## 4 Discussion  
The amplitude and phase spectra courses for the ideal semiconductor are known [25]. To measure against them, the temperature distribution in the tested sample and the waveforms for the absorption coefficient below and above the band gap were required. The expression for the absorption coefficient is one of the parameters of the temperature distribution. The expression for the phase and amplitude of the photothermal signal depends on this distribution. Details are presented in prior work [25]. The changes observed in the experimental spectra were interpreted as originating from defects located on the surface of the samples, as they were observed to be strongly dependent on the method of surface preparation. To simulate the changes, it was assumed that the defects could be simulated in temperature distributions with Gauss-shaped expressions. In the simulations, parameters such as energy, thermal diffusivity, and thermal conductivity were determined, and their courses were compared with the obtained experimental spectra. The modified [PERSON]'s model [26; 29; 30] was applied to interpret the obtained spectra. The heat conduction equation describes the sample's temperature distribution as previously described [30]. The modified model considers a damaged subsurface layer on both surfaces of the sample with significantly different thermal parameters from the main part of the sample. The absorption coefficient due to the presence of the defects has the Gaussian character. \[\beta=A_{d}\cdot exp\left(\frac{E-E_{d}}{\beta_{1}}\right)^{2} \tag{1}\]  
Figure 8: Phase spectra of Cd\({}_{0.95}\)Be\({}_{0.05}\)Te for front and rear detection and illumination of different surfaces at 12 Hz (blue lines), 76 Hz (green lines), and 126 Hz (red lines). (**a**) Surface 1 illuminated, rear detection. (**b**) Surface 1 illuminated, front detection. (**c**) Surface 2 illuminated, rear detection. (**d**) Surface 2 illuminated, front detection. where \(E_{d}\) is the value of the energy of the defect, \(\beta_{1}\) is the parameter describing the width of Gaussian shape maximum, and \(A_{d}\) is the amplitude of the maximum. The defect is located at the surfaces of the sample, and its nature can be associated with the quality of the surface after the preparation process (grounding, polishing, etching). For the energy \(E_{d}\) of radiation, the layer strongly absorbs, while the volume of the sample is transparent. The temperature distribution in the sample is the sum of temperatures generated on the surface and the volume of the sample:  
\[T^{\prime}(x)=T(x)+T_{1}^{d}(x)+T_{2}^{d} \tag{2}\]  
The piezoelectric signal is given by the expression [24]  
\[V\sim\left(\frac{1}{l}\int\limits_{-l/2}^{l/2}T^{\prime}(x)dx\pm\frac{6}{l^{2 }}\int\limits_{-l/2}^{l/2}T^{\prime}(x)xdx\right) \tag{3}\]  
Two terms in the expression represent piston and drum effects [26]; they add up in the case of front detection and subtract in the case of rear mode. Assuming the proper expressions for the absorption coefficient in the direct bandgap semiconductors (Urbach tail thermal broadening and absorption connected with the band-to-band electron transitions) [26], one can simulate the amplitude and phase spectra for the semiconducting sample with the presence of the defects localized on the subsurface damaged layer. The nature of the amplitude and phase spectra is influenced by thermal bulk and layer parameters, the most important of which are thermal diffusivities, energy gaps, and the thicknesses of the sample and the near-surface layer. These basic parameters characterizing the material were used to simulate both amplitude and phase spectra. Figure 9 presents amplitude (a) and phase (b) spectra of ground Cd\({}_{0.95}\)Be\({}_{0.05}\)Te mixed crystal. Experimental data are shown together with simulations according to the above-given model.