**2. Materials and Methods**

Crystals investigated in this work were grown by using the vertical Bridgman technique. Before the growth process, starting mixtures were prepared from high-purity CdTe (6 N) and Be (99.9%) powders and put into a graphite crucible. The crucible was placed into a growth chamber, sealed, and evacuated. After evacuation, the external pressure of argon gas (around 90 atm.) was applied to reduce evaporation of the material during the growing. The temperature in the hot zone was set to 1600 K, with a stability better than 0.1 K. We used a 4 mm/h pulling rate to grow the crystal within two days. Typically, our crystals grown by the Bridgman high-temperature and high-pressure technique were 4–6 cm in length and 1 cm in diameter. We could cut 15–20 plates 1–1.5 mm thick from one crystal rod. Four specimens of beryllium content (in ingot) were measured for x = 0.01, 0.03, 0.05, and 0.1. Pure CdTe crystals were also measured for the same procedure of surface preparation. More details concerning the growth procedure can be found elsewhere [22].

The beryllium concentration in the samples was determined after crystal milling (in agate mortar) by applying the powder X-ray diffraction technique (Empyrean diffractometer, Malvern Panalytical) with a Cu anode used as a source of CuKα X-ray radiation (λ = 1.5406 Å). More details about the measurement were presented in previous work [23]. The diffraction data were fitted using the ReX v. 0.91 Rietveld analysis software. The following parameters were fitted: scale factor, 2-theta offset, background coefficients, and cell constant a for the CdTe structure. In this case, the beryllium in the CdTe was treated as a solid solution of the first type, and thus the main changes were mainly observed for the cell dimension. All U factors were isotropic and set to 0.5. The reflection shape was described by the pseudo-Voight function. For analysis, the necessary crystal structure file of CdTe (cif) was downloaded from the American Mineralogist Crystal Structure Database [24].

The XRD patterns of example CdBeTe mixed crystals (CdTe and Cd0.9Be0.1Te) powdered are presented in Figure 1a. Characteristic diffraction reflections from (111), (220), (311), (400), (331), (420), and (511) planes of the cubic phase (type of zinc blende structure) are visible on the patterns for both CdTe (black) and Cd0.9Be0.1Te (red) samples. In the case of a mixed crystal, the diffraction peaks are shifted towards higher 2 θ in comparison to the position of these signals in the CdTe. Such behavior demonstrates the presence of mixed crystals, so the beryllium was successfully incorporated into the crystal lattice of CdTe. The absolute values of the lattice constant were calculated by the Rietveld method and the results that were obtained as the function of the composition are displayed in Figure 1b. Linear dependence of the lattice constant versus Be content confirms the composition of the grown crystals.

**Figure 1.** The XRD patterns of CdTe (black) and Cd0.9Be0.1Te (red) powders (**a**) and lattice constant versus beryllium concentration (**b**).

The cut samples were ground in a suspension of water and Al2O3 powder on flat glass parallel plates. The grain diameter of the grinding powder was approximately 10 μm. Then, the samples were polished with diamond paste on polishing discs until a mirror surface was obtained. The grain diameter in the polishing paste was between 0.1 and 1 μm.

The samples were subjected to two different etching processes. First, the samples were etched using a mixture containing 48% HF (hydrofluoric acid), 30% H2O2, and H2O. Digestion took place at room temperature. The samples were subjected to photothermal tests. Then, the surfaces of the samples were ground and polished again to use a mixture of K2Cr2O7, 96%H2SO4, and H2O for etching. The etching took place at a temperature of about 80 ◦C. After etching, the samples were briefly immersed in a 50% NaOH solution, then rinsed in water, and finally in ethyl alcohol.

The typical experiment setups for piezoelectric detection, piezoelectric cell allowing front and rear detection, and lock-in detection were used [25]. A 150 W xenon lamp was used as the light source. The beam passed through a computer-controlled spectrometer; 90% of the beam fell on the photothermal cell and 10% on the photodiode, whose task was to monitor the light intensity. Cell and photodiode signals were measured by two lock-in Stanford SR 510 units. In piezoelectric detection, there are two possible ways of mutual arrangement of the detector and the measured sample. The detector is located behind the illuminated sample in the more commonly used rear configuration. In the front configuration, the detector is placed on the illuminated surface. Depending on the configuration, different course amplitude and phase spectra are observed.

#### **3. Results**

#### *3.1. Cut and Grounded Samples*

First, cut and grounded samples were examined. Figure 2 presents the experimental amplitude (blue) and phase (green) spectra of Cd0.97Be0.03Te in the rear configuration at the frequency modulation of 126 Hz. In both spectra, the theoretical simulations for the ideal sample are presented (in black). The different characters of both experimental and simulated spectra are visible. There are two additional maxima in the sub-bang gap region for the amplitude and the significant change (at the energy of E = 1.46 eV) of the phase in the same area. The amplitude signal in the above bandgap area is increasing in comparing stable values in simulated amplitude spectra. Similar behavior was previously observed for Zn1−x−yBexMnySe compounds [19]. It was associated and interpreted as coming from the defects located on the surface of the sample and strictly connected with the method of surface preparation.

**Figure 2.** (**a**) Experimental amplitude (blue) and (**b**) phase (green) spectra of Cd0.95Be0.05Te in the rear configuration at the frequency modulation of 126 Hz. The solid black lines simulate the ideal crystal's theoretical amplitude and phase spectra.

Figure 3 presents amplitude (a, b) and phase (c, d) spectra for Cd0.99Be0.01Te grounded mixed crystals for different frequencies of modulation frequency and the rear (a, c) and front (b, d) configurations. In this case, the character of amplitude and spectra deviates from the theoretical predictions. For the lowest frequency (12 Hz), the additional maximum visible for higher frequencies is not visible. The higher the frequency, the higher the intensity of the maximum below the energy gap will be compared to the area above the energy gap: as the modulation frequency increases, the thermal diffusion length decreases, and the signal is generated from a smaller thickness. For low frequencies, the signal comes from a large sample thickness, and the signal from the surface is not dominant. It is worth noting that

regardless of the frequency, the points of inflection of the curves are observed in the phase spectra for the same energies.

**Figure 3.** Amplitude (**a**,**b**) and phase (**c**,**d**) spectra for Cd0.99Be0.01Te grounded mixed crystal for different frequencies of modulation frequency for the rear (**a**,**c**) and front (**b**,**d**) configurations at 12 Hz (blue lines), 76 Hz (green lines), and 126 Hz (red lines).

The different amplitude and phase spectra characters were observed for the Cd0.9Be0.1Te mixed crystal. Figure 4 presents amplitude (a) and phase (b) spectra for this sample.

**Figure 4.** Amplitude (**a**) and phase (**b**) spectra for Cd0.9Be0.1Te grounded mixed crystal for different frequencies of modulation frequency for the front configuration at 12 Hz (blue lines), 36 Hz (cyan line), 76 Hz (green lines), and 126 Hz (red lines).

Two maxima are observed for this sample in the amplitude spectra of E1 = 1.51 eV and E2 = 1.59 eV. The first one is present for all the frequencies, and its intensity is not changed compared to the intensity of the signal in the region above the energy gap. The behavior of the second maximum is similar to the one observed in the previous sample. A probable cause is that the thickness of the damaged layers on both surfaces is different. In the phase spectra, one must analyze the maxima and bending points to identify the localization of defects and their energetic positions.

Beryllium and defects related to its presence in the subsurface layer are undoubtedly responsible for changes in spectra and the formation of additional peaks. A strong correlation between surface preparation for Zn1−x−yBexMgySe [26] was previously observed, but no explanation has yet been found for the mechanisms of the formation of defects on the surface; research is ongoing to clarify their nature.

A decrease in amplitude spectra in the region above Eg (not a constant signal as in theory) was observed by Kuwahata et al. [27] in studies of implanted Si + ions in InP. According to them, silicon ions are responsible for defects in the crystal lattice and suppress the propagation of an elastic wave, which causes a decrease in the amplitude above the energy gap region. This is related to an increase in the number of free carriers in the conduction band states in the annealed samples. When these states are filled, photons of the energy close to the energy gap are not absorbed, and the photothermal signal is not generated.

A similar effect was also reported by Matsumori et al. [28] in studies of the impact of damage caused by ion implantation in Si. The photothermal signal was sensitive to the size and structure of damage in the layer with implanted ions. The authors attributed the signal reduction below the energy gap of the surface quality and the defects present on it. Its damage suppresses the generation of elastic waves. The authors came to conclusions that can also be drawn from the current research: the increased number of defects on the surface causes a more significant generation of thermal energy in the sub-bandgap region and the opposite effect for the area above the gap. Here, the thermoelastic waves are suppressed.

#### *3.2. The Change of the Energy Gap with the Be Content*

The series of Cd1−xBexTe samples was measured to obtain the energy gap values' dependence on the beryllium content described by the composition parameter (x). The amplitude and phase spectra were measured for the samples: x = 0.01, 0.03, 0.5, 0.1. A pure CdTe sample was also measured and subjected to the same surface treatment procedure. The amplitude and phase spectra for the modulation frequency of 126 Hz are presented in Figure 5. There was an increase in the value of Eg with the rise of beryllium content (clearly visible). Calculating the energy gap value from the phase and amplitude spectra was possible. The values could be estimated directly from the spectra or calculated as a parameter from the theory.

**Figure 5.** Amplitude (**a**) and phase (**b**) spectra of Cd1−xBexTe for different beryllium content. Black line: x = 0, red: x = 0.01, blue: x = 0.03, green: x = 0.05, magenta: x = 0.1. The color arrows indicate the values of energy gaps.

The phase spectra course may differ for different samples and frequencies. Still, the most important are the changes (inflection points) at which these changes occur: they indicate additional photothermal signal sources and the energetic position of the defects on the surface.

The obtained values of energy gaps are presented in Table 1.

**Table 1.** The experimental values of Eg for Cd1−xBexTe.


#### *3.3. Etched Samples*

One of the sample preparation goals was to obtain a perfect-quality surface. First, the polished samples were subjected to etching using a mixture containing 48% HF (hydrofluoric acid), 30% H2O2, and H2O. This procedure caused the photothermal signal to be wholly quenched for mixed samples, making it impossible to measure the spectra. A possible explanation for this will be discussed later in this article. Therefore, it was decided to grind the samples again and further etch them in a new solution. The surfaces of the specimens were ground and polished to use a mixture of K2Cr2O7, 96% H2SO4, and H2O for the etching.

Figure 6 compares the amplitude spectra for the ground and etched Cd0.95Be0.05Te sample.

**Figure 6.** Amplitude (**a**) and phase (**b**) spectra for the ground (green lines) and etched (blue lines) Cd0.95Be0.05Te sample at 126 Hz of modulation frequency.

The expectation was to obtain the spectra close in shape to the ideal crystal (black in Figure 2). The applied method of etching did not improve the surfaces of the sample. In the amplitude spectrum, an additional maximum still exists below the energy gap, which is not expected for an ideal sample. Although the phase has a different shape, it is worth noting that phase changes take place at the same energy values (indicated in the figure with vertical lines). This proves that the defects on the surface were present at a different depth of the damaged layer (by etching) or that additional effects had been achieved, e.g., with phenomena associated with the carriers. The same changes in phase are manifested differently in amplitude; with different maximums, it is also worth emphasizing that piezoelectric spectroscopy allows for studying the differences on both surfaces of the sample prepared with the same treatment procedure.

Figures 7 and 8 present the experimental spectra of the amplitude and phase of Cd0.95Be0.05Te after the etching process was obtained for the illumination of different surfaces of the sample. The sample was measured in rear and front configurations. The surfaces of the samples were assigned numbers 1 and 2 and then measured after illumination of surface 1, then 2. The aim was to examine and compare the surfaces after an identical treatment procedure.

**Figure 7.** Amplitude spectra of Cd0.95Be0.05Te 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.

Complementarity, especially in the amplitude spectra, is evident. Whether rear or front detection is considered, the strong maximum associated with the surface defect is observed for the illumination at surface 2. Its intensity is much higher in comparison to the above bandgap region, which indicates that etching negatively affects the quality of the surfaces, and the defects strengthen the photothermal signal. In the case of illumination of surface 1, the amplitude spectra have a similar character with a smaller maximum in the sub-bandgap region. The maximum has a higher intensity for rear detection and is associated with subtracting the piston and drum effects.

The phase spectra for the illumination of surface 2 show the changes at the same energy values despite the curves' different characters. The more significant differences are observed for phase spectra for front detection and the illumination at surface 1. It should be emphasized that both phase and amplitude must be analyzed to interpret piezoelectric spectra correctly.

The same change of character was also observed for the rest of the samples, which proved that the chosen etching procedure introduced additional defects on the surfaces of the samples.

**Figure 8.** Phase spectra of Cd0.95Be0.05Te 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.
