Two possible experimental arrangements for FDTR. (a) A system based on cw lasers. Laser 1 (the pump laser) is passed through an EOM and provides the modulated heat source, while laser 2 (the probe laser) measures the thermoreflectance signal. Both beams are directed coaxially through a single objective lens onto the sample. A matched reference detector is used to determine the true phase of laser 1 at the sample. (b) A system based on a pulsed laser. Each pulse is split into pump and probe pulses. Probe pulses are delayed relative to the pump pulses with a mechanical stage. The pump beam passes through an EOM and a second harmonic generation crystal before being directed onto the sample.
The calculated phase response for cw and pulsed FDTR measurements of 100 nm of Al on sapphire over the range 50 kHz–20 MHz.
Sensitivity parameter for , the substrate thermal conductivity; , the substrate volumetric heat capacity; and , the metal-substrate thermal boundary conductance calculated for three substrates: (a) silicon, (b) sapphire, and (c) Pyrex.
Sensitivity parameter for , the cross-plane thermal conductivity, , the in-plane thermal conductivity, and , the metal-substrate thermal boundary conductance, calculated single-crystal quartz.
Sample phase data and best-fit curves for three substrates: (a) silicon, (b) sapphire, and (c) Pyrex glass. Also shown are solutions obtained by varying substrate thermal conductivity by ±25%.
Phase data and best fit for single-crystal quartz with the -axis parallel to the optical axis. Also shown are solutions obtained by varying ratio of in-plane to cross-plane substrate thermal conductivity by ±25%.
Sensitivity calculation for 100 nm of Al on sapphire for the sensitivity parameters of the pump spot radius and substrate thermal conductivity. Pump and probe spots are taken as having a radius.
Best-fit values obtained from the data in Fig. 5.
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