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Abstract
Photonic memory provides optics the opportunity for upgrading data storage hardware and shows great promise in future computing hardware due to its innate superiority in speed, power consumption and bandwidth. Chalcogenide phase-change materials (PCMs) such as Ge2Sb2Te5 (GST) are one of the most promising non-volatile storage materials and have been used for on-chip photonic integration circuits (PIC). Here, we explore the transmission contrast and the thermal distribution produced by different spatial structures of GST cells in photonic memory including geometric shapes, vertical positions and array distributions. We design the geometric shape of GST cells in photonic memory that matches the optical field distribution profile, causing a more than 20% increase in transmission contrast. We then set the vertical position of GST cells embedded in waveguides where the GST cell is overlapping most with the waveguide propagation mode, increasing the transmission contrast by more than 50%. Engineering the surrounding cladding layer is also an effective method to improve the transmission contrast (>10%). Beyond that, selecting a suitable size of the gap can obtain a better balance between the storage capacity and the thermal management in uniform GST arrays while the non-uniform array can further improve the thermal uniformity. Our studies indicate that spatial distribution optimization of light storage media is necessary to develop low-energy-consumption on-chip PIC.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-performance memories are essential to drive the rapid development of the Internet of Things (IoT), big data analytics and cloud computing. However, the existing electronic memory hardware cannot fully meet the requirements of ultrafast large-scale data processing, although PCRAM [1,2], RRAM [3], MRAM [4], FeRAM [5] and two-dimensional (2D) material memories [6,7] have been substantially optimized for speeding up data storage. Optics is proved to be a better way to achieve fast data transmission, and optical interconnects [8] have been developed for multicore on-chip low-latency communications in the last decade. Attributing to the advantages of high speed, low energy consumption, low heat dissipation and high bandwidth [9,10], optical technology has provided an alternative opportunity for memory, which can significantly advance the parallel data processing [11–14].
PCMs have been widely used in optical rewritable storage and solid-state memory technologies due to their substantial optical and electrical contrasts [15] between their metastable amorphous and crystalline phases. The phase transition can be achieved by electrical, optical and thermal stimulations, with nanosecond switching speed [2,16,17], high durability [18] and long retention time [19]. Non-volatile photonic memory with the above superiority has been successfully demonstrated by the incorporation of thin-film PCMs on top of optical waveguides [20–23] and used for on-chip PIC such as photonic neural network [24,25] and photonic tensor core [13]. For the PCMs-based photonic memory, the crystalline PCMs absorb most optical signals representing minimum level while the amorphous PCMs transmit most optical signals representing maximum level with intermediate levels achieved in-between them [20]. Additionally, in a fully optical addressing photonic memory, information is written or erased by optical thermal switching of PCMs [26,27]. Optical transmission contrast and the dynamic heating profile uniformity during the switching, notably affecting the storage density (number of memory levels) and the switching energy, determine the performance of photonic memory.
Here, we propose a scheme for optimizing the spatial structure of PCMs in photonic memory from geometric shapes, vertical position and array distribution. By rational design of geometric shapes, we can increase the transmission contrast by more than 20%. The vertical position of PCMs in the waveguide can be optimized to further enhance the transmission contrast (∼ 50%), significantly improving the storage capacity and the optical modulation ability. On the other hand, using an isolated PCM array especially a non-uniform array rather than a thin film patch leads to a more uniform temperature distribution under optical pulse switching, which could potentially reduce the switching energy and enhance the switching controllability. The proposed optimization strategies on the spatial structure of PCMs are experimentally practical to increase the storage capacity while lowering the switching energy of photonic memory for high-performance applications in on-chip PIC.
2. Methods
All simulations are done in Lumerical DEVICE Suite (Ansys). The simulation of optical field distribution is obtained by using the FDTD module. A 1550-nm laser with TE fundamental mode is employed to investigate optical field distribution after modulating by PCM. The input power of the light source is 15 mW. The TE polarization fraction is 99.08% and the waveguide TE / TM fraction is 90.72% / 76.52% in the mode source. The length (optical field propagation direction), width and height of the straight Si3N4 waveguide are 10 µm, 1.3 µm and 0.33 µm in turn. The material of the substrate and the cladding layer are SiO2 and air, respectively. We use Ge2Sb2Te5 (GST) as the modulator and its thickness is 10 nm. All the boundary conditions of simulation regions are set as Perfectly Matched Layer (PML). The investigation of temperature distribution in these photonic memory units is employed using the HEAT module. In the thermal simulations, the programming optical pulse is 80-ns width and the heat absorption of GST cells as the heat source can be obtained in the power absorbed analysis of the FDTD module. The boundary condition of the thermal simulation region in the z-min direction is constant at 300 K. And the convection between any two of the above materials is constant at 300 K and 10 W/m2 K. The optical and thermal performance parameters of materials in the FDTD and Heat simulation are all shown in Table 1.
Table 1. Optical and thermal parameters of the materials used in the simulations including refractive index (n), thermal conductivity (k), specific heat capacity (c) and density (ρ), which are taken from reference 21.
3. Results and discussions
3.1 Geometry shapes of PCMs
Firstly, we compared the optical modulation ability of PCM patches with different geometry shapes by Finite Difference Time Domain (FDTD) simulations. The well-studied Ge2Sb2Te5 (GST) is used as a non-volatile modulator and a 1550-nm light with transverse electric (TE) polarization is set as the input light source in the simulations. Figure 1(a)-(c) show the schematic of photonic memory units, where GST patches are placed above the Si3N4 waveguides and the patches are rectangular, triangular and elliptical, respectively. The GST patches with different geometry shapes have the same thickness (10 nm) and the contact surface area. For the case of amorphous GST (aGST), the electric field (E-field) distributions of the photonic memory units with different shapes show a very similar profile (the upper pictures in Fig. 1(d)-(f)) with the optical transmission (Tra) variation at the output of the waveguide less than 0.5%. Whereas, crystallization forces absorption of the triangular and elliptical GST patches (cGST) to become stronger than that of the conventional rectangular patch, resulting in less optical transmission (Trc).
Fig. 1. FDTD simulations of the photonic memory units with the single GST patch. (a)-(c), Schematics show the photonic memory units with rectangular (a), triangular (b) and elliptical (c) GST patches, respectively. Optical transmission is labeled by the red arrow. (d)-(f), E-field distributions on the surface of the waveguides with the aGST (top) and cGST (bottom) cells, with rectangular (d), triangular (e) and elliptical (f) patches corresponding to (a)-(c) in turn.
To uncover the difference more obviously, we calculated the transmission ratio α (α = 10lg(Tra/Trc)) in these photonic memory units, shown in Fig. 2(a). The length L of GST patches in Fig. 2(a) is intentionally selected to keep the area unchanged (L × W = W × L1/2 = W × L2/4 = constant). With the width W increasing from 0.8 to 1.3 mm, the corresponding length (L2) of elliptical GST decreases from 1.3 to 0.8 µm and a significant decrease in the transmission ratios α of the rectangular and elliptical devices is observed, whereas the α of the triangular patch is barely changed. For the width W less than 1.15 µm, the elliptical patch is superior in the α to the other two shapes. On the contrary, the triangular patch shows the highest α when W is larger than 1.15 µm. The influence of geometry on the transmission contrast is caused by the inhomogeneous optical field distribution along the waveguide as well as in the cross-section of the waveguide, which is the strongest in the middle gradually decaying to the edges [27]. It is obvious that the larger the overlapping of patches with high optical fields, the higher the transmission difference can be achieved. The overlap integral (OI) of the optical mode with the GST patches are calculated by the following expression Eq. (1):
Fig. 2. Performance of the photonic memory units with the single GST patch. (a)-(c), Transmission ratio Tra/Trc (a), overlap integral OI (b) and insertion loss (c) as a function of the width W of the patches with the same area and different shapes. (d) and (e), Transmission ratio Tra/Trc (d) and insertion loss (e) as a function of the area of the patches with the same width W and different shapes. (f), Transmission Tr of the rectangular cGST (solid black square) and aGST (hollow black square) patches with W = 1.3 µm in Fig. 2(a), and their transmission ratio Tra/Trc (red disk) with the change of wavelength λ.
We further analyzed the influence of the length L during optical transmission. Similarly, the widths of GST patches (W = 1.3 µm) remained and the length L increased, i.e. L1 = 2L and L2 = 4L/π, keeping the same surface area of different shapes. The result of simulations (Fig. 2(d)) indicate that the transmission ratio α increases as the area (length) increases. Meanwhile, the α values of triangular and elliptical devices keep similar, and both are larger than that of regular rectangular devices. Although the expansion of GST area produces a significant increase in the transmission contrast, the insertion loss also increases rapidly as shown in Fig. 2(e). On the contrary, the geometry shapes of GST patches have little effect on insertion loss. For most applications based on large-scale photonic networks, GST patches with strong insertion loss are not preferable. For this reason, geometry optimization is essential to enhance the transmission contrast. To make our conclusions more general, we calculated Tra, Trc and Tra/Trc of the rectangular GST patch operated in the C-band (1525-1565 nm) in Fig. 2(f). The size of the rectangular GST patch is the same as the one with W = 1.3 µm in Fig. 2(a). Trc of the rectangular patch is less than 55% and the transmission contrast is over 2 dB, which indicates the designed photonic memory units have enough transmission contrast to support the function of reading and writing.
The above simulations indicate the structural engineering of GST patches is efficient in enlarging the optical transmission contrast which determines the storage capacity of photonic memory units. A larger transmission contrast can be achieved by optimizing the PCM shape to match the optical field distribution profile. By replacing the regular rectangular PCM (the same width as the waveguide, i.e. W = 1.3 µm in Fig. 2(a), α = 2.175 dB) used for conventional photonic memory [20] with triangular and elliptical patches, the transmission contrast is 2.467 dB and 2.622 dB respectively with an increase more than 20%. Further engineering of the waveguide structure (e.g. photonic crystals and plasmonic) together with the shape optimization, we expect an even larger storage capacity of photonic memories.
3.2 Spatial position optimization of PCMs
Next, we examined the effect of the vertical position of PCM cells embedded in waveguides on the transmission contrast. Figure 3(a) and 3(b) show the schematic of the photonic memory unit with a GST patch embedded inside the waveguide. Both W and L were set as constant (W = 1.3 µm and L = 1 µm), while the depth d of patches varied. Starting from the top surface (d = 0) of the waveguide, we gradually increased the vertical depth until the patch touched the SiO2 layer (d = 330 nm). From Fig. 3(c) and 3(d), we can see that the optical field distributions are heavily dependent on the vertical location of the GST patch. We keep the widths and areas of different GST shapes the same as the rectangular patches, i.e. W = 1.3 µm, L = 1 µm, L1 = 2L and L2 = 4L/π. With the increase of d, the transmission ratio presents a trend which ascends at first and then descends independent of the geometry shape of GST patches, with the maximum value obtained at d = 140 nm, as shown in Fig. 3(e). Notably, the maximum transmission ratio corresponds to the d where the GST patch is overlapping most with the waveguide propagation mode (see the middle panel of Fig. 3(d)). The optical absorption of the crystalline patch at the bottom (d = 330 nm) is much higher than the case at the top surface of the waveguide (d = 0) due to the asymmetric cladding layers below and above the waveguide. By replacing the top cladding layer (air) with SiO2, the optical absorption of the crystalline modulation media on top of the waveguide can be significantly increased resulting in an improved optical transmission contrast of more than 10% (Table 2). Notably, the embedded device can be fabricated by conventional nanofabrication techniques. Firstly, PCM film is deposited on a silicon or silicon nitride wafer, followed by the growth (e.g. PECVD) of the waveguide material resulting in a sandwiched structure with embedded PCM film. Afterwards, the waveguide structure can be defined by electron beam lithography (EBL) and reactive ion etching (RIE).
Fig. 3. Photonic memory units with GST patches in different embedded positions. (a) and (b), Schematics show the photonic memory unit with the GST patch embedded inside the waveguide with 3D (a) and cross-section (b) views. (c), E-field distributions at the surface of waveguide with cGST at different locations of the waveguide: surface (top chart), center (middle chart) and bottom (bottom chart) of the waveguide. Dashed boxes denote the boundary of cGST. (d), E-field profiles of the waveguide cross-section with cGST at the surface (top), center (middle) and bottom (bottom chart) of the waveguide, denoted by dashed lines. (e), Transmission ratio Tra/Trc changes along with the depth d of GST in the waveguide.
Table 2. Tra, Trc, Tra/Trc and insertion loss in GST photonic memory units, with different cladding layers.
3.3 Optimization of the thermal uniformity of PCM arrays for practical optical switching
Compared with a single patch, PCM arrays have stronger light-matter interaction resulting in larger optical contrast, which has been used for photonic memory realizing multi-level storage even analog information storage by amplitude modulation [28,29] and mode conversion [25], etc. In this section, we studied the light modulation and dynamic temperature distribution under switching of PCM arrays with various structures. While the optical modulation contrast determines the storage capacity, the thermal uniformity is related to the recrystallization process and the energy consumption [21]. We place three GST patches along the direction of optical transmission (x-direction) with a gap g (Figs. 4(a) and (b)). The widths of patches are fixed at W = 1.3 µm with different lengths, l1, l2 and l3, respectively. We investigated two different photonic memory structures with uniform (l1 = l2 = l3) and non-uniform (at least one length is different from others) GST arrays, defined as structure S2 and S3 respectively. Above all, we compared the light modulation of array-based photonic memory units with the conventional type of single patch (S1), and the total areas were same, as shown in Fig. 4(c). For the case of cGST, S2 and S3 show similar optical transmission slightly higher than S1. Figure 4(d) illustrates that the optical transmission of S2 depends on gap size (g). With the increasing of g, the optical transmission of the aGST arrays is nearly unchanged while that of crystalline arrays is slightly increasing yet with enough optical contrast between amorphous and crystalline states.
Fig. 4. Photonic memory units with rectangular GST arrays. (a) and (b), Schematics show the perspective (a) and cross-section (b) views of the photonic memory unit with the GST array along the x-axis. (c) E-field distributions on the surface of the waveguides with different GST structures (S1, S2 and S3): the cGST film (S1, L = 1 µm), the uniform distributed cGST array (S2, l1 = l2 = l3 = 0.333 µm, g = 0.3 µm) and the non-uniform distributed cGST array (S3, l1 = 0.31 µm, l2 = 0.29 µm, l3 = 0.4 µm, g = 0.3 µm). (d) Transmission Tr of the uniform distributed cGST (solid black square) and aGST (hollow black square) arrays, and their transmission ratio Tra/Trc (red disk) with the change of g.
Subsequently, we investigated the thermal uniformity of PCM arrays programmed by optical pulses. Figure 5(a)-(c) show the temperature distribution of GST cells with different structures after 80-ns laser modulation. As described in Fig. 5(a), the non-uniform thermal effect caused by light absorption will result in a large temperature difference between the center section and the edge section of S1, which leads to poor control of the crystallization process and energy waste. Relatively, the temperature profile of S2 is more uniform with multiple temperature peaks in the whole array (Fig. 5(b)). For S3, we intentionally reduced the length of the GST patch with higher temperature distribution (i.e. L1 and L2) and increased that with the lowest temperature distribution (i.e. L3) appropriately, which indeed has raised the temperature distribution in the rightmost GST patch. The temperature uniformity can be further increased by replacing the uniform S2 structure with the non-uniform S3 structure (Fig. 5(c)). Under the stimulation of an 80-ns single optical pulse, the dynamic temperature response in the time domain of different positions in S1, S2 and S3 are calculated in Fig. 5(d). After the pulse is generated, the trend of temperature change is very similar for different structures where the temperature at the center point is always the highest and that at the edges is much lower. However, the temperature discrepancy in S2 and S3 is smaller than in S1, indicating a better temperature uniformity in GST arrays. In search of the optimal structure, we statistically analyzed the temperature distribution of these photonic memory units, the results of which were shown in Fig. 5(e). With the increase of g, the standard deviation (SD) of the temperature distribution in uniform GST arrays descends gradually. Only when g is greater than 0.2 µm, the standard deviation (SD) of the uniform GST arrays is less than that of the GST patch. Considering the tradeoff between the transmission ratio (Fig. 4(d)) and the thermal uniformity, the appropriate gap is 0.2 ∼ 0.3 µm. The temperature distribution of the non-uniform array (S3, g = 0.3 µm) is also calculated and shows a smaller SD than S2 (g = 0.3 µm). Thus, the optical modulation ability and the thermal uniformity of PCM arrays need to be balanced by controlling the size of gaps. Besides, the non-uniform structure can further improve the thermal uniformity with the same optical modulation ability of the uniform structure. The statistical results of optical modulation ability and thermal uniformity of S1, S2 and S3 are summarized in Table 3, which shows the above conclusion more clearly. We need to clarify that the results on PCM array are based on a very small area (1.3 µm × 1.0 µm in total) of GST patches and the array parameters (such as number of patches and patch size) have not been optimized. With a larger area of GST patches and optimized array parameters, the uniformity of the temperature distribution could be further improved, while keeping the transmission contrast (mainly depends on the area) at a high level. With a better thermal uniformity of GST, the energy efficiency and damage threshold of the device can be improved. Moreover, PCM arrays have more optical field penetration and weaker resonance effects resulting in better switch controllability [28], which is suitable for photonic memory realizing multi-level storage even analog information storage.
Fig. 5. Heat simulations of the photonic memory units. (a)-(c), Temperature distribution on the waveguide surface after 80-ns laser modulation, and corresponding temperature profiles along the center lines (white dotted lines) of the waveguide surface. These photonic memory units have different structures: single patch S1 (a), uniform array S2 (b) and non-uniform array S3 (c). (d), The transient temperature profiles of S1 (top panel), S2 (middle panel) and S3 (bottom panel) at three different positions, denoted by the hollow disks in the bottom panels of (a), (b) and (c) respectively. (e), Statistical results of the temperature distribution along the centerline of the GST as a function of g with different GST structures. The insert shows the standard deviation (SD, Tstd) of the temperature distribution and its x-axis corresponds to that of the figure. S1: black, S2: blue, S3: red.
Table 3. Comparison of optical modulation ability and temperature distributions of S1, S2 and S3.
4. Conclusion
In summary, we develop strategies to improve the storage capacity and the thermal efficiency of photonic memory by optimizing the spatial structure and array distribution of PCM cells with numerical methods. For the single patch, the triangular and elliptical cells are superior to the conventional rectangular one in optical contrast due to the larger overlapping area with the optical field distribution. The optical contrast can be further enhanced by adjusting the vertical location of PCM cells or adding a cladding layer. Going even further, selecting a suitable size of the gap can obtain a better balance between the storage capacity and the thermal performance in uniform PCM arrays while the non-uniform structure can further improve the thermal uniformity effectively. Our studies provide a practicable methodology to increase the storage capacity, improve the damage threshold, facilitate the switching controllability and lower the energy consumption of photonic non-volatile memory using PCMs, which is beneficial for developing applicable on-chip PIC.
Funding
National Key Research and Development Program of China (2020YFA0308800); National Natural Science Foundation of China (62074042); Science and Technology Commission of Shanghai Municipality (20501130100); the Young Scientist Project of MOE Innovation Platform; the start-up funding from Fudan University.
Acknowledgments
This research was sponsored by National Key Research and Development Program of China (2020YFA0308800), National Natural Science Foundation of China (62074042), Science and Technology Commission of Shanghai Municipality (20501130100), the Young Scientist Project of MOE Innovation Platform and the start-up funding from Fudan University.
Disclosures
The authors declare no conflict of interest.
Data availability
All data underlying the results are presented in this article. Additional data related to the study may be obtained from the corresponding author.
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