Evolution of Low‐Frequency Vibrational Modes in Ultrathin GeSbTe Films

GeSbTe (GST) phase‐change alloys feature layered crystalline structures made of lamellae separated by van der Waals (vdW) gaps. This work sheds light on the dependence of interlamellae interactions at the vdW gap on film thickness of GST alloys as probed by vibrational spectroscopy. Molecular beam epitaxy is used for designing GST layers down to a single lamella. By combining density‐functional theory and Raman spectroscopy, a direct and simple method is demonstrated to identify the thickness of the GST film. The shift of the vibrational modes is studied as a function of the layer size, and the low‐frequency range opens up a new route to probe the number of lamellae for different GST compositions. Comparison between experimental and theoretical Raman spectra highlights the precision growth control obtained by the epitaxial technique.

DOI: 10.1002/pssr.202000434 GeSbTe (GST) phase-change alloys feature layered crystalline structures made of lamellae separated by van der Waals (vdW) gaps. This work sheds light on the dependence of interlamellae interactions at the vdW gap on film thickness of GST alloys as probed by vibrational spectroscopy. Molecular beam epitaxy is used for designing GST layers down to a single lamella. By combining density-functional theory and Raman spectroscopy, a direct and simple method is demonstrated to identify the thickness of the GST film. The shift of the vibrational modes is studied as a function of the layer size, and the low-frequency range opens up a new route to probe the number of lamellae for different GST compositions. Comparison between experimental and theoretical Raman spectra highlights the precision growth control obtained by the epitaxial technique. Table S1, Supporting Information). The symmetric scan of the bulk-like sample (top red curve) confirms that the layer is oriented along (111) with Bragg reflection of the Si substrate at Q z ¼ 2.00 Å À1 and the (00. 15) and (00. 30) reflections of GST225 at Q z ¼ 1.83 and 3.67 Å À1 , respectively. [12] The reflections (00.12) and (00.27) at Q z ¼ 1.38 and 3.22 Å À1 , respectively, have been assigned in our previous work [8] to the first-order peaks of the vacancy layers (VLs) and prove the layered nature of the film even though the larger full width at half maximum (FWHM) is an indication of compositional disorder [8] (see Figure S1, Supporting Information). In addition, they allow for the estimate of the average block size of 16.2 Å, which means a total number of lamellae (N) of %21 in the bulk-like sample (the number of lamellae reported in the text has been obtained by the thickness/block size ratio; see Table S1, Supporting Information, and the values have been approximated either to full-or half-filled lamella for the sake of clarity). Furthermore, the HRTEM analysis of this sample (Figure 1b) highlights the areas with mainly nine-layer blocks (GST225) separated by vdW gaps and a lattice stacking compatible with the trigonal phase. [13] The determination of the stacking has been possible only in local areas of the TEM specimens due to a clear contrast between vdW gaps and atoms (see Figure S2, Supporting Information). The discrepancies in other regions are attributed to slight deviation from the high symmetry orientation or to the presence of bilayer (BL) defects. [14] The dependence of the structural properties on the thickness of the film has been investigated by XRD. The diffraction pattern of seven samples with different thickness, reported in Figure 1a, shows two main changes with the thickness of the film; namely, the FWHM of the GST(00.30) reflections increases from 0.03 Å À1 (N % 21) to 0.22 Å À1 (N % 2), and the VL peak intensity decreases by reducing the number of vdW gaps. HRTEM images correlate with XRD data and demonstrate the successful realization of GST films down to 3, 2, and 1 lamellae, as shown, respectively, in Figure 1c-e. However, TEM studies establish that the crystal structure becomes more perfect with a regular arrangement of vdW gaps with increasing GST film thickness. It should also be pointed out that the 1-2 lamellae GST films could vary somewhat in the thickness and contain amorphous regions. Albeit the average composition corresponds to GST225 throughout the series and no significant change of the in-plane lattice constant is detected down to N % 3.5 (1.6941 Å vs 1.6935 Å for bulk-like; see Figure S3, Supporting Information), HRTEM evidences a local tendency to form Ge-poor configurations such as GST124 and Sb 2 Te 3 close to the Si substrate, which is also confirmed by the results of energy-dispersive X-ray (EDX) microanalysis on the average stoichiometry of the GST films (see Table S2, Supporting Information). This can be ascribed to kinetic effects during the shutter transient at the beginning of the growth, and examples are reported in Figure 1c-e for N % 3-1, respectively. In particular, the XRD spectrum for two lamellae shows the smearing out of the VL peak (see arrows in Figure 1a).

nm (estimated by X-ray reflectivity (XRR) measurements; see
Raman spectra of the layered GST225 as a function of layer thickness are reported in Figure 2a. From DFT calculations and polarization resolved measurement at 10 K, the symmetry of the vibrational modes is assigned. Bulk phonons at the Γ-point actually correspond to the irreducible representa- High-frequency modes can be identified in the bulk-like sample, such as E g (3), A 1g (2), and A 1g (4) at 107.4, 110.7, and 175.1 cm À1 , respectively (the peak positions have been obtained by the low-temperature measurements at 10 K of Figure S5, Supporting Information). Interestingly, two other modes are visible in the low-frequency region: E g (1) at 36.7 cm À1 and A 1g (1) at 53.7 cm À1 . Although these modes have been already observed in a previous work, [15] in the following, we will show that their dependence on the sample thickness allows estimating the number of lamellae, which represents the main result of this work.
Overall, Figure 2b shows a good agreement between experiment and theory for the intensity and position of www.advancedsciencenews.com www.pss-rapid.com Raman peaks. The inversion of the relative position of the theoretical E g (3) and A 1g (2) modes (predicted only 8.3 cm À1 apart) with respect to the experiment (see Figure S4, Supporting Information) can be attributed to the lack of both disorder within the cationic sublattice and compositional disorder [16] in the theoretical models. The E g (2), A 1g (3), and E g (4) modes present in the theoretical Raman spectra are hidden in the experimental spectra at room temperature (RT) due to low signal-to-noise ratio. Raman spectra at low temperature, however, allow for resolving a shoulder on the lower energy side of the A 1g (4) peak, which can be attributed to the A 1g (3) mode (see Figure S5, Supporting Information). Figure 2a evidences two different trends for low-and highfrequency Raman peaks as a function of thickness down to two lamellae. The weak signal for N % 1 is due to the reduced amount of material, and the smearing out of the peaks resembles the spectrum of the disordered cubic phase reported in the previous study. [17] In addition, XRD and HRTEM data (see Figure 1) show only the GST diffraction peaks and no clear vdW gap. Albeit the high-frequency modes (E g (3), A 1g (2), and A 1g (4)) are almost not affected by the film thickness (see also Figure S4, Supporting Information), the low-frequency modes (E g (1) and A 1g (1)) nicely show a clear shift. We define now the nomenclature E g B (1) and A 1g B (1) for the low-frequency modes in thin layers that evolve into the E g (1) and A 1g (1) bulk modes by increasing the thickness. The frequency evolution reported in Figure 3 for the measurement at 10 K (full symbols) shows that both E g B (1) and A 1g B (1) soften by reducing the thickness (for the 1/N values, see Table S1, Supporting Information). The total shift for E g B (1) is %2 cm À1 between N % 21 (bulk-like) and N % 2, whereas the decrease in intensity of A 1g B (1) makes the tracing of the peak possible only down to three lamellae (see Figure 2a) with a total shift of %1 cm À1 . The theoretical calculations performed for bulk and N ¼ 3, 2, and 1 (the phonon modes data for GST225 are reported in the Supporting Information) confirm the experimental redshift between bulk and N ¼ 2 for E g B (1) of 2.5 cm À1 and a slightly larger value between bulk and N ¼ 3 for A 1g B (1) of 2.6 cm À1 . At the same time, the maximum theoretical shift (between bulk and N ¼ 1) for E g B (1) and A 1g B (1) is %3.5 and %11.6 cm À1 , respectively. The not perfect matching of the A 1g B (1) for N % 3 with theory can be explained by the compositional disorder due to the Ge depletion occurring in some areas of the film (see Figure 1c) that can affect the vibrational frequencies.
Useful insights into the frequency change of the E g B (1) and A 1g B (1) modes can be found by looking at their displacement patterns ( Figure 3b). The low-frequency modes consist, respectively, of in-plane and out-of-plane vibrations where the two edges of the lamella move in opposite direction and modulate more the weaker interactions between the lamellae (interlamellar) than the stronger ones within the lamella (intralamellar). The different behavior of the high-frequency modes with thickness is attributed to the antiphase vibrations of the atoms near the edge of the lamella (see Figure S4, Supporting Information), which reduce the overall effect. Interestingly, the sensitivity to the vdW gap of the E g (1) and A 1g (1) allows for probing the layer thickness, and analogies can be found, respectively, with the interlayer shear (LSM) and breathing (LBM) modes in 2D materials, such as MoS 2 , [18] Bi 2 Te 3 , [19] graphene, [9] and vdW heterostructures. [20] In fact, LSMs and LBMs are also present in bulk GST225, but at variance with MoS 2 , they are Raman-silent, being zone-boundary modes in the primitive trigonal cell. Nonetheless, the breaking of the lattice translational symmetry due to finite thickness along the c-axis activates these modes in the Raman spectrum at E g B (1) ¼ 7.1 (10) cm À1 and A 1g B (1) ¼ 9.3 (13.9) cm À1 for the N ¼ 3 (2) case, respectively (see the gray area of Figure 2b). Unfortunately, this frequency region is very close to the Rayleigh peak, and it is not experimentally accessible by our setup. In the rest of the manuscript, we will then focus on the low-frequency modes in the region 30-40 cm À1 as a probe for the number of lamellae in GST materials with different compositions.
To strengthen the observation of the thickness dependence of the low-frequency Raman modes in GST materials due to their  (1) mode is attributed to coherent anti-Stokes Raman scattering of air. [38] b) Raman intensity of GST225 in bulk and thin-film geometries calculated with DFT phonons and the bond polarizability model (BPM) in the z(y,xy)-z scattering geometry. Modes at ultralow frequencies (LBM/LSM) become active as long as translational symmetry is broken along the c-axis and at least two lamellae are present.
www.advancedsciencenews.com www.pss-rapid.com interlamellar character, the analysis reported for GST225 has been repeated for a different composition of the alloy that was obtained by rapid thermal annealing (RTA) of the GST225 series at 300 C for 30 min in N 2 atmosphere. This results for the bulklike sample in the formation of GST124, [21,22] which has a lower formation energy than GST225, [13] as confirmed by the average block size of 1.4 Å (N % 23.5; see Figure S6, Supporting Information). The irreducible representation of phonons at the Γ-point for GST124 bulk is five active modes are visible in the spectrum at RT of Figure 4a (red curve), namely, E g (1) and A 1g (2) at 36.5 and 55.6 cm À1 (low frequency), respectively, and A 1g (2), E g (3), and A 1g (3) at 106.7, 112.5, and 173.5 cm À1 (high frequency), respectively. The peak positions for A 1g (2) and E g (3) were obtained from polarization resolved Raman spectra, whereas a low signal-to-noise ratio makes the assignment for E g (2) difficult. Similar to the GST225 case, there is an inversion of the theoretical A 1g (2) with E g (3) peak positions as compared with experimental data. The Raman spectrum for bulk GST124 reported in Figure 4a matches (1) mode (filled black squares) and A 1g B (1) (filled red circles) that evolve into the E g (1) and A 1g (1) bulk modes, respectively, as a function of inverse number of lamellae (see Table S1, Supporting Information, for the full dataset). The corresponding theoretical DFT frequencies at 0 K are shown by open symbols. The continuous and dashed lines are polynomial fits. (1) mode (filled black squares) and A 1g B (1) (filled red circles) that evolve into the E g (1) and A 1g (1) bulk modes, respectively, as a function of inverse number of lamellae (see Table S1, Supporting Information, for the full dataset). The corresponding theoretical DFT frequencies at 0 K are shown by open symbols. The continuous and dashed lines are polynomial fits. The dotted line is a guide to the eye. b) Displacement patterns for the E g (1) and A 1g (1) modes in the bulk.
www.advancedsciencenews.com www.pss-rapid.com well with the DFT calculations (see Figure S7, Supporting Information). Most importantly, the overall spectrum is characterized by sharper peaks, especially in the low-frequency region. For example, the FWHM for A 1g (1) in the bulk-like sample measured at 10 K decreases from 5.9 cm À1 (as-grown GST225) to 4 cm À1 (annealed GST225). This is due to the improved ordering of the VLs [12,14] resulting in the reduction of chemical disorder. [23] Down to N % 7, the low-frequency modes redshift, whereas the high-frequency modes do not show a significant change (see Figure 4, and Figure S8, Supporting Information, and the 1/N values are reported in Table S1, Supporting Information). In the case of GST124 as well, the E g (1) and A 1g (1) vibrations mostly modulate the interaction across the vdW gap than those inside the lamella. Besides the similarities with the as-grown case, new features appear for N % 3.5 at 46.3, 69.5, and 113 cm À1 . These peaks correspond to the E g (1), A 1g (1), and E g (2) Raman modes of bulk Sb 2 Te 3 , respectively. [24] The tendency to form Sb 2 Te 3 at the beginning of the growth was already observed for as-grown GST225 (see Figure 1, N % 2), but no clear features were measured in the Raman spectrum, probably due to the reduced amount of material. In the annealed case, by decreasing the thickness down to N % 1, the Sb 2 Te 3 features become even more pronounced in the overall spectrum with the redshift of the high-frequency mode to 169.7 cm À1 at N % 3, corresponding to the A 1g (2) mode in Sb 2 Te 3 . This phase separation might be ascribed to a decrease of the energy gain of GST with respect to Sb 2 Te 3 and GeTe by reducing the film thickness. [25] In our case, annealing might lead to material segregation, such as Ge or formation of GeTe BLs, whose evaporation is prevented by the capping layer. Contrary to Sb BLs, whose Raman features are easily detected in epitaxial Sb 2 þ x Te 3 films, [26] a poor GeTe signal for ultrathin films below four BLs has been shown by Wang et al. [27] to be driven by the suppression of Peierls distortions in the thinner samples. Recently, Lotnyk et al. observed Ge evaporation during deposition of GST225 at higher temperature with the formation of GST124, GeTe 2 , and Sb 2 Te 3 , [28] but no additional modes are visible in our spectrum that could be attributed to GeTe 2 . Further studies are needed to shed light on the stacking in the annealed samples in the presence of capping. Even though Sb 2 Te 3 dominates the full spectrum, it is still possible to follow the low-frequency GST modes between N % 23.5 (bulk-like) and N % 3: softening of the modes with decreasing thickness is observed with a total shift for E g B (1) and A 1g B (1) of %3.3 and 5.2 cm À1 , respectively (see Figure 4b, and the 1/N values are reported in Table S1, Supporting Information). The polarization resolved Raman spectra of the sample with N % 3 allowed for discriminating the E g (1) of Sb 2 Te 3 from the A 1g B (1) of GST124. An increased Rayleigh scattering due to a larger surface roughness prevented instead a good fit of the E g B (1) peak at N % 2. The peak positions from the theoretical calculations of GST124 in bulk and in thin layers with N ¼ 1, 2, and 3 (see Supporting Information for the data) evidence softening with a total shift between bulk and N ¼ 1 for E g B (1) and A 1g B (1) of %4 and %11.6 cm À1 , respectively. The comparison of the fits for the experimental and theoretical data shows a good agreement down to N ¼ 3.5, where the Sb 2 Te 3 signature becomes visible. The larger softening of the experimental frequencies between N ¼ 3.5 and N ¼ 3 is qualitatively ascribed to the Ge deficiency resulting in the increase of the atomic distances between blocks and the decrease of the restoring forces. It is important to note that LBM and LSM are Ramansilent also in bulk GST124, because they correspond to zoneboundary modes in the primitive cell, but they become Raman active for N ¼ 3 (E g (1) ¼ 8.9 cm À1 , A 1g (1) ¼ 11.4 cm À1 ) and N ¼ 2 (E g (1) ¼ 12.2 cm À1 , A 1g (1) ¼ 16.5 cm À1 ), as a result of the breaking of translational symmetry along the c-axis (see Figure S7, Supporting Information).
In conclusion, we have investigated the dependence on the sample thickness of the vibrational properties of ultrathin GST films epitaxially grown by MBE. A method for probing the number of lamellae in layered GST materials has been proposed by means of Raman spectroscopy, a tool for nondestructive characterization that has been already used for PCM materials. [12,8,29,30] Indeed, we have demonstrated that the number of lamellae can be measured by following the change of low-frequency Raman modes with the film thickness down to a single lamella. This has been shown for GST225 and for GST124 obtained, in turn, by post-growth annealing of a GST225 series. The methodology is quick and robust and highlights the advantages of the MBE technique for the precise control of the layer size.

Experimental Section
MBE Growth: The studied samples consist of GST films with the thicknesses between 34.3 and 2.3 nm grown by solid-source MBE on Si(111)-( p 3 Â p 3)R30 -Sb passivated surfaces with 0.03 miscut. All the substrates are cleaned, and the surfaces are prepared using the methods described in previous works. [11,31] According to flux calibration by XRR measurements on amorphous Ge, Sb, and Te films grown at RT, the cell temperatures correspond to a Ge/Sb/Te flux ratio of %2/2/5. The substrate temperature was %250 C for all the growths. A reflection highenergy electron diffraction (RHEED) technique was used for confirming the formation of the Si(111) À (7 Â 7) reconstruction prior the Sb termination of the substrate.
XRD and XRR: Ex situ structural characterization of the films was performed by high-resolution XRD and XRR. The system consists of a fourcircle PANalytical X'Pert Pro Materials Research diffractometer equipped with a Ge (220) hybrid monochromator and Cu Kα 1 (λ ¼ 1.540598 Å) X-ray radiation. For ω-2ϑ scans, a 1 mm slit at the detector side was used. The cubic unit cell has been adopted for indexing the XRD pattern of the Si substrate, whereas the choice of the trigonal unit cell in the case of the epilayer accounts for the study of the rhombohedral layered GST structure with space group R-3m.
DFT: Phonons are calculated at Γ-point within density-functional perturbation theory (DFPT) [32] as implemented in the Quantum-Espresso suite. [33] We used the Perdew-Burke-Ernzerhof (PBE) exchange and correlation functional [34] and the semiempirical correction due to Grimme (D2) [35] to include vdW interactions. We used norm conserving pseudopotentials and a plane wave expansion of Kohn-Sham orbitals up to an energy cutoff of 30 Ry. Brillouin zone integration is performed on Monkhorst-Pack [36] grids with a minimal k-point linear density of 4.6 Å. Bulk GST124 and GST225 are modeled in the fully relaxed primitive cells with 3D periodic boundary conditions. Thin films are instead modeled by trigonal cells at the theoretical bulk in-plane lattice parameter (a ¼ 4.191 Å for GST225 and a ¼ 4.290 Å for GST124), containing N ¼ 1, 2, and 3, seven-layer (GST124) or nine-layer (GST225) blocks plus a vacuum 12 Å wide separating the periodic images of the layers along the c-axis. The cationic layers close to the vdW gaps are fully occupied by Sb atoms, [37] and intermixing in the cationic sublattices is neglected in the present work. The theoretical Raman spectra are computed from ab initio phonons, and Raman tensors in nonresonant conditions are obtained, in turn, from the BPM developed previously for GST225. [30] A z(x,xy)-z www.advancedsciencenews.com www.pss-rapid.com backscattering geometry is considered with z along the c-axis of the trigonal representation of all models. A Lorentzian broadening of 3 cm À1 is assigned to all peaks. The Bose factor is computed at 300 K. The theoretical atomic positions and the size of the vdW gaps in bulk and multilayers of GST225 and GST124 are given in Table S3-S6 and Table S11-S14, Supporting Information. Theoretical phonons at the Γ-point in bulk and multilayers of GST225 and GST124 are given in Table S7-S10 and  Table S15-S18, Supporting Information. HRTEM: HRTEM studies were carried out in an FEI Titan Themis 80-200 transmission electron microscope operated at 200 kV and equipped with spherical aberration image corrector, FEI Ceta 16M complementary metal-oxide-semiconductor (CMOS) camera, and Super-X EDX detector. Cross-sectional TEM specimens in Si[110] zone axis were prepared by a focused ion beam technique in a dual-beam workstation Helios NanoLab 650.
Micro-Raman Spectroscopy: The Stokes scattering of the samples was obtained by means of micro-Raman spectroscopy. The systems were excited by a continuous wave He-Ne laser 632.8 nm equipped with an LN 2 -cooled charge-coupled device (CCD) detector in backscattering z(y,xy)-z geometry. The emission was focused by a microscope objective with 0.9 (0.55) numerical aperture at 295 K (10 K), the power densities of 10 4 W cm À2 (25 kW cm À2 ), and an acquisition time of 180 s. The same objective was used for the collection of the signal. The achieved spectral resolution is 0.7 cm À1 , and a notch filter suppressed the stray light. The character of the vibrational modes was assigned by means of polarizationresolved spectroscopy.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.