Absolute value of the sensitivity parameter of the TDTR ratio signal (ratio of the in-phase and out-of-phase signals of the rf lock-in amplifier) at modulation frequencies (a) and (b) for a hypothetical sample consisting of an Al transducer layer with thickness ; a thin film with thermal conductivity , heat capacity , and thickness ; a substrate with and and an interface thermal conductance between the Al transducer layer and the film of . Each curve is labeled by the corresponding parameter in the thermal model; is the phase of the reference channel of the rf lock-in amplifier.
The product of steady-state temperature rise and the uncertainty in setting the absolute value of the phase of the reference channel of the rf lock-in amplifier , as a function of modulation frequency . The data in figure were measured on an Al-coated thick layer doped with 3% ErAs (solid circles) and a Pt-coated thick doped with 0.3% ErAs (open circles).
(a) Comparison of thermal conductivity measurements by TDTR at a modulation frequencies of (open diamonds) and 0.6 MHz (open circles) on thick layers with 0.3% ErAs doping. The uncertainty of TDTR measurements at is about the size of the symbols and the error bars are omitted for clarity. (b) Comparison of thermal conductivity of the same samples measured by the method (solid circles) and TDTR at (open circles). For and 40%, TDTR and the method measurements are essentially identical. TDTR measurements at agree with measurements by the method within experimental uncertainty.
(a) Thermal conductivity of with 0.3% (circles) and 3% (squares) ErAs doping measured by TDTR at (open symbols) and the method (solid symbols) plotted as a function of film thickness . Labels are percentage of ErAs. Measurements by TDTR (open circle) and the method (solid circle) on a with 0.3% ErAs overlap. In the plot, prior measurements by Kim et al. (Ref. 7) on a doped with 0.3% ErAs (solid diamond) and a (solid triangle), and prior TDTR measurements at low modulation frequencies by Koh and Cahill (Ref. 14) on epitaxial films (open triangles) are included for comparison. (b) Thermal conductivity of doped with (circles) and without (triangles) 0.3% ErAs. Open symbols are TDTR measurements while solid symbols are the measurements. Labels are the percentage of ErAs. The measurements indicate 25% reduction in due to 0.3% doping of ErAs while TDTR measurements are essentially identical with and without ErAs doping.
(a) Frequency dependence of the thermal conductivity of films measured by TDTR plotted as a function of thermal penetration depth . The data are for three samples: Al-coated doped with 0.3% ErAs (diamonds), Pt-coated doped with 0.3% ErAs (circles), and Al-coated doped with 3% ErAs (squares). The dashed line is frequency dependence of TDTR measurements on a film from Ref. 14. The labels are percentage of ErAs doping. (b) Frequency dependence of thermal conductivity of films measured by TDTR plotted as a function of thermal penetration depth . The data are for three samples: two films doped with 0.3% ErAs, coated with Al (open diamonds) and Pt (open circles), and one sample without ErAs doping coated with Pt (open triangles). Thermal conductivities of films with 0.3% ErAs measured by TDTR from part (a) are reproduced here as the dashed line.
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