1. Introduction

In the rapidly evolving landscape of information technology, the demands for computational power are experiencing an exponential surge, far outpacing our ability to scale the performance of current-generation computing technologies [1]. In this context, neuromorphic computing emerges as a solution to address the latency and power consumption issues associated with the Von Neumann architecture. It utilizes a bio-inspired paradigm where the processing unit serves dual roles as both the processor and the memory, giving rise to a concept known as in-memory computing [2]. In this context, integrated photonics offers a well-suited technological platform for building neuromorphic computing hardware. Indeed, photonics unique advantages, such as minimal interference between wavelengths of information propagating through a fast-light medium with minimal losses, facilitate large-scale parallel operations with comparatively lower latency and power consumption [3–6].

The hybrid barium titanate (BTO) – silicon nitride (SiN) platform may offer significant advantages for neuromorphic computing by combining the unique properties of BTO and SiN to enable high-performance photonic integrated circuits with high operation speeds and low transmission losses [7,8]. This novel platform developed for datacom is particularly noteworthy due to the incorporation of the Pockels effect provided by the BTO and its compatibility with standard silicon processing techniques [9]. However, despite one of the largest Pockels coefficients among the non-centrosymmetric electro-optic materials, device footprints in the order of millimeters are necessary to achieve substantial modulation depths, which may compromise the scalability requirements for neuromorphic computing [10]. To address this challenge, we propose incorporating an additional active material into the SiN/BTO platform to provide amplitude switching with ultra-compact footprints. The family of phase change materials (PCMs), which have garnered considerable interest recently, are compelling for neuromorphic photonics [11–15]. Their interest lies in the possibility of changing their phase reversibly, usually by heating the material. The phase change implies a large contrast in refractive index and absorption. This transition can be triggered either all-optically—optical heating—or electronically using a microheater configuration [16]. The family of PCMs for photonics comprises various alloys, the most popular being the chalcogenides [17] and metal-transition oxides such as VO₂ [18]. Vanadium dioxide (VO₂) showcases a reversible transition known as the insulator-to-metal transition (IMT). The phase transition manifests at an approximate temperature of 70 °C, in which a strong modulation of the complex refractive index occurs (Δn > 1, Δκ > 2) with broadband response [19], as compared with the ∼ 600 °C phase transition of chalcogenide PCMs. Such a feature would enable neuromorphic systems with much lower energy consumption per synaptic event. Furthermore, the analogic and hysteretic behavior of the IMT transition can be leveraged to enhance functionalities. Thus, devices based on VO₂/Si and VO₂/SiN waveguide devices, such as modulators, photonic memories or optical limiters, have already been demonstrated in the literature [20–25].

Within this context, we propose the integration of VO₂ in the BTO/SiN platform to enable new building blocks with ultra-compact footprints for large-scale neuromorphic computing hardware. An electronically reprogrammable switching device is proposed to provide a scalar multiplication functionality with multilevel operation. A design strategy to achieve high accuracy and large-scale implementation is provided. The hybrid VO₂/SiN/BTO device operates by controlling the absorption variation of the VO₂ by locally heating with a microheater. The modelling of the VO₂ for designing the multilevel response of the hybrid device is also tackled. Furthermore, the use of a transparent conducting oxide for the microheater for a more efficient thermo-optical performance and strategies to improve the switching time and energy are discussed. Overall, such a new building block holds promise for expanding the use of the BTO/SiN platform for photonic neuromorphic computing in large-integration schemes.

2. Results and discussion

2.1 Description of the proposed device with scalar multiplication functionality

The proposed device and the cross-section are depicted in Figs. 1(a) and 1(b). It comprises an 80-nm-thick bottom layer of BTO overlaid with a SiN layer patterned to form a rib waveguide. To enable the scalar multiplication functionality, i.e., amplitude switching, a small patch of VO₂ is deposited on top of the SiN. The loss strength is determined by the state of the VO₂. For the insulating state (i-VO₂), the optical loss is low, whereas in the metallic state (m-VO₂) is high. Intermediate values with bistable (volatile memory) response can be obtained by partially triggering the insulator-metal transition of VO₂ and leveraging its hysteresis loop. In this case, the insulator-metal transition is controlled by locally heating the VO₂ using a microheater and Joule heating. On the other hand, the considered cross-section dimensions of the SiN/BTO waveguide (1.1 µm × 150 nm) are taken from [26]. The associated optical mode is shown in Fig. 1(c) for the transverse electric (TE) polarization.

 

Fig. 1. (a) Illustration and working principle of the proposed device with scalar multiplication functionality based on a hybrid VO₂/SiN/BTO waveguide. The multiplication feature is based on the absorption variation of the VO₂ caused by the insulator-metal transition, whereas its hysteresis loop is leveraged for bistable memory functionality. A multilevel operation can be achieved based on the analogic change of the VO₂ patch between its insulating and metallic phases. The VO₂ state is controlled by a microheater placed close and on top of the hybrid waveguide. Holding power is necessary to bias the temperature of the VO₂ within the hysteresis loop (see inset) to maintain the optical level. Heating and cooling electrical switching pulses are used to program and erase the optical level. (b) Cross-section of the proposed device. (c) Optical mode, E_x field component, of the SiN/BTO waveguide at λ = 1550 nm. The effective refractive index is 1.614.

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Theoretically, an infinite number of intermediate values could be achieved due to the analogic response of the IMT of VO₂ thin films. However, for practical purposes, the achievable number of optical levels is limited by the noise of other devices such as the laser stability or the thermal noise of the photodetector. Recent work on neuromorphic computing using photonic integrated circuits sets the quantization level between 0.1 and 0.2 dB [27,28]. The lower the quantization level, higher the computation accuracy but the weaker the signal-to-noise ratio (SNR), which could be for critical applications such as image recognition [28]. Therefore, for this work, we will consider 0.2 dB/level. On the other hand, the extinction ratio of the device is crucial because it determines the accuracy, i.e., the maximum number of levels (bits) that can be encoded, as shown in Fig. 2(a).

 

Fig. 2. (a) Required extinction ratio (ER) as a function of the number of bits. (b) Minimum achievable insertion loss (IL) as a function of the extinction ratio-insertion loss ratio, ER/IL, for a different number of bits. All results are calculated considering a quantization value of 0.2 dB/level.

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In absorption-based devices, large extinction ratios (ER) usually come with high insertion (IL), thereby limiting scalability. Such a limitation is illustrated in Fig. 2(b), where the minimum achievable insertion loss is plotted as a function of the extinction ratio-insertion loss ratio for different numbers of encoded bits considering 0.2 dB/level. In this regard, to achieve high accuracy and large-scale implementation (500-1000 components) [29], technologies such as VO₂ that deliver large value of ER/IL are required.

Usually, in photonic computing, scalability also is accompanied by cascadability, such as in photonic tensor cores to perform matrix-vector-multiplication or in neural networks to connect a certain number of layers. In this context, to allow cascadability an insertion loss below 1 dB per device is desired [5,30]. Therefore, according to Fig. 2(b) and considering that VO₂-waveguide devices could reach ER/IL between 10 and 20, we target 5-bit (ER = 6.2 dB) for our device, corresponding to an insertion loss of around 0.5 dB.

2.2 Design of the VO₂/SiN/BTO waveguide and multilevel operation

The dimensions of the VO₂ (width and thickness) are investigated to reach the required value of ER while minimizing the IL and footprint. To this end, we carried out finite element method (FEM) simulations using FemSIM tool from RSoft to obtain the optical modes of the hybrid VO₂/SiN/BTO waveguide and the associated complex effective refractive indices (${n_{\textrm{eff}}} + i{\kappa _{\textrm{eff}}}$). We consider the fundamental TE mode at a wavelength $\lambda = 1550$ nm. Simulations were carried out for the insulating and metallic state of the VO₂ and varying the thickness and width of the VO₂. The thickness was varied between 10 and 100 nm, whereas the width was swept between 100 and 500 nm. The refractive indices of the materials are BTO = 2.285, SiN = 1.996, SiO₂ = 1.45, i-VO₂ = 3.21 + i0.17 and m-VO₂ = 2.15 + i2.79 [26,31]. The simulation grid was non-uniform and set to 30 × 30 × 30 nm in bulk sections with 10 minimum divisions in each dimension.

By setting ER = 6.2 dB, we derived the corresponding length as $L = ER/|{{\alpha_m} - {\alpha_i}} |$, where α_m/i is the propagation loss constant in dB/µm for the metallic/insulating states of the VO2, which is obtained from the effective extinction coefficient, ${\kappa _{\textrm{eff}}}$, as ${\alpha _{i/m}} = 10{\log _{10}}(e )4\pi {\kappa _{\textrm{eff},i/m}}/\lambda $. Based on these lengths, the optical loss in the insulating state caused by the absorption of the VO₂ was calculated to select the optimal width-thickness configurations that fulfill our insertion loss requirements of 0.5 dB. Results are shown in Fig. 3(a). The optical loss shows a clear increase with the VO₂ width, higher than 0.5 dB, for values above 200 nm. On the other hand, the impact of the thickness becomes more pronounced as the VO₂ widens. This behavior is explained by the larger dependence of the propagation loss with the VO₂ thickness for wider than narrower patches. Figures 3(b) and 3(c) show the optical mode and the propagation loss value for 150-nm-wide VO₂, and 30 nm and 100 nm of thickness, respectively. Although the optical mode is quite different, which may give rise to coupling losses, the difference between the propagation losses is smaller than for wide VO₂ patches. This is showcased in Figs. 3(d) and 3(e), where we consider the same thickness values but for a 500-nm-wide VO₂. The difference between these values is much larger than in the previous case, as the optical field interacts more with the VO₂. Moreover, both values of propagation loss are significantly higher than for narrower VO₂ patches, resulting in large optical losses. Consequently, we restricted further optical analysis for VO₂ films narrower than 200 nm.

 

Fig. 3. (a) Optical loss of the hybrid VO₂/SiN/BTO waveguide as a function of the VO₂ width and for different thicknesses. The optical loss is calculated for the insulating state and the length required to fulfill an ER = 6.2 dB (5-bit). (b)-(e) Optical modes, E_x component, of the hybrid waveguide for different VO₂ widths and thicknesses. (b) 150 nm wide and 30 nm thick. (c) 150 mn wide and 100 nm thick. (d) 500 nm wide and 30 nm thick. (e) 500 nm wide and 100 nm thick. All results are calculated at λ = 1550 nm.

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We carried out 3D finite-difference time-domain (3D-FDTD) simulations using FullWAVE tool from RSoft to calculate the coupling loss between the reference SiN/BTO waveguide and hybrid VO₂/SiN/BTO waveguide for 100 nm, 150 nm, and 200 nm wide VO₂ films [see Fig. 4(a)]. Overall, low coupling losses (CL) are obtained for these widths and thin values because of the large field profile similarity between the reference and hybrid waveguide [see Figs. 1(c) and 3(b)]. As the VO₂ becomes thicker, the optical field interacts more with the VO₂ giving rise to a larger optical mismatch [see Figs. 1(c) and 3(c)]. Next, we calculated the insertion loss of the device as $IL = {\alpha _i}L + 2CL$. Such values and the associated length of the device are shown in Figs. 4(b) and 4(c), respectively. 100-nm-wide VO₂ patches deliver the lowest insertion losses of less than 0.5 dB and the longest lengths larger than 10 µm. By contrast, a width of 200 nm achieves devices as compact as 4 µm long but results in insertion losses higher than 0.5 dB. Therefore, a 150-nm-wide and 30-nm-thick VO₂ patch provides the best trade-off between insertion loss and footprint, resulting in an insertion loss as low as 0.45 dB in a hybrid waveguide length of just 9 µm. It is worth mentioning that possible deviations in the x-axis position of the VO₂ patch would not significantly affect the device specifications. The optimal design would exhibit robust performance even with a significant deviation of ±100 nm. In this scenario, the insertion loss is nearly unaffected, and the extinction ratio would drop from 6.2 to 6 dB. Hence, considering that the step difference between levels is 0.2 dB, this would imply losing just 1 level.

 

Fig. 4. Analysis of the optical loss and length of the hybrid waveguide as a function of the VO₂ thickness and for 100 nm, 150 nm, and 200 nm of VO₂ width. (a) Coupling loss. (b) Insertion loss. (c) Length of the device. Results are given at λ = 1550 nm and considering an ER = 6.2 dB (5 bit). The optimal configuration is selected for VO₂ width and 150 and 30 nm thickness, respectively.

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Once the geometry of the VO₂ has been established, the next step is to model the multilevel response of the hybrid waveguide by leveraging the analogic and hysteretic response of the IMT and determining the temperature of each level. To this end, the dielectric constant of mixed insulator-metal states, ${\varepsilon _{\textrm{EMT}}}$, occurring during the IMT of VO₂ are modeled based on Maxwell-Garnett effective medium theory [32], described as

The complex effective refractive index of the VO₂ as a function of the temperature during heating and cooling is shown in Fig. 5(a). Based on the values, we obtained the effective refractive indices of the hybrid waveguide for the intermediate states of the VO₂ patch and the associated optical loss from the effective extinction coefficient. Figure 5(b) shows the optical loss of the designed hybrid waveguide as a function of the temperature. 32 different hysteretic curves (levels) are obtained by changing the maximum temperature when the VO₂ is heated. The quantization value is around 0.2 dB/level. The holding temperature is established at 62.84 °C to retain a certain level, thereby enabling memory functionality. On the other hand, the switching temperature for each level is shown in Fig. 5(c), and the smallest switching temperature increment is around 0.2 °C.

 

Fig. 5. (a) Effective complex refractive index, ${n_{EMT}} + i{\kappa _{EMT}}$, of the VO₂ calculated using the Maxwell-Garnett effective medium theory. (b) 5-bit multilevel response of the hybrid waveguide as a function of the VO₂ temperature. The dashed line stands for the holding temperature (62.84 °C). (c) Necessary temperatures of the VO₂ to set the optical levels.

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We verified the multilevel response of the designed hybrid waveguide by 3D-FDTD simulations for the insulating state (level 1), a mixed insulator-metal state (level 17), and the metallic state (level 32). Figure 6 shows the Poynting vector, S_z, in linear scale for the three cases when the light comes from the SiN/BTO waveguide and passes through the 9-µm-long VO₂/SiN/BTO waveguide and the associated normalized S_z profile of the hybrid waveguide. For the insulating state (level 1), 3D-FDTD simulations [see Fig. 6(a)] give an insertion loss of 0.49 dB, which is in fair agreement with the value given by Fig. 5(b) (0.45 dB). In the mixed insulator-metal state (level 17), there is also good agreement between 3D-FDTD [Fig. 6(b)] (3.99 dB) and the value of Fig. 5(b) (4.09 dB). Such a small difference is because the field distribution suffers little change between levels 1 and 17, as can be noticed by comparing both S_z profiles [Figs. 6(a) and 6(b)]. Finally, for the metallic state (level 32), a slightly higher discrepancy in the insertion loss is found between 3D-FDTD (7.12 dB) and FEM (7.29 dB) simulations. This difference is attributed to the small variation in the S_z profile, as shown in Fig. 6(c). Nevertheless, differences in the insertion loss remain below the quantization level for all cases.

 

Fig. 6. 3D-FDTD simulations (Poynting vector, S_z) of the 9-µm-long VO₂/SiN/BTO waveguide in different states when the light comes from the SiN/BTO waveguide, producing scalar multiplication operation with different levels. The right plots show the associated optical mode, S_z, of the hybrid waveguide. (a) Insulating state (level 1). (b) Mixed insulating-metallic state (level 17). (c) Metallic state (level 32). Results are given at λ = 1550 nm.

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2.3 Design of the microheater

As shown in Fig. 1(a), a microheater is used in the proposed device for triggering the temperature of the VO₂ and enabling the multilevel operation. Microheaters have a compact footprint and offer a broad temperature range with precise control [35]. Metallic microheaters require relatively large gaps between the metal and hybrid waveguide, reducing the efficiency in the heat transmission and thus leading to higher power consumption and lower speeds [36]. A possible solution to reduce the gap and increase the thermo-optical performance is to replace the metal with a transparent conductive oxide (TCO) [37,38]. Therefore, the impact of the heater material on the optical performance was first analyzed by comparing titanium and a high-mobility TCO such as hydrogen-doped indium oxide (IHO) [39].

The dimensions for the microheater were 60 nm, 150 nm, and 11 µm for the thickness, width, and length, respectively. The complex refractive indices are n_Ti = 3.685 + i4.61 [40] and n_IHO = 1.755 + i0.01 [39]. Figs. 7(a) and 7(b) show the influence of the gap on the ER and IL, respectively, for the 9-µm-long VO₂/SiN/BTO waveguide with titanium and IHO microheaters placed on top. The IHO heater has a negligible influence on the IL, whereas the ER is only slightly reduced for small gaps. Such a small impact is caused by the negligible absorption of IHO. By contrast, IL and ER are drastically affected for the titanium heater because of its large extinction coefficient compared with IHO. Thus, the IHO heater is selected for the final device with a gap of 100 nm to avoid undesired coupling losses, i.e., keep the same performance as the hybrid waveguide without the heater.

 

Fig. 7. Comparison between a TCO-based heater using IHO and a titanium heater in terms of (a) ER, and (b) IL for the 9-µm-long VO₂/SiN/BTO waveguide. The dotted line stands for the optical response without the heater.

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The thermal response of the device was investigated by using COMSOL Multiphysics. Simulations were carried out using 3D-FEM in the steady-state and temporal domains. The microheater was set as the heat source, Q, and modeled as $Q = P/({{w_h}{t_h}{l_h}} )$, where P is the electrical power consumed by the microheater, and w_h, t_h, and l_h the microheater width, thickness, and length, respectively. The obtained thermo-electrical coefficient, i.e., the relation between the temperature increment of the VO₂ patch and the applied electrical power, is as high as ∼26.49 °C/mW for a background temperature of 20 °C.

Figure 8 shows the temperature distribution of the device in the steady-state regime for reaching level 32 (metallic state), which requires the highest temperature (76.5 °C) in the VO₂. The estimated electrical power is ∼2.13 mW. By estimating ∼4.87 kΩ for the resistance of the IHO microheater [39], we prospect a maximum voltage of ∼3.22 V, thereby being compatible with standard CMOS voltage levels used in microelectronics. On the other hand, the VO₂ patch is homogenously heated, as shown in Fig. 8(a). The temperature of the IHO heater reaches a value of 109 °C with a large temperature gradient [see Fig. 8(b)], requiring just ±3 µm in the x-axis to reach the background temperature. Hence, this would minimize possible thermal crosstalk to adjacent devices. Moreover, as heating is very localized and produced in compact regions of the chip, it is not foreseen an increment of the overall chip’s temperature and, thereby, undesired switching effects.

 

Fig. 8. Temperature distribution of the device in the steady-state regime for reaching level 32. (a) 3D and (b) XY cross-section representation of the hybrid waveguide with the IHO heater.

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Figure 9 showcases an example in the time domain of the multilevel operation of the device with memory functionality when switching among levels 1, 15, and 25 by applying 100-µs-long electrical pulses. The 10-90% heating/cooling time of VO₂ is ∼11.25 µs, and a holding power of ∼1.62 mW (62.84 °C) is required to maintain the VO₂ optical response within the hysteresis loop. An electrical pulse of ∼1.85 mW is first applied to switch from level 1 to level 25. This electrical power increases the temperature to the desired level (69.05 °C), as shown in Fig. 9(a), and thus the optical losses of the device increase to 5.75 dB of level 25, as depicted in Fig. 9(b). To switch to level 15, first, the VO₂ must be cooled down to reach level 1 (insulating state) and then heated again to the corresponding temperature for level 15. To this end, an electrical pulse with a power of ∼0.94 mW is applied, which sets the erasing threshold temperature to 45 °C, thus ensuring that the VO₂ has completely transitioned to the insulating state. In this manner, level 15 is reached by applying a new electrical pulse with lower power.

 

Fig. 9. Simulation of the multilevel operation of the hybrid VO₂/SiN/BTO waveguide with the IHO microheater showing: (a) the temperature evolution (solid blue line) associated with the electrical signal applied to the heater (dotted red line), and (b) the optical response of the device.

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Further improvements on the switching time and switching energy could be attained by engineering the electrical pulse. By increasing the heating rate, i.e., the peak power of the electrical pulse, the necessary time to reach a specific temperature as well as the generated heat volume would be decreased, yielding faster switching times and a reduction of the switching energy [19].

3. Conclusions

In conclusion, we have proposed utilizing VO₂ technology for enhancing the SiN/BTO integrated photonics platform with application in large-scale neuromorphic computing. Specifically, the insulator-metal transition of VO₂ and its hysteresis loop have been leveraged for developing an ultra-compact and low-loss scalar multiplication device with multivelel operation functionality. Our proposed device, based on a hybrid SiN/BTO waveguide with a 30-nm-thick and 150-nm-wide VO₂ patch placed atop, features a 5-bit amplitude resolution with an insertion loss of ∼0.5 dB in just 9 µm length. Efficient switching between optical levels is achieved by placing a transparent microheater based on IHO near the VO₂, thus increasing the thermo-optical efficiency without compromising the optical response in comparison with metallic heaters. Our device could be programmed using electrical pulses below 2.2 mW of a few microseconds and CMOS-compatible voltages. Therefore, the SiN/BTO platform could be benefited from a much higher integration density thanks to the dramatic reduction in the footprint of multiplication scalar devices from ∼mm to ∼µm lengths, thereby opening a path for implementing large-scale neuromorphic photonic computing.