## 4 Results  
It is worth emphasizing that the in-plane thermal conductivity can be measured by either changing the spot-size of the laser on the sample or spatially separating the position of the pump and probe spots [21; 35]. Moreover, using the TD-TR method it is not possible to measure the in-plane thermal conductivity by changing its spot size, but one can perform measurements using separation of beams or by the elliptical-beam method [36]. It was found that for time-domain methods the recommended method is to spatially separate the position of the pump and probe spots [35]. In this paper we demonstrate that, using the frequency-domain method, it is possible to measure in-plane thermal conductivity. To test that the thermoreflectance is able to measure in-plane thermal conductivity, we performed the measurement of isotropic AlGaAs thin-layer sample and calculated the sensitivity. Figure 6 shows the relation between the relative sensitivity vectors of these parameters calculated using Equation (1). These relative sensitivity vectors are calculated as SPhase, \(p=\partial(\rm Phase)/\partial ln(p)\), where SPhase,p is phase sensitivities to parameter \(p\) of the model, respectively [26]. After theoretically demonstrating that is it possible to measure in-plane thermal conductivity, we used the 2 um thick AlGaAs sample to experimental validation of the method. 2 um thick AlGaAs is thermallly isotropic. Figure 7 shows the measured TR phase of sample #2. In order to decrease the number of unknown parameters, we use the cross-plane thermal conductivity, diffusivity and thermal interface boundary of the Al0.33 Ga0.67 As thin film from the literature (k = 12 W/mK, \(\alpha\) = 6.5 \(\times\) 10\({}^{-6}\) m\({}^{2}\), RAlGaAs/GaAs = 1 \(\times\) 10\({}^{-9}\) (m\({}^{2}\) KW\({}^{-1}\)) [29; 37]. The fitting results using Matlab function lsqcruvefit using Equation (1) yield the value of in-plane thermal conductivity to be 16 \(\pm\) 4 W/mK. This demonstrates that the sample is thermally isotropic. It is worth to notice that the thermal boundary resistance between gold and the layer was found to be one order of magnitude higher than in the interface Ti-GaAs (RAu/AlGaAs = (2.0 \(\pm\) 0.5) \(\times\) 10\({}^{-7}\) (m\({}^{2}\) KW\({}^{-1}\))), as expected [36]. Figure 8 presents the PTR results for temperatures \(-\)50, 0 and 50 \({}^{\circ}\)C measured for sample #3. The fitting procedure was identical as in our previous paper [24]. We used Matlab function lsqcurvefit for numerical calculations. First, we estimate Rth between Ti layer GaAs (sample #1). We found out that with changing temperature between \(-\)50 \({}^{\circ}\)C and 50 \({}^{\circ}\)C thermal interface boundary remains constant within the estimated error. Secondly, we use these values and data for sample #1 in estimating cross-thermal transport properties of sample #3. For the latter calculation, we used the parameters presented in Table 2.  
Figure 8: PTR experimental results (points) for sample#3 in three different temperatures: \(-\)50 \({}^{\circ}\)C, 0 \({}^{\circ}\)C and 50 \({}^{\circ}\)C. Additionally, the best fittings are presented as solid lines using Equation (8). Figure 7: Measured TR phase of 2 \(\upmu\)m AlGaAs thin layer covered by 100 nm of gold layer between 100 Hz and 500 kHz. The best fits are obtained using Equation (1). Note that the experimental results are consistent with the sensitivity analysis. The sensitivity to frequency about 1 kHz is 0, while the experimental phase to frequency of about 1 kHz is also close to 0 degs. As can be seen, the in-plane thermal conductivity values are two times larger than the cross-plane thermal conductivity, as expected. The value is also consistent with those reported by authors for room temperature [36]. On the other hand, the thermal boundary resistance between gold layer and SL is within the error the same as for AlGaAs sample (sample #2). It is worth mentioning that, as with the Rth of Ti/SL layer, the thermal boundary resistance with changing temperature is constant with the estimation errors.