The transient thermoreflectance (TTR) method consists of measuring changes in the reflectivity of a material (thin film) under pulsed laser heating, and relating these changes to the corresponding surface temperature variations. Analytical solutions of the diffusion problem are then used to determine the thermal conductivity of the material following an iterative matching process between the solutions and the experimental results. Analytical solutions are attainable either when the material absorbs the laser energy volumetrically or when the material absorbs the laser energy at the surface. Either solution allows for the determination of only one thermal property (thermal conductivity or diffusivity), with the other one assumed to be known. A new, single, analytical solution to the transient diffusion equation with simultaneous surface and volumetric heating, found using fractional calculus, is presented in a semi-derivative form. This complete solution provides the means to determine the two thermal properties of the material (thermal conductivity and diffusivity) concomitantly. In this preliminary study, the solution component for surface heating is validated by comparison with experimental data for a gold sample using the classical thermoreflectance method. Further results, for surface and volumetric heating, are obtained and analyzed considering a GaAs sample.
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A Fractional-Diffusion Theory for Calculating Thermal Properties of Thin Films From Surface Transient Thermoreflectance Measurements
Vladimir V. Kulish, Assistant Professor, ASME Associate Member,
Vladimir V. Kulish, Assistant Professor, ASME Associate Member
School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore 639798
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Jose´ L. Lage, Professor, Mem. ASME,
e-mail: JLL@SEAS.SMU.EDU
Jose´ L. Lage, Professor, Mem. ASME
Box 750337, Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337
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Pavel L. Komarov, Research Fellow, Assoc. Mem. ASME,
Pavel L. Komarov, Research Fellow, Assoc. Mem. ASME
Box 750337, Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337
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Peter E. Raad, Professor, Mem. ASME
Peter E. Raad, Professor, Mem. ASME
Box 750337, Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337
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Vladimir V. Kulish, Assistant Professor, ASME Associate Member
School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore 639798
Jose´ L. Lage, Professor, Mem. ASME
Box 750337, Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337
e-mail: JLL@SEAS.SMU.EDU
Pavel L. Komarov, Research Fellow, Assoc. Mem. ASME
Box 750337, Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337
Peter E. Raad, Professor, Mem. ASME
Box 750337, Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division August 28, 2000; revision received May 4, 2001. Associate Editor: R. Skocypec.
J. Heat Transfer. Dec 2001, 123(6): 1133-1138 (6 pages)
Published Online: May 4, 2001
Article history
Received:
August 28, 2000
Revised:
May 4, 2001
Citation
Kulish, V. V., Lage, J. L., Komarov, P. L., and Raad, P. E. (May 4, 2001). "A Fractional-Diffusion Theory for Calculating Thermal Properties of Thin Films From Surface Transient Thermoreflectance Measurements ." ASME. J. Heat Transfer. December 2001; 123(6): 1133–1138. https://doi.org/10.1115/1.1416688
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