Size effect of the Ge₂Sb₂Te₅ cell atop the silicon nitride O-ring resonator on the attenuation coefficient

The switching between amorphous (a-GST) and crystalline (c-GST) states of the Ge₂Sb₂Te₅ (GST) thin films initiated by low-energy pulses occurs quite fast and is accompanied by significant changes in their phase and optical properties and the possibility to remain in the metastable states for tens of years.

Over the past five years, the prospective applications and devices of GST thin films for reflective displays,¹ active antennas in the middle IR range,² and thermal camouflage³ were demonstrated. In addition, special attention is paid to the use of GST in nanophotonic elements based on silicon nitride, operated in the telecommunication range (C-range) at about 1550 nm.⁴ In this wavelength range, the difference in the refractive indices of a-GST and c-GST is significant.⁵ However, there is still a difference in the extinction coefficient, which also affects optical switching and optical contrast efficiency.

The opportunity of using GST in telecom is caused by the significant contrast of optical properties at 1550 nm between states with different phases. This contrast makes GST a very suitable material for controlling the signal parameters of waveguide structures. For this purpose, a local region of coating by the GST thin film (GST cell) should be formed on the surface of the slab waveguide on a chip. A change in the phase state of this GST coating, and hence the signal passing parameters through the waveguide, can be initiated by heating the GST with laser pulses passing through the waveguide. The greater the absorption, the lower the optical power is capable of heating the GST to the melting point and crystallization temperature when the device is switched. For this reason, the absorption coefficient is one of the key parameters for the development of nanophotonic devices.

By varying the fluence of the programmable laser pulse, the GST thin films with multiple phases and different amorphous to crystalline volume ratios can be realized.^6,7 As a result, controlling the amount of amorphous and crystalline fractions in the GST material by changing the parameters of the programmable pulse allows one to create several nonvolatile reliable and repeatable memory levels (up to 34).⁸ A further increase in the number of levels can be implemented using a materials science approach, for example, through the additional use of “the transition from the metastable cubic to the stable trigonal phase,”⁹ or through the engineering and technological approaches, for example, by increasing the cell size. The larger the cell size on the waveguide, the greater the optical effect of switching and the optical contrast.⁵ However, a decrease in the cell size might potentially lead to an increase in the device energy efficiency, which opens the way for the creation of hundreds and thousands of devices on a single chip, for example, for the realization of the neuromorphic computing schemes.^10–12 Thus, it is necessary to find the optimal size of the GST cell for the design of nanophotonic elements, providing suitable contrast, especially in the case of multilevel systems, without degraded power consumption.

It should be taken into account that along with a significant decrease in the GST cell size in the waveguide structure, the attenuation coefficient per unit length will sufficiently change because of the variation in the contribution of scattering and reflection at the ends of the GST-covered area in comparison with the absorption in the GST itself. In addition, the size effect can be observed in the GST cells when the optical parameters¹³ begin to change with a decrease in the size of the GST cell. This effect is not well understood and is difficult to take into account when creating a device design. In particular, this relation becomes important when the dimensions of the GST cell on the waveguide become comparable with the wavelength of the light. In this case, enhanced light scattering⁵ should be observed, which will reduce the overall absorption of GST per unit length, which will lead to a decrease in the switching energy efficiency. Thus, the GST-based nanophotonic device optimization requires a clear understanding of the effect the GST cell size has not only on the parameters of waveguide structures but also on the scattering and absorption contribution to the attenuation coefficient.

This research deals with the numerical calculation and experimental study of the attenuation coefficient dependence of the waveguide integrated GST cell size and the experimental identification of the GST cell range with dominating light scattering. Complementing the previous works on the study of the GST attenuation coefficient on silicon^8,14,15 and silicon nitride^8,16–18 waveguides, the novelty of our work is associated with the experimental observation of the dependence of the attenuation coefficient on the GST in a wide range of lengths (100 nm–20 μm), enabling us to estimate the regions of the Ge₂Sb₂Te₅ cells, where light scattering or absorption dominates. We used previously tested O-ring resonators (ORRSs)¹⁹ with low loss and high sensitivity to a small refractive index deviation.

We prepared two 15 × 15 mm² chips using commercially available silicon wafers with wet thermal silicon oxide (2.6 μm) and stoichiometric low-pressure chemical vapor deposited (LPCVD) silicon nitride with a thickness of 450 nm and a set of O-ring resonators (ORRs) with GST cells atop.

The fabrication process included three main steps. At the first stage, alignment marks were formed via photolithography, subsequent thermal evaporation of Ti/Au (4 nm/200 nm), and the lift-off process. At the second stage, an image of the waveguides in the positive resist ZEP 520 A was formed using e-beam lithography. After the development in O-xylene, the waveguide layer was completed by reactive ion etching in a CHF₃ environment. At the third stage, e-beam lithography was used to mark the place for further GST deposition. After 20 nm GST film and 60 nm SiO₂ cap layer deposition and the lift-off process, one chip was crystallized by heating up to 250 °C, and the other one was left unchanged [see also the supplementary material (Fig. S13)]. The set of O-ring resonators with diameters of 127.46 μm was fixed on each chip, providing the free spectral range (FSR) of 3 nm. However, the lengths of the GST cells and the gaps between the ring and the bus waveguide were varied.

The optical micrograph of one of the fabricated ORRs with a GST cover is shown in Fig. 1(a). The fabricated device includes two focusing grating couplers (FGCs) connected via the bus waveguide separated from the ORR by the gap.²⁰ The couplers were previously optimized for 1550 nm wavelength operation with about 20% coupling efficiency.²¹ The white lines in the figure schematically show the propagation of light.

The initial amorphous GST films with a thickness of 20 nm were obtained by magnetron sputtering of the polycrystalline target in a vacuum chamber. The profile distribution of the chemical elements for the GST films was controlled by Auger electron spectroscopy and TOF-SIMS.²² 

The investigations were focused on films with amorphous and cubic crystalline structures. It should be noted that the hexagonal phase (hcp) is the stable phase for thin GST films. However, the greatest change in optical properties occurs during the phase transformation between the amorphous phase and the metastable cubic phase (fcc), which is a lower-temperature phase of the GST compared to the hcp phase.²³ 

The crystallization of the as-deposited amorphous thin films was carried out using the heating stage HFS600E-PB4 Linkam at the temperature of 250 °C for 30 min in the argon flow. The choice of the annealing temperature was based on the previous investigation results of the thermal crystallization process for GST thin films.²⁴ The a-GST and annealed (c-GST) thin films were characterized by x-ray diffraction (XRD). The broad halo ring and diffraction peaks were obtained for the as-deposited and annealed GST thin films, respectively [Fig. 2(a)], which confirms their amorphous and crystalline (fcc) states, respectively.

The spectroscopic ellipsometer HORIBA UVISEL 2 was used to determine the spectral dependences of the refractive index and extinction coefficient for the GST thin films in the wavelength range of 210 nm (5.9 eV)–2100 nm (0.59 eV). Measured spectra were evaluated by a Psi Delta program using a five-layered model (air–surface–GST–SiO₂–Si). The surface rough layer was defined by effective medium approximation [a mixture of the film (50%) and void (50%)]. A single Tauc–Lorentz (TL) oscillator was applied to obtain the optical properties of the a-GST and c-GST films [Figs. 1(b) and 1(c)]. The crystallization of the a-GST thin films into the fcc structure is accompanied by significant changes in the optical properties. The refraction index (n) and the extinction coefficient (k) at the telecommunication wavelength of 1550 nm increased after the crystallization from 4.2494 and 0.0524 to 6.5201 and 0.758 52, respectively.

The extracted values of n and k for the amorphous state are close to the data in a number of other studies,^25–27 while the spectra of these parameters for the films in the crystalline state are somewhat different from the studies in Refs. 23, 28, and 29. This discrepancy may be due to the use of different crystallization regimes, for example, the annealing temperature and the heat treatment time.

At the first stage of the numerical simulations, the TE mode within the 2D cross section of the silicon nitride rib waveguide was calculated. We found a change in the effective mode index of the rib waveguide from 1.587 to 1.735 and 2.047 when it is covered with a 20 nm a-GST and c-GST layer, correspondingly [see the supplementary material (Figs. S1–S4)]. The distributions of the normalized electric field in the cross section for the TE mode of the waveguide covered by the amorphous and crystalline GST are shown in Figs. 3(b) and 3(d). Because of the small real part of the refractive index of the a-GST, the optical mode mostly remains in the waveguide in contrast to the c-GST-covered waveguide, which provides a strong TE-mode capture by the 20 nm GST layer.

At the second stage, for more precise analysis, the 3D Finite Element Method (FEM) in COMSOL Multiphysics was applied. In Figs. 3(a) and 3(c), the 3D rib waveguide is shown, in which the optical waveguide mode interacts with the amorphous and crystalline GST via the evanescent optical field. We calculated the S-parameters, i.e., the elements of a scattering matrix connecting linearly the complex amplitudes of the scattered waves with incident ones³⁰ for GST cells (including 100 nm of uncovered, original waveguide from each side) with different lengths and thicknesses at the wavelength in vacuum λ₀ = 1550 nm. The transmitted and reflected powers were obtained as |S₂₁|² and |S₁₁|², respectively. The absorbed power was found by integrating the loss density of power over the GST volume. The scattering was calculated by subtracting the total absorption, transmission, and reflection from the input power.

The dependences of the found parameters on the length of the a-GST and c-GST cells are shown in Figs. 3(e) and 3(f). For the crystalline GST with high real and imaginary parts of the complex refractive index, at small cell lengths up to 2 μm, scattering dominates (about 40% of the light at the peak). Above 2 μm length, the scattering reaches a level of about 14%, slightly decreasing with the increasing GST cell size. The reflection from the GST cell qualitatively shows a similar behavior, but its contribution is much less than 0.7% and 0.1% at short and long GST lengths, respectively. At these cell sizes, the main contribution is made by absorption (about 85%).

For the amorphous GST with smaller real and imaginary parts of the complex refractive index, the situation is qualitatively similar; scattering strongly dominates at short GST lengths (about 30% of light at the peak and 25% at higher GST lengths) with a negligible contribution of reflection (<0.5%). However, up to 10 μm length, the absorption contribution is still less than 25%. For a more detailed analysis of a-GST and c-GST S-parameters, see the supplementary material (Figs. S5–S12).

To identify the regions of the GST length, in which either scattering or absorption dominates, their ratio was investigated. Figures 4(a)–4(d) show the dependences of the scattering/absorption ratio for a-GST and c-GST, respectively. If the ratio is 1, both processes contribute equally to the efficiency of the device. If the ratio is greater than 1, then the contribution of scattering is higher, whereas at ratio values less than 1, the absorption process dominates.

Figures 4(e) and 4(f) show that the behavior of a-GST and c-GST cells is qualitatively similar. A peak in the scattering/absorption ratio is observed at cell length lower than 2 μm and slowly decreases at higher values. However, if for a-GST, the scattering/absorption ratio is lower than 1 in the entire range of investigated cell lengths up to 10 μm, then for c-GST, which has a higher extinction coefficient, absorption begins to dominate from about 1 μm.

Since the ranges of the dominance of absorption and scattering in amorphous and crystalline materials are different, a more complex characteristic should be used to design energy-efficient devices with optical switching. Figures 4(e)–4(g) show the dependence of losses for transfer from the amorphous to the crystalline state, defined as the product of the ratios in Figs. 4(a) and 4(b). It can be seen from the figure that starting from about 2 μm, the switching losses are less than 1 and are determined mainly by absorption rather than scattering, thereby determining an optimal energy-efficient region.

We calculated the attenuation coefficients for our devices to compare the numerical calculations with the experimental data based on optical transmission. Thus, the attenuation coefficient (μ) includes the total losses in the circuit, reflection (r), scattering (s), and absorption (α), and can be easily extracted from the experimental data. The attenuation coefficient $μGSTth$ (dB/μm) can be found from the numerically calculated transmission as

where L is the length of the a-GST or c-GST cell and S₂₁ is the transmitted power.

An O-ring resonator is a susceptible device to study the optical loss of material deposited on top of it in detail. The position of the resonance peak substantially depends on the environment. For the covering with a higher than air refractive index, the peak is shifted to larger wavelengths. The measured transmission spectra for the two fabricated ORRs before and after a-GST/SiO₂ and c-GST/SiO₂ formation are shown in Figs. 5(a)–5(c). Because of the evanescent coupling, the presence of GST leads to both a shift of the resonance peak toward longer wavelengths and a change in its full width at half maximum (w). Before the a-GST and c-GST fabrication, the quality factor of an ORR is limited by several reasons, namely, scattering ion irregularities, sidewall roughness, absorption of the material, leakage on a bending radius, etc. Assuming that all these losses of the ORR do not change after the transfer from a-GST to c-GST, we can write the attenuation coefficient change (Δμ) as follows:

where μ_a and μ_b are the attenuation coefficients, n_g is the group mode index, λ₀ is the wavelength in a vacuum, and Q_a and Q_b are the unloaded quality factors before and after the GST thin film deposition,²⁰ 

Here, T_a,b are the part of transmitted powers and w_a,b are the full widths at half maximum for resonance wavelengths λ_a,b. Assuming that the length of the GST is much shorter than the O-ring length L ≪ 2πR, the attenuation coefficient of the GST (μ_GST) can be found as

where R is the O-ring radius.

We analyzed the obtained Q-factors for O-ring resonators with different a,c-GST widths. The values of the attenuation coefficient from the width of the GST calculated using Eq. (5) are shown in Figs. 5(d) and 5(e). To date, several works have been related to the experimental determination of the GST attenuation coefficient on silicon,^14,15,31 silicon nitride,^16,18,31 and silicon on insulator¹⁷ waveguides. Balanced splitters,¹⁶ Mach–Zehnder interferometers,^15–17 and O-ring¹⁵ and race-track¹⁶ resonators were used for this purpose. The direct comparison of these results is a difficult task due to the difference in GST cell sizes (length/thickness/covered cap material and thickness) and waveguide parameters (width/thickness/etching depth) in the works (see Table I). Moreover, in all listed studies, the attenuation coefficients were found from the linear slope of the output optical power on the GST cell length, which implies simplifying the relationship and finding the average value of the attenuation coefficients. The average value of the attenuation coefficients for devices with the parameters closest to us^14,18,31 is 0.064–0.99 and 0.87–2.96 dB/μm for a-GST and c-GST, respectively. However, our experimental data and numerical calculations show that the attenuation coefficient depends on the length of the GST. For GST cell sizes equal to 0.1, 1, and 5 μm, the measured a-GST attenuation coefficients are 0.24, 0.5, and 0.14 dB/μm, and c-GST attenuation coefficients are 1.15, 9.25, and 4.8 dB/μm, respectively.

In a general method for all listed papers, the attenuation coefficients were found from the linear slope of the output optical power on the GST cell length, which implies simplifying the relationship and finding the average value of the attenuation coefficients. Similar to the predicted dominance of scattering, the attenuation coefficient is not constant but depends on the cell size. For small c-GST cells (0.1–1 μm), the attenuation coefficient has a peak, the height of which is determined mostly by scattering. At large values of the a-GST cells (>1 μm), when absorption dominates, the dependence flattens out, and the attenuation coefficient is mainly determined by the absorption coefficient (μ ≈ α).

For the amorphous GST with a cell of up to 10 μm long, the attenuation coefficient is determined by the scattering coefficient [Fig. 4(a)].

Although the experimental results of the work are in good agreement with our calculations and the other previous studies,¹⁶ the best fit with the numerically calculated data was obtained for the GST films of incompatible thicknesses. The best fits were found for a-GST and c-GST thicknesses of 10 and 15 nm, respectively. These values differ from the measured thickness of 20 nm grown atop the waveguide [broken and solid lines in Figs. 5(d) and 5(e)]. We attribute these discrepancies to the possible formation of the native oxide on the surface of the films before covering them with the protective layer,³² which leads to the partial oxidation of the GST cell and a change in the real and imaginary parts of the refractive index.³³ It should be noted that the discrepancy between the data can be influenced by a change in the film thickness (on the order of 1.5 nm) due to a change in density during crystallization. However, the difference in the thickness between our a-GST and c-GST thin films can be on the order of 1.5 nm (density changes upon crystallization of 6.8%³⁴), which cannot fully explain the discrepancy in the data, but it is also undoubtedly a significant factor.

Our results are important for developing nanophotonic devices, including energy-efficient fully optical attenuators, switchers, and large neuromorphic circuits.³⁵ 

We have performed numerical and experimental investigations of the dependence of the attenuation coefficient on the length of a-GST and c-GST on the silicon nitride rib waveguide. We have also carried out detailed numerical calculations of the dependence of the reflection, transmission, scattering, and absorption at the telecom wavelength of 1550 nm on both a-GST and c-GST lengths and thicknesses. With the help of numerical calculations, we have found that the contribution of scattering prevails over absorption for the amorphous and crystalline GST up to 10 and 1 μm cell length, respectively. Using the data obtained, we have calculated the dependence of the optical losses for the transition from the amorphous to the crystalline state. In this case, the most energy-efficient devices should operate with GST cell lengths of more than 2 μm. The transmission spectra of ORRs in the C-range have been measured. The change in the Q-factor of the O-ring resonators with a cell length of a-GST and c-GST has been found and compared with the theoretical calculation of the attenuation coefficient. The comparison shows that the change in the attenuation coefficient depends on the length of the GST cell, for both the amorphous and crystalline GST. It also qualitatively confirms the dominance of various mechanisms of energy loss. We attribute the quantitative difference to the difficult-to-account oxidation of the films. The results of this research can be used to develop nanophotonic devices with GST cells. On the one hand, the reduction in the GST cell size leads to a smaller device footprint. On the other hand, the reduction in the GST cell size below 2 μm leads to enhanced light scattering and suppression of absorption. This leads to the necessity to compromise during the nanophotonic device development and approach each specific task differently.

See the supplementary material for simulation data and experimental determination of the GST attenuation coefficient on different waveguide material and devices.

We acknowledge support from the Russian Science Foundation, Project No. 20-79-10322. The authors are grateful to Anna Dedkova and Maria Fedyanina (MIET) for their assistance in performing the thin film studies via the equipment of the shared research facilities “Microsystem Technics and Electronic Component Base,” “Diagnostics and Modification of Microstructures and Nanoobjects,” and “STI Sensory” of MIET.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.