Ab initio Investigation of Structural Units and Raman Vibrational Characteristics in Ge-Se-Te Glasses

1 Introduction

Chalcogenide glasses in the Ge-Se-Te system represent an important class of amorphous semiconductors with exceptional infrared transmission, large optical nonlinearities, and high refractive indices [1,2,3]. Their compositional flexibility allows continuous tuning of structural and optical properties, which makes them attractive for infrared photonics, sensing, and information storage applications. Among these systems, the substitution of selenium by tellurium plays a pivotal role in modifying both the bonding character and network connectivity, thereby influencing vibrational and electronic behaviors [4,5]. At the atomic scale, Ge-Se-Te glasses consist of diverse structural motifs, including Ge-centered tetrahedra, edge-sharing tetrahedral units, and Ge–Ge–linked ethane-like units (Ge2Ch6, Ch = Se, Te). Substituting Se with the heavier Te atom not only alters bond lengths and bond angles but also changes the force constants and local symmetry of these units. These structural modifications have a pronounced impact on the Raman-active vibrational modes, often manifested as systematic redshifts in the stretching and breathing frequencies. Experimental studies have observed such spectral trends [6,7,8], but the detailed evolution of specific local vibrational modes with Te→Se substitution still requires more quantitative clarification.

To address this issue, this study employs ab initio calculations to analyze the structural and vibrational evolution of representative Ge-Se-Te building blocks. The investigation focuses on three fundamental units: mixed GeSexTe4−x (x = 0–4) tetrahedra, edge-sharing tetrahedral pairs, and Ge–Ge–bonded ethane-like structures to explore how the gradual substitution of Se by Te affects local geometry and characteristic vibrational modes. While cluster-level models have inherent limitations in capturing medium-range glass disorder, they are widely used in chalcogenide research to probe local coordination environments and allow a controllable way to isolate substitution effects [9,10,11,12,13]. Through this approach, this work aims to provide complementary microscopic insight into how local structural changes influence Raman-active vibrational modes in Ge-Se-Te units. The resulting analysis supports more reliable Raman spectral assignments and helps improve understanding of the composition-dependent vibrational behavior of Ge-Se-Te glasses.

2 Computational Methods

Geometry optimizations and vibrational frequency analyses were carried out using density functional theory (DFT) with the B3LYP hybrid functional and LANL2DZ effective core potentials augmented with polarization functions (d) without any scaling factor. The maximum deviation of 7 cm−1 (≈5.19%) between our computed and literature experimental Raman modesconfirms that this level of theory already reproduces the literature experimental frequencies within their intrinsic uncertainty. The structural models included three representative types of Ge-Se-Te units: (i) mixed GeSexTe4−x (x = 0–4) tetrahedra, (ii) edge-sharing tetrahedral pairs containing Ge-Se-Ge-Se, Ge-Se-Ge-Te, and Ge-Te-Ge-Te four-membered rings, and (iii) ethane-like units with systematically varied Se/Te substitution. All cluster models were terminated with hydrogen atoms to saturate dangling bonds, maintain charge neutrality, and preserve realistic local coordination environments of Ge and chalcogen atoms, consistent with established cluster-based approaches for chalcogenide glasses [10,14]. The optimized structures were verified by the absence of imaginary frequencies. Raman activities were obtained from analytical frequency calculations normalizing the intensity of each Raman vibrational mode simultaneously.

3 Results

3.1 Isolated Tetrahedral Unit

The optimized geometries of the GeSexTe4−x (x = 0–4) tetrahedral units obtained in this work show strong consistency with structural parameters reported in previous experimental and theoretical studies, confirming the reliability of the present computational results. The calculated Ge-Se bond lengths range from 2.40 Å to 2.43 Å, while the Ge-Te bond lengths lie between 2.62 Å and 2.67 Å, which are showed in Table 1. These values are in close agreement with the reported averages of ~2.40 Å for Ge-Se and ~2.60 Å for Ge-Te bonds in amorphous Ge-Se and Ge-Te systems, respectively [15,16]. The slight overestimation observed here may be attributed to the use of hybrid functional and effective core potential basis sets, which tend to marginally elongate heavy-atom bonds due to relativistic and polarization effects. Meanwhile, the internal bond angles within the tetrahedra deviate slightly from the ideal 109.5°. The bond lengths and angles of the overall structure are within acceptable ranges. In addition, the isolated tetrahedral unit structure of the GeSexTe4−x (x = 0, 1, 2, 3, 4) clusters are shown in Fig. 1.

Figure 1: The isolated tetrahedral unit structure of the GeSe_xTe_4−x (x = 0, 1, 2, 3, 4) clusters.

The number and types of vibrational modes in the GeSexTe4−x tetrahedral units can be further rationalized based on molecular symmetry and the general 3N − 6 rule [17,18], where N represents the number of atoms in a nonlinear molecule. For a tetrahedral cluster such as GeSe4 (five atoms), this leads to 3 × 5 − 6 = 9 fundamental vibrational degrees of freedom. Group theoretical analysis within the Td point group predicts that these nine modes transform as A1 + E + 2F2, all of which are Raman active, while only the F2 modes are also infrared active. The A1 mode corresponds to the symmetric stretching of the four Ge-Se (Ge-Te) bonds, whereas the triply degenerate F2 modes involve asymmetric stretching and bending motions of the tetrahedron. As Te atoms are introduced, the molecular symmetry is progressively reduced (to C3v, C2v), leading to the splitting and mixing of degenerate F2 modes. This symmetry lowering results in additional Raman-active components and a noticeable redistribution of vibrational intensities. All the Raman vibrational modes of GeSexTe4−x clusters are shown in Table 2.

The calculated Raman-active vibrational frequencies of the GeSe4 and GeTe4 tetrahedral units exhibit excellent consistency with experimental observations reported for GeSe2 and GeTe2 glasses. For the GeSe4 tetrahedron, the computed A1 symmetric stretching mode (ν1) appears at 194 cm−1, which closely matches the experimentally observed Raman band centered around 201 cm−1 attributed to the breathing vibration of corner-sharing GeSe4/2 tetrahedra in Ge-Se glasses [19,20]. For the GeTe4 tetrahedron, the computed A1 mode appears at 123 cm−1, which is in excellent agreement with the main Raman peak of GeTe2 glasses observed between 127 cm−1, corresponding to the symmetric stretching of Ge-Te bonds [21,22,23]. The consistency between the main vibrational frequencies of the GeSe4 and GeTe4 tetrahedral units and the corresponding literature values verifies the reliability of the calculations. On this basis, we further investigated the Raman vibrational frequencies of the GeSexTe4−x mixed tetrahedra and their gradual evolution behavior.

The calculated Raman vibrational modes of the GeSexTe4−x tetrahedra exhibit distinct frequency distributions with normalized intensity in Fig. 2, which reflect the local bonding environment around the Ge center. The symmetric stretching vibrations extracted from all GeSexTe4−x mixed tetrahedra, as illustrated in Fig. 3, can be clearly categorized into two groups: (i) modes primarily associated with Ge-Se bonds and (ii) modes dominated by Ge-Te bonds. A systematic trend is observed in both categories, indicating that the vibrational frequency of the symmetric stretching mode strongly depends on the number of equivalent bonds of a given type within the tetrahedral unit. For the Ge-Se related symmetric stretching modes, the frequency gradually decreases as the number of Ge-Se bonds in the tetrahedron increases. Specifically, the mode involving a single Ge-Se bond (in GeSeTe3) exhibits the highest frequency at 271 cm−1, followed by 266 cm−1 for two Ge-Se bonds (GeSe2Te2), 251 cm−1 for three Ge-Se bonds (GeSe3Te), and 194 cm−1 for four Ge-Se bonds (GeSe4). A similar frequency-decreasing trend is also observed for Ge-Te related symmetric stretching modes, which shift from 167 cm−1 for a single Ge-Te bond (in GeSe3Te) to 123 cm−1 for four Ge-Te bonds (GeTe4).

Figure 2: The vibrational mode frequencies of GeSe_xTe_4−x clusters with normalized intensity.

Figure 3: The symmetric stretching vibrational mode frequency shift with Ge-Se and Ge-Te bands related.

3.2 Edge-Sharing Tetrahedral Unit

In addition to the isolated tetrahedral units, edge-sharing tetrahedral (EST) structures in the Ge-Se-Te system were also investigated. Owing to the different proportions of Se and Te atoms, a variety of mixed edge-sharing configurations can be formed. To ensure a systematic and comparable analysis, this study adopted a symmetric substitution approach. Specifically, substitutions were introduced in pairs at equivalent atomic sites within the symmetric edge-sharing tetrahedral framework, thereby maintaining the overall structural symmetry and allowing a clear observation of compositional evolution. Following this substitution scheme, nine distinct symmetric configurations were constructed, as illustrated in Fig. 4. The optimized structural parameters, including Ge-Ch (Ch = Se, Te) bond lengths and inter-tetrahedral bond angles, are summarized in Table 3.

Figure 4: The edge-shared structure of the Se_2−xTe_x-Ge₂Se_nTe_2−n-Se_2−xTe_x (n = 0, 1, 2; x = 0, 1, 2) cluster.

Fig. 5 presents the normalized-intensity vibrational-mode frequencies of the edge-sharing clusters. Given the complexity and the large number of vibrational modes in edge-sharing tetrahedral (EST) structures, the present study focuses on the breathing vibration of the four-membered rings as the primary subject of analysis, which considered as the most intense Raman active mode of the edge-sharing Ge2Ch6 (Ch = Se, Te) structure arises from the in-phase symmetric stretching (breathing) vibration ν(A1) of the two GeCh4 tetrahedra. Table 4 collects the computed symmetric breathing frequencies ν(A1) of the four-membered rings formed in edge-sharing clusters. Three distinct ring types occur in the dataset: (i) Ge-Se-Ge-Se, (ii) Ge-Se-Ge-Te, and (iii) Ge-Te-Ge-Te. For each ring type the calculations were performed for a series of clusters in which Se atoms occupying the ring-corner (top-corner) positions are progressively replaced by Te.

Figure 5: The vibrational mode frequencies of Edge-Sharing Se_2−xTe_x-Ge₂Se_nTe_2−n-Se_2−xTe_x (n = 0, 1, 2; x = 0, 1, 2) clusters with normalized intensity.

The results show two clear and mutually consistent trends in Fig. 6. First, comparing the three ring chemistries at equivalent degrees of substitution demonstrates that the ring breathing frequency systematically decreases as the average chalcogen changes from Se, mixed Se/Te to Te. The pure Ge-Se-Ge-Se rings give the vibrational mode frequencies from 213, 205 to 198 cm−1 for 0, 1 and 2 Te substitutions at the specified corner sites, respectively, the mixed Ge-Se-Ge-Te rings occupy an frequency shift from 182, 176 to 170 cm−1, and the pure Ge-Te-Ge-Te rings present the frequencies decreasing from 166, 157 to 142 cm−1, which can be seen that the ring breathing frequency decrease with the increasing of Te substitutions at the specified corner sites. Second, within each ring class ((i) Ge-Se-Ge-Se, (ii) Ge-Se-Ge-Te, and (iii) Ge-Te-Ge-Te.) the breathing frequency decreases monotonically as the number of Te atoms in the ring local environment increases. the breathing frequency is highest for Ge-Se-Ge-Se rings, the middle for Ge-Se-Ge-Te rings and lowest for Ge-Te-Ge-Te rings.

Figure 6: The Breathing vibrational mode frequency of Edge-Sharing Se_2−xTe_x-Ge₂Se_nTe_2−n-Se_2−xTe_x (n = 0, 1, 2; x = 0, 1, 2) clusters.

3.3 Ethane-Like Clusters

For the ethane-like “Ch3Ge-GeCh3” structural motifs with a central Ge-Ge bond and six terminal Ch atoms (Ch = Se or Te).in the Ge-Se-Te system, the analysis primarily focused on the stretching vibration modesand their dependence on the Se/Te ratio at the terminal sites. To ensure structural symmetry and to systematically reveal the compositional evolution, a symmetric even-substitution scheme was adopted, in which two equivalent terminal atoms were simultaneously replaced in each step. This approach yielded four representative configurations, as illustrated in Fig. 7, and the optimized bond lengths and bond angles for these structures are summarized in Table 5.

Figure 7: The Ethane-like structure of Ge₂Se_2xTe_6−2x (x = 0, 1, 2, 3) clusters.

Fig. 8 shows the frequencies of vibrational modes in ethane-like Ge2Se2xTe6−2x (x = 0, 1, 2, 3) clusters with intensity normalization. From all the vibrational modes of the above structure, the main two vibrational modes in terms of intensity are selected based on their D3d symmetry classification using point-group analysis, as shown in Table 6. The strongest feature arises from the A1g breathing mode, in which all six Ge-Ch (Ch = Se or Te) bonds extend and contract in unison while the two GeCh3 fragments remain collinear; this in-phase motion produces the largest change in molecular polarizability and therefore dominates the spectrum. The second-stronging contribution is the Eg antisymmetric stretch, where the two GeCh3 units oscillate out of phase: as one Ge-Ch bond lengthens, its counterpart across the Ge–Ge axis shortens. According to literature [24], the ethane-like Se3Ge-GeSe3 structural unit is characterized by the peak at 175 cm−1, which is well matched with the calculated vibration frequency of Se3Ge-GeSe3 cluster attributed to ν(A1g) mode (173 cm−1)—in Table 6. The close agreement between the calculated results and the literature data validates the scientific rationality of the computational approach.

Figure 8: The vibrational mode frequencies of Ethane-like Ge₂Se_2xTe_6−2x (x = 0, 1, 2, 3) clusters with normalized intensity.

A comparative analysis of the main stretching modes with ν(A1g) and ν(Eg) in Fig. 9 revealed a clear and consistent trend: the stretching vibration frequency decreases progressively with increasing Te content in the terminal positions. These results further demonstrate that the substitution of Se by Te significantly alters the local bonding environment and vibrational response of ethane-like clusters in chalcogenide glass networks.

Figure 9: The main vibrational mode frequency in Ethane-like Ge₂Se_2xTe_6−2x (x = 0, 1, 2, 3) clusters.

4 Discussion

Table 7 summarises the deviations between our calculated values and the literature frequencies for the principal symmetric-stretching modes of Ge-Se and Ge-Te clusters. Overall, the calculated wavenumbers track the experimental ones within ±7 cm−1, corresponding to relative errors of −3.48% to +5.19%. The largest discrepancy (+7 cm−1, 5.19%) is observed for edge-sharing Ge2Te6. In addition, no experimental data is listed for the ethane-like Ge2Te6 unit in Table 7, To the best of our knowledge, experimental Raman measurements specifically identifying the ETH-Ge2Te6 structural motif have not been reported in the literature, which is consistent with previous structural studies reporting a low fraction of Ge-Ge homopolar bonds in Ge-Te glasses [25,26].

The compositional evolution of vibrational features in Ge-Se-Te systems can be reasonablyinterpreted based on vibrational spectroscopy theory and bond polarizability models [28,29,30], which together indicate that frequency shifts typically involve contributions from changes in bond force constants, atomic masses, and bond-polarizability effects. The systematic redshift of the main Raman-active symmetric stretching modes in Ge-Se-Te clusters (GeSexTe4−x tetrahedra, edge-sharing tetrahedra, and ethane-like units) is are therefore better understood as the collective outcome of these three contributions. Under the harmonic approximation, the frequency (ν) of a stretching vibration is shown in Eq. (1): v=12πkμ(1) where k is the bond stretching force constant and μ is the reduced mass. The substitution of Se (MSe = 78.96) with the heavier Te (MTe = 127.60) increases μ and simultaneously reduces the Ge–Ch restoring force due to weaker Ge 4p–Ch np (n = 4, 5) orbital overlap.

In GeSexTe4−x tetrahedra, all symmetric stretching vibrations can be grouped into two main types: Ge-Se related and Ge-Te related modes. The frequency of each group systematically decreases as the number of identical bonds within a tetrahedron increases. This trend primarily reflects the redistribution of vibrational energy among equivalent oscillators, leading to a smaller effective restoring force constant (keff). Additionally, our calculated bond-angle variations (e.g., Se-Ge-Se decreasing from ≈109.5° to ≈99.2° in mixed Se/Te tetrahedra) and bond-distance variations from ~2.4 Å(Ge-Se) to ~2.6 Å(Ge-Te) further reduce keff by enabling softer angular restoring forces, consistent with established central-force models. Consequently, tetrahedra with more identical bonds exhibit lower symmetric stretching frequencies than those containing fewer.

For edge-sharing tetrahedra, the vibrational behavior is dominated by the breathing modes of the four-membered rings (Ge-Se-Ge-Se, Ge-Se-Ge-Te and Ge-Te-Ge-Te).

The frequency hierarchy indicates a gradual softening of the breathing motion as Te atoms replace Se at the bridging sites. This can be attributed to the smaller bond-bending force constant (kθ) and lower ring strain in Te-rich configurations, which facilitate angular relaxation and mode coupling across the shared edge. Our calculated breathing frequencies follow this hierarchy with typical decreases of ~4–15 cm−1 for each symmetric 2Te-for-2Se substitution step in Table 4, supporting the interpretation that both mass and angular-force reductions are operative.

In the ethane-like structures, the focus is placed on the stretching modes with ν(A1g) and ν(Eg). The substitution of terminal Se atoms by heavier and less electronegative Te atoms monotonically red-shifts both the A1g and Eg vibrational modes. This effect can be described by the local mode-coupling model, in which heavy-atom substitution enhances mass loading and redistributes energy between stretching and bending coordinates.

5 Conclusion

This work provides a systematic DFT analysis of how Te → Se substitution affects the vibrational behavior of representative Ge-Se-Te structural units. By examining a complete series of GeSexTe4–x (x = 0–4) tetrahedra together with edge-sharing and ethane-like motifs, the study establishes a coherent microscopic picture linking bond-length/angle variations to the observed Te-induced redshifts of Raman-active modes. The results clarify how reduced mass, Ge-Ch (Ch = Se or Te) bond weakening, and local geometric relaxation collectively shape the compositional evolution of vibrational frequencies. These trends offer a unified reference for interpreting Raman features in Ge-Se-Te glasses and provide a structural basis for subsequent experimental or computational investigations.