KR100916623B1 - Three-fold polarization modulator for modulating input light of a high numerical aperture lens - Google Patents

Abstract

The present invention relates to a three-layer polarization modulator for modulating the incident light of a high aperture lens. The apparatus of the present invention comprises: a three-layer polarization modulator for modulating the incident light of linearly polarized light to pass through itself into three different polarization states; And a high-aperture lens that polarized modulated incident light passing through the three-layer polarization modulator passes through itself to generate a focus light having a light intensity distribution close to a circle. Therefore, the device of the present invention has a circular light intensity distribution on the focal plane by adjusting the polarization of the incident light so that it can have a uniform resolution and can deepen the DOF, thereby providing an effect of improving the yield in the lithography process of the semiconductor. do.

Polarization Modulation, Three-Layer Polarization, High-Aperture Lens

Description

Three-fold polarization modulator for modulating input light of a high numerical aperture lens

1A and 1B are views illustrating polarization states of a typical high-aperture lens;

2A and 2B are diagrams showing an intensity distribution of focus light by a general high-aperture lens;

3 is a schematic diagram of a polarization modulator for modulating incident light of a high-aperture lens according to an embodiment of the present invention;

4 is a view showing a three-layer polarization modulator according to an embodiment of the present invention;

5A and 5B show the intensity distribution of the focus light by the high-aperture lens of the present invention.

* Explanation of symbols for main parts of the drawings

31: High-Length Number Lens

32: three-layer polarization modulator

The present invention relates to a polarization modulator for modulating light incident on a high aperture lens.

       The directivity of semiconductors continues to improve in order to store large amounts of information in a limited size. In order to realize such integration, the line width of the pattern to be obtained through the lithography process during semiconductor manufacturing must be reduced. In the semiconductor process, the line width of the pattern is determined by the wavelength of the laser used for lithography, the numerical aperture (NA) of the lens for lithography, and the k1 factor called the process constant in the lithography process as follows.

       The line width (or resolution) of the pattern = k1 × wavelength / NA

       Here, k1 is determined by a photoresist commonly used in lithography, and the wavelength represents 193 nm of an ArF laser used for line width reduction in current semiconductor lithography processes. Changing to a shorter UV wavelength can reduce the line width, but due to the material problems of the optical elements for this purpose, it is difficult to expect a decrease in the line width due to the wavelength reduction.

       For this reason, the wavelength can be reduced by increasing the performance of the optical devices while using the 193 nm, which makes it easy to make optical elements, in particular, it is currently desired to reduce the line width of the pattern by increasing the numerical aperture (NA) of the exposure machine. Is the trend.

       However, as the numerical aperture increases, not only the line width but also the depth of focus (hereinafter referred to as DOF) is also reduced.

Depth of focus (DOF) = k2 × wavelength / NA ² (where k2 is the process variable for DOF)

       In particular, since the DOF is inversely proportional to the square of the numerical aperture, the reduction ratio is larger than the line width in an exposure machine having a numerical aperture of 1 or more. Reducing the DOF eventually reduces the process margin in the lithography process. Basically, each process variable changes little by little as the work progresses. In addition, the position of the semiconductor wafer located on the upper surface of the exposure machine also does not always have a fixed value, but varies with some degree of scattering. Such minute mechanical change may be caused by a problem of positional accuracy of the process stage, a flatness error of a photomask corresponding to a subject of an exposure machine, and a flatness error of a wafer.

       Eventually, as the process proceeds, there is an error scatter. Only the wafers in the DOF produce the desired pattern, otherwise the pattern does not occur or the size of the pattern is different from the target value. This affects the yield over the entire lithography process.

       When performing this lithography process, a lens is used to collect light into one point. In particular, high-aperture lenses with high numerical aperture (NA) are usually used to achieve high resolution or very small focal size.

The numerical aperture NA is a value obtained by multiplying the sine of the focal angle a formed by the light emitted from the lens by the refractive index n of the medium through which the light passes to the focal point.

       In general, linearly polarized incident light incident on the high-aperture lens has a polarization direction inclined by the refractive angle of the lens, unlike the original polarization direction after the lens has been transmitted by the refraction of the lens.

       Hereinafter, a description will be given with reference to FIGS. 1A and 1B.

1A and 1B are diagrams illustrating polarization states of a general high aperture lens.

       Referring to FIG. 1A, an example in which incident light that is linearly polarized on the x-axis and travels along the z-axis is incident on the high aperture lens. In this case, as shown in FIG. 1A, when viewed on an xz plane including a polarization vector, the polarization direction is not only the x-axis direction, but also the tilted polarization on the optical path where incident light of the x-axis polarization passes through the high-aperture lens and is focused. It also has a z-axis direction.

      When viewed on the y-z plane as shown in FIG. 1B, the polarization direction on the optical path in which incident light of x-axis polarization passes through the high-aperture lens and focuses is maintained on the x-axis polarization.

       The focus light intensity distribution by the high-aperture lens has a different distribution from the focus light intensity by the low-aperture lens (or circular aperture).

       Hereinafter, the focus light intensity distribution of the high aperture lens will be described with reference to FIGS. 2A and 2B.

Referring to Figure 2a, Figure 2a is passed through the high numerical aperture lens having a wavelength of 1, λ is the x-axis linearly polarized incident light is focused each a is 60 degrees in the refractive index is 1, the medium formed in the focal plane (xy plane in focus) Density graph showing light intensity distribution. 2A, it can be seen that the intensity of the focus light has an elliptical shape on one side of the focal plane.

       2B is an intensity distribution graph before and after focus on the z-axis or optical axis.

In FIG. 2B, the units of the x, y, and z axes are lambda . Since the distribution of the focus light intensity on the focal plane has an elliptic shape, the ratio of the major axis (0.74 λ ) to the minor axis (0.56 λ ) in the region of 50% (half width) of the intensity is 1.321 and the half width of the intensity on the z-axis. Is 1.8 λ . The DOF extension can be seen from the increase in half width of the intensity distribution on the optical axis.

       As such, the light intensity distribution in the focal plane by the high-aperture lens has an elliptical shape, but also has a disadvantage in that the DOF is drastically shortened. The elliptical light intensity distribution inhibits having a uniform resolution, and short DOF causes the yield to be bad in the semiconductor lithography process as mentioned above.

Accordingly, an object of the present invention is to modify the polarization of the incident light in the high-aperture lens to solve the above-mentioned problems by making the light intensity distribution on the elliptic focal plane circular to deepen the DOF without degrading the resolution. It is to provide a three-layer polarization modulation device for modulating the incident light of the lens.

The three-layer polarization modulator for modulating incident light of a high-aperture lens according to the present invention for achieving the above object is a polarization modulator for modulating the polarization state of the incident light, the incident light of linearly polarized light is transmitted through three A three-layer polarization modulator for modulating a polarization state different for each region; And a high-aperture lens that polarized modulated incident light passing through the three-layer polarization modulator transmits itself to generate a focus light having a light intensity distribution close to a circle.

In addition, the three-layer polarization modulator includes a first region for modulating the incident light to have polarized light parallel to the X-axis; A second region for modulating the incident light to have polarization parallel to the Y axis; And a third region for modulating the incident light to have polarized light parallel to the X axis.

In addition, the outer diameter w3 of the third region is characterized in that the beam size of the incident light.

In addition, the first to third regions may be defined as an angle with a focus of each region of the focus light passing through the high-aperture lens.

Further, the high aperture lens is characterized by having a focal angle a defined by the numerical aperture value.

In addition, the focal angle a of the high-aperture lens is an angle with the focal point with respect to the first to third regions.

In addition, the focal angle a of the high-aperture lens is an angle a1 forming a boundary between the focus and the first region, an angle a2 forming a boundary between the focus and the second region, and the focus and the first angle. It is characterized by the sum of the angle (a3) and the boundary with the three areas.

In addition, the outer diameter w1 of the first region of the three-layer polarization modulator is

Where a is the focal angle, w3 is the outer diameter of the third region, and a1 is the angle forming the boundary between the focal point and the first region.

Further, the outer diameter w2 of the second region of the three-layer polarization modulator is

Here, a is a focal angle, w3 is an outer diameter of the third region, and a3 is obtained by being an angle formed between a boundary between the focal point and the third region.

In addition, the high-aperture lens may be focused at a polarization state in which the high-aperture lens is inclined by the incident angle from the vertical to the focal point at an angle a1 that forms the boundary between the focus and the first region.

In addition, the high-aperture lens is focused on the focal point in a polarized state that is maintained horizontally from an angle a1 between the focal point and the boundary between the first region and an angle a2 between the focal point and the boundary between the second region. It features.

In addition, the high-aperture lens has a polarization state inclined by the incident angle from the vertical to the focal point from the angle (a2) forming the boundary between the focus and the second region to the angle (a3) forming the boundary between the focus and the third region. It is characterized by gathering in focus.

A polarization modulator for modulating incident light of a high aperture lens according to the present invention for achieving the object of the present invention is a polarization modulator for modulating the polarization state of the incident light incident on the high aperture lens having a focal angle (a) The polarization modulator includes a three-layer polarization modulator for modulating the incident light of linearly polarized light so that the incident light passes through the polarized light into three different polarization states, wherein the three-layer polarization modulator is configured to modulate the incident light to have polarization parallel to the X-axis. And a second region for modulating the incident light to have polarization parallel to the Y axis, and a third region for modulating the incident light to have polarization parallel to the X axis.

In addition, the outer diameter w3 of the third region is characterized in that the beam size of the incident light.

In addition, the first to third regions may be defined as an angle with a focus of each region of the focus light passing through the high-aperture lens.

In addition, the outer diameter w1 of the first region of the three-layer polarization modulator is

Where a is the focal angle, w3 is the outer diameter of the third region, and a1 is the angle forming the boundary between the focal point and the first region.

Further, the outer diameter w2 of the second region of the three-layer polarization modulator is

Here, a is a focal angle, w3 is an outer diameter of the third region, and a3 is obtained by being an angle formed between a boundary between the focal point and the third region.

Hereinafter, with reference to the accompanying Figures 3 to 5 will be described in detail a preferred embodiment of the present invention.

3 is a schematic diagram of a polarization modulator for modulating incident light of a high aperture lens according to an embodiment of the present invention.

Referring to FIG. 3, the linearly polarized incident light I ₁ having the size of w 3 is incident to the high-aperture lens 31 by the polarized modulated incident light I ₂ through the three-layer polarization modulator 32. Here, the linearly polarized incident light I ₁ shows a circular cross section in a polarization state before entering the three-layer polarization modulator 32. It can be seen that the cross-section of the linearly polarized incident light I ₁ is a linearly polarized state of 45 degrees on the X and Y axes. When the linearly polarized incident light I ₁ passes through the three-layer polarization modulator 32, the linearly polarized incident light I ₁ is emitted as the polarized modulated incident light I ₂ . In this case, the polarized modulated incident light I ₂ may emit light in which the polarization state is modulated for each of the first to third regions 1, 2, and 3 of the three-layer polarization modulator 32. That is, looking at the cross section of the polarized modulated incident light I ₂ , the first to third regions are vertically polarized-modulated in parallel to the X-axis, and the second region is horizontally polarized-modulated in parallel to the Y-axis. When the polarized modulated incident light I ₂ passes through the high-aperture lens 31, the polarization state is inclined by the incident angle from the vertical to the focal point with respect to the high-aperture lens 31 having a focal angle of a from 0 to a1. And a1 to a2 are in a polarized state that is kept horizontal, and a2 to a3 are focused at a polarized light inclined by the incident angle from the vertical to the focus.

In this way, the intensity distribution made through the high-aperture lens 31 and made in the three-layer polarization focal plane can be made close to the circle and the DOF can be expanded without degrading the diffraction resolution. This will be described through graphs in FIGS. 5A and 5B below.

Such a polarization modulator will be described in more detail with reference to the three-layer polarization modulator of FIG. 4.

4 is a view showing a three-layer polarization modulator according to an embodiment of the present invention.

Referring to FIG. 4, the three-layer polarization modulator 32 includes a first region 1 for modulating incident light to have polarization parallel to the X axis and a second region for modulating incident light to have polarization parallel to the Y axis ( 2) and a third region 3 for modulating the incident light to have polarization parallel to the X axis. In this case, each of the first to third regions is defined as an angle with a focus of each region of the focus light passing through the high-aperture lens 31. In Fig. 3, the focal angle a defined by the numerical aperture value of the high aperture lens 31 is equal to the sum of the angles formed between the focal point and the boundary of each area. That is, a = a1 + a2 + a3. Here, the focal angle (a) is an angle (a1) formed by the boundary between the focus and the first area, an angle (a2) formed by the boundary between the focus and the second area, and an angle formed by the boundary between the focus and the third area ( is the sum of a3). A1, a2, and a3 for the optimal circular focal plane light intensity distribution and the expanded DOF for the focal angle a are obtained by using the tripolar vector diffraction calculation formula for the high-aperture lens 31. Here, the trigonometric vector diffraction integration formula is described in the well-known book by E. wolf, "Electromagnetic diffraction in optical systems. II. Structure of th image field un an aplanatic system". From the beam size w3 of the incident light and the outer diameter of each region of the three-layer polarization modulator 32 from each of a1, a2, and a3, the following equations (1) and (2) can be obtained.

Equation 1

Equation 2

Where a is the focal angle, w3 is the outer diameter of the third region, a1 is the angle that forms the boundary between the focus and the first region, and a3 is the angle that forms the boundary between the focus and the third region.

Equation 1 is the outer diameter w1 of the first region 1 of the three-layer polarization modulator 32, and Equation 2 is the outer diameter w2 of the second region 2 of the three-layer polarization modulator 32. The outer diameter of the third region 3 of the three-layer polarization modulator 32 is w3, which is the beam size of incident light.

The following is the use of the three-layer polarizer 32 when the linearly polarized incident light I ₁ having a wavelength of 1λ passes through the high aperture lens 31 having a focal angle a of 60 degrees, a numerical aperture of 0.86, and n = 1. It will be described as an experimental example according to. That is, it is an experiment showing how the intensity distribution and DOF of the optimized focus light through the three-layer polarizer 32 are improved compared to the intensity distribution and the DOF of the unfocused polarized light for the high-aperture lens under the same conditions. Optimization of a1, a2, a3 to obtain an optimized three-layer polarization modulator 31 by trigonal vector diffraction integration calculation for the high aperture lens 31 for the focal light a at 60 degrees (a = 60 degrees). The calculated values are a1 = 15 degrees, a2 = 32 degrees and a3 = 13 degrees.

5A and 5B are diagrams showing the intensity distribution of the focus light by the high-aperture lens of the present invention.

5A shows the intensity distribution of the focus light on the focal plane (X-Y plane), and it can be seen that it has a nearly circular distribution. That is, the ratio of long axis (0.68 lambda) to short axis (0.64 lambda) of the region having 50% intensity on the focal plane obtained by the optimized a1, a2, a3 as described above is 1.058.

5B shows the distribution of light intensity near the focus on the optical axis (Z axis). The distance between the points where the intensity is 50%, that is, the half width on the optical axis (Z axis) is 2.7 lambda. The ratio of long axis to short axis and optical axis obtained by polarization modulation can obtain circular intensity distribution and increased half width or extended DOF with little influence on the focus light distribution size or diffraction limit.

Table 1 below shows the degree of oval on the focal plane for each of the high-aperture lenses with a focal angle of 60 degrees when the unmodulated preceding polarized light enters and when the modulated three-layer polarized light enters through the three-layer polarization modulator. And DOF (half width on the Z axis).

Table 1

Unmodulated linearly polarized light Modulated Trilayer Polarization Increase and decrease Long axis (λ) 0.74 0.68 -0.06           Single axis (λ) 0.56 0.64 +0.08 Long axis vs short axis 1.321 1.058 0.263 Full width at half maximum on the Z axis (λ) 1.8 2.7 0.9

As can be seen from Table 1, when the incident light incident on the high-aperture lens is polarized-modulated, the intensity distribution of the focus light on the high-aperture lens is closer to a circle, and an expanded DOF can be obtained.

Therefore, the device of the present invention has a circular light intensity distribution on the focal plane by adjusting the polarization of the incident light so that it can have a uniform resolution and can deepen the DOF, thereby providing an effect of improving the yield in the lithography process of the semiconductor. do.

Claims (17)

In the polarization modulator for modulating the polarization state of the incident light, The incident light of the linearly polarized light is modulated so as to have different polarization states for each of the three regions, and the light traveling direction is Z-axis, and the axis orthogonal to the cross section of the light traveling direction is about the coordinate axis defined by the X-axis and Y-axis. Three regions may include a first region for modulating the linearly polarized incident light to have polarization parallel to an X axis; A second region for modulating the linearly polarized incident light to have polarization parallel to a Y axis; And a third layer polarization modulator having a third region for modulating the linearly polarized incident light to have polarization parallel to an X axis. And Three-layer polarized light for modulating the incident light of the high-numbered lens, characterized in that it comprises a high-numbered lens that the polarized modulated incident light passing through the three-layer polarization modulator passes through it to produce a focus light having a circular light intensity distribution Modulation device. delete The method of claim 1, The outer diameter w3 of the third region is A three-layer polarization modulator for modulating incident light of a high aperture lens, characterized in that the beam size of incident light. The method of claim 3, wherein The first to third regions are 3. The three-layer polarization modulator for modulating incident light of a high aperture lens, wherein the angle is defined as an angle with a focal point for each region of the focal light passing through the high aperture lens. The method of claim 4, wherein The high aperture lens A three-layer polarization modulator for modulating incident light of a high-aperture lens, characterized in that it has a focal angle (a) defined by a numerical aperture value. The method of claim 5, The focal angle (a) of the high aperture lens is And an angle with a focal point for the first to third regions. The method of claim 6, The focal angle (a) of the high aperture lens is An angle a1 formed by the boundary between the focal point and the first area, an angle a2 formed by the boundary between the focal point and the second area, and an angle formed by a boundary between the focal point and the third area (a3) The three-layer polarization modulator for modulating the incident light of the high aperture lens. The method of claim 7, wherein The outer diameter w1 of the first region of the three-layer polarization modulator is

Where a is the focal angle, w3 is the outer diameter of the third region, and a1 is the angle forming the boundary between the focal point and the first region A three-layer polarization modulator for modulating incident light of a high-aperture lens, characterized in that obtained. The method of claim 8, The outer diameter w2 of the second region of the three-layer polarization modulator is

Where a is the focal angle, w3 is the outer diameter of the third region, and a3 is the angle formed by the boundary between the focal point and the third region A three-layer polarization modulator for modulating incident light of a high-aperture lens, characterized in that obtained.      The method of claim 9,        The high aperture lens        3. The three-layer polarization modulator for modulating incident light of a high-aperture lens, wherein the light is focused at an angle a1 formed between the focal point and the boundary between the first area and the focal point in a polarized state tilted from the X axis to the focal point.       The method of claim 10,        The high aperture lens        The angle a1 between the focal point and the boundary between the first area and the angle a2 between the focal point and the second area between the focal point and the second area are focused in a polarized state maintained in the Y axis. Three-layer polarization modulation device for modulating the incident light of the water lens.      The method of claim 11,        The high aperture lens        The angle a2 between the focal point and the boundary between the second region and the angle a3 between the focal point and the boundary between the third region and the focal point are focused in a polarized state maintained on the X axis. Three-layer polarization modulation device for modulating the incident light of the water lens. A polarization modulator for modulating the polarization state of incident light incident on a high aperture lens having a focal angle (a), It includes a three-layer polarization modulator for modulating the incident light linearly polarized parallel to the X-axis transmitted through it into a different polarization state for each of the three regions, The three-layer polarization modulator includes a first region that modulates incident light to have polarization parallel to the X axis, a second region that modulates incident light to have polarization parallel to the Y axis, and a polarization parallel to the X axis. And a third region for modulating to have an incident light of the high aperture lens. The method of claim 13, The outer diameter w3 of the third region is A three-layer polarization modulator for modulating incident light of a high aperture lens, characterized in that the beam size of incident light. The method of claim 14, The first to third regions are 3. The three-layer polarization modulator for modulating incident light of a high aperture lens, wherein the angle is defined as an angle with a focal point for each region of the focal light passing through the high aperture lens. The method of claim 15, The outer diameter w1 of the first region of the three-layer polarization modulator is

Where a is the focal angle, w3 is the outer diameter of the third region, and a1 is the angle forming the boundary between the focal point and the first region A three-layer polarization modulator for modulating incident light of a high-aperture lens, characterized in that obtained. The method of claim 16, The outer diameter w2 of the second region of the three-layer polarization modulator is

Where a is the focal angle, w3 is the outer diameter of the third region, and a3 is the angle formed by the boundary between the focal point and the third region A three-layer polarization modulator for modulating incident light of a high-aperture lens, characterized in that obtained.

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