The most straightforward approach to obtain flexible memristive arrays is directly depositing inorganic materials onto flexible substrates via thin-film fabrication processes, such as evaporation and sputtering. Until now, a large number of inorganic materials, such as AlO_x (Lee et al., 2017; Jang et al., 2018b), SiO_x (Yoon et al., 2018), WO_x (Lin et al., 2018), and HfAlO_x (Wang et al., 2020d; Wang et al., 2021c), have been fabricated as flexible resistive switching dielectrics by using this approach. For instance, J. Yoon et al. reported a 8 × 8 flexible SiO_x-based one diode–one resistor (1D-1R) memristive crossbar array on a plastic substrate by employing physical vapor deposition (PVD) technology (Yoon et al., 2018). The schematic of the SiO_x-based 1D-1R array is shown in Figure 2A. The fabricated 1D-1R devices exhibited robust electrical characteristics under the bending state with a radius of 8 mm, indicating an excellent mechanical flexibility (Figure 2B).

Most inorganic materials require high-temperature processes to guarantee the nucleation of particles and the quality of grown thin film. However, the extensively used flexible substrates only show low temperature tolerance (Wang et al., 2021c; Wang et al., 2021d), which limits the choice of inorganic materials. Hence, it is vital to develop low-temperature manufactural processes to prepare flexible memristive arrays for in-memory computing. Recently, Zhang’s group reported a series of studies on the use of low-temperature atomic layer deposition (ALD) technology to fabricate flexible memristive devices (Wang et al., 2021c; Wang et al., 2019; Wang et al., 2020d). This approach not only provides an atomically dense resistive switching layer with a precise control of thickness, but also is compatible with flexible fabrication process. Based on this method, a three dimensional (3D) flexible memristive crossbar array with the platinum (Pt)/HfAlO_x/tantalum mononitride (TaN) stack structure was fabricated on a PET substrate at 130°C (Figure 2C) (Wang et al., 2021c). Typical forms of synaptic plasticity, such as long-term potentiation (LTP), long-term depression (LTD), and paired pulse facilitation (PPF), have been successfully demonstrated in the electronic synapses. In addition, the memristive devices in the flexible 3D array could also maintain reliable LTP and LTD behaviors under the bending state with the bending radius of 10 mm. These developed flexible memristive arrays offer a promising way to implement the wearable in-memory computing system.

Organic materials often show better flexibility than inorganic materials, which are potential candidates for fabricating flexible memristive devices and arrays. Common organic materials, such as albumin (Chen et al., 2015), collagen (Zeng et al., 2019), silk fibroin (Kook et al., 2020; Wang et al., 2016a), polyethyleneimine (PEI) (Yang et al., 2020) and poly(1,3,5-trivinyl-1,3,5-trimethylcyclotrisiloxane) (pV₃D₃) (Jang et al., 2019; Jang J. et al., 2018a), have demonstrated their promising application in flexible memristive devices and arrays. By employing wafer-scale ultraviolet photolithography technology, a silk fibroin-based memristive array was successfully fabricated on a parylene-C film with robust flexibility (Kook et al., 2020). The fabricated memristive crossbar array shows robust flexibility (bendable to a radius of 1.3 mm) and reliable electrical performance (Figure 2D). With the utilization of initiated chemical vapor deposition (iCVD) approach, Jang et al. demonstrated a flexible memristive crossbar array with a copper (Cu)/pV₃D₃/aluminum (Al) structure for in-memory logic computing (Jang et al., 2018a). Each memristive unit in the array is connected to one selector to construct the one-selector–one-memristor (1S1M) architecture to alleviate the leakage current of the array. Typical logic operations such as NOT and NOR, were successfully implemented in the flexible pV₃D₃-based memristive crossbar array (Figures 2E,F).

Although organic materials often show excellent flexibility, the chemical stability of most organic materials is usually poor. The inferior chemical stability hinders the practical application of flexible organic memristive devices and arrays, e.g. medical equipment typically need to withstand a high temperature of 121°C during steam sterilization (Kuribara et al., 2012). In addition, the implementation of large-scale memristive arrays leads to inevitable heat dissipation, which further affects the reliability and stability of organic materials. Among various organic materials, copper phthalocyanines have been intensively explored due to their reliable chemical and thermal stability (Choi et al., 2008; Lv et al., 2019; Wang et al., 2016b; Wang et al., 2017; Zhou et al., 2021). Recently, as shown in Figures 2G,J. Zhou et al. reported a highly chemically and thermally stable flexible memristive array by using monochloro copper phthalocyanine (ClCuPc) materials (Zhou et al., 2021). Benefitting from the intrinsic high thermal stability of CuPc and the further improvement of air stability caused by chlorination, the fabricated memristive device could exhibit reliable resistive switching behavior at 300°C. Typical synaptic behaviors, such as PPF, paired-pulse depression (PPD), and spike-rate-dependent plasticity (SRDP), have been implemented in ClCuPc-based memristive devices. Furthermore, a 7 × 7 memristive crossbar array was constructed based on the ClCuPc memristive synapses, which was used to implement in-memory computing for game Tetris.

Apart from weak thermal stability, most organic materials are vulnerable to moisture, making organic-based memristive devices and arrays hard to maintain stable performance in a humid environment (Lee et al., 2020; Yuan et al., 2021). For instance, commonly reported organic memristive devices based on chitosan (Hosseini and Lee, 2015), pectin (Xu et al., 2019), perovskite materials (Hwang and Lee, 2017), and glucose (Park et al., 2018) usually exhibit poor water-resistance, and even water soluble. Hence, it is necessary to develop water-resistance organic flexible memristive devices and arrays for harsh environments (Lee et al., 2015). Lee et al. recently reported a flexible nitrocellulose-based memristive array with high water-resistance and mechanical flexibility (Lee et al., 2020). The fabricated memristive devices could exhibit reliable electrical switching behaviors after submersion in phosphate-buffered saline solution, artificial perspiration, and deionized water (Figures 2H,I). Moreover, the flexible memristive devices showed stable operations under the bending state with a radius of 10 mm (Figure 2J).

In addition to inorganic and organic materials, 2D materials have recently received extensive attention due to their unique structural characteristics, good mechanical flexibility, and excellent electrical properties (Kim et al., 2021a; Meng et al., 2021). Plenty of 2D materials such as graphene (Sun et al., 2017), transition metal dichalcogenides (TMD) (Feng et al., 2019; Zhao et al., 2018) and boron nitride (BN) (Ge et al., 2021; Qian et al., 2017; Siddiqui et al., 2017) have been well studied for flexible memristive arrays. For example, Wang et al. reported a flexible memristive array with the graphene/MoS_2–xO_x/graphene structure, which has good mechanical property and fabulous thermal stability (Figure 3A) (Wang et al., 2018a). The fabricated memristive device could exhibit reliable electrical performance after 1,200 bending cycles at a radius of curvature of 1 cm (Figure 3B). Recently, a flexible BN-based memristive array for in-memory computing was developed (Figure 3C) (Meng et al., 2021). The fabricated flexible BN-based memristive devices realized both in-memory digital and analogue computing, breaking the limitation caused by the difference in information form between digital data and analog data. The flexible memristive devices could implement FALSE,material implication (IMP) and NAND operations for in-memory digital computing (Figure 3D). In addition, the flexible memristive devices could also be used to realize the synaptic plasticity such as PPF, LTP/LTD and spike-timing-dependent plasticity (STDP) for in-memory analogue computing. Sneak current in the array is one of the primary issues limiting the high-density integration of memristive crossbar arrays. To solve this issue, Sun et al. developed a flexible self-selective memristive device based on a van der Waals heterostructure with the hexagonal boron nitride (h-BN)/graphene/h-BN structure (Figure 3E) (Sun et al., 2019). The middle graphene layer enables the volatile and non-volatile resistive behaviors in the same device, resulting in the self-selective effect. Based on the self-selective devices, a 12 × 12 memristive crossbar array was built, showing a promising application on future data storage in wearable artificial intelligence (Figure 3F).

Developing novel materials with ideal electrical and mechanical properties is an effective way to obtain stretchable memristive arrays. Recently, a stretchable SrTiO_3−x-based memristive crossbar array was successfully fabricated on a PDMS substrate via thin film deposition process (Rahman et al., 2018). In addition, a stretchable Ag₂S thin film-based memristive array has also been developed (Figure 4A) (Jo et al., 2021). The solution-processed Ag₂S film demonstrated excellent mechanical properties and could withstand a strain of 14.9%. Based on the stretchable memristive devices, a wearable self-powered healthcare-monitoring system was successfully constructed (Figure 4B).

In contrast to inorganic materials, organic materials have inherent advantages in terms of lighter weight and better stretchability, thus they are more appropriate for realizing stretchable electronics (Fu et al., 2019; Yuan et al., 2021). Organic-based stretchable memristive devices such as PDMS/carbon nanotubes (CNTs)/maltoheptaose-block-polyisoprene (MH-b-PI)/Al (Hung et al., 2017) and Cu@GaIn/PDMS/Cu@GaIn (Lu et al., 2021) have been extensively studied. For instance, Lu et al. successfully demonstrated stretchable and twistable PDMS-based memristive devices for in-memory digital computing (Lu et al., 2021) (Figure 4C). On the basis of majority-inverter graph (MIG) logic, the fabricated stretchable memristive devices realized a one-bit full adder for digital computing.

Despite great progress has been made in organic materials, stretchable organic-based devices cannot offer reliable resistive switching properties. In the light of this, researchers attempt to exlpore novel materials that have both the good electrical characteristic of inorganic substances and the excellent stretchability of organic substances (Yang et al., 2018; Yi et al., 2019). Recently, by employing Ag nanoparticle-doped thermoplastic polyurethanes (TPU: Ag NPs) as the resistance switching material, Yang et al. demonstrated a stretchable memristive crossbar array constructed on a PDMS substrate for in-memory computing (Yang et al., 2018). The stretchable memory cell of the fabricated array implemented synaptic plasticity under stretching strain (Figures 4D,E).

Besides material innovation, designing a specific structure to withstand applied strain is another powerful approach for stretchable memristive arrays. Over the years, researchers have developed various effective structures, such as wave, island and serpentine-shaped, to enhance the stretchability of the system. Using an island-structure strategy, a stretchable in-memory computing system was developed by embedding rigid TiO₂-based memristive units into soft interconnects (Kim et al., 2021b) (Figure 5A). Benefitting from this structure, the fabricated in-memory computing system could exhibit reliable electrical performance under a strain of 25%. The TiO₂-based memristive array in the system was used to implement artificial neural network for learning and inferencing. A stretchable HfO₂-based memristive array with excellent damage endurance has also been demonstrated by using the island structure (Wang et al., 2021b). Moreover, each memristive unit in the stretchable array is also consisted of many discrete HfO₂-based sub-units (Figure 5B). This discrete structure enables the stretchable memristive device to have a large stretchability of 40% strain and good mechanical damage endurance.

Apart from the island-structure, the wavy-structure has also been developed to design stretchable memristive devices. Based on this strategy, stretchable HfO₂-based memristive devices were recently developed by directly laminating the Cu/HfO₂/Au/PI film onto a pre-stretching PDMS substrate (Wang et al., 2020a). After releasing the pre-stretching substrate, wavy-structured memristive devices were formed (Figure 5C). The structure could significantly improve the stretchability of HfO₂-based memristive devices, exhibiting reliable switching characteristics up to 20% strain (Figure 5D).

Moreover, the mechanical flexibility of the system can also be effectively improved by configuring the system as a serpentine structure. Based on the serpentine-shaped configuration, a stretchable wearable device integrated with indium zinc oxide (IZO) nanomembrane-based memristive array was developed, where the Au electrode was made into a serpentine shape (Figure 5E) (Sim et al., 2019). Owing to the serpentine-shaped metal electrode (Figure 5F), the memory cell can be isolated from the strain under mechanical contortion, so that the system could exhibit stable electrical performance under 30% stretching strain. These structural designs can significantly enhance the mechanical flexibility of the rigid memristive array, providing a promising way to extend current stretchable memristive devices and arrays.