Determination of Modulus of Metal Films Using Thermoreflectance
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UCTION
THE different methods of determining elastic moduli are recently reviewed.[1] These methods include static tests such as four-point-bend and nanoindentation and dynamic tests such as resonant ultrasound spectroscopy and impulse excitation. The standard test method ASTM E 1876[2] for measurement of elastic moduli of a material is based on impulse excitation of vibration wherein the sample is excited mechanically and longitudinal vibrations parallel to the length of the rod are detected. The fundamental resonant frequency is measured and used to determine the different moduli.[3,4] This method is also used to study the vibration damping properties of materials using standard ASTM 756[5] test. Thermally generated acoustic waves by laser incidence in dispersive elastic solids have been studied both experimentally and analytically.[6,7] The displacement at the surface of the solids has been measured by different techniques including piezoelectric transducers[7] and interferometry.[8,9] Ultrasonic attenuation and sound velocity measurements in thin films are studied by picosecond acoustic interferometry wherein a picosecond pump laser pulse is used to generate acoustic waves and the optical reflectivity is measured by a probe laser.[10–13] The pump laser pulse sets up an isotropic thermal stress that launches a strain wave that propagates in the solid. The interaction of the reflected probe beam at interfaces with that reflected from the strain pulse has been used to determine the velocity of sound and the damping rate.[10] The time scale of these pulses is in the range of picoseconds. Picosecond lasers are not as easily available as the nanosecond lasers. Secondly, the measurement techniques for the thermoreflectance from the sample require K. JAGANNADHAM, Associate Professor, is with the Materials Science and Engineering Department, North Carolina State University, Raleigh, NC 27695. Contact e-mail: [email protected] Manuscript submitted May 10, 2014. Article published online October 8, 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A
additional set up to measure the time periods in picoseconds after the beam incidence. In the present work, a Q-switched Nd-YAG laser beam with pulse duration in few nanoseconds has been used as the pump beam to generate the acoustic pulses. Thus, the acoustic pulses are generated by impulse heating of the metal film using the laser with pulse duration in nanoseconds. A second, continuous red laser was used to measure the thermoreflectance signal from an indium metal film that is pressed on to a sapphire substrate or from a tungsten film deposited on Si wafer. The acoustic response was measured from the variation of transient thermoreflectance signal (TTR) with time. The acoustic velocity in the medium was obtained from the TTR signal variation with time. The time scale of acoustic oscillations in the present measurements was in the range of a fraction of a microsecond. These measurements are made very easily with a photodetector and an amplifier coupled to a digital oscilloscope to recor
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