Measuring Birefringence in Calcium Fluoride at 157 nm

Bob Wang, Mike Ward, Rick Rockwell and Jennifer List

As a practical matter, residual birefringence is supplanting intrinsic birefringence as a more important parameter for product quality control.

In recent years, leading-edge optical lithography has been moving to ever-shorter wavelengths: from 248 nm (KrF excimer laser) to 193 nm (ArF excimer laser) and now to 157 nm (F₂ excimer laser). At 157 nm, calcium fluoride (CaF₂) is the primary lens material used in step-and-scan systems because of its optical properties and its readiness for mass production.

These systems require extremely high quality material. Three parameters are especially critical: low absorption, high homogeneity of index of refraction and low-level linear birefringence, which we will hereafter call simply birefringence. This last parameter in particular has taken on increased significance with the push toward shorter wavelengths.

Exploring birefringence

Birefringence is an anisotropy in refractive indices along different crystal axes when working with linearly polarized light.¹ For example, calcite, one of the most common uniaxial crystals in polarization optics, has two principal indices of refraction. CaF₂ is a single crystal belonging to the cubic group characterized by a high degree of symmetry (four- and threefold rotation axes).

One assumption used to be that single crystals in the cubic group have isotropic optical properties, particularly, the index of refraction.¹ Last year, however, John Burnett and colleagues at the National Institute of Standards and Technology in Gaithersburg, Md., determined the intrinsic birefringence in CaF₂ at 157 nm to be Δn = _—110 — n₀₀₁ = -1.12 x 10^—6, or 11.2 ±0.4 nm/cm.

The scientists believe this intrinsic birefringence at short wavelengths comes from a symmetry-breaking effect of the finite wave vector of the photon on the symmetry of the light-matter interaction in cubic crystals.^2,3 This level of birefringence is more than 10 times higher than the tolerance of the optical lithography industry. Only by applying complicated correction designs is the industry able to reduce the effect of intrinsic birefringence to an acceptable level.⁴
Stress factors

Besides intrinsic birefringence, external mechanical stress or residual stress in bulk materials, which may be introduced during the materials’ growth and production phase, can also induce birefringence via the photoelastic effect. The increasingly stringent requirements for low-aberration optics used in step-and-scan systems have mandated improved specifications and control of birefringence at extremely low levels (preferably <0.5 nm/cm).

Although positioning optical components at different crystal orientations can correct for intrinsic birefringence, this is not the case for residual birefringence, which is subsequently emerging as a more critical parameter for product quality control.

For industrial quality control, instead of using Δn, it is easier to express birefringence according to retardation magnitude (nm) and fast-axis angle. It also is possible to normalize retardation to the thickness of the sample (nm/cm) through which the light beam passes. The relationship between retardation values δ (nm), Δn and the thickness of the measured sample, D (cm), is

δ (nm) = Δn x D (cm)x 10⁷.
Since the discovery of intrinsic birefringence at 157 nm, the optical lithography industry has developed a critical interest in measuring birefringence at that and other lithography wavelengths. In response to this need, International Sematech awarded Hinds Instruments a contract to expedite the development of a deep-UV birefringence measurement system to characterize birefringence in CaF₂ at 157 nm.

The resulting deep-UV birefringence measurement system uses a deuterium lamp as the light source and a monochromator to select the wavelength, with the light from that device collimated by a CaF₂ lens (Figure 1). The lens is followed by a Rochon polarizer at —45°, a photoelastic modulator at 0°, a sample mounted on an X-Y scanning stage, another photoelastic modulator at 45°, another Rochon polarizer at 90° and, finally, a photomultiplier tube. The optical train arrangement is vertical to minimize any birefringence that horizontal mounting might induce. All of the optical components reside in a nitrogen environment (O₂ < 10 ppm) because oxygen absorbs light at 157 nm.

Figure 1. The optical setup of the deep-UV birefringence measurement system developed at Hinds is vertical to eliminate any birefringence induced by horizontal mounting of the sample.

The electronic signals generated at the detector have both AC and DC components. The AC signal containing the birefringence information is processed using two lock-in amplifiers. The equipment processes the DC signal, representing the average light intensity reaching the detector, using a special function of one of the two lock-in amplifiers, which is equivalent to passing the detector signal through an electronic low-pass filter and an analog-to-digital converter. A PC records resulting data and calculates retardation magnitude and fast-axis angle.

The key optical components in the instrument are the photo-elastic modulators.⁵ Such resonant devices produce polarization modulation of a light beam with a precise sinusoidal waveform. This, in turn, provides high sensitivity and accuracy in measuring birefringence.⁶

The system can measure birefringence in any optical material transparent at 248, 193 or 157 nm.⁷ This includes quantification of both residual and intrinsic birefringence problems. In-house testing indicates the device also provides high repeatability (3 σ/mean <1 percent) at a low noise level (0.01 nm).

To determine the noise level of the system, we first took a series of measurements with no sample present. This data set of approximately 450 data points gives an average of 0.0092 nm and a standard deviation of 0.0046 nm.⁷ To test the repeatability, we measured samples at different retardation levels repeatedly at fixed sampling spots. The data set of more than 400 data points has a mean of 5.64 nm and a standard deviation of 0.014 nm. The 3 σ (three times the standard deviation) value is about 0.7 percent of the mean for this test, which represents a high level of instrumental repeatability. Furthermore, the measured fast-axis angles of the same sample are within ±0.1°.

Mapping birefringence

Using the deep-UV birefringence measurement system called Exicor, researchers have mapped the retardation of several CaF₂ cubes at 157 (Figure 2a), 193 and 248 nm (Figure 2b). In these maps, the light beams were propagating along the (110) axis, this being the orientation in which the intrinsic birefringence (n_—110 — n₀₀₁) is measured. The birefringence map at 193 nm has a similar birefringence pattern.

Figure 2. Birefringence maps indicate magnitude and fast-axis angle of a CaF₂ cube measured at (a) 157, (b) 248 and (c) 633 nm, with light propagating along the (110) crystal axis.

It is important to note that the 157-nm map illustrates a sample with significant variation in retardation values. The 441 data points have an average retardation value of 27.0 nm (or 11.3 nm/cm), a maximum value of 29.2 nm (or 12.2 nm/cm), a minimum value of 25.0 nm (or 10.5 nm/cm) and a standard deviation of 0.8 nm. The retardation varies as much as ±8 percent from the average value. If not handled properly, such a high level of retardation variation will affect how accurately one can determine the intrinsic birefringence in CaF₂ at 157 nm.

In principle, the intrinsic birefringence in a single crystal should be constant at a given wavelength. The observed variation in retardation values over the scanned areas could result from the presence of both intrinsic and residual birefringence in the CaF₂ cubes measured.

If it is assumed that the residual birefringence in a sample is random, then sufficient averaging over a large number of data points should minimize the contribution of residual birefringence. The average of 441 data points measured at 157, 193 and 248 nm leads to average values of normalized retardation of 11.3, 3.55 and 1.13 nm/cm, respectively. These data are in good general agreement with the previously reported values.

The birefringence map measured at 633 nm using a HeNe birefringence measurement system (Figure 2c) illustrates dramatically different birefringence patterns from the other images, particularly with regard to fast-axis angles. There is a somewhat random angular distribution, with localized areas of high retardation dominated by angles around 0° (for example, the two high-retardation ridges at the low right corner) and 90° (for example, near the central area). In contrast, fast-axis angles around 0° (horizontal) dominate the other images. The irregularity of the fast-axis angles for the 633-nm map also indicates a dominance of residual birefringence. The average of 441 data points measured at 633 nm leads to a low averaged value of normalized retardation of 0.258 nm/cm. The intrinsic birefringence in CaF₂ should become much smaller at 633 nm, according to the 1/—λ² dependence.

The 633-nm map helps explain what is happening in the other images. The two high-retardation ridges in its lower right corner (presumably residual birefringence) appear as high-retardation ridges in the other images, because the fast-axis angles in those two ridges are nearly parallel to the fast-axis angles of the intrinsic birefringence. At 633 nm, the fast-axis angles in the central area of the sample are closer to vertical than horizontal. Therefore, it appears that residual birefringence with a fast-axis orientation close to 90° cancels a substantial portion of the intrinsic birefringence, which is shown as lower retardation regions in the other images.

Figure 3. Figures 3a and b. Besides mapping with light propagating along the (110) crystal axis, scientists also mapped residual birefringence at 157 nm in CaF₂ samples at nonintrinsic birefringence crystal axes. The difference in birefringence quality is obvious from even a cursory examination of the two data maps.

This instrumental approach also allowed mapping of residual birefringence at 157 nm in a variety of CaF₂ samples with the light beam propagating along (111) and (100) crystal axes (Figures 3a and b, respectively). Here we see two examples with average retardation values of 5.44 nm (1/4-in. thickness) and 0.66 nm (1-in. thickness), respectively. The difference in birefringence quality is obvious from even a cursory examination of the two data maps, and illustrates the measurement system’s capability as an at-wavelength tool for quality control of lens materials that are used in 157-nm optical lithography.

References

1. E. Hecht and A. Zajac (1974). OPTICS, Addison-Wesley, London, p. 251.

2. J.H. Burnett, Z.H. Levine and E.L. Shirley (2001). PHYS. REV. B, 64 241102(R).

3. J.H. Burnett, Z.H. Levine, E.L. Shirley and J.H. Bruning, JM3, in print (2002).

4. N. Shiraishi, et al (2002). Progress of Nikon’s F₂ exposure tool development. Proc. SPIE, Vol. 4691, p. 594.

5. J.C. Kemp (1969). J. Opt. Sci. Amer. 59, p. 950.

6. B. Wang and T.C. Oakberg (1999). REV. SCI. INSTRUM. 70, p. 3847.

7. B. Wang (September 2002). Exicor DUV birefringence measurement system at optical lithography wavelengths. Third International Symposium on 157-nm Lithography.

Acknowledgments

This project has partial funding from International Sematech. The authors would like to thank John Burnett at the National Institute of Standards and Technology for his valuable discussions and for offering samples, and the entire Hinds team involved in developing the birefringence measurement system for their help.

Meet the authors

Bob Wang, Rick Rockwell and Jennifer List are with the Applications Research Group of Hinds Instruments Inc. in Hillsboro, Ore. Mike Ward is the marketing manager.