Photo-thermal measurement of absorptance losses, temperature induced wavefront deformation and compaction in DUV-optics

Bernd Schäfer; Jonas Gloger; Uwe Leinhos; Klaus Mann

doi:10.1364/OE.17.023025

1. Introduction

In modern DUV wafer steppers operating at the wavelength of 193nm fused silica and CaF₂ are employed as optical materials. Despite considerable quality improvements achieved in recent years, the combination of high photon energies, increasing fluencies and high radiation doses can still result in intolerable changes of the optical properties. In addition, ever increasing demands on resolution and throughput in semiconductor microlithography call for an ongoing optimization of the relevant optical parameters, in particular with respect to linear and non-linear absorption losses, long-term stability, and imaging quality. This puts also new challenges on the sensitivity and reliability of the applied characterization techniques.

The high energy of 193nm photons causes the optical properties of fused silica and CaF₂ to change with time. Apart from degradation mechanisms as color center formation [1] or compaction and rarefaction [2, 3], the absorption within the bulk and on the surfaces or dielectric coatings raises the temperature of an optical element, which leads to local changes of the refractive index, and, thus, results in the development of a thermal lens. In order to estimate the influence of thermal lensing on optical quality, and, possibly, taking it into account in the design of lithography objectives, the comprehensive knowledge of material absorption at the operation wavelength is highly demanded. Unfortunately, the most commonly used techniques in this field, i.e. laser calorimetry [4, 6] and ratiometric transmission measurements, suffer from several problems, as e.g. long measurement times, missing spatial resolution, or limited accuracy at low absorption levels. This can be avoided by direct inspection of the laser-induced wavefront deformation a test beam accumulates when passing the sample. The advantages of this photo-thermal approach, as compared to calorimetry, are the fast measurement, the more flexible sample dimensions, better spatial resolution and the direct measurement of an optically relevant quantity. Moreover, the temporal dynamics of the process can be evaluated. Compared to a ratiometric transmission measurement, the photo-thermal method is more sensitive, gives more stable values for low absorption samples, and, in particular, only probes the absorptance and not the scatter losses. In contrast to laser induced deflection (LID) of a single ray [5] probing the complete irradiated part of the specimen with a large number of beamlets in parallel is insensitive to spatial adjustments and facilitates calibration.

The effect of laser-induced densification (compaction) of fused silica on the transmitted or reflected wavefront has been investigated already by various groups [7,8], and a couple of attempts to link the experimental findings to compaction data based on theoretical modelling or numerical simulation have been made [1,7,8]. However, until now wavefront measurements were always performed by interferometric techniques, which in contrast to Hartmann-Shack sensors, are more complex in design and require higher effort for wavefront reconstruction.

In this paper we present a novel setup for quantitative determination of laser-induced wavefront deformations, absorption and compaction in DUV optics. Following a brief section on theoretical fundamentals of Hartmann-Shack wavefront sensing and thermal lensing, the experimental setup is presented and results for DUV grade fused silica and CaF₂ are discussed.

2. Theory

2.1 Hartmann-Shack wavefront sensor

The Hartmann principle as sketched in Fig. 1 [9–11] is based on an orthogonal or hexagonal array of lenses (Hartmann-Shack) or pinholes (Hartmann), which divides the incoming beam into a large number N of sub-rays. The total irradiance I_ij and the position of the individual spots are monitored with a position sensitive detector placed at a distance f behind the array. The displacement of the spot centroid x_c with respect to a plane wave reference position x_r measures the direction of the time averaged transverse Poynting vector and thus the wavefront gradient β_ij, averaged over a sub-aperture (i,j), according to

Fig. 1 Principle of the Hartmann-Shack wavefront sensor (cf. text)

Download Full Size | PDF

{(\begin{matrix} β_{x} \\ β_{y} \end{matrix})}_{i j} = {(\begin{matrix} \partial w / \partial x \\ \partial w / \partial y \end{matrix})}_{i j} = \frac{1}{f} {(\begin{matrix} x_{c} - x_{r} \\ y_{c} - y_{r} \end{matrix})}_{i j} .

A series expansion (degree M) of the wavefront w(x,y) in, e.g., Zernike polynomials P_l with expansion coefficients c_l i.e.:

w (x, y) = \sum_{l = 0}^{M} c_{l} P_{l} (x, y),

in combination with a familiar least square approach

\sum_{i, j} [{(\sum_{l} c_{l} \frac{\partial P_{l}}{\partial x} (x_{i}, y_{j}) - β_{x, \exp .}^{i j})}^{2} + {(\sum_{l} c_{l} \frac{\partial P_{l}}{\partial y} (x_{i}, y_{j}) - β_{y, \exp .}^{i j})}^{2}] \overset{!}{=} \min

leads to a linear system of equations for c_l, which can efficiently be solved by standard techniques of linear theory.

From the reconstructed wavefront the global parameters peak-valley deformation w_PV and rms deformation w_rms

w_{P V} = \max_{i j} w_{i j} - \min_{i j} w_{i j} and w_{r m s} = N^{- 1 / 2} \sqrt{\sum_{i, j} {(w_{i j} - \bar{w})}^{2}}

can be determined to quantify the amount of the photo-thermal lensing effect.

2.2 Thermal lensing

Consider a cylindrical sample G irradiated by a circular laser beam traveling in z-direction as shown in Fig. 2 . The transient temperature change δT(r,t) of the sample encountered during irradiation is obtained by the solution of the heat equation with appropriate boundary conditions on ∂G:

Fig. 2 Geometry and notations characterizing a cylindrical optical element during laser irradiation

Download Full Size | PDF

\begin{array}{l} c_{p} ρ \partial_{t} δ T (r, t) + \nabla \cdot (λ \nabla δ T (r, t)) + μ \cdot I_{P} (r, t) = 0 r \in G \\ n \cdot (λ \nabla δ T (r, t) + κ δ T (r, t) n - β I_{p} (r, t) e_{z}) = 0 r \in \partial G . \end{array}

In Eq. (5) μ and β denote the bulk and surface absorption coefficients, respectively, I_p(r,t) denotes the laser power density distribution, κ the coefficient of heat transfer, λ the thermal conductivity, c_p the specific heat, ρ the density, and n the outward directed surface normal Given certain initial and irradiation conditions, sample dimensions and material parameters, as shown in Table 1 for fused silica and calcium flouride, Eq. (5) can be solved numerically for any instant of time. However, usually μ⋅l_s << 1 and β << 1 holds, and from a linear superposition the solution δT(r,z,t) can be expressed as:

δ T (r, z, t) \overset{μ l_{s}, β < < 1}{=} P [μ \cdot V (r, z, t) + β \cdot S (r, z, t)],

where P is the average laser power. In (6) the bulk and surface terms V(r,z,t) and S(r,z,t) depend on sample dimension, laser profile as well as on λ/c_pρ and κ, respectively. However, they are independent of P, μ and β.

Table 1. Material parameters of fused silica and CaF₂ used in finite difference simulations

View Table

As a consequence of the inhomogeneous temperature distribution, the refractive index varies locally according to

n (δ T (r, z, t)) = n_{0} + \frac{\partial n}{\partial T} δ T (r, z, t),

and the elongation of the sample δl(r,t) writes:

δ l (r, t) = \int_{0}^{l_{s}} \frac{\partial u_{z}}{\partial z} (r, z, t) d z .

The displacements u = (u_x, u_y, u_z)^T are determined by the condition of elastic equilibrium:

\begin{array}{l} Δ u (r, t) + \frac{1}{1 - 2 σ} \nabla (\nabla \cdot u) = \frac{2 + 2 σ}{1 - 2 σ} α \cdot \nabla δ T (r, t) r \in G \\ n \cdot (C (U - α δ T)) = p r \in \partial G . \end{array}

In (8) σ denotes the Poisson number, α the coefficient of thermal expansion, p the external forces per unit area and C resp. U is the elastic stiffness resp. strain tensor. Furthermore it is assumed that the temperature distribution is averaged over time intervals Δt>>c_s·l_s, with c_s the mean speed of sound.

According to Eq. (7)a, b the wavefront of a well collimated probe beam, traveling parallel to the specimen z-axis, picks up a wavefront deformation δw(r,t):

δ w (r, t) = (n_{0} - 1) \cdot \int_{0}^{l_{s}} \frac{\partial u_{z}}{\partial z} (r, z, t) d z + \frac{\partial n}{\partial T} \cdot \int_{0}^{l_{s}} δ T (r, z, t) d z \overset{l i n e a r i t y}{~} P [μ V' (r, t) + β S' (r, t)] .

As in Eq. (6), the form factors V’ and S’ are independent of P, μ and β. An oblique incidence of the test beam at angle γ within the xz-plane requires a slight modification of Eq. (9):

δ w (x \cos γ - d_{v}, y, t) = \cdot \int_{0}^{l_{s}} [(n_{0} - 1) \frac{\partial u_{z}}{\partial z} (h, z, t) + \frac{\partial n}{\partial T} δ T (h, z, t)] \sqrt{1 + \tan^{2} γ'} d z,

were

h = \sqrt{y^{2} + {(x + z \tan γ')}^{2}} w i t h γ' = arc \sin (\frac{\sin γ}{n_{0}})

denotes the tilt of the test beam inside the specimen and

d_{V} = l_{s} \frac{\sin (γ - γ')}{\cos (γ')}

is the lateral displacement behind the sample due to refraction.

3.2 Compaction

So far only transient wavefront distortion have been considered. Irreversible compaction or densification of fused silica, on the other hand, is assumed to originate from a local weakening of Si-O-Si bonds followed by a structural rearrangement [1]. As a consequence of the band gap of ~10eV, a two-photon mechanism is usually considered to be responsible for this damage process in fused silica under 193nm irradiation. Thus, the density change with pulse number N and peak intensity I can be written as:

\frac{ρ - ρ_{0}}{ρ_{e q} - ρ_{0}} = 1 - \exp [- {(a I ² N)}^{b}],

with ρ₀ and ρ_eq the initial and equilibrium density, and a, b < 1 model parameters, respectively. For small values of I²·N the exponent in (10) can be expanded, leading to an I² N-power law for compaction:

\frac{δ ρ}{ρ} = {(c I^{2} N)}^{b},

Equation (11) with an exponent b~0.6-0.7 has frequently been reported [1,2,7]. The influence of a densification δρ/ρ on the wavefront deformation can easily be considered by introducing in Eq. (7a) an additional term $\frac{\partial n}{\partial (δ ρ / ρ)} {(\frac{δ ρ}{ρ})}_{c}$ and a negative fictitious temperature contribution $δ T = - \frac{1}{3 α} (\frac{δ ρ}{ρ})$ in Eq. (8), were the subscript c refers to a situation where the sample is inhomogeneously irradiated and the contraction is constrained by the un-irradiated outer parts of the specimen. The experimental value for δρ/ρ, which cannot be measured directly, may be determined by comparing the results from finite difference (FD) wavefront simulations according to Eq. (5), (8) and (9) with varying input compaction to the experimental wavefront distortion δw_{pv, rms}.

3. Experimental

3.1 Setup

The setup used for photo-thermal measurements is shown in Fig. 3 . It consists of a nitrogen purged Al chamber which contains all optically relevant components. A collimated ArF excimer laser irradiates the sample collinearly; for defined conditions the excimer laser beam is expanded and confined by an aperture to a circular flat-top profile of Ø 7mm. The probe beam, a 639 nm fiber coupled diode laser, intersects the specimen under an angle of 8°. For homogeneous illumination the probe laser is expanded 25 times, and, after passing the sample, demagnified again to fit the detector area of the Hartmann-Shack sensor. This consists of a 12bit digital CCD camera with 1280 x 1024 pixels behind an orthogonal quartz microlens array (plano-convex lenslets, pitch 0.3mm, focal length f=40mm). Both camera data and laser power readings obtained from a power monitor (Ophir) are fed into a PC for online data processing. Furthermore, the beam line is equipped with a PC controlled shutter in order to accomplish variable heating and cooling intervals. For noise reduction up to 256 frames per record are sampled. The oxygen pressure is monitored with a respective sensor (Zirox) and kept below 100ppm during the measurements.

Fig. 3 Setup for measurement of the laser induced photo-thermal wavefront deformation

Download Full Size | PDF

A typical spot pattern from the Hartmann-Shack sensor during ArF excimer laser irradiation of a quartz sample with 100mW/cm² is shown in Fig. 4 (left). The arrows indicate the local displacements of the spots during heating as compared to the unirradiated sample. The right picture shows the reconstructed wavefront, exhibiting a peak-valley deformation of ~2nm. For a spherical surface this would correspond to a defocus term of approximately 5km.

Fig. 4 Recorded spot diagram (left) and reconstructed wavefront (right) of a quartz cylinder (Ø 25mm × 45mm), irradiated at 193nm with an intensity of ~ 100mW/cm²

Download Full Size | PDF

A standard measurement protocol for acquisition of the photo-thermal signal is displayed in Fig. 5 . The left diagram shows the temperature difference (averaged in z direction) between the axis and the boundary of the sample, calculated according to Eq. (5) for consecutive periodic measurement cycles succeeding a pre-conditioning interval. The measurement protocol starts with a cooling period of 54s; during the next 27s a reference is taken by sampling and averaging 64 camera frames for noise reduction. Thereafter, the ArF laser is switched on and the photo-thermal signal recorded. All in all, a complete cycle lasts about 100s. This short measurement time compared to calorimetry stems from the fact that only wavefront gradients are detected, and thus no equilibrium conditions are required. Indeed, although the mean temperature certainly increases, the temperature difference between sample axis and boundary virtually undergoes no change in consecutive periods. The time constant for a 40mm long quartz sample can be estimated from the decay of the peak-valley wavefront deformation just after terminating the irradiation, yielding about 5s (Fig. 5, right), which is in good agreement with the calculated temperature decay time according to Eq. (5).

Fig. 5 , left: z-averaged temperature difference between axis and boundary vs. time calculated for a quartz cylinder (length 40mm) during alternate irradiation and cooling intervals of 27 and 81 s, respectively. Right: Measured decay of the wavefront distortion of a cylindrical quartz sample (length 40mm) after stopping irradiation.

Download Full Size | PDF

3.2 Calibration

In order to gain absolute values of absorption coefficients the setup had to be calibrated, which can be achieved in various ways. One option is to measure the photo-thermal signal of a resistor heated sample as sketched in Fig. 6 (left). A sample of same material and dimensions as the samples under test was provided with a central bore corresponding to the laser beam diameter, and heated by a resistor chain glued within the bore. Thus, assuming that heat production is approximately constant in z-direction, the temperature distribution in the outer zone is the same as in the laser heated case, provided the surface absorption can be neglected. Assuming further that elastic constraints are small, the rms or peak-valley deformations of a wavefront extrapolated into the obscured area can be plotted over the absorbed power, and from the coefficients a and b of a linear fit a calibration factor is obtained, permitting the absolute determination of the absorption coefficient k (base 10) according to:

Fig. 6 , left: Calibration of the photo-thermal measurement setup using quartz sample (d=25mm, l_c=45mm) with central bore (=dia. of laser beam) and resistor chain; right: peak-valley and rms wavefront deformation plotted vs. electrical power. Solid lines represent the linear fit to the measured data.

Download Full Size | PDF

k = \frac{w_{r m s} - b}{a \cdot P \cdot l_{s}} \lg (e) .

The fit parameters of a_rms=140nm/W and b_rms=0.02nm indicate a detection limit of ~40 pm for the wavefront rms, corresponding to 0.2 mW absorbed power.

Alternatively, a calibration is possible from results of numerical simulations. According to Eq. (9) the wavefront distortion w_rms can be calculated for various sample geometries, any set of material coefficients, as well as arbitrary laser parameters. Then, as a consequence of linearity, a straight line $w_{r m s} = a \cdot k + b$ and therefore the k-factor for a given laser fluence can be determined from w_rms.

4. Results

4.1 Absorption of fused silica at 193nm

In Fig. 7a (left) the rms wavefront deformation is plotted vs. single pulse fluence for three quartz samples of equal size taken from different charges of the same vendor. The samples exhibit non-linear absorption which shows up in the parabolic increase of the deformation with laser fluence. The resulting absorption coefficient k is shown on the right, ranging from 1·10⁻⁴ to 5·10⁻⁴ cm⁻¹. The coefficients of linear absorption, given by the intercept with the ordinate, are even lower, e.g. 5·10⁻⁵ cm⁻¹ as extrapolated for sample 3. The results from a calibration based on numerical simulations of Eq. (6-8) are shown in Fig. 7b . As compared to Fig. 7a, the absorption vs. fluence shows qualitatively the same behaviour, the absolute values, however, are about 20-40% smaller.

Fig. 7a (left): Measured w_rms data as a function of laser fluence (@ 150 Hz, λ=193nm, average over 5 measurements) for three uncoated quartz substrates of equal size. Right: Corresponding absorption coefficients k (calculated with calibration factors from resistor heated sample). The slopes indicate the presence of two-photon non-linear absorption

Download Full Size | PDF

Fig. 7b Absorption coefficients k for three uncoated quartz substrates of equal size calculated with calibration factors from numerical simulations assuming a surface absorption of 0.01%.

Download Full Size | PDF

Considering the small magnitude in the measured w_rms values, the unknown surface absorption, uncertainties in material parameters as well as errors introduced by wavefront extrapolation into the obscured region in the case of resistor heated calibration samples, the results are quite satisfactory. Further improvements of signal-to-noise ratio – especially by an increase of the pulse repetition rate into the multi-kHz region - as well as more accurate numerical calculations in combination with an additional calibration procedure based on a reference “gray” sample, will certainly yield a better consistence of future results.

4.2 Laser-induced wavefront distortion in CaF₂

Figure 8 shows measurements of laser-induced wavefront deformations in two CaF₂ samples of different lengths, recorded during irradiation at λ = 248nm. In contrast to fused silica, which always exhibits a positive lens effect, a sign reversal is observed for CaF₂ in specific cases (Fig. 8, left). Although the thermal expansion is almost 40 times larger as compared to quartz, the change of refractive index with temperature is negative (cf. Tab. 1) and may overcompensate the specimen expansion.

Fig. 8 Photothermal measurement of CaF₂ samples (left: l_s=20mm, right: l_s=70mm) using an irradiation wavelength of 248nm and 50mW/cm² power density. A sign reversal of the thermal lens is observed.

Download Full Size | PDF

However, no such sign reversal is observed in finite difference (FD) calculations performed for different sample dimensions, bulk absorptions, laser beam diameters and crystal orientations. Only a strong surface absorption can result in a positive lens effect, as shown in Fig. 9 .

Fig. 9 FD calculations of the wavefront distortion w_pv for two CaF₂ samples (z axis oriented || [001]) which exhibit different signs of thermal lensing. A circular flat-top beam (Ø7mm) of 5·10³ W/m² cw power and a sample diameter of 25mm were used for calculation.

Download Full Size | PDF

Unfortunately, the large dependence of the photo-thermal signal on surface absorption renders calibration much more cumbersome compared to fused silica. Instead of resistor heating, different techniques based on reference samples, thickness series and numerical calculations must be considered. These attempts will be evaluated in the near future.

4.3 Densification in fused silica

Figure 10 shows the permanent wavefront distortion induced in a quartz sample (l_s=25mm) after 9·10⁶ pulses at 193nm, as well as the peak-valley irregularity w_pv as a function of the pulse number. In this experiment the ArF laser beam cross-section was reduced by a telescope to 3mm x 1.5mm in order to achieve sufficient power density for compaction. The w_pv value seems to saturate at a level of about 45nm. In order to obtain the same deformation within the FD simulations, an unconstrained compaction of δρ/ρ of 7·10⁻⁶ has to be considered. The thick line in the right diagram of Fig. 10 represents an a·x^b-power law fit through the first 4 measured points, the observed exponent b being 0.63.

Fig. 10 , left: Wavefront deformation of a quartz sample (l_s=25mm) after 9 million 193nm pulses of 0.1J/cm². The entrance and exit positions of the heating beam, projected on a plane perpendicular to the test beam axis are marked as rectangles. right: peak-valley wavefont irregularity as a function of pulse number.

Download Full Size | PDF

Compaction induced birefringence could be investigated by introducing two crossed polarizers in the test laser beam path (cf. Figure 3), both in front of and behind the sample, and removing the microlens array from the Hartmann-Shack camera. Figure 11 shows the pattern of the test beam after passing the quartz sample irradiated with 1.2·10⁶ pulses at 0.1 J/cm².

Fig. 11 , left: Test beam pattern of a quartz sample between crossed polarizers after 1.2·10⁶ pulses (193nm) at 0.1 J/cm². The rotated coordinate axes indicate the orientation with respect to the camera reference frame; right: simulated test beam pattern for δρ/ρ=4·10⁻⁶ and a flat-top beam of 3mmx1.5mm. The isolines represent transmitted intensities of 9·10⁻⁵ −9·10⁻⁴ relative to the test beam intensity.

Download Full Size | PDF

Assuming a constant sample temperature and unsaturated compaction, the following proportionalities can be considered [7]:

n_{r} - n_{ϕ} ~ σ_{r} - σ_{ϕ} ~ \frac{Δ ρ}{ρ} ~ {(I ² N)}^{b} .

In Eq. (13, 14) φ is the azimuth, n_r and n_φ the refractive indices for radial and azimuthal polarization, σ_r and σ_φ the corresponding stresses, N the number of laser pulses and I their peak intensity. Hence, the observed intensity distribution $I_{⊥}$ , normalized to the test beam intensity without sample and at parallel orientation of the polarizers, can be written as [12]:

\frac{I_{⊥}}{I_{| |}} = \sin^{2} ϕ \cos^{2} ϕ \cdot (1 - \cos (\frac{2 π (n_{r} - n_{ϕ}) l_{s}}{λ})) \overset{(n_{r} - n_{φ}) \cdot l_{s} < < λ}{~} {(I ² N)}^{2 b} .

reported literature values of the empirical exponent b vary in the range of 0.6-0.7, which is in excellent agreement with the experimental parameter 2b_exp=1.255 of a power fit to

{(I_{⊥} / I_{| |})}_{\max}

over N (shown in Fig. 12 ) as well as with the exponent in a power fit of w_pv over N (cf. right diagram of Fig. 10).

Fig. 12 Ratio: maximum intensity between crossed polarizers to maximum intensity without sample and parallel polarizers as a function of pulse number for a quartz sample of l_s=25mm. Laser parameters were ν=1kHz, fluence H=0.1J/cm².

Download Full Size | PDF

5. Conclusion

A novel photo-thermal measurement technique was developed, allowing to monitor laser induced thermal lens as well as compaction effects. The technique uses a high-sensitivity Hartmann-Shack sensor which can detect in real time wavefront distortions with a resolution of about λ/10,000, corresponding to < 100pm. The quantitative evaluation of the thermal lens data accomplishes a fast assessment of both absorptance properties and imaging quality of the optics under test. An absolute calibration of the measured data is possible by comparison with signals from a resistor heated specimen as well as from numerical simulation. The advantages of the novel setup in comparison to calorimetry are the much faster measurement (no equilibrium, only wavefront gradients), the more flexible sample dimensions and the possibility to investigate the dynamics in imaging quality. In comparison to transmission measurement the setup gives more stable values and there is no bias from scattering. Thus, the new method may be regarded an alternative to both techniques.

Acknowledgement

The authors like to thank Michael Stolz from Carl Zeiss SMT for many fruitful discussions.

References and links

1. R. E. Schenker, L. Eichner, H. Vaidya, S. Vaidya, P. M. Schermerhorn, D. R. Fladd, and W. G. Oldham, “Ultraviolet damage properties of various fused silica materials,” Proc. SPIE 2428, 458–468 ( 1994). [CrossRef]

2. W. Primak and R. Kampwirth, “The Radiation Compaction of Vitreous Silica,” J. Appl. Phys. 39(12), 5651–5658 ( 1968). [CrossRef]

3. C. Van Peski, “Behavior of Fused Silica under 193nm Irradiation”, Technology Transfer # 00073974A-TR, International SEMATECH (2000)

4. E. Eva and K. Mann, “Calorimetric measurement of two-photon absorption and color-center formation in ultraviolet-window materials,” Appl. Phys., A Mater. Sci. Process. 62(2), 143–149 ( 1996). [CrossRef]

5. M. Guntau and W. Triebel, “Novel method to measure bulk absorption in optically transparent materials,” Rev. Sci. Instrum. 71(6), 2279–2282 ( 2000). [CrossRef]

6. C. Görling, U. Leinhos, and K. Mann, “Comparative studies of absorptance behaviour of alkaline-earth fluorides at 193 nm and 157nm,” Appl. Phys. B 74(3), 259–265 ( 2002). [CrossRef]

7. N. F. Borrelli, C. Smith, D. C. Allan, and T. P. Seward, “Densification of fused silica under 193-nm excitation,” J. Opt. Soc. Am. B 14(7), 1606–1625 ( 1997). [CrossRef]

8. J. M. Algots, C. Steinbrecher, H. Jinbo, and S. Chuckravanen, “Optical Materials: Compaction and rarefaction affect photolithography system lifetimes,” Laser Focus World , 41(11) ( 2005).

9. D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72 ( 1996). [CrossRef]

10. B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71(7), 2663 ( 2000). [CrossRef]

11. B. Schäfer and K. Mann, “Determination of beam parameters and coherence properties of laser radiation by use of an extended Hartmann-Shack wave-front sensor,” Appl. Opt. 41(15), 2809–2817 ( 2002). [CrossRef] [PubMed]

12. M. Born, and E. Wolf, Principles of Optics, (Cambridge University Press, 7th Ed.), Sect. 15.4, 823pp (2001)

	Fused Silica	Calcium Fluoride
n₀ (λ=633nm)	1.457	1.433
α	5·10⁻⁷ [1/K]	1.885·10⁻⁵ [1/K]
λ	1.38 [W/mK]	9.71 [W/mK]
Young’s modulus E	71.7 [GPa]	75.8 [GPa]
Poisson ratio σ	0.17	0.26
dn/dT (λ=633nm)	8.5·10⁻⁶ [1/K]	−10.5·10⁻⁶ [1/K]
dn/d(δρ/ρ)^[5]	0.4504	-
Elastic constants C₁₁, C₁₂, C₄₄	77.1, 15.8, 30.6 [GPa]	164.2, 43.98, 33.7 [GPa]
Elastooptic constants q₁₁, q₁₂, q₄₄	4.2, 0.65, 1.78 [10⁻¹² Pa]	−0.038, 1.08, 0.71 [10⁻¹² Pa]

Photo-thermal measurement of absorptance losses, temperature induced wavefront deformation and compaction in DUV-optics

Abstract

1. Introduction