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Phase shifting diffraction interferometry (PSDI) was adapted to provide real-time feedback control of a laser-based chemical vapor deposition (LCVD) process with nanometer scale sensitivity. PSDI measurements of laser heated BK7 and fused silica substrates were used to validate a finite element model that accounts for both refractive index changes and displacement contributions to the material response. Utilizing PSDI and accounting for the kinetics of the modeled thermomechanical response, increased control of the LCVD process was obtained. This approach to surface tracking is useful in applications where extreme environments on the working surface require back-side optical probing through the substrate.
© 2014 Optical Society of America
1. Introduction
Fused silica optics replacement costs in demanding laser applications [1] mandate research and development of technologies that mitigate laser-induced damage [2, 3]. Damage mitigation strategies include global processing to refinish the entire surface and local processing to extend optic lifetime. For one such local technique a laser ablates millimeter-diameter flaws into designed conical shapes [3]; however, the accumulation of these pits eventually limits the optic’s lifetime. A recently developed novel approach deposits silica over the damaged area using laser-based chemical vapor deposition (LCVD) and shapes the final surface with nanometer-scale accuracy [4]. This approach uses a CO2 laser to heat damaged regions above ~1000 K, which thermally activates and spatially constrains the polymerization of a tetraethylorthosilicate (TEOS) precursor in order to form silica on the surface. LCVD parameters are adjusted to optimize precursor deposition kinetics and material transport, resulting in a silica layer with high damage threshold and a desired surface profile.
High energy laser systems typically require nanometer scale flatness of mitigated optical surfaces in order to minimize perturbations to the laser light [3]. To meet this requirement, real-time measurements of the surface profile are needed to serve as feedback to control LCVD parameters. Contact metrology such as stylus profilometry and atomic force microscopy are too slow for measuring millimeter-sized areas and are impractical to mount in a LCVD setup. Noncontact approaches such as confocal microscopy and focus stacking do not meet the 10-nm depth resolution requirement. We concluded that interferometry was the best approach to measure surface profiles in real time and meet the requirements imposed by the LCVD system.
Phase-shifting diffraction interferometry (PSDI) is an attractive approach offering a fiber-coupled configuration, wide field of view (several mm’s), and high axial resolution (<10 nm) [5, 6]. Using techniques related to digital holography, multiple interferograms are collected at sub-wavelength phase delays to generate a surface profile. We use optical fibers to separate the vibration-sensitive components from the sample measurement region and a form of common-mode noise rejection at the sample in order to achieve the needed depth precision. Previous work has used PSDI to measure surface figure for many applications, including extreme ultraviolet lithography (EUVL) mirrors [6], crystal growth metrology [7] and laser fusion targets [8].
This work describes the implementation of PSDI for in situ monitoring of laser material processing, specifically by adapting PSDI to an LCVD mitigation system. The interferometer reference and probe beams are launched from two single mode fibers and interfered through sample surface reflection at a CCD camera. The PSDI hardware is placed in a back-side location with an off-axis viewing angle that looks through the bulk of the fused silica to prevent interference with the front surface LCVD system. Phase retrieval, back propagation and phase unwrapping is implemented in a real-time processing algorithm. Thermal expansion of laser-heated BK7 and fused silica is used to calibrate the system. Because transmission interferometry is sensitive to refractive index which varies with temperature the measured height of the thermally expanded region is exaggerated by this variation. We used a thermomechanical model to better understand this effect and remove it from the measurement. We also confirmed these simulation results by experiment. The deposition kinetics of fused silica using LCVD is measured and defect mitigation is demonstrated using PSDI. In addition, we used the expanded region in order to register the center of the deposition profile to the center of the damaged region. We found this registration to be difficult using other techniques.
The paper is organized as follows: sections 2 and 3 detail the PSDI measurement system and surface profile retrieval using Fourier optics; sections 4 and 5 discuss the thermally induced phase change measurements and a model to account for the thermally-induced optical path increase; lastly, section 6 presents the implementation of PSDI and above models to provide feedback into the LCVD process, resulting in a flat surface and registered (to damage pit) deposition volume.
2. PSDI measurement system
The PSDI measurement system shown in Fig. 1 is an interferometer utilizing a 532-nm continuous wave (CW) laser source (Spectra Physics, Millennia II). The laser delivers a 1 mm 1/e2 diameter beam at 200 mW, which is expanded 1:2 and attenuated to a few mW in the optical apparatus shown. We selected this laser for its short coherence length, which prevents unwanted interference among system components.
Fig. 1 The PSDI measurement system is composed of an open air interferometer shown at the top of the diagram, a single mode fiber transport shown in the middle and a two fiber launch that creates a sheared interferogram of the sample on the camera. A separate control system (not illustrated) processes the interferogram and adjusts the LCVD process parameters in a feedback loop.
One leg of the interferometer is manually adjustable to compensate for large optical path differences between the two legs. The other leg is attached to a piezoelectric driver that ramps the phase linearly over 1.5 wavelengths. The output from each leg of the interferometer is collected into a single-mode fiber and passed through a fiber polarization adjuster. The contrast in the fringes of the interferogram that is created by the light leaving the fibers is maximized when the polarization of the light is aligned and the amplitude of the light is balanced between each fiber. The balance of light can be adjusted by rotating a half wave plate located before the polarization beam cube, while the polarization is aligned using the fiber polarization adjusters. The entire assembly is set up on a vibration-isolated table. The fibers carrying the two light signals then terminate at the LCVD table, where the cleaved ends are mounted in a fixture. This fixture stacks the fiber ends vertically and allows for adjusting their pointing and their separation along a vertical line. The light from the fibers passes through the transparent sample from the back side, reflects off the surface under study, and continues to the camera where the interferograms are captured in a 30-ms exposure per frame. All samples measured 50 mm in diameter by 10 mm thick, λ/20 flatness and were anti-reflection coated on the back-side air-glass reflecting surface. Twelve interferograms are captured during the piezo ramp and a phase shift is associated with each one. When plotted versus phase the intensity of each pixel in the interferogram is a sinusoidal function. We use a numerical algorithm to retrieve the amplitude and phase shift of the curve [9]. This is the first step in the processing chain shown in Fig. 2 which yields a sample surface profile.
Fig. 2 The software processing algorithm used as the feedback loop in the LCVD surface monitoring system.
This recovered phase shift measures the optical path difference (OPD) between the two paths that each originate at one of the cleaved fiber ends and terminate at a common pixel on the camera. Because the fibers ends are separated vertically, a spatially linear phase (a tilt) appears in the measurement in addition to any phase generated by the test sample. To better understand this relation between pixel phase shift and path length consider a column of pixels that are aligned parallel to the line that runs between the fibers ends. There is one pixel in this line where the difference in path length to each fiber is a minimum. As you move away from this pixel towards one fiber, the difference increases, and as you move toward the opposite fiber the difference changes in the opposite direction. In addition, if the line between the fiber ends is not parallel to the plane of the CCD (Dalsa DS-1B), a spatially spherical distortion will appear in the phase.
The recovered phase at the camera is modulo 2π radians, or wrapped. In order to make measurements on the laser-driven phase change, the continuous unwrapped phase is needed. Unwrapping consists of adding integer multiples of 2π radians to the wrapped phase values in order to improve the phase continuity. There are a number of unwrapping algorithms that can be used for this purpose. We tested both the Goldstein method and that of Flynn et al. [10]. Goldstein’s was the only algorithm that could be computed in a time suitable for using in our feedback loop (approximately 10 s or less), but that algorithm became too slow for patches of 103 to 104 pixels having non-zero residues. (Non-zero residues result from closed loops of camera pixels whose total integrated phase is not zero.) Such residues can be generated by camera noise or artifacts, or by portions of the sample that generate OPD variation between two adjacent pixels greater than the 532-nm laser wavelength. For single measurements of a nearly static surface where the measurement time is not critical and for cases where the number of non-zero residues is large, we found that the slower Flynn algorithm is more accurate.
Because of the high grade polish of the samples used, errors in phase due to flatness are estimated to be less than 2.5 nm. However, smoothly varying phase aberrations caused by the arrangement of the fiber sources were present for all measurements. One way we removed them was to record the phase for a flat region of the sample, unwrap this phase, and then fit the phase profile with Zernike polynomials as an orthogonal basis set. We then stored the fitted phase and for each measurement subtracted it from the phase recovered at the CCD.
3. Obtaining a surface profile using Fourier optics approximation
The retrieved amplitude and phase at the camera location does not lead directly to a measurement of the test area on the sample. Diffraction causes the complex envelope formed by the amplitude and phase to change as the light propagates to the camera, in our case obeying the approximation given by Fourier optics. We can therefore use the principle of Fourier optics to reverse this process and determine the complex envelope at the test region, as described in the Appendix.
In order to find the exact propagation distance to the sample we placed a small 60-µm-diameter feature in the field of view. Initially we set the propagation distance Z to the measured distance between the camera and the sample’s test surface. We then made an interferogram, executed the software propagation algorithm, and analyzed the amplitude of the light at the presumed sample plane. Because the feature was a small phase object, we could adjust Z until the amplitude became uniform with no apparent diffraction rings, thereby finding the correct value of Z.
At the end of the software processing chain, the phase of the light at the test sample needed to be extracted and scaled to physical dimensions. We verified our estimate of this scaling factor by measuring with a confocal microscope the depth of a pit generated in fused silica and comparing this depth with the PSDI-measured phase. The pit was 300 µm in diameter and 750 nm deep. The 1024 pixel square images at the sample plane were found to have a pixel size of 4.9 µm and a scaling of height to phase of 0.194 µm per wave.
The system software is written in LabVIEW and implements all the features needed to calibrate and run the software analysis chain. The final phase unwrapping was reduced to a sub-frame region of interest (ROI) in order to decrease the processing time. This ROI shows in Fig. 3, where areas outside the ROI remain wrapped. The volume and peak height inside the ROI were recorded along with time-stamped snapshots of the surface profile. For the size of region of interest shown in Fig. 3 (~2x2mm2), the instrument generates a surface profile every four seconds. This acquisition rate could be further increased with computer hardware upgrades.
Fig. 3 Surface profile of laser heated fused silica derived from PSDI measurements (both x- and y-scales are in mm). The asymmetry from left to right is due to interferometry setup. The 2D phase plots show a region of interest that has been unwrapped and scaled to a height which would be accurate if the sample were at room temperature. Vertical lineouts through the surface profiles illustrate the shape of the expanded region.
4. Thermally-induced phase change measurements
The interferometry setup is used to measure the change in surface profile during LCVD processing. The measurement requires taking into account the change in surface profile due to heating the substrate material in order to distinguish between the apparent surface profile and new material added through deposition. The change in surface profile from laser heating is a result of thermal expansion of the material and depends on the material type and its associated coefficient of thermal expansion. In addition, the photo-thermal response of the material—which affects the measured phase through changes in refractive index—must be taken into account. To separate these effects from our real-time deposition measurements, a thermal model of the heating was created and experiments were conducted on different substrate materials for calibration purposes. The result is a software algorithm that can determine the background surface profile caused by laser heating and subtract it from the measurement. The algorithm requires the real-time measured laser power, the pre-experiment measured beam diameter and the substrate material properties.
A CW CO2 laser (Coherent Gem C-30, maximum output power of 20 W) is employed to heat the substrate. A detailed specification of the laser heating test bed can be found elsewhere [11]. The output of the laser passes through an acousto-optic modulator and beam formatting optics that allow various combinations of power and beam size to be incident on the test samples. Laser light passing through a leaker mirror is measured and used in a feedback loop to stabilize the power to <2%, but this feedback results in a time of 30 s or greater to ramp to the power set point. The power can be set as high as 8 W at the sample and can be shaped slowly in time to produce various envelopes.
The two materials tested were fused silica and BK7. Fused silica has a relatively low coefficient of thermal expansion (α = 0.55 ppm/K) and when heated above the glass transition point (Tg~1350 K) leaves a densified pit after cooling due to structural relaxation effects during cooling [12]. Conversely, BK7 has a relatively high expansion coefficient (α = 7.1 ppm/K) and leaves a bump after heating above Tg due to an arrest in the viscoelastic axial strain during cooling [13]. If a high enough temperature is reached, both materials begin to evaporate, e.g. >2500 K for fused silica [14]. In the results shown below, the power where evaporation occurs is used as the upper limit for temperatures that are reasonable to use in LCVD for each material, PFS = 5 W and PBK7 = 1.75 W for silica and BK7 respectively.
We selected twelve different evenly spaced power levels up to the experimentally determined evaporation power for each material. Two different temporal functions for power, P(t), were used: a nominally square pulse exposure and another with a power ramp-down. The square pulse shape function included a 30 s rise due to power stabilization in the feedback loop along with a steady-state portion of ~100 s, followed by an abrupt power shutoff. The ramp-down function is identical to the first square pulse, followed by a 30 s ramp to zero power at the end. The gradual ramp to zero power allows the material to cool slowly and results in a smaller pit for fused silica and a smaller bump and BK7, as we discuss later.
The measured apparent height of the heated region of the sample comes from two sources, expansion of the material and a change in index of refraction with temperature. The refractive index change affects the measurement because PSDI measures relative optical path length that also includes laser-heated material as shown in Fig. 1. The height of the thermally expanded region follows the power envelope closely, which is expected because the elastic response (i.e. speed of sound) is much faster than the power variations in the envelope.
The maximum height near the end of the flat portion of the power envelope increases with the power set points used among different test sites. At a set point of 0.18 W, the height is 1.5 µm while a set point of 5.95 W leads to a height of 8 µm. Figure 3 shows two-dimensional profiles of the thermally expanded region at two different power set points. Due to the two-fiber arrangement of the PSDI setup, there are two surface profiles generated for each object on the test sample: a primary and a “ghost”. For LCVD depositions smaller than 1 mm the second surface is outside the field of view, but the thermally expanded regions extend from the location of the peak temperature to the edge of the sample and hence affect the profile in the field of view. The peak of the ghost profile is reversed in height and would appear to the right (horizontal shift) of the profiles shown in Fig. 3. This ghost causes the sharp drop off and the asymmetric horizontal profile. Vertical lineouts do not have this asymmetry and are shown for the same four powers below the two dimensional profiles in Fig. 3. For each of the twelve power set points used on each material a vertical lineout was used to determine the height difference between the peak and a point 1 mm away in radius. Some of the higher set points above the evaporation threshold were removed from the final data set that was used to compare to the model in Fig. 4.
Fig. 4 Measured peak OPD (solid circles) as a function of laser power for BK7 (left panel) and fused silica (right panel) along with simulated total OPD (solid line), the thermal expansion component of the OPD (dashed line), and the refractive index component of the OPD (dotted line).
5. Simulating the thermally-induced optical path increase
In order to compare our experimental results to the predicted photothermal behavior, finite element modeling is used. A detailed description of the modeling details is found in the Appendix and in Ref [15]. A laser beam with an 814-µm Gaussian spatial profile is used to heat a cylindrically shaped disk 50.4 mm in diameter and 10 mm thick. Measured power traces, P(t), are fit to a logistic analytic function (to capture the ~30 s ramp portion of the power exposure) and input to the model. The calculated temperature field T(r,z,t) is used to evaluate the change in index, Δn, while the axial displacement, ΔL due to thermal expansion captures the length change. The total OPD change as a function of radial position caused by laser heating is
where Tref = 293.15 K is the reference temperature and dn/dT is the derivative of refractive index with respect to temperature at 532 nm. The room temperature refractive indices are 1.52 for BK7 and 1.46 for fused silica. In simulating OPD, the thermal expansion coefficient that drives the displacement is fixed while the effective dn/dT is determined by varying dn/dT in simulations to match OPD with the experimental data at a power level of 1 W. For laser powers above ~1 W, the total OPD expressed in mm varied linearly with dn/dT as 0.226 mm.K for BK7 and 0.281 mm.K for silica. The OPD difference between the peak of the expansion and a location 1 mm in radius is calculated from simulations. This OPD is compared to the PSDI measured OPD where a vertical lineout through the optical path surface profile (Fig. 3) is extracted and an average difference from the peak to a point 1 mm in radius in both direction is calculated.Figure 4 displays the measured OPD for BK7 and fused silica as a function of peak incident laser power at a laser beam size of 814 µm. Data for BK7 were only collected for powers less than 2 W to prevent evaporation. Data for fused silica were collected for powers up to 6 W due to its higher evaporation temperature relative to BK7 (3000 K vs. 1500 K). Also shown in Fig. 4 are simulated OPD for both materials, along with the individual contributions due to changes in the refractive index (ΔnL) and the thermal expansion (ΔLn). The simulations agreed well for the BK7 case using literature values of 3.5 ppm/K [16]. However, using a literature value of 9 ppm/K for fused silica [17] results in a ~40% overestimate. Therefore, a slightly lower value of 7.2 ppm/K was used for the simulation shown in Fig. 4. As expected, the contribution to OPD from the thermal expansion term of Eq. (1) dominated the OPD for BK7, accounting for ~79% of the total signal, while the inverse was true for fused silica where thermal expansion accounted for only ~10% of the total signal. Thus, in the case of fused silica, the fact that the measurement occurs through the bulk of the glass served to amplify the photothermal signal, greatly facilitating the use of PSDI in laser alignment.
6. LCVD characterized with PSDI
Tetraethylorthosilicate (TEOS) silica precursor is applied by LCVD on a fused silica surface and monitored using the PSDI setup by probing through the fused silica substrate. A focused ~0.7-mm-diameter Gaussian beam from a CO2 laser [18] is used to heat a surface to a temperature higher than the thermal decomposition point of the TEOS precursor (923 K). Simultaneously, a co-incident gas containing the precursor is injected with a nozzle. The precursor (~0.2%) is carried from a bubbler using nitrogen as the carrier gas and impinges on the surface at atmospheric pressure, displacing the ambient air. As the surface is heated, material accumulates on the surface as a result of the local decomposition of the TEOS within the heated region and polymerization of SiO2 monomers occurs to form fused silica. This LCVD material is amorphous silica with optical properties near those of the fused silica substrate, including high transmission and high damage threshold at UV wavelengths.
Figure 5 shows the peak height of the silica deposited relative to the substrate surface over a 1000-second exposure. The peak height and a surface profile are captured every four seconds using a tracking algorithm implemented in the LabVIEW software, which controls both the LCVD and PDSI systems. Small perturbations in the time profile in Fig. 5 are a result of phase errors in the PSDI measurements, errors such as those caused by vibration independently affecting the PSDI fibers. Phase errors can also occur because the measured surface is moving during laser exposure and silica deposition; these errors can result in inaccurate phase unwrapping. By applying a rolling average over ten measurements the effect of these errors on measurements of deposition rates are reduced. The main consequence of applying such a filter to the measurements is a reduction in overall time response of the system.
Fig. 5 A plot of the height of a silica deposition as a function of time. The first 100 s show the height measured by PSDI if the thermal expansion of the material is not subtracted. From 100 to 1000 s, silica is deposited at a linear rate. After the laser exposure ends at 1000 s, the deposited material cools to its final profile. The inset image shows a surface plot of the final surface profile.
Pyrolytic LCVD deposition at a rate of ~1.3 nm/sec is observed consistent with previously reported ex situ measurement [18]. Using this dynamic measurement as feedback to turn off the LCVD laser prevents over- or under-filling a pit that might otherwise occur from using a constant exposure time based on ex situ measurements. This accurate filling highlights PSDI’s ability to track 10-nm-scale vertical displacement in laser-reactive heated environments. The PSDI measurements can therefore provide insight into subtle additive processes and material dynamics.
Another capability enabled by real-time PSDI profiling is the indirect registration of the deposited material to the location of the pit, as illustrated in Fig. 6. Before deposition, a thermally expanded region is created by operating the LCVD laser at low power with no precursor gas. The large deformation shown in Fig. 6 is the result of the laser-induced thermal expansion and the associated photothermal exaggeration of this expansion. The pit to be filled is superimposed on the expanded surface and its apex is off-center relative to the location of maximum deformation from laser heating. By translating the sample, the peak of the thermally deformed surface and the apex of the pit can be aligned. Since the peak of the thermally expanded region occurs at the location of highest temperature, the thermally activated LCVD deposition is naturally registered to the center of the pit. More detailed results of these experiments will be reported elsewhere.
Fig. 6 A small pit (green outline) in a fused silica sample to be filled by LCVD is aligned to the thermal bump caused by heating with the LCVD beam resulting in registration to an accuracy of a few microns.
7. Conclusions
PSDI is a useful technique for nanometer-scale real-time profiling and feedback control of laser-based processes. Arranging the interferometer hardware in an off-axis viewing direction from the back side of the sample results in a system where no space restrictions are placed on hardware that must be placed near the working surface. In addition, the backside viewing through the heated substrate enables registration of the LCVD deposition with the targeted pits, while avoiding the extreme thermal and gaseous environment above the treated site. A model was developed allowing the comparison of measured profiles to simulated profiles based on material properties. Using such a model one could envision using measured surface profiles to extract the temperature dependence of the mechanical and optical properties of a material. By treating the unknown material property as a parameter in the simulation and finding the value which matches experiment a temperature dependence could be inferred. This technique could be used at temperatures much greater than 1000K where the coefficient of thermal expansion and change in index of refraction are difficult to measure by other means in a furnace configuration. These results illustrate that significant control over LCVD is realizable based on PDSI real-time measurements and offer insights into the dynamics of many important processes, including CVD and thermomechanical material response.
Appendix
Thermomechanical model
A 2D axisymmetric geometry is used to describe the volumetric energy deposited into the silica as a function of time t, radial position from the center of the beam r, and depth into the sample z:
In Eq. (3), P(t) is the deposited time-dependent laser power (reduced by Fresnel reflection at the surface), β(T) is the temperature-dependent laser absorption coefficient and r0 is the 1/e2 radius of the Gaussian beam. The reflectivity at normal incidence of fused silica at 10.59 µm is 15% and varies less than 1% over the temperatures ranges considered in our experiments [18]. The temperature-dependent absorption coefficient for the 10.59-µm CO2 laser radiation was measured by McLachlan and Meyer to vary as β(T) = –7.64 mm−1 + [12.43x10−2 mm−1K−1]T between 298 K and 2073 K [19]. For transient analysis the energy deposition is sufficiently resolved within the laser absorption depth (4 µm at 2000 K) by using a highly non-uniform finite-element mesh of 8,270 elements (7911 domain elements and 359 boundary elements). The element size ranged from 1 µm directly below the laser to 500 µm at the opposite boundary of the sample. With the volumetric heat source Q, defined above in Eq. (3), the quasi-static nonlinear heat equation can then be described aswhere ρ, Cp and κ are the mass density, heat capacity at constant pressure and thermal conductivity, respectively. Convective heat transport from material displacement is ignored.Once the laser deposits heat into the silica, thermal expansion and contraction causes the material to deform and stress to develop. The deformation and stress are obtained by solving the elastic equations
where σ and ε are the isotropic Cauchy stress and strain tensors respectively, C is the elasticity tensor and α is the coefficient of thermal expansion. Equations (4) and (5) are thus coupled through the temperature field T(r,z,t). In Eq. (7), ε is written in terms of the displacement vector u. The thermal expansion coefficients for fused silica and BK7 were taken from [15, 20] and from [16] for BK7, respectively. Note that α = 7.1 ppm/K for BK7 and was held constant while α for fused silica varied as 0.97 ppm/K = 0.49 ppb/K2 × T where T is in K. From the laser-induced temperature field the change in refractive index is calculated, and from the axial displacement the path length increase due to thermal expansion is determined. In preliminary simulations, the inertial term in Eq. (5) was included but was found to have less than a 0.02% effect on the OPD calculations and was subsequently dropped.Fourier optics propagation model
The discrete fast Fourier transform (FFT) of the complex field envelope is
where r and s are array indices running from 0 to M–1 and N–1, respectively; is the complex array of amplitude and phase values at the camera’s location; and M and N are the array sizes. In the spatial frequency domain the properties of the light at an upstream location are back propagated by multiplying the FFT by a transfer function [21]where and where z is the propagation distance, R is the wavefront radius at the camera (which equals the distance from the fibers to the camera), p is the camera pixel size, and θ is the incidence angle of the light propagating into the CCD. To reduce distortions, the camera was placed parallel to the test sample as shown in Fig. 1. This results in the wavefronts of the propagating light impinging on the CCD at an angle; therefore, the FFT of the phase array represents different spatial frequency ranges for the two camera axes, which necessitate calculating T[r][s] for different ranges of u and v. The distance over which the light is propagated between the camera and the sample does not change during an experiment, hence T[r][s] can be calculated and stored once and reused to improve the speed of the software processing. In the transfer function we neglected the change in index from air to glass as the light propagates back to the test surface. Finally the inverse FFT is applied to the product of the FFT and transfer function to obtain the complex envelope at the sample.Acknowledgments
The authors express deep gratitude to R. Negres for her careful reading and input to this manuscript. Enlightening conversations with C. Grigoropoulos, J. Yoo and D. Lee of the UC Berkeley Thermal Lab regarding LCVD are gratefully acknowledged. The authors thank N. Nielsen, J. Hughes and F. Ravizza for technical assistance. S. Elhadj and M. Matthews acknowledge support from UCFR grant #12-LR-237713. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.
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Thalangunam Krishnaswamy S.
07/21/2014 1:11 AM
It made a good reading of the paper.