1. Introduction

The combination of chalcogenide phase-change materials (PCM) and integrated photonics produces a synergy that has led to groundbreaking optical non-volatile reconfigurable devices [1–6]. Placing the PCM, which is switched and accessed optically, directly on top of the waveguide has enabled on-chip non-volatile memories [2,7], all-optical switches [8,9], optical computing [10,11], electro-optical modulators [12], and neuromorphic computing elements [4], thus bridging gaps towards all-photonic chip-scale information processing [13,14]. This kind of device relies on the evanescent coupling between the propagating electromagnetic wave inside the waveguide and the material, which is a conventional method commonly used in light modulators [15], sensors [16], detectors [17,18], etc. Because most PCMs possess a non-negligible imaginary refractive index in the visible and near-IR for both states, light is attenuated in different amounts depending on the PCM phase-state [19,20], which implies a differentiable transmitted signal. This simple yet powerful architecture has proven to be a promising solution for optical applications, given that light is attenuated without directly blocking the transmission. An alternative approach, having the PCM embedded inside the waveguide, would provide a larger contrast between states, but would reduce the optically transmitted signals [21]. Moreover, devices with PCMs deposited on top, rather than embedded inside the waveguide, are obtained with a much simpler nanofabrication process.

In the experimental implementations thus far, the optical read-out makes use of the above mentioned evanescent-coupling. However, the optical switching between the amorphous and crystalline states, and therefore the modulation of the light transmission, has been triggered by a variety of approaches including the use of external (i.e. out of chip) laser pulses to heat up the material [22,23], by electrical heaters [12] or by the same evanescent-field coupling using a pump-probe scheme [2,4,8,10,11]. External pulses, in a method that resembles the write and erase processes in re-writable optical disks (such as DVD-RW, blu-ray RE etc.), are not optimum for future integration, although it facilitates the switching of memory cells at any location throughout the chip. Evanescent-field coupling for both write and erase, on the other hand, is a novel on-chip switching technique that allows full integration and all-optical operation. Nevertheless, light routing techniques are hard to scale [2,11] and require further development before any cell at any position within the chip can be switched independently using this method.

Achievements of this architecture include operation speeds approaching 1GHz, wavelength selective multi-bit operation, and more than 10 levels for non-volatile storage. Controllable and reliable intra-level transitions corresponding to different mixtures of crystalline and amorphous material has also been achieved. All this has been possible because of the fast crystallization kinetics, room-temperature stability, and the large refractive-index contrast between the amorphous and crystalline states of compounds such as Ge₂Sb₂Te₅ (GST). However, the process that drives the reversible phase switching using evanescent field, especially the attainability of reliable intermediate levels, is still unclear—questions such as why a power-decreasing train of pulses is needed to recrystallize while a single-shot is sufficient to amorphize have not been examined. Herein, we address this problem by studying the amorphization and recrystallization processes in computational simulations and by comparing our results to both new and previous experimental results. To do so, we investigate the evanescent-field coupling and power (heat) transfer between the guided light and the GST, using Si₃N₄ photonic devices operating in the C and L band with 10 nm GST capped with 10 nm indium-tin oxide (ITO) to avoid oxidation. For the experimental analysis, we employ the same pump-probe scheme as in [2,4,10]. We also make use of the attenuation coefficient values obtained experimentally for GST on balanced-splitter photonic devices for $\lambda =1595 \text{nm}$, using TE modes in [7]:

2. Evanescent-field coupling to phase-change materials

Amorphous GST (am-GST) on top of the waveguide offers low light attenuation due to its small extinction coefficient in the C and L-band wavelength range [7]. This means that the optical mode inside the waveguide remains mostly unaltered and the evanescent coupling to the GST cell is weak. Crystalline GST (cry-GST), on the other hand, possesses a larger complex refractive index at these bands. In this case, the light is partially guided by the material due to the significantly large real part of the refractive index. This creates a strong overlap between the highly absorptive GST and the optical field, which induces strong attenuation of the optical signal. We study this evanescent-field coupling between the guided mode—inside the rib waveguide—and the GST, qualitatively using Finite Element Method (FEM) modelling in COMSOL Multiphysics. In doing so, we used 2D simulations to calculate the cross-sectional mode and therefore, the strength of the interaction. In particular, we consider a transverse electric (TE) mode within half-etched Si₃N₄ photonic circuits, considering only GST sections completely covering the waveguide, $\lambda =1550 \text{nm}$, and the same materials parameters as in [1]. The effect of the phase transition on the normalized electric field amplitude was analyzed along a vertical line cutting the center of GST/ITO capping, as shown in the inset of Fig. 1(a). Upon crystallization, the maximum amplitude of the electric field moves from the center of the Si₃N₄ waveguides, to the vicinity of the GST. Given the large real and imaginary part of the refractive index of cry-GST, the propagating mode couples to and propagates inside the GST, where its magnitude is maximum, thus experiencing a strong attenuation. In Fig. 1(b), on the same vertical line, the normalized absorbed power (P_abs) was calculated along the GST and ITO layers. It was found that for cry-GST, there is two orders of magnitude more power absorbed from the mode than for am-GST, consistent with their large difference in the extinction coefficients. The influence of the thickness of the GST can also be observed as an exponentially slow decay of the electric field. Also, considering that the GST layer is only 10 nm thick, it is reasonable to assume that upon pulse excitation the whole of the GST will be at a similar temperature, thus fully switched along this axis. More interestingly, considering a horizontal cut on the same plane of the waveguide, plotted at the mid-point of the GST thickness (i.e. 5 nm into the material) in Fig. 1(c), shows how the power absorbed is maximum at half of the width of GST, being two orders of magnitude larger for cry-GST than for am-GST. The results in this figure also show the influence of ITO, given that at $\lambda =1550 \text{nm}$ ITO has a complex refractive index of $n_{ITO}=0.6+0.04i$, with an extinction coefficient comparable to that for am-GST [24]. Therefore, ITO will also absorb energy, giving rise to larger attenuation coefficients than if there were no capping or absorptive material atop.

 

Fig. 1 Electric field and power transfer to the GST/ITO capping for a mode with λ = 1550nm. a) Normalized electric field amplitude across the vertical cut-line shown in the inset. b) Normalized power absorbed by the GST with respect to the maximum power that can be transferred to GST (i.e. P_abs^cry−GST for fully crystalline GST) on the same vertical cut of a). c) Normalized P_abs on a horizontal line cut shown in the inset, which is traced at half the thickness of the GST. d) Simulated optical intensity of a guided wave travelling from left to right through a 5 µm long GST in the crystalline state (cf. zoom-in on the right). e) Phase (upper panel) and amplitude (lower panel) of the S₁₂ scattering parameter of the optical mode in d). f) Derived overall power flow for different GST-cell length: power transmitted through the phase-change photonic cell (black), power absorbed within the GST (red), and power scattered out of the waveguide (blue). Reflections at the bare waveguide/GST interface are at least as small as −30 dB and therefore negligible. g) Effective attenuation coefficient calculated from the scattering parameter according to Eq. (2). For longer cell-lengths the result match well the ones obtained experimentally in Eq. (1). For lengths below 2 µm, in contrast, a clear deviation can be observed due to mode transition effects between the bare waveguide and the phase-change element whose size is comparable to the wavelength.

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The mode simulations in Figs. 1(a)-1(c) offer relevant information about the effective refractive index and the evanescent coupling in our device. However, the results describe the interaction assuming an infinitely long GST cell, which leaves us with no information about the edge effects in the few micrometers long cells considered in this paper. To study these effects, we implemented a 2D slab-waveguide simulation using frequency domain solver in COMSOL Multiphysics as shown in Fig. 1(d). In this figure, the results are shown for crystalline GST with an incident mode propagating from left to right. Low scattering at the input was achieved by first deriving the mode pattern numerically before exciting it by a waveguide port. In the zoom-in image shown in Fig. 1(d), the propagating light is pulled upwards by the GST as result of its large real refractive index, as expected. However, it is also visible that the light does not fully interact with the first ~300 nm of the cell before coupling to the material, an effect that will be relevant later when observing SEM micrographs of actual devices. Scattering out of the waveguide into both the substrate and the air can also be observed, which arises from the transition at the beginning and the end of the cell. For a more quantitative analysis, the scattering parameters of the system were derived from different cell-sizes by placing an exact replica of the excitation port behind the GST cell. This analysis reveals that the reflections at the interface between the bare waveguide and the phase-change material—derived from the S₁₁ reflection parameter—are as small as −30 dB and can therefore be neglected. The amplitude and phase of the S₁₂ (transmission parameter), which is our main interest, is plotted in Fig. 1(e). It is found that for longer cells the phase increases linearly and the amplitude decreases exponentially. For GST cells shorter than 2 µm, the scattering is not negligible in comparison with the total absorption, reason why there is slightly more attenuation of the transmitted light, which is reflected in the change of slope of abs(S₁₂) in Fig. 1(e). The higher scattering losses in this case is likely due to GST being a perturbation on the same scale as the wavelength of light in the waveguide. This is further demonstrated in Fig. 1(f) in which not only the transmitted light, but also the power absorbed within the GST and the scattered power are plotted. Here, the transmitted power was derived from the S₁₂ parameter, the absorbed power was obtained by integrating the power loss density over the area of GST, and the scattered power was calculated by subtracting both transmitted and absorbed power from the incident power. For GST cells shorter than 1 µm scattered and absorbed power are on the same order of magnitude which causes the aforementioned deviation of the exponential attenuation. For longer cells, the overall scattered power—the sum of power scattered at the front and at the end—decreases because the total power reaching the rear of the GST is much smaller. If we assume that each cell can be modelled by a uniform effective refractive index, then we can calculate the attenuation coefficient from

2.1 Influence of the geometrical parameters on the effective refractive index

The evanescent interaction between the waveguide mode and the GST cell depends on both the dimensions of the waveguide and the size of the cell itself. Since the waveguide mode and its impact on the properties of the cell do not depend strongly on the exact waveguide structure, only the influence of the dimensions of the GST cell are investigated. To do so, the effective complex refractive index (ñ_eff = n_eff -ik_eff) of the cells are derived using a mode analysis using COMSOL. In the simulations, the waveguide was 1 µm wide and 330 nm high and the wavelength was fixed to 1550nm. In Fig. 2, we show both the real and the imaginary part of the effective refractive index as a function of the width (panel a) and the height (panel b) of the GST cell. With decreasing cell area, both the real and imaginary part decrease substantially. At cell heights and widths below approximately 10 nm and 400 nm, respectively, the effective refractive index varies significantly with small changes in the geometric parameters. In terms of the GST-cell length, in Figs. 1(e)-1(g) it can be observed that the longer the cell the higher the attenuation of the optical mode. Therefore, to obtain good signal-to-noise ratios (SNR) while maintaining sufficient contrast between states, cells with lengths in the 1-5 µm have been preferred, as demonstrated later. However, using several short GST islands has been proposed as an alternative solution to increase the contrast between transmission levels [4].

 

Fig. 2 Simulated dependence of the effective refractive index (upper panels) and the effective extinction coefficient (lower panels) of the GST cell at λ = 1550 nm by varying a) the width (for 10 nm thick cell), and b) the height (for 1 µm wide cell).

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Although recent experiments have used different lengths and widths for the GST cells, 10 nm has been the thickness chosen in most of them. This is because there is a trade-of between the attenuation and the total transmission in devices. For memory applications, for instance, thicker films will induce too much attenuation (i.e. poor SNR) but offer good contrast between the multiple transmission levels. Thinner GST will have exactly the opposite situation. Devices with <10 nm thick GST can be employed in applications in which low attenuation is required, such as phase modulation.

2.2 Thermo-optical effect

Under pulse excitation, the GST cell heats up. Afterwards, it cools down until reaching the room temperature at which it is operated. During this time, the light transmission undergoes different responses as result of the varying temperature of GST before reaching either higher or lower levels if amorphization or crystallization take place. This effect can be measured experimentally by detecting the real-time response during and after the evanescent coupling between pulse and material, which has been done extensively in [3] to measure the thermo-optical parameters of GST. This effect is the combination of the optical response to a change in the complex refractive index (which depends on the GST temperature) and the generation, by the pulse, of free carriers inside the material. The latter is thus an electronic contribution that effects light attenuation by contributing to the intraband absorption rate. The former, is the optical response due to the changes in refractive index as function of the temperature, given by the equations:

3. Amorphization

We describe the partial amorphization mechanism with FEM models in COMSOL, and compare to pump-probe experimental results using the setup described in [2]. To do so, we used devices in which the GST, covering completely a 1.3 μm wide waveguide, was prepared in the crystalline state by annealing at 250°C for 2-5 min after sputtering. The switching to the amorphous state was obtained by means of a pump pulse with enough energy and with a trailing edge in the 0.5-5 ns range to rapidly melt-quench the GST, thus favoring a disordered state [20,25]. In detail, if P_min is the minimum pulse power able to amorphize GST, then, when a pump pulse with fixed width and with power $P_n \ge P_{min}$ is sent to the GST cell (prepared in the crystalline state with transmission T₀), amorphization is induced. Consequently, the transmission of the probe signal increases from the baseline transmission T₀ to a characteristic value T_n, the transmission level n. We found that T_n is unique to the pulse power P_n, therefore, the level n can be accessed every time that this same pump pulse is sent to a fully crystalline GST cell. The more energetic the pulse, the deeper—along the waveguide—and broader the area that is melt-quenched (amorphized), as shown in Fig. 3(a). In this figure, the normalized absorbed power, shown previously in Fig. 1(c), was projected over the propagation direction using the experimental value for the attenuation of the TE mode given in the Eq. (1), and considering a 5 μm long cry-GST cell. The isosurfaces of the power absorbed by GST provide good insight about the pulse penetration along the GST and the areas that would be switched to the amorphous state if the power absorbed is higher than the threshold to melt-quench it. This model, however, does not account for the edge effects observed in Fig. 1(d).

 

Fig. 3 Amorphization by evanescent coupling in a GST cell. a) Projection of the mode in Fig. 1(c) into the cry-GST, along the propagation direction, and using the experimental value for the optical attenuation in Eq. (1) (not accounting for edge effects). b) 3D FTDT and heat transfer simulation of a 100 ns, 15 mW pulse at λ = 1580 nm propagating through a waveguide with a 2 μm fully crystalline GST on top. The temperature profile is shown at four times during the pulse excitation reaching its maximum at the end of the pulse (t = 100 ns). The area that is amorphized is the area with T>890 K. c) Thermo-optic effect and amorphization by varying pulse power and fixing pulse length to 100 ns, and d) varying pulse length and fixing pulse power to 6.1 mW for a 5 μm long GST and λ = 1580 nm. e) Change in transmission (ΔT) as a function of the pulse power and pulse width for devices with GST cells with a length of 1 μm. f) same as e) but for a 5 μm long GST. g-j) SEM images of 5 µm long phase-change photonic memories after pump-probe measurements. g) In the fully crystalline state. h) Amorphization and recrystallization with the same pump-pulse. i) Differential amorphization from the two opposite directions (after several back and forth cycles). j) Ablation after a very energetic pulse of ~30 nJ.

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To understand the time evolution of the temperature upon pulse excitation, and to include the effect of the GST edges, we performed 3D simulations using Lumerical. In doing so, we calculated the power absorbed in the GST and ITO layers using FDTD for a 2 μm long GST-cell. Then, we used this three-dimensional power profile as a source in a heat transfer simulation, employing the material properties summarized in Table 1. In Fig. 3(b), we show the evolution of the thermal profile under the excitation of a 100 ns, 15 mW pulse. It can be observed, as expected from our analysis in the previous section, that the edge does play an important role: we obtain a profile as in Fig. 3(a), but shifted around 300 nm into the GST when the temperature is above 890 K, enough to amorphize the material. For more information on the temperature evolution of the GST and further discussions on the thermo-optical effect refer to Refs [2,3].

Table 1. Thermal material coefficients user for the FEM and FDTD simulations.

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In order to compare our model with experimental results, we show in Fig. 3(c) the real-time response of the probe transmission, corresponding to a combination of the thermo-optical effect and free-carrier absorption [3]. This is plotted when amorphization takes place in a 5 μm long GST cell for different P_in. For a fixed pulse length of 100 ns with 500 ps rise/fall times, it is shown how the higher the energy absorbed, due to an increase in pulse power, the higher the final transmission level. As GST absorbs more energy—seen in the thermo-optical curve shown in Fig. 3(c) as it gets deeper, i.e. hotter—the pulse amorphizes a larger area of the GST, which can be related to the thermal isosurfaces in Fig. 3(a). Furthermore, tuning the power is not the only way to reach an energy that is enough to amorphize GST. By fixing power to 6.1 mW and controlling pulse width, a similar output with several different transmission levels was achievable as plotted in Fig. 3(d). The final level of transmission is therefore dependent on the amorphous/crystalline areal ratio, which is deterministically controlled by tuning the switching pulse energy. If pump pulses with energies that can heat up the GST far beyond its melting point are used, the material composition may be modified and it may even get destroyed as ablation takes place. For this reason, pulse widths shorter than 100 ns are commonly employed, and rather the pulse energy is controlled by tuning the pulse power [2,4,8]. For the experiments reported here, a variety of pulse generators were used, some offering 500 ps rise/fall times, others with 5 ns, and even arbitrarily created pulses with 50 ns rise/fall times. All such pulses were able to amorphize GST, indicating that the important parameters for controlling amorphization here were the pulse power and pulse width at max power (i.e. the pulse energy). It is perhaps a little surprising that pulses with fall times as long as 50 ns led to successful amorphization (since shorter required fall times are usually reported [27]). This finding may be related to the different way (cf. conventional optical/electrical excitation) energy is transferred to the GST via the evanescent coupling mechanism in this architecture, but further research is required to clarify this apparent discrepancy.

The contrast of the transmission levels before and after switching to the amorphous state depends on the dimensions of the PCM element. Short PCM sections (shorter than 800 nm) require lower energies to switch and provide low optical attenuation and therefore high transmission and SNR. This configuration may sound ideal, however, the contrast in transmission between the amorphous and the crystalline state is notably small, thus making difficult the differentiation of transmission levels unless very high SNR detectors are employed.

On the other hand, when using very long GST cells, such as 10 μm, the probe signal is almost completely absorbed. Accordingly, the SNR for the readout pulse is poor and the transmission measurements become challenging. Thus, high energy pump pulses may be required to amorphize enough GST to induce a significant increment in transmission. This is the reason why cells with lengths in the 1 to 5 μm have been preferred. We now compare the performance of devices in the two extremes of this range in terms of the required switching energy and read-out contrast in Figs. 3(e) and 3(f). These GST dimensions allowed for fast operation where pump pulses between 10 ns and 200 ns were successfully employed with switching energies as low as 13.4 pJ. The results plotted in Fig. 3(e) for 100 ns pulses correspond to the traces illustrated in Fig. 3(c). The measurements in this figure were carried out on the same two devices (one per each GST length), after every pump pulse towards a fixed transmission point in the plot, followed a re-crystallization process towards level 0 (as explained in the following subsection) before achieving the next level. With this approach, every level can be independently addressed with high reproducibility, a feature that enabled the multilevel memory operation in [2]. A remarkably high contrast of 60% was obtained for 5 μm long GST devices in Fig. 3(f) as the pulse energy reached nearly 1200 pJ.

Four different SEM images for phase-change based photonic devices are shown in Figs. 3(g)-6(j), before and after pump pulses with different conditions. An extensive amorphization area with a high-power pulse is shown in Fig. 3(h) in a device that was cycled several times and was operating correctly right before SEM imaging—the contrast between the two areas is due to the difference in conductivity between am- and cry-GST. Moreover, Fig. 3(i) shows areas that have undergone both amorphization and recrystallization from opposite sides, enabling two active areas with different responses in a single device. The larger amorphous area shows crystalline stripes, a property of the recrystallization process as explained below. Lastly, the micrograph in Fig. 3(j) shows a device that was ablated with a very energetic (~30 nJ) pulse.

Up to this point, we have only considered GST-cells covering completely the width of the waveguide. However, Fig. 4(a) (together with the results shown above in Fig. 3) suggests that the energy exchange between the mode and the cry-GST takes place around the center of the waveguide, while being mostly constant along the vertical axis (thickness), as shown in Fig. 4(b). A way to reduce the energy consumption could be using smaller GST and waveguide widths, so that a higher ratio of the used energy is concentrated in the area which is subsequently switched. Moreover, we keep the GST thickness fixed at 10 nm as this provides a good attenuation/transmission trade-off while maintaining an almost uniform thermal profile—see Fig. 2 for more details on the influence of the geometrical parameters on n_eff and k_eff. Aiming to optimize the energy consumption, we made 1 μm wide waveguides and studied the effect of reducing the GST width in the profile of the power absorption, which is shown in Fig. 4(c). As the GST width decreases, the evanescent mode coupling is weaker, as expected from the values of k_eff in Fig. 2, in addition to the maximal absorbed power at the center of the waveguide. The ratio of maximally to minimally absorbed power (within each width value) exceeds a factor of two for all cells wider than 200 nm. Neglecting thermal diffusion, this means that the pump power required to switch the outer part of the cell exceeds the power required to switch the center by at least a factor of two. Therefore, switching the entire area of a >0.5 μm cell with a single pulse is not possible without risking severe destruction of the central part of the cell, as shown in Fig. 4(d), in which a GST cell with irreversible degradation is shown (the sample was annealed in a hotplate to make sure the rest of GST was recrystallized). Even with less GST, the power to switch might have to be larger since most of the mode does not couple to the material and the switching will take place in a confined area of the GST. Hence, the switching energy (i.e. the energy absorbed by GST) might be lower because of better confinement, but the pulse energy that does not couple would be wasted.

 

Fig. 4 Power absorbed by GST with varying widths at λ = 1550nm. a) Simulated power absorption (power loss density) of a waveguide with cry-GST on top. b) Plot of P_abs in a) along a vertical line through the 10 nm thick GST. c) Power absorbed by GST along a horizontal line through the have thickness of GST for different widths of centrally positioned cells. d) SEM micrograph of GST after excitation with a high-power picosecond pulse that cause irreversible degradation.

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The smaller the GST cell, the more significant the scattering effects when comparing both the amorphous and the crystalline states due to the differences in n_eff. This is another option to minimize energy and form factor, given that the optical transmission can be switched between two distinguishable levels by combining both attenuation and scattering, thus enabling good optical contrast despite the size.

4. Recrystallization

To regain long-range order in the GST molecular structure, the material needs to be heated above the crystallization temperature (~160°C) for a critical amount of time. Although the target temperature is significantly lower than the melting temperature, this process has proved more challenging than the amorphization under evanescent-field coupling. While a single pulse is enough to induce amorphization, to achieve a $T_n\to T_0$ transition (i.e to switch from a high transmission level n back to the fully crystalline state), several pulses or a single structured pulse are required for crystallization. In particular, a train of consecutive pulses with gradually decreasing power [2,8], multiple pulses with the same energy [4,11,28], and recently a single double-step pulse [10] have been experimentally demonstrated. Given that amorphous GST exhibits nearly ten times lower optical attenuation compared to crystalline GST (See Eq. (1)), we use optical pulses within the same energy range when switching back-and-forth between states: one pulse can initially induce amorphization, while a subsequent, identical pulse will either keep the same state or partially crystallize a small amount of the PCM device. This is possible, because the resulting temperature from a pulse that heats amorphous GST over the crystallization temperature (~150°C) can also induce amorphization of the GST remaining in the crystalline state, given that it reaches temperatures of nearly 750°C, enough to melt-quench the material.

Considering our results in Figs. 3 and 4, if a first pulse amorphizes an area within the fully cry-GST, which is proportional to its power, then a subsequent pulse would interact with the resulting mixture between am-GST in the center, and cry-GST at the edges and the rear of the cell. This mixture is the key to understand the multi-step recrystallization process. Figure 5(a) shows the attenuation coefficient calculated from the cross-sectional optical mode of the rib-waveguide, considering varying partial amorphous sections embedded between crystalline areas. This, in turn, shows the differential absorption by the material because of the amorphous/crystalline areal proportions, which leads to unique responses. The strong variations are the result of the power being absorbed in the crystalline areas, which becomes weaker as the amorphous central area expands towards the edges, as plotted in Fig. 5(b). For this reason, if further pulses are sent when GST is in any of these intermediate states, higher temperatures will be reached at the boundaries between am-GST and cry-GST where the absorbed power is greatest. Furthermore, if parabolic-like amorphous areas are considered along the light propagation axis—based on the simulations in Fig. 3—then one recrystallization step can be understood as the small crystallization that takes place at the edges and at the end of the amorphous area (when only cry-GST is facing the pulse, thus having a higher extinction coefficient). The case of amorphous areas along the entire GST cell is also possible provided the right amorphization pump pulse power; this is common for shorter GST cells too, as in the case of 1 µm in Fig. 3(d). Multiple recrystallization steps will then be required; given that it is not possible to heat up the center of the amorphous material directly. Instead, several pulses, each one crystallizing a bit of the amorphous material are required until the whole amorphous area is back to fully crystalline.

 

Fig. 5 Recrystallization scheme computational modelling and experiments using λ = 1580nm. a) Normalized attenuation coefficient as function of the amorphous section width, embedded into crystalline GST, as shown in the inset. The α_cry corresponds to the attenuation when GST is fully crystalline, which can be measured experimentally. b) Normalized power absorbed (P_abs)—with respect to the maximum power absorbed when GST is fully crystalline P_abs^cry-GST—traced on the horizontal line parallel to the substrate and crossing the GST at half-height (at 5 nm, as shown in the inset), including the embedded amorphous section. c) Light absorption calculated for 5 μm long GST considering: 1) an initial amorphization depth of 4.5 μm with 0.9 μm of width; 2) the experimental attenuation calculated for fully amorphous and fully crystalline GST; and 3) the partial-amorphous attenuation values reached in intermediate recrystallization steps, calculated using a) until the amorphous area is completely recrystallized (i.e. the amorphized area depth is equal to zero). The bars indicate the pulse energies required to transfer the same energy E to the material via absorption, as a function of the energy required to heat-up over the crystallization temperature (and below the melting temperature) when the material is in a fully-crystalline state, which can be experimentally measured. d) Sketch of the full recrystallization as understood from the simulations, requiring thus an energy-decreasing train of pulses. The GST sections sketches are plotted as seen from the top representing both 5 μm and 1 μm GST long devices. e) Top view of the temperature profile of the GST-cell calculated from FDTD and heat simulations. Pump pulses with lower, equal, and higher power than that used to amorphize the marked elliptical area (P = 15 mW, see Fig. 3(b)) are studied. Using 100 ns pulses, the temperature is plotted for 5 ns, 50 ns, and 100 ns into the pulse excitation. f) Similar thermal simulations considering a smaller GST cell: 0.7 μm wide and 1 μm long, and a fully amorphized area that extends along the entire GST cell. g) SEM micrographs of cells with 0.7 μm wide and 1 μm long GST, featuring off-centered amorphous lines. h) Transmission measured in real time during the pulse excitation, thus carrying the information of the thermo-optical effect that leads to partial recrystallization in small steps. i) Amorphization followed by a full recrystallization with a single double-step pulse.

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While the explanation presented above provides an answer to why several pulses are used in the recrystallization process, as done in [4,28], it does not explain why a train of energy-decreasing pulses are necessary if we are to minimize the total number of pulses, as done in [2]. To find a reasonable answer to this, we raise a hypothesis based on the results in Fig. 5(a). As the GST recrystallizes, the attenuation increases, given that there will be a higher portion of cry-GST than of am-GST (i.e. the amorphous volume decreases). Therefore, the attenuation that the first recrystallizing pump pulse undergoes is much lower than that of any of the following pulses; thus, more energy is required for this pulse than for the subsequent ones to reach the same temperature (crystallization temperature, for instance). Hence, pulse-energy requirements decrease as the attenuation increases. If considering the case of a memory cell of 5 μm and a pump pulse that amorphizes GST to a depth of 4.5 μm and a width of 0.9 μm, the evolution of the attenuation of the entire GST cell in the recrystallization process can be studied by calculating the total amount of light that is absorbed after each pulse. This is done by reducing the area of amorphous GST following the isothermal curves in Fig. 3(a) and calculating the attenuation of differential areas using the values in Fig. 5(a). The results for the absorbed light in this case are shown in Fig. 5(c), together with the modulation in pulse energy required to obtain the same absorption in every intermediate state. These results show that there is an exponentially decreasing pulse energy required to obtain the same absorption from the material, i.e. to heat it up to the same temperature, as recrystallization takes place from the edges. This process is sketched in Fig. 5(d) for a better visualization. This method represents the less time consuming process for individual square pulses as the energy modulation implies the minimum number of pulses to be used [2,8]. Alternatively, a larger number of pulses of constant but lower energy can be used to recrystallize GST in even smaller steps [4,28]. This alternative may require less energy per pulse, but would increase the total duration of the total recrystallization as many more pulses are required, thus slowing the device cyclability. Also, given that the attenuation is calculated for differential sections, which could have been taken in different order with the same result, then the actual place where recrystallization takes place—including different recrystallization areas to that near the edges as considered in the hypothesis above—would lead to similar train of pulses with decreasing energy. Tailoring the size and geometry of the waveguides and the GST cells, like that demonstrated in [11] where the GST is switched with two picosecond pulses hitting the cell from two perpendicular sides, might lead to optimized switching mechanisms with smaller number of pulses.

To further analyze our hypothesis on the differential recrystallization at the edges of the amorphous area, we carry out 3D light propagation FDTD and heat simulations on Lumerical. We use the results of the simulations shown in Fig. 3(b) to establish the amorphous area size embedded in the crystalline cell, which we approximate to an ellipse for simplicity. We first calculate the P_abs at the interface between the waveguide and the partially amorphous GST using 3D FDTD simulations assuming a 2 µm long GST covering all the waveguide, i.e. 1.3 µm wide. We then use this P_abs as the heat source and study the temperature evolution for a 100ns excitation. In Fig. 5(e) we study three scenarios, when the power of the pulse is smaller, the same, and larger than the pulse power P_n used in the previous step (see. Figure 3(b)) to amorphize. In this figure, pulses with P<P_n would reach a temperature higher than T_c near the edges of the amorphous GST even after the first 5 ns, thus recrystallizing the area of interaction and reducing the size of the amorphous area. For P = P_n, the pulse would induce high temperatures close to the melting point but not over, therefore, it also recrystallizes the edges of the amorphous area, where most of the heat concentrates due to the large contrast in extinction coefficient between am- and cry-GST. This demonstrates why sending a pulse to cry-GST (covering the entire waveguide) induces amorphization initially, but sending a second identical pulse results in a small recrystallization, as shown experimentally in [2]. On the other hand, larger pulse powers would induce further amorphization into the cry-GST, not fulfilling the goal of recrystallizing and instead achieving a higher transmission state. We repeat the same simulation but assuming a structure like that shown in Fig. 4(d) for smaller GST cells: 0.7 µm wide and 1 µm. If the amorphous area extends completely from one end to the other, then the recrystallization should take place from the side edges toward the inner part. In this case, shown in Fig. 5(f), it is clear how the temperature is higher along the edges in the totality of the extension of the amorphous area. Thermal diffusion can play an important role in this effect, its action on the material may be the reason of the long cooling times before the transmission levels stabilize, especially when recrystallizing as the temperature required is lower.

The fact that the heating occurs along areas close to the edges of the amorphous area (see Fig. 5(b)) might be the cause of the lines observed in the SEM micrographs in Figs. 3(h) and 3(i) for GST covering the entire waveguide, and the ones in Fig. 5(g) for smaller cells. They might be the result of areas that fail to recrystallize properly, which can be avoided by using smaller energy gaps between consecutive pulses in the train of recrystallizing pulses. However, their effect on the reliability of transmission levels can be diminished by pre-conditioning the material before actual operation. That is, the GST cell should be cycled several times beforehand so that transmission levels reach stable values [2].

For an experimental implementation, this pre-conditioning process can be performed using a train of power decreasing pulses, a method found empirically in [2], consisting of k pulses with powers $P_{n\to m}=P_n-m\Delta P$, where n stands for the starting transmission level and $m=0,1,2\dots , k-1$. Such pulses are sent consecutively in time intervals limited only by the cooling rate of GST. It was found that the smaller $\Delta P$ the smaller the error in attaining a specific level n, when switching back-and-forth several times. This is because lines such as those in Figs. 3(h) and 3(i) are avoided if progressive recrystallization is done with pulses whose energy are closer to each other. In this pulse sequence, all the pulses recrystallize in small steps—each step representing a unique transmission level—but all together drive the transmission towards $T_0$. The number k will be given by the condition $P_{k-1}\approx P_{min}$ for which $T_0$ should be reached. Pulses beyond this condition should not modify the transmission as the material is transformed to the fully crystalline state. Pulse powers and widths can be chosen accordingly, if the energy (pulse width multiplied by power) remain in the same range. An experimental demonstration is shown in Fig. 5(h), in which the thermo-optical response was recorded in real time for 100 ns pulses with decreasing powers sent to a cell previously amorphized by a 5.62 mW pulse. All the small changes towards less transmissive states add up until the base transmission for fully cry-GST is once again reached.

A novel alternative to overcome the energy and speed concerns when using multiple pulse schemes has recently been proposed in [10]. In this case, shown in Fig. 5(i), a single double-step pulse was used to heat the material over the crystallization temperature and keep it hot, yet below the melting point, until full recrystallization from the edges to the inside takes place. The first step of the pulse consisted of a pulse with the same power ($P_n$) and width as that used to amorphize. Without this high-power part of the pulse, even if using longer excitations, recrystallization was not obtained. The second step consisted of a power between 0.3 $P_n$ and 0.4 $P_n$ for times between 100 and 150 ns. This scheme was successfully demonstrated to pulses up to 100 ns width and resembles the double-step pulse scheme successfully demonstrated in PCM-based optical disks [29].

5. Comparison between real-time switching dynamics

As explained in the previous section, two consecutive pulses may have different effects on the GST cell, even if they have the same energy. This is due to the modulation of the refractive index of the GST cell that occurs after every pulse excitation. To analyze this effect, we show the real-time change in transmission displaying the thermo-optical response of the GST cell using the same pulse energy in two cases: one in which the energy is barely enough to switch and another in which the switching is large. In Fig. 6, we plot the transmitted 100ns pump pulses measured after the interaction with the GST, which were captured simultaneously for the amorphization and the crystallization processes in a 5 µm-long GST cell. It is observed that a pump pulse with the same initial energy (372 pJ or 561 pJ inside the waveguide) can induce amorphization in a GST cell that was originally prepared in crystalline state. In this case, there is an increase in the transmission measured from the probe signal, which becomes larger as the pulse gets more energetic, i.e. as more material is amorphized inside the GST section, as explained above. After the amorphization, the same pulses were sent to the GST cell where recrystallization takes place in a smaller step. The relaxation of the material towards a lower transmission level, after pulse excitation, shows that the recrystallization needs to be done in several steps to compensate the large change in transmission obtained previously in the amorphization process. This becomes more obvious as the amorphization is larger using a high energy pulse.

 

Fig. 6 Real-time pump pulse and probe signal measurements on 5 μm-long GST, using 100 ns pulses with energies of 373 pJ and 561 pJ (inside the waveguide) and λ = 1580nm.

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The transmitted pump pulse measured and plotted in Fig. 6 provides information on how the GST absorbs energy during the pulse excitation. Such pulses correspond to the resulting pulse after propagating inside the device containing the GST cell. This pulse also provides information about how much light is being absorbed. For instance, in such figure, during amorphization, the transmitted pump pulse displays less peak power than in the same measurement for the crystallization process, which is due to a larger attenuation in the former case. The shape of the pulse, in turn, offers information on the rate at which the GST is being heated up and the transition that is taking place. During amorphization, the pulse is largely absorbed (lower peak power) but the effect is constant over time as the melting is taking place because the quenching would only happen once the pulse has passed. During crystallization, on the other hand, as the pulses propagates through the material, this crystallizes and changes the attenuation in real time, thus changing the pulse shape and displaying the rate at which the crystallization happens. Changes in the morphology of the pulse can thus offer valuable information towards understanding the intrinsic phase-transition dynamics and the time-scales of the process.

6. Summary

In this paper, we have described the mechanism for the controlled all-optical switching of a phase-change material on integrated photonic circuits. We considered evanescent coupling between the confined optical mode and a GST cell placed directly on top of the waveguide. To circumvent the elusive full and repeatable switching cycle—the major obstacle in photonic and plasmonic applications of phase-change materials—the amorphization and stepwise recrystallization schemes proposed originally in [2] were computationally studied and compared to experimental results. We found that a single pump pulse is enough to amorphize a fraction of the cell, in parabolic-like shapes that depend on the pulse energy. Moreover, we explained the stepwise process to fully recrystallize the material from the dynamic modulation of the GST absorption as result of recrystallization happening only at the boundaries of the amorphous area. We found that during back-and-forth switching the areas that are heated up either over the crystallization or the melting temperature are well delimited and depend only on the pulse energy and the amorphous/crystalline areal distribution before an incoming pulse. This is the source of the controllable transmission levels and deterministic switching using evanescent coupling: the well-defined areas for light-matter interaction, which is not the case of the filaments created with electrical current switching, for instance. We also compared the real-time responses during both amorphization and crystallization.

Although this paper considered a simple geometry consisting of a rib-waveguide and a rectangular section of GST, tailoring the size and geometry of the different components can lead to new and more efficient switching mechanisms, as done in [4]. One example was recently demonstrated in [11] where the GST is switched with two picosecond pulses hitting the cell from two perpendicular sides, which might lead to optimized switching mechanisms with smaller number of pulses. There is indeed plenty of room to optimize this architecture in terms of energy and operation times. Not only from geometrical aspects, but also by trying different light sources, different wavelengths, and by finding better phase-change materials with lower losses and faster switching, while having good optical contrast. However, the already demonstrated controllable non-volatile light modulation has filled a longstanding gap in integrated photonics platforms. Its potential in applications such as collocated data storage and processing [2,10,11], optical switches [8], and neuromorphic computing units [4], positions the growing phase-change photonics as one of the most promising applications in integrated photonics.