The bulk scattering of synthetic fused silica for 193 nm lithography was investigated using an instrument for high-sensitive total and angle resolved scattering measurements at 193 nm. Bulk scattering coefficients α between 0.6×10-3 and 1.7×10-3 cm-1 (base e) depending on the hydroxyl (OH) content and fictive temperature of the samples were measured using a total scattering (TS) technique. The results are interpreted with regard to a model which relates scattering in fused silica to structural disorder in the material. From angle resolved scatter (ARS) measurements at 193 nm, a Rayleigh type scattering distribution was found. Using TS and ARS at 633 nm, 532 nm, and 325 nm in addition to the results at 193 nm, wavelength scaling ~n 8/λ 4 as predicted by theory is obtained. Thus, the model is demonstrated to hold from the visible spectral range down to the deep ultraviolet.
©2006 Optical Society of America
In recent years high-purity synthetic fused silica has become more and more important as an optical material for deep ultraviolet applications. As the semiconductor industry employs ever shorter wavelengths and sophisticated imaging techniques to manufacture smaller structures using optical lithography, the demands on suitable materials are drastically increasing. Besides low optical losses and high laser damage resistance, the materials have to fulfill demanding requirements concerning ultra-low stress birefringence and a smooth and homogeneous refractive index distribution.
At the same time, because of the large number (~20) and the large dimensions (~300 mm) of optical elements in commercial lithography systems, the costs of the optical materials play a non-negligible role. For 193 nm, only two materials have been established, calcium fluoride and synthetic fused silica. In particular for projection optics, nearly without exception fused silica is used as optical material.
The light scattering of optical materials for DUV applications is critical particularly for two reasons. First, scattering leads to reduced intensity and therefore reduced throughput of a wafer scanner in production and also to reduced image contrast which is of crucial importance for lithography applications.
Second, in particular for DUV wavelengths, scatter losses can be expected to be of the same magnitude as absorption because of the strong wavelength dependence. The latter plays a significant role for the estimation of thermally induced refractive index change and the image distortion of high-end optical elements. Thus, scattering has to be quantified and separated from transmission-drop measurements in order to achieve accurate absorption values.
The first investigations of light scattering in glasses were motivated by the need for extremely low-loss media for optical waveguides in the infrared. For these applications, light scattering in the bulk material is the dominating loss mechanism. Because of the amorphous structure of glasses, scatter losses can only be reduced down to intrinsic minimum values which depend on their chemical and structural properties which in turn depend on the manufacturing processes. In the 1960s and 70s, theories were developed to describe the scattering in glasses by “frozen-in” density fluctuations resulting in structural inhomogeneities [1,2]. A good review of these models is given in Ref. . The structural disorder is interpreted as a result of thermal fluctuations corresponding to a fictive temperature T f at which the equilibrium configuration is equivalent to the structure in question. If a fused silica sample is annealed at a temperature T a for a sufficiently long period of time so that the material can reach thermal equilibrium, quenching results in a lower absolute temperature of the material T << T a. However, the density fluctuations are “frozen-in” around Ta such that the actual structure corresponds to a fictive temperature T f ≈ T a. However, these models have so far only been validated in the visible and near infrared spectral regions. The shorter the wavelength the more likely these theories will fail. Therefore, accurate at-wavelength measurements of scatter losses of fused silica are needed. Moreover, in order to receive reliable results, a traceable standardized measurement technique has to be used.
There are only few papers reporting on scatter measurements of fused silica:
In Ref  scatter measurements at 442 nm and at 633 nm were performed to separate the contributions of surface, subsurface and bulk scattering of fused silica from total scattering. A Rayleigh type scatter distribution was reported. However, by quantitative comparison of the scatter levels at the two wavelengths, the expected 1/λ 4 scaling did not hold. Therefore, extrapolation of the data to shorter wavelengths is not possible.
In Ref. , the linear dependence of Rayleigh scattering in glasses on fictive temperature has been investigated. However, the scatter measurements were performed at 488 nm and the scattering intensities were measured relative to a “standard silica glass”. No quantitative values were given.
Up to 2003, no measurements of the bulk scattering of fused silica down to 193 nm were reported in the literature. From attenuation values which are common in the optical fiber community, the scatter losses at 193 nm could be roughly estimated: In Ref.  a total scatter loss of 0.14 dB/km at 1550 nm was extrapolated to 193 nm using a simple ~1/λ 4 wavelength scaling. The obtained value of 1.3×10-3 cm-1 was in good agreement with values around 1.5×10-3 cm-1 measured at 193 nm for Corning HPFS (high purity fused silica). However, as will be shown below, when extrapolating over such a wide spectral range, the dispersion of the refractive index can not be neglected. Using the more accurate wavelength scaling ~n 8/λ 4 following Ref. , the lower limit for the total scatter losses at 193 nm would yield 2.6×10-3 cm-1 at 193 nm. Assuming the measured values reported in Ref.  being correct, the IR losses of the material used for the estimation were significantly underestimated.
In our work the bulk scattering coefficients of various synthetic fused silica samples with different physical and chemical properties were measured at 193 nm. As was discussed e.g. in Ref. , the ratio between inelastically to elastically scattered light is about 0.04 for pure fused silica, i.e. the total scatter loss is by far dominated by the elastic component. Therefore, we focused on quantifying the elastically scattered light. For thorough investigation two different and independent measurement techniques were used.
Following ISO 13696  total backscattering (TSb) is defined as the power P b scattered into the backward hemisphere divided by the incident power P i:
A similar definition exists for total forward scattering, TSf. In the following the sum of TSb and TSf is regarded as the total scatter loss TS.
Angle resolved scattering (ARS) is defined as the power ΔP s scattered into the solid angle ΔΩ s normalized to the incident power P i and ΔΩ s :
where θ s is the polar angle of scattering defined with respect to the backward surface normal of the sample under investigation. For the sake of simplicity in Eq. (2), we assumed isotropic scattering.
ARS is equal to the cosine corrected bidirectional scatter distribution function (BSDF) . It can be converted into TS values by integration over the forward and backward hemispheres.
2.2 Measurement set-up
In the past years, light scattering measurement systems were developed at the Fraunhofer IOF in Jena which cover a wide range of wavelengths from the visible extending up to the infrared and down to the deep ultraviolet and vacuum ultraviolet spectral regions [10,11]. The main components of our DUV/VUV light scattering measurement system described in detail in Ref.  are schematically shown in Fig. 1.
The whole optical system is housed in two vacuum chambers. Operation in vacuum is necessary in order to avoid absorption in air and to suppress Rayleigh scattering on gas molecules. The light source (1) is an excimer laser which can be operated at 157 nm and 193 nm. After attenuation using neutral density filters (2) and passing a spatial filter consisting of two spherical VUV-enhanced aluminum mirrors and a 100 μm diameter pinhole (3) a reference beam is coupled out by a superpolished CaF2 substrate and reflected onto the reference detector (4) in order to compensate for laser power fluctuations and contamination effects. As detectors side-on photomultiplier tubes (PMTs) are used with calcium fluoride diffusers in front of them to homogenize the angular and position sensitivity. For TS as well as for ARS measurements the sample is illuminated by a 1 mm diameter spot and with an maximum energy density of approximately 3 mJ/cm2.
For TS measurements, a Coblentz sphere based set-up is used. The sample (5) is illuminated at normal incidence. For TSb, the radiation scattered back (6) between 2° and 85°, according to ISO 13696, is focused by the Coblentz sphere (7), an aluminized glass hemisphere, onto the detector (8). The specular reflected and transmitted beams are directed out of the Coblentz sphere and absorbed by beam dumps (9). For TSf measurements, the Coblentz sphere together with the sample positioning and the detector systems is rotated about a horizontal axis through the sample surface to switch to forward scatter mode. TS background scattering levels measured at 193 nm and at 157 nm using an empty sample holder below 1×10-6 have been achieved in backward as well as in forward scattering modes.
The sample (1) is mounted onto the inner goniometer arm (2). The outer goniomter arm (3) contains an adjustable aperture stop (4) which allows solid angles ΔΩ s between 1×10-6 sr and 1×10-4 sr to be selected. A lens (5) is used to focus the scattered light onto the detector aperture (6) in front of the PMT (7) which acts as field stop and defines the field of view of the detector at the sample position. A narrow-band spectral purity filter (8) for 193 nm was developed which is used to suppress inelastically scattered light. ARS instrument signatures measured at 193 nm and at 157 nm using an empty sample holder were below 10-5 sr-1 at 157 nm and 10-6 sr-1 at 193 nm. The measurement system therefore exceeds 12 orders of magnitude.
For both ARS and TS measurements calibration is performed via measurement of a calcium fluoride diffuser with known absolute scatter values .
2.3 Samples and measurements
To investigate the nature of the bulk scattering of fused silica at 193 nm angle resolved scatter measurements were performed. For this purpose a sample disc with a diameter of 200 mm was prepared of type IIIa (see below) glass with an OH content of about 300 ppm and a fictive temperature of about 1050 °C. Figure 3 shows the sample geometry and the illumination conditions. On two opposing sites of the cylindrical surface, flat entrance (1) and exit (2) windows for the specular beam (3) were prepared. These window as well as the circular areas of the sample were mechanically polished while the residual side surfaces were flame polished. The sample was radially illuminated. ARS measurements were performed with light polarized parallel (p) and perpendicular (s) to the measurement plane. The curves were multiplied with sinθ s to correct for the detected scattering volume varying with the direction of observation.
For TS measurements at 193 nm, several synthetic fused silica rods with a diameter of 25 mm were taken from three types of homogenized and annealed fused silica, denoted by A, B, and C. Each type had been fabricated by a different manufacturing process resulting in different amounts of hydroxyl.
Material A is a type III quartz glass  which is produced by hydrolysis of SiCl4 in a H2/O2 flame, soot deposition and immediate vitrification to a OH rich silica glass. Material B is a type IIIa glass where the soot deposition and vitrification are two separate steps. This allows additional drying procedures before consolidation resulting in a lower OH content compared to Material A. Material C is also a type IIIa glass with extended drying leading to an even lower hydroxyl content.
The OH content was determined via Raman spectroscopy by measuring the strength of the 3695 cm-1 band which represents the O-H stretching .
For each material, rods with different fictive temperatures T f were generated by annealing at the desired temperature for at least 30 min with a subsequent quenching in water mist. The fictive temperature of each sample was estimated by evaluation of the 606 cm-1 Raman band . The accuracy of the OH and T f measurement is ± 5% resp. ± 10 °C.
In order to separate surface from bulk effects, a set of samples with thicknesses of 2 mm, 5 mm, 10 mm, 15 mm, and 20 mm respectively was fabricated from each rod. In order to reduce the influence of surface scattering as far as possible, the front and rear surfaces were super polished . The surfaces were inspected by atomic force microscopy within 10×10 μm2 scan areas which contain the spatial frequencies relevant for light scattering at 193 nm. Table 1 gives an overview of the examined sample sets.
3.1 Scatter distribution at 193 nm
Figure 4 shows the resulting curves of the ARS measurement on the sample disc together with the theoretical fits according to a Rayleigh scattering distribution.
In the angular ranges around the specular reflected and transmitted beams at 0° and 180°, the entrance and exit points of the specular beam lies within the field of view of the detector. In these regions the ARS is dominated by surface scattering leading to the marked peaks. In the off-specular regions, however, an ARS following a Rayleigh scatter distribution can be observed having the form :
where C is a constant used as fit parameter in Fig. 4.
Integration of the ARS curves over the whole sphere and normalization to the field of view of the detector being 0.7 cm yields a total scatter loss of (1.14±0.21)×103 cm-1.
Although the ARS method proved to be successful for quantifying total scatter losses, it is less suited for larger numbers of samples because of the complex sample geometry required and the need of polishing not only the directly illuminated but also the complete cylindrical side surfaces. Hence, for directly determining the scatter losses in different materials with varying chemical and physical properties, TS measurements were performed allowing samples with easier geometry and less effort to be investigated.
3.2 Scattering coefficients at 193 nm via TS measurements
The total scattering of a given sample is the sum of the actual bulk scatter TSvol and the components TSsurf and TSsubsurf resulting from scattering induced by surface nanoroughness and subsurface defects. Thereby TSvol is a function of sample thickness d:
where α is the scattering coefficient. It has the dimension cm-1 and can be converted into the scattering related part k = α/ln10 of the extinction coefficient. For TSVol << 1, which is fulfilled in the present study, Eq. (4) can be approximated as:
Thus, plotting measured TS values against the sample thickness should yield a linear function with slope α. This technique is, in principle, independent of contributions from surface and subsurface scattering. However, these contributions have to be constant throughout all samples with varying d. From AFM measurements, the rms roughness values were calculated as described in Ref. . The values varied between 0.09 nm and 0.11 nm. Thus, the contributions of surface scattering at 193 nm could be estimated using the theoretical approach described in Ref.  to be below 1×10-5.
For each sample set, TSb and TSf measurements were performed. The measurements were carried out as 2D mappings to check for homogeneity of the samples and to suppress the influence of local defects. In Fig. 5, the results of TSb mappings are exemplarily shown for sample set A3.
For each mapping, an average TS value was determined after applying a data reduction algorithm according to ISO 13696.
To determine the total scatter values TS, the sum of the measured values TSb and TSf has to be corrected for those parts of the internal scattered radiation that are not transmitted through the front or rear surfaces but leave the sample through the sidewalls. Correction factors between 1.8 and 2.5 were calculated by raytracing for each sample geometry separately. In Fig. 6 the resulting TS values are plotted versus sample thickness.
A linear trend can be observed for samples up to a thickness of 10 mm. For thicker samples, a more or less pronounced drop of the detected scatter signal can be found. This could be expected because of the imaging properties of the Coblentz sphere. Only light scattered from a definite volume located conjugate to the detector position is completely detected causing a deviation from the linear relationship for thicker samples. Measuring samples with a thickness up to 20 mm allowed us to determine the turning point up to which the measured values accurately represent the total scattered power. Hence, the slopes of the linear fits for all samples using the first three data points yield the scattering coefficients α summarized in table 2 for all samples. In addition, fig. 6 reveals that the extrapolated scatter values for d = 0 mm are approximately zero indicating negligible surface and subsurface scattering. The uncertainty values Δα include the uncertainties of the TS measurements (16% maximum relative error ) as well as the uncertainties of the linear fits.
In Fig. 7 the scattering coefficients are plotted versus fictive temperature.
Two important results can be derived from this diagram:
- For samples with similar hydroxyl content the scattering coefficient grows with the fictive temperature. The relationship can be regarded as linear within the uncertainty bars.
- The samples with high OH content reveal significantly lower scatter losses.
The ARS measurement on the sample disc confirms that the scattering distribution follows Rayleigh scattering. This is a qualitative validation of the model discussed in Ref. . Furthermore, although the TS measurements are insensitive to the actual scatter distribution, the calculation of the correction factors discussed above is based on a Rayleigh scattering distribution. Moreover, a Rayleigh type ARS is the precondition for the determination of the scattering coefficient by inspecting only a limited angular range as is a wide-spread practice [5,6,18].
The correlation found between the fictive temperature and the scattering coefficient confirms the theory presented in Ref. [1,2] which relates the optical scattering coefficient to thermally driven fluctuations of the local dielectric constant. The random structure of glass is determined by structural disorder “frozen-in” around the transition temperature as the material is cooled down. The actual state corresponds to the fictive temperature T f. The scattering coefficient can be expressed as:
with the index of refraction n, the photoelastic coefficient p, the isothermal compressibility ftT at T f, and the Boltzmann constant k B.
Following Ref  the term n 8 p 2 can be approximated by (n 2-1)2, with n ≈ 1.561 for fused silica at 193 nm. β T values between 5.7×10-11 m s2/kg and 6.2×10-11 m s2/kg are given in Ref. , depending on T f. Thus, theoretical values for or α are obtained between 1.41×10-3 cm-1 for T f = 1050 °C and 1.54×10-3 cm-1 for T f = 1300 °C. This is in good agreement with the values measured for the high-purity fused silica (material C).
Regarding the fact that we found lower scatter losses for higher OH contents, the only contribution in Eq. (6) that could explain this dependence is the isothermal compressibility which is not only a function of T f but can be influenced even by small amounts of impurities in the material. This effect has been explained in Ref.  as the result of additional structural relaxation.
In order to validate the wavelength scaling behavior predicted in Eq. (6) we determined the scattering coefficients at 325 nm, 532 nm, and at 633 nm for all samples in analogy to the experiments at 193 nm using the set-up described in Ref. . The results are shown in Fig. 8 together with a fit function that follows an n 8/λ 4 dependence.
The wavelength scaling according to Eq. (6) holds even down to 193 nm in the deep ultraviolet spectral range. The slightly higher values at 532 nm turned out to be the result of systematic errors because of enhanced background scatter signal at this wavelength.
To recheck the results with an independent technique, ARS measurements were performed on sample C2 at different wavelengths. In contrast to the measurements presented in Sec. 3.1, the sample was illuminated through the super polished circular surfaces at normal incidence. The ARS was measured with unpolarized incident light and integrated over the whole sphere assuming isotropic scattering. The results are shown in Fig. 9.
In addition to confirming a wavelength scaling ~n 8/λ 4, the absolute values measured via the ARS technique are in good agreement with the results retrieved from TS measurements.
Our results show that the model discussed in Ref. [1,2,3] with regard to the visible and near infrared spectral regions holds in the spectral range from the visible down to the deep ultraviolet. When extrapolating the values measured at 193 nm up to 1550 nm using the correct wavelength scaling ~n 8/λ 4, we obtain scattering induced attenuation values around 0.08 dB/km. The difference to 0.14 db/km used in Ref.  is most likely caused by underestimated absorption contribution in Ref..
In Section 3.1 the scattering coefficient of a disc sample was measured via ARS to be (1.14±0.21)×10-3 cm-1. With an OH content of about 300 ppm and a T f of about 1050 °C, the disc material corresponds to sample B1 for which a scattering coefficient of (1.07±0.18)×10-3 cm-1 was measured via TS. Although completely different techniques were used, the measured values are in good agreement demonstrating the accuracy of each of the measurements.
5. Summary and conclusions
An instrument for high-sensitive total and angle resolved scatter measurements at 193 nm and 157 nm has been developed at the Fraunhofer Institute in Jena. The system enabled the investigation of the bulk scattering properties of synthetic fused silica for 193 nm lithography at the wavelength of application.
Angle resolved scatter measurements revealed a Rayleigh type scattering distribution. From ARS, total scattering losses were obtained by integration.
A technique based on total scatter (TS) measurements at 193 nm allowed the direct determination of the scattering coefficient α. Because it is robust, fast and undemanding concerning sample geometry, the TS technique is well suited for larger number of samples. In addition, TS is a quantity well defined in the international standard ISO 13696.
Thus, the scattering coefficients of various fused silica samples were measured at 193 nm using the TS technique. Values between 0.6×10-3 cm-1 and 1.7×10-3 cm-1 were obtained depending on the OH contents and the fictive temperature of the materials. The results were checked using ARS as independent technique for selected samples. Both methods yielded comparable results.
The theoretical model established in the fiber optics community which relates scattering in fused silica to structural disorder resulting from thermal history of the material has been demonstrated to hold down to 193 nm: A linear dependence of or on the fictive temperature has been observed and the wavelength scaling of α follows a ~n 8/λ 4 law from the visible to the deep ultraviolet spectral region. Furthermore, a scatter reduction effect for samples with considerable OH content has been observed and quantified.
The dependence of the actual scatter loss of the materials on their chemical and physical properties imposes the need for accurate measurements for each material type. The results presented in this paper suggest that the scattering coefficients of fused silica at 193 nm can be estimated by extrapolating from values measured at longer wavelengths. However, it has to be thoroughly tested, if the wavelength scaling predicted by theory holds for the material at hand.
This work was supported by the Thüringer Kultusministerium, project OPTOMATRONIK (B507-02004) and by the Deutsche Forschungsgemeinschaft, SPP 1159 StraMNano project NanoStreu.
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