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Abstract
In this paper, we propose and demonstrate electrical switching of a 4% tungsten-doped Ge2Sb2Te5 (W-GST) pixel in a lateral configuration without the need for an auxiliary resistive heater. The phase transition between an amorphous and poly-crystalline state is achieved by Joule heating directly through the 4 μm × 4 μm × 350 nm active volume of the chalcogenide phase change pixel. While undoped GST would be challenging to switch in a lateral configuration due to very large resistance in the amorphous state, W-GST allows for switching at reasonable voltage levels. The pixel temperature profile is simulated using finite element analysis methods to identify the pulse parameters required for a successful electrical actuation. Experimentally, a 1550 nm light source is used for in-situ optical reflection measurements in order to verify the crystallization and re-amorphization of the pixel. As a result of the W doping, we identify volatile and non-volatile regimes with respect to bias voltage and pulse width during crystallization. During amorphization, we observe irreversible material failure after one complete cycle using in-situ optical monitoring, which can be attributed to a migration or segregation process. These results provide a promising path toward electrically addressed devices that are suitable for optical applications requiring amplitude modulation in a reflective geometry, such as spatial light modulators.
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1. Introduction
The modulation of both amplitude and phase of light is a critical component of modern optical devices for high-speed communications [1] and beam steering, LIDAR [2], spatio-temporal pulse shaping [3,4], and other applications. Currently, most of the spatial light modulation (SLM) work relies on Liquid Crystal on-Silicon (LCoS) or micro-mechanical adaptive mirrors (MEMS) to achieve the necessary light control. These two techniques, while viable, generally rely on non-scalable fabrication techniques and suffer from limited reconfiguration speeds due to the nature of the active switching mechanism for light control. Chalcogenide phase change materials (PCMs) such as the family of Ge-Sb-Te ternary alloys, offer an alternate path for high-speed light modulation [5]. PCMs alter their atomic structure via a thermal stimulus, typically an electrical or optical pulse, leading to a drastic change in refractive index at the telecom wavelength between a low-index amorphous state (n = 4.44 + 0.28i) and a high-index crystalline state (n = 6.93 +1.28i). For SLMs, the core idea is to implement an electrically actuated device where the optical refractive index of each pixel can be tuned. PCMs can serve this purpose given the remarkably large change in index, $\Delta$n; however, due to the high electrical impedance of the amorphous state coupled with the high contact resistance at the interface with metallic electrodes, electrical actuation of large pixels (a) requires large actuation voltages and (b) cannot rely on off-the-shelf radio-frequency (RF) components due to the incompatibility with standard 50 $\Omega$ termination. In this work, we focus on doped germanium-antimony-telluride (GST) [6] and, more specifically, tungsten-doped GST (W-GST) as the underlying PCM.
To date, many demonstrations have investigated the optical switching properties at the pico- and nanosecond time scales [7] showing the optical multi-level functionality based on the partial crystallization mechanisms [8–10]. However, demonstrations of truly integrated photonic devices with electrical addressability using scalable fabrication techniques have been few and far between. In general, there are three configurations for electrically addressing phase change pixels: (1) top and bottom contacts in a sandwich configuration [11,12], (2) lateral electro-thermal auxiliary resistive heater [13,14], and (3) lateral through-pixel, in which the current passes through the PCM layer placed in the gap between two electrodes [15]; this is the approach we take in this work. One major advantage is that a through-pixel geometry lowers the energy requirements dramatically as all the heat is dissipated within the material itself. This avoids the losses that stem from thermal boundaries, allowing for switching of thick films well beyond what has been reported in literature [16].
Here, we design gap sizes between 3-5 $\mu$m to investigate the upper limit of electrical switching over large volumes that are comparable to the standard pixel size in high-definition spatial light modulators. Given the large PCM thickness needed for both amplitude and phase modulation applications, our study falls within the dreaded "filamentation regime" [17,18] in which Joule heating mechanisms fail to switch large PCM pixels due to an arc-like conductive path that acts as a short circuit and prohibits further switching. Therefore, we explored large pixels whereby electrical switching is a major challenge, with the aims of (a) further understanding the switching limitations and their origins, and (b) exploring possible solutions for which switching such pixels is viable.
In our previous work, we demonstrated that tungsten doping/alloying substantially reduces the electrical resistivity contrast and reduces the amorphous state resistivity by over three orders of magnitude [19] while minimally affecting its optical properties. Additionally, introducing tungsten lowers the contact resistance, improves the optical contrast, and extends the face-centered-cubic state up to 350$^{\circ }$C, with a minimal impact on thermal conductivity. Together, this results in a lower voltage requirement for electrically actuating W-GST pixels in a through-pixel geometry. Thus, W-GST serves as a promising candidate for electro-optic PCM (EO-PCM) for high-speed dual-mode operation in a lateral through-pixel configuration. In this Letter, we extend the investigation by demonstrating a dual-mode electrically addressable lateral pixel for optical amplitude modulation at 1550 nm. To characterize the pixels, we developed an in situ optical monitoring setup to capture the time dynamics during an electrical pixel actuation. Fast switching rates were achieved with the ability to crystallize several microns of W-GST using a single 26 V, 1 $\mu$s electrical pulse.
While we demonstrate the ability to crystallize large pixel sizes, switching such pixels comes at the expense of material cyclability, where we show that a single cycle of amorphous-crystalline-amorphous transition is possible, but further cycling is prohibited due to material degradation. This degradation can be attributed to thermal or electronic transport which leads to elemental segregation [20,21] Nevertheless, this work presents a clear evidence that large volume W-GST through-pixels are a viable path towards PCM-based SLMs once the problem of degradation is solved, which will form the basis of follow-up work based on polarity switching [22] during reconfiguration.
2. Device design
The W-GST pixel was designed to be large enough (10 $\mu$m x 10 $\mu$m) for ease of alignment and patterning using standard optical photolithography. The switchable pixel area, however, varied in size from 3-5 $\mu$m. This was dictated by the width of the tungsten electrodes and the gap between them (Fig. 1(a)). Additionally, the thin film structure was designed via the transfer matrix method (TMM) to provide maximum reflected contrast between the amorphous and crystalline states at 1550 nm. We define the optical visibility (OV) given by
where $R_a$ and $R_c$ are the reflectances for W-GST pixel in the amorphous and crystalline states, respectively. The film structure was SiO$_2$/W-GST/SiO$_2$ on a silicon (Si) substrate. TMM was used to design the layer thicknesses to achieve the highest possible optical visibility. The resulting stack consisted of 300 nm SiO$_2$/350 nm W-GST/10 nm SiO$_2$ capping, which produced a 78% optical visibility at 1550 nm (Fig. 1(b)). To electrically switch the device and optically measure the pixel visibility, a custom-built setup was built. More explicit explanation of the experimental setup is presented in Section 4.
Fig. 1. (a) Schematic diagram of the designed device. (b) Optical visibility at 1550 nm for a parametric sweep of the SiO$_2$ passivation and W-GST thicknesses. (c)-(f) Transient temperature (blue), input electrical pulse profiles (red), and temperature profile at three discrete times (black circles) after the pulse turns off for (c)-(d) crystallization and (e)-(f) amorphization of the W-GST pixel.
3. Electro-thermal model
To better understand the transient thermal properties and Joule heating, we conducted a finite element analysis using COMSOL Multiphysics with the AC/DC and the Heat Transfer in Solids modules [23]. The equation used to model the heat generated by Joule heating, Q$_j$ is given by
where $\sigma$ is the electric conductivity and $J$ is the electric current density. This is then substituted into the time dependent equation for heat transfer by conduction given by the heat flux $Q$ defined as where $\rho$ is the density, $C$ is the heat capacity, $T$ is the temperature, $t$ is time, and $k$ is the thermal conductivity.By assigning one of the tungsten electrodes as the ground and the other electrode as the electric potential source, current passes from one electrode to another through the W-GST pixel. Since W-GST is a resistive material, it will heat and transition from amorphous to crystalline, and vice versa provided sufficient local heat dissipation. To convert from amorphous to crystalline, a simple heating of the material to a temperature above 625 K is sufficient [19]. However, to revert the pixel back to amorphous, a higher voltage with a short pulse duration is required to melt and quickly quench the GST before the molecules rearrange into a crystalline form. All pulses used in this work have a 3 ns rise time and a 5 ns fall time.
A 1 $\mu$s pulse with an amplitude of 40 V was used to crystallize W-GST (Fig. 1(c)). The maximum temperature in the W-GST was well above the required 625 K (Fig. 1(d)). On the other hand, the pulse used to re-amorphize the pixel was 70 V, 300 ns (Fig. 1(e)). This enabled the pixel to melt as it reached a temperature higher than the required 925K (Fig. 1(f)). Due to the thickness of the GST and thermal interface, the cooling rate was $\approx$2 K/ns which is lower than the typically observed $\approx$10 K/ns [24]. However, for many GST-based alloys, a cooling rate in the range 1-10K/ns is sufficient to achieve the desired melt-quench [25,26], which makes W-GST a good candidate for the experimental demonstration of large volume PCM-based SLM pixels.
4. Device fabrication and experimental setup
The devices (Fig. 2(a)) were fabricated using standard i-line contact photolithography. First, a 300 nm thick SiO$_2$ passivation layer was deposited on to a 3" silicon substrate using the plasma enhanced chemical vapor deposition (PECVD) technique, as it provides higher quality films. Next, i-line photolithography was used to pattern the electrodes, followed by a 100 nm sputter deposition of tungsten and a lift-off protocol. A secondary lithography step was then used to pattern the pixels. A co-sputtering technique was employed using 4N GST225 and W targets. A perforated shield is used for reducing the W particle flux enabling a 4% W doping concentration to be achieved. Additional details on growth and material characterization can be found in our previous study [19]. The alloying scheme reduced the electrical resistivity of the amorphous state yet increased it for the crystalline state, causing a reduction in the electrical resistivity contrast between the two states (Fig. 2(b)). Additionally, the optical contrast necessary for the visibility measurements remained consistent with that of GST. Without breaking vacuum and prior to the final lift-off step, we deposited a 10 nm capping layer of SiO$_2$ using RF magnetron sputtering to prevent oxidation and material degradation over time [27]. The resulting wafer contained over 100 devices. Figure 2(a) shows a high-magnification image of a typical as-deposited pixel. We also deposited undoped GST225 on to a separated wafer for comparison.
Fig. 2. (a) Perspective view SEM of the PCM pixel. (b) Resistor model describing the resistivity reduction caused by W doping. (c) Schematic of the dual experimental setup showing electrical (actuation) and optical (probe) components.
The fabricated devices were then characterized using the custom-built configuration shown in Fig. 2(c). The dual-mode electro-optical experimental setup included a white light source and a microscope to visualize the switching phenomena with a conventional silicon camera. A secondary InGaAs camera was swapped during the laser alignment. Single or bursts of microsecond pulses (or less) were generated and amplified using a multichannel pulse delay generator with maximum 5 V output pulses, and 3 ns and 5 ns rise and fall times, respectively. The electrical pulses were amplified up to 100 V. The resulting pulses were transmitted through a set of tungsten contacts using high-speed probes that were electrically connected through a 16 $\mu$m$^2$ W-GST pixel. As stated earlier, tungsten doping was a key factor that enabled us to impedance-match this pixel to an RF pulse generator by lowering the electrical contrast while preserving the refractive index contrast at 1550 nm. Coherent infrared light from a fiber-coupled laser is channeled via a 80:20 splitter and sent to a circulator (port 1 $\rightarrow$ 2 of circulator) to one input of a compound microscope and focused with a 20X, 0.40 NA objective onto the active area of the W-GST optical pixel. The time varying reflected light propagates back through the microscope through the 2 $\rightarrow$ 3 port of the circulator and on to one arm of a high-speed balance detector where the second arm is directed from the initial 80:20 splitter. By matching the signal in both arms pre-phase change, our system is only sensitive to the changes in reflectivity due to the phase transitions and yields a high signal-to-noise ratio.
5. Results
The plot in Fig. 3(a) shows the in-situ reflectivity measurements captured in order to confirm the phase transition. The input voltage was monotonically increased from 13 V to 23 V at increments of 1 V. Prior to reaching the crystallization temperature threshold, we observe a volatile regime where a 37% increase in reflectivity can be observed only when the pulse train is on. This regime could be further investigated in the future to serve applications where volatile transition is desired. To crystallize the W-GST pixel, an input voltage of 23 V with a pulse duration of 20 $\mu$s was used. An optical microscope image of the crystallized device is shown in Fig. 3(b). Further tuning of the electrical excitation was performed to ascertain pulse characteristics comparable to the modelled values. To re-amorphize the pixels, voltages in the range of 70-80 V with a pulse width as low as 37ns were used (limited by our electronic pulse generator). As mentioned in Section 3, we believe that these pulses should be sufficient to melt-quench the doped PCM, thus achieving reversibility of large and thick W-GST pixels (Fig. 3(b) inset). This is a critical breakthrough as it shows that the limitation due to heat trapping that prevents melt-quenching of large pixels is lifted in through-pixel doped geometries leading to three obvious advantages over demonstrations that rely on microheaters: a) it enables thick pixels that could serve both amplitude and phase operations, b) it leads to dramatically lower energy consumption due to lack of thermal boundaries, and c) the speed is only limited by the material response time, which leads to a full cycling in a few microseconds.
Fig. 3. (a) Transient optical reflectivity for monotonically increasing input voltage for 16 input electrical pulses. (b) Optical image captured on VIS camera after the 23V multi-pulse sequence and an inset image showing the re-amorphized pixel.
Although the pixel switching seemed promising, reversibility over multiple cycles was not optimally achieved. As individual re-amorphization pulses were sequentially induced, a dark filament was observed (Fig. 4(a)) along the crystallization path, further indicating that large area switching comes at a cost. This ultimately creates a conductive path of least resistance making the device irreversible after two cycles. One potential reason for the irreversible failure is the strong electric field accompanying the large, long-duration voltages during crystallization [21]. Failure analysis is reserved for future work due to the complexity and need for further metrology and modeling, however, possible answers to the irreversible damage and promising solutions are discussed in the next section.
Fig. 4. Images of the degraded W-GST pixel captured using (a) bright-field microscopy and (b) SEM after the second amorphization cycle. (c) Bright-field microscopy and (d) SEM images of the exploded undoped GST pixel after a 90 V, 500 ns pulse.
6. Discussion
While we have shown that, in principle, W-GST large area through-pixels allow for efficient and high-speed optical reconfiguration, they are prone to failure due to material degradation. To better understand the device failure, the failed pixel was imaged using a high-resolution scanning electron microscope (SEM) (Fig. 4(b)). We believe that the filament seen could be due to several reasons: (1) the GST evaporated during the re-amorphization process as observed in other doped GST devices [15], (2) mechanisms of thermally-driven transport [20], or (3) electrical material migration and segregation reported by other groups [18,22]. This is a complex problem (e.g, is the segragation that of the dopant or of tellurium?), that would require further investigation and materials-focused research in order to answer questions regarding material degradation.
We suspect the solution that should be taken will involve multiple modificaitons that don’t affect the main conclusion of this paper. To that end, we plan future investigations based on three possible avenues: (1) Looking at other dopants that might be more stable while maintaining similar optical/electrical properties, (2) Reversing the polarity of the switching pulse (possibly mid-cycle) to prevent electric-field driven drift, or (3) Engineering the thermal bath (e.g, switching the SiO$_2$ with a more conductive material such as SiN) to improve thermal quenching rates.
Although this device ultimately failed, as shown in the images of Fig. 4(a)-b, doped-GST devices seem to still be a promising path towards large area lateral pixels, due to their reasonable voltage requirements and the ability for crystallization/amorphization in large areas and thicknesses. In fact, a similarly configured device with undoped GST pixels was fabricated and tested for comparison, but it exploded and failed during the crystallization process at 90 V, 500 ns pulse due to high voltage breakdown (Fig. 4(c)-d). This is not too surprising, as previous work utilizing Joule heating (through-pixel) performed by other groups showed GST failure during crystallization [21], through a similar geometry of much smaller dimensions. Hence, re-amorphization was not even attempted. Therefore, W-GST is a more desirable material for reversible large pixel switching in lateral geometries, provided the issue of irreversible degradation could be solved.
7. Conclusions
We were able to achieve electrical switching of W-GST by reducing the electrical resistivity contrast between aGST and cGST by doping the material with tungsten at 4% concentration. This allowed the electrical resistivity contrast of the PCM to drop by several orders of magnitude while still maintaining the desired optical contrast between the amorphous and crystalline phases. GST was deposited and patterned as a large pixel (10 $\mu$m × 10 $\mu$m) with the active pixel size being 4 $\mu$m x 4 $\mu$m. Pulses were transported through 4 $\mu$m wide tungsten electrodes and, with the help of Joule heating, allowed the pixel switching. A 40 V, 1 $\mu$s pulse with a rise time of 3 ns and fall time of 5 ns was used to revert from aW-GST to cW-GST. On the other hand, a 70 V, 300 ns pulse with the same rise and fall times was used to re-amorphize the pixel. Although the pixel starts degrading upon amorphization and is rendered completely irreversible after a few cycles, W-doping allowed for switching (a) a lateral geometry that cannot be achieved with undoped GST due to field-induced breakdown and (b) PCM thicknesses that cannot be reached with the current generation of auxiliary microheater geometries. Research into irreversible filament formation is ongoing, with potential solutions ranging from improving the thermal conductivity of the substrate to alternating the polarity of the switching pulse, which could reduce heat trapping and material segregation, respectively, hence improving the overall endurance of the device.
Funding
Ford Foundation; National Science Foundation (1710273).
Acknowledgments
We acknowledge M.D. Shah Alam for his help in setting up the finite element modeling of the system. This work was supported in part by the National Science Foundation (Collaborative Research, Grant No 1710273) and Thorlabs, Inc. J.A.B. gratefully acknowledges financial support from the National Academies under the Ford Foundation Fellowship Program.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. F. Feng, I. H. White, and T. D. Wilkinson, “Free space communications with beam steering a two-electrode tapered laser diode using liquid-crystal SLM,” J. Lightwave Technol. 31(12), 2001–2007 (2013). [CrossRef]
2. B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017). [CrossRef]
3. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000). [CrossRef]
4. A. Chong, C. Wan, J. Chen, and Q. Zhan, “Generation of spatiotemporal optical vortices with controllable transverse orbital angular momentum,” Nat. Photonics 14(6), 350–354 (2020). [CrossRef]
5. H.-S. P. Wong, S. Raoux, S. Kim, J. Liang, J. P. Reifenberg, B. Rajendran, M. Asheghi, and K. E. Goodson, “Phase change memory,” Proc. IEEE 98(12), 2201–2227 (2010). [CrossRef]
6. S. W. Ryu, H.-K. Lyeo, J. H. Lee, Y. B. Ahn, G. H. Kim, C. H. Kim, S. G. Kim, S.-H. Lee, K. Y. Kim, J. H. Kim, W. Kim, C. S. Hwang, and H. J. Kim, “SiO2 doped Ge2Sb2Te5 thin films with high thermal efficiency for applications in phase change random access memory,” Nanotechnology 22(25), 254005 (2011). [CrossRef]
7. K. Zhang, S. Li, G. Liang, H. Huang, Y. Wang, T. Lai, and Y. Wu, “Different crystallization processes of as-deposited amorphous Ge2Sb2Te5 films on nano- and picosecond single laser pulse irradiation,” Phys. B 407(13), 2447–2450 (2012). [CrossRef]
8. G. A. Sevison, S. Farzinazar, J. A. Burrow, C. Perez, H. Kwon, J. Lee, M. Asheghi, K. E. Goodson, A. Sarangan, J. R. Hendrickson, and I. Agha, “Phase change dynamics and two-dimensional 4-bit memory in Ge2Sb2Te5 via telecom-band encoding,” ACS Photonics 7(2), 480–487 (2020). [CrossRef]
9. M. Zhu, K. Ren, L. Liu, S. Lv, X. Miao, M. Xu, and Z. Song, “Direct observation of partial disorder and zipperlike transition in crystalline phase change materials,” Phys. Rev. Mater. 3(3), 033603 (2019). [CrossRef]
10. A. Heßer, I. Bente, M. Wuttig, and T. Taubner, “Ultra-thin switchable absorbers based on lossy phase-change materials,” Adv. Opt. Mater. 9(24), 2101118 (2021). [CrossRef]
11. G. Rodriguez-Hernandez, P. Hosseini, C. Ríos, C. D. Wright, and H. Bhaskaran, “Mixed-mode electro-optical operation of Ge2Sb2Te5 nanoscale crossbar devices,” Adv. Electron. Mater. 3(8), 1700079 (2017). [CrossRef]
12. M. Wimmer and M. Salinga, “The gradual nature of threshold switching,” New J. Phys. 16(11), 113044 (2014). [CrossRef]
13. Y.-Y. Au, H. Bhaskaran, and C. D. Wright, “Phase-change devices for simultaneous optical-electrical applications,” Sci. Rep. 7(1), 9688 (2017). [CrossRef]
14. Y. Zhang, C. Fowler, J. Liang, B. Azhar, M. Y. Shalaginov, S. Deckoff-Jones, S. An, J. B. Chou, C. M. Roberts, V. Liberman, M. Kang, C. Ríos, K. A. Richardson, C. Rivero-Baleine, T. Gu, H. Zhang, and J. Hu, “Electrically reconfigurable non-volatile metasurface using low-loss optical phase-change material,” Nat. Nanotechnol. 16(6), 661–666 (2021). [CrossRef]
15. Y. Yin, A. Miyachi, D. Niida, H. Sone, and S. Hosaka, “A novel lateral phase-change random access memory characterized by ultra low reset current and power consumption,” Jpn. J. Appl. Phys. 45(28), L726–L729 (2006). [CrossRef]
16. Y. Zhang, C. Ríos, M. Y. Shalaginov, M. Li, A. Majumdar, T. Gu, and J. Hu, “Myths and truths about optical phase change materials: A perspective,” Appl. Phys. Lett. 118(21), 210501 (2021). [CrossRef]
17. M. L. Gallo and A. Sebastian, “An overview of phase-change memory device physics,” J. Phys. D: Appl. Phys. 53(21), 213002 (2020). [CrossRef]
18. L. Martin-Monier, C. C. Popescu, L. Ranno, B. Mills, S. Geiger, D. Callahan, M. Moebius, and J. Hu, “Endurance of chalcogenide optical phase change materials: a review,” Opt. Mater. Express 12(6), 2145–2167 (2022). [CrossRef]
19. P. Guo, J. A. Burrow, G. A. Sevison, H. Kwon, C. Perez, J. R. Hendrickson, E. M. Smith, M. Asheghi, K. E. Goodson, I. Agha, and A. M. Sarangan, “Tungsten-doped Ge2Sb2Te5 phase change material for high-speed optical switching devices,” Appl. Phys. Lett. 116(13), 131901 (2020). [CrossRef]
20. G. Bakan, N. Khan, H. Silva, and A. Gokirmak, “High-temperature thermoelectric transport at small scales: Thermal generation, transport and recombination of minority carriers,” Sci. Rep. 3(1), 2724 (2013). [CrossRef]
21. S.-W. Nam, D. Lee, M.-H. Kwon, D. Kang, C. Kim, T.-Y. Lee, S. Heo, Y.-W. Park, K. Lim, H.-S. Lee, J.-S. Wi, K.-W. Yi, Y. Khang, and K.-B. Kim, “Electric-field-induced mass movement of Ge2Sb2Te5 in bottleneck geometry line structures,” Electrochem. Solid-State Lett. 12(4), H155 (2009). [CrossRef]
22. A. Padilla, G. W. Burr, C. T. Rettner, T. Topuria, P. M. Rice, B. Jackson, K. Virwani, A. J. Kellock, D. Dupouy, A. Debunne, R. M. Shelby, K. Gopalakrishnan, R. S. Shenoy, and B. N. Kurdi, “Voltage polarity effects in Ge2Sb2Te5-based phase change memory devices,” J. Appl. Phys. 110(5), 054501 (2011). [CrossRef]
23. A. E. Aboujaoude, “Nanopatterned phase-change materials for high-speed, continuous phase modulation,” Master’s thesis, University of Dayton (2018).
24. S. Abdollahramezani, O. Hemmatyar, M. Taghinejad, H. Taghinejad, A. Krasnok, A. A. Eftekhar, C. Teichrib, S. Deshmukh, M. A. El-Sayed, E. Pop, M. Wuttig, A. Alù, W. Cai, and A. Adibi, “Electrically driven reprogrammable phase-change metasurface reaching 80% efficiency,” Nat. Commun. 13(1), 1696 (2022). [CrossRef]
25. A. Redaelli, A. Pirovano, A. Benvenuti, and A. L. Lacaita, “Threshold switching and phase transition numerical models for phase change memory simulations,” J. Appl. Phys. 103(11), 111101 (2008). [CrossRef]
26. S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alù, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 9(5), 1189–1241 (2020). [CrossRef]
27. R. Lawandi, R. Heenkenda, and A. Sarangan, “Switchable distributed Bragg reflector using GST phase change material,” Opt. Lett. 47(8), 1937–1940 (2022). [CrossRef]
