MEASURING transient surface temperatures of substrates

Transcription

1 116 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 21, NO. 1, FEBRUARY 2008 Transient Thermoelastic Response of Nanofilms Under Radiation Heating From Pulsed Laser-Induced Plasma M. D. Murthy Peri, Dong Zhou, Ivin Varghese, and Cetin Cetinkaya Abstract Measuring transient surface temperatures of substrates excited by nanosecond impulsive-type thermal sources is a nontrivial problem due to limited response times of many current sensors and the thinness of thermal skin at the nanosecond-time scale. An indirect transient surface temperature measurement technique for nanofilms subjected to a nanosecond dynamic loading is presented and demonstrated. The intensity profile calibrated based on the plasma radiation energy measurements is used as a boundary condition for finite-element analysis to estimate the transient surface temperature and the stress tensor induced in a 100-nm chromium film bonded to a quartz substrate due to the thermal radiation heating of the laser-induced plasma. The current approach is useful for predicting the damage threshold of nanofilms in laser-induced plasma (LIP) particle cleaning, as the direct and indirect transient temperature measurements currently available are unreliable for nanosecond impulsive thermal excitations. Particle cleaning techniques based on LIP have been under development for damage-free removal of sub-100-nm particles. The plasma core formed in this cleaning approach is a source of nanosecond-range impulsive radiation and subsequent thermomechanical excitation of the substrate and, consequently, possible substrate damage. The transient temperature measurements are used to estimate the peak surface temperature and the thermomechanical stresses induced in the substrate. Index Terms Nanofilms, nanosecond radiation excitation, photomask, surface temperature measurements, thermoelastic response. I. INTRODUCTION MEASURING transient surface temperatures of substrates excited by nanosecond impulsive-type thermal sources is a nontrivial problem due to limited response times of many current sensors and the thinness of thermal skin at the nanosecondtime scale. In this paper, an indirect transient surface temperature measurement technique for bonded nanofilms subjected to a nanosecond dynamic loading, generated during a pulsed laser-based sub-100-nm particle removal process, is presented and demonstrated. Removal of sub-100-nm particles from substrates without damage is a major challenge in various industries such as semiconductor, nanomanufacturing, and MEMS fabrication. With the demand for faster and efficient integrated circuits, the Manuscript received October 26, 2006; revised September 10, The authors are with the Department of Mechanical and Aeronautical Engineering, Center for Advanced Materials Processing, Wallace H. Coulter School of Engineering, Clarkson University, Potsdam, NY USA ( cetin@clarkson.edu). Digital Object Identifier /TSM feature sizes are shrinking to nanometer scale and, as a result, the tolerable particle size on the substrates is currently being reduced to sub-100-nm levels. According to the 2006 update of the International Technology Roadmap for Semiconductors (ITRS), the minimum diameter of spherical defect size that can be tolerated (in polystyrene latex sphere equivalent dimensions) on the substrate is 35 nm by 2010 and the defect size on the EUV masks is 36 nm for the year 2010 [1]. Manufacturable solutions for removal of defects due to foreign particles from EUV masks, of size nm, are classified as unknown by the ITRS roadmap, while the sub-100-nm particle removal remains a challenge. The main source of removal difficulty in the sub-100-nm range is due to the fact that while the removal force required for detachment is directly proportional to the characteristic geometric dimension of a particle (i.e., its diameter for spherical particles), the mechanical strength of the features patterned on a substrate depends on their cross-sectional areas and aspect ratios. The industry reports on substrate damage during cleaning in recent years often indicate that the required detachment force for nanoscale particles has been converging to the characteristic strength of features [2], [3]. Among the techniques that are being investigated for sub-100-nm nanoparticle removal along with the laser-induced plasma (LIP) removal technique are brush scrubbing, megasonic cleaning, and CO snow cleaning. In recent years, the shock waves generated by LIP have been demonstrated for removal of sub-100-nm particles, i.e., 60-nm PSL particles and nm PSL particles from silicon substrates [4], [5]. In LIP cleaning, a pulsed laser beam is focused and the plasma is formed at the focal point of the lens due to dielectric breakdown of air. The formed plasma expands to a limit size and then saturates while emitting a thermal radiation field. The hot core of air surrounding the plasma emerges as a shock wave and detaches after a certain period of time. In the current procedure, this emerging shock wave is directed onto the surface with the particle to break the nanoparticle-substrate adhesion bond. This approach could be considered as a selective nanoparticle removal technique as the shock pressure can be imparted on the locality of the particle that has to be removed rather than targeting the entire substrate. Larger areas could be cleaned with the help of a scanning system. In the conventional cleaning techniques, the entire substrate surface is imparted by the dynamic force magnitude and thus precise control of forces is not possible. The LIP technique could reduce the concern of adding particles due to post-cleaning processes, which is a disadvantage in conventional cleaning techniques in various applications, where the substrate would be dipped in a fluid and the /$ IEEE

2 PERI et al.: TRANSIENT THERMOELASTIC RESPONSE OF NANOFILMS UNDER RADIATION HEATING 117 contaminant particles in the fluid would deposit on the substrate, i.e., to remove a small number of particles they tend to add more particles or to shift particles around due to the post-cleaning processes. As with the other nanoparticle removal techniques, due to radiative and convective heat effects, substrate damage is also a possible concern with the LIP nanoparticle removal technique when smaller nanoparticles are targeted below the threshold gap distance, defined as the safe distance between the center of the plasma and the substrate at which no substrate damage is observed. This distance would change from substrate to substrate and the target particle on the substrate and the safe distance for removal of sub-100-nm PSL particles from silicon substrate without any damage has been reported [4]. The potential causes for the possible damage below the threshold distance include shock wave temperature, pressure, and the plasma radiation-induced damage as well as the direct contact of the LIP core with the substrate. The transient pressures available from the LIP technique are on the order of kilo-pascal levels [5], [6]. The pressure levels are typically too low to result in any mechanical substrate damage, as the strength of the substrate is often three orders of magnitude higher than the shock pressure. The effect of shock temperature and pressure on a film bonded to a substrate is determined by a computational analysis based on the finite-element (FE) method and it is reported in [6] and [7]. From the results of the previous FE simulations it can be concluded that the surface stresses induced due to surface temperature were dominating the stresses induced due to shock pressure loading. However, the induced stresses, radial (a peak level of approximately 650 MPa), shear ( 120 kpa), and axial ( 200 kpa) stress components with both thermal and mechanical loadings, were within the damage limits of the material when the effect of the level of dynamic strain rate is taken into consideration [7]. It is then concluded that the substrate damage could be caused by the radiation heating generated by the LIP. The measurement of the substrate surface temperature and estimation of stresses induced when the substrate is subjected to nanosecond-scale excitation due the radiation heating of the plasma requires giga-hertz frequency range sensing. The peak pressure of the shock wave could be measured by the microsecond rise time shock transducers as reported in [5], as the shock wave expansion takes place in the time scale of microseconds. However, the measurement of the substrate surface temperature due to the radiation of plasma which is a nanosecond phenomenon requires substantially faster rise time sensors. The most commercially available transient temperature measurement sensors, for both direct and indirect techniques, have rise times ranging from microsecond to milliseconds. For instance, the direct measurement technique employing thermocouples has rise time in milliseconds [8] and the rise time of a fiber optic temperature probe is approximately 1 s [9]. II. EXPERIMENTAL PROCEDURE FOR RADIATION ENERGY MEASUREMENTS The direct measurement of transient surface temperature, when a thin film or a substrate is excited by a nanosecond electromagnetic (radiative) pulse, is currently not possible by commercial sensors. In order to measure surface temperature Fig. 1. (a) Laser induced-optical emission profile in time (t) measured by [17] and (b) normalized intensity profile of (a) for first 45 ns. by a high-frequency excitation, a nanosecond rise time temperature sensor is required and the difficulty of attaining thermal equilibrium in short time (nanosecond) is a major measurement difficulty. In the current paper, an indirect noncontact technique for approximating the surface temperature rise under a nanosecond LIP radiation exposure is presented and demonstrated. In this technique, the LIP radiation energy per pulse is measured and the measured energy is superimposed over the known LIP irradiation profile, and this renormalized intensity profile is then used as input to the fully coupled FE analysis (commercial package ABAQUS V6.6) to predict the transient thermoelastic response of the surface of the film and/or the substrate. The induced thermoelastic stresses which could be used further to estimate the onset of damage of the nanofilm are of practical interest. In generating an LIP core, a nanosecond Gaussian profile pulse from a laser is focused with the aid of a convex lens, to initiate rapid plasma formation in the air. So, when the laser energy is being pumped as a Gaussian pulse, the intensity of the plasma would increase until almost all the laser energy is absorbed in a given pulse. Thus, it is reasonable to approximate that the plasma intensity would attain its maximum at the

3 118 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 21, NO. 1, FEBRUARY 2008 Fig. 2. Schematic of laser-induced plasma radiation energy measurement experimental setup. end of the pulse duration of the laser. As reported in [10], the laser intensity and the temporal profile of the laser induced optical-emission can be obtained by collimating the optical emission using uncoated quartz lens and measured by a biplanar phototube. The laser pulse and the temporal intensity profile of the laser induced optical-emission measured by [10] are plotted in Fig. 1(a). Fig. 1(b) depicts the normalized radiation intensity profile of the generated plasma which is used as a boundary condition in the present paper. The profile reported in [10] was normalized in the first 45-ns period and then approximated by a function to extrapolate the profile for 400 ns, as the plasma intensity diminishes [11]. To obtain the transient temperature response of the surface subjected to the LIP radiation, calibrating the peak of the intensity profile is nontrivial. This is due to the reason that attaining thermal equilibrium in such short time scale is difficult and the unavailability of nanosecond rise time sensors to measure the surface temperature directly. In the current paper, the radiation profile was calibrated by calculating the peak intensity based on the plasma radiation energy, measured with the aid of a volume absorber energy/power meter. A set of experiments similar to those reported in [12] were designed and conducted to determine radiation energy from the LIP core. In these experiments, a pulsed Nd: YAG (Quantel Brilliant) laser at 1064 nm with 5-ns pulsewidth, 5-mm beam diameter, and 370 mj was employed. The laser beam was focused using a 100-mm focal length convex lens with a 1064-nm anti-reflective coating. The thermal head used to measure the radiation energy of the plasma was a medium power volume absorber power/energy meter (Ophir, Model: 30(150) A-HE). The medium power meter has a spectral bandwidth that ranges from 190 nm to 3 m except nm. The display unit coupled to the power meter was a radiant power energy meter (Newport, Oriel Series, Model: 70260). The schematic of the experimental setup is depicted in Fig. 2. The critical parameter for particle removal is the gap distance (i.e., the distance between the center of the plasma and the surface of the substrate). The smaller the gap distance, the higher are the pressure and the temperature, which might result in damage of the probe. To avoid damage to the active surface of the power meter, initially it was placed at a gap distance of 22 mm. The laser was fired in single-shot mode and the corresponding total radiation energy deposited on the sensor area was recorded. This procedure was repeated for firing distances ranging from 22 to 3 mm. In Fig. 3, the measured radiation energy (milli-joules) as a function of gap distance is summarized. The average corresponding peak intensity (in gigawatts per squared meters) obtained in Fig. 3. Radiation energy (E ) deposited on volume absorber energy meter of mm area, as a function of firing distances (d). single-shot mode at these firing distances was then calculated based on the dimensions of the sensor area (diameter of the sensor area, mm). Further, the intensity was fitted to estimate the intensity of the plasma at any firing distance. The fitted peak intensity as a function of firing distance, obtained from the radiation energy measurements, is presented in Fig. 4. It was approximated that the radiation intensity profile acting at all the firing distances would arrive uniformly at the probe surface, as the radiation of the plasma propagates with the speed of electromagnetic waves except that the magnitude would be a function of firing distance. III. COMPUTATIONAL ANALYSIS FOR TRANSIENT THERMOELASTIC RESPONSE OF FILM SURFACE In the current paper, based on the plasma radiation energy measurements and the intensity profile, the temperature of the surface is indirectly estimated by a transient FE analysis. A fully coupled thermomechanical analysis based on FE was performed to obtain the surface temperature and the stress tensor induced on the surface of a 100-nm chromium film bonded to a quartz substrate irradiated by an LIP core. For verification purposes, a test simulation was performed to compare the simulation results with the 1-D heat conduction formulation for laser irradiation. The 1-D heat conduction equation for laser irradiation described in [13] and [14] was used to estimate the rise in surface temperature and to verify the FE model for the plasma ir-

4 PERI et al.: TRANSIENT THERMOELASTIC RESPONSE OF NANOFILMS UNDER RADIATION HEATING 119 (thickness) 100 nm to compare the rise in surface temperature of the film obtained by the 1-D heat conduction equation and the FE simulations. The chromium layer was meshed and the intensity was uniformly loaded on the surface of the film in FE simulation. The transient temperature rise was then analyzed. The transient temperature rise obtained from finite element simulations is also plotted in Fig. 5. The peak temperature rise observed was 9.94 K. From Fig. 5, the difference between responses after the peak is attributed to the fact that the FE analysis is based on a fully coupled thermomechanical model while the closed form solution holds only for heat conduction with no mechanical effect. Thus, the FE model can be used for the surface temperature estimation. Fig. 4. Measured intensity profile (I ) of laser-induced plasma as a function of gap distance (d) deposited on the radiation energy meter. Fig. 5. Transient temperature profile (1T) of chromium film irradiated by square pulse with t =20ns. Solid represents temperature rise obtained from 1-D heat conduction solution and transient temperature rise obtained from FE simulations is denoted by dashed line. FE simulations were carried on 1000-nmthick chromium film. radiation analysis when an irradiation profile is absorbed uniformly by a surface. For the verification simulations, the temperature of the film was estimated by assuming that a square pulse with a pulsewidth of 20 ns was imposed on a chromium surface. The chromium film with the thermal diffusivity m s, the intensity GW/m, and the thermal conductivity W/m K was used for the calculation of surface temperature rise, based on 1-D heat conduction. From the closed-form solution of the 1-D heat conduction equation when the laser flux density is absorbed uniformly by the film surface, the temperature rise of the surface of the film as a function of time due to the thermoelastic response of the film, for a pulsewidth ns, is plotted in Fig. 5. The peak temperature rise attained is obtained as 9.4 K (Fig. 5). The square pulse with a pulsewidth ns and intensity GW/m was then imposed on a chromium layer of dimensions 1000 nm IV. TRANSIENT THERMOELASTIC RESPONSE OF A SURFACE TO RADIATION HEATING An axi-symmetric domain with m (in the radial and axial directions) chromium layer on a m quartz substrate (Fig. 6) was meshed for obtaining its response under the thermal excitation approximated in Fig. 1(b). The properties of the chromium film and the quartz substrate used in the linear, fully coupled thermoelastic FE analysis are tabulated in Table I. Infinite elements were used at the right edge and at the bottom of the quartz substrate to minimize the reflection of the acoustic wave. The length of the model in radial direction is selected as 100 m, to ensure that no boundary effects would be present in the FE domain. The minimum element size in the mesh was selected considering the thermal thickness and the minimum acoustic wavelength criterion. When a surface is excited by a high-frequency (short) heat pulse, a thin thermal skin is generated on the surface where the pulse is applied. The thickness of thermal skin for 100-nm chromium film excited by a 10-ns pulse is approximated as nm and the maximum element length in thickness direction (using ten elements per the length of skin depth) is calculated as nm. The minimum wavelength that can be excited by the input pulse acoustically is approximately m and the maximum element dimension in acoustic wave propagation (using six elements per the minimum wavelength) is obtained as m. It can be observed that the thermal skin is thicker than the chromium film itself. In order to capture the effect of the thermal skin thickness, a 500-nm quartz substrate bonded to the chromium film is used in the FE mesh. Since the quartz substrate s thermal conductivity is nearly two orders of magnitude less than chromium film, it is reasonable to have a 500-nm quartz substrate to capture the thermal skin in this model. The element size used in the FE mesh for the chromium film and the quartz substrate considering the thermal skin thickness and minimum acoustic wavelength criteria are finally determined as nm and nm, respectively. The normalized intensity profile (Fig. 3) prescribed as dynamic heat boundary condition for the 100-nm chromium film top surface and heat transfer analysis, using dynamic temperature displacement coupling with distributed flux loading, was performed for the prediction of the surface temperature and the

5 120 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 21, NO. 1, FEBRUARY 2008 Fig. 6. Axisymmetric FE mesh for 100-nm chromium film on 500-nm quartz substrate. Bottom and right boundary of domain is meshed with infinite elements. TABLE I PROPERTIES OF 100-nm CHROMIUM FILM AND QUARTZ SUBSTRATE USED IN FE ANALYSIS induced stresses (,, and ) in the film due to the radiation of the plasma. Note that due to the axisymmetric nature of the problem the shear components and are zero. Later, the intensity profile was estimated at a gap distance of mm by multiplying the normalized intensity profile with a factor of 9.09 and this profile was prescribed on the film. The axisymmetric elements used were four node, continuum, reduced integration, and temperature-displacement type. A time step of was used for the transient thermoelastic simulations. The simulations were run for 325 ns for the peak intensity of GW/m and 400 ns for the case with GW/m. The results of the FE simulations were analyzed on the surface of the chromium film, when subjected to two different peak intensities. V. RESULTS OF TRANSIENT THERMOELASTIC ANALYSIS The transient thermoelastic response of the chromium film under nanosecond-scale (impulsive) radiation excitation was obtained and analyzed. It can be seen from Fig. 7(a) that the peak temperature rise on the surface film for a peak intensity of 1 GW/m is 49.5 K. The peak radial, shear, and axial stresses attained on the surface of the nanofilm are 212 MPa, 64.6 Pa, and 5.1 kpa, respectively. The magnitude of the peak transient stresses induced on the surface appear to be low, but the total stresses components on the film could be high enough to cause surface damage. The results indicate that the stress state in the film is dominated by the radial expansion Fig. 7. FE simulations results for temperature rise (1T) and radial stress ( ), when 100-nm chromium film bonded to quartz substrate is irradiated with LIP profile with maximum intensity I =1GW/m. (a) Transient surface temperature rise and (b) radial stress induced on surface of film. of the film. The CTE of the chromium film is two orders of magnitude higher than the quartz substrate, on which the chromium film is bonded (Table I). This bonding results in less

6 PERI et al.: TRANSIENT THERMOELASTIC RESPONSE OF NANOFILMS UNDER RADIATION HEATING 121 TABLE II ESTIMATED SURFACE TEMPERATURE (1T), MAXIMUM RADIAL STRESS ( ), MAXIMUM AXIAL STRESS ( ), AND MAXIMUM SHEAR STRESS ( ) INDUCED ON SURFACE OF A 100-nm CHROMIUM FILM BONDED TO LOW CTE SUBSTRATE (QUARTZ) reported in [18], there would not be any damage at a threshold firing distance of 2.5 mm. Fig. 8. FE simulations results for temperature rise (1T) and radial stress ( ), when 100-nm chromium film bonded to quartz substrate is irradiated with LIP profile with maximum intensity I = 9:09 GW/m. (a) Transient surface temperature rise and (b) radial stress induced on surface of film. shear stress and higher radial stresses on the surface of the film. The temperature rise and the radial stresses obtained for a peak radiation of GW/m are plotted in Fig. 7(a) and (b), respectively. The transient surface temperature rise at peak intensity of 9.09 GW/m, obtained at a gap distance of 2.5 mm, is 450 K and the peak radial, shear, and axial stresses induced are 1.92 GPa, 840 Pa, and 46.4 kpa, respectively. The transient temperature and the radial stresses attained on the surface of the film are presented in Fig. 8(a) and (b), respectively. The peak surface temperature, the radial, the shear, and the axial stress at different firing distances are approximated based on linearity and tabulated in Table II. It is interpreted that the damage in the 100-nm chromium film could be due to the radial stress induced (thermoelastic stress) by the laser-induced plasma irradiation rather than the temperature rise directly. The static yield stress of chrome film is 362 MPa. However, considering the experimental studies and the dynamic strain rate factor VI. CONCLUSION AND REMARKS Thermomechanical responses of thin film under nano-second time scale radiation loading conditions are investigated for estimating the surface temperature and the thermomechanical stresses induced, which could be used for damage analysis of thin films bonded to a substrate. As the direct and indirect temperature measurements are unreliable for nanosecond thermal excitations, the experimentally measured plasma radiation energy is used to estimate the surface temperature and the stresses induced in a 100-nm chromium film on low thermal expansion coefficient substrate using the FE method. The radiation energy of the plasma per pulse was measured using a volume absorber energy meter. The intensity at each gap distance was calculated based on the energy measured and the dimensions of the energy meter sensor. The intensity profile was approximated and normalized using the data from the literature. The measured intensity data was fitted to estimate the intensity of the laser induced plasma at a range of gap distances. The normalized intensity profile was imposed on a 100-nm chromium film and the surface temperature and the stresses induced in the surface were predicted via an FE analysis. This measurement approach can be used for predicting the damage threshold of nanofilms, as the direct and indirect temperature measurements currently available are not reliable for nanosecond-rise time dynamic loading conditions, i.e., impulsive thermal loads such as pulsed lasers. The induced stresses can be compared with the dynamic yield stress of the substrate to predict the damage of various substrates. It is concluded that even though the temperature rise on the surface is not sufficient to cause thermal damage (i.e. melting, phase transformation) the thermally induced stresses could cause damage to the substrate. This technique could be potentially used for predicting

7 122 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 21, NO. 1, FEBRUARY 2008 the onset of damage (material alteration) for a variety of substrates using the LIP technique, by determining the threshold (experimentally) and then matching this gap distance with the FE analysis to determine the maximum radial stress which the film can withstand. Comparing this maximum stress obtained from the FE simulations with the yield stress (static case) of the film gives the dynamic stress of the film due to the loading of the nanofilm by impulsive radiation heating liberated by plasma irradiation. Thus, utilizing the presented approach, the damage initiation/material alteration and ultimately the strength of the material (both in films and substrates) subjected to impulsive loading such as pulsed lasers can be predicted. [17] Thermal and mechanical properties of 100 chromium film and quartz substrate Intel Corp. Santa Clara, CA. [18] I. Varghese, D. Zhou, M. D. M. Peri, and C. Cetinkaya, Onset of material alteration due to laser induced plasma exposure in nanofilms deposited on photomasks, J. Thin Solid Films, submitted for publication. M. D. Murthy Peri, received the B.Tech. degree in mechanical engineering from Jawaharlal Nehru Technological University, Hyderabad, India, in 2001, and the M.S. and Ph.D. degrees in mechanical engineering from Clarkson University, Potsdam, NY, in 2004 and 2007, respectively. REFERENCES [1] The International Technology Roadmap for Semiconductors (ITRS) 2005 ed. International SEMATECH. [2] A. Hand, Damage-free cleaning beyond 65 nm, Semiconduct. Int., Jan [3] L. Peters, Wafer cleaning needs damage control, Semiconduct. Int., Nov [4] I. Varghese and C. Cetinkaya, Non-contact removal of 60 nm latex particles from silicon wafers with laser induced plasma, J. Adhesion Sci. Technol., vol. 18, pp , [5] D. Zhou, A. T. J. Kadaksham, M. D. M. Peri, I. Varghese, and C. Cetinkaya, Nanoparticle detachment using shock waves, J. Nanoeng. Nanosyst., vol. 219, pp , [6] J. Kadaksham, D. Zhou, M. D. M. Peri, I. Varghese, F. Eschbach, and C. Cetinkaya, Nanoparticle removal from EUV photomasks using laser induced plasma shockwaves, in Proc. SPIE, Apr. 18, 2006, vol. 6283, p C. [7] I. Varghese, D. Zhou, M. D. M. Peri, and C. Cetinkaya, Thermal loading of laser induced plasma shockwaves on thin films in nanoparticle removal, J. Appl. Phys., vol. 101, p , [8] D. Rittel, Transient temperature measurement using embedded thermocouples, Experimental Mechanics, vol. 38, no. 2, pp , [9] M. D. Paul and W. A. David, Survey of temperature measurement techniques for studying underwater shock waves, in Proc. Int. Symp. Interdisciplinary Shock Wave Res., Sendai, Japan, [10] M. Ogura et al., Myocardium tissue ablation with high-peak-power nanosecond 1,064-and 532-nm pulsed lasers: Influence of laser-induced plasma, Lasers Surgery Med., vol. 31, pp , [11] Y. L. Chen, J. W. L. Lewis, and C. Parigger, Spatial and temporal profiles of pulsed laser-induced air plasma emissions, J. Quantitative Spectroscopy Radiative Transfer, vol. 67, pp , [12] F. Ferioli, Experimental characterization of laser-induced plasmas and application to gas composition measurements, Ph.D. dissertation, Univ. Maryland, College Park, [13] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids. Oxford, U.K.: Clarendon, [14] C. B. Scruby and L. E. Drain, Laser Ultrasonics Techniques and Applications. New York: Adam Hilger, [15] Chromium Film and Bulk Chromium Properties, CRC Materials Science and Engineering Handbook. [16] Fused quartz properties [Online]. Available: Dong Zhou, received the B.S. and M.S. degrees in engineering mechanics from Tsinghua University, Beijing, China, in 1990 and 1999, respectively, and the Ph.D. degree in mechanical engineering from Clarkson University Potsdam, NY, in He worked as a Research Associate for a year at Clarkson University. He is currently an Assistant Professor at the Institute of Civil Engineering, Chongqing Jiaotong University, Chongqing, China. Ivin Varghese, received the B.Tech. degree in mechanical engineering from the Indian Institute of Technology, Madras, India, in 2002, and the M.S. and Ph.D. degrees in mechanical engineering from Clarkson University, Potsdam, NY, in 2004 and 2007, respectively. Cetin Cetinkaya, received the B.Sc. degree in aerospace engineering from Istanbul Technical University, Istanbul, Turkey, in 1986, and the M.Sc. and Ph.D. degrees in aeronautical and astronautical engineering from the University of Illinois, Urbana Champaign, in 1991 and 1995, respectively. He is currently an Associate Professor of mechanical engineering in the Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY. His research interests include ultrasonic testing and monitoring, laser ultrasonics, thermoelastic wave propagation, nanoadhesion, and computer algebra.