JP2011061164A - Lighting condition determining method, program and device manufacturing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a lighting condition determining method whose calculation time is short. <P>SOLUTION: The lighting condition determining method that determines a polarization direction of light illuminating an original plate in an exposure apparatus configured to project a pattern of the original plate on a substrate by a projection optical system includes: a step of determining a principal interference term representing a light intensity distribution formed on the substrate by interference of diffracted light contributing principally to formation of the image formed on the substrate with diffracted light from the illuminated original plate among a plurality of terms of an expression showing the image formed on the substrate; and a step of determining a polarization direction meeting an allowable standard by evaluating the relation between the polarization direction of the light illuminating the original plate and a value of the principal interference term. The principal interference term is a term left in the expression when one diffracted light group between two diffracted light groups forming the image by interference is limited to diffracted light of some order having an amplitude larger than a predetermined value. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an illumination condition determination method, a program, and a device manufacturing method.

  Currently, various devices (for example, semiconductor devices and liquid crystal display devices) are manufactured using an exposure apparatus. In order to manufacture higher performance devices, an exposure apparatus having higher resolution performance is required. One technique for increasing the resolution of an exposure apparatus is to increase the NA of a projection optical system using an immersion technique. The immersion technique is a technique for increasing the numerical aperture (NA) in proportion to the refractive index (N> 1) of the liquid by filling the space on the photosensitive member with a liquid (for example, water) having a refractive index of 1 or more. It is. A light wave having a larger incident angle forms an image by increasing the NA by the immersion technique. For this reason, the need to control the polarization of light waves is increasing. As a technique for controlling the polarization of illumination light, for example, there is a proposal of a method for determining the direction of polarized light with the highest image performance by calculating the image by changing the direction of polarized light (see Patent Document 1).

JP 2005-183938 A

In the conventional method for optimizing the illumination conditions, the amount of calculation is enormous because the image formed on the image plane of the projection optical system is strictly calculated, which increases the calculation time.
An object of the present invention is to simplify the calculation in the determination of the illumination condition and reduce the calculation time.

  One aspect of the present invention relates to an illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system, and the illumination condition determining method is illuminated. Among the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the original plate, the main represents the light intensity distribution formed on the substrate by interference of diffracted light that mainly contributes to the formation of the image Determining an interference term and determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term, wherein the main interference term comprises: This is a term that remains in the above equation when one of the two sets of diffracted light groups that form an image by interference is limited to orders of diffracted light having an amplitude greater than a predetermined value.

  According to the present invention, the calculation in determining the illumination condition can be simplified and the calculation time can be shortened.

It is a figure which shows the flow of the illumination condition determination method (polarization direction optimization method). It is a figure which illustrates effective light source (a), target pattern (b), diffracted light distribution (c), diffracted light distribution (d) of Sx1, and diffracted light distribution (e) of Sa1. It is a figure which illustrates the main interference term (a) of Sx1 in the polarization direction 0 degree, and the main interference term (b) of Sx1 in the polarization direction 90 degrees. It is a figure which illustrates the value in the center position of the main interference term. It is a schematic diagram of the optimal polarization direction. It is a figure which illustrates an evaluation position. It is a figure which illustrates CD curve. It is a figure which illustrates a NILS curve. It is a figure which illustrates target pattern (a), diffracted light distribution (b), diffracted light distribution (c) of Sx1, and diffracted light distribution (d) of Sa1. It is a figure which illustrates the value of a main interference term. It is a figure which illustrates CD curve. It is a figure which illustrates a NILS curve. It is a figure which illustrates a target pattern and an effective light source. It is a figure which illustrates CD curve. It is a figure which illustrates a NILS curve. It is a figure which illustrates the structure of an exposure apparatus. It is a figure which shows roughly the structure of the computer which performs the illumination condition determination method (polarization direction optimization method) shown in FIG.

  The present invention is useful for manufacturing various devices such as semiconductor devices such as IC and LSI, display devices such as liquid crystal panels, detection devices such as magnetic heads, and imaging devices such as CCDs. In the present invention, for example, immersion exposure is performed in which a liquid is filled between a final surface of a projection optical system and a substrate coated with a resist (photosensitive material), and an original pattern is projected onto the substrate through the projection optical system and the liquid. It is suitable for.

  The exposure apparatus generally includes an illumination system that illuminates an original (also called a mask or a reticle) and a projection optical system that projects a pattern of the original onto a substrate (for example, a wafer). In this specification, the light intensity distribution formed on the pupil plane of the illumination system is referred to as an effective light source distribution. The effective light source distribution is equivalent to the light intensity distribution formed on the pupil plane of the projection optical system in a state where the original is not disposed on the object plane of the projection optical system.

  Hereinafter, a method for determining the illumination condition, more specifically, a method for determining the polarization direction of light for illuminating the original plate will be described. As a specific example, let us consider forming the target pattern shown in FIG. 2B using the effective light source shown in FIG. The mask pattern is assumed to be the pattern shown in FIG. 2B when converted to the size on the image plane. In the effective light source distribution shown in FIG. 2A, the optimum polarization directions for the six light source elements at the positions Sx1, Sx2, Sa1, Sa2, Sa3, and Sa4 are obtained. Here, since the target pattern is a combination of rectangular patterns having sides parallel to the x axis and the y axis, the optimum polarization direction at each effective light source position is considered to be symmetric with respect to the x axis and the y axis. It's okay. Since Sx1 and Sx2 are symmetric with respect to the y-axis, the optimum polarization direction of Sx2 is symmetric with respect to the y-axis with respect to the optimum polarization of Sx1. Similarly, from the symmetry of the position of the light source element, the optimum polarization direction of Sa2 is symmetric with respect to the y axis with respect to the optimum polarization direction of Sa1. Furthermore, the optimum polarization direction of Sa3 is equal to the optimum polarization direction of Sa1, and the optimum polarization direction of Sa4 is symmetric about the x axis with respect to the optimum polarization direction of Sa1. Therefore, if the optimal polarization directions of the light source elements Sx1 and Sa1 are determined, the optimal polarization directions of the other four light source elements are also determined. In this specification, the optimum polarization direction means a polarization direction that satisfies an acceptance criterion.

  First, in order to determine the optimum polarization direction for Sx1, in the light wave emitted from Sx1, a term (main interference term) that mainly contributes to imaging is determined. FIG. 2C shows a diffracted light distribution of the mask pattern shown in FIG. Diffracted light (see FIG. 2D) within a circle having a radius NA (NA is the NA of the projection optical system) centered at the position of Sx1 is obtained when the mask (original) is illuminated obliquely by the light source element Sx1. It can be considered that diffracted light taken into the pupil of the projection optical system is shown in FIG. Since the light source element Sx1 has a spread on the pupil plane, Sx1 may be divided into a plurality of calculation elements, but here, the spread of the light source element Sx1 is ignored and considered as one point. At this time, in the image I formed by illuminating the mask pattern by the light source element Sx1, any two sets of diffracted lights E1 and E2 interfere among the diffracted lights in the range of FIG. Formed by. When the intensity of the light source element Sx1 is 1, when the projection optical system has no aberration, the image I is expressed by Expression (1).

... (1)
* Represents a complex conjugate. (F1, g1) and (f2, g2) are pupil coordinates (coordinates in the pupil of the projection optical system). Here, E1 and E2 are the amplitudes of the diffracted light having the distribution shown in FIG. All indicates that the range in which the sum of f1, g1, f2, and g2 is taken is the entire pupil plane of the projection optical system. The sum of f1, g1, f2, and g2 can be obtained over the entire pupil plane when the diffracted lights E1 and E2 in the diffracted light distribution of FIG. 2D are obliquely illuminated by the light source element Sx1. This is because it is limited to the diffracted light taken into the pupil of the projection optical system. In addition to f1 and g1, E1 depends on the polarization direction P in the exit pupil, but the variable P is not explicitly shown for the sake of simplicity.

  In the conventional polarization optimization, the image I is calculated by calculating the image I for each polarization using the amount determined by the equation (1) (or the amount essentially equivalent to the amount determined by the equation (1)). A method of selecting polarized light having a high value is used (see Patent Document 1). In one embodiment of the present invention, instead of calculating the image I, the main interference term M is calculated, and M is used to determine the polarization with high imaging performance, resulting in computational complexity (and consequently calculation time). To reduce. The main interference term is diffraction that mainly contributes to the formation of the image among a plurality of terms in an expression (for example, Expression (1)) indicating an image formed on the substrate by the diffracted light from the illuminated original. It is a term representing a light intensity distribution formed on a substrate by light interference. Here, the main interference term can be expressed by, for example, Expression (2), Expression (3), or Expression (4).

... (2)

... (3)

... (4)

The diffracted light D1 (or D2 ^* ) in Expression (2) is obtained by setting the value of the diffracted light whose amplitude is smaller than a predetermined value (for example, 0.1) in the diffracted light E1 (or E2 ^* ) to zero. By not calculating diffracted light having a small amplitude, it is possible to calculate a term (main interference term) that mainly contributes to imaging. Here, instead of replacing both E1 (f1, g1) and E2 ^* (f2, g2) in Eq. (1) with D1 and D2 ^{* as} in Eq. (2), either one is replaced. May be. The right side of Expression (2) remains in Expression (1) when diffracted light having an amplitude smaller than a predetermined value is excluded from at least one of the two sets of diffracted light groups that form an image by interference. This is an example of the main interference term. Here, the two sets of diffracted light groups include a first set of diffracted light groups and a second set of diffracted light groups. In this embodiment, the first set of diffracted light groups is a set of E1 (f1, g1) at each of a plurality of pupil coordinates (f1, g1), and the second set of diffracted light groups is a plurality of pupil coordinates. A set of E2 ^* (f2, g2) in each of (f2, g2).
(F1, G1) in Expression (3) represents that (f1, g1) is limited to an arbitrary value (for example, 0) in Expression (1). By limiting one diffracted light of the two sets of diffracted light that interferes to a diffracted light of an order having an amplitude larger than a predetermined value (for example, 0th order light), a term that mainly contributes to imaging ( The main interference term) can be calculated. Here, as in Expression (3), not only one of (f1, g1) and (f2, g2) in Expression (1) is limited, but both may be limited. The right side of Equation (3) is obtained when Equation (1) is used when one of the two diffracted light groups forming an image by interference is limited to a diffracted light of an order having an amplitude larger than a predetermined value. It is an example of the remaining main interference term.

Formula (4) includes both the concept shown in Formula (2) and the concept shown in Formula (3). The right side of Equation (4) is
(A) limiting one diffracted light group of two sets of diffracted light groups forming an image by interference to orders of diffracted light having an amplitude greater than a predetermined value; and
(B) When diffracted light having an amplitude smaller than a predetermined value is excluded from at least one of the two sets of diffracted light groups,
It is an example of the main interference term which remains in Formula (1).

  Thus, by calculating only the main interference term (a term that mainly contributes to imaging), the amount of calculation can be reduced, and the polarization direction suitable for imaging can be determined efficiently. Here, when all the terms that contribute to imaging are calculated according to the equation (1), the calculation time is naturally long, and the polarization direction suitable for imaging cannot be determined within the required time. It may be. On the other hand, by calculating only the main interference term as in this embodiment, for example, the range of the polarization direction suitable for imaging is roughly determined while roughly swaying the polarization direction, and then the polarization direction is within that range. It is easy to precisely determine the polarization direction suitable for imaging while finely shaking the lens. As a result, it may be possible to improve the accuracy of the determination of the polarization direction as compared with the conventional technique for a limited time or a limited calculation ability. There are various calculation methods such as equations (2), (3), and (4) for calculating the main interference term. In addition, for example, (f1, g1) is not limited to one arbitrary value (F1 = 0, G1 = 0), but a plurality of values (for example, three for F1 and three for G1). You may limit to (F1 = 0, 1, -1, G1 = 0, 1, -1) etc. In this case as well, it goes without saying that it is within the scope of the present invention as long as terms that mainly contribute to imaging are selectively calculated. For simplicity of explanation, the case where the projection optical system has no aberration has been discussed. However, when there is an aberration, it can be dealt with by adding aberration information to the diffracted light distribution.

  Hereinafter, an example will be described in which the main interference term used when determining the polarization direction of the light source element Sx1 is calculated as (F1 = 0, G1 = 0) in Expression (3). Here, it is assumed that the polarization direction in the exit pupil coincides with the polarization direction of the light source element and is uniform on the exit pupil. The fact that the imaging performance is improved by determining the optimum polarization in this way will be confirmed in Examples described later. FIG. 3 shows an example of calculating the main interference term. FIG. 3A shows an example in which the polarization direction is 0 degree (parallel to the x-axis). FIG. 3B shows an example when the polarization direction is 90 degrees (parallel to the y-axis). Here, the optimum polarization direction is evaluated by the value of the main interference term at the center position (evaluation position) of the center hole pattern in FIG. 2B, and the polarization direction having the largest value is set as the optimum polarization direction. As shown in FIG. 4A, the value of the main interference term changes according to the polarization direction. In FIG. 4A, the horizontal axis represents the polarization direction (degrees), and the vertical axis represents the value of the main interference term. From this result, the optimum polarization direction of Sx1 can be determined to be 90 degrees. Here, the index for determining the optimum polarization direction is the peak value of the central pattern, but is not limited thereto, and may be an average value of values at a plurality of positions, or may be weighted for each of a plurality of positions. A value representing the steepness of the gradient of the main interference term at the pattern boundary position may be used as an index. In addition, from the result of FIG. 4A, with respect to Sx1, the optimum polarization candidate is set to 80 degrees to 100 degrees, and image formation calculation is performed for the selected range of polarization, and the final optimum polarization is obtained. You may choose. Furthermore, as shown in Example 3 described later, the polarization direction in which the main interference term takes an extreme value may be obtained by calculation. For example, the polarization direction P in which the main interference term M has a maximum value can be determined as a value satisfying the expressions (5) and (6).

... (5)

... (6)

  Similarly, the polarization direction of the light source element Sa1 can be optimized. As described above, when the light source elements Sx1 and Sa1 are determined, the optimum polarization of all the light source elements is determined in consideration of symmetry with respect to the x axis and the y axis.

  FIG. 1 shows a flow of an illumination condition determination method (polarization direction optimization method). FIG. 17 schematically shows the configuration of a computer 10 that executes the illumination condition determination method (polarization direction optimization method) shown in FIG. The computer 10 can include, for example, a CPU 11, a main memory 12, an input device 13, an output device 14, and a nonvolatile memory 15. The main memory 12 can include a DRAM, for example. The non-volatile memory 15 can include, for example, a hard disk device, an EEPROM, or the like. The input device 13 can include, for example, a keyboard, a communication device, and the like. The output device 14 can include, for example, a display, a printer, a communication device, a memory, and the like. The nonvolatile memory 15 can store a program 16 for causing the computer 10 to execute the polarization optimization method shown in FIG. The program 16 is configured as an application program, for example, and can be read into the main memory 12 in accordance with an activation request. The CPU 11 executes the steps shown in the flow of FIG. 1 by executing the program 16.

  In step S01 in FIG. 1, the wavelength of exposure light, the NA of the projection optical system, the target pattern, the effective light source distribution, the mask pattern, and the refractive index at the image plane of the projection optical system where the diffracted light interferes are specified via the input device 13. Is done. In step S02, an evaluation method for determining optimum polarization is determined. In the example already described, the position of the center hole pattern is evaluated by the value of the main interference term at the evaluation position. Determination of the evaluation method includes determination of an evaluation position and a main interference term (for example, any one of the equations (2), (3), and (4)). In step S03, the diffracted light distribution of the mask pattern is calculated. In step S04, the light source element for calculating the optimum polarization direction is determined. In the above example, two of Sx1 and Sa1 are determined as light source elements for calculating the optimum polarization direction. In FIG. 1, the light source element is specified by the value of the parameter i. In step S05, the first light source element is designated (i = 1). In step S06, a circular area CSi having a radius NA around the designated light source element is determined. In step S07, the main interference term is calculated using the diffracted light in CSi. Specifically, for a plurality of polarization directions P, the value of the main interference term is calculated according to, for example, Expression (3). In step S08, the result of calculating the value of the main interference term for a plurality of polarization directions is evaluated, and the optimum polarization direction is determined. For example, in the example shown in FIG. 4A, the optimum polarization direction is determined as 90 degrees. In steps S07 and S08, an optimal polarization direction may be determined according to, for example, equations (5) and (6). As described above, in this embodiment, the optimum polarization direction (the polarization direction satisfying the acceptance criterion) is determined by evaluating the relationship between the polarization direction of the light illuminating the original and the value of the main interference term. In step S09, the value of i is changed to specify a different light source element, and the process returns to step S06. Therefore, the processing from step S06 to S09 is executed for each light source element. In the example already described, calculation is performed for two of Sx1 and Sa1.

  In step S10, based on the already calculated result, the optimal polarization direction of all the light source elements is determined using the symmetry of the arrangement of the light source elements. In the above-described example, the optimum polarization direction degree with respect to the light source elements Sx2, Sa2, Sa3, and Sa4 is determined using the results of Sx1 and Sa1. Of course, calculation may be performed for all light source elements Sx1, Sa1, Sx2, Sa2, Sa3, and Sa4. In step S11, the optimum polarization is adjusted as necessary. In the above-described example, with respect to Sx1, the optimum polarization candidate is set to 80 degrees to 100 degrees, and image calculation is performed for the selected optimum polarization, and the final optimum polarization direction is selected. It is. In step S12, the mask pattern is adjusted as necessary. This is because if the mask pattern has an auxiliary pattern, it may be necessary to adjust the size of the auxiliary pattern according to the optimum polarization. Further, OPC adjustment of the main pattern may be performed. You may adjust optimal polarization | polarized-light with respect to the mask pattern after adjusting in this way as needed. This flow ends in step S13.

Hereinafter, the result of optimizing the polarization direction of the light source and the effect of optimizing the polarization direction will be described through examples.
Hereinafter, the features of the present invention will be exemplarily described through examples. The present invention can also be applied to optical systems other than liquid immersion, for example. Further, the present invention can be implemented with various modifications such as application to a halftone mask and a line pattern.

[Example 1]
The exposure apparatus was an immersion exposure apparatus. The immersion liquid was water (refractive index n = 1.44), the wavelength was 193 nm, and the NA was 1.35. The projection optical system had no aberration and the magnification was 0.25 times. The refractive index n of the resist was 1.70. The effective light source was a hexapole shown in FIG. For the light source element Sx1 on the x axis, the inner σ was 0.80, the outer σ was 0.98, and the opening angle was 20 degrees. For the light source element Sa1 centered in the direction of 55 degrees from the positive x-axis to the positive y-axis, the inner σ was 0.83, the outer σ was 0.95, and the opening angle was 15 degrees.

  The target pattern was a rectangle having a side of 50 nm in terms of the size on the image plane. The individual rectangles were assumed to be shown in FIG. The mask pattern when converted to the size on the image plane is the same as the target pattern in FIG. FIG. 2C shows the diffracted light distribution of the mask pattern shown in FIG. FIG. 2D shows a region for calculating the main interference term for the light source element Sx1, and FIG. 2E shows a region for calculating the main interference term for the light source element Sa1. FIG. 3A shows the result of calculating the value of the main interference term for the light source element Sx1 with the polarization direction set to 0 degree. Here, the main interference term was calculated as (F1 = 0, G1 = 0) in Equation (3). FIG. 3B shows the result of calculating the value of the main interference term for the light source element Sx1 with the polarization direction set at 90 degrees. FIG. 4A shows the value of the main interference term at the center position of the hole pattern as an example. The polarization direction in which the main interference term takes a maximum value is 90 degrees in all hole patterns, not limited to the center hole pattern center position. 90 degrees is the optimum polarization direction for the light source element Sx1.

  Using a method similar to that for the light source element Sx1, the main interference term is calculated for the light source element Sa1 from the diffracted light in FIG. For example, the value of the main interference term at the center hole pattern position changes as shown in FIG. The polarization direction having the highest value is 140 degrees. At this time, even if the evaluation positions are different hole positions, the polarization direction in which the main interference term takes the highest value is in the range of 125 degrees to 155 degrees. From this, the optimum polarization direction of the light source element Sa1 is determined to be 140 degrees. With the method already described, the optimum polarization directions of all the light source elements are determined from the optimum polarization directions of the light source elements Sx1 and Sa1 in consideration of symmetry. It is determined that Sx2 is 90 degrees, Sa2 is 40 degrees, Sa3 is 140 degrees, and Sa4 is 40 degrees. FIG. 5 schematically shows the optimum polarization direction.

  In order to confirm the validity that the optimum polarization determined by the exit pupil is the optimum polarization of the effective light source, the imaging performance in the case of non-polarization and the case of optimum polarization is compared. In FIG. 6, two hole patterns for evaluating the imaging performance are indicated by A and B. In the effective light source distribution shown in FIG. 2A, the change in the imaging performance of A and B was examined between the optimal polarization shown in FIG. 5 and the non-polarization (sum of orthogonal polarizations). The imaging performance is evaluated by a change in hole diameter (CD) with respect to defocus and NILS (Normalized image log slope) with respect to defocus. The defocus change of the hole diameter was evaluated under the constant intensity value (slice value) at which the diameter in the x-axis direction of the hole indicated by A in FIG.

  FIG. 7A shows the CD change with respect to the defocus of the hole shown by A in FIG. CD is an average value in the x-axis direction and the y-axis direction. FIG. 7B shows a CD change with respect to the defocusing of the hole shown by B in FIG. The decrease due to CD defocusing is larger for the A hole than for the B hole. From FIGS. 7A and 7B, it can be seen that the imaging performance evaluated by CD is the same between the optimal polarization and the non-polarization.

  FIG. 8A shows the NILS change with respect to the defocusing of the hole indicated by A in FIG. NILS is an average value in the x-axis direction and the y-axis direction. In the best focus, the unpolarized NILS is 1.12, whereas the optimally polarized NILS is 1.15, which is an improvement of about 3% NILS. FIG. 8B shows the NILS change with respect to the defocusing of the hole indicated by B in FIG. In the best focus, the unpolarized NILS is 1.55, whereas the optimally polarized NILS is 1.81, which is an improvement of about 17% NILS. 8 (a) and 8 (b), it can be seen that the imaging performance evaluated by NILS is improved by optimizing the polarization. By optimizing the polarization, it was possible to improve the NILS while maintaining the depth of focus by the CD evaluation. From this, it can be seen that in this embodiment, it is possible to improve the imaging performance by giving the light source the optimum polarization at the exit pupil.

[Example 2]
In this embodiment, a polarization optimization is considered when the mask pattern has a main pattern equal to the target pattern and an auxiliary pattern. The effective light source distribution (see FIG. 2A) and the target pattern (see FIG. 2B) are the same as those in the first embodiment. FIG. 9A shows a mask pattern of this embodiment. The auxiliary pattern is determined by an existing method. The size of the auxiliary pattern was 32 nm in terms of the size on the image plane. FIG. 9B shows the diffracted light distribution of the mask pattern of FIG. FIG. 9C shows an area for calculating the main interference term for the light source element Sx1, and FIG. 9D shows an area for calculating the main interference term for the light source element Sa1. FIG. 10A is a value at the center position of the hole pattern A of the main interference term calculated using the diffracted light of FIG. 9C. The main interference term was calculated in the same manner as in Example 1. From FIG. 10A, the optimum polarization direction of the light source element Sx1 is determined to be 90 degrees. FIG. 10B is a value at the center position of the hole pattern A of the main interference term calculated using the diffracted light of FIG. From FIG. 10B, the optimum polarization direction of the light source element Sa1 is determined to be 145 degrees. From the optimum polarization directions of the light source elements Sx1 and Sa1, the optimum polarization directions of all the light source elements are determined in consideration of symmetry. Specifically, Sx2 is determined to be 90 degrees, Sa2 is determined to be 35 degrees, Sa3 is determined to be 145 degrees, and Sa4 is determined to be 35 degrees. FIG. 11 and FIG. 12 show the results of comparing the imaging performance in the case of optimal polarization and non-polarization. FIG. 11A shows the defocus change of the hole diameter (CD) for the hole shown by A in FIG. 6, and FIG. 11B shows the defocus change of the hole diameter (CD) for the hole shown by B in FIG. It is a focus change. It can be seen that both have the same performance even when the polarization is optimized. 12A shows a change in NILS with respect to the defocus for the hole shown in FIG. 6A, and FIG. 12B shows a change in NILS with respect to the defocus for the hole shown in FIG. 7B. From FIG. 12A, the NILS is improved by about 7% by optimizing the polarization in the best focus. From FIG. 12B, the NILS is improved by about 9% by optimizing the polarization in the best focus. By polarization optimization, NILS could be improved without reducing the depth of focus.

[Example 3]
The exposure apparatus was an immersion exposure apparatus. The immersion liquid was water (refractive index n = 1.44). The wavelength was 193 nm and NA was 1.35. The projection optical system had no aberration and the magnification was 0.25 times. The refractive index n of the resist was 1.70. The effective light source was a quadrupole as shown in FIG. The light source element Sa1 in the first quadrant is a rectangle whose center is x = 0.35, y = 0.20, the length in the x direction is 0.10, and the length in the y direction is 0.07. is there. There is a light source element Sa2 in the second quadrant at a position symmetric with respect to Sa1 and the y axis, a light source element Sa4 in the fourth quadrant and a light source element Sa3 in the third quadrant at a position symmetric with respect to Sa1 and Sa2. There is.

  The target pattern was a hole pattern having a side of 65 nm in terms of the size on the image plane (see FIG. 13A). The mask pattern when converted to the size on the image plane is assumed to be the same as the target pattern in FIG. The main interference term was calculated as (F1 = 0, G1 = 0) in equation (3). In this embodiment, the polarization direction in which the main interference term M takes the maximum value is set as the optimum polarization direction. The condition that M takes a maximum value is that the first-order differentiation by Mol of M (x, y, Pol), which is a function of the position (x, y) of the main interference term on the image plane and the polarization direction Pol, becomes zero. And the second derivative by Pol becomes negative. An expression in which the first derivative is zero can be expressed as Expression (7).

... (7)
As Pol that satisfies Expression (7), two solutions shown in Expression (8), Pol_1 and Pol_2, are obtained.

... (8)
Of these two Pols

... (9)
The Pol that satisfies the above is the Pol that M takes the maximum value.

  In this embodiment, A, B, and C in FIG. 13B are selected as (x, y). The hole positions of A, B, and C are in units of μm, and A (x = 0.00, y = 0.00), B (x = −0.13, y = 0.00), C (x = 0.20, y = 0.13). In the light source element Sa1, the polarization direction in which M has a maximum value can be determined as 126.6 degrees for A, 125.2 degrees for B, and 147.3 degrees for C by the method described above. The optimum polarization direction may be the average of these values, may be a weighted linear sum, or may be selected by performing image formation calculation in four polarization directions. In addition, a value closest to the optimum polarization direction obtained by calculation may be selected as the optimum polarization direction from a plurality of polarization directions that can be realized in manufacturing. Here, 147.3 degrees which is the polarization direction in C is selected as the optimum polarization direction. From the symmetry of the x-axis and y-axis, the light source element Sa2 is 32.7 degrees, the light source element Sa3 is 147.3 degrees, and the light source element Sa4 is 32.7 degrees.

  FIG. 14 and FIG. 15 show the results of comparing the imaging performance in the case of optimal polarization and non-polarization. FIG. 14A shows a change in hole diameter (CD) with respect to defocusing with respect to the holes indicated by A and B in FIG. 13B. FIG. 14B shows a change in CD with respect to defocusing with respect to the hole indicated by C in FIG. 13B. It can be seen that both have the same performance even when the polarization is optimized. FIG. 15A shows a change in NILS with respect to defocus for the A and B holes shown in FIG. FIG. 15B shows a change in NILS with respect to the defocus for the hole C in FIG. 13B. From FIG. 15A, the NILS is improved by 5.5% for A and 8.0% for B by optimizing the polarization in the best focus. From FIG. 15B, NILS is improved by 4.7% in C by optimizing the polarization in the best focus. By polarization optimization, NILS could be improved without reducing the depth of focus.

[Exposure equipment]
Next, an exposure method to which the present invention can be applied will be exemplarily described with reference to FIG. The exposure apparatus 100 includes an illumination system 110, a mask stage 132 that holds a mask (original) 130, a projection optical system 140, a main control unit 150, a monitor and input device 152, and a wafer stage 176 that holds a wafer 170. With. In the exposure apparatus 100, the liquid 180 is supplied between the final surface of the projection optical system 140 and the wafer 170, and the pattern of the mask 130 is projected onto the wafer 170 via the projection optical system 140 and the liquid 180. In this example, the exposure apparatus 100 is a step-and-scan projection exposure apparatus (that is, a scanner), but a step-and-repeat system and other exposure systems may be applied.

  The illumination system 110 includes a light source unit and an illumination optical system. The light source unit includes a laser 112 as a light source and a beam shaping system 114. The type and number of lasers are not limited, and the type of light source unit is not limited. As the beam shaping system 114, for example, a beam expander including a plurality of cylindrical lenses can be used. The beam shaping system 114 shapes the beam shape to a desired one by, for example, converting the aspect ratio of the cross-sectional shape of the parallel light from the laser 112 to a desired value (for example, changing the cross-sectional shape from a rectangle to a square). To do. The beam shaping system 114 forms a light beam having a size and a divergence angle necessary for illuminating an optical integrator 118 described later.

  The illumination optical system is configured to illuminate the mask 130. The illumination optical system includes, for example, a condensing optical system 116, a polarization control unit 117, an optical integrator 118, an aperture stop 120, a condensing lens 122, a bending mirror 124, a masking blade 126, and an imaging lens 128. Including. The illumination optical system can realize various illumination modes such as modified illumination. The condensing optical system 116 is composed of a plurality of optical elements, and efficiently introduces a light beam having a desired shape into the optical integrator 118. For example, the collection optics 116 includes a zoom lens system and controls the distribution of the shape and angle of the incident beam to the optical integrator 118. The condensing optical system 116 includes an exposure amount adjustment unit that can change the exposure amount of the illumination light to the mask 130 for each illumination. The exposure adjustment unit is controlled by the main control unit 150. For example, the exposure amount monitor can be placed between the optical integrator 118 and the mask 130 or at another location, and the exposure amount can be measured and the result can be fed back.

  The polarization control unit 117 includes, for example, a polarizing element, and is disposed at a position substantially conjugate with the pupil plane 142 of the projection optical system 140. The polarization control unit 117 controls the polarization state in a predetermined region of the effective light source formed on the pupil plane 142. A polarization control unit 117 composed of a plurality of types of polarization elements may be provided on a turret that can be rotated by an actuator (not shown), and the main control unit 150 may control driving of the actuator. The polarization control unit 117 can realize a polarization direction suitable for imaging determined by the above method.

  The optical integrator 118 is configured as a fly-eye lens that uniformizes the illumination light that illuminates the mask 130, converts the angular distribution of the incident light into a position distribution, and emits it. The fly-eye lens is configured by combining a large number of rod lenses (that is, microlens elements) with its entrance and exit surfaces maintained in a Fourier transform relationship. However, the optical integrator 118 is not limited to a fly-eye lens, and includes an optical rod, a diffraction grating, and a plurality of sets of cylindrical lens array plates arranged so that each set is orthogonal.

  Immediately after the exit surface of the optical integrator 118, an aperture stop 120 having a fixed shape and diameter is provided. The aperture stop 120 is disposed at a position substantially conjugate with the effective light source shown in FIG. 2B formed on the pupil plane 142 of the projection optical system 140, and the aperture shape of the aperture stop 120 is the same as that of the projection optical system 140. This corresponds to the intensity distribution of the effective light source on the pupil plane 142. The aperture stop 120 controls the intensity distribution of the effective light source. The aperture stop 120 can be switched by an aperture replacement mechanism (actuator) 121 so that the aperture stop is positioned in the optical path according to the illumination conditions. Driving of the actuator 121 is controlled by a drive control unit 151 controlled by the main control unit 150. The aperture stop 120 may be integrated with the polarization control unit 117.

  The condensing lens 122 is emitted from a secondary light source in the vicinity of the exit surface of the optical integrator 118, condenses a plurality of light beams that have passed through the aperture stop 120, and is reflected by a mirror 124 to form a masking blade 126 surface as an illuminated slope. Illuminate uniformly with Koehler illumination. The masking blade 126 is composed of a plurality of movable light shielding plates, and has an approximately rectangular arbitrary opening shape corresponding to the effective area of the projection optical system 140. The light beam transmitted through the opening of the masking blade 126 is used as illumination light for the mask 130. The masking blade 126 is an aperture whose opening width is automatically variable, and can change the transfer area. In addition, the exposure apparatus 100 may further include a scan blade having a structure similar to the above-described masking blade, which makes it possible to change the transfer region in the scan direction. The scanning blade is also a diaphragm whose opening width can be automatically changed, and is provided at a position optically conjugate with the mask 130 surface. By using these two variable blades, the exposure apparatus 100 can set the size of the transfer region in accordance with the size of the shot to be exposed. The imaging lens 128 irradiates and transfers the opening shape of the masking blade 126 onto the surface of the mask 130, and reduces and projects the pattern on the surface of the mask 130 onto the surface of the wafer 170 placed on a wafer chuck (not shown).

  The mask 130 has a main pattern corresponding to the pattern to be transferred and, if necessary, an auxiliary pattern that does not resolve itself, and is supported and driven by the mask stage 132. Diffracted light emitted from the mask 130 passes through the projection optical system 140 and is projected onto the wafer 170. The mask 130 and the wafer 170 are arranged in an optically conjugate relationship. Since the exposure apparatus 100 is a scanner, the pattern of the mask 130 is transferred onto the mask 130 by synchronously scanning the mask 130 and the wafer 170. In the case of a step-and-repeat type exposure apparatus (ie, “stepper”), exposure is performed with the mask 130 and the wafer 170 being stationary. As the mask 130, any of a binary mask, a halftone mask, and a phase shift mask can be used.

  The mask stage 132 supports the mask 130 and is connected to a moving mechanism (not shown). The mask stage 132 and the projection optical system 140 are provided, for example, on a stage barrel surface plate that is supported by a base frame placed on a floor or the like via a damper or the like. Any configuration known in the art can be applied to the mask stage 132. A moving mechanism (not shown) includes a linear motor or the like, and the mask 130 can be moved by driving the mask stage 132 in the XY directions. The exposure apparatus 100 scans the mask 130 and the wafer 170 in a synchronized state by the main control unit 150.

  The projection optical system 140 has a function of forming an image on the wafer 170 of diffracted light that has passed through the pattern formed on the mask 130. The projection optical system 140 can be an optical system including only a plurality of lens elements. The projection optical system 140 can also be an optical system (catadioptric optical system) having a plurality of lens elements and at least one concave mirror. The projection optical system 140 may also be an optical system having a plurality of lens elements and at least one diffractive optical element such as a kinoform. When correction of chromatic aberration is required, a plurality of lens elements made of glass materials having different dispersion values (Abbe values) can be used, or the diffractive optical element can be configured to generate dispersion in the opposite direction to the lens element. To do. Otherwise, chromatic aberration compensation is achieved by narrowing the spectrum of the laser.

  The main control unit 150 performs drive control of each unit, and particularly performs illumination control based on information input from the monitor and the input device of the input device 152 and information from the illumination system 110. Control information by the main control unit 150 and other information are displayed on the monitor of the monitor and input device 152.

  In the wafer 170, an antireflection film 172 is formed on the substrate 174, and a resist (photoresist) 171 is applied on the antireflection film 172. The antireflection film 172 may be a multilayer. Further, the antireflection film 172 may not be formed. Wafer 170 is supported by wafer stage 176. The wafer stage 176 can be applied with any configuration known in the art, and therefore a detailed description of the structure and operation is omitted here. For example, the wafer stage 176 moves the wafer 170 in the XY directions using a linear motor. The mask 130 and the wafer 170 are scanned in synchronization, for example, and the positions of the mask stage 132 and the wafer stage 176 are monitored by, for example, a laser interferometer. Mask 130 and wafer 170 are driven at a constant speed ratio. The wafer stage 176 is provided on a stage surface plate supported on a floor or the like via a damper, for example. For example, the mask stage 132 and the projection optical system 140 are provided on a lens barrel surface plate (not shown) supported on a base frame placed on a floor or the like via a damper or the like.

  For the liquid 180, a substance that has good exposure wavelength transmittance, does not cause contamination on the projection optical system, and has good matching with the resist process is selected. The final surface of the projection optical system 140 is coated to protect the influence from the liquid 180.

  In the exposure, the light beam emitted from the laser 112 is introduced into the optical integrator 118 via the condensing optical system 116 after the beam shape is shaped by the beam shaping system 114. The optical integrator 118 makes the illumination light uniform, and the aperture stop 120 sets the intensity distribution of the effective light source. Such illumination light illuminates the mask 130 under optimum illumination conditions via the condenser lens 122, the bending mirror 124, the masking blade 126, and the imaging lens 128. The light beam that has passed through the mask 130 is reduced and projected onto the wafer 170 at a predetermined magnification by the projection optical system 140.

  Since the final surface of the projection optical system 140 on the wafer 170 is immersed in the liquid 180 having a refractive index higher than that of air, the NA of the projection optical system 140 becomes high, and the resolution formed on the wafer 170 becomes fine. Further, by controlling the polarization, an image with high contrast can be formed on the resist 171. Thereby, the exposure apparatus 100 can provide a high-quality device (semiconductor element, LCD element, imaging element (CCD, etc.), thin film magnetic head, etc.) by transferring the pattern onto the resist with high accuracy.

  The device manufacturing method according to a preferred embodiment of the present invention is suitable for manufacturing a device such as a semiconductor device or a liquid crystal device. The method may include a step of exposing a substrate coated with a photosensitive agent using the above exposure apparatus, and a step of developing the exposed substrate. Furthermore, the device manufacturing method may include other well-known steps (oxidation, film formation, vapor deposition, doping, planarization, etching, resist stripping, dicing, bonding, packaging, and the like).

Claims (9)

An illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system,
Of the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the illuminated original plate, the light intensity distribution formed on the substrate by the interference of diffracted light that mainly contributes to the formation of the image. Determining a principal interference term to represent;
Determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term, and
The main interference term is a term that remains in the above formula when one of the two sets of diffracted light groups forming an image by interference is limited to a diffracted light of an order having an amplitude larger than a predetermined value. Is,
A lighting condition determination method characterized by the above. An illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system,
Of the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the illuminated original plate, the light intensity distribution formed on the substrate by the interference of diffracted light that mainly contributes to the formation of the image. Determining a principal interference term to represent;
Determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term, and
The main interference term is a term that remains in the above equation when diffracted light having an amplitude smaller than a predetermined value is excluded from at least one of the two sets of diffracted light groups that form an image by interference. is there,
A lighting condition determination method characterized by the above. An illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system,
Of the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the illuminated original plate, the light intensity distribution formed on the substrate by the interference of diffracted light that mainly contributes to the formation of the image. Determining a principal interference term to represent;
Determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term, and
The main interference term limits one diffracted light group of the two sets of diffracted light groups that form an image by interference to orders of diffracted light having an amplitude larger than a predetermined value, and the two sets of diffracted light When the diffracted light having an amplitude smaller than a predetermined value is excluded from at least one diffracted light group of the group, it is a term remaining in the formula.
A lighting condition determination method characterized by the above. Determining the polarization direction comprises:
A calculation step of calculating a light intensity distribution formed on the substrate by calculating a value of the main interference term for each polarization direction while changing a polarization direction of light illuminating the original;
Determining a polarization direction satisfying an acceptance criterion by evaluating a light intensity distribution calculated for a plurality of polarization directions in the calculating step;
The illumination condition determination method according to any one of claims 1 to 3, characterized by comprising: The step of determining the polarization direction determines a polarization direction satisfying the acceptance criterion by calculating an expression giving a polarization direction in which the main interference term takes an extreme value;
The lighting condition determination method according to claim 1, wherein the lighting condition is determined. A program for causing a computer to execute an illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system,
Of the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the illuminated original plate, the light intensity distribution formed on the substrate by the interference of diffracted light that mainly contributes to the formation of the image. Determining a principal interference term to represent;
Determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term,
The main interference term is a term that remains in the above formula when one of the two sets of diffracted light groups forming an image by interference is limited to a diffracted light of an order having an amplitude larger than a predetermined value. Is,
A program characterized by that. A program for causing a computer to execute an illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system,
Of the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the illuminated original plate, the light intensity distribution formed on the substrate by the interference of diffracted light that mainly contributes to the formation of the image. Determining a principal interference term to represent;
Determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term,
The main interference term is a term that remains in the above equation when diffracted light having an amplitude smaller than a predetermined value is excluded from at least one of the two sets of diffracted light groups that form an image by interference. is there,
A program characterized by that. A program for causing a computer to execute an illumination condition determining method for determining a polarization direction of light for illuminating an original in an exposure apparatus that projects the pattern of the original onto a substrate by a projection optical system,
Of the plurality of terms in the equation representing the image formed on the substrate by the diffracted light from the illuminated original plate, the light intensity distribution formed on the substrate by the interference of diffracted light that mainly contributes to the formation of the image. Determining a principal interference term to represent;
Determining a polarization direction satisfying an acceptance criterion by evaluating a relationship between a polarization direction of light illuminating the original plate and a value of the main interference term,
The main interference term limits one diffracted light group of the two sets of diffracted light groups that form an image by interference to orders of diffracted light having an amplitude larger than a predetermined value, and the two sets of diffracted light When the diffracted light having an amplitude smaller than a predetermined value is excluded from at least one diffracted light group of the group, it is a term remaining in the formula.
A program characterized by that. A device manufacturing method for manufacturing a device, comprising:
Determining illumination conditions by the illumination condition determining method according to any one of claims 1 to 5,
Exposing the substrate while illuminating the original under the determined illumination conditions;
Developing the substrate;
A device manufacturing method comprising: