1. Field of the Invention
The present invention relates to an illumination optical system, an exposure apparatus, and a device manufacturing method.
2. Description of the Related Art
Devices such as a semiconductor device can be manufactured by a lithography process. A projection exposure apparatus is used in the lithography process. The lithography process includes a process of projecting a circuit pattern onto a substrate (e.g., a silicon substrate or glass substrate) coated with a photosensitive material, thereby transferring the circuit pattern onto the photosensitive material.
Along with the recent advance of the micropatterning of semiconductor devices, a pattern having a line width of 0.15 μm or less is transferred onto a substrate. The advance of the micropatterning of semiconductor devices improves the packing density, which makes it possible to manufacture low-power, high-performance semiconductor devices. Under the circumstances, a high demand has arisen for further advance of the micropatterning of semiconductor devices. Along with this demand, another high demand, in turn, has arisen for an improvement in the resolving power of the projection exposure apparatus.
The relationship among a resolving power R (a line & space pitch that can be transferred), a numerical aperture NA of the projection optical system, and a wavelength λ of the exposure light is given by:R=k1×λ/NA  (1)where k1 is a coefficient.
As is obvious from equation (1), to increase the resolving power (to decrease the value of R), it is only necessary to shorten the wavelength λ of the exposure apparatus or increase the numerical aperture NA of the projection optical system. For this reason, conventionally, the NA of the exposure apparatus has been increasing and the wavelength of the exposure light has been shortening.
Unfortunately, the recent study has revealed that along with an increase in NA, p-polarized light (a light component whose electric field vector lies on a plane including the light component and the normal to the substrate when it strikes the substrate) decreases the contrast of interference fringes in the resist. In view of this, to improve the resolving power by increasing the NA, it is necessary to attain polarized illumination which uses only s-polarized light (a light component whose electric field vector is perpendicular to that of the p-polarized light) by eliminating the p-polarized light along with an increase in NA.
This is because the resist is exposed depending on the strength of the electric field component of the light. As the NA increases, the electric field vector of the p-polarized light generates no interference fringes, resulting in an intensity distribution having a uniform intensity irrespective of the position on it.
Assume a coordinate system as shown in FIG. 2, on which interference fringes are formed by interference between two diffracted light beams E+ and E−. This specification assumes the z direction as the optical axis direction, and the z-axis as the normal to the x-y plane. Note that when the optical axis is bent by a mirror, the z direction is also bent. That is, this specification defines the x, y, and z directions on a relative coordinate system which uses the optical axis direction as a reference.
Referring to FIG. 2, the diffracted light beams E+ and E− each include s-polarized light (amplitude: Es) whose electric field vector is parallel to a substrate W, and p-polarized light (amplitude: Ep) perpendicular to the s-polarized light.
The diffracted light beams E+ and E− are given by:
                              E          +                =                              (                                                                                                                                                                                    -                            Ep                                                    ⁢                                                                                                          ⁢                          cos                          ⁢                                                                                                          ⁢                          θ                                                                                                                                    Es                                                                                                                                                                                    -                      Ep                                        ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    θ                                                                        )                    ⁢                      ⅇ                          2              ⁢                              πⅈ                ⁡                                  (                                      vt                    -                                                                  z                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        θ                                            λ                                        +                                                                  x                        ⁢                                                                                                  ⁢                        sin                        ⁢                                                                                                  ⁢                        θ                                            λ                                                        )                                                                                        (        2        )                                          E          -                =                              (                                                                                                      -                      Ep                                        ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    θ                                                                                                Es                                                                                                  Ep                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    θ                                                                        )                    ⁢                      ⅇ                          2              ⁢                              πⅈ                ⁡                                  (                                      vt                    -                                                                  z                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        θ                                            λ                                        -                                                                  x                        ⁢                                                                                                  ⁢                        sin                        ⁢                                                                                                  ⁢                        θ                                            λ                                                        )                                                                                        (        3        )            where ν is the frequency, and λ is the wavelength. For the sake of simplicity, the diffracted light beams E+ and E− are assumed to be 45° linearly polarized light beams in each of which the s-polarized light is in phase with the p-polarized light.
The sum of the diffracted light beams E+ and E− is the amplitude of interference fringes and given by:
                                          E            +                    +                      E            -                          =                              (                                                                                                      -                      2                                        ⁢                    Ep                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                                                    x                              ⁢                                                                                                                          ⁢                              sin                              ⁢                                                                                                                          ⁢                              θ                                                        λ                                                                          )                                                                                                                                                              2                    ⁢                    Es                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                                                    x                              ⁢                                                                                                                          ⁢                              sin                              ⁢                                                                                                                          ⁢                              θ                                                        λ                                                                          )                                                                                                                                                                                    -                      2                                        ⁢                    iEp                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                                                    x                              ⁢                                                                                                                          ⁢                              sin                              ⁢                                                                                                                          ⁢                              θ                                                        λ                                                                          )                                                                                                                  )                    ⁢                      ⅇ                          2              ⁢              π              ⁢                                                          ⁢                              ⅈ                ⁡                                  (                                      vt                    -                                                                  z                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        θ                                            λ                                                        )                                                                                        (        4        )            
The square of the absolute value of this amplitude is the intensity of the interference fringes and given by:
                                                                                                                                                      E                      +                                        +                                          E                      -                                                                                        2                            =                            ⁢                                                4                  ⁢                                      Ep                    2                                    ⁢                                      cos                    2                                    ⁢                  θ                  ⁢                                                                          ⁢                                                            cos                      2                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                                              x                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                            θ                                                    λ                                                                    )                                                                      +                                                                                                      ⁢                                                4                  ⁢                                      Es                    2                                    ⁢                                                            cos                      2                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                                              x                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                            θ                                                    λ                                                                    )                                                                      +                                  4                  ⁢                                      Ep                    2                                    ⁢                                      sin                    2                                    ⁢                                                            θsin                      2                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                                              x                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                            θ                                                    λ                                                                    )                                                                                                                                              =                            ⁢                                                4                  ⁢                                      (                                                                  Es                        2                                            +                                                                        Ep                          2                                                ⁢                        cos                        ⁢                                                                                                  ⁢                        2                        ⁢                        θ                                                              )                                    ⁢                                                            cos                      2                                        ⁡                                          (                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                                              x                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                            θ                                                    λ                                                                    )                                                                      +                                                                                                      ⁢                              4                ⁢                                  Ep                  2                                ⁢                                  sin                  2                                ⁢                θ                                                                        (        5        )                                          In          ⁢                                          ⁢          equation          ⁢                                          ⁢                      (            5            )                          ,                  the          ⁢                                          ⁢          term          ⁢                      :                                                                                        cos          2                ⁡                  (                      2            ⁢            π            ⁢                                                  ⁢                                          x                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                θ                            λ                                )                                    (        6        )            expresses the oscillation amplitude of the interference fringes. In this case, the intensity distribution of a line & space pattern has a period λ/sin θ in the x direction.
When a micropattern is projected using a high-NA projection optical system, the angle θ between the z-axis and the diffracted light beam becomes larger than when a normal one is used. For example, FIG. 3 shows the angle θ between the z-axis and the diffracted light beam in a photosensitive material (the refractive index in a resist: 1.7) when a line & space pattern having a period of L nm is projected using an ArF laser beam having a wavelength λ=193 nm. The angle θ between the z-axis and the diffracted light beam becomes 45° when the period roughly falls below 160 nm.
As the angle θ becomes 45°, cos 2θ in the coefficient of the term expressed by equation (6) becomes zero, and the term expressed by equation (6) therefore becomes zero. For this reason, the amplitude Ep of the p-polarized light is not reflected on the term of the oscillation amplitude of the interference fringes at all, but is reflected on only sin2 θ that expresses interference fringes which do not oscillate in the x direction. The above-described fact demonstrates that the p-polarized light merely decreases the contrast of the interference fringes.
Whether the diffracted light beam is p-polarized or s-polarized is determined in accordance with the relationship between the diffracted light beam and the substrate. In other words, since the above description is given assuming s-polarized light and p-polarized light for a pattern which extends in the y direction and has a periodicity in the x direction, the s-polarized light is a Y-polarized light component whose electric field vector points in the y direction, and the p-polarized light is an X-polarized light component whose electric field vector points in the x direction. Conversely, when a pattern which extends in the x direction and has a periodicity in the y direction is used, a diffracted light beam is generated in the y direction. In this case, the s-polarized light is an X-polarized light component whose electric field vector points in the x direction, and the p-polarized light is a Y-polarized light component perpendicular to the s-polarized light. In other words, an incident light beam which is s-polarized for a pattern having a periodicity in the x direction turns into that which is p-polarized for a pattern having a periodicity in the y direction. Note that the polarization state changes depending on the reference surface and the light beam incident direction.
As described above, the p-polarized light decreases the contrast of an image in an exposure apparatus having a high-NA projection optical system. To obtain a high-contrast image, it is effective to perform exposure using exposure light including a relatively small amount of p-polarized light and a relatively large amount of s-polarized light. An illumination system which provides polarized illumination, that illuminates the mask in a predetermined polarization state, is therefore important for high-NA lithography in the future.
FIG. 4 is a view showing the polarization states on the pupil plane of an illumination system attained by the illumination system which provides polarized illumination. Y-polarized low-σ illumination is effective in transferring a repetitive pattern in the x direction when used together with an Alt-PSM. Note that σ is called a coherence factor, which is obtained by dividing the NA of the illumination optical system on its exit side by that of the projection optical system on its incident side. X-polarized low-σ illumination is effective in transferring a repetitive pattern in the y direction when used together with an Alt-PSM. Y-polarized X-dipole illumination is advantageous to transferring a repetitive pattern in the x direction when used together with a binary mask or a halftone mask (also called an Att-PSM). X-polarized Y-dipole illumination is effective in transferring a repetitive pattern in the y direction when used together with a binary mask or Att-PSM. Tangentially polarized crosspole illumination is effective in transferring a pattern as a mixture of repetitive patterns in both the x and y directions when used together with a binary mask or Att-PSM. Tangentially polarized annular illumination is effective in transferring a pattern as a mixture of repetitive patterns in various directions when used together with a binary mask or Att-PSM. The tangential polarization means a polarization state in which the electric field vector points in a direction nearly perpendicular to the direction of the center of the optical axis at each point on the pupil of the illumination system. Radially polarized 45°-quadrupole illumination is effective in transferring a contact hole pattern when used together with a Cr-less PSM. The radial polarization means a polarization state in which the electric field vector points in the direction of the center of the optical axis at each point on the pupil of the illumination system.
FIG. 5 is a view showing an arrangement example of a projection exposure apparatus having an illumination optical system which illuminates an original with polarized light. An example of this projection exposure apparatus is disclosed in, e.g., PCT(WO) 2004/051717.
A light source 1 provides light to the illumination optical system. The light source 1 is, e.g., an excimer laser. A waveplate (polarization control unit) 2 is, e.g., an optical element made of a birefringent glass material such as quartz crystal or magnesium fluoride. The waveplate 2 collectively converts polarized light provided by the light source 1 into that in a predetermined polarization state.
A neutral density filter (ND) 3 is used to change the illuminance of the illumination light in accordance with the sensitivity of a photosensitive material applied on a substrate 17.
A microlens array 4 makes the incident light emerge with a specific angular distribution so that it enters an optical system, which is set at the succeeding stage of the microlens array 4, while maintaining the same properties, even if the light from the light source 1 is shifted or decentered from the optical axis of the illumination optical system due to vibration of the floor or exposure apparatus. A condenser lens 5 projects the light which has emerged from the microlens array 4 onto a CGH (Computer Generated Hologram) 61. The CGH 61 generates arbitrary diffracted light to form a desired light distribution on the A plane via a condenser lens 7. A microlens array 62 is set to be exchangeable with the CGH 61. When the microlens array 62 is inserted in the optical path, it forms a uniform light distribution on the A plane via the condenser lens 7. A variable magnification relay lens 8 enlarges or reduces the distribution formed on the A plane, and projects it onto an optical integrator 10.
A polarization control unit 9 is formed by arraying a plurality of waveplates, and is used to form effective light sources, which have a plurality of polarization states, on the pupil plane of the illumination optical system. FIG. 4 is a view illustrating effective light sources having a plurality of polarization states.
FIG. 9 is a view showing an arrangement example of the polarization control unit 9. FIG. 9 shows the polarization control unit 9 when seen from the optical axis direction. The region on the pupil is divided into eight partial regions. In each partial region, a waveplate compatible with a polarization state to be formed in it is arranged.
The optical integrator 10 forms a plurality of secondary sources at the position of the pupil of the illumination optical system (on the exit surface of the optical integrator 10). The optical integrator 10 can be formed as, e.g., a fly-eye lens or microlens array.
A condenser lens 11 superposes light beams obtained by wavefront splitting of the incident light by the optical integrator 10 to form a nearly uniform intensity distribution on the B plane. A half mirror 12 splits the light toward an exposure amount sensor 13 for controlling the exposure amount. A relay optical system 14 projects the light having the nearly uniform intensity distribution formed on the B plane onto an original (reticle) 15.
A projection optical system 16 projects a circuit pattern drawn on the original 15 onto the substrate (wafer) 17 coated with a photosensitive material. A substrate stage 19 aligns the substrate 17. The substrate stage 19, for example, drives the substrate 17 by scanning for scanning exposure or moves the substrate 17 step by step to switch the shot region. The substrate stage 19 mounts an illuminometer 18. The illuminometer 18 drives the substrate stage 19 at an arbitrary timing so as to be inserted into the exposure region, thereby measuring the illuminance in the exposure region. A control device 20 controls the light source 1 so that the exposure amount of the substrate 17 reaches a target one, on the basis of the output from the exposure amount sensor 13.
To perform polarized illumination by controlling the light polarization state by a waveplate, the waveplate must be fabricated so as to generate a precise phase difference. Details of this fabrication will be explained with reference to FIG. 6. Letting d be the substrate thickness, and ΔN be the birefringence amount of a birefringent glass material, a ½-waveplate 101 made of this material must be fabricated so as to satisfy a phase difference δφ of (180+360×m) degree (m: natural number) with respect to light having a wavelength λ. The phase difference significantly changes even when the thickness d of the waveplate 101 shifts from a target value by only several micrometers, so the thickness d must be controlled precisely.
To generate a precise phase difference by the waveplate 101 made of a birefringent glass material, it is also necessary to set the incident angular range with respect to the waveplate 101 to be relatively narrow. When the light enters the waveplate 101 at an angle θ with respect to the normal incident light as shown in FIG. 6, the length of an optical path that passes through the waveplate 101 increases more than when the light vertically enters the waveplate 101. Therefore, the exit light from the waveplate 101 exhibits a phase error of Δ degree.
Consider a case in which light enters a pair of waveplates (0th-order ½-waveplates) made of a birefringent glass material as shown in FIG. 7 with a certain angle. FIG. 8 shows the result of simulating the purity of polarization while changing the thickness of the waveplates.
Letting Ix be the intensity of light which oscillates in the x direction, and Iy be that of light which oscillates in the y direction, the purity of polarization is defined as Ix/(Ix+Iy). The polarization state of light which enters the waveplates is Y-polarization (Iy=1 and Ix=0), and the waveplates each are a ½-waveplate whose fast axis is in the 45° direction with respect to the X-axis. Since incident light having an incident angle of 0° (Y-polarized light) is converted into X-polarized light by the ½-waveplates into X-polarized light, the purity of polarization is 1.
FIG. 8 shows the relationship between the thickness d (mm) of the waveplates and the purity of polarization. The ordinate and abscissa indicate the incident angles of the incident light with respect to the waveplates in the x and y directions, and the color density represents a change in the purity of polarization. The white color indicates high purity of polarization, and the black color indicates low purity of polarization. The result shown in FIG. 8 reveals that the purity of polarization of the exit light depends on the incident angle and the thickness of the waveplates. The larger the thickness of the waveplates and the larger the incident angle, the larger a change in the purity of polarization.
The above-described fact reveals that the purity of polarization on the target illumination surface decreases when a thick waveplate is used and a waveplate is arranged at a position at which the incident angular distribution exhibits a large incident angle in a projection exposure apparatus. In this case, the image contrast decreases and therefore an ED window reduces, resulting in degradation in the yield of a chip. When a waveplate made of a birefringent glass material is used for an exposure apparatus, it is desirable to arrange a thin waveplate (which, preferably, has a thickness of 0.5 mm or less) at a position at which the incident angle is small (preferably, ±3° or less).
Birefringent glass materials such as quartz crystal and fluoride magnesium each have a limit of a fabricable outer diameter from the viewpoint of limitations associated with a furnace to grow its crystal. In general, the diameter of the fabricable crystal of quartz crystal is up to about 70 mm. A crystal of quartz crystal having a diameter larger than that value takes much time for crystal growth, and it is difficult to control impurities contained in it. For these reasons, such a crystal is very expensive and is therefore hard to supply stably. To use a waveplate made of quartz crystal produced commercially, it is necessary to set the light beam effective diameter of the waveplate to 70 mm or less.
The incident angle and the light beam diameter have a tradeoff relationship in the optical path. This is known as the general principle of optics and is introduced as the Smith-Helmholtz formula in, e.g., Max Born and Emil Wolf, “Principles of Optics I” trans. Toru Kusakawa and Hidetsugu Yokota, Tokai University Press, pp. 225-228.
To obtain a good purity of polarization, a waveplate must be arranged at a position at which the incident angle is small. However, at the position at which the incident angle is small, the light beam diameter is large, so a required size of the waveplate is large. The size of the waveplate is subject to the limitations on the manufacture of the birefringent glass material, as described above. In view of this, a position to arrange the polarization control unit 9 has conventionally been determined to satisfy the limit of the outer diameter of the birefringent glass material and obtain its largest shape, as shown in the right view of FIG. 9.
In recent years, however, it is demanded to attain optimal polarization states for individual exposure conditions, e.g., special polarization states as shown in FIG. 10.
When the polarization state in a relatively large partial region distributed on the pupil of the illumination optical system is controlled by a waveplate arranged near the pupil, a required outer shape of the waveplate exceeds the limit of the outer shape of the birefringent glass material. On the other hand, when a waveplate is arranged at a position at which the light beam effective diameter is small to be able to fabricate the waveplate, the incident angle with respect to the waveplate increases. This makes it impossible to obtain a good purity of polarization.