Optical Design Works

The first high-aperture UV optical systems were developed in the beginning of the XXth century when the first monochromatic UV micro-objectives for ultra-high resolution microscopy were introduced. These objectives had a NA value as large as 0.35, the working wavelength was at 280 nm (magnesium line) and lenses were made from fused quartz.

The intensive research on lithographic optics design started in the 1960s together with the integral circuits invention. The pioneers of lithography used photographic objectives for the lithographic projection. However in the late 1960s companies like CERCO, Carl Zeiss and IBM started developing ultraviolet reduction lenses for production of masks and later for projection onto the wafer. These schemes were based on photographic objectives as well but they had a significant difference required by the orthoscopic condition. Most of them were realized on the base of classical Gauss-type objective with adding several correction components. One of these objectives introduced by IBM in 1974 and called Lentar is shown in Figure 1. The materials for the lenses were glasses from the Schott catalog.

Figure 1. Lithographic objective Lentar (1974) with image side NA = 0.2,

image field size 15 × 15 mm², working wavelength 405 nm,  reduction ratio 0.2.

In optical projection lithography, the resolution d of an objective (feature size) at the diffraction limit is given by the expression

.                                                    (1)

In this equation l is the wavelength, NA is numerical aperture of the objective, and k₁ is an empirical constant. NA is defined by the formula

,                                                 (2)

whereq is the half-angle of the image-forming light cone at the image side and n is the index of refraction of the medium in image space. It is known from optics theory that in the case of idealized conditions for two incoherent point sources, the Rayleigh criterion implies that k₁ = 0.61 and then d is a distance between the central maximum of the Airy distribution and its first minimum. In lithographic practice, this coefficient depends on lens aberrations, illumination conditions (such a degree of coherence and intensity distribution in the aperture plane), mask structure, resist properties, process conditions, operator skills etc. It follows from the expression (1) that resolution can be improved in three ways: by increasing the numerical aperture, by shortening the exposure wavelength, and by decreasing the value of k₁.

Figure 2. Depth of focus of optical system. The depth of focus is defined by permissible spot size at  the image plane.

Optical resolution depends also on the depth of focus (DOF), because with the increase of NA the optical system becomes very sensitive to defocus. In common case the depth of focus for diffraction limited optical system is defined as half the distance along the optical axis between the central diffraction maximum and the first zero of the Airy distribution and it is given by the approximate expression

.                                                            (3)

However in lithography an effective depth of focus is defined as

,                                                        (4)

where k₂ is also an empirically determined constant (it is a specific lithographic process-related factor as well) and n is the index of refraction of the medium in image space. Eliminating NA from (1) and (4) we obtain

.                                                         (5)

In practice, the coefficients k₁ and k₂ are experimentally determined for each exposure tool. At high numerical aperture, the formulae above have to be adopted.

As it follows from equations (1) and (4) the resolution can be improved by increasing NA, and by decreasing the factors k₁, k₂ and the wavelength. Since 1960s lithographers have been developing technologies at progressively shorter wavelengths. In the past, the used wavelengths were 436 nm (g-line), 405 nm (h-line) and 365 nm (i-line). In the 1970s and early 1980s, optical exposure tools operated at 400 nm on average, and the feature sizes were always larger than the working wavelength of the exposure tool. Currently, most systems use 248 nm and 193 nm. The sources of radiation are a KrF excimer laser at 248 nm and an ArF excimer laser at 193 nm. In the future, wavelengths could be shortened to 157 nm (F₂ laser) or less. At each step to lower wavelength and higher NA, besides other issues, lithographers should find solutions for the source, the lens material, and the required polishing accuracy. An example of an optical system working at a wavelength of 248 nm is shown in Figure 3.

Figure 3. Lithographic objective from US Patent 5,805,344 (1998) with image side NA = 0.56,

image field size 15 × 15 mm², working wavelength 248 nm, reduction ratio 0.25.

The development of polishing and measurement techniques allowed a decrease of number and of the size of components in the optical layout by using lens surfaces with an aspherical shape (aspheres). The design possibilities were widened as well by using catadioptric objectives, e.g. by combining reflective mirror surfaces and refractive lens elements. In the system shown in Figure 4 the plane mirror allows to produce a compact objective and the combination of a beam splitter and a concave mirror allows a reduction of astigmatism and chromatic aberrations.

Figure 4. Lithographic objective from US Patent 4,953,960 (1990) with image side NA = 0.45,

image field size 15 × 15 mm², working wavelength 248 or 193 nm,  reduction ratio 0.25.

Recent breakthroughs in optical fabrication technology enable high-volume production of ultra-high-precision glass optics. Fused silica, a glass produced by melting crystal quartz, is the primary optical material used for 365-, 248- and 193-nm lithography. Calcium fluoride is used as a companion material to fused silica for achromatization at 193 nm and it is also used in areas of high flux because of its high laser damage resistance. Only this material can be used for optical systems working at 157 nm because of the high absorption of fused silica at this wavelength. However, usage of calcium fluorideis limited by its birefringence and inhomogeneity. These difficulties reflected on the design solution shown in Figure 5, which has small number of lenses but has a disadvantage because of mirror obscuration.

Figure 5. Lithographic objective from US Patent 6,757,051 Embodiment 1 (2002) with image side NA = 0.75, field size 20 × 20 mm², working wavelength 157 nm, reduction ratio 0.25.

It can be observed that, in parallel with the decreasing working wavelength, optical designers are vigorously developing systems having higher numerical apertures (from  0.2 in 1970s up to 0.9 nowadays). An example of such a system with NA=0.8 is shown in Figure 6. With the increase of NA and decreasing wavelength, different design challenges are encountered; in particular because of the shallow depth of focus, the distance between the surface of the last lens and the wafer should be controlled with high accuracy. The field size is also currently increasing in order to produce larger chips. This can be achieved either by optical design adaptation or by scanning object and image through the highly corrected objective field.

Figure 6. Lithographic objective from US Patent 6,757,051 Embodiment 5 (2002) with image side NA = 0.8, field size 15 × 15 mm², working wavelength 157 nm, reduction ratio 0.25.

The alternative for increasing NA is changing the refractive index of the medium in front of the wafer as it can be seen from relation (2). This immersion technique seems to be a very promising technology which can postpone or even make superfluous the 157 nm lithography generation.

Lithographers are also working on decreasing coefficients k₁ and k₂. Nowadays tool vendors and process developers are pushing k₁ to the value of 0.3 (very close to the theoretical value of 0.25) and k₂ to 1, which is usually achievable with good-quality objectives. Equation (5) shows explicitly that at the same NA and the same lens resolution, a shorter wavelength gives a larger depth of focus. From the viewpoint of lens resolution, this is the incentive for exploring shorter wavelengths, even when a longer wavelength seems adequate. Another observation is that a smaller value of k₁ increases the depth of focus quadratically. Since different resolution enhancement techniques are used such as phase-shift masks, better photoresists, improved  process control and off-axis illumination schemes, it is possible to achieve a smaller k₁  and extend the depth of focus.

Currently immersion lithography generations are under development. The next generation will be the Extreme Ultra Violet (EUV) lithography. This generation operates with a wavelength in the range of 10 to 14 nm (Xe-laser). There is no material that can be transparent at this wavelength and optical systems should consist of mirrors only. The number of mirrors should be minimized because the value of the reflectivity of a single reflector doesn't exceed 70%. In order to provide the designer with enough parameters to correct aberrations these mirrors should be extremely high-order aspheres. The example of this optical system is shown in Figure 7. The first operational EUV system is expected around the year 2010.

Figure 7. Lithographic objective from US Patent 5,815,310 (1998) with image side NA = 0.25, annular width of the field 1.5 mm, working wavelength 13 nm, reduction ratio 0.25.

Lithographers consider the possibility of X-ray lithography as well, but at the moment it is difficult to predict its future.