## 2 Materials and Methods  
### Frequency Domain Photothermal Infrared Radiometry Set Up  
The PTR experimental set-up is presented in Figure 1[24]. The DPSS laser (\(\lambda\) = 532 nm, 800 mW CW power, model CNI laser MGL-FN-532-1W) is intensity-modulated by an acoustic-optical modulator (model Crystal Technology, Inc. AOM 3080-120) in the frequency range between 100 Hz and 10 MHz using a 30 MHz waveform generator (Agilent 33522A). The beam spot (1/e2) has a diameter of 1.8 mm. Two Au-coated off-axial parabolic mirrors are used to collect and collimate the emitted IR radiation from the sample, focusing it on a photoconductive mercury cadmium telluride (MCT) detector (Kolmartech KMPV 11-1J1/DC/Ge). The detector has peak sensitivity at a wavelength of 9.6 \(\upmu\)m and an active area of 1 mm\({}^{2}\) (with sensitivity between 2 \(\upmu\)m and 12 \(\upmu\)m). It is cooled with liquid nitrogen and has an antireflection-coated Ge window. Finally, the signal from the detector is processed by a lock-in amplifier (LIA, SR865 from Stanford Research, able to work in the frequency range between DC and 2 MHz and SR844 in the frequency range of 2 MHz and 10 MHz). Additionally, the system is prepared for temperature-dependent measurements using a Linkam System (LTS420) able to work between \(-\)200 \({}^{\circ}\)C and 420 \({}^{\circ}\)C.  
The disadvantage of the PTR method is that the signal strongly decreases with the temperature with law \(\Delta E\sim\sigma T^{3}\Delta T\) (where \(\sigma\) is Stefan-Boltzmann constant) as shown in Figure 2. For comparison, the results from frequency-domain thermoreflectance (FD-TR) measurements are also presented.  
Although the PTR signal can be increased by decreasing the beam size, we should bear in mind that there is a trade-off between one-dimensional heat propagation in the sample and the beam spot size. Thus, there is an optimum spot-size that maximizes the PTR signal while keeping the heat-transport one-dimensional. From Figure 2 one can see that at low temperature (below \(-\)100\({}^{\circ}\) C/173 K), the PTR signal is very small and measurements cannot be taken in frequency-scans up to MHz. On the other hand, thermoreflectance can be measured down to 50 K [33]. The thermoreflectance signal can be described by the formula [33]:  
\[\text{S}_{\text{TR}}=\frac{\Delta\text{R}}{\text{R}}=\left(\frac{1}{\text{R} }\frac{\partial\text{R}}{\partial\text{T}}\right)\Delta\text{T}=\text{C}_{ \text{TR}}\Delta\text{T} \tag{1}\]  
where \(\Delta\text{T}\) is the thermal wave oscillations (which depends on the temperature via thermal transport parameters) and CTR is the thermoreflectance coefficient. In paper [16], authors show that signals above room temperature increase linearly with temperature. In our paper we show that this trend is also observed for lower temperatures for a layered sample. The deviation from linear behavior was already observed by other authors [34].  
Figure 1: Frequency-domain photothermal infrared radiometry set-up with temperature cell. The beam size was 1.8 mm.  
Figure 2: Temperature-dependent of the PTR and TR amplitudes at 1 kHz for a GaAs wafer covered by 50 layer of Ti and 2 μm AlGaAs thin layer with 100 nm of gold layer, respectively. The data are not normalized. The signals were depicted for 1 kHz. Note that PTR amplitude is very stable with error bars within experimental points.