Raman Spectra of PbTe-and GeTe-Based Monocrystalline Epitaxial Layers

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Introduction
Lead telluride and germanium telluride are well-known IV-VI semiconductors [1].Tey found their place in a large number of electronic devices and sensors, such as rewritable optical memory (CD, DVD) and electronic nonvolatile memory (NVM) technology [2,3].Recently, these materials are again in the focus of research due to the perspective of application as thermoelectrics for midrange temperatures (600-800 K) [4].Very recent renewal of interest to (Pb, Ge)Te thin layers deposited on BaF 2 (111) substrates is related to their function as a novel ferroelectric Rashba semiconductor [5].GeTe is a IV-VI narrow-gap semiconductor that, upon illumination or passing current, can transform between amorphous (resistive) and crystalline (metallic) states.Crystalline germanium telluride exists at room temperature in α (rhombohedral R3m) structure and at high temperatures in β (rocksalt-type phase-face centred cubic Fm3̅ m) at above 700 K [6].PbTe has the cubic NaCl structure, where Pb and Te atoms form the cation and the anion sublattices.Properties of PbTe that depend on the dopants, such as an energy gap of 0.32 eV and the ability to be either n-or p-type, allowing it to be used for power generation applications.More recently, eforts have been made to improve the thermoelectric properties of PbTe by nanostructuring [4].PbTe-based nanostructures have very favorable thermal and charge-transport properties.However, despite the promising results of new nanostructures based on PbTe, alloying in solid solution remains an active area of research [7].
Laboratory demonstrations showed highly efcient thermoelectric conversion parameters in mixed composite material (Pb, Ge)Te-Bi 2 Te 3 [8].Introduction of Eu in (Pb, Ge)Te is expected to open the band gap with a high rate of about 30 meV/at.%Eu, thus providing a way to tune the optimal operation temperature of thermoelectric converters.
Importantly, good thermoelectric materials must possess a very low thermal conductivity of the order of (1-2) W/mK.Te engineering of thermal properties proved very successful in improving thermoelectric materials.However, this approach requires a detailed knowledge of phonon energies in binary, ternary, and quaternary IV-VI semiconductor alloys.
In this paper, we focused on the Raman spectra of PbTe, GeTe, (Pb, Ge)Te, and (Pb, Ge, Eu)Te layers that were grown on BaF 2 (111) monocrystalline substrates by the molecular beam epitaxy (MBE) technique.Our goal is to determine the phonon properties of this type of material in the form of thin flms and provide guidelines for further synthesis that can lead to application as thermoelectrics.

Materials and Methods
PbTe, GeTe, (Pb, Ge)Te, and (Pb, Ge, Eu)Te layers on BaF 2 (111) monocrystalline substrates were grown by the molecular beam epitaxy (MBE) technique.Efusion cells with PbTe, GeTe, Eu, and Te solid sources were used, and the obtained layers were about 1 µm thick.Many growing processes were performed to obtain high crystalline-quality epitaxial heterostructures.Diferent samples with one or more layers (bufer layer at about 20-200 nm thick each) deposited on the BaF 2 (111) surface were produced.Te layer growth was monitored in situ using the refection high-energy electron difraction (RHEED) technique.Typical RHEED difraction observed during (Pb, Ge, Eu)Te deposition on BaF 2 presented in Figure 1(a) reveals the layer-by-layer 2D epitaxial growth regime.For composition determination of both Ge and Eu contents, we used XRD data and known Vegard law as well energy-dispersive X-ray fuorescence EDXF method.Te content of Eu as well as the charge (2+) and spin state (S � 7/2) of Eu ions in (Pb, Ge, Eu)Te was verifed by electron paramagnetic resonance experiments also.
In Figures 1(b)-1(d), we present representative XRD spectra for each group of flms we analyzed.From this analysis, one draws the conclusion that all the samples where homogeneous, high quality crystalline layers.More details about obtaining this thin flm type by the MBE method can be found in [9].
Te micro-Raman spectra were taken in the backscattering confguration and analyzed by Jobin Yvon T64000 spectrometer, equipped with a nitrogen-cooled chargecoupled device detector.As an excitation source, we used the 514.5 nm (2.41 eV) line of an Ar-ion laser.A microscope lens with a magnifcation of 100x was used to focus the laser beam.Te spectrum was recorded with a laser power density of 1.5 mW/μm 2 on the sample and the measurement time of 5 s, which did not cause structural changes in the sample.
Figures 2 and 3 show the Raman spectra of diferent layers based on PbTe and GeTe on the BaF 2 substrate at room temperature.Te spectra were measured in a wide range, but only the results up to 1100 cm −1 are shown because the spectra are fat afterwards, without any specifcs.Te penetration depth of the laser radiation is such that the characteristics of both the flm and the bufer layer can be seen on the spectra.
Te modes at 126 and 143 cm −1 are registered in all spectra.In addition, for samples with GeTe as the upper layer, phonons at 93, 160, 220, and 265 cm −1 were also registered.Te spectra of PbTe/GeTe/BaF 2 and Pb 0.745 Ge 0.255 Te/BaF 2 are presented in Figure 2(b).In the case of PbTe/GeTe/BaF 2 , in addition to the phonons registered in Figure 2(a), a new structure can be seen at around 73 cm −1 and 181 cm −1 as well as its second, third, and fourth order Raman scattering.For both samples, the phonon at 93 cm −1 is missing.It is interesting to note that in the PbTe/ GeTe/BaF 2 sample, each harmonic has a diferent shape, i.e., there was a change in the shape of the harmonics relative to the Pb 0.745 Ge 0.255 Te/BaF 2 sample.
Te spectra of Ge 0.989 Eu 0.011 Te/BaF 2 and representative sample of the (Ge, Eu)Te/GeTe/BaF 2 type are shown in Figure 3(a).
Te addition of Eu did not lead to changes in the spectra compared to Figure 2(a).Te exception is the shift of the phonon at 93 cm −1 -87 cm −1 .Te efect of adding Eu to the PbGeTe solid solution is shown in Figure 3(b).For the Pb 0.697 Ge 0.259 Eu 0.044 Te/PbGeTe/BaF 2 sample, the spectrum has all the characteristics of the spectra from Figure 2.However, for samples Pb 0.94 Ge 0.049 Eu 0.011 Te/BaF 2 and Pb 0.91 Ge 0.046 Eu 0.044 Te/BaF 2 , it is characteristic that the phonons at 93, 126, and 143 cm −1 gave one broad structure, which occupies the range from 80 to 160 cm −1 .In addition, in all cases, the harmonics for the 181 cm −1 phonon have the same shape as for the PbTe/GeTe/BaF 2 sample.

Discussion
Te results can be explained as follows.PbTe has a cubic structure of the NaCl type (Fm3̅ m space group symmetry) and no active Raman modes.Phonon at about 73 cm −1 (see Figure 2(b)) is the Brillouin zone edge mode because the phonon density of PbTe [10] has a maximum at these frequencies.Tis mode has already been observed in many PbTe-based alloys.PbTe at the top of the structure or in a large percentage in the alloy (see Figure 3(b)) does not allow the 93 cm −1 phonon GeTe to be seen.Te broad but weak structure at about 100 cm −1 in Figure 3(b) is the sum of phonons from GeTe at about 93 cm −1 and phonons from PbTe at about 104 cm −1 .In both cases, they phonons were registered for violating the selection rules.Regarding phonons at 126 and 143 cm −1 , registered in Figure 2(a) for PbTe/ BaF 2 , but also on most other spectra from the literature [11,12], it is known that these modes originate from the TeO 2 , which is always formed on the sample surface.Tese modes can weaken if the single crystal sample is polished immediately before the measurement.Also, TeO 2 is much thinner than the penetration depth of the laser light, so it does not afect the accuracy of the Raman spectrum.Of course, polishing is out of the question for samples obtained by MBE.However, this is not the main topic of this paper.

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Journal of Spectroscopy In the case of GeTe spectra, the situation is somewhat more complicated.In the high temperature cubic phase of GeTe, Raman scattering by optical phonons is forbidden, as in the case of PbTe.However, in the case of the room temperature phase of the rhombohedral structure with cation-anion sublattice shift (ferroelectric distortion), scattering is allowed due to the absence of inverse symmetry.Tere are several works on this topic [13][14][15].Based on this, it can be concluded that the mode at 93 cm −1 originates from the distorted octahedrally coordinated Ge atoms.Also, the mode at about 160 cm −1 corresponds to the vibrations of Ge atoms on defective octahedral sites [16].Te weak structures around 220 cm −1 and 265 cm −1 can be related to Ge vibrations in the GeTe 4-n Ge n environment [14,15] or the sum of TeO 2 vibrations, which are now seen as the second harmonic.
We labeled the structure at ω 0 � 181 cm −1 from Figure 3 as a local Ge mode.It is known that if the semiconductor is doped with impurities that take the place of a heavier atom and are lighter than it; in our case, Ge takes the place of Pb in PbTe and then two new modes appear.Tese are the local mode, which appears above the optical band, and the gap mode, located between the acoustic and optical bands of the host material [17].In the case of PbTe, that gap does not exist, so the gap mode does not appear.
Te impurity mode can appear due to the electronphonon interaction [18].Still, most often, it occurs due to the diference in the masses of the original ion and the impurity that comes in its place, known as the isotope like or mass efect [19].In our case, lattice ions are replaced with lighter ones, and we approximate no change in the force constants.
If only the mass efect is taken into account, the position of the local mode can be estimated in the simplest way, which is described in detail in [20].
In this way, the value for ω 0 � 175.7 cm −1 was determined.Tat value is in very good agreement with the experimental values from Figures 2(b Figures 2(b) and 3(b), we note that the third harmonic is signifcantly weaker in intensity than the second and fourth.For the sample Pb 0.745 Ge 0.255 Te/BaF 2 , all harmonics have only phononic character, i.e., there are no features related to the electron-phonon interaction, such as broadening relative to the natural form, change of position regarding the basic multiplied value, and formation of a new structure near the multiphonon.However, the fourth harmonic in the PbTe/GeTe/BaF 2 sample has all these characteristics.
Te explanation for this situation can be as follows: during the growth of this heterostructure by the MBE method, there is no sharp transition from the GeTe layer to the upper PbTe layer, but rather the formation of a PbTe-GeTe transition layer.Tis spatial inhomogeneity has nanometer dimensions and plays a very active role.Because of its dimensions, it causes changes in the electronic structure, which can lead to electron-phonon interaction, as in our case.One of the consequences of the electron-phonon interaction on the Raman spectra is the change in the shape of the harmonic (in our case, the fourth) [21].Te energy of this harmonic is close to the energy of the electronic transition, so the conditions for interaction between them have been created.Te energy of the fourth harmonic is about 100 meV.In the energy spectrum of PbTe, several transitions exist in this energy range [1].Terefore, the conditions for electron-phonon interaction were created in this way.Tis efect is desired when designing new thermoelectrics.
Te same efect with the fourth harmonic can be seen in the samples from Figure 3(b).However, the reason for registering the electron-phonon interaction is the addition of Eu ions.Tese ions do not create new levels or resonance states [9].Still, they change the electronic spectrum of the basic material, so similarly, the energy of the fourth phonon and electronic transitions in the PbTe alloy are brought closer together.As a result, the shape of the fourth harmonic changes again.
Further research should focus on the thermoelectric properties of these heterostructures and the search for the optimal level of Eu doping, which will be the subject of our future work.

Conclusion
In this paper, we have focused on the Raman spectra of PbTe, GeTe, (Pb, Ge)Te, and (Pb, Ge, Eu)Te layers grown on BaF 2 (111) monocrystalline substrates.Phonon features originating from the bulk material and a local mode of Ge in PbTe at about 181 cm −1 were registered.Te position of this local mode can be explained by a model that only considers the diference in the masses of the constituent elements.Multiphonon processes registered for this phonon are a consequence of the change in the electronic structure of PbTe.Te shape of the fourth harmonic of the Ge local mode in PbTe in the PbTe/GeTe/BaF 2 heterostructure and (Pb, Ge, Eu)Tebased flms is a consequence of the infuence of electronphonon interaction on the intensity of Raman scattering lines.