Pressure sensing is indispensable in a wide range of scenarios, e.g., physiological signal detection, environmental signal monitoring, etc. The rigid single-point sensor, such as load cells, have been maturely applied with high accuracy and stability for decades, integrated with dedicated designs. However, their large volume limits their spatial arrangement and installation. With the development of micro/nanomaterials and design strategies, endowing pressure sensors with flexibility and high spatial resolution properties have been hot research topics over the years, which not only are essentials in frontier scientific and technological fields (e.g., robotic tactile perception and prosthesis [1,2]^[1][2], human-interactive interfaces [3,4]^[3][4], wearable healthcare devices [5,6]^[5][6], etc.) but also have the potential as an alternative and complement to traditional single-point sensors. Flexibility enables easy and fine attachment on curved surfaces and less discomfort for biological measurement. The arrayed structure provides spatial pressure distribution, thus being able to extract abundant information. There are multiple mechanisms for flexible pressure sensing arrays that convert pressure into different electrical quantities, including piezoresistive [7^[7][8],8], capacitive [9^[9][10],10], piezoelectric [11^[11][12],12], triboelectric [13^[13][14],14], etc. Among them, piezoelectric and triboelectric sensors demonstrate high sensitivity to dynamic pressure; however, they have more complicated electronic designs and suffer from inaccuracy when measuring static pressure. For measurements including both static and dynamic pressure, capacitive sensors and piezoresistive sensors are mostly preferred. Although capacitive sensors can achieve high sensitivity and stability, they are susceptible to parasitic capacitance and noise. In comparison, piezoresistive sensors have the advantages of easy material preparation, simple readout circuits, low-cost, and anti-electrical interference capacity in measurements.

2. Piezoresistive Materials and Microstructures

2.1. Performance Metrics of Pressure Sensors

The evaluation of pressure sensors requires a series of performance metrics, including sensitivity, working range, linearity, hysteresis, response time, relaxation time, and spatial resolution ^[15]. These indicators are important for understanding the physical properties of the sensor and the sensor selection for specific scene requirements. The sensitivity of the piezoresistive pressure sensor is defined as the slope of the relative change in resistance or current versus pressure. The quantitative description of sensitivity is as follows, having the unit kPa⁻¹ or Pa⁻¹. In general, the sensitivity of many pressure sensors decreases with pressure, and the resistive response saturates beyond the working range; thus, maintaining high sensitivity and linearity over a wide pressure range is an important issue. Hysteresis influences measurement inaccuracy, manifested as the variation between the loading curve and the unloading curve. The quantitative indicator of hysteresis is defined as where 𝐴𝑢𝑛𝑙𝑜𝑎𝑑𝑖𝑛𝑔 and 𝐴𝑙𝑜𝑎𝑑𝑖𝑛𝑔 are the areas under the unloading and loading curve [16^[16][17],17], Δ𝐻𝑚𝑎𝑥Δ is the maximum difference between the loading and unloading curve at the same pressure, and is the full-scale output [15,18,19]^[15][18][19]. The intrinsic cause of the hysteresis phenomenon includes viscoelasticity of the material, adhesion between the conductive material and substrate, etc. Additionally, most piezoresistive materials based on polymer composite materials have relatively high hysteresis. This is due to the inability of its internal conductive network to fully recover after rearranging under stress ^[20]. In addition to developing low hysteresis materials, circuitry ^[21] and algorithms ^[22] can be applied to compensate for the hysteresis. Response time and relaxation time (also known as recovery time) are crucial factors for dynamic measurement scenarios. They are used to quantitatively describe the delay of resistance change to pressure change when loading and unloading. Mechanical viscoelasticity is the main cause of the delay [15,23]^[15][23]. For the sensor array, the spatial distribution of measurement points can be characterized by spatial resolution, which is represented in the form of N × N ^[24], the spatial period of the arrangement (center-to-center distance between adjacent pixels) ^[25], or the number of measuring points per unit area (in dots per inch or pixels per inch) ^[26]. 

2.2. Piezoresistive Materials and Microstructure Design

Piezoresistive sensors convert pressure into a change in resistance. The resistance can be measured by either sandwiched between the positive and negative electrodes or placed on coplanar electrodes, dominated by either vertical or lateral resistance, respectively. The resistance can be considered as the combination of bulk resistance and contact resistance [27,28]^[27][28]. Bulk resistance is related to material properties, including geometry and internal electrical property. Contact resistance is related to the contact area and interface between the material and the electrodes. To enable sensors with better performance, various materials and sensing structures have been extensively studied. In terms of piezoresistive materials, besides metal strain gauges and semiconductor devices ^[7], polymer composite materials have been a focus in the literature [15^[15][29],29], which shows great prospects in large areas and flexible sensor devices. Polymer composite materials are usually composed of plastic matrix and conductive components. For polymer composites consisting of conductive fillers and insulating substrates, bulk resistance is related to both its geometry and the conductive pathways inside the material, explained by the percolation theory and the tunneling effect [30,31]^[30][31]. The percolation theory analyzes the pressure-induced percolation pathways formed by conductive components, and the tunneling effect refers to the tunneling of charge carriers without contact between particles ^[7]. Common choices for elastic bases are polymers, e.g., polydimethylsiloxane (PDMS) [32^[32][33],33], polyurethane (PU) ^[34], and thermoplastic polyurethane (TPU) [35,36]^[35][36]. Hydrogels ^[37] are preferred for biocompatible requirements. Conductive components usually include (1) carbon-based materials, e.g., carbon black (CB) [35^[35][38],38], carbon nanotubes (CNTs) [39,40]^[39][40], graphene [41^[41][42],42], hybrid carbon fillers ^[43], etc.; (2) metal materials, e.g., metal nanowires [34,44]^[34][44] and metal particles ^[26]; (3) others include MXene [45^[45][46],46], conductive polymers, e.g., polypyrrole (PPy) [16^[16][47],47], polyaniline (PANI) ^[48], poly(3,4-ethylene dioxythiophene) (PEDOT) ^[49], etc. For the electrode material connecting each measurement point of the array, metal materials are usually selected, e.g., Au-based serpentine connections ^[50] and spay-coated Ag nanowire electrode strips ^[26]. Adjusting the ratio and concentration of substrates and conductive fillers will lead to different sensor characteristics. Shi et al. reported a pressure sensor with extremely low loading (<1.5 wt.%) of urchin-like hollow carbon spheres in PDMS fabricated by the spin-coating method. The sensor relied on the Fowler–Nordheim tunneling effect, which enabled a large tunneling distance and resulted in an ultrahigh sensitivity of 260.3 kPa⁻¹ at 1 Pa. The minimal amount of filler material also endowed the sensor with desirable properties such as high transparency, high elasticity, biocompatibility, and ease of fabrication. Furthermore, the hollow structure contributed to the resistance to temperature variations ^[51]. By adjusting the ratio of ink components (which consists of conductive carbon nanotubes, insulating silica nanoparticles, and silicone elastomer polymer), Tang et al. proposed a soft and porous composite pressure sensor fabricated by 3D printing technology which can be tuned between negative and positive piezoresistive effect. At a lower CNTs content, a positive piezoresistive pressure sensor with a sensitivity of 0.096 kPa⁻¹ across a 0~175 kPa pressure range can be produced with good linearity ^[52]. In addition to the selection and proportion of materials, the performance of sensors can be further improved by designing three-dimensional microstructures on the surface. The microstructures enhance the material’s compressibility and stress concentration in terms of mechanical properties and facilitate changing the contact area of the conductive interface, thereby improving the sensor’s pressure-sensing performance. In terms of specific surface morphology, both regular and irregular microstructures can be applied. Regular surface structures include microdome ^[53], micropyramid ^[54], micropillar arrays ^[55], conical frustum-like surface structures ^[56], etc., improving the sensitivity by increasing the contact area under pressure. These microstructures can be fabricated by casting or coating onto templates. The templates can be silica molds prepared by photolithography ^[57], laser engraved mold ^[58], etc. Additional surface morphology can also be added to the 3D structure for further improvement. For example, Yao et al. developed a piezoresistive sensor with cracked metallic film coated on the micropyramidal elastomer, which exhibited a sensitivity of more than 10⁷ Ω kPa⁻¹ and a low hysteresis of 2.99 ± 1.37% over 0~20 kPa. To create the cracked morphology, they deposited a thin Pt film on PDMS with a micropyramid surface structure and compressed the material. The key to creating regular and annular is by using a soft low-tack adhesive during compression ^[59]. According to Li et al., the sharp microstructure can be combined with a short electrode channel length to enhance the sensitivity of the piezoresistive pressure sensor. Based on this, they fabricated a sensor with a sharp micropyramid structure and short-channel coplanar Au electrodes (with a channel length of 300 μm and channel width of 1 mm), achieving a sensitivity of 1907.2 kPa⁻¹ in the 0~100 Pa range and 461.5 kPa⁻¹ in the 100~1000 Pa range, as well as a detection limit of 0.075 Pa and a fast response time of 50 μs ^[53]. To further improve the sensor performance, irregular surface structures attract interest from researchers, including wrinkles ^[60], plant-inspired structures using natural biomaterial templates (e.g., leaves ^[46]), and human skin-inspired structures using randomly distributed spinosum templates (e.g., abrasive paper ^[42]). Additionally, Zhao et al. reported a self-formed microstructure for a piezoresistive film with a surface roughness of about 8~10 μm, which is much smaller than the controllable microstructures (typically 15~100 μm). The piezoresistive film (PRF) was synthesized by mixing multi-walled carbon nanotubes (MWCNTs) with thermoplastic polyurethane (TPU) elastomer at low temperatures ^[36]. These irregular surface structures generally have higher performance but are not as good as regular structures in terms of controllability, uniformity, and mass production capacity. Further, a multilayer structure can be designed by stacking two layers of microstructure face-to-face, resulting in an interlocked structure. Examples of multilayer structures include both regularly arrayed microstructures ^[8] and irregular microstructures stacked face-to-face ^[42], corresponding to the categories of surface morphologies mentioned above. The internal porous structure is another way to improve sensitivity and working range, owing to its lower modulus and higher compressibility. Preparation strategies include freeze-drying ^[35], salt or sugar template ^[61], etc. The pores close when applied with pressure, and the conductive surfaces on the pores contact each other to form conductive paths. Conductive components can be additionally coated to enhance performance. For example, Park et al. fabricated low hysteresis porous piezoresistive material with conductive MWCNTs particles coated at the inner surface of the PDMS pores. They explored both the mechanical and piezoresistive hysteresis of the material with values less than 21.7% and 6.8%, respectively ^[17]. The pores can have uniform arrangement and size, which enhances the sensor-to-sensor consistency compared to structures with random sizes. Oh et al. presented a piezoresistive sensor with uniform porosity, achieving a coefficient of variation of 2.43%. The microfluidic emulsion droplet self-assembly technique was used to fabricate the porous PDMS elastomer, which exhibited uniformly sized pores arranged in a highly ordered, close-packed manner. They also addressed the problem of bonding strength between elastic substrates and conductive materials by chemically grafting conductive polymer (PPy) on the surface of porous elastomer (PDMS) to establish stronger covalent bonds than physical adhesion, achieving a low hysteresis of 2% ^[16]. Hierarchical pores can also be applied. Inspired by bamboo, Dai et al. developed a hierarchical pore structure in conductive carbon nanofibers (CNFs)/PDMS foam materials to address the conflict between sensor sensitivity and mechanical reliability in porous structures ^[62]. The hierarchical pore structures, which consist of large-scale pores of several hundred micrometers, hollow structures of several micrometers, and micro/nanoscale irregular pores on the hollow skeleton, respond to tiny pressures by forming additional conductive paths and exhibit high sensitivity of ~0.6 kPa⁻¹ at 0~1 kPa. The synergy of porous structure and surface microstructure has also been explored. The synergistic effects of the surface microstructure and the porous structure can enhance the contact area and the number of conductive pathways under applied pressure. For example, Li et al. fabricated a piezoresistive material with high porosity and elliptical surface microstructure by using a mixture of PDMS and MWCNTs, stacking two layers to form an interlock structure. The material exhibited a sensitivity of 10.805 kPa⁻¹ in the 1~1000 Pa range and 2.015 kPa⁻¹ in the 1 k~100 kPa range ^[63].

3. Piezoresistive Array Design

3.1. Passive and Active Arrays

At the analog front end, the pressure-modulated resistance array is sequentially scanned and converted to a voltage signal by readout circuitry for further analog-digital conversion. According to the readout method, matrix sensor arrays can be classified into passive and active-matrix arrays ^[64]. In passive arrays, electrodes are laid directly on the piezoresistive material, while in active arrays, active components (e.g., transistors) are tightly integrated with each pixel element. Active arrays have advantages in signal transduction and integration, but passive arrays are easier to fabricate. For passive-matrix array construction, electrodes are laid directly on the piezoresistive material. The positive and negative ends can be individually led out for each pixel. For larger array density, a row-column structure is preferable due to the reduced number of wires. Resistors in the same row and column share the same wire. Row lines and column lines are selected sequentially to complete a scan of the whole pressure distribution map. Signal reading and conditioning are carried out in the external circuit design. A voltage divider, negative-feedback amplifier structure, and Wheatstone bridge are three principles for resistor-voltage conversion. Operational amplifiers can be applied to decrease the output impedance, thus reducing the loading effect ^[6]. Note that for the row-column mode in the passive matrix, electrical crosstalk may exist inside the array, leading to inaccurate measurement of the resistance. However, they usually involve more operational amplifiers in the circuit design, increasing the hardware volume when higher pixel density is applied. 

3.2. Structure Designs and Measuring Mechanisms

Spatial resolution is the primary performance metric for evaluating a pressure distribution detection array. There are several structures to measure spatial pressure distribution, and the definition of spatial resolution varies according to the array structure. One direct way is to arrange discrete material elements and corresponding electrodes on substrates. The resolution is commonly reported as the number/density of pixel materials, informs of 3 × 3 [48^[48][52][65],52,66], 4 × 4 [8,46^{[8][46][63][66][67]},63,67,68], 5 × 5 ^[62], 6 × 6 ^[45], and 8 × 8 ^[25]. However, the uniformity of pixel property and the gaps between pixels need to be considered [16,69]^[16][68]. For some scenarios, such as decease diagnostic, it is preferable to place individual pressure sensing elements at several feature points (e.g., arches and joints) and interpret the information through further algorithms without a neat row-column array ^[6]. Another way is to cover the electrodes of the array with a continuous piece of piezoresistive materials to form the array [26^[26][36],36], which is capable of achieving much higher spatial resolution. Their resolution is often reported as the density of readout points, that is, the density of electrode intersections in passive arrays and the density of transistors in active arrays. For this configuration, the spatial resolution is limited by both the sensing material and the electrodes. For example, Shi et al. developed a pressure sensor based on Fowler–Nordheim tunneling effect by spin-coating urchin-like hollow carbon spheres in polydimethylsiloxane (PDMS) with concentration far below the percolation threshold. The material forms a vertical conduction path under pressure while being horizontally insulated, thereby reducing transverse interference. Theoretically, the sensing density can be 2,718,557 per cm²; however, limited by electrode size, a 64 × 64 passive matrix was fabricated in a 32 × 32 mm area by photolithography, reaching a sensing density of 400 cm⁻². The thin-film pressure sensor exhibits a high sensitivity of 260.3 kPa⁻¹, high transparency, and reduced temperature interference ^[51]. Improving resolution while maintaining other good performances is of great importance. As mentioned previously, microstructures commonly involve an increase in sensitivity by introducing variations in the contact area. The size of the microstructure influences pixel density, considering uniformity and flatness. Regular structures (e.g., micropyramids) typically fall in the range of 15~100 μm. Irregular structures based on special molds, such as plants, exhibit better performance but are not suitable for large-scale production; thus, the array demonstrations in these essays are usually individual elements arranged in individual forms. Recently, Zhao et al. developed a large-scale piezoresistive sensor with a high spatial resolution of 0.9 mm (28.2 ppi) by applying a kind of MWCNTs/TPU material with a self-formed surface structure on the scale of 8~10 μm. The microstructure was flat enough for the 0.9 mm pixel size and had a high sensitivity of ~385 kPa. The material was integrated into a 64 × 64 active matrix using CNT TFTs, covering a 4-inch area ^[36]. Researchers also focus on other features, such as air permeability which is required for wearable applications. Pei et al. fabricated a high-resolution array with a porous structure by 3D printing. Silicone ink was extruded by gas to form a porous structure, and graphene was attached to the surface as the piezoresistive material. The sensor had a linear response in the range of 0~12 kPa and a sensitivity of 4 Pa⁻¹. The pitch distance between each sensing unit is 1 mm, equivalent to a resolution of 100 cm⁻² [70]^[69]. Besides higher resolution, multiple resolution, an important sensing characteristic of human skin, was also researched. Mimicking real tactile sensing of human fingers, Kim et al. developed a multiple-resolution piezoresistive sensor by arranging pitch-varying electrodes on a single piece of piezoresistive material. Using aligned Ni/PDMS material, the resolution of their sensor can be adjusted up to 100 dpi with a pitch distance from 0.25 mm to 1 mm ^[26]. In addition to focusing on sensor structure, appropriate processing algorithms will greatly improve the sensing limit under the same hardware conditions [71]^[70]. Besides fabricating pixel structures by either assembling discrete material elements or arranging electrodes, there are also pixel-less methods that do not employ patterned pixels on physical structures. One is a light-omitting sensor device with visible output. Lee et al. proposed a two-layer structure consisting of a pressure-sensing film lying on an electroluminescent film capable of displaying high-resolution images corresponding to the pressure distribution. The top film was coated with a kind of cathode and cellulose/nanowire nanohybrid network for pressure sensing, which controls the current flowing through the quantum-dot light-emitting diode on the bottom film, thus influencing the image display. The spatial resolution was over 1000 dpi (evaluated by loading the micro-bumps array). The sensor had a sensitivity of over 5000 kPa⁻¹ and a response time of less than 1 ms. The displayed image was captured by high-resolution cameras in real-time, and the pressure data can be resolved by pre-calibrated image data, which avoided local data acquisition and processing electronics [72]^[71]. Another is the electrical impedance tomography (EIT) method. It is a technique that can reconstruct the conductivity of the internal area only through electrodes at the boundary. Current is injected into the conductive film, and the voltage is analyzed to reconstruct the impedance distribution [73,74]^[72][73]. The quality of the result depends largely on the reconstruction algorithm. The EIT method simplifies the internal wiring of the sensing material, thus making it much easier for manufacturing. However, it suffers from poor spatial resolution and low temporal frequency [76]^[74]. In summary, a generic strategy is to attach sensing elements separately to substrates, providing flexible choices for sensor displacement. For pixel-based structures, most previous works stuck at millimeter range resolution with a resolution of no higher than 100 dpi in the literature. This is probably limited by the distance between the conductive path or microstructure size of the material and the fabrication ability of flexible electronics. Pixel-less methods ease the requirement of locally arrayed electronics but involve additional devices or complex algorithm analysis.

3.3. Crosstalk and Suppression

It is worth noting that the spatial resolution of the pressure detection array is not only determined by the array structure. All arrays face the challenge of crosstalk. The coupling between the array elements may introduce errors in the pressure measurement of each point, known as crosstalk interference. Thus, for the evaluation of the sensor array, it is necessary to determine maximum resolution under the condition that interference among pixels falls below a certain level ^[26] and to reduce crosstalk to achieve higher measurement accuracy. Since both the mechanical and electrical response of each sensing pixel may be influenced by other pixels, the sources of crosstalk issues can be categorized into mechanical crosstalk and electrical crosstalk ^[25]. Mechanical crosstalk is derived from deformation coupling. A force applied to one pixel would generate deformation of the adjacent pixels, resulting in the resistance change in the unloaded pixels. This is a noteworthy problem for the common sensor structure that covers a whole piece of piezoresistive material on arrayed electrodes [77]^[75]. Arranging discrete sensing elements is a direct solution ^[33], but the elastic supporting layer may still be a cause. To evaluate this issue, Li et al. studied three interconnection methods: serpentine, straight line, and unpatterned piece. They found that serpentine interconnects could best suppress crosstalk between adjacent pixels ^[25]. Electrical crosstalk was caused by unintended conductive pathways or current leakage, resulting in an inaccurate readout of the resistance. The electrical crosstalk paths have two sources. One is the lateral conductive path inside the material at different measuring points, and the other is the crosstalk loop of the external resistance reading circuit of the material. A detailed introduction and countermeasures are presented in the following paragraphs. For the first condition, an isolated piezoresistive pixel structure can be applied [50,78]^[50][76]. Coplanar electrodes, such as comb structures, can also suppress crosstalk [25,33]^[25][33]. Apart from attaching individual sensing elements, researchers also find some solutions by designing special geometry structures. Park et al. introduced a grooved structure between parallel electrodes through the molding process, which increased the leakage resistance between adjacent electrodes, thus effectively attenuating the crosstalk interference ^[17]. Kyubin Bae et al. further developed a mesh-structured anisotropic material to reduce lateral conduction sensor array using the dip-coating method. The CNT/PDMS composite was uniformly patterned in the holes and isolated by the mesh layer, eliminating the electrical crosstalk effect and mechanically connecting the sensing elements [79]^[77]. From the perspective of developing new material, Kim et al. presented an anisotropic material to reduce lateral conduction. They prepared Ni/PDMS mixture and applied a magnetic field to align the nickel particles in the field direction, forming filamentous conduction paths. They discovered that after alignment, the composite had less densely connected conduction paths in the lateral direction. There was virtually no crosstalk at pitches beyond 0.25 mm, achieving tunable resolutions up to 100 dpi ^[26]. In summary, crosstalk derives from both mechanical and electrical aspects. The suppression can focus on novel materials ^[26], geometry structure design [25^[25][77],79], external circuit design [60^[60][62],62], or backend algorithmic compensation [85]^[78].