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.

1.
O¨zisik, M. N., 1980, Heat Conduction, Wiley, New York.
2.
Kakac¸, S., and Yener, Y., 1985, Heat Conduction, Hemisphere, Washington, DC.
3.
Poulikakos, D., 1994, Conduction Heat Transfer, Prentice Hall, New Jersey.
4.
Xu
,
X.
,
Grigoropoulos
,
C. P.
, and
Russo
,
R. E.
,
1995
, “
Transient Temperature During Pulsed Excimer Laser Heating of Thin Polysilicon Films Obtained by Optical Reflectivity Measurement
,”
ASME J. Heat Transfer
,
117
, pp.
17
24
.
5.
Chen
,
G.
,
Tien
,
C. L.
,
Wu
,
X.
, and
Smith
,
J. S.
,
1994
, “
Thermal Diffusivity Measurement of GaAs/AlGaAs Thin-Film Structures
,”
ASME J. Heat Transfer
,
116
, pp.
325
331
.
6.
Goodson
,
K. E.
, and
Flik
,
M. I.
,
1994
, “
Solid Layer Thermal Conductivity Measurement Techniques
,”
Appl. Mech. Rev.
,
47
, pp.
101
112
.
7.
Kulish
,
V. V.
, and
Lage
,
J. L.
,
2000
, “
Fractional Diffusion Solutions for Transient Local Temperature and Heat Flux
,”
ASME J. Heat Transfer
,
122
, pp.
372
376
.
8.
Kamke, E., 1959, Differentialgleichungen: Lo¨sungsmethoden und Lo¨sungen, Leipzig.
You do not currently have access to this content.