1. Field of the Invention
The present invention relates to a hologram, a hologram data generation method, and an exposure apparatus.
2. Description of the Related Art
A projection exposure apparatus has conventionally been employed to fabricate a micro-patterned semiconductor device such as a semiconductor memory or a logic circuit by using photolithography (printing). The projection exposure apparatus projects and transfers a circuit pattern formed on a reticle (mask) onto a substrate such as a wafer via a projection optical system.
A resolution R of the projection exposure apparatus is given by:
where λ is the exposure light wavelength, NA is the numerical aperture of the projection optical system, and k1 is a process constant determined by, for example, a development process.
The shorter the exposure light wavelength or the higher the NA of the projection optical system, the better the resolution. However, it might be difficult to further shorten the current exposure light wavelength because the transmittance of a glass material generally decreases as the exposure light wavelength shortens. It might be also difficult to further increase the NA of the projection optical system available at present because the depth of focus decreases in inverse proportion to the square of the NA of the projection optical system, and because it might be difficult to design and manufacture lenses to form a high-NA projection optical system.
Under the circumstances, there have been proposed resolution enhanced technologies (RETs) of improving the resolution by decreasing the process constant k1. One of these RETs is the so-called modified illumination method (or oblique illumination method).
The modified illumination method generally inserts an aperture stop, which has a light-shielding plate on the optical axis of an optical system, in the vicinity of the exit surface of an optical integrator which forms a uniform surface light source, thereby obliquely irradiating a reticle with exposure light.
The modified illumination method includes, for example, an annular illumination method and quadrupole illumination method that are different in the aperture shape of an aperture stop (i.e., the shape of the light intensity distribution). There has also been proposed another modified illumination method which uses a computer generated hologram (CGH) in place of an aperture stop, in order to improve the use efficiency (illumination efficiency) of the exposure light.
Along with an increase in the NA of the projection optical system, a polarized illumination method which controls the polarization state of exposure light is also required to increase the resolution of the projection exposure apparatus. The polarized illumination method illuminates a reticle with, for example, S-polarized light alone, which has a component in the circumferential direction of concentric circles about the optical axis. A contrast of the image to be formed might be enhanced by using the S-polarized light alone.
In recent years, there has been proposed a technique which exploits both the modified illumination method (the formation of a light intensity distribution having a desired shape, e.g., a quadrupolar shape) and the polarized illumination method (i.e., polarization state control).
For example, Japanese Patent Laid-Open No. 2006-196715 discloses a technique which implements both the modified illumination method and polarized illumination method using a light beam conversion element composed of a plurality of pairs of a form birefringence region and a diffraction region. Japanese Patent Laid-Open No. 2006-196715 describes controlling the polarization state using the form birefringence region and the shape (i.e., a reconstructed image) of the light intensity distribution at the predetermined plane using the diffraction region. The number of the pairs depends on kinds of polarization states formed on the predetermined plane.
U.S. Pat. No. 7,265,816 (or Japanese Patent Laid-Open No. 2006-5319) discloses a technique which can control the balance among four poles of a quadrupolar light intensity distribution typically formed by the modified illumination method and the polarized illumination method. U.S. Pat. No. 7,265,816 refers, after converting four circularly polarized lights into four linearly polarized lights different from each other with a quarter wave plate, to change the light intensity distribution at a predetermined plane by controlling the balance with using four separated CGHs which function as a diffractive optical element corresponding to each linearly polarized light.
A CGH design technique is disclosed in “Iterative method applied to image reconstruction and to computer-generated holograms”, OPTICAL ENGINEERING, Vol. 19, No. 3, May/June 1980, 297-305.
The conventional technique requires a plurality of the separated CGHs to form a reconstructed image composed of a plurality of polarization states, and the number of separated CGHs to be required depends on the number of a variety of polarization states.
When a plurality of CGHs combined with each other are used, an irradiance variation might occur in a reconstructed image if an optical integrator cannot sufficiently correct the intensity distribution of the incident light (for example, if the light impinges on only some of these CGHs).
The present invention provides a hologram which can reduce the irradiance variation.
According to an aspect of the present invention, a hologram which forms a light intensity distribution on a predetermined plane by using an incident light is provided. The hologram includes a plurality of cells configured to control both a phase of a first polarized light component, in a first polarization direction, of the incident light and a phase of a second polarized light component in a second polarization direction perpendicular to the first polarization direction. The plurality of cells are designed to form a portion, in an overlap region in which a first light intensity distribution region formed on the predetermined plane by the first polarized light component and a second light intensity distribution region formed on the predetermined plane by the second polarized light component are superposed on each other, having a polarization state different from the first and second polarized light components. A phase difference between the phase of the first polarized light component and the phase of the second polarized light component is a constant value in the portion, and the phase of the first polarized light component is diffused in the portion.
Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.
Exemplary embodiments according to the present invention will be described below with reference to the attached drawings. The same reference numerals denote the same members throughout the drawings, and a repetitive description thereof will not be given.
As shown in
The hologram 100 controls a phase of a first polarized light component (e.g., a first linearly polarized light component IL1), in a first polarization direction (e.g., X-polarization), of an incident light. The first linearly polarized light component IL1 forms a first light intensity distribution region on the predetermined plane PS.
The hologram 100 also controls a phase of a second polarized light component (e.g., a second linearly polarized light component IL2), in a second polarization direction (e.g., Y-polarization) perpendicular to the first polarization direction. The second linearly polarized light component IL2 forms a second light intensity distribution region on the predetermined plane PS.
The hologram 100 includes a plurality of cells 110 (e.g., a collection of cells 110) as shown in
The plurality of cells might be designed so that there is an overlap region in which the first light intensity distribution region formed on the predetermined plane PS and the second light intensity distribution region formed on the predetermined plane PS are superposed on each other.
For example, when the first linearly polarized light component IL1 forms the first light intensity distribution region LI1 as shown in
The plurality of cells 110 might be designed so that a portion PA is formed in the overlap region MA. In
A phase difference between the first linearly polarized light component and the second linearly polarized light component in each portion (e.g., PA1) might be a constant value. A value of the phase difference in each portion might be similar to or different from each other. The value of the phase difference can be selected from, but is not limited to, −π/2, 0, π/2, π, π/4, −π/4, 3π/4, and −3π/4.
The plurality of cells 110 might be designed to form such portions in the overlap regions (e.g., MA1). A phase difference between the phase of the first linearly polarized light component and the phase of second linearly polarized light component might be a constant value in the each portion. It is possible that the phase difference of each of the portions adjacent to each other might be different from or similar to each other.
The phase of the first linearly polarized light component is diffused in the portion (e.g., PA1). The diffused phase means that a phase distribution on the predetermined plane PS has a random phase. In other words, the diffused phase means that the phase distribution has a plurality of spatial frequencies. Regarding a reconstructed image, the phase distribution having the plurality of spatial frequencies means that the reconstructed image is formed by a light emitted from every point of the hologram. When the phase difference between the phase of the first polarized light component and the phase of second polarized light component is a constant value in a portion, if the phase of the first polarized light component is diffused in the portion, the phase of the second polarized light component is also diffused in the portion.
To form a polarization state different from the first and second linearly polarized light components in the portion, the hologram 100 might be designed in consideration of a phase difference between the first and second linearly polarized light components on the predetermined plane PS, or amplitude ratio (intensity rate) between the first and second linearly polarized light components on the predetermined plane PS, or both.
For example, when an incident light is a linearly polarized light in a polarization direction of +45° with respect to an X-axis, the polarization direction of the linearly polarized light is changed in a range from more than 0° to less than +90° with respect to an X-axis by controlling the amplitude ratio (the intensity rate). And also, the polarization direction of the linearly polarized light is changed in a range from less than 0° to more than −90° with respect to an X-axis by giving the phase difference of π and controlling the amplitude.
When an incident light is a linearly polarized light in a polarization direction of +45° with respect to an X-axis, the polarization direction of the linearly polarized light is converted into a circularly polarized light by giving the phase difference of π/2 or −π/2 between the first and second linearly polarized light components on the predetermined plane PS.
Shapes of the first light intensity distribution region LI1 shown in
A data generation method used to manufacture a computer generated hologram 100 is described next.
First, a desired light intensity distribution LI on the predetermined plane PS in
Second, a phase difference between a phase of the first linearly polarized light component in the first light intensity distribution region LI1 and a phase of the second linearly polarized light component in the second light intensity distribution region LI2. The phase difference is determined in accordance with a relationship between a polarization direction of the incident light and a polarization state of the light intensity distribution LI to be formed on the predetermined plane PS so that a portion which has a designed polarization state is formed in the overlap region MA.
Third, a first hologram data to form the first light intensity distribution region LI1 and a second hologram data to form the second light intensity distribution region LI2 is generated under an admissibility condition of diffusing the phase of the first linearly polarized light component (e.g., X-polarization) while maintaining the phase difference which is determined. The first and second hologram data can be called as a hologram data for X and Y-polarizations. When a phase distribution of the first linearly polarized light component on the predetermined plane PS is diffused under maintaining the phase difference, a phase distribution of the second linearly polarized light component on the predetermined plane PS is also diffused. The phase of the first linearly polarized light component might be diffused in the first light intensity distribution region LI1 entirely, and a diffused area might be optionally limited to the overlap region MA.
Finally, the hologram data for the first and second linearly polarized light components (e.g., X and Y-polarizations) are integrated with each other.
When the second light intensity distribution region is related to the first light intensity distribution region in symmetry for a light intensity distribution and a phase distribution, the second hologram data might be easily obtained in consideration of the symmetry after the first hologram data is generated.
The hologram data generation method is described in detail in examples below.
The hologram 100 which gives different phase distributions to the wavefronts of the first linearly polarized light component (e.g., X-polarization) and the second linearly light component (e.g., Y-polarized light) is explained in detail below.
To give different phase distributions to the wavefronts of X-polarization and Y-polarized light, the hologram 100 might independently control the wavefronts in the respective polarization directions. For example, in order to form two phase levels for each of the X- and Y-polarizations, it is possible to give binary phases to the wavefronts in each of the two polarization directions. For this purpose, four types of cell structures might be included in the hologram 100. Each of cells 110a to 110d shown in
As shown in
The plurality of cells 110 might include an anisotropic cell which has an anisotropic medium configured to change a polarization state of the incident light as described above.
The steps among the cells 110a to 110d in the Z direction can be represented by using a refractive index n of the isotropic medium 114, a refractive index nx of the anisotropic medium 112 with respect to X-polarization, and a refractive index ny of the anisotropic medium 112 with respect to Y-polarized light. This embodiment exemplifies a case in which n=nx>ny.
To configure a two-phase-level computer generated hologram as the hologram 100, a cell to shift a phase of π is necessary. To attain this state, thicknesses H1 of the anisotropic medium 112 of the cell 110a and the isotropic medium 114 of the cell 110c need satisfy:
A thickness H2 of the isotropic medium 114 of the cell 110b, that is, a difference H2 between the thickness of the cell 110c and that of the cell 110b or 110d (a difference H2 between the thickness of the isotropic medium 114 of the cell 110c and that of the isotropic medium 114 of the cell 110d) need satisfy:
Assuming X-polarization which impinges on the cell 110c as a reference, X-polarization which impinges on the cell 110a is in phase with the reference. Also, assuming Y-polarized light which impinges on the cell 110c as a reference, Y-polarized light which impinges on the cell 110a is π out of phase from the reference.
Assuming X-polarization which impinges on the cell 110c as a reference, X-polarization which impinges on the cell 110b is π out of phase from the reference. Also, assuming Y-polarized light which impinges on the cell 110c as a reference, Y-polarized light which impinges on the cell 110b is in phase with the reference.
Assuming X-polarization which impinges on the cell 110c as a reference, X-polarization which impinges on the cell 110d is π out of phase from the reference. Also, assuming Y-polarized light which impinges on the cell 110c as a reference, Y-polarized light which impinges on the cell 110d is also π out of phase from the reference.
In this manner, the computer generated hologram can give binary phases to the wavefronts in the two polarization directions respectively by using the cell structures of four types (cells 110a to 110d) shown in
A case in which nx=n=1.6 and ny=1.4 will be exemplified as a concrete numerical example. In this case, letting X be the wavelength of the incident light, the thicknesses H1 and H2 are 2.5λ and 0.833λ, respectively, that fall within few multiples of the wavelength λ. These values are realistic as the thicknesses of the cells of a computer generated hologram.
In one example, the anisotropic media 112 might include an anisotropic layer. The anisotropic media 112 of all cells may have identical optic axis directions. If the anisotropic media 112 of all the cells shown in
The optic axis means herein an axis along a direction in which, because the refractive indices in all directions perpendicular to a propagation direction of an incident light are constant in the anisotropic medium 112, no birefringence occurs even if non-polarized light impinges on the anisotropic cell so that ordinary and extraordinary rays match each other or have a minimum deviation if any.
In another example, the anisotropic media 112 might be included in an anisotropic cell. The anisotropic media 112 of respective cells may have different optic axis directions.
As described above, the plurality of cells 100 might include anisotropic cells including an anisotropic medium configured to change a polarization state of the incident light, and isotropic cells including an isotropic medium configured not to change a polarization state of the incident light.
Note that a function of setting light components in two polarization directions of the incident light to be in phase with, or π out of phase from each other, in the cells 110a0 to 110d0 of four types of the computer generated hologram 100 shown in
Thicknesses (the thicknesses in the Z direction) h1 of the first anisotropic cell 110a0 and second anisotropic cell 110b0, a thickness h2 of the first isotropic cell 110c0, and a thickness h3 of the second isotropic cell 110d0 can be represented by using the following three refractive indices (first to third refractive indices). The first refractive indices are a refractive index nE of the first anisotropic cell 110a0 with respect to X-polarization, and a refractive index nE of the second anisotropic cell 110b0 with respect to Y-polarized light. The second refractive indices are a refractive index no of the first anisotropic cell 110a0 with respect to Y-polarized light, and a refractive index no of the second anisotropic cell 110b0 with respect to X-polarization. The third refractive indices are refractive indices n of the first isotropic cell 110c and second isotropic cell 110d. This embodiment exemplifies a case in which nO>nE.
To configure a two-step computer generated hologram 100, a phase shift of π is necessary. To attain this state, the thicknesses h1 of the first anisotropic cell 110a0 and second anisotropic cell 110b0 need satisfy:
To form a wavefront matching the one obtained at the refractive index no of the first anisotropic cell 110a0 with respect to Y-polarized light and the refractive index no of the second anisotropic cell 110b0 with respect to X-polarization, the thickness h2 of the first isotropic cell 110c0 need satisfy:
Also, to form a wavefront matching the one obtained at the refractive index nE of the first anisotropic cell 110a0 with respect to X-polarization and the refractive index nE of the second anisotropic cell 110b0 with respect to Y-polarized light, the thickness h3 of the second isotropic cell 110d0 need satisfy:
A case in which nO=1.6, nE=1.4, and n=1.5 will be exemplified as a concrete numerical example. In this case, letting λ be the wavelength of the incident light, the thicknesses h1, h2, and h3 are 2.5λ, 2λ, and 3λ, respectively, that fall within few multiples of the wavelength λ. These values are realistic as the thicknesses of the cells of a computer generated hologram.
Each of the first anisotropic cell 110a0 and second anisotropic cell 110b0 may be formed from a diffraction grating (three-dimensional structure) which generates form birefringence. In other words, the anisotropic medium may include one of a birefringent material and a three-dimensional structure which generates form birefringence.
Each of the first anisotropic cell 110a1 and second anisotropic cell 110b1 is formed from a diffraction grating which generates form birefringence, as described above. Each of the first anisotropic cell 110a1 and second anisotropic cell 110b1 is formed, for example, from a one-dimensional diffraction grating having a periodic structure with a pitch P smaller than the wavelength of the incident light in order to prevent the generation of diffracted light components of orders other than the 0th order.
The first anisotropic cell 110a1 and second anisotropic cell 110b1 are configured such that the direction of the pitch of the periodic structure of the first anisotropic cell 110a1 is different from that of the second anisotropic cell 110b1. This makes it possible to attain a cell which advances the wavefront of X-polarization from that of Y-polarized light, and a cell which retards the wavefront of X-polarization from that of Y-polarized light.
Japanese Patent Laid-Open No. 2006-196715 discloses a diffraction grating made of quartz as an example of the diffraction grating which generates form birefringence. According to Japanese Patent Laid-Open No. 2006-196715, when quartz has a refractive index of 1.56 with respect to a wavelength of 193 nm, and the duty ratio of the diffraction grating in the form birefringence region is 1:1 (=0.5), a refractive index n⊥ of the diffraction grating in the direction of the pitch is 1.19, and a refractive index nII of the diffraction grating in a direction perpendicular to the pitch is 1.31.
Even when each anisotropic cell is formed from a diffraction grating which generates form birefringence, thicknesses h1′ of the first anisotropic cell 110a1 and second anisotropic cell 110b1 need satisfy equation (4) upon substituting h1′ for h1. Likewise, a thickness h2′ of the first isotropic cell 110c1 need satisfy equation (5) upon substituting h2′ for h2, and a thickness h3′ of the second isotropic cell 110d1 need satisfy equation (6) upon substituting h3′ for h3.
A case in which the first anisotropic cell 110a1 and second anisotropic cell 110b1 are made of quartz compatible with a wavelength λ=193 nm will be exemplified as a concrete numerical example. The refractive index of the quartz is assumed to be 1.56, a refractive index n⊥ of the diffraction grating in the direction of the pitch is assumed to be 1.19, and a refractive index nII of the diffraction grating in a direction perpendicular to the pitch is assumed to be 1.31, as described above. To obtain the thicknesses h1′ of the first anisotropic cell 110a1 and second anisotropic cell 110b1, the thickness h2′ of the first isotropic cell 110c1, and the thickness h3′ of the second isotropic cell 110d1 using equations (4) to (6), it is only necessary to substitute n⊥ for nE and substitute nII for nO. In this case, the thicknesses h1′ of the first anisotropic cell 110a1 and second anisotropic cell 110b1 are 4.17λ from equation (4). This value is equal to the thickness of a λ/2 plate as one type of wave plate. From equations (5) and (6), the thickness h2′ of the first isotropic cell 110c1 and the thickness h3′ of the second isotropic cell 110d1 are 1.41λ and 2.31λ, respectively, that are smaller than the thicknesses h1′ of the first anisotropic cell 110a1 and second anisotropic cell 110b1. In this manner, the thicknesses h1′ of the first anisotropic cell 110a1 and second anisotropic cell 110b1, the thickness h2′ of the first isotropic cell 110c1, and the thickness h3′ of the second isotropic cell 110d1 fall within the thickness of the λ/2 plate. 4.17λ is realistic as the thickness of the cell of a computer generated hologram.
This embodiment has exemplified a two-phase-level computer generated hologram as the hologram 100, so the hologram 100 can be formed from anisotropic cells having one thickness and isotropic cells having two thicknesses. However, the present invention is not particularly limited to the two-phase-level computer generated hologram, and is applicable to a computer generated hologram of a multiple of steps more than two phase levels which is formed from anisotropic cells having more than one thickness, and isotropic cells having more than two thicknesses. In this embodiment, the one-dimensional diffraction grating is used as the diffraction grating which generates form birefringence, and a two-dimensional diffraction grating may be used. The phase of the computer generated hologram is not limited to quantized levels (i.e., discrete levels), and the phase of the hologram might be changed continuously by changing the thickness of each cell continuously.
Note that although this embodiment has exemplified only the cell structure of the hologram 100, it may not be easy to bond materials having different properties, as shown in
In the
In this embodiment, it is described that the incident light is linearly polarized light including X-polarized light and Y-polarized light having the same amplitude assuming a case in which the hologram 100 forms a light intensity distribution including X-polarized light and Y-polarized light at the same ratio as in annular illumination. A hologram optionally can be designed to be compatible with the formation of a light intensity distribution including X-polarization and Y-polarization at different ratios by using polarized light including X-polarized light and Y-polarized light having different amplitudes as the incident light in order to obtain high efficiency. A partially coherent light can be used as the incident light. Circularly polarized light or elliptic polarization can also be used as the incident light, and in that case the thickness of each cell of the hologram 100 might be required to change.
A detailed design example of a computer generated hologram as the hologram 100 will be explained below with reference to a flowchart of
An example to design the light intensity distribution LI shown in
This target image illustrated in
Referring to
In the portion formed by S-polarization, the method to divide the light intensity distribution depends on the angle of S-polarization. In the portion formed by circularly polarized light, the light intensity distribution is divided on even for X and Y-polarizations.
In step S1004, the phase difference between X and Y-polarizations on the predetermined plane is determined. More specifically, values are applied into each portion of MA in
Therefore, the target image (
In step S1006, hologram data for X and Y-polarizations are generated under an admissibility condition of diffusing the phase of X-polarization while maintaining the phase difference as shown in
The phase difference in the overlap region is limited to maintain the determined value, but a phase itself is not limited. Therefore hologram data can be generated with optimization using iterative Fourier transform (i.e., Gerchberg-Saxton algorithm). More specifically, the admissibility condition of diffusing the phase means that random distribution might be used for the initial data for hologram data. In each iterative calculation step, hologram data for X and Y-polarizations are generated separately, then the phase in the overlap region on the predetermined plane might be shifted to maintain the phase difference condition shown in
The phase difference shown in
The phase other than the overlap region is replaced with 0 in
The diffused phase on the predetermined plane as shown in
In step S1008, the hologram data for X and Y-polarizations generated in step S1006 (
In
The structure of the whole hologram area can be generated by the same process.
There are four combinations of the phases of the X-polarization and Y-polarized light in the computer generated hologram, that is, (0, π), (π, 0), (0, 0), and (π, π). The cell structure shown in
The cell structure of a computer generated hologram compatible with four phase combinations will be shown in detail. For example, if the combination of the phases of the X-polarization and Y-polarized light is (0, π), the cell 110a shown in
When a hologram is formed by combining a plurality of CGHs such as described in the background of the present invention, an irradiance variation might occur in the reconstructed image if the optical integrator cannot sufficiently correct the intensity distribution of the incident light (for example, if the light impinges on only some of these CGHs.) According to the example 1, the illumination variation can be decreased.
When a plurality of separated CGHs are combined, unnecessary diffracted light might be generated due to structural discontinuity at the boundary between the separated-CGHs. According to the example 1, a deterioration of the reconstructed image due to the unnecessary diffracted light can be reduced.
A detailed design example of the hologram 100 is described next with reference to a flowchart of
An example that is line symmetric with respect to the line y=x (wherein x means the polarization direction of the X-polarization IL1, and γ means the second polarization direction of Y-polarization IL2) is described here. The hologram can be designed so that a phase distribution of the Y-polarization intensity distribution is equal to a phase distribution which is realized by flipping a phase distribution of the X-polarization IL1 intensity distribution along the axis. In other words, the hologram data for Y-polarization can be obtained by flipping the hologram data for X-polarization with respect to the line of Y=X.
The example describes y=x as the line symmetric axis. When the line symmetric axis is y=−x, the hologram will be designed by using the similar technique.
Referring to
In step S2004, the phase difference between X and Y-polarizations on the predetermined plane is determined.
In step S2006, phase symmetry between a phase distribution of the X-polarization and a phase distribution of the Y-polarization is determined.
In step S2008, hologram data for X-polarization are generated under an admissibility condition of diffusing the phase of X-polarization while maintaining the phase symmetry shown in
In step S2010, hologram data for Y-polarization is obtained by flipping the hologram data for X-polarization shown in
In step S2012, the hologram data for X and Y-polarizations generated in step S2008 and S2010 shown in
The phase state in the overlap region might be determined on the basis of a light intensity ratio between X and Y-polarizations. It is required to consider speckles for X and Y-polarizations to maintain the light intensity ratio because constructed images obtained by using the generated hologram is formed by speckles. The speckles for X and Y-polarizations might be similar to each other because the hologram data for X and Y-polarizations are symmetric each other. The speckles similar to each other can enhance degree of polarization of the reconstructed image.
In the design method described in the example 2, the light intensity ratio of the target image is always 1:1 because the symmetric axis in the method is y=x. Then, the light intensity ratio of the incident light is also always 1:1. Therefore, a degree of +45° as the polarization direction with respect to the X-axis of the incident light can always available.
The case of the light intensity distribution LI including phase distribution is four times rotational symmetric will be explained below. A flowchart shown in
The hologram comprising the plurality of cells can be designed so that a phase distribution of the Y-polarization light intensity distribution is equal to a phase distribution which is realized by rotating a phase distribution of the X-polarization light intensity distribution by an angle of 90 degrees. In other words, the hologram data for Y-polarization can be obtained by rotating the hologram data for X-polarization by an angle of 90 degrees.
Referring to
In step S2004, the phase difference between X and Y-polarizations on the predetermined plane is determined.
In step S2006, phase symmetry between a phase distribution of the X-polarization and a phase distribution of the Y-polarization is determined.
In step S2008, hologram data for X-polarization are generated under an admissibility condition of diffusing the phase of X-polarization while maintaining the phase symmetry shown in
In step S2010, hologram data for Y-polarization is obtained by rotating the hologram data for X-polarization shown in
In step S2012, the hologram data for X and Y-polarizations generated in
In the examples regarding symmetric targets, the described targets comprise only S-polarization, but target images might comprise not only S-polarization but also circularly polarized light and so on. In this case, phase symmetry on the predetermined plane is different from the phase symmetry shown in
A calculation time by using the symmetric data generating method shown in
The hologram may be also optionally generated with the flowchart shown in
In the above described examples, the design method for the target images whose portions in the overlap region MA formed by a linear polarization of which has a polarization direction different from the X and Y-polarizations or a circular polarization is explained. The target image may also optionally comprise an elliptic polarization. In this case, the phase difference to form a required target image on the predetermined plane PS may be selected from a value which is different from 0, π/2, π and −π/2.
Because the conventional arts require separated CGHs of types in a number equal to that of polarization directions of the target image, it might not be easy for the conventional arts to continuously change the polarization direction in each pixel. In contrast, this embodiment according to the present invention can provide a computer generated hologram which can continuously change the polarization direction in each pixel, as described above.
Although this embodiment has exemplified a case in which the computer generated hologram includes few cells, a light intensity distribution with a desired shape and polarization state can be formed even by increasing the number of cells of the computer generated hologram. Increasing the number of cells of the computer generated hologram may make it possible to decrease the sizes of pixels which divide the light intensity distribution (target image), thus forming a uniform light intensity distribution.
An exposure apparatus 1 to which the hologram 100 is applied will be explained below with reference to
The exposure apparatus 1 is a projection exposure apparatus which transfers the pattern of a reticle 20 onto a wafer 40 by the step & scan scheme. However, the exposure apparatus 1 can adopt the step & repeat scheme or another exposure scheme.
As shown in
The illumination apparatus 10 illuminates the reticle 20 on which a circuit pattern to be transferred is formed, and includes a light source 16 and illumination optical system 18.
The light source 16 is, for example, an excimer laser such as an ArF excimer laser with a wavelength of about 193 nm or a KrF excimer laser with a wavelength of about 248 nm. However, the light source 16 is not particularly limited to an excimer laser, and may be, for example, an F2 laser with a wavelength of about 157 nm or a mercury lamp with a narrow wavelength range.
The illumination optical system 18 illuminates the reticle 20 with light from the light source 16, and performs modified illumination on the reticle 20 in a predetermined polarization state while ensuring a predetermined illuminance. In this example, the illumination optical system 18 includes a light extension optical system 181, beam shaping optical system 182, polarization controller 183, phase controller 184, exit angle saving optical element 185, relay optical system 186, multibeam generation unit 187, polarization state adjusting unit 194, and the hologram 100. The illumination optical system 18 also includes a relay optical system 188, aperture 189, zoom optical system 190, multibeam generation unit 191, aperture stop 192, and irradiation unit 193.
The light extension optical system 181 deflects light from the light source 16 to guide it to the beam shaping optical system 182. The beam shaping optical system 182 shapes the section of the light from the light source 16 into a desired shape by converting the horizontal to vertical ratio of the section of the light from the light source 16 into a desired value (e.g., by changing the sectional shape from a rectangle to a square). The beam shaping optical system 182 forms a light beam with a size and an angle of divergence which are required to illuminate the multibeam generation unit 187.
The polarization controller 183 includes, for example, a linear polarizer and has a function of removing unnecessary polarized light components. It is possible to efficiently convert light from the light source 16 into desired linearly polarized light by minimizing polarized light components removed (shielded) by the polarization controller 183.
The phase controller 184 converts the linearly polarized light obtained by the polarization controller 183 into circularly polarized light by giving a phase difference of λ/4 to it.
The exit angle saving optical element 185 includes, for example, an optical integrator (e.g., a fly-eye lens or fiber bundle including a plurality of microlenses), and outputs the light at a predetermined angle of divergence.
The relay optical system 186 converges the light which emerges from the exit angle saving optical element 185 on the multibeam generation unit 187. The relay optical system 186 adjusts the exit surface of the exit angle saving optical element 185 and the incident surface of the multibeam generation unit 187 to hold the Fourier transform relationship (the relationship between the object plane and the pupil plane or that between the pupil plane and the image plane).
The multibeam generation unit 187 includes an optical integrator (e.g., a fly-eye lens or fiber bundle including a plurality of microlenses) for uniformly illuminating the polarization state adjusting unit 194 and computer generated hologram 100. The exit surface of the multibeam generation unit 187 forms a light source surface including a plurality of point light sources. The light which emerges from the multibeam generation unit 187 impinges on the polarization state adjusting unit 194 as circularly polarized light.
The polarization state adjusting unit 194 converts the circularly polarized light obtained by the phase controller 184 into linearly polarized light having a desired polarization direction by giving a phase difference of λ/4 to it. The light which emerges from the polarization state adjusting unit 194 impinges on the computer generated hologram 100 as linearly polarized light.
More specifically, in one example, the incident light generated from the light source 16 might include X and Y-polarizations, and an amplitude of X-polarization might be equal to an amplitude of Y-polarization.
The hologram 100 forms a light intensity distribution (e.g., a light intensity distribution LI as shown in
The aperture 189 has a function of passing only a light intensity distribution formed by the hologram 100. The computer generated hologram 100 and aperture 189 are set to hold the Fourier transform relationship.
The zoom optical system 190 enlarges a light intensity distribution formed by the hologram 100 at a predetermined magnification, and projects it onto the multibeam generation unit 191.
The multibeam generation unit 191 is inserted on the pupil plane of the illumination optical system 18, and forms, on its exit surface, a light source image (effective light source distribution) corresponding to the light intensity distribution formed at the position of the aperture 189. In this example, the multibeam generation unit 191 includes an optical integrator such as a fly-eye lens or cylindrical lens array. The aperture stop 192 is inserted near the exit surface of the multibeam generation unit 191.
The irradiation unit 193 includes, for example, a condenser optical system and illuminates the reticle 20 with an effective light source distribution formed on the exit surface of the multibeam generation unit 191.
The reticle 20 has a circuit pattern and is supported and driven by the reticle stage (not shown). Diffracted light generated by the reticle 20 is projected onto the wafer 40 via the projection optical system 30. Since the exposure apparatus 1 is of the step & scan scheme, it transfers the pattern of the reticle 20 onto the wafer 40 by scanning them.
The projection optical system 30 projects the pattern of the reticle 20 onto the wafer 40. The projection optical system 30 can be a dioptric system, catadioptric system, or catoptric system.
The wafer 40 is a substrate onto which the pattern of the reticle 20 is projected (transferred), and is supported and driven by the wafer stage (not shown). However, it is also possible to use a glass plate or another substrate in place of the wafer 40. The wafer 40 is coated with a resist.
As described above, the computer generated hologram 100 does not give a phase distribution to the wavefront of light polarized in a single direction, but two-dimensionally gives different phase distributions to the wavefronts of both X-polarization and Y-polarization. This makes it possible to form a light intensity distribution LI almost without generating any loss in light amount.
In exposure, light emitted by the light source 16 illuminates the reticle 20 by the illumination optical system 18. The light which bears the information of the pattern of the reticle 20 forms an image on the wafer 40 by the projection optical system 30. The illumination optical system 18 used for the exposure apparatus 1 can suppress any illumination variation and loss in light amount, and form a light intensity distribution with a desired shape and polarization state by the hologram 100. Hence, the exposure apparatus 1 can provide high-quality devices (e.g., a semiconductor device, an LCD device, an image sensing device (e.g., a CCD), and a thin-film magnetic head) with a high throughput and a good economical efficiency.
While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.