for the X-axis and Y-axis.

First embodiment.
FIG. 1 is a perspective view schematically showing an example of the appearance of the pattern measuring device 1, and FIG. 2 is a diagram schematically showing an example of the configuration of the pattern measuring device 1. As shown in FIG.

The pattern measuring device 1 measures the pattern shape of the photomask 80 . Here, before describing the pattern measuring apparatus 1, the photomask 80 will be described first.

The photomask 80 is a photomask used for exposing a substrate (not shown) such as a liquid crystal display. This photomask 80 includes a substrate 81 and a light shielding film 82, as illustrated in FIG. The base material 81 has a plate-like shape. The base material 81 has translucency and is made of quartz, for example. The light shielding film 82 is formed on one main surface (for example, the +Z side main surface) of the base material 81 . The light shielding film 82 is formed in a predetermined pattern in plan view. The light shielding film 82 is a film that blocks light, and is, for example, a metal film such as a chromium film. By forming the light shielding film 82 on one main surface of the base material 81, the photomask 80 is formed with a light transmitting portion 80a and a light shielding portion 80b in plan view.

This photomask 80 is attached to an exposure device (not shown). In this exposure apparatus, a light source, a photomask 80, an exposure lens, and a substrate are arranged in this order. The light source irradiates the photomask 80 with light for exposure. This light passes through the transparent portion 80a of the photomask 80 and is irradiated onto the photoresist on the substrate via the exposure lens. This allows the photoresist on the substrate to be exposed. In other words, the pattern of the transparent portion 80a of the photomask 80 can be transferred onto the photoresist of the substrate. Accuracy of the pattern shape of the photomask 80 is important for exposing the photoresist on the substrate in a desired pattern.

Therefore, the pattern measuring apparatus 1 measures the pattern shape of the photomask 80 . As illustrated in FIGS. 1 and 2, the pattern measuring apparatus 1 includes an irradiation section 10, a detection section 20, a moving mechanism 40, a control section 50, an elevating mechanism 60, a display section 70, and a holding section 90. FIG.

The holding part 90 is a member that holds the photomask 80 . The holding part 90 holds the photomask 80 such that the thickness direction of the photomask 80 is along the Z-axis direction. In the example of FIG. 1, the holding part 90 holds only the peripheral portion of the photomask 80 . Note that the holding part 90 may support the entire lower surface of the photomask 80 with a translucent member.

The irradiation unit 10 and the detection unit 20 are provided on opposite sides of the photomask 80 in the Z-axis direction. In the examples of FIGS. 1 and 2, the irradiation section 10 is provided on the −Z side with respect to the photomask 80, and the detection section 20 is provided on the +Z side with respect to the photomask 80. FIG.

The irradiation unit 10 irradiates light along the Z-axis direction and causes the light to enter part of the photomask 80 . As the light, for example, light having a wavelength similar to that of exposure light (for example, i-line) is used. The irradiation unit 10 includes, for example, a light source 11 , a condenser lens 12 , a bandpass filter 13 , a relay lens 14 , a pinhole plate 15 , a reflector 16 and a condenser lens 17 .

A light source 11 emits light. The light source 11 is, for example, an ultraviolet irradiator. A mercury lamp, for example, can be used as the ultraviolet irradiator. Light irradiation/stop of the light source 11 is controlled by the controller 50 .

Condenser lens 12 , bandpass filter 13 , relay lens 14 , pinhole plate 15 , reflector plate 16 and condenser lens 17 are arranged in this order between light source 11 and photomask 80 .

The condensing lens 12 is a convex lens and is arranged so that its focal point is positioned at the light source 11 . Light emitted from the light source 11 is converted into collimated light or light with a small spread angle by the condenser lens 12 , and this light enters the bandpass filter 13 . The bandpass filter 13 transmits only light having a predetermined wavelength band (transmission band) out of the light. As this wavelength band, the wavelength band of light for exposure (for example, the wavelength band including the i-line) can be adopted. The wavelength band of the band-pass filter 13 is set narrow, and substantially monochromatic light (so-called monochromatic light) passes through the band-pass filter 13 . Light transmitted through the bandpass filter 13 enters the relay lens 14 .

The relay lens 14 is a convex lens and converges the incident light on the field diaphragm 151 of the field diaphragm plate 15 . The field diaphragm 151 penetrates the field diaphragm plate 15 in its thickness direction. The field stop 151 and the pattern surface of the photomask 80 are arranged at positions having an imaging relationship with the relay lens 14 . Light passing through the field stop 151 is incident on the reflecting surface of the reflecting plate 16 . A reflector 16 is provided to change the traveling direction of light, and causes the light to enter a condenser lens 17 . The condenser lens 17 is a convex lens and forms an image of the incident light on the photomask 80 with an appropriate NA (numerical aperture). The aperture stop 171 adjusts the NA (numerical aperture) of the illumination light to an appropriate size. The irradiation unit 10 irradiates a portion of the photomask 80 with this light along the Z-axis direction.

The detector 20 detects light that has passed through the photomask 80 . The detection unit 20 includes, for example, an objective lens 21, an imaging lens 22, a relay lens 25, and image sensors (optical sensors) 27 and .

The objective lens 21, the imaging lens 22, the relay lens 25 and the image sensor 27 are arranged in this order as they are separated from the photomask 80 in the Z-axis direction. The relay lens 25 and the image sensor 27 are built in the optical head 30 of FIG. The light transmitted through the part of the photomask 80 is magnified by the objective lens 21 and the imaging lens 22 , and is imaged on the imaging surface of the image sensor 27 via the relay lens 25 .

The image sensor 27 is, for example, a CCD image sensor or the like, generates a captured image IM1 based on the light imaged on its own imaging surface, and outputs the captured image IM1 to the control unit 50 . In other words, the image sensor 27 obtains the captured image IM1 by forming an image on the imaging surface of light from the photomask 80 through a predetermined optical system (objective lens 21, imaging lens 22, etc.). The image sensor 27 is, for example, a monochrome image sensor.

FIG. 3 is a diagram showing a schematic example of a captured image IM1 obtained by capturing a pattern to be imaged in this embodiment. A captured image IM1 of FIG. 3 includes a part of the pattern P1 (translucent portion 80a) of the photomask 80 . In the example of FIG. 3, the pattern P1 extends in one direction (vertical direction in the drawing) from end to end of the captured image IM1. The pattern P1 is also called a line pattern. A pixel value corresponding to the pattern P1 reflects the intensity of light transmitted through the pattern P1. More specifically, the pixel value is the intensity distribution of light transmitted through the photomask 80 and the optical system of the pattern measuring apparatus 1 (objective lens 21, imaging lens 22, etc.) shows the intensity distribution of the light. In the example of FIG. 3, the captured image IM1 includes only one pattern P1, and the pixel values are substantially zero in areas other than the pattern P1.

The moving mechanism 40 moves the holder 90 within the XY plane. As a result, the photomask 80 held by the holding portion 90 also moves within the XY plane. The moving mechanism 40 has, for example, a ball screw mechanism and is controlled by the controller 50 . By moving the photomask 80 within the XY plane, the irradiation unit 10 and the detection unit 20 can be scanned with respect to the photomask 80 . Therefore, the image sensor 27 can image the pattern P1 in a plurality of measurement areas of the photomask 80. FIG. It should be noted that the moving mechanism 40 only needs to have a function and structure to move the photomask 80 relative to the irradiation unit 10 and the detection unit 20. For example, the irradiation unit 10 and the detection unit 20 can be moved integrally. You may let

The elevating mechanism 60 elevates the holding portion 90 in the Z-axis direction. As a result, the photomask 80 held by the holding portion 90 also moves up and down. The lifting mechanism 60 has, for example, a ball screw mechanism and is controlled by the controller 50 . The photomask 80 can be moved to the focal point of the objective lens 21 by the elevating mechanism 60 elevating the photomask 80 . The elevating mechanism 60 only needs to have the function and structure to elevate the photomask 80 relative to the detection unit 20, and may elevate the detection unit 20, for example.

The display unit 70 is a display device such as a liquid crystal display or an organic EL display, and the display content thereof is controlled by the control unit 50 . For example, the control section 50 outputs an image signal including the measurement result to the display section 70 . A display unit 70 displays the measurement result based on the image signal.

The control unit 50 can control the pattern measuring apparatus 1 as a whole. For example, the control unit 50 controls irradiation by the irradiation unit 10, movement by the moving mechanism 40, and elevation by the lifting mechanism 60, as described above. The control unit 50 also functions as an arithmetic processing unit that calculates a value (for example, line width) regarding the pattern shape based on the captured image IM1 generated by the image sensor 27 .

The control unit 50 is an electronic circuit device, and may have, for example, an arithmetic processing unit and a storage medium. The arithmetic processing unit may be an arithmetic processing unit such as a CPU (Central Processor Unit). The storage unit may have a non-temporary storage medium (eg, ROM (Read Only Memory) or hard disk) and a temporary storage medium (eg, RAM (Random Access Memory)). The non-temporary storage medium may store, for example, a program that defines processes to be executed by the control unit 50 . When the processing device executes this program, the control section 50 can execute the processing specified in the program. Of course, part or all of the processing executed by the control unit 50 may be executed by hardware.

<Overview of Functions of Control Unit 50>
The control unit 50 obtains the pattern shape of the pattern P1 using the captured image IM1. As a specific example, the control unit 50 calculates the line width W1 of the pattern P1.

FIG. 4 is a diagram schematically showing an example of pixel values (that is, light intensity distribution) of the captured image IM1 in the width direction of the pattern P1. The example of FIG. 4 shows a plurality of light intensity distributions when the line width W1 of the pattern P1 is changed. The line width W1 is wider in the light intensity distribution shown on the right side.

In a region where the line width W1 is wide, the intensity increases at both ends and takes a substantially constant value at the center. In the region where the line width W1 is wide, the maximum value of intensity does not much depend on the width of the line width W1, and the constant value (intensity) in the central portion does not much depend on the width of the line width W1. Therefore, if the threshold value Th is set based on this constant value (pixel reference value Iref in the drawing), the line width W1 of the pattern can be calculated with relatively high accuracy by a threshold method generally well known in image processing. can be done. The threshold Th may be set to 50% of the pixel reference value Iref1, for example.

On the other hand, in a region where the line width W1 is close to the resolution limit of the objective lens 21, the intensity distribution has an upwardly convex shape, and the maximum value of the intensity depends on the width of the line width W1. increase or decrease significantly. Moreover, the maximum value of the intensity does not have a constant correlation with the line width W1. Therefore, in such a region where the line width W1 is narrow, the set value of the threshold Th becomes unstable and it becomes difficult to calculate the line width W1 by the threshold method described above.

In other words, although the line width calculation by the threshold method based on the pixel reference value Iref1 is effective in areas where the line width W1 is wide, it is not effective in areas where the line width W1 is narrow. More specifically, this technique is not effective in areas where the line width W1 is about 2 [μm] or less. Therefore, in the present embodiment, the control unit 50 calculates the line width W1 of the pattern by a method different from the method described above in order to measure the line width W1 with high accuracy regardless of the width of the line width W1.

FIG. 5 is a functional block diagram schematically showing an example of the internal configuration of the control section 50. As shown in FIG. The control section 50 includes a model generation section 51 , an image simulator 52 and a determination section 53 .

The model generator 51 generates model data MD1. The model data MD1 represents the distribution of light transmitted through the pattern P1 having a certain pattern shape (hereinafter referred to as light distribution) as discrete values. The light distribution here is information including the intensity distribution and phase distribution of light (for example, information represented by complex numbers).

FIG. 6 is a diagram schematically showing an example of the light intensity distribution of model data MD1. FIG. 6 illustrates the light intensity distribution in the width direction of the pattern P1. The pixel number x on the horizontal axis indicates the pixels arranged in the width direction of the pattern P1. This light intensity distribution is hereinafter also referred to as a model intensity distribution. As illustrated in FIG. 6, the model intensity distribution has a substantially trapezoidal shape. Note that in the example of FIG. 6, the model intensity distribution is indicated by continuous values, but in reality it is indicated by values for each pixel (that is, discrete values). Therefore, more precisely, the waveform connecting the model intensity distributions (discrete values) has a substantially trapezoidal shape. Note that in the example of FIG. 6, the maximum value of intensity in the model intensity distribution is normalized to 1.

Here, the line width W1 of the pattern P1 is defined as follows. That is, the line width W1 is defined by the interval between a pair of points when the intensity takes an intermediate value (here, half value = 0.5) between the minimum value (here, 0) and the maximum value (here, 1). be done.

Although the model intensity distribution is shown as a one-dimensional light intensity distribution in FIG. 6, it may have a two-dimensional light intensity distribution like the captured image IM1. Specifically, a distribution obtained by extending the light intensity distribution of FIG. 6 in the longitudinal direction of the pattern P1 may be employed as the model intensity distribution. In this case, the model data MD1 may have the same size as the captured image IM1. The position of the pattern P1 in the model data MD1 is set to be substantially equal to the position of the pattern P1 in the captured image IM1.

A phase distribution of the model data MD1 (hereinafter also referred to as a model phase distribution) is set in advance to a constant value (eg, zero).

The model generation unit 51 outputs this model data MD1 to the image simulator 52 . The image simulator 52 calculates the light intensity distribution (hereinafter referred to as simulation intensity (also called distribution). That is, the image simulator 52 calculates the simulated intensity distribution based on the model data MD1 and the optical characteristics of the optical system of the pattern measuring apparatus 1. FIG. The optical properties are, for example, the numerical aperture of the lens, the wavelength of the light and the sigma. As an algorithm for the image simulator 52, a known one may be adopted. For example, in this algorithm, fast Fourier transform and inverse fast Fourier transform are performed on model data MD1. The image simulator 52 outputs data SD1 representing the calculated simulation intensity distribution to the determination section 53 .

The determination unit 53 obtains the difference between the data SD1 from the image simulator 52 and the captured image IM1 from the image sensor 27 . In other words, the determination unit 53 obtains the difference between the simulated intensity distribution calculated by the image simulator 52 and the actual light intensity distribution obtained by imaging with the image sensor 27 . Below, the light intensity distribution of the captured image IM1 is also referred to as the captured image intensity distribution. Further, since the maximum value of the intensity in the data SD1 is normalized to 1, it is preferable to normalize the maximum value to 1 also in the imaging intensity distribution to be compared. As the difference, for example, a sum of absolute values of differences in corresponding pixel values (light intensity) may be used. The smaller the sum, the smaller the difference.

The determination unit 53 determines whether the difference between the simulated intensity distribution and the captured intensity distribution is greater than a reference value. When the difference is large, it is considered that the model data MD1 does not reflect the actual pattern P1. Therefore, when the difference is larger than the reference value, the determination section 53 outputs difference data DD1 indicating the difference to the model generation section 51 . The difference data DD1 indicating the difference in the shape of the intensity distribution includes, for example, the value of the difference in the intensity distribution and the amount of difference in the line width W1 calculated from the difference in the intensity distribution. In response to the input of the difference data DD1, the model generator 51 corrects the pattern shape (here, the line width W1) and generates (updates) model data MD1 corresponding to the corrected pattern shape. The model generator 51 outputs this model data MD1 to the image simulator 52 again.

The image simulator 52 performs simulation processing again on the corrected model data MD1 to calculate the simulation intensity distribution, and outputs the data SD1 to the determination section 53 .

The determination unit 53 performs the same processing again. That is, the determination unit 53 obtains the difference between the data SD1 and the captured image IM1, and determines whether or not the difference is greater than a reference value. When the difference is greater than the reference value, the controller 50 repeats the above operation.

When the difference is smaller than the reference value, it is considered that the model data MD1 reflects the actual pattern P1. Therefore, when the difference is smaller than the reference value, the determination unit 53 recognizes the pattern shape adopted in the model data MD1 as the shape of the actual pattern P1. That is, the determination unit 53 regards this pattern shape as the measurement shape. The determination unit 53 may output data WD1 indicating the pattern shape (here, data indicating the line width W1). The control unit 50 may display this data WD1 on the display unit 70 as measurement data.

<Model generating unit 51>
Next, a more specific example of the shape of the model intensity distribution will be described. As illustrated in FIG. 6, the edge portions at both ends of the model intensity distribution change smoothly. In other words, the model generator 51 generates the model intensity distribution so that the shape of the intensity distribution does not include high spatial frequency components.

Now, in the example of FIG. 6, the model intensity distribution has a flat section R2 in which the intensity is substantially constant and an intensity change section in which the intensity changes compared to the flat section R2. In the example of FIG. 6, the intensity change section has an increase section R1 and a decrease section R3. The increasing section R1 is a section in which the intensity increases as the pixel number x increases. A flat section R2 is a section in which the intensity is constant regardless of the increase in the pixel number x. The decreasing section R3 is a section in which the intensity decreases as the pixel number x increases.

The increasing section R1 and the decreasing section R3 correspond to edge portions of the model intensity distribution. The waveform along which this edge portion primarily determines how much high spatial frequency content the model intensity distribution contains. The smoother the waveform, the less the model intensity distribution contains high spatial frequency components.

Therefore, in the present embodiment, attention is paid to the waveform along which the edge portion of the model intensity distribution follows. Here, the flat section R2 is removed and a function obtained by connecting together the waveforms of the increasing section R1 and the decreasing section R3 is introduced. This is because this function represents the waveform of the edge portion of the model intensity distribution. In this embodiment, the cutoff frequency fc0 of this function is defined as follows. That is, the cutoff frequency fc0 is set to a quarter or less of the reciprocal of the spatial resolution of the captured image IM1 (hereinafter referred to as the spatial frequency f0). The spatial resolution of the captured image IM1 is also the spatial resolution of the image sensor 27, and is the actual spatial width (for example, 32 [nm]) corresponding to one pixel width. Further, since the discrete values of the model data MD1 are set corresponding to each pixel of the captured image IM1, the spatial resolution of the captured image IM1 is also the spatial resolution of the discrete values of the model data MD1.

As such a function, for example, a Hann function (also called a Hann filter) may be employed. FIG. 7 is a graph showing the Hann function W(u). The Hann function W(u) is represented by the following formula when the value u is made dimensionless by the pixel dimension.

W(u)=0.5·cos(2·π·u)+0.5 −0.5≦u≦0.5
... (1)
The maximum value of this Hann function W(u) is normalized to one. The value u is represented by actual dimension [μm]/pixel dimension [μm] and is a dimensionless quantity. This Hann function W(u) is divided into an increasing section R11 and a decreasing section R12 with the position where the value u takes 0 as a boundary. That is, in the increasing section R11, the Hann function W(u) smoothly increases from 0 to 1 along the waveform of the cosine wave as the value u increases, and in the decreasing section R12, the Hann function W(u ) smoothly decreases from 1 to 0 along a cosine waveform as the value u increases.

Here, the increasing section R11 of the Hann function W(u) is adopted as the increasing section R1 of the model intensity distribution, and the decreasing section R12 of the Hann function W(u) is adopted as the decreasing section R3 of the model intensity distribution. That is, the Hann function W(u) is adopted as a function obtained by connecting the increasing section R1 and the decreasing section R3 of the model intensity distribution.

Here, introducing the ratio OSR (=f0/fc0) between the cutoff frequency fc0 of the Hann function W(u) and the spatial frequency f0 of the captured image IM1, the intensity E[x ] can be expressed, for example, as follows.

- When OSR/2 ≤ x < 0 (increase interval R1)
E[x]=0.5·cos(2·π·x/OSR)+0.5
When 0≤x<W1-OSR/2 (flat section R2)
E[x]=1
When W1-OSR/2≤x≤W1 (lowering section R3)
E[x]=0.5·cos{2·π·(x−W1+OSR)}/OSR)+0.5
... (2)
As can be understood from the increase section R1 in Equation (2), the ratio OSR indicates the width (number of pixels) of the increase section R1. For example, if the cutoff frequency fc0 of the Hann function W(u) is set to 1/9 of the spatial frequency f0, the ratio OSR is 9, and the number of pixels in the increased section R1 of the model intensity distribution is also 4.5. Since the waveform of the decreasing segment R3 is symmetrical to the waveform of the increasing segment R1, the ratio OSR also indicates the width of the decreasing segment R3. This ratio OSR is preset, for example.

The model generator 51 can generate the model intensity distribution of the model data MD1 based on the initial value of the line width W1 and Equation (2). By adopting such a method, it is possible to generate a model intensity distribution that does not contain high spatial harmonic components without being limited by the spatial resolution of the captured image IM1. The initial value of the line width W1 may be set in advance, or may be generated based on the captured image IM1. For example, the model generation unit 51 estimates the line width W1 based on the number of pixels between two points that intersect a threshold value calculated from a predetermined pixel reference value Iref (see FIG. 4) in the captured image IM1, and initializes the estimated value. value. According to this, a value close to the actual line width W1 can be adopted as the initial value.

Note that the model generation unit 51 creates the model intensity distribution such that the position of the pattern P1 in the model intensity distribution substantially matches the position of the pattern P1 in the captured image IM1. More specifically, the model generation unit 51 generates a model so that the maximum intensity of the captured image IM1 substantially matches the maximum intensity of the model intensity distribution, and the center of the pattern in the captured image IM1 substantially matches the center of the model intensity distribution. , to generate the model intensity distribution.

The model generator 51 outputs model data MD1 to the image simulator 52 . The image simulator 52 calculates the simulated intensity distribution as described above, and outputs data SD1 representing the simulated intensity distribution to the determination section 53 . As described above, the determination unit 53 obtains the difference between the data SD1 and the captured image IM1, and outputs the difference data DD1 to the model generation unit 51 when the difference is greater than the reference value.

The model generator 51 corrects the estimated value of the line width W1 in response to the input of the difference data DD1, and updates the model data MD1 based on the corrected estimated value of the line width W1.

FIG. 8 is a diagram schematically showing an example of model intensity distributions before and after updating. The example of FIG. 8 shows two model intensity distributions with different line widths W1. Here, in order to make it easier to see the difference in the line width W1, two model intensity distributions are schematically shown by aligning the waveforms of the increasing section R1. In the example of FIG. 8, one model intensity distribution is indicated by black circles. Since the discrete values of the increasing interval R1 and the flat interval R2 are identical to each other in both model intensity distributions, only the discrete values in the decreasing interval R3 of the other model intensity distribution are indicated by black squares.

A correction width ΔW1 of the line width W1 is set smaller than the spatial resolution of the captured image IM1. The spatial resolution of the captured image IM1 is several tens [nm] (for example, 32 [nm]), and the correction width ΔW1 is set to a value of several [nm] or less (for example, 0.5 [nm]). According to this, the line width W1 can be changed with much higher precision than the spatial resolution of the captured image IM1. In other words, the line width W1 can be calculated with much higher accuracy than the spatial resolution.

As described above, according to the present embodiment, the line width W1 is calculated by a method different from the conventional calculation method. Specifically, by specifying the model data MD1 when the simulated intensity distribution and the actual captured intensity distribution are substantially equal, the pattern shape (here, the line width W1) adopted in the model data MD1 is measured. (measured value). As a result, even if the shape of the luminance distribution of the captured image changes in the vicinity of the resolution limit, the line width W1 can be accurately measured regardless of the changed shape.

Moreover, the model intensity distribution of this model data MD1 does not contain high spatial frequency components. Specifically, the cutoff frequency fc0 is set to a quarter or less of the spatial frequency f0 of the captured image IM1. Therefore, as described below, it is possible to improve the calculation accuracy of the simulation intensity distribution.

For comparison, consider the case of adopting a single rectangular pulse as the model intensity distribution. In this case, the model intensity distribution is binary data. However, with this rectangular pulse, the line width is limited to the spatial resolution of the pixel, and the line width cannot be modified with an accuracy smaller than this spatial resolution. Therefore, the accuracy of the measured value of the line width W1 obtained by the control unit 50 is also about the same as the spatial resolution. Therefore, it is not possible to meet the demand for advanced measurement in the near future.

On the other hand, the model intensity distribution can express the line width more precisely by the pixel values in the increasing section R1 and the decreasing section R3 (see FIG. 8). In other words, the line width W1 can be set to any value in the model data MD1 without being limited by the spatial resolution of the captured image IM1.

Here, as a further comparative example, the case of adopting a perfect trapezoidal wave is also considered. FIG. 9 is a schematic diagram of an example of a model intensity distribution based on a trapezoidal wave. Here, the model intensity distribution of the light transmitted through the pattern P1 is constructed by the intensities from the pixel number x to the pixel number xn. In the example of FIG. 9, a plurality of trapezoidal waves having different line widths W1 are indicated by solid lines, broken lines, one-dot chain lines, and two-dot chain lines, respectively. However, the portions where these overlap are indicated by solid lines. In FIG. 9, the model intensity distribution is constructed by n discrete values. Also in the example of FIG. 9, the model intensity distribution is shown by aligning the waveforms in the increase section R1 in order to make it easier to see the difference in the line width W1.

In this model intensity distribution, the difference in line width W1 is represented by the intensity of pixel number xn−1. For example, the intensity at pixel number xn−1 is indicated by black circles, black squares, black triangles, and white circles. For the model intensity distribution with the widest line width W1, the black circle is adopted, and for the model intensity distribution with the narrowest line width W1, , white circles are adopted. In FIG. 9, the narrowest trapezoidal wave is labeled with the line width W1.

FIG. 10 is a graph showing the relationship between the designed line width of the model and the line width calculated as described above. FIG. 10 shows line widths calculated using the model intensity distribution of FIG. It should be noted that the simulation conditions (for example, optical system parameters, etc.) in FIGS. 9 and 10 are the same. As illustrated in FIG. 10, it can be seen that the calculation accuracy when using this model intensity distribution is low. Here, deviation is introduced as an index indicating calculation accuracy. The deviation here is the maximum value of the difference between the straight line VL1 obtained by linearly approximating the plotted points in FIG. 10 and each plotted point. The smaller the deviation, the higher the calculation accuracy. In the result of FIG. 10, the deviation was 7 [nm]. That is, if the simulation intensity distribution is calculated using the model data MD1 of the present embodiment, the simulation intensity distribution is close to the actual light intensity distribution (captured image IM1) transmitted through the pattern of the designed line width. In short, by adopting the model data MD1 of the present embodiment, it is possible to calculate a simulation intensity distribution close to the actual light intensity distribution.

Now, the reason why the accuracy of the calculation result using the model intensity distribution of FIG. 9 is low is considered as follows. That is, since the model intensity distribution is represented by discrete values for each pixel, the creation of this model intensity distribution is equivalent to the process of sampling a pattern (or light distribution), which is a continuum, at a predetermined sampling frequency. can be considered. In this sampling process, the spatial frequency f0 is grasped as the sampling frequency.

If the creation of the model intensity distribution is equivalent to the sampling process, then the creation of the model intensity distribution is also bound by the sampling theorem in the same way as the sampling process of signals that change in the time domain. The sampling theorem is a theorem that indicates at what interval sampling should be performed when sampling a signal. According to this sampling theorem, it is shown that the original data can be restored from the discretized data if the sampling frequency is set higher than twice the highest frequency contained in the signal that changes in the time domain. This makes it possible to avoid aliasing errors.

Note that the sampling theorem is a theorem applied to communication, for example, and at first glance seems to be unrelated to image processing. , and an image also has a characteristic value with a similar concept of spatial frequency unit [LP (line pair)/mm]. Therefore, the applicant has the view that the sampling theorem holds even in the field of images as long as digital data is handled.

Conversely, in the model intensity distribution of FIG. 9, the sampling frequency (that is, the spatial frequency f0) is lower than twice the highest spatial frequency contained in the model intensity distribution, thus causing aliasing errors. It is considered that there are Therefore, it is considered that the calculation accuracy is degraded.

Now, in this embodiment, the spatial frequency f0 is the reciprocal of the spatial resolution of the captured image IM1. That is, the sampling spatial frequency (=spatial frequency f0) used for sampling the continuum (pattern or light distribution) is predetermined and difficult to increase.

Therefore, in this embodiment, the maximum frequency is reduced in order to increase the difference between the maximum spatial frequency included in the model intensity distribution and the sampling frequency (spatial frequency f0). That is, the control unit 50 (model generating unit 51) generates the model intensity distribution so as not to include high spatial frequency components. More specifically, the model generator 51 generates the model intensity distribution such that the cutoff frequency fc0 of the above function is less than or equal to 1/4 of the spatial frequency f0.

FIG. 11 is a graph showing the relationship between the designed line width of the model and the line width calculated as described above. The simulation conditions are the same as those of FIG. FIG. 11 shows the line width W1 calculated using the model intensity distribution of FIG. 6 under the same simulation conditions as in FIG. It can be seen that the line width W1 can be calculated with high accuracy by using the model data MD1. In the example of FIG. 11, the deviation, which is an index of calculation accuracy, is 1.2 [nm]. This deviation is about one-sixth of the deviation for the comparative example.

FIG. 12 is a diagram showing an example of the relationship between the ratio OSR (=f0/fc0) and the deviation. The simulation conditions for FIG. 12 are the same as described above. As can be understood from FIG. 12, the deviation tends to decrease as the ratio OSR becomes larger than the limit value of 2 indicated by the sampling theorem. The deviation reduction rate in the region where the ratio OSR is less than 4 is higher than the deviation reduction rate in the region where the ratio OSR is 4 or more. Therefore, it can be seen that deviation can be effectively reduced if the ratio OSR is 4 or more. In other words, if the cutoff frequency fc0 is 1/4 or less of the spatial frequency f0, the deviation can be effectively reduced. If the ratio OSR is 6 or more, the deviation can be 2 [nm] or less, and if the ratio OSR is 10 or more, the deviation can be 1 [nm] or less.

As described above, the image simulator 52 can calculate the simulated intensity distribution with high accuracy without causing an aliasing error because the model intensity distribution does not include spatial frequency components. In other words, the model data MD1 contributes to improving the calculation accuracy of the simulation intensity distribution. Moreover, since the estimated value of the line width W1 can be corrected with a correction amount smaller than the spatial resolution of the captured image IM1, the control unit 50 can obtain the measured value of the line width W1 with high accuracy.

<Update of model data MD1>
As described above, the model generator 51 updates the model data MD1 according to the input of the difference data DD1. At this time, the model generator 51 updates the model data MD1 so that the difference between the simulated intensity distribution and the imaged intensity distribution is reduced.

As a more specific example, the following method may be adopted. That is, the model generation unit 51 may determine the line width W1 to be adopted as the next model data MD1 based on changes in the past difference data DD1. As a specific example, consider a case where the line width W1 of the first model data MD1 is wider than the captured image IM1. The control unit 50 creates second model data MD1 in which the line width difference calculated from the difference data DD1 is corrected, or second model data MD1 in which the line width is excessively corrected. After that, the second model data MD1 is input to obtain a simulation result, and the difference between the obtained simulation intensity distribution and the imaging intensity distribution is obtained. As a result, if the simulation result is still wider than the imaging intensity distribution IM1, the third model data MD1 corrected to have a smaller line width is generated, and similar calculations are performed. On the other hand, when the simulated intensity distribution becomes narrower than the imaging intensity distribution IM1, the third model data MD1 with a larger line width is generated and similar calculations are performed. The method of excessively correcting the difference in line width as described above is well known as one method of numerical analysis as SOR (successive over-relaxation), and the coefficient for excessive correction is determined by tests and experience. ing.

Note that the model generation unit 51 may correct not only the line width W1 but also the position of the model intensity distribution of the light transmitted through the pattern P1. That is, the position of the model intensity distribution may also be corrected so that the position of the pattern P1 in the captured image IM1 and the position of the pattern P1 in the simulation intensity distribution substantially match each other. As a more specific example, the determination unit 53 calculates the difference between the simulated intensity distribution and the imaged intensity distribution for each increase section R1 and decrease section R3. The model generator 51 corrects the position of the model intensity distribution so that the difference in the increase interval R1 approaches the difference in the decrease interval R3.

<Image simulator algorithm>
The image simulator 52 may calculate the simulated intensity distribution according to the procedure described below, as is well known. FIG. 13 is a diagram for explaining simulation processing. Here, it is assumed that the captured image IM1 has n×n pixels, and the model data MD1 also has a light distribution in an n×n area.

In a general method, the image simulator 52 first performs a two-dimensional fast Fourier transform to calculate the diffraction pattern of the pattern P1 formed on the pupil plane (Fourier transform plane FS1) of the objective lens 21 . In the example of FIG. 13, this fast Fourier transform is schematically shown by the Fourier transform lens FFT1. The Fourier transform plane FS1 in the simulation also has n×n pixels (areas) like the captured image IM1. The diffraction pattern DP1 is arranged so that the center of the diffraction pattern DP1 coincides with each of the regions of .

Next, the image simulator 52 erases the data outside the circle AP1 corresponding to the aperture stop of the optical system on the Fourier transform plane FS1. In other words, the values outside the circle AP1 are set to zero. Next, the image simulator 52 performs a two-dimensional inverse fast Fourier transform on each of the n×n diffraction patterns DP1 for each light beam incident on the pattern P1. In the example of FIG. 13, this two-dimensional inverse fast Fourier transform is schematically shown by an inverse Fourier transform lens IFFT1. Then, a two-dimensional inverse fast Fourier transform is performed on all rays incident on the pattern P1, and the obtained results are integrated to calculate the light intensity distribution (that is, the simulated intensity distribution) on the imaging plane IS1.

However, according to such a general method, the fact that the number of calculations is extremely large is a factor that reduces the practicality of the method. Therefore, in this embodiment, considering that the patterns to be measured are limited to linear patterns, the following calculation method is used to perform calculations with a small number of calculations.

Now, in the example of FIG. 3, one pattern P1 extends from end to end of the captured image IM1. In this case, even in the model data MD1, the light distribution is substantially uniform in the longitudinal direction of the pattern P1. Therefore, in this case, as illustrated in FIG. 13, the diffraction pattern DP1 exhibits strength in the width direction of the pattern P1, and substantially one-dimensional data having a significant value in the longitudinal direction of the pattern P1. Become.

Therefore, in the image simulation, the image simulator 52 may perform processing as follows. In other words, since the diffraction pattern DP1 is substantially one-dimensional data, the image simulator 52 calculates the diffraction pattern DP1 so that the center of the diffraction pattern DP1 coincides with the area of the Fourier transform surface FS1 determined for each light beam incident on the pattern P1. , and after aperture stop processing is performed on the circle AP1, one-dimensional inverse Fourier fast transform is performed on a data string having a significant value. This operation is performed for all rays incident on the pattern P1, and the results are integrated to obtain the light intensity distribution (that is, the simulated intensity distribution) on the imaging plane IS1. With such a calculation method, although a general method performs a two-dimensional inverse fast Fourier transform for each ray, in the present embodiment, a one-dimensional inverse fast Fourier transform can be performed, so the total amount of calculation is reduced. Clearly an order of magnitude less.

FIG. 14 is a flow chart showing an example of the above operation of the image simulator 52. As shown in FIG. In step S1, the image simulator 52 performs fast Fourier transform on the model data MD1 to calculate a diffraction pattern DP1. In the present embodiment, as described above, the model intensity distribution does not contain high spatial frequency components, so the high order components in the diffraction pattern DP1 are small and substantially zero.

Next, in step S2, the image simulator 52 places this single diffraction pattern DP1 on the Fourier transform plane FS1 for the illumination light beam.

Subsequently, a circle AP1 corresponding to an aperture stop is set on this Fourier transform plane FS1. This circle AP1 is arranged at the center of the Fourier transform surface FS1, and its diameter is preset according to the characteristics of the optical system. At step S3, the image simulator 52 erases the data outside the circle AP1 among the diffraction patterns DP1 on the Fourier transform plane FS1. That is, the data is set to zero. In the example of FIG. 14, this processing is referred to as aperture diaphragm processing.

Next, in step S4, the image simulator 52 temporarily stores the result obtained by performing the one-dimensional inverse fast Fourier transform on the diffraction pattern DP1 placed on the Fourier transform plane FS1. Specifically, the image simulator 52 stores the result in a temporary storage medium of the control unit 50 .

Next, in step S5, the image simulator 52 determines whether or not the processes of steps S2 to S4 have been executed for all illumination light rays. When the processing has not been executed for all illumination rays, the image simulator 52 executes step S2 again for the next illumination rays.

When the processing has been performed for all the illumination rays, in step S6, the image simulator 52 adds all the temporarily stored calculation results for the illumination rays to calculate the simulation intensity distribution.

According to this process, the image simulator 52 may perform one-dimensional inverse fast Fourier transform on one ray of illumination light in step S4. In other words, when the two-dimensional inverse fast Fourier transform is performed by a conventional general method, if the number of data is n×n, it is necessary to perform the one-dimensional fast Fourier transform 2·n times. Therefore, in the above-described process, only one operation is required. Therefore, the number of calculations can be greatly reduced.

<Function adopted for model data>
In the above example, the Hann function W(u) is used as the function along which the edge portion of the model intensity distribution of the model data MD1 follows. However, it is not necessarily limited to this. For example, various window functions (Blackman window, Kaiser window, etc.) having a cutoff frequency fc0 equal to or less than a quarter of the spatial frequency f0 of the captured image IM1 may be employed.

<How to generate model data>
In the above example, values of a predetermined function (for example, Hann's function W(u)) are used as the discrete values forming the model intensity distribution of the model data MD1. However, it is not necessarily limited to this. For example, the model generation unit 51 may generate the model data MD1 based on design drawing data (for example, CAD (computer-aided design) data) of the pattern of the photomask 80 . More specifically, the model generation unit 51 may perform a removal process for removing high spatial frequency components on the design drawing data to generate the model data MD1. As the removal processing, processing such as filtering, which is also called blur processing, or low-pass filtering can be employed. As the cutoff frequency for this removal processing, a frequency equal to or lower than 1/4 of the spatial frequency f0 may be used.

Although the design drawing data is used in the above example, it is not necessarily limited to this. In short, image data reflecting the pattern of the photomask 80 should be adopted. For example, the above removal processing may be performed on a captured image obtained by capturing a model diagram of a pattern formed on the photomask 80 .

<Model data>
The captured image IM1 of FIG. 3 includes one pattern P1, and the model data MD1 also employs a model intensity distribution corresponding to the one pattern P1.

However, the captured image IM1 may include corners of the pattern. FIG. 15 is a diagram schematically showing another example of the captured image IM1. In the example of FIG. 15, the pattern P1 has a rectangular shape extending in the vertical direction. The pattern P1 extends vertically from the lower end of the captured image IM1, and its upper end is included in the captured image IM1. That is, the upper edge of the pattern P1 is positioned below the upper edge of the captured image IM1. Therefore, corners are formed on both sides in the left-right direction of the upper end of the pattern P1.

The model generator 51 may generate the model data MD1 so that the intensity changes smoothly even on a plane. FIG. 16 is a diagram schematically showing an example of model intensity distribution. FIG. 16 shows the model intensity distribution of the model data MD1 in a contour map. Specifically, contour lines A1 to A4 are shown. The intensity indicated by the contour lines A1 to A4 is higher as the number of the sign is smaller. That is, the contour line A1 indicates the highest intensity, and the contour line A4 indicates the lowest intensity.

Each of the contour lines A1 to A4 has an elongated shape along the extending direction of the pattern P1, and the corners of the upper ends are along arcs. The centers of the circular arcs at both corners of each contour line A1 to A4 are set to be the same. In this model data MD1, the model intensity distribution in the lateral direction D1 is set in the same manner as described above. The model intensity distribution in the longitudinal direction D2 is also set in the same manner as described above, except that it has only one edge portion.

Although the model intensity distribution in the horizontal direction D1 is set in the same manner as described above, the maximum value of the model intensity distribution is smaller than 1 at the upper edge portion (eg, line D11). Although the model intensity distribution in the vertical direction D2 is set in the same manner as described above, the maximum value of intensity is less than 1 at each of the right edge portion and the left edge portion (eg, line D21).

According to this, high spatial frequency components can be removed compared to the case where the model intensity distribution forms an angle in plan view. Therefore, the image simulator 52 can calculate the simulation intensity distribution with high calculation accuracy.

Note that the upper edge position of the pattern P1 can be defined as follows. That is, the edge position is defined as the intermediate value (for example, half value = 0.5) between the maximum value (here, 1) and the minimum value (here, 0) in the upper edge portion of the model intensity distribution. can be stipulated. According to this, the distance between the lower end of the model intensity distribution and the edge position can be defined as the length L1 of the pattern P1.

The model generator 51 may generate the model data MD1 based on the line width W1 and the length L1 of the pattern P1, for example. Then, when the difference data DD1 is input from the determination unit 53, at least one of the line width W1 and the length L1 is corrected, and based on the line width W1 and the length L1 after correction, the model data MD1 should be updated.

According to this, the image simulator 52 can calculate the simulation intensity distribution with higher calculation accuracy, so that the line width W1 and the length L1 can be obtained with higher accuracy.

According to the model data MD1 of FIG. 16, the diffraction pattern DP1 of the Fourier transform plane FS1 has two-dimensional data, so it is better to adopt a conventional algorithm instead of the algorithm of FIG.

<Reuse of calculation results>
FIG. 17 is a functional block diagram schematically showing another example of the configuration of the control section 50. As shown in FIG. The control unit 50 can write data to the storage medium 55 and read data from the storage medium 55 . This storage medium 55 stores data SD1 indicating the simulation intensity distribution calculated in the past by the image simulator 52 . Specifically, the image simulator 52 associates the data SD1 with the data WD1 described below and stores them in the storage medium 55 . The data WD1 is data indicating the pattern shape used to generate the model data MD1, and is data indicating the line width W1, for example.

As a specific example, when the image simulator 52 performs simulation processing on the model data MD1 generated using the initial value of the line width W1 and calculates the simulation intensity distribution, the data WD1 indicating the initial value , and the data SD1 representing the simulated intensity distribution are associated with each other and stored in the storage medium 55 . By repeating this process, storage medium 55 stores a plurality of sets of data WD1 and data SD1 as a database.

When the data SD1 is stored in the database, the control unit 50 uses the data SD1 in the database instead of recalculating the simulation intensity distribution. Thereby, the number of calculations of the control unit 50 can be reduced.

Specifically, the image simulator 52 receives the data WD1 from the model generator 51 . Image simulator 52 determines whether data SD1 corresponding to received data WD1 is stored in storage medium 55 or not. That is, it is determined whether or not the simulation intensity distribution corresponding to the line width W1 employed in generating the model data MD1 has already been stored in the database. When the corresponding data SD1 is not stored in the storage medium 55, that is, when the corresponding simulation intensity distribution is not stored in the database, the image simulator 52 calculates the simulation intensity based on the model data MD1 as described above. Calculate the distribution. The image simulator 52 outputs the data SD1 to the determination unit 53 and stores the data WD1 and the data SD1 in the storage medium 55 in association with each other.

On the other hand, when the data SD1 corresponding to the data WD1 is stored in the database, the image simulator 52 does not perform simulation processing for the model data MD1, and reads the corresponding simulation intensity distribution (data SD1) from the database (storage medium 55). , to the determination unit 53 . The determination unit 53 determines whether or not the difference between the simulated intensity distribution read from the database and the captured intensity distribution is greater than the reference value.

In short, the data SD1 indicating the simulation intensity distribution once calculated is stored in the storage medium 55, and the simulation intensity distribution is not calculated again when it becomes necessary for subsequent determination. Data SD1 is used. According to this, the number of calculations in the control unit 50 can be reduced.

Note that in the first embodiment, the model generator 51 and the image simulator 52 are utilized for measuring the pattern shape of the photomask 80. FIG. However, it is not necessarily limited to this. In the present embodiment, the image simulator 52 can calculate the simulation intensity distribution with high calculation accuracy by the model generator 51 generating the model data MD1 that does not include high spatial frequency components. The simulated intensity distribution may be used not only for pattern measurement but also for other purposes. A specific example of another utilization method will be described in the second embodiment.

Also, in the first embodiment, the cutoff frequency fc0 is set to 1/4 or less of the spatial frequency f0. However, it is not necessarily limited to this. The algorithm itself of the present embodiment for identifying the model data MD1 in which the difference between the data SD1 and the captured image IM1 is equal to or less than the reference value is different from the conventional algorithm. This difference in algorithm can bring about an improvement in measurement accuracy. In other words, this embodiment also proposes a new algorithm.

In particular, when a linear pattern is assumed, the algorithm for performing a one-dimensional inverse fast Fourier transform on the diffraction pattern DP1 placed on the Fourier transform plane FS1 is also different from the conventional one. The effect (reduction of the number of calculations) is not premised on the condition that the cutoff frequency fc0 is one-fourth or less of the spatial frequency f0.

Modification.
As described above, the control unit 50 can calculate the simulation intensity distribution with high calculation accuracy by using the model data MD1. By the way, various algorithms are used as algorithms for pattern position measurement or line width measurement. Different algorithms may have different measurement accuracies. Therefore, the calculation accuracy of pattern position measurement or line width measurement may be measured using this model data MD1. For example, based on the calculation result of the image simulator 52 using the model data MD1, the deviation serving as an index of the calculation accuracy may be calculated for each algorithm. This allows, for example, verification of the performance of pattern position measurement or line width measurement algorithms.

That is, by using the model data MD1 according to the present embodiment, it is possible to obtain a simulation image with high positional resolution and high positional accuracy. I am using it. In short, highly reliable model data MD1 is used for algorithm evaluation.

Second embodiment.
FIG. 1 is a diagram schematically showing an example of the configuration of the correction pattern generation device 2. As shown in FIG. The configuration of the correction pattern generation device 2 is the same as that of the pattern measurement device 1 . However, as will be detailed later, the internal configuration of the control unit 50 differs from that of the first embodiment.

Now, the pattern of the photomask 80 may have defects. For example, patterns may be missing. FIG. 18 is a diagram schematically showing another example of the captured image IM1 (hereinafter referred to as captured image IM1A). In the example of FIG. 18, the captured image IM1A includes the pattern P2. The pattern P2 has a translucent portion 80a and a semi-translucent portion 80c. The light transmittance of the translucent portion 80a is higher than that of the semi-translucent portion 80c. The translucent portion 80a is formed of a base material 81, for example. The semi-translucent portion 80 c is formed by forming a semi-translucent film (for example, a chromium oxide film) on one main surface of the base material 81 .

In the example of FIG. 18, the semi-transparent portion 80c has a substantially L-shaped shape. That is, the translucent portion 80c has a first portion extending in the vertical direction and a second portion extending rightward from the lower end of the first portion. The first portion is of equal width and extends longitudinally, while the second portion is not of equal width. Specifically, a white defect PD1 occurs at the tip (right end) of the second portion. A white defect PD1 is a chipped portion in which a semi-transparent film is not formed in an originally necessary portion. In the example of FIG. 18, the white defect PD1 has an elongated shape elongated in the horizontal direction.

Although such a photomask 80 is defective, there is a technique for correcting the white defect PD1 of this photomask 80. FIG. Specifically, the photomask 80 is corrected by forming the light shielding film 82 with a predetermined correction pattern in a partial area of the white defect PD1. FIG. 19 is a plan view schematically showing an example of the configuration of a photomask 80 on which a correction pattern RP1 is formed. The correction pattern RP1 has an elongated shape extending in the horizontal direction in a partial region of the white defect PD1.

By forming the correction pattern RP1 in an appropriate shape and at an appropriate position, the photomask 80 can be produced as a regular product. However, if this repair is repeated many times, the substrate 81 of the photomask 80 will be damaged. Therefore, I would like to complete the repair once. Therefore, it is desirable to obtain the optimum correction pattern RP1 in advance.

FIG. 20 is a functional block diagram schematically showing an example of the configuration of a control section 50 (hereinafter referred to as control section 50A) according to the second embodiment. The control section 50A includes a model generation section 51A, an image simulator 52A, a determination section 53A, and a synthesis section 54A.

The model generation unit 51A generates model data MD1A indicating candidates for the correction pattern RP1. The model data MD1A indicates the distribution of light transmitted through the correction pattern RP1 formed on the base material 81. FIG. Since the correction pattern RP1 is formed of the light shielding film 82, the model intensity distribution of the model data MD1 has a shape obtained by vertically inverting the model intensity distribution of FIG. Each discrete value (initial value) of this model intensity distribution may be entered by the user. This model data MD1A also has high spatial frequency components removed as in the first embodiment.

The model generator 51A outputs the model data MD1A to the synthesizer 54A. The captured image IM1A is also input to the synthesizing unit 54A. Synthesis unit 54A synthesizes captured image IM1A and model data MD1A to generate input data ID1A. Specifically, the synthesizing unit 54A embeds the model data MD1A in a predetermined area of the captured image IM1A. In other words, the synthesizing unit 54A replaces the value of each pixel in the predetermined area with the value of each pixel of the corresponding model data MD1A. The predetermined area is an area that matches the shape of the candidate for the correction pattern RP1, and is arranged at a predetermined position within the white defect PD1. In order to match the maximum value of the model intensity distribution and the maximum pixel value of the captured image IM1A, the maximum pixel value of the captured image IM1A may be normalized to 1.

FIG. 21 is a graph schematically showing an example of light intensity distribution in captured image IM1, and FIG. 22 is a graph schematically showing an example of light intensity distribution in input data ID1A. 21 shows the light intensity distribution on line y in FIG. 18, and FIG. 22 shows the light intensity distribution on line y in FIG. Although the light intensity distributions in FIGS. 21 and 22 actually have discrete values, they are schematically shown as continuous values. In FIG. 22, the part where the intensity exhibits a valley shape is the model intensity distribution corresponding to the candidate of the correction pattern PR1.

Based on the input data ID1A, the image simulator 52A calculates the intensity distribution of the light on the substrate when the light indicated by the input data ID1A passes through the optical system of the exposure device (not shown) and is irradiated onto the substrate. do. The image simulator 52A, like the image simulator 52, performs fast Fourier transform and inverse fast Fourier transform, and the optical characteristics of the exposure apparatus are adopted for various parameters used for the transform.

Incidentally, the light intensity distribution of the captured image IM1A is not the light immediately after passing through the photomask 80, but the light passing through the optical system (objective lens 21, imaging lens 22, etc.) of the correction pattern generation device 2. FIG. However, in the above-described example, the light intensity distribution of the captured image IM1A is approximated to the light immediately after passing through the photomask 80 and is used as the input data ID1A. This is because the numerical aperture (NA) of the optical system of the correction pattern generator 2 is much larger than the numerical aperture of the optical system of the exposure device. Therefore, such an approximation does not introduce significant error.

Moreover, since the light intensity distribution of the captured image IM1A is part of the input data ID1A of the image simulator 52, it is desirable that this light intensity distribution also not contain high spatial frequency components. Here, the resolution of the objective lens 21 and the imaging resolution of the image sensor 27 are set in advance so that the light intensity distribution does not contain high spatial frequency components. Thereby, the calculation accuracy of the simulation intensity distribution can be improved.

The image simulator 52 outputs data SD1A representing the simulated intensity distribution to the determination section 53A.

Reference data RD1A is also input to determination unit 53A. The reference data RD1A is data representing the intensity distribution of light on the substrate when the substrate is exposed using the regular photomask 80 (hereinafter referred to as the reference intensity distribution). The reference data RD1A is preset, for example.

Determination unit 53A obtains the difference between data SD1A and reference data RD1A, and determines whether the difference is greater than a reference value. When the difference is greater than the reference value, the determination unit 53A outputs difference data DD1A indicating the difference to the model generation unit 51A. The model generator 51A updates the model data MD1A in response to the input of the difference data DD1A. Specifically, the model generator 51A modifies at least one of the shape and position of the correction pattern RP1 candidate to update the model data MD1A. The correction width is smaller than the spatial resolution of the captured image IM1A. The model generator 51A outputs the updated model data MD1A to the synthesizer 54A again.

Synthesis unit 54A synthesizes captured image IM1A and model data MD1A to generate input data ID1A, and outputs input data ID1A to image simulator 52A. The image simulator 52A calculates a simulated intensity distribution based on the input data ID1A, and outputs data SD1A representing the simulated intensity distribution to the determination section 53A.

The determination unit 53A obtains again the difference between the data SD1A and the reference data RD1A, and determines whether or not the difference is greater than the reference value. When the difference is greater than the reference value, the controller 50 repeats the above operation. That is, when the difference between the data SD1A and the reference data RD1A is large, the candidate for the correction pattern RP1 is corrected because the photomask 80 cannot be corrected appropriately depending on the candidate for the correction pattern RP1.

When the difference is smaller than the reference value, the determination unit 53A outputs the correction pattern RP1 candidate indicated by the model data MD1A as correction pattern data indicating the correction pattern RP1.

FIG. 23 is a graph showing an example of simulation results. Graphs G1 to G3 are shown in FIG. A graph G1 shows the light intensity distribution when the substrate is exposed using the photomask 80 on which the white defect PD1 is formed. Specifically, graph G1 shows the light intensity distribution corresponding to line y in FIG. A graph G2 shows a reference intensity distribution when a substrate is exposed using a regular photomask 80 in which no white defect PD1 exists. Specifically, it shows the light intensity distribution corresponding to a line equivalent to line y in FIG. Graph G3 shows the simulated intensity distribution. Specifically, the light intensity distribution corresponding to line y in FIG. 19 is shown. FIG. 21 shows the graph G3 when the difference between the graphs G2 and G3 is smaller than the reference value. The control unit 50A outputs the correction pattern RP1 candidate corresponding to this graph G3 as correction pattern data representing the correction pattern RP1.

As described above, the correction pattern generation device 2 can generate correction pattern data representing a more appropriate correction pattern RP1. Even if the semi-transmissive portion 80c is a retardation film, the semi-transmissive portion 80a and the semi-transmissive portion 80c are separately modeled, and after fast Fourier transform, they are superimposed on the Fourier transform plane. Then, the simulation of the projected image and other operations described above can be performed by similar operations.

By the way, in the above example, the model intensity distribution of the model data MD1A is set so as not to contain high spatial frequency components, like the model data MD1. Therefore, the portion corresponding to the model intensity distribution of the light intensity distribution (FIG. 22) indicated by the input data ID1A does not contain high spatial frequency components. Thereby, the calculation accuracy of the simulation intensity distribution can be improved. Moreover, in the above example, the resolution of the objective lens 21 and the spatial resolution of the image sensor 27 are set so that the light intensity distribution in the captured image IM1 does not contain high spatial harmonic components either. According to this, high spatial frequency components are not included not only in the model intensity distribution but also in other portions of the light intensity distribution indicated by the input data ID1A. More specifically, in the input data ID1A (see FIG. 22), the cutoff frequency of the function obtained by connecting the functions along which the intensities in the intensity change sections R21 to R25 are in this order is the reciprocal of the spatial resolution of the captured image IM1. The resolution of the objective lens 21, the spatial resolution of the image sensor 27, and the model data MD1 are preferably set so as to be one fourth or less of . According to this, it is possible to appropriately improve the calculation accuracy of the simulation intensity distribution.

Reference example.
The position of the projected image by the image simulator 52 (the portion corresponding to the light transmitted through the pattern in the simulation intensity distribution) is the phase difference distribution of the diffracted light paired with the intensity distribution of the diffracted light (diffraction pattern DP1). can be shifted in the image space with high spatial resolution and high precision by performing tilting operation with . However, with this method alone, the shape of the model data MD1 is restricted on a pixel-by-pixel basis, so a model with the optimum line width cannot always be used. Alternatively, since it is necessary to process the left and right edge portions separately, there is an unfavorable point in that the amount of calculation associated with the processing increases approximately twice.

As described above, the model data generation method and the model data generation device have been described in detail, but the above description is illustrative in all aspects, and the present disclosure is not limited thereto. Moreover, the various modifications described above can be applied in combination as long as they do not contradict each other. And it is understood that many variations not illustrated can be envisioned without departing from the scope of this disclosure.

51, 51A model generator 80 photomask fc1 cutoff frequency MD1, MD1A model data P1, P2 pattern RP1 correction pattern

Claims (8)

Model data that is input to an image simulator that calculates the intensity distribution of light that has passed through a given optical system using fast Fourier transform and inverse fast Fourier transform. A method of generating model data represented by a value,
generating the model data such that the cutoff frequency of the predetermined function is equal to or less than a quarter of the reciprocal of the spatial resolution of the discrete values;
The method of generating model data, wherein the predetermined function is a function obtained by connecting waveforms along which the intensity change portion of the light intensity distribution included in the model data is connected. A method for measuring the shape of a photomask pattern, comprising:
a first step of obtaining a captured image by forming an image of light from the photomask that has passed through a predetermined optical system on an imaging surface;
a second step of generating model data representing the distribution of light transmitted through a pattern having a certain pattern shape by using the method for generating model data according to claim 1;
A simulated intensity distribution, which is a light intensity distribution on the imaging plane when the light indicated by the model data is imaged on the imaging plane via the optical system, is fast Fourier transformed and applied to the model data. A third step of calculating by performing an inverse fast Fourier transform;
a fourth step of determining whether the difference between the simulated intensity distribution and the light intensity distribution in the captured image is greater than a reference value;
a fifth step of correcting the pattern shape of the model data and repeating the second to fourth steps when the difference is greater than the reference value;
and a sixth step of regarding the pattern shape of the model data as the measured shape when the difference is equal to or less than the reference value. The pattern measurement method according to claim 2,
The pattern measurement method, wherein the correction width of the pattern shape in the fifth step is narrower than the spatial resolution of the discrete values. The pattern measurement method according to claim 2 or 3,
The captured image includes a line pattern extending in one direction from end to end of the captured image,
The third step is
performing a fast Fourier transform on the model data to calculate a diffraction pattern;
a step of two-dimensionally arranging the diffraction pattern in each region of a Fourier transform plane;
and performing an inverse Fourier transform on the diffraction pattern of each region of the Fourier transform surface. The pattern measurement method according to any one of claims 2 to 4,
further comprising a seventh step of associating the simulation intensity distribution calculated in the third step with the pattern shape of the model data employed in the second step, and storing them in a storage medium as a database;
When the simulation intensity distribution corresponding to the pattern shape of the model data adopted in the second step after the seventh step is stored in the database, the third step is not performed, and the fourth step is performed. In the step, the pattern measurement method determines whether or not a difference between the simulated intensity distribution read from the database and the intensity distribution in the captured image is greater than the reference value. A method for generating correction pattern data indicating a correction pattern for repairing a defective photomask, comprising:
a first step of acquiring a captured image based on light from the photomask that has passed through a predetermined first optical system;
a second step of generating model data representing a distribution of light transmitted through a mask on which correction pattern candidates are formed, by the method of generating model data according to claim 1;
a third step of synthesizing the captured image and the model data to generate input data;
A simulated intensity distribution, which is the intensity distribution of light on the substrate when the light indicated by the input data is irradiated onto the substrate via a second optical system having a numerical aperture smaller than that of the first optical system, a fourth step of calculating by performing a fast Fourier transform and an inverse fast Fourier transform on the input data;
a difference between a reference intensity distribution indicating an intensity distribution of light on the substrate when light transmitted through a regular photomask is irradiated onto the substrate via the second optical system, and the simulation intensity distribution; A fifth step of determining whether the value is greater than the reference value;
a sixth step of correcting the shape of the correction pattern candidate and repeating the second to fifth steps when the difference is greater than the reference value;
and a seventh step of adopting the correction pattern candidate as the correction pattern data when the difference is equal to or less than the reference value. The correction pattern data generation method according to claim 6,
The method of generating correction pattern data, wherein a correction width for the shape of the correction pattern candidate in the sixth step is narrower than the spatial resolution of the discrete values. Model data that is input to an image simulator that calculates the intensity distribution of light that has passed through a given optical system using fast Fourier transform and inverse fast Fourier transform. A device that generates model data represented by a value,
a model generation unit that generates the model data such that the cutoff frequency of a predetermined function is equal to or less than a quarter of the reciprocal of the spatial resolution of the discrete values;
The model data generation device, wherein the predetermined function is a function obtained by connecting waveforms along which intensity change portions of the light intensity distribution included in the model data are connected.

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