Electrically driven reprogrammable phase-change metasurface reaching 80% efficiency

Phase-change materials (PCMs) offer a compelling platform for active metaoptics, owing to their large index contrast and fast yet stable phase transition attributes. Despite recent advances in phase-change metasurfaces, a fully integrable solution that combines pronounced tuning measures, i.e., efficiency, dynamic range, speed, and power consumption, is still elusive. Here, we demonstrate an in situ electrically driven tunable metasurface by harnessing the full potential of a PCM alloy, Ge2Sb2Te5 (GST), to realize non-volatile, reversible, multilevel, fast, and remarkable optical modulation in the near-infrared spectral range. Such a reprogrammable platform presents a record eleven-fold change in the reflectance (absolute reflectance contrast reaching 80%), unprecedented quasi-continuous spectral tuning over 250 nm, and switching speed that can potentially reach a few kHz. Our scalable heterostructure architecture capitalizes on the integration of a robust resistive microheater decoupled from an optically smart metasurface enabling good modal overlap with an ultrathin layer of the largest index contrast PCM to sustain high scattering efficiency even after several reversible phase transitions. We further experimentally demonstrate an electrically reconfigurable phase-change gradient metasurface capable of steering an incident light beam into different diffraction orders. This work represents a critical advance towards the development of fully integrable dynamic metasurfaces and their potential for beamforming applications.


Note 1: 3D electrothermal simulation model of metadevices
We perform the electrothermal analysis for the meta-switch by creating a 300 µm × 300 µm × 1000 µm 3D finite element model in COMSOL Multiphysics (see Fig. S2a). To consider a real practical model, we assume the heterostructure device is attached to a 500 µm silicon substrate. In our simulations, Electric Currents module is employed to calculate the voltage and current distribution in the device, and Heat Transfer in the Solid module is used to predict the temperature profile. The two modules are coupled via Joule heating and the temperature dependence of material properties.
Electrical phenomena in the device are modeled via Poisson and continuity equations, ∇.[σ(x, y, z, t)∇V ] = 0, in which σ is the electrical conductivity of the microheater material.
If the thermal characteristic of the microheater is modeled as a first-order system comprising a parallel thermal resistance (R t ) and thermal capacitance (C t ), the cooling rate follows an exponential relation with a time constant of τ = R t C t . R t and C t depend on the length and the width of the microheater as well as the thermal properties of the ambient. Therefore, judicious selection of the contributing materials and design of the heterostructure metadevice can guarantee successful repeatable, reversible, and multi-state phase transformation of the PCM. W is used as a well-known refractory material for the heating element due to the moderate electric conductivity, good thermal conductivity, high temperature endurance, good metal barrier properties, and high resistance to electromigration 1,2 . The electrical resistivity obtained from four-point probe measurements (at room temperature) of a 50-nm-thick sputtered W is 500 nΩ.m, which is consistent with experimental data reported in the literature 1 . We set 0.0015 1/K as the resistivity temperature coefficient of W as the temperature and resistance of the microheater increase when the voltage across the microheater evolves with time 3,4 . The governing transient heat transfer equation is described by 5 where C s is the specific heat capacity, ρ is the density, k is the thermal conductivity, T is the time-and space-dependent temperature, and Q s is the Joule heat source per volume. which is typical for many systems 15,16 . The thermal conductivity of GST depends both on the temperature and phase as detailed in the literature 17 .
Quantitative analysis of the crystallization kinetics of the GST element exposed to the annealing pulses is crucial for precise control of the properties of the light. Fig. S2b  Temperature uniformity is a crucial measure for successful operation of large-scale phasechange metasurfaces. The magnified spatial distribution of the reflected beam from the meta-switch in Fig. 2a in two different states of GST, i.e., C-GST and A-GST, at λ = 1440 nm are shown in Fig. S2c. These rather uniform profiles across the device are expected since a nonpatterned GST patch with an even topography is used, which significantly reduces the surface-induced scattering loss. This evenness is also suggested by the electrothermal simulations presented in Fig. 1b showing a fairly uniform heat profile is across the microheater at the end of the set/reset pulse. In contrast to the A-GST case, where a trace of jags appears at the circumference after amorphization, the C-GST case has a more uniform boundary.
This follows the rationale that long nature of the set pulse allows uniform formation and growth of crystalline zones in the background of A-GST; however, the fast reset pulse randomly leaves some partially amorphized zones at the edge of the metasurface far from the center of the microheater.
To further study the heat distribution evenness, the temperature map of the microheater (studied in the main text) in the cross section and across the center of the GST film perpendicular to the current flow are shown in Figs. S2d and S2e, respectively. Evidently, the minimum temperature of GST upon stimulation with a set/reset pulse is more than 250 • C/770 • C confirming that GST can indeed be fully crystallized and melted, respectively.
In addition, the difference between the maximum and minimum induced temperature across the center of the GST film is less than 10 • C and 20 • C for the former and latter cases, respectively, which suggests complete phase transition of GST after the process. Since large probing pads act as heat sink during Joule heating process, heat dissipates faster along the microheater. One way to gain higher temperature uniformity is increasing the edge clearance between the metasurface and the pads by elongating the microheater. Figures S2f and S2g display the temperature profiles for a device with 1.6 µm clearance between the edge of the metasurface and that of the probing pads. This modification can address the undesired effect of temperature deviation and decay rate from the center of microheater.
In addition, we explore the correlation between the metadevice size and the spatial nonuniformity in the reflection value through eletrothermal simulations conducted for a metasurface with a larger aperture size that can tolerate 20% reflectance contrast at λ = 1640 nm. According to Fig. 3a(ii), such a contrast corresponds to 40% crystallization change between the center (with 100% crystallization fraction) and edges (with 60% crystallization fraction) of the GST film. In order to comply with this criterion, the temperature variation should be limited to ∼ 50 • C between the center and edges of the GST film, with temperatures equal to ∼ 260 • C and ∼ 212 • C, respectively (see Fig. S2b). Though microheaters with larger footprints improve the temperature uniformity across the device, for the sake of miniaturization, we have considered the area of the microheater 15% larger than the meta- Addressing individual meta-atoms is an important yet challenging step that can empower dynamic multifunctional metasurfaces to prevail over conventional spatial light modulators (based on liquid crystal or microelectromechanical structures). This would be more demanding when dealing with subwavelength meta-atoms whose reconfiguration mechanism depends on Joule heating. Since stimulation of each meta-atom relies on the precise control over biasing of the laterally extended pixelated heater elements, the performance measure of the metasurface is affected by the lossy nature of the wires network. At the expense of losing addressability over one direction, this negative effect could be fairly alleviated by relying on a 1D array of resistive nanoribbons (i.e., nanoheaters) homogeneously heating meta-atoms in the orthogonal direction. In this way, gate biassing can be applied to the end faces of individual micro-electrodes through compact contact pads without interfering with the optical beam. Along this direction, a simple prototype of tunable gated field-effect metasurfaces consisting of 96 independently addressable elements with pitch size of 400 nm has been recently demonstrated 18 . This along with the potential of robust sub-micrometer width tungsten electrodes as a high-temperature high-speed heater hold the promise for the realization of dense micro-electrodes externally controlled through an electrical signal (e.g., a voltage provided by a printed circuit board).
To figure out the feasibility of local addressing of GST cells using Joule heating, electrothermal simulations are carried out for a 1D array of heterostructure ribbons (600-nmwidth, 10-µm-long) comprising tungsten nanoheaters and the reflective meta-atoms (see Fig. S4). We study the impact of the reset pulse on the phase transition of GST by applying a 200-ns-long 3.1 V electrical pulses to the micro-electrode. Figure S4a shows the heat profile in a cross section at the center of the array at the end of the reset pulse. It is evident that the center pixel can be homogenously heated above 630 • C that ensures complete re-amorphization. The transient temperature profiles in Fig. S4b shows that during the entire heating process, the temperature of neighboring GST cells remains well below the onset crystallization temperature (i.e., ∼ 160 • C). Such a negligible thermal crosstalk between the neighboring elements guarantees the successful addressability of the phase-change metasurface at the pixel level.
Note 2: Effective medium theory for the optical charac-

terization of intermediate states of GST
Amongst the existing effective-medium theories, we use the Lorentz-Lorenz relation to model the optical constants of GST in the intermediate states as follows 19 : in which A (λ) and C (λ) are the permittivities of A-GST and C-GST, respectively, at wavelength λ, and m, ranging from 0 (associated with 0% crystallinity (or A-GST)) to 1 (associated with 100% crystallinity (or C-GST)), is the crystallization fraction of GST. The

Reset Set
Cont'd. Figure S7: Repeatability of the phase-change meta-switch. Reflectance spectra from the studied meta-switch collected after applying individual set/reset pulse for 50 consecutive cycles. The shaded red and blue areas clearly verify the good consistency after each cycle of operation. The average reflectance spectra for A-GST and C-GST (shown in Fig. 2c) are represented by blue and red dashed lines, respectively, as a baseline for a better comparison.    The embeddings corresponding to A-GST and C-GST in the latent space (rotated with respect to the center of Fig. 5a for a better view). The reduced-dimensional reflectance responses of metasurfaces in panel (a) are depicted using color-coded shapes.  Figure S18: X-ray diffraction spectra of the GST film. Each diffraction peak of C-GST is attributed to the scattering from a specific set of parallel planes of atoms. Inset: a generic scheme of the atomic distribution of (a) A-GST and (b) C-GST.