Terahertz spectroscopic characterization of Ge₃Sb₂Te₆ compounds for active applications

Abstract

A study of the optical and dielectric properties of the non-volatile chalcogenide phase change material Ge₃Sb₂Te₆ in the terahertz band (0.5–2.5 THz) is presented. Thermally annealed thin films of this material have been characterized with THz time-domain spectroscopy (THz-TDS), in addition to X-ray diffraction (XRD) and Raman spectroscopy. Optical constants, dielectric properties, and THz conductivity were derived from the THz-TDS data using a numerical method that takes into account the strong etalon effect of the thin film. The results are compared to the properties of Ge₂Sb₂Te₅, which is commonly employed in photonics. Remarkably, Ge₃Sb₂Te₆ exhibits considerably lower losses along the metal-to-insulator (MIT) transition. It has also been found that Ge₃Sb₂Te₆ is more robust and that its optical constants are less affected by the substrate material. These results suggest that Ge₃Sb₂Te₆ is potentially a more suitable candidate for high-performance applications requiring high contrast in the refractive index and low loss, such as in THz beam steering.

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1 Introduction

Chalcogenide phase change materials (ChPCM) composed of germanium (Ge), antimony (Sb) and tellurium (Te) with various stoichiometries exhibit remarkable tunability in their optical, electrical, and dielectric properties.^1,2 These materials exhibit non-volatile highly stable intermediate phases in addition to the amorphous (dielectric, low-loss) and the crystalline (metallic, high-loss) states,¹ reachable upon external stimuli, making them promising candidates for reconfigurable photonic applications.^3–5 This metal-to-insulator transition (MIT), which induces significant optical contrast, arises from the rearrangement of chemical bonds, from covalent bonding in the amorphous state to resonant bonding in the crystalline state.⁶ However, the optical constants of these compounds depend on the material stoichiometry¹ and fabrication conditions.⁷

Among these PCMs, Ge₂Sb₂Te₅ has been extensively studied and widely applied.^8,9 However, across the literature, its optical and dielectric properties vary significantly.^8–11 Although the phase transitions in Ge₂Sb₂Te₅ are ultra-fast (typically 1 ns) and stable for up to 10 years, the material exhibits high losses upon thermal annealing and cannot be annealed at temperatures exceeding 320 °C,⁸ limiting the achievable optical contrast. This has driven the search for alternative materials that can reach higher optical contrast with lower losses. Recent studies suggest that similar compounds such as Ge₃Sb₂Te₆, Ge₁Sb₂Te₄, Ge₁Sb₄Te₇, Sb₂Se₃, and Sb₂S₃ exhibit promising characteristics in the optical region,^12–17 but have yet to be explored in the THz domain.

To address this gap, we investigate here the thermally induced electromagnetic properties associated with the MIT transition in the non-volatile chalcogenide compound Ge₃Sb₂Te₆. To this end, we used a combination of terahertz time-domain spectroscopy (THz-TDS), X-ray diffraction (XRD), and Raman spectroscopy, with a particular focus on the potential of this material for next-generation programmable THz technologies. We compare the results with the properties of Ge₂Sb₂Te₅. THz-TDS is employed to directly measure the time-domain electric field response, providing critical insights into conductivity changes associated with phase transitions in thermally annealed thin films deposited on thick substrates. XRD analysis identifies thermally induced phases and their degree of crystallinity. Raman spectroscopy tracks microstructural changes related to molecular vibrations. In addition, we examine the influence of substrate selection on the optical and dielectric properties of Ge₃Sb₂Te₆ across its amorphous, crystalline, and intermediate (mixture-phase) states. The combination of these techniques offers a comprehensive understanding of the temperature-induced structural, optical and electronic transitions in Ge₃Sb₂Te₆, advancing its potential for active THz photonic applications.

2 Materials and methods

2.1 Preparation of chalcogenide compounds

Thin films of Ge₃Sb₂Te₆ and Ge₂Sb₂Te₅ were deposited on 625 ± 25 μm-thick highly resistive silicon (HR-Si) substrates and 450 ± 25 μm sapphire (Al₂O₃) substrates via electron beam (e-beam) evaporation using stoichiometric targets of the respective chalcogenide compounds. The reason for using two different substrates was to systematically assess how the substrate material influences the optical constants of the PCMs under study, as it is known that it may affect film growth, crystallinity, and measurements. For instance, the complex refractive index of Ge₂Sb₂Te₅ deposited on sapphire was estimated to be 25 + 5i at 260 °C and 21 + 1i at 180 °C,⁹ whereas for Ge₂Sb₂Te₅ on a quartz substrate, reported values were 18 + 13i at 260 °C and 10 + 2i at 180 °C,⁸ all measured at 1 THz.

Prior to deposition, the substrates were cleaned using acetone, ethanol, and O₂ plasma treatments. The evaporation process was carried out at a 4 kV high voltage and a 2.5 mA current under vacuum conditions, with a base pressure of 2–3 × 10⁻⁷ mbar and a working pressure of 0.3–3 × 10⁻⁶ mbar. The deposition rate was monitored using a water-cooled quartz crystal microbalance. The thin films were measured via profilometry (DEKTAK XT), which determined a thickness approximately 110 nm ± 10 nm.

To ensure accurate extraction of the optical properties, which depend on the THz transmission ratio between the sample (thin film + substrate) and the bare substrate,^8,9,18 only half of each substrate was coated with the GST thin film, while the other half was left uncoated for reference. Post-deposition, each sample was annealed at different temperatures: 155 °C, 205 °C, 255 °C, 305 °C, 355 °C, and 405 °C, to induce various crystalline phases.

The material composition of the fabricated GST films was verified by scanning electron microscope energy dispersive X-ray (SEM-EDX) measurements. To this end, we used a field emission scanning electron microscope (FE-SEM Joel IT1800 SHL) with a fully embedded energy dispersive X-ray spectrometer (EDS), operated at beam energies ranging from 10 and 30 kV and probe currents from 0.20 to 5.65 nA. As a result, we obtained a measured composition of Ge_2.9Sb₂Te_6.1 for nominal Ge₃Sb₂Te₆ and Ge_1.7Sb_2.2Te_5.1 for nominal Ge₂Sb₂Te₅, both of which were found to remain stable post annealing, supporting the results of our study.

The uniformity of thin films post-annealing was confirmed through Raman spectroscopy at three different spatial locations on each sample and by optical imaging, which shows no sign of degradation for Ge₃Sb₂Te₆, whereas spatial non-uniformity was observed for Ge₂Sb₂Te₅ samples annealed above 305 °C (as shown in Fig. 1). Thermally induced MIT transitions were analyzed through XRD and Raman spectroscopy, as detailed in the subsequent sections.

Fig. 1 Optical images of as-grown and annealed (at 405 °C) samples of (a) Ge₃Sb₂Te₆ and (b) Ge₂Sb₂Te₅, both deposited on HR-Si substrate. Scale bar: 20 μm.

2.2 XRD

The XRD patterns of Ge₃Sb₂Te₆ and Ge₂Sb₂Te₅ thin films, both deposited on silicon substrates and annealed at a temperature of 155 °C, 205 °C, 255 °C, and 305 °C, as well as in the as-grown state, are presented in Fig. 2. Highly intense and broad diffraction peaks corresponding to the HR-Si substrate were observed around 2θ = 14° (not shown in Fig. 1), where 2θ is the angle between the incident X-ray beam and the diffracted beam. For the as-grown films, only a broad peak was observed around 2θ = 30°, indicating an amorphous⁹ or partially disordered phase.¹ In contrast, distinct diffraction peaks emerged in the annealed films, reflecting the structural changes associated with the phase transition at higher temperatures.

Fig. 2 X-ray diffraction (XRD) patterns of (a) Ge₃Sb₂Te₆ and (b) Ge₂Sb₂Te₅ compounds, recorded at annealing temperatures of 155 °C, 205 °C, 255 °C, and 305 °C. The observed diffraction peaks correspond to the characteristic reflections associated with the amorphous and crystalline phases of these materials. These results indicate a transition from an insulating to a metallic state as thermal annealing progresses. The peak assignment was made in accordance with reported literature data,^1,8,9,21 providing insight into the structural transformations induced by annealing.

For the common Ge₂Sb₂Te₅ (Fig. 2b) samples annealed between 155 °C and 205 °C, the broader peak around 2θ = 30° (corresponding to the crystallographic plane 200) grows sharply indicating the presence of face-centered cubic (FCC) phases. In samples annealed above 205°, new peaks appear at lower 2θ values (103), corresponding to the development of hexagonal close-packed (HCP) phases.^8,9 In contrast, Ge₃Sb₂Te₆ (Fig. 2a) exhibited a slightly different thermal response. The broader peak at 30° (200) grows slowly compared to Ge₂Sb₂Te₅, suggesting a higher transition temperature from as-grown to cubic phases in Ge₃Sb₂Te₆.¹ In addition, no new peak evolution was detected near 30° for samples annealed up to 205 °C. However, samples annealed above 255 °C showed new peaks at higher 2θ values, slightly higher than 30°, indicating the coexistence of mixed (FCC and trigonal) crystalline phases. This kind of coexistence of different phases within the same PCM can be understood from the following fact. As the annealing temperature of an as-grown sample is increased towards the amorphous–crystalline phase change temperature, small crystalline nuclei are formed in the amorphous matrix, and these nuclei grow to eventually make the material fully crystalline. For annealing temperatures between those associated with the initiation and completion of crystallization, the material exists as a mixture of two different phases (phase coexistence). If uniform heating is applied, these intermediate states involve crystalline precipitates uniformly dispersed throughout an amorphous matrix.^7,19 In this situation, the material behaves as an effective homogeneous medium whose optical properties are approximately a weighted average of those associated with the purely amorphous and crystalline phases, with weights that depend on the degree of crystallization (which in turn depends on the annealing temperature).²⁰ Something similar happens between two crystalline phases.¹⁹

Secondary peaks emerged at 43° (220) and 53° (222) for samples annealed at 155 °C and 205 °C, respectively. These correspond to the formation of cubic phases in both Ge₃Sb₂Te₆ and Ge₂Sb₂Te₅ samples.^1,8,9 For Ge₂Sb₂Te₅ samples annealed above 205 °C, additional peaks around 40° (106) and 47° (210) appeared, indicating the formation of HCP lattices. In contrast, the XRD peaks of Ge₃Sb₂Te₆ samples grow slowly compared to those of Ge₂Sb₂Te₅. The samples annealed above 205 °C showed a distinct behavior, with the emergence of a peak around 53° (222) without any additional peaks near 40° and 47°. These differences in the rate of growth of XRD peaks with annealing temperature indicate different crystallization pathways in addition to the different crystallization phases of Ge₂Sb₂Te₅ and Ge₃Sb₂Te₆. These observations were found to be consistent with previous studies of similar materials.^1,8,9,21

2.3 Raman analysis

To further investigate the phase transitions linked to thermally-induced microstructural changes in Ge₃Sb₂Te₆ thin films and compare its features with those of Ge₂Sb₂Te₅, Raman spectra were measured for samples annealed at 155 °C, 205 °C, 255 °C, 305 °C, and 355 °C, as shown in Fig. 3. Raman spectra were obtained using a Jobin Yvon T64000 triple spectrometer equipped with a laser operating at 785 nm, and a grating of 600 gr mm⁻¹, allowing spectral data collection over a range of 50 to 250 cm⁻¹ with a resolution of 3.03 cm⁻¹.

Fig. 3 Raman spectra of (a) Ge₃Sb₂Te₆ and (b) Ge₂Sb₂Te₅ compounds, recorded at annealing temperatures of 155 °C, 205 °C, 255 °C, 305 °C and 355 °C (only for Ge₃Sb₂Te₆). The Raman spectrum of Ge₂Sb₂Te₅ annealed at 355 °C is not shown. The broad spectral envelope arises from the superposition of multiple peaks associated with lattice vibrational modes, whereas shifts in the envelope peak with increasing annealing temperature reflect thermally induced microstructural changes, signifying the transition from the as-grown amorphous phase to a crystalline state. The observed Raman modes are consistent with the vibrational modes previously reported in the literature,^4,8 further supporting the structural evolution of the materials with thermal annealing.

No Raman peaks were observed from the HR-Si substrate within the recorded range, while both the as-grown (amorphous) and annealed (crystalline) thin films showed broad spectral envelopes, which is an indication of overlapping of multiple peaks. However, distinct features within these envelopes were identified that show similarities with earlier reported literature for Ge₃Sb₂Te₆^4,22,23 and Ge₂Sb₂Te₅.^8,22,24,25 In Ge₂Sb₂Te₅, these bands originate due to transitions from amorphous to cubic and then to hexagonal phases with increasing annealing temperature,^8,9 and in Ge₃Sb₂Te₆ due to transitions from amorphous to cubic and subsequently to trigonal phases.^4,26

Specifically, the as-grown amorphous Ge₂Sb₂Te₅ film shows three distinct spectral bands [Fig. 3(b), blue curve]. A low intensity Raman band around 88 cm⁻¹ can be attributed to the Sb–Sb bonds vibrations in Te₂Sb–SbTe₂,²² or to the E-modes of GeTe₄.²⁷ The second and the most dominant band appears near 150 cm⁻¹, can be attributed to the Sb–Te vibrations in SbTe₃ pyramidal units^22,28 or potentially from the defective octahedra co-ordination of Sb atoms.^29,30 The third peak, near 129 cm⁻¹, corresponds to the A₁ mode of GeTe_4−nGe_n (n = 1, 2), related to the corner sharing GeTe₄ tetrahedra modes.^31,32 This peak may also corresponds to the B-band of vibrational modes in a-GeTe.²⁷ Similarly, the as-grown amorphous Ge₃Sb₂Te₆ films show three distinct spectral bands with slightly shifted frequencies and different peak strengths [Fig. 3(a), blue curve], consistent with the findings reported by K. Shportko et al.²³ Compared to the as-grown amorphous Ge₂Sb₂Te₅, the first band near 88 cm⁻¹ appears stronger and can be attributed to the Γ₃(E) vibrational mode, similar to one found in single crystalline α-GeTe.²³ This increase in intensity is likely due to the higher Ge-content in Ge₃Sb₂Te₆, which enhances weaker bands around 88 cm⁻¹ and 215 cm⁻¹ (not clearly visible). Additionally, the second and the third bands near 127 cm⁻¹ and 148 cm⁻¹ now have similar peak strength, unlike in as-grown amorphous Ge₂Sb₂Te₅. Once again, the weak features (near 129 cm⁻¹) of amorphous Ge₂Sb₂Te₅ gain intensity due to the increased Ge content in Ge₃Sb₂Te₆, which leads to the weakening of the Sb–Te vibrations associated with SbTe₃ pyramidal units or the defective octahedral configurations of Sb-atoms.²³

Upon thermal annealing, the peak near 148 cm⁻¹ gradually decreases in intensity for Ge₂Sb₂Te₅ samples annealed between 155 °C (orange curve) to 205 °C (yellow curve), indicating a transition to the cubic phase. This peak disappears completely in samples annealed above 205 °C. Instead, two new band emerges at 112 and 172 cm⁻¹ (violet and green) similar to those previously observed during the crystallization of Sb₂Te₃ films.³² These bands may be attributed to bulk Sb₂Te₃, typically the E_g(2) and A_1g(2) vibrational modes of the hexagonal phase. Additionally, the 129 cm⁻¹ band splits into two weaker closely overlapping bands at 109 cm⁻¹ and 145 cm⁻¹. These are due to vibrational modes of the cubic (FCC) crystalline phase and are observed in samples annealed at 155 °C (orange curve) and 205 °C (yellow curve).³² The band at 109 cm⁻¹ can be attributed to the softened A₁ mode of corner-sharing GeTe₄ tetrahedra, while the one at 145 cm⁻¹ is linked to the A₁ mode of GeTe_4−nGe_n (n = 1, 2).

In contrast, for Ge₃Sb₂Te₆, the as-grown sample and the one annealed at 155 °C show nearly identical Raman features, except for a weak broadband near 88 cm⁻¹ that slightly increases in intensity. This suggests that the crystallization temperature for the amorphous-to-cubic phase transition exceeds 155 °C,³³ likely due to the increase in Ge content in Ge₃Sb₂Te₆.

Samples annealed at 205 °C (yellow curve) and 255 °C (violet curve) exhibit nearly identical Raman spectra, though with a reduced intensity of the 148 cm⁻¹ band compared to the as-grown sample. In addition, two new bands emerge: one clearly visible at 103 cm⁻¹ and another broad one near 160 cm⁻¹, indicating the transition to the characteristic metastable cubic phase.⁴ The 103 cm⁻¹ band can be assigned to the E_g mode and the 160 cm⁻¹ to the A_1g mode.³⁴

Annealing above 255 °C causes further reduction in the 148 cm⁻¹ band, with the most significant decrease observed at 355 °C. Meanwhile, the band at 103 cm⁻¹ becomes narrower while maintaining its peak intensity in samples annealed at 305 °C and shifts towards higher frequencies in those annealed at 355 °C. At 355 °C, the Raman spectrum exhibits three characteristic bands: a nearly resolved peak at 79 cm⁻¹, another near 110 cm⁻¹ and a third at 172 cm⁻¹.⁴ These can be attributed to the E mode of α-GeTe,²³ the A₁ mode of GeTe₆³⁵ and the A_1g(2) mode of Sb₂Te₃, respectively. The latter may be linked to vacancy ordering into layers, which breaks the local symmetry and transforms into van der Waals gaps as the trigonal phase forms.

2.4 THz spectroscopic data processing

The transient electric fields transmitted through the sample (thin film + substrate, E_sample(t)) and the bare substrate (E_substrate(t)) used as reference were measured using an in-house-built all-fiber THz-TDS spectrometer based on a femtosecond laser (Toptica FemtoFErb 1560) at 1550 nm and photoconductive switches (MENLO TERA15). The time-domain scanning was performed with a voice coil optical delay line with an approximate range of 50 ps at a speed of 5 traces per s. Measurements were performed in a laboratory at 25 °C with dry air (humidity < 10%) purged in the propagation path to eliminate the effects of water vapor, i.e., ringing after the main THz pulse in the time domain, resulting in sharp absorption lines in the spectra. The optical properties of the material were derived from the transfer function. This transfer function is defined as the ratio of the Fourier transforms of E_sample(t) and E_substrate(t), allowing for analysis in the frequency domain. Because of the finite thickness of both the thin film and the substrate, etalon effects were observed, producing interference patterns in the measured transmission spectra.

To mitigate substrate-induced etalon effects, a Tukey apodization filter with a width of 18 ps and a smoothness parameter of 0.9 was applied during the post-processing. However, it does not remove the etalon effect of the thin film, given its small thickness in terms of the THz wavelength λ_THz, which results in the etalon response overlapping with the main pulse. This effect can be taken into account by the transfer function:^18,36

where ω is the agular frequency, N is the complex refractive index of the thin film, n_sub is the refractive index of the substrate, d is the thin-film thickness, and c is the speed of light in vacuum.

To determine the complex refractive index N from the experimentally measured transfer function, T(ω), the above equation can be solved, either analytically under the thin-film approximation,³⁷ or numerically.⁸ Analytical solutions rely on the assumptions d ≪ λ_THz, corresponding to the conditions |nωd/c| ≪ 1 and |n_subωd/c| ≪ 1.³⁸ While these approximations are valid for thin films on thick substrates, they may not hold for high-refractive-index n thin-films with significant optical contrast, where |nωd/c| approaches unity, rendering the thin-film approximation unreliable.

To address this challenge, we numerically solve the equation for T(ω) using the MATLAB fsolve function, enabling precise determination of N. From N, the dielectric permittivity ε can be calculated as ε = N².

The extracted optical constants were further validated by simulating the transmission function using CST Microwave Studio (MWS) and comparing the results with the experimental data. The simulation results showed excellent agreement with the measured transmission spectra.

3 Results

3.1 Transmittance

Fig. 4 shows the transmittance spectra of Ge₂Sb₂Te₅ and Ge₃Sb₂Te₆ thin films within the frequency range of 0.5–2.5 THz at increasing annealing temperatures.

Fig. 4 THz-transmittance spectra of Ge₃Sb₂Te₆ (110 ± 10 nm, solid curve with circles) and Ge₂Sb₂Te₅ (110 ± 10 nm) deposited on a silicon substrate (dashed curve with crosses), as well as Ge₃Sb₂Te₆ (115 ± 10 nm, solid curve with stars) and Ge₂Sb₂Te₅ (95 ± 10 nm, dashed curve with plus signs) deposited on Al₂O₃ substrates, were measured over a broad frequency range of 0.5–2.5 THz using a THz-TDS instrument. The spectra of each sample were recorded following annealing at various temperatures: 155 °C, 205 °C, 255 °C, 305 °C, 355 °C and 405 °C.

The transmittance decreases monotonically with increasing annealing temperature, exhibiting a rather flat response over the measured frequency range. However, the reduction in transmittance is more pronounced for Ge₂Sb₂Te₅ as compared to Ge₃Sb₂Te₆. Ge₂Sb₂Te₅ demonstrates a more significant drop in transmittance with increasing annealing temperature, approaching nearly 15% transmittance for Ge₂Sb₂Te₅ on Al₂O₃ (plus, purple) and nearly 5% for Ge₂Sb₂Te₅ on silicon (cross, purple) for samples annealed at 255 °C. Further annealing Ge₂Sb₂Te₅ samples does not alter the transmittance and it remains same, nearly 5% (cross, cyan). In contrast, approximately 75% transmittance is observed for Ge₃Sb₂Te₆ annealed at 255 °C (star and circle, purple) and nearly 10% transmittance for the sample annealed at 405 °C (circle, red). We have considered Ge₂Sb₂Te₅ annealed up to 355 °C and Ge₃Sb₂Te₆ up-to 405 °C, for which the transmittance is above 5%.

3.2 Complex refractive index and permittivity

Fig. 5 presents a comparison between the numerically extracted (solid lines) and analytically extracted (dashed lines) complex refractive indices of Ge₃Sb₂Te₆. Both indices closely overlap for the as-grown sample and those annealed up to 255 °C closely. However, the analytical method tends to overestimate the real part of the refractive index for the sample annealed at 405 °C (by 9.5% at 1 THz) and the imaginary part for the sample annealed at 355 °C (by 9% at 1 THz). This suggests that the analytical solution is more reliable for thin films with lower refractive indices, although both methods yield similar results. Therefore, for further analysis, we consider only the numerically extracted values.

Fig. 5 A comparison of numerically and analytically extracted (a) refractive index, n, and (b) extinction coefficient, k, is presented for Ge₃Sb₂Te₆ thin films deposited on a silicon substrate.

Fig. 6 illustrates the extracted values for (a) the refractive index (real part of), n, and (b) the extinction coefficient, k, of thermally annealed GST thin films, with N = n + ik being the material complex refractive index (see SI1, SI, for a comparison of these data with the optical constants of Ge₂Sb₂Te₅ reported in previous works at 1 THz). An exponential increase in n at lower frequencies strongly suggests a metallic behavior for Ge₃Sb₂Te₆ samples annealed above 255 °C, as well as for Ge₂Sb₂Te₅ samples annealed above 155 °C. For Ge₃Sb₂Te₆ films deposited on silicon and Al₂O₃ substrates, the refractive index curves overlap throughout the annealing temperature range, suggesting that the choice of substrate has no significant effect on the optical properties of this material. In contrast, a slight difference is observed for Ge₂Sb₂Te₅, consistent with earlier findings reported in the literature.^8–11 Specifically, Ge₂Sb₂Te₅ deposited on silicon shows a faster rate of increase in the refractive index compared to the same material deposited on a Al₂O₃ substrate. Furthermore, when comparing the two composites, Ge₂Sb₂Te₅ exhibits a sharper increase in refractive index compared to Ge₃Sb₂Te₆ on both silicon and Al₂O₃.

Fig. 6 Numerically extracted (a) refractive index, n, and (b) extinction coefficient, k, are presented for thin films of Ge₃Sb₂Te₆ deposited on Si (solid curve with circles), Ge₂Sb₂Te₅ on Si (dashed curve with crosses), Ge₃Sb₂Te₆ on Al₂O₃ (solid curve with stars), and Ge₂Sb₂Te₅ on Al₂O₃ (dashed curve with plus signs) at annealing temperatures of 155 °C, 255 °C, 355 °C and 405 °C.

Ge₃Sb₂Te₆ exhibits a lower thermo-optic coefficient – defined as the rate of change of refractive index with respect to temperature (dn/dT) – compared to Ge₂Sb₂Te₅. For example, at 1 THz, the refractive index of Ge₂Sb₂Te₅ increases sharply from 16 in its as-grown state to 60 at an annealing temperature of 255 °C, while Ge₃Sb₂Te₆ shows a more gradual increase, rising from 6.5 to 52 at 405 °C (see inset in Fig. 6a). The higher thermo-optic coefficient of Ge₂Sb₂Te₅ makes it well suited for frequency-agile terahertz applications that require a shift in the resonance frequency. However, this high thermo-optic coefficient in Ge₂Sb₂Te₅ is accompanied by a large thermal extinction coefficient – defined as the rate of change of the extinction coefficient with respect to temperature (dk/dT). This large thermal extinction coefficient (see inset in Fig. 6b) can be a drawback in applications where it is important to shift the resonance frequency without affecting the resonance strength, for instance, in beam steering using phase-arrayed antennas.

In comparison, due to its lower thermo-optic coefficient, Ge₃Sb₂Te₆ could serve as a better alternative to Ge₂Sb₂Te₅, offering more control over its optical properties within the MIT, which makes it advantageous for THz photonics applications that require a gradual shift in the complex refractive index without significant absorption changes. This enhanced flexibility comes at the cost of a higher annealing temperature.

Another important aspect of the considered materials is the complex dielectric function, which is defined as ε = N², where ε = ε′ + iε′′. The real part of the dielectric function, ε′, is given by ε′ = n² − k², and the imaginary part, ε′′, is expressed as ε′′ = 2nk. The accuracy of ε′ is highly dependent on the extracted complex refractive index, which, in turn, relies on the precision of the measured thickness of both the thin film and the substrate. Any slight variation in thickness introduces changes in the extracted refractive index (N), with real and imaginary components becoming n + Δn and k + Δk, respectively. This results in an additional term for the real part of the dielectric function which, to first order, reads:

Δε′ ≈ 2nΔn − 2kΔk (2)

Since Δn and Δk typically have opposite signs, their contributions combine, leading to significant errors in the calculated real part of the dielectric function.^36,39 For example, as evident from Fig. 6, the n and k curves for the Ge₃Sb₂Te₆ samples annealed above 255 °C and the Ge₂Sb₂Te₅ samples annealed above 155 °C (corresponding to the crystalline phase of these PCMs), exhibit similar shapes and values, especially in the case of the sample annealed at 405 °C. Therefore, even small errors in n and k (typically less than one unit) can lead to a significant deviation in the calculated value of ε′. As a result, we successfully extracted the complex dielectric permittivity of Ge₃Sb₂Te₆ for all annealing temperatures except for 405 °C, for which n ≈ k and the values recovered for ε′ are not reliable for the reasons mentioned above. Both, Ge₃Sb₂Te₆ on silicon and Ge₃Sb₂Te₆ on Al₂O₃ samples exhibited similar permittivity magnitudes and trends as depicted in Fig. 7. The results demonstrated an increase in the permittivity with increasing annealing temperatures. The as-grown amorphous sample and the sample annealed at 155 °C showed comparable permittivity values, indicating the dominant amorphous phase of Ge₃Sb₂Te₆ at these temperatures. In contrast, the pronounced increase in the permittivity observed for the sample annealed at 255 °C is consistent with a phase transition from the amorphous to the cubic phase at this temperature. A larger increase in permittivity for the sample annealed at 355 °C indicates the coexistence of cubic and trigonal phases in Ge₃Sb₂Te₆. To gain deeper insight into the transformation from amorphous (insulating) state to the metallic (crystalline) state, we have investigated the conductive properties of the studied PCMs, as discussed in next section.

Fig. 7 (a) The real (ε′) and (b) imaginary (ε′′) components of the dielectric permittivity of Ge₃Sb₂Te₆ thin-film, deposited on silicon (solid line with circles) and Al₂O₃ (solid line with stars) substrates, are presented for samples annealed at 155 °C, 255 °C, 355 °C and 405 °C in addition to the as-grown amorphous samples.

4 Conductivity

THz frequencies, with energies comparable to thermal energy, can stimulate the dynamics of charge-carrier quasi-particles, such as free electrons, holes, surface plasmons, excitons, and polaritons, while also triggering collective excitations like optical phonons. To investigate the leading mechanisms underlying charge transport in the considered PCMs, we extracted their THz conductivity from the measured complex refractive index, expressed as σ = iε₀ωN² = σ′ + iσ′′, where ε₀ is the permittivity of vacuum. Therefore, the real part of the conductivity σ′ depends solely on the imaginary part of the dielectric function (σ′ = ε₀ωε′′). This implies that σ′ typically exhibits a lower relative error than σ′′ and provides meaningful information on the transition from metal to insulator in thermally annealed samples.^36,39 We calculated σ′ for the thermally annealed GST samples, as shown in Fig. 8. In the same way as the transmittance, the extinction coefficient (k), and the imaginary part of the dielectric function (ε′′), the THz conductivity of Ge₃Sb₂Te₆ demonstrates a gradual increase with increasing annealing temperature. Additionally, the retrieved conductivity values are similar to the ones previously reported for other Ge–Sb–Te chalcogenide compounds.^9,39,40

Fig. 8 Numerically extracted real component of THz conductivity for Ge₃Sb₂Te₆ deposited on Si (solid curve with circles), Ge₂Sb₂Te₅ on Si (dashed curve with crosses), Ge₃Sb₂Te₆ on Al₂O₃ (solid curve with stars), and Ge₂Sb₂Te₅ on Al₂O₃ (dashed curve with plus signs) at annealing temperatures of 155 °C, 255 °C, 355 °C and 405 °C in addition to the as-grown amorphous samples.

To further analyze these observations, the THz conductivity spectra were fitted using a Drude–Lorentz model described by the following equation:

where σ_DC represents the DC or static conductivity, and τ is the scattering time associated with the Drude term, which corresponds to the contribution from non-local free charge carriers in the material. The Lorentz term, expressed as a summation over up to 4 Lorentz oscillators, accounts for localized optical phonons oscillating at specific frequencies ω_i with oscillator strength A_i and damping constant γ_i.

The numerically extracted real part of the THz conductivity obtained from THz transmission measurements (solid lines) and the Drude–Lorentz fitted THz conductivity (dashed lines) are presented in Fig. 9. The fitting parameters (with error intervals corresponding to standard deviations) for the Lorentz oscillators are summarized in Table 1. Note that the values of σ_DC and τ for the as-grown and 155 °C annealed samples are very small, indicating a largely insulating behavior. In these cases, in which the Drude term contributes minimally (it was not possible to calculate the error bar for them for this reason), we used it as a fitting placeholder to capture any residual low-frequency behavior, although its physical interpretation is limited and its omission would hardly alter the results.

Fig. 9 Drude–Lorentz fitted THz conductivity of Ge₃Sb₂Te₆ deposited on Si. Solid lines represent the numerically extracted real part of the THz conductivity (mean values) obtained from THz transmission measurements at three different spots on the sample. Black dashed lines represent Drude–Lorentz model fits.

Table 1 Drude–Lorentz model fitting parameters for Ge₃Sb₂Te₆ at different annealing temperatures with error bars (standard deviation)

Annealing temp. (°C)	Thickness (nm)	σ DC (S m^−1)	τ (ps)	f j = ωj/2π (THz)	γ j (THz)
As-grown	117	2.3 × 10^−14	3.4 × 10^−6	1.85 ± 0.05, 4.57 ± 0.24	4.21 ± 2.67, 19.26 ± 3.52
155	112	4.0 × 10^−14	0.1 × 10^−4	1.22 ± 0.08, 2.05 ± 0.06	4.16 ± 4.11, 21.06 ± 5.64
205	86	10 446 ± 974	0.1164 ± 0.06	1.97 ± 0.02, 3.09 ± 0.02	34.67 ± 5.11, 2.40 ± 0.90
255	112	9166.5 ± 3510	0.0461 ± 0.11	2.09 ± 0.02, 3.63 ± 0.05	35.43 ± 10.12, 17.62 ± 10.67
305	101	22 447.9 ± 8246	0.1015 ± 0.09	2.08 ± 0.07, 3.5 ± 0.01	70.78 ± 24.24, 10.84 ± 1.62
355	111	111 366.5 ± 14 723	0.0851 ± 0.04	1.82 ± 0.05, 3.43 ± 0.02	39.08 ± 14.22, 28.27 ± 3.047
405	92	257 243.8 ± 42 907	0.0670 ± 0.05	1.69 ± 0.01, 3.43 ± 0.01	26.56 ± 17.50, 41.94 ± 14.22

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To analyze the conductivity behavior of Ge₃Sb₂Te₆, we investigated the physical meaning of its DC conductivity values, as obtained from the Drude–Lorentz fits. As shown in Table 1, both the as-grown sample and the one annealed at 155 °C exhibit nearly zero DC conductivity, consistent with their amorphous state. Within this phase, the conductivity exhibits a relatively slow increase with temperature as more carriers are excited,¹⁹ which justifies the slight difference between the as-grown and 155 °C-annealed samples. In contrast, samples annealed above 155 °C show a much more drastic increase in DC conductivity, from near-zero to approximately 10⁴ S m⁻¹, typical of the transition to the FCC phase, for which the material experiences the highest conductivity increment (of 2–3 orders of magnitude).¹⁹ The samples annealed at 205 °C and 255 °C exhibit comparable DC conductivity values (also evident from Fig. 9), suggesting they are likely in the same (FCC) structural phase. Further, the sample annealed at 305 °C results in a 2.5× increase in the DC conductivity, of the same order of the 4.4× increase reported for Ge₂Sb₂Te₅ in its cubic phase upon annealing from 200 °C to 280 °C, based on Hall measurements.⁴¹ Again, this slower conductivity growth is common within a given phase, although, in crystalline phases, it is due to the increase of mobility (rather than carrier concentrations as in the amorphous phase), as crystal grains grow during heating and the scattering by grain boundaries decreases.¹⁹ At 355 °C and 405 °C, the DC conductivity increases by 12× and 28×, respectively (relative to 255 °C), indicating progression towards the trigonal phase. This overall 28 factor is of the same order of magnitude as that associated with the FCC-hexagonal Ge₂Sb₂Te₅ transition.¹⁹ It is also consistent with the 76× increase reported for Ge₂Sb₂Te₅ between 180 °C to 400 °C,⁴¹ taking into account that Ge₃Sb₂Te₆ requires a higher annealing temperature to achieve a fully trigonal phase (at least over 355 °C in our case) than Ge₂Sb₂Te₅ to achieve a fully hexagonal phase (340 °C as reported in ref. 41) together with the fact that optical constants in fully crystalline phases continue to evolve during heat treatment due to vacancy ordering.⁷

In addition, we conducted variable-temperature electrical measurements to further strengthen our study on the MIT transition behavior of the two considered GST compositions and support the presence of phase co-existence in Ge₃Sb₂Te₆. In particular, we used an in-line four-point probe (4PP) method⁴² to measure the sheet resistance (R_sh) of the studied PCMs and calculated the corresponding DC conductivity (σ^4PP_DC) for both as-grown amorphous and thermally annealed crystalline samples. The full results are included in Table S1 of SI2 (SI) and reveal a significant contrast in R_sh between the amorphous and crystalline phases for both compositions, consistent with a clear MIT. For instance, the as-grown amorphous Ge₃Sb₂Te₆ film exhibits an extremely high R_sh value of ∼42 × 10⁶ Ω □⁻¹, while the Ge₃Sb₂Te₆ sample annealed at 405 °C shows a drastic reduction in R_sh down to ∼64 Ω □⁻¹, indicating full crystallization. To further understand the electrical switching behavior, we compared the σ^4PP_DC of crystalline Ge₃Sb₂Te₆ with its DC conductivity inferred from THz-TDS measurements viaeqn (3) (σ^TDS_DC). For the as-grown samples, the THz-TDS measurements yielded a negligible conductivity value, in accordance with 4PP measurements. For samples annealed at 405 °C, σ^TDS_DC ≈ 1.51 σ^4PP_DC, which is reasonable given that THz-TDS captures both localized and non-local free charge carriers, and is consistent with fact that the DC and Drude-fitted conductivity of hexagonal Ge₂Sb₂Te₅ are also similar.¹⁹

The conductivity behavior at intermediate phases is also worth studying. In this case, when a constant voltage is applied to the PCM, the increase of current depends on the nucleation level (associated with the applied annealing temperature). If nuclei are not yet in physical contact (initial nucleation stage) such that they form a low resistance current path through the sample, the increase in current is small. When multiple crystallites meet each other (percolation) and form a continuous crystalline path between electrodes, the current immediately becomes much larger.¹⁹ To analyze this mixed-phase regime, we examined a Ge₃Sb₂Te₆ sample annealed at 355 °C, representing an intermediate cubic-trigonal (polycrystalline) state. In this case, σ^TDS_DC ≈ 1854 σ^4PP_DC. This large discrepancy strongly suggests a scenario where the material contains partially crystallized regions without fully connected percolation paths. As a result, 4PP detects poor long-range DC transport, as carriers driven by low-frequency fields undergo significant scattering at grain boundaries. Contrarily, the latter are not a dominant factor at THz frequencies, as carriers can mode inside grains,⁹ and THz-TDS remains sensitive to localized carrier motion within isolated crystalline domains, as discussed in previous works for other PCMs. For instance, the DC conductivity of a thin-film polycrystalline Ge₂Sb₂Te₅ sample, where grain boundary scattering significantly inhibits current flow, is much lower than the value determined by the Drude model.¹⁹ The difference between the THz-TDS and DC measurements decreases with increasing annealing temperature because of the enhancement in grain size and the decrease of scattering at grain boundaries, as we observed for an annealing temperature of 405 °C, and in agreement with previous studies on Ge₂Sb₂Te₅.^9,19

Finally, it is worth mentioning that THz transmission measurements (from which all optical and electrical properties were obtained) were performed at three different spots on each sample, allowing us to average out potential inhomogeneities, which can arise from nanoscale thickness variations, partial crystallization, and mixed-phase regions. Additionally, systematic errors arising from setup misalignment, particularly those caused by mechanical instabilities in the delay stage, cannot be ruled out. As an illustration of the characterization uncertainty induced by these factors, we quantified standard deviation values in the extracted transmittance, and complex refractive index of Ge₃Sb₂Te₆ over a Si substrate at 1 THz, which are included in Table 2, along with the corresponding mean values of these quantities. Standard deviation values for the full studied spectrum are shown in Fig. S2 of SI3 (SI).

Table 2 Numerically extracted optical constants at 1 THz for Ge₃Sb₂Te₆ samples (Si substrate) annealed at various temperatures. Each value is presented as the mean ± standard deviation across three measurement spots

Annealing temp. (°C)	Transmittance (%)	Refractive index (n)	Extinction coefficient (k)
As grown	99.3 ± 0.08	8.7 ± 3.20	0.2 ± 0.19
155	92.4 ± 0.13	9.5 ± 0.67	3.8 ± 0.25
205	71.7 ± 0.03	17.5 ± 3.11	12.7 ± 2.59
255	68.3 ± 0.24	21.5 ± 1.19	8.4 ± 0.77
305	46.4 ± 0.86	25.9 ± 1.08	18.4 ± 0.74
355	17.1 ± 0.69	40.8 ± 1.15	32.5 ± 1.95
405	8.6 ± 0.41	53.1 ± 1.72	51.7 ± 3.23

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Conclusions

We have systematically investigated the effect of thermal annealing on the optical, electrical and conductive properties of a non-volatile chalcogenide compound Ge₃Sb₂Te₆ and compared its performance with the well-established Ge₂Sb₂Te₅ compound. Our results demonstrate that Ge₃Sb₂Te₆ exhibits lower losses compared to Ge₂Sb₂Te₅. Furthermore, the influence of the substrate on the optical properties is less pronounced for Ge₃Sb₂Te₆, whereas Ge₂Sb₂Te₅ shows significant substrate-dependent variations. Notably, the maximum annealing temperature for which Ge₂Sb₂Te₅ films did not exhibit spatial non-uniformity was limited to 305 °C, which constrains the maximum achievable refractive index. In contrast, Ge₃Sb₂Te₆ samples were studied for annealing temperatures up to 405 °C, with no signs of degradation. These results suggest that Ge₃Sb₂Te₆ could sustain even higher annealing temperatures, potentially leading to greater optical contrast and enhanced performance.

Author contributions

C. G.-M conceived and proposed the study. M. K. fabricated the samples at Nanophotonics Technology Center (NTC) of Universitat Politecnica de Valencia (UPV). M. K. Z. and J. A. A.-S. performed the THz-TDS transmission measurements at the NTC facility of UPV. M. K. Z. and D. O. D. Z. D. conducted the XRD and Raman spectroscopy measurements at the University of Valencia. K. K. carried out the Fourier transform analysis, implemented the required analytical and numerical computational techniques for data processing, extracted the optical properties, and performed material model fitting including optimizations of the Drude and Lorentz models. K. K. also validated the extracted parameters using electromagnetic wave simulation software, CST Studio Suite, conducted comparative analyses, and wrote the manuscript. B. V. and C. G.-M supervised the project and reviewed the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

Supplementary information: Comparison with previous reported data on the optical properties of Ge-Sb-Te compounds, DC electrical characterization, and measurement uncertainty quantification. See DOI: https://doi.org/10.1039/d5tc01667c.

Data for this article, including THz-TDS, Raman, and XRD data, are available at The Materials Data Facility at https://doi.org/10.18126/1v02-w971.

Acknowledgements

The authors wish to acknowledge support from the TERAOPTICS project (grant no: 956857) funded by the European Union's research and innovation program and projects PID2019-111339GBI00 and TED2021-132259B-I00 from the Agencia Estatal de Investigacion of the Spanish Ministerio de Ciencia e Innovacion. The authors would also like to thank Surya Revanth Ayyagari and Irmantas Kasalynas from FTMC, Lithuania, for their help in taking the optical images of the samples. Funding for open access charge: CRUE-Universitat Politècnica de València.

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