Pixelated non-volatile programmable photonic integrated circuits with 20-level intermediate states

In order to apply Sb₂S₃ in the field of pixelated programmable PICs, it is essential to determine the refractive index (real part n and imaginary part k) of amorphous Sb₂S₃ (aSbS) and crystalline Sb₂S₃ (cSbS) and the crystallization temperature. A 10 nm-thick Sb₂S₃ film was deposited by radio frequency (RF) sputtering on a standard 500 μm-thick silicon substrate. After that, a 20 nm-thick SiO₂ film, which acts as the protective layer, was deposited by PECVD at 100 °C to prevent sulfur loss during the phase transition process. The schematic diagram of the multi-layer sample is shown in figure 2(a). The deposited Sb₂S₃ material at the very beginning was in the amorphous state. To crystallize the Sb₂S₃ film and determine the crystallization temperature, four Sb₂S₃ samples were annealed at different temperatures (starting from 240 °C to 360 °C with an increment of 40 °C) for 5 min. As shown in figure 2(b), the film surface shows a non-uniform pattern when the heating temperature reaches up to 320 °C, which is due to the nucleation and growth of crystals. The optical constants of the originally deposited Sb₂S₃ sample and four Sb₂S₃ samples heated at different temperatures are measured by a spectroscopic ellipsometer, as illustrated in figure 2(c). More details on the ellipsometer can be found in the supplementary material. As expected from the Sb₂S₃ micrographs, the Sb₂S₃ starts to crystallize at 320 °C, after which the refractive index changes dramatically. According to the measurement results, the fitted bandgaps of cSbS and aSbS are 1.53 eV and 2.04 eV, respectively. The bandgaps of amorphous and crystalline Sb₂S₃ are much larger than those of GST, which means that Sb₂S₃ could significantly reduce optical loss compared to GST in the visible and near-IR wavebands [36]. As shown in figure 2(d), the refractive indexes of aSbS and cSbS were compared with other measurement results from [35]. The slight difference may be caused by the material roughness, the fabrication process, or the measurement error.

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A programmable multi-level Sb₂S₃ matrix consists of a large number of Sb₂S₃ elements. The fine phase transition and the footprint of a single Sb₂S₃ element are crucial for the performance of the programmable PICs and metasurfaces. In this section, we investigate the laser-writing multi-level intermediate states of a single Sb₂S₃ element at the microscale. A 70 nm-thick Sb₂S₃ film was deposited on the silicon substrate, after which a 700 nm-thick SiO₂ was deposited as the protective layer. The experimental setup of the in-house developed pulsed laser writing system for the multi-level phase transition of Sb₂S₃ matrix can be found in figures 3(a) and S1: a high-power laser beam generated by a continuous wave laser (CWL) at 520 nm wavelength is focused by a 50×/0.6NA objective lens on single Sb₂S₃ elements to perform phase transition. The full width at half maximum (FWHM) of the focused laser spot size is 1.2 μm. According to the transfer matrix method, the degree of crystallization of Sb₂S₃ elements can be characterized by the reflectance of the phase-change region [42, 43]. An optical brightfield microscope was then added to the laser-writing setup in order to navigate the region of interest and measure the reflectance of phase-transition regions in-situ. The illumination and imaging light paths are shown in blue in figure 3(a). The central wavelength and the bandwidth (FWHM) of the LED are 455 nm and 18 nm, respectively. The power of the LED is too low to impact the phase transition. More details about the experimental setup can be found in supplementary materials.

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Single laser pulses with different powers were used to induce different degrees of crystallization of Sb₂S₃ elements. The laser power generated by the laser diode changes from 30.5 mW to 58.5 mW, and the laser pulse duration is 10 ms. The reflectance difference ($\Delta R$) is used to determine the crystallize fraction given by

$$\begin{align}\Delta R = \frac{{R - Ra}}{{Ra}}\end{align} \tag{ 2 }$$

where R is the measured reflectance of intermediate states of Sb₂S₃ elements, and R_a is the reflectance of aSbS. The ΔR of the phase-change regions at different laser powers was measured and shown in figure 3(c). When the laser power is too low (less than 30.5 mW) to reach the crystallization temperature, there is no change in the reflectance of the Sb₂S₃, and the Sb₂S₃ pixel remains in the amorphous state. As the laser power increases from 37.5 mW to 51.5 mW with a step of 7 mW, the aSbS starts to partially crystallize and the reflectance increases before reaching up to the peak reflectance (i.e. the point where full crystallization happens). A slight variation in the reflectance of intermediate states of Sb₂S₃ can be observed when the laser power is increased from 37.5 mW to 51.5 mW. The underlying physics of why ΔR remains the same at pulse power ranging from 37.5 mW to 51.5 mW, unfortunately, is unknown as of now, but it again demonstrates the fact that the relationship between laser power and the reflectance difference is nonlinear [44]. Hence, we would like to leave this as an open question for future study and discussion, while focusing on the demonstration of the multi-level intermediate states of Sb₂S₃ alongside its potential applications in this paper. As we increase the pulse power from 51.5 mW to 58.5 mW, we observe a further increase in the reflectance difference, which indicates the generation of more intermediate states. In addition, the central damage of phase-change regions affects the stability of crystallization [32, 36]. Due to the low absorption of aSbS and the burn-in-effect, local damage and defects can be induced by the high-power and long-period laser pulse illumination in the phase-change regions. The central damage images of Sb₂S₃ elements after high laser power excitation are shown in figure S2. As a result, the crystallization stability of Sb₂S₃ induced by a single high-power and long-duration laser pulse limits the applications of multi-level intermediate states.

To improve the crystallization stability, we use different numbers of low-power laser pulses to crystallize aSbS pixels (from 0 to 350 pulses). The power of the laser beam is 28.4 mW, and the pulse period and duty cycle of the square pulses are 80 ms and 50%, respectively. The reflectance of the Sb₂S₃ induced by different numbers of pulses was measured, as shown in figure 4(a). The microscopic images of the phase-transition pixel under different numbers of pulses (0, 160, 240, 350) are shown in figure 4(b). The microscopic images of 20-level intermediate states are illustrated in figure S3. When the number of pulses is less than 120, the reflectance remains constant because the temperature of the laser heating area does not reach the crystalline temperature (around 320 °C). As the number of pulses exceeds 120, the reflectance gradually increases. The increase in reflectance is linearly related to the number of pulses. The reflectance difference reaches its peak value of 0.58 after 320 laser pulses. In comparison, the reflectance difference of cSbS heated on a heating panel is 0.60, which is slightly higher than that of cSbS pixels induced by the focused laser. This indicates that the reflectance difference between Sb₂S₃ induced by thermal annealing and the focused laser demonstrates the complete crystallization after 320 laser pulses. The gradual increase in reflectance and absence of darker points in the phase-change region exclude the influence of local damage induced by high-power laser pulses. In addition, we performed the measurement of Raman spectrum to demonstrate the cSbS induced by laser pulses, as shown in figure 4(c). The Sb₂S₃ processed by thermal annealing and laser heating has the same set of peak wavelengths corresponding to known vibration modes that affirm crystallization [32]. The experimental results demonstrate the efficiency of the laser heating process in the crystallization of PCMs. The 20-level intermediate states of single Sb₂S₃ pixels were realized in the range of 120–320 pulses. The diameter of the phase-transition pixels is about 1.2 μm, which is caused by the focused laser. Compared with the single-pulse crystallization strategy, the partial crystallization strategy using low-power, multi-pulse lasers is much more stable. The longer period and pulse interval allow for a longer duration of heat transfer from the center to the edge in the phase-transition region, alleviating the issue of excessive temperature in the center of the phase-transition region. Therefore, the multiple low-power pulse crystallization approach is more suitable for achieving multi-level intermediate states. Moreover, the multi-pulse crystallization approach has also been demonstrated to greatly improve cycling durability [34]. We set 10 pulses as the crystallization step to guarantee the distinct reflectance difference of 20-level intermediate states and improve the stability of crystallization. The slope of $\Delta R$ with the number of pulses could go down with a proper reduction in optical power. The more intermediate states of Sb₂S₃ pixels could be realized by optimizing the pulse power and pulse duration. In addition, more precise measuring instruments are required to distinguish the minor reflectance differences of different intermediate states of Sb₂S₃ pixels. While the main focus of this paper is the crystallization of Sb₂S₃, it is worth noting that multi-level intermediate states during the amorphization process can also be realized in a similar way [34, 44]. Compared to the crystallization process, the amorphization process requires higher temperature and shorter laser pulse width (from femtoseconds to nanoseconds). The parameters of laser pulses, including the laser power, the pulse width and the repetition frequency, need to be optimized through experiments to realize multi-level intermediate states. In terms of cyclability, there were some studies discussing the cycling duration of PCMs, especially Sb₂S₃ [34, 36]. Delaney et al [36] demonstrated a fast degradation of Sb₂S₃ after around 1000 switching cycles. To improve the cycling durability, [34] demonstrated a multi-pulse irradiation-based method to obtain greater cycling durability. It is worth noting that the region irradiated by laser pulses tends to form irreversible deformation due to local melting and surface tension, while lowering pulse energy reduces the deformation and thus improves cycling durability. Compared with a single pulse with high energy, the method of using multiple pulses with lower pulse power tends to improve the cycling durability.

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The programmable integrated photonic circuits based on programmable MZIs have been proposed to perform various linear functions, such as MVM, which behaves similarly to the field programmable gate arrays in electronic integrated circuits [45]. The MZIs, as basic building blocks, consist of thermal phase shifters with a large footprint, which impede very large-scale integration of PICs. In this section, we propose pixelated non-volatile programmable PICs based on the multi-level intermediate states of Sb₂S₃ pixels, as shown in figure 5(a). The low-loss Sb₂S₃ is first deposited on the multimode interferometer (MMI) and waveguide, after which a movable laser spot is focused on the different Sb₂S₃ pixels to induce partial crystallization. The Sb₂S₃ pixels are then switched to intermediate states to affect light propagation. In this paper, we simulated two fundamental pixelated programmable photonic integrated devices, i.e. programmable MZI and MMI, to demonstrate the feasibility of the programmable Sb₂S₃ matrix in PICs, as shown in figures 5(b) and (c). The multi-level intermediate states of Sb₂S₃ used in the simulation are determined by our experimentally characterized Sb₂S₃ thin film. The cross-section of the sample is shown in figure 6(a), which is consistent with the structure used in simulation. The thickness of Sb₂S₃ film is 10 nm, which was determined through simulation optimization. Additionally, a 200 nm-thick Si₃N₄ film was prepared for waveguides. Five-level intermediate states of 10 nm-thick Sb₂S₃ pixels were realized experimentally; see the micro images in figure 6(b). The diameter of phase-transition pixels is 1 μm, which corresponds to the spot size of the focused laser. Based on the reflectance of the Sb₂S₃ pixels at intermediate states, the crystalline fraction can be determined, and the effective permittivity (${\varepsilon _{{\text{eff}}}}$) and the refractive index of intermediate Sb₂S₃ pixels can be calculated according to the effective medium theory [46] (see more details in the supplementary materials).

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Firstly, we simulated the symmetrical MZI at 785 nm wavelength. A Sb₂S₃ film was assumed to be deposited on two arms of the MZI to modulate the optical phase without damaging the unitary properties. The width and height of the Si₃N₄ waveguide are 500 nm and 200 nm respectively, to determine the single-mode condition. Because the thickness of the Sb₂S₃ film affects the optical mode in the waveguides and therefore, the phase modulation and the optical loss, we simulated Sb₂S₃ films of different thicknesses (from 10 nm to 30 nm) on the waveguides to determine the appropriate thickness of the Sb₂S₃ layer for phase modulation. The figure of merit (FOM) $\Delta {n_{{\text{eff}}}}/\Delta {k_{{\text{eff}}}}$ was used to estimate the loss of the cSbS phase shifters, and $L\pi$ is the length of the Sb₂S₃ patch to realize the π phase shift in each waveguide arm. The simulated results are shown in figure 7(b). Apparently, a thinner Sb₂S₃ film with a larger $L\pi$ corresponds to a higher FOM. In addition, the mode overlaps between bare waveguides and waveguides covered with Sb₂S₃ are higher for thinner Sb₂S₃ films. The simulated results of mode overlaps are shown in figure S5. This means that the 10 nm-thick Sb₂S₃ film has a lower optical insertion loss. Thus, a 10 nm-thick Sb₂S₃ matrix was applied in the MZIs, and the simulation electric field intensity profile can be seen in figure 7(a). By combining the 5-level intermediate states and the number of laser-writing Sb₂S₃ pixels, we simulated the 30-level transmission of bar and cross output (E_{o 1} and E_{o 2}), as shown in figure 7(c). It is worth noting that the simulated MZI can return to the initial state by inducing Sb₂S₃ pixels to the initial amorphous state [29].

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In addition, we studied the programmable Si₃N₄ MMI based on the Sb₂S₃ matrix to perform a 1 × 2 switch at a 785 nm wavelength in simulation. As shown in figure 8, the width and length of Sb₂S₃ matrix are 4 μm and 17 μm, respectively. The size of a reconfigurable Sb₂S₃ pixel is 1 × 1 μm, and the thickness of Sb₂S₃ film remains the same as before (i.e. 10 nm). The total number of pixels is 68 (4 × 17). The Sb₂S₃ pixels are in the initial amorphous state, and the MMI performs a 50:50 power split, as shown in figures 8(a) and (b). To switch the optical power to the lower waveguide, we optimize the intermediate states of the Sb₂S₃ matrix in the MMI region based on a multiple-value search algorithm. Each Sb₂S₃ pixel has six intermediate states, which correspond to six refractive index values, i.e. 2.75 (aSbS), $3.042 + 0.000777i$ (iSbS₁), $3.355 + 0.00182i$ (iSbS₂), $3.561 + 0.002635i$ (iSbS₃), $3.643 + 0.002985i$ (iSbS₄), $3.819 + 0.0038i$ (cSbS), which have been experimentally determined in the previous section. Similar to the direct-binary-search algorithm, we provide a random pattern as the initial guess. The state of one Sb₂S₃ pixel is switched, and the FOM is simulated in one simulation. The state of the pixel is retained if the FOM is improved; otherwise, the pixel is brought back to its previous state. In this way, all 68 pixels with 6 values are simulated in one iteration. When the FOM stops improving after several iterations, we can ensure that the best results are obtained. As shown in figures 8(c) and (d), 84.50% transmission of the lower waveguide is obtained. For comparison, we also optimized the same Sb₂S₃ matrix size but with only two states for each pixel, i.e. aSbS and cSbS. The simulated results along with the pattern of the Sb₂S₃ matrix are shown in figures 8(d) and (f). The transmission (77.47%) of the binary Sb₂S₃ matrix configuration is apparently lower than that of the multi-level Sb₂S₃ matrix. The simulated results of the programmable MMI demonstrate the superior performance achieved with the multi-level Sb₂S₃ compared to binary Sb₂S₃. Moreover, the multi-level Sb₂S₃ induced by the focused laser pulses has more potential applications in programmable PICs and metasurfaces than the Sb₂S₃ with only binary states. As an example, we proposed and simulated a single-layer continuous varifocal metalens based on multi-level Sb₂S₃ pixels. More details of the metalens can be found in the supplementary materials.

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To validate the proposed pixelated PICs, an MZI-based photonic linear processor that uses Sb₂S₃-based pixelated phase shifters is realized by simulation, as shown in figure 9. The structure of the photonic linear processor is shown in figure 1, and the Sb₂S₃-based phase shifters with 30-level/π accuracy are used in the photonic linear processor. The photonic linear processor is used to perform convolution between kernels and an image, as shown in figure 9(a). The photonic system with nine inputs can perform simultaneous convolution on an image with nine 3 × 3 kernels. Each 3 × 3 kernel filter is flattened into a 1 × 9 row vector, and the resulting nine kernel vectors form the 9 × 9 kernel matrix M. Then the kernel matrix M is decomposed as $M = U\Sigma {V^{\,\dagger} }$ based on singular value decomposition. U and ${V^{\,\dagger} }$ are unitary matrices, which can be decomposed into multiple cascaded MZIs using the Clements' scheme [47], and the diagonal matrix Σ is implemented by a column of MZIs. The raw image is divided into multiple 3 × 3 patches, and then flattened into column vectors as inputs. The input signals propagate through the Sb₂S₃-based kernel matrix to realize MVM and convolution. The nine outputs from o₁ to o₉ correspond to nine kernel filters, and the sequence of outputs is reshaped into processed images. The raw image and processed images are shown in figure 9(a). The whole pixelated kernel matrix and Sb₂S₃-based phase shift values are shown in figure S7.

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To validate the accuracy of pixelated kernel matrix in very large-scale PICs, we generated random unitary matrices U(16) and U(64). The unitary matrices are decomposed into cascaded MZIs, and the phase shifters are discretized into multi-level phase values. The inner phase shifts θ (range from 0 to π) are discretized to 30-level phase values, and the outer phase shifters φ (range from −π to π) are discretized into 60-level phase values. Then the discrete matrices (U_P(16) and U_P(64)) and the error matrices are shown in figure 9(b). Moreover, a standard measure of fidelity is used to quantify the performance of the pixelated matrix. The fidelity is given by

$$\begin{align}F = {\left| {\frac{{tr\left(U{P^\dagger }U\right)}}{{\sqrt {N \times tr\left({U^\dagger }U\right)} }}} \right|^2},\end{align} \tag{ 3 }$$

where N is the number of inputs. The simulated fidelity of pixelated matrices is shown in figure 9(c). The fidelity of the very large-scale MZI mesh (100 × 100) is maintained at above 90%. Overall, the simulation results indicate that the pixelated programmable MZI-based photonic linear processor has the potential to be scaled up to a large size.

Sb₂S₃ thin films were deposited on the silicon substrates (N-type, 100) under vacuum by RF magnetron sputtering using an Sb₂S₃ target. Ar gas was introduced into the chamber at a flow rate of 20 sccm, and the magnetron sputtering power was 20 W. The deposited speed was 1.37 nm·min⁻¹, which was measured by an optical ellipsometer. Then, a SiO₂ cladding layer was deposited by PECVD at 100 °C, which is lower than the crystalline temperature of Sb₂S₃.

The proposed pixelated PICs can be fabricated based on the existing silicon photonics fabrication technology. The suggested fabrication process can be detailed as follows.

A 200 nm-thick Si₃N₄ film is deposited on SiO₂ (2 μm) on the silicon substrates by PECVD process, after which the photonic circuits can be fabricated using three-step deep ultraviolet lithography or electron-beam lithography process. The first lithography step is prepared for fabricating alignment markers. The resist that is spin-coated on the wafer is selectively exposed for making the alignment markers. Then the resist is developed using specific solvents. The gold and chromium are evaporated over the whole wafer by electron-beam evaporation. The sacrificial layer (unexposed resist) is washed away in acetone, and the gold on the sacrificial layer is lifted off together with the sacrificial layer. Then, the gold in direct contact with the substrate remains and is formed into alignment markers. The second lithography step is used to fabricate the Si₃N₄ waveguides. The lithography process is similar to the first lithography step. The distinct steps involve replacing the lift-off process with an etching process. The Si₃N₄ film is etched by the inductively coupled plasma etching. Then the resist is removed in acetone. The third lithography process is used to fabricate the Sb₂S₃ pixels. The fabrication process is similar to the first step. The Sb₂S₃ material is deposited by RF magnetron sputtering (in the section 5.1). Finally, the chip is cladded by the SiO₂ as a protective layer via low-temperature PECVD.

After fabricating PICs, the pulsed laser writing system can be used to create pixelated non-volatile programmable PICs, see more details in section 3.2. By controlling the position of the laser beam with the objective lens and the sample stage, a programmable Sb₂S₃ matrix can be achieved. The resolution of the laser writing system is only limited by the optical diffractive limit. The laser power and the number of laser pulses are controlled to induce multi-level intermediate states of the Sb₂S₃ pixels. The states and phase values of the Sb₂S₃ pixels are determined by the calibration experiments, as detailed in sections 2 and 3.