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Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions
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Image of FIG. 1.
FIG. 1.

(a) Schematic of traditional FDTR. (b) Schematic of BB-FDTR. The pump beam undergoes intensity modulation at frequency and gets focused on the sample. EOM2 induces an additional modulation in the reflected probe beam, heterodyning the thermal signal, allowing for higher heating frequencies at a lower measurement frequency, thereby increasing the measurement range of . (c) Schematic of BB-FDTR with alternate location for EOM2. In this configuration, the heterodyning occurs at the sample surface but the thermal phase response cannot be isolated. Labels identifying the make and model of the components can be found in Table I .

Image of FIG. 2.
FIG. 2.

Normalized temperature and phase response from traditional FDTR with an unamplified photodiode from 200 kHz to 200 MHz and an amplified photodiode up to the bandwidth of the photodiode and BB-FDTR experiments with an amplified photodiode for c-Si at = 311 K. In the low frequency regime, the data from traditional FDTR and BB-FDTR is the same and indicates no effect from using different photodiodes. As the frequency increases ( > 20 MHz), signal to noise ratios decrease in traditional FDTR. Heterodyning the signal allows for large signal to noise ratios up to a heating frequency of 200 MHz.

Image of FIG. 3.
FIG. 3.

(a) Sensitivity to a 1% change in nominal sample parameters, found in Table II , as defined by Eq. (5) . The effect on the sensitivity from (b) decreased interface thermal conductance and (c) decreased sample thermal conductivity.

Image of FIG. 4.
FIG. 4.

(a) A constant fit to the phase response over the entire frequency range under predicts the bulk value of Si at = 311 K and motivates a window fitting scheme. (b) Fitting in different windows of the phase response yields a heating frequency dependent thermal conductivity. The last 15 points of the phase data are fit to determine (inset), based on the sensitivity analysis. Minimizing mean square error yields a value of = 210 ± 10 MW/m K.

Image of FIG. 5.
FIG. 5.

Transforming the x-axis of Fig. 4(b) yields for c-Si at = 311 K. The data is normalized to = 143 W/m K and compare favorably with our prior results and numerical predictions from Ref. .


Generic image for table
Table I.

Component list for schematics in Fig. 1 .

Generic image for table
Table II.

Nominal values for fitting and the sensitivity analysis and the uncertainty ranges used to generate the shaded error regions in Fig. 5 .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions