Failure mechanisms in flexible electronics

ABSTRACT

The rapid evolution of flexible electronic devices promises to revolutionize numerous fields by expanding the applications of smart devices. Nevertheless, despite this vast potential, the reliability of these innovative devices currently falls short, especially in light of demanding operation environment and the intrinsic challenges associated with their fabrication techniques. The heterogeneity in these processes and environments gives rise to unique failure modes throughout the devices’ lifespan. To significantly enhance the reliability of these devices and assure long-term performance, it is paramount to comprehend the underpinning failure mechanisms thoroughly, thereby enabling optimal design solutions. A myriad of investigative efforts have been dedicated to unravel these failure mechanisms, utilizing a spectrum of tools from analytical models, numerical methods, to advanced characterization methods. This review delves into the root causes of device failure, scrutinizing both the fabrication process and the operation environment. Next, We subsequently address the failure mechanisms across four commonly observed modes: strength failure, fatigue failure, interfacial failure, and electrical failure, followed by an overview of targeted characterization methods associated with each mechanism. Concluding with an outlook, we spotlight ongoing challenges and promising directions for future research in our pursuit of highly resilient flexible electronic devices.

GRAPHICAL ABSTRACT

KEYWORDS:

• Flexible electronic devices
• failure mechanisms
• characterization methods

1. Introduction

With the significant advancements in cutting-edge electronics and flexible materials, there has been a substantial increase in both experimental and theoretical research in the field of flexible electronic devices. These efforts aim to meet emerging requirements in various domains, including health-care applications [1–4], human motion monitoring [5–7], electronic skin [8–11], and engineering applications [12–15]. Consequently, several prototypes of diverse flexible devices have been developed. Nevertheless, the current reliability of the majority of flexible electronics remain insufficient due to limitations in fabrication techniques and stringent application requirements.

The reliable performance of these devices necessitates consistent electrical properties, such as resistance, capacitance [16] and response speed [17], even under deformation. However, over their lifecycle, flexible electronic devices often endure intricate mechanical deformations, potentially leading to material failure or signal distortion. Such deformations may entail exceedingly high strains during integration with human skin or organs [18], or when embedded in textiles [19]. Additionally, they might undergo small, repetitive strain cycles during roll-to-roll fabrication processes [20–22], and experience thermal expansion from fluctuations in ambient temperature or Complex monitoring requirements in engineering applications [15,23]. Furthermore, fabrication-induced defects, such as those resulting from transfer printing [24,25] and encapsulation processes [26–28], are likely to accelerate device failure. These primary failures often occur in flexible electronics with semiconductors and conductors. Conversely, for devices without such components, such as flexible electrodes with doped nanomaterials, unique degradation patterns arise under stress. For example, electrodes with 0D nanomaterials (nanoparticles) [29–31] might crack along grain boundaries, while those with 1D nanomaterials (nanowires) [32–35] can face resistance spikes due to brittle nanowire breaks. Devices with 2D nanomaterials (nanosheets) [36–39] see declining performance, with contact and tunneling resistances between nanosheets being pivotal considerations.

Given their extensive range of practical applications, flexible electronic devices are fabricated through diverse fabrication techniques and are designed to function in varied environmental conditions. This heterogeneity in fabrication and functionality results in distinctive failure modes throughout their service lifetimes. These failure modes can be broadly categorized into four classes: strength, fatigue, interfacial, and electrical failure, as depicted in Figure 1. These modes significantly affect their long-term utility in crucial sectors such as engineering and biomedical sciences. Noteworthy studies have been undertaken to investigate the failure mechanisms of flexible electronics, ranging from analytical models to numerical methods and advanced characterization methods. As a result, it is vital to closely examine the latest advancements in various failure modes of flexible electronic devices to enhance our understanding of these failure mechanisms.

Figure 1. Overview of failure of flexible electronic devices from perspective of failure mode, characterization methods, fabrication process and operating environment. Strength failure: Adapted with permission. Copyright 2010, Elsevier BV [40]. Interfacial failure: Adapted with permission. Copyright 2014, Elsevier BV [41]. Fatigue failure: Adapted with permission. Copyright 2021, Wiley-VCH Verlag [42]. Electrical failure: Reproduced with permission. Copyright 2022, American chemical Society [43]. Bending strength test: Adapted with permission. Copyright 2018, Elsevier BV [44]. Peel-off test. Adapted with permission. Copyright 2018, Elsevier BV [44]. Laser-induced interfacial spallation. Adapted with permission. Copyright 2020, American chemical Society [45]. Bending fatigue test. Adapted with permission. Copyright 2013, Elsevier BV [46]. Tensile fatigue test. Adapted with permission. Copyright 2022, Nature Publishing group [47]. Electromigration test. Adapted with permission. Copyright 2019, Springer Verlag [48].

In this study, we present an exhaustive review of these four failure modes in flexible electronics, concentrating on their respective failure mechanisms and characterization methods. This review begin with an overview of the triggers of device failure, namely, the fabrication process and operating environment, followed by an in-depth discussion of the failure mechanisms concerning strength, fatigue, interfacial, and electrical failure, which are detailed in Sections 3 to 7. We conclude by presenting a perspective on the prevalent challenges and prospective avenues for future research.

2. The influence of fabrication processes and operating environments

The multistage fabrication process coupled with diverse operating environments present potential risks to flexible electronic devices. This section delves into the negative impacts of these fabrication processes and operating environments on the stability of flexible electronic devices.

2.1. Fabrication processes

The standard fabrication techniques (Figure 2) for flexible electronic devices include photolithography, soft lithography, inkjet printing, transfer printing, encapsulation technology, and mechanically guided assembly. These techniques are described in detail below.

Figure 2. Schematic illustration of representative fabrication process for flexible electronic devices. (a) Photolithography process. Adapted with permission. Copyright 2016, Elsevier BV [49]. (b) roll-to-roll printing. Reproduced with permission. Copyright 2018, American chemical Society [50]. (c) deterministic assembly. Adapted with permission. Copyright 2021, Wiley-VCH Verlag [51]. (d) inkjet printing process. Adapted with permission. Copyright 2018, American chemical Society [52]. (e) mechanically guided 3D assembly of a resistive vibration sensor. Adapted with permission. Copyright 2021, Wiley-VCH Verlag [42]. (f) encapsulation of a flexible microfluidic electronic system. Adapted with permission. Copyright 2014, American Association for the Advancement of Science [53].

Photolithography is a predominant technique for producing flexible electronic devices, offering superior resolution. Despite its widespread use in device patterning, its complexity and environmental demands, can be challenging. As depicted in Figure 2a, the process begins with the application of a photoresist to the substrate surface, forming a protective coating. Subsequently, UV light is directed through a mask plate onto the photoresist, triggering a chemical reaction that results in either photodecomposition (for positive photoresists) or photocrosslinking (for negative photoresists). The subsequent development phase involves dissolving the photoresist to either remove the exposed region (positive photoresist) or the unexposed region (negative photoresist), effectively replicating the mask pattern onto the coated substrate. The pattern is then etched onto the substrate to produce the desired design. A notable concern in this fabrication approach is that while the photoresist forms the device’s pattern and the residual etchant eliminates specific material, solvents may persist on the device surfaces. This residual presence can compromise the electrical performance or introduce imperfections in the final products [49].

Roll-to-roll printing, demonstrated in Figure 2b, facilitates the continuous production of flexible, biocompatible electrode arrays on polyethylene-terephthalate (PET) substrates. The procedure involves the deposition of silver, carbon, and insulator ink layers into the grooves of a gravure plate, which are subsequently transferred to a substrate via rotation of a roll or carrier on a roll core [50]. Both the operating temperature and humidity significantly influence the fabrication process. Fluctuating conditions may disrupt ink fluidity and coating uniformity, impacting device quality and stability [22]. Furthermore, insufficient adhesion between the printed material and the substrate could lead to circuit delamination or failure [21].

Transfer printing technology involves the strategic arrangement of micro and nano materials into spatially structured functional modules. It encompasses three primary types: additive transfer, subtractive transfer, and deterministic assembly. In the deterministic assembly, for instance, the structure is transported from the donor substrate to the stamp and finally to the receiver substrate by manipulating the adhesion and fracture mechanisms at the critical ink/receptor interface, as depicted in Figure 2c [51]. The technology’s essence lies in its ability to efficiently and precisely select and arrange functional components for device structure. These components span intricate molecular-scale materials such as self-assembled monolayers, nanotubes, graphene, and functional polymers, to high-performance rigid substances like single-crystalline inorganic semiconductors, metals, and oxide thin films. They also include fully integrated device structures, encompassing thin film transistors (TFTs), light-emitting diodes (LEDs), CMOS circuits, sensing arrays, and solar cells [51]. Despite its benefits, it can experience failures due to insufficient adhesion during production, similar to roll-to-roll printing [54]. The transfer process might also result in uneven substrate surfaces, which can negatively impact circuit quality and stability [55].

Inkjet printing, a non-contact patterning method, facilitates rapid structuring of intricate designs. Figure 2d presents a schematic of this process, encompassing ink ejection, droplet flight, ink-substrate impact, spreading, and drying [52]. The performance of fabricated flexible devices hinges on spray conditions including solvent type, concentration, and substrate surface properties. Ink diffusion from the print head can cause short circuits, impacting electronic lifespan and stability [56]. Moreover, uneven particle size distribution in the ink could cause precipitation, compromising the device’s reliability and stability [57].

Mechanically guided assembly, a versatile method for creating three-dimensional (3D) structures, leverages a prestrained elastomer platform to drive 2D to 3D conversions via buckling (Figure 2e) [42]. Nonetheless, this approach poses challenges. Missteps in strain release during fabrication could induce excessive curvature in certain areas, risking localized damage. Furthermore, the assembly process often necessitates interactions across multiple material interfaces. This may provoke interfacial delamination in the bonding area or total structure adhesion, consequently undermining successful 3D formation [58].

Encapsulation technology, as shown in Figure 2f, is vital in fabricating flexible electronic devices, because it selectively prevents or allows the entry of external environmental factors, including water and oxygen, while mitigating the impact of both internal and external heat exchange on device performance [53]. However, it presents certain challenges. For instance, interfacial adhesion can affect the encapsulation quality, and poor adhesion between the encapsulation material and the flexible electronics could result in inadequate protection [59]. The stiffness of the encapsulation material affects the flexibility and bendability of the flexible electronic device. Moreover, disparities in physical properties between materials can introduce various issues [53]. For example, if the thermal expansion coefficients of the encapsulation and substrate materials are mismatched, temperature variations could create stress disparities, leading to device failure.

2.2. Operating environments

Here, we investigates diverse operating environments for flexible devices and systems. Importantly, the categorization of flexible devices in Figure 3 is guided by their distinct usage contexts: epidermal electronics, implantable devices, textile-based systems, and engineering monitoring devices. Each device type encounters distinct challenges within its operating context:

Figure 3. Operating environments of flexible electronic devices and their influencing factors. (a) Epidermal electronics. 1) flexible sensor arrays that can be used for pressure monitoring on human surfaces. Reproduced with permission. Copyright 2016, Nature Publishing group [60]. 2) 3D-printed soft neural probe with nine channels by the conducting polymer ink and the PDMS ink. Reproduced with permission. Copyright 2020, Nature Publishing group [61]. 3) Fractal device structure of the EEG measurement system, where the left image represents the device cascade on the auricle and mastoid, and the right image represents the amplified interconnections. Adapted with permission. Copyright 2015, Proceedings of the National Academy of Sciences [62]. (b) implantable devices. 1) wireless biodegradable sensor wrapped around the femoral artery and secured with sutures. Adapted with permission. Copyright 2019, Nature Publishing group [18]. 2) Implanted pressure sensor in front of the eye model. 3) wireless implanted pressure sensor with an external coil in front of the eye model. Reproduced with permission. Copyright 2008, IEEE [63]. (c) textile-based devices. 1) Solid-state textile-based micro-supercapacitors. 2) the scanning electron microscopy (SEM) image of a solid-state textile- based micro-supercapacitors. Adapted with permission. Copyright 2016, Wiley-VCH Verlag [19]. 3) textile-based pressure sensor. 4) LEDs lit by a DC source through knotted textile conductive circuits. Reproduced with permission. Copyright 2017, Wiley-VCH Verlag [64]. (d) flexible electronic devices in engineering applications. 1) flexible skin for Boundary layer state measurement and flight Attitude Identification on unmanned aerial vehicle (UAV). Reproduced with permission. Copyright 2023, IOP Publishing [13]. 2) schematic diagram of the UAV equipped with smart sensing skin for sensing wind pressure. Adapted with permission. Copyright 2020, Springer Verlag [65].

1. Load: Epidermal electronics experience mechanical loads such as external pressure and impact [60]. Implantable devices within the human body endure biological loads like bodily fluid pressure, and muscular contractions [18]. Textile-integrated devices must withstand mechanical stresses like clothing friction and pulling [19]. These loads may cause deformation and damage to the devices.

2. Humidity Change: Fluctuating internal and external humidity levels can destabilize and compromise the reliability of flexible electronic components. High humidity can lead to water absorption by device materials, resulting in short circuits or component failure [66]. In addition, Humidity changes can also weaken flexible electronics adhesion, causing delamination or deformation [67].

3. Temperature Variation: Devices, whether on the surface or inside the body, are influenced by ambient temperature changes, potentially causing shape alterations and performance instability. For example, high temperatures might trigger material thermal expansion, impacting the device’s form and characteristics [68].

4. Chemical Substances: Chemicals present in the human body may affect implantable flexible devices’ materials and components [69]. Epidermal electronics may be influenced by sweat, sebum, and other substances [70], causing corrosion, oxidation, and potentially, device failure.

5. Light Exposure: Devices exposed to the natural environment are susceptible to light effects. Sustained UV light exposure may cause material aging, deterioration, or deformation in flexible electronics [71].

6. Extreme environments: Flexible sensors deployed in engineering applications often encounter severe conditions. For instance, flexible electronics used on aircraft skin need to endure extreme temperature changes, wing vibrations during high-speed flight [23,72,73], and interference from aircraft radar radio frequency radiation [74]

In summary, unfavorable factors during manufacturing can lead to device defects and potential failure, while adverse operational conditions can directly or indirectly impair device performance and stability. Therefore, when designing and manufacturing flexible electronic devices, it’s crucial to account for these potential failure mechanisms and apply corresponding characterization methods. This ensures device stability, reliability, and safe operation within their intended environments

3. Strength failure

In flexible electronics, conductive materials such as metal-based materials [75–78], carbon-based materials [75,79,80], and conductive polymers [81–86]), along with semiconductors including semiconducting NWs [87,88], semiconducting organics [86,89–91], light-absorbing semiconductors [92–94], field-effect transistors [75,79]) serve as functional components. Elastomeric polymers like PDMS [95–97], PI [98,99], PET [20,100], PEN [101], PES [102], PGS [103], PAR [26] form the flexible platform. As these electronics are fabricated from thin films of flexible and stretchable materials, they present unique properties and damage mechanisms under force, distinct from traditional rigid electronics [104]. Various strength failure modes can occur, with the characteristics influenced by the choice of materials and their structures [105–108]. This section will discuss strength failure modes, including tension, bending, and impact-induced damage, as well as damage from mismatched material properties in multi-layer structures.

3.1. Tensile-induced damage

The durability of flexible electronics under intense tensile loading is significantly influenced by the formation and propagation of cracks [109,110]. Such cracks typically develop and expand gradually to relieve considerable localized stress [111,112]. Consider a uniaxial tensile test (Figure 4a) as an example: a brittle film on a flexible substrate typically experiences three stages as the tensile strain escalates. Initially, cracking begins at the critical strain; this is followed by the onset of midpoint cracking and transverse fragment buckling as the strain increases; finally, once a certain strain threshold is surpassed, no additional cracks form, marking the achievement of saturation crack density [109]. However, the load-bearing capacity of brittle layers is inherently constrained by their functional and material characteristics, typically resulting in the appearance of cracks within functional layers prior to substrate failure [117,118]. Consequently, the brittle film invariably fractures at a strain lower than the flexible polymer substrate. Instances of such systems with low fracture strains encompass chromium on polydimethylsiloxane (<1%) [119], silica on polyethylene terephthalate (<3%) [28], tantalum on polydimethylsiloxane (<0.5%) [120] and titanium oxide/carbon nanofibers on polyacrylonitrile/polyvinyl pyrrolidone (<1.5%) [121].

Figure 4. Strength failure mechanisms. (a) illustration of the three stages of brittle film fragmentation under uniaxial loading; the insets show the progression of cracks of a 20 nm thick SiOx coating on a 12 μm thick PET substrate. Adapted with permission. Copyright 2002, Elsevier BV [109]. (b) Demonstration of the failure of a flexible accelerometer upon impact. Adapted with permission. Copyright 2014, Elsevier BV [113]. (c) analytical model of stretchable electronic devices with viscoelastic packages and soft substrates subjected to impact loads on the surface of human skin. Adapted with permission. Copyright 2016, ASME [114]. (d) flexible microfluidic electronic systems under stretch and twist configurations. Adapted with permission. Copyright 2014, American Association for the Advancement of Science [53]. (e) left, schematic illustration of a flexible sensor with a non-bonded interface, exhibiting a notable mechanical mismatch between the layers. Right, SEM image of the sensor in its bent state, highlighting stable bonding between the microcones and the dielectric layers. Adapted with permission. Copyright 2022, Nature Publishing group [115]. (f) left, SEM image of the cross-section of an organic–inorganic multilayer permeation barrier. Right, the evolution of defects: beginning as pin-holes, escalating to channel cracks, and culminating in the delamination of the oxide-organic interface. Adapted with permission. Copyright 2010, Elsevier BV [116].

Progressive damage in flexible thin-film devices under tensile loading, as numerous studies indicate, arises predominantly from the differing mechanical properties of the conductive metal film and its flexible polymer substrate (Figure 4d). George et al. examined the crack propagation in metal films on flexible polymer substrates using in-situ atomic force microscopy (AFM) and finite element stress calculations. They categorized damage mechanisms during the tensile test into two phases: initial sprouting and random development of cracks forming a network across the film, followed by depth-oriented development of cracks at maximum stress within the multilayer structure [122]. Heinrich et al. and Stephan Frank et al. conducted in-situ tests on the fragmentation and buckling of thin coating layers on elastomeric substrates. They found that tensile loading caused a mismatch in elastic deformation between the coating and substrate due to different Poisson’s ratios. This induced significant compressive stresses, leading to film bending, continuous delamination, and extensive system damage. They also noted that orthogonal tensile strain allowed for controlled induction of parallel cracking [123]. M.J. Cordill et al. quantified the Poisson effect on thin film structures under tensile load, illustrating the sequence of film cracking in tension: initial perpendicular cracks form a single crack band, followed by bending in the same direction, growth of the bent section, and cracking at the apex [43].

The failure of flexible films under tensile loading is primarily determined by the crack onset strains (COS) [109,124], which denote the strain at initial crack detection. Two analytical methods, the weakest link and shear lag models, have been instrumental in related studies. The former considers fracture toughness is determined by the most brittle region (‘weakest link’) along the crack front [124,125], whereas the latter the shear stress is proportional to the relative displacement of the flexible substrate to the metal layer [126,127].

Utilizing the weakest link model, Y. Leterrier et al. [124] proposed a crack initiation strain model based on fragmentation tests on uniaxial silicon oxide-coated polyethylene terephthalate (PET) films. This model identifies the strength distribution of a coating fragment under stress $\sigma$, characterized by length $l$, width $w$ and thickness $h$, using the equation:

(1) $\begin{array}{c}F\left(\sigma \right)=1-exp\left[-\frac{lwh}{V_0}{f}_V\left(\sigma \right)-\frac{lw}{S_0}{f}_S\left(\sigma \right)\right],\end{array}$(1)

where $f_V$ and $f_S$ represent the distribution of flaws within the functional layer’s volume and on its surface, respectively. Moreover, Assuming the initial fracture as a random event, the crack onset strains are dependent on the coating’s surface area, and the average fracture strain are calculated by

(2) $\begin{array}{c}\bar{\epsilon }=\frac{{\beta }_V}{E}{\left(\frac{\lambda h}{l_0{h}_0}\right)}^{-1/{\alpha }_V}\cdot \mathrm{\Gamma }\left\{1+1/\alpha \right\},\end{array}$(2)

where ${\beta }_V$, ${\alpha }_V$ and $\alpha$ represent strength distribution parameters derived from the early linear extrapolation of partial experimental results, $\lambda$ signifies the film portion’s length being inspected for the first crack, $E$ denotes the functional layer’s modulus of elasticity, and $l_0$ and $h_0$ are normalizing factors, $\mathrm{\Gamma }$ represents the gamma function.

The shear lag model provides an additional analytical method to compute stress redistribution [127]. Upon applying the energy release rate relationship derived from Laws and Dvorak’s work to the functional layer-substrate system (assuming residual stresses are negligible), the crack initiation strain can be determined by [128,129]:

(3) $\begin{array}{c}\epsilon =\sqrt{\frac{2G_c\xi h_s{E}_s}{h\left(h_s+h\right)E{E}_0}},\end{array}$(3)

where $G_c$, $E_s$, $E$ and $E_0$ represent the fracture toughness of the functional layer, the elastic modulus of the substrate, functional layer, and the entire film, respectively, while $h_s$ and $h$ indicate their corresponding thickness.

Several studies have leveraged these principles to enhance the COS of brittle metal films supported by flexible polymers. Tanja Jörg et al. studied the deformation behavior of 40–500 nm thick sputter-deposited Mo films, correlating fracture strength and COS with decreasing film thickness [130]. They also assessed the impact of deposition conditions on the structure-stress relationship, establishing that residual stress tailoring can reduce the COS [131]. Similarly, M.J. Cordill et al. investigated fracture, flexure, and delamination of Cr films on polyimide (PI) under tensile strain using the shear hysteresis model. Their findings suggest that film fracture and delamination are thickness-dependent and a thinner film with high crack density may be less reliable than a thicker adherent layer [132,133]. Furthermore, V.M. Marx et al. explored the strain-induced phase transition in two-phase Co films on PI, concluding that the strain-induced phase transition can enhance the ductility of cobalt films, thereby delaying the onset of cracking [134].

Efforts have been made to delay the onset of cracking in rigid films on flexible substrates under tension through microstructural optimization of the rigid films themselves. Inhwa Lee et al. improved the weak cracking resistance of flexible nanoparticle films by integrating very long nanowires, demonstrating that nanowires longer than 90 μm inhibit the overall film cracking and significantly reduce resistivity [135]. Impressive mechanical properties under tensile and compressive bending were displayed by a novel nanocomposite of nanowire-reinforced nanoparticle matrix film developed by Young D. Suh et al., offering an inspired alternative for flexible and transparent electrode applications [136]. Furthermore, Chullhee Cho et al. fabricated durable thin-film electrodes by implanting an ultra-thin interlayer (graphene, molybdenum disulfide, or hexagonal boron nitride) between a metal film and a flexible substrate, thereby increasing the allowable strain before electrical failure by 400% [137].

Under tensile loading, flexible films doped with nanomaterials exhibit a distinctive failure mechanism. Nanoparticle-coated flexible films display a pattern of crack development analogous to that of individual metallic films under tensile load. Sanghyeok Kim et al.‘s exploration of Ag nanoparticle (Ag NP) films on flexible substrates showed that with increasing tensile strain, cracks develop perpendicular to the tensile load and grow along Ag NP grain boundaries [138]. This aligns with past studies on crack extension in nanocrystalline metal films [139].

3.2. Bending-induced damage

In flexible devices, unavoidable operation under bending conditions can significantly affect performance and reliability. Brittle materials within these devices are susceptible to stress concentration during bending, often leading to rupture [140]. This damage mechanism can also manifest at interconnects [141]. Further, bending stresses can deform or destabilize features like micro-bending structures and three-dimensional elements in flexible electronic devices, compromising their performance [42].

Structures subjected to bending loads experience two distinct stress states: tensile stresses on convex surfaces and compressive stresses on concave ones [142,143]. The relative position of the brittle structure to the flexible polymer substrate dictates two potential failure modes under flexural loading. Under tension, channel cracking of the film occurs, similar to the damage under tensile stress. Conversely, under compression, the functional layer might experience tunnel buckling, delamination, and cracking [144]. Contrary to the effects of uniaxial stretching, flexible devices undergoing bending deformation do not experience failures from coupled compressive and tensile stress. Such combined stresses typically result in a sequence of film cracking, buckling, and eventually delamination.

The location of the neutral plane, the dividing line between compression and tension, is of significant importance. The ‘plane sections remain plane’ assumption yields an analytical solution for the neutral plane location as follows [145]:

(4) $\begin{array}{c}z=\frac{\sum _{i=1}^n{E}_i{d}_i^2+2\sum _{i=2}^n\left(E_i{d}_i\sum _{j=1}^{i-1}{d}_j\right)}{2\sum _{i=1}^n{E}_i{d}_i},\end{array}$(4)

where $z$ represents the neutral plane axis location, $E_i$ the material’s modulus of elasticity, $d_i$ the layer thickness, and $i$ the layer index. This equation suggests that a similar thickness of the encapsulation layer and the polyimide substrate can counteract the mechanical strain applied to the functional layer [146].

Nonetheless, the classical beam theory ceases to be applicable in cases with a substantial difference in elasticity modulus between layers. When a flexible layer with a small modulus of elasticity is sandwiched between two stiff layers, the central soft layer undergoes significant shear deformation during bending, decoupling the deformations of the top and bottom stiff layers [147]. Consequently, the entire multilayer structure has multiple zero-stress surfaces; each stiff layer has its neutral axis and bending center. Lan Li et al. analytically determined these neutral axis locations during the design and fabrication of a flexible, high-refractive-index contrast 3D photonic device [148].

Determining the neutral plane proves instrumental in optimizing flexible device design under bending loads. Seung-Yoon Kim et al. utilized analytical and numerical simulations to position the neutral mechanical plane (NMP) optimally, achieving high-performing mechanically flexible silicon nanomembranes (NMs) completely depleted of silicon field-effect transistors on an insulator. The device demonstrated robust mechanical and electrical stability even under a 1 mm bending radius [149]. Sangmin Lee et al. proposed a design rule – neutral axis (NA) engineering – that controls the neutral plane’s position using a buffer layer on the ITO layer, improving the bendability of organic solar cells to a bending radius of approximately 1 mm [150]. Recognizing flexible displays often comprise several thin films with varied thicknesses and linear elastic mechanical properties, Chang-Chun Lee et al. proposed an analytical solution for bending stress/strain in multilayer thin-film flexible displays. They estimated specific outcomes for alternating layered systems, revealing core trends in the normalized bending strain and neutral axis position’s dependence on the modulus and thickness ratio of relevant layers [151].

Flexible films doped with nanowires exhibit a distinct destruction process under bending deformation. The failure criterion of silver nanowire (Ag NW) electrodes on polymer substrates in flexible devices was proposed by Donggyun Kim et al., using in-situ mechanical tests on individual Ag NWs. The findings reveal that Ag NW electrodes undergo strain-dependent electrical failures linked to unique deformation properties and the size-dependent brittle-ductile transition of the fivefold twinned Ag NWs. All Ag NWs above 40 nm in diameter display brittle fracture, with consistent stress-strain responses, regardless of size. Conversely, Ag NWs beneath 40 nm in diameter show increased strain- at-break figures, with smaller diameters correlating with higher ductility and enhanced deformability in subsequent flexible electrodes. Additional in-situ tensile tests demonstrated that Ag NWs exceeding 40 nm in diameter experience brittle fracture at roughly 2.6% lattice strain due to localized necking, potentially causing the steep resistance increase in flexible electrodes under bending pressure. Therefore, the fracture threshold for bending-induced failure in conductive electrode films is premised on the lattice strain of Ag NWs, which triggers brittle fracture, resulting in an evident size effect [141].

Flexible electronic devices often experience performance alterations due to bending strain prior to outright failure. Liu et al. studied this using a flexible single-crystal silicon p-eigen-n diode, finding that bending-induced physical deformation leads to misalignment of electrodes and the intrinsic region. This reduces the effective horizontal electric field, thereby decreasing the diode’s current density, with the effect amplifying as bending strain increases [152]. In a similar vein, Yang et al. explored the physical mechanisms of flexible microwave passive components under mechanical bending. Their findings revealed a direct relationship between a decreasing bending radius and increasing inductance and capacitance values of the component [153].

3.3. Impact-induced damage

Flexible engineering devices, epidermal devices, and textile-based devices are prone to unexpected impacts or collisions, potentially leading to device failure (Figure 4b) [154–158]. Notably, a trade-off exists between mechanical robustness and functional performance in flexible electronics like e-skins. Enhancements in resilience to external mechanical shocks often compromise their sensing capabilities, monitoring functionality, flexibility, and stretchability [159,160].

Advances have been made in designing impact-resistant devices. J. H. Yuan et al. introduced a viscoelastic encapsulation layer atop a stretchable electronic device to counter impact loads and diffuse energy through viscoelastic properties. Their theoretical model (Figure 4c) suggests that the impact resistance of such devices depends on the encapsulation layer’s thickness and viscoelastic attributes, as well as the impact’s duration [114]. Yanan Wang et al. engineered a Mechanical Shock Tolerant (MST) e-skin that spontaneously replicates the protective and sensory functions of natural skin. This e-skin, comprising a Conductive Collagen Fiber Sponge (CFS) enveloped in an Elastic Non-Newtonian Gel (ENG), efficiently dissipates mechanical energy when subject to impact load, leading to a 455% extension in buffer time and a 76.5% decrease in peak force [161].

3.4. Destruction caused by the mismatch of material properties of multi-layer structures

Flexible electronic devices often utilize multilayer structures to maintain diverse functionalities such as monitoring, stretchability, and hermeticity [162–164]. Nevertheless, these structures can present drawbacks, primarily due to the distinct physical properties of different layers. For instance, the modulus of elasticity can differ up to five orders of magnitude between layers [115,165–169], and materials can have varied sensitivities to humidity and temperature fluctuations [170–172]. Thus, interface disruption or delamination may occur under complex mechanical deformation or environmental changes.

Even without external changes, flexible devices may degrade or fail due to the mismatch in physical properties within their multilayer materials. Given the stringent encapsulation requirements of these devices, any mechanical defects in the brittle oxide film within the multilayer structure can severely impact performance. While the polymer layers in these structures can recover from large strains, the metal oxide layers are brittle and can fracture under minor strains from internal hygroscopic expansion. Typical fracture modes include oxide layer channel cracking and delamination at the oxide-organic interface. Moisture mainly penetrates the structure through pinhole-like defects in the oxide layer [173,174]. However, channel cracks can exacerbate moisture penetration by providing a line source rather than a point source from the initial pinhole. When delamination at the oxide-organic interface is accompanied by channel crack expansion and increased hygroscopic expansion, the situation worsens [66,175]. Moisture absorption at the delamination interface creates a regional moisture source, significantly accelerating humidity penetration into the multilayer structure, which can be fatal for the flexible device [116].

3.5. Characterization methods and experiments for strength failure

Strength failure characterization methods, their corresponding procedures, and instruments are detailed in Table 1. Notably, we currently lack characterization methods for destruction caused by material property mismatches in multi-layer structures.

Table 1. Characterization methods of strength failure.

Failure modes	Test procedures	Measuring Instruments	Advantage	Disadvantage
Tensile-induced damage	Fragmentation testing (Uniaxial tensile testing)	OM, AFM, SEM	In-situ observation techniques integration possible.	Only qualitative data on sample’s surface condition.
Bending-induced damage	Rod bending test	Digital multimeter	Simple, versatile procedure for all flexible thin film devices.	Direct rod contact allows only tensile strain; manual handling may cause damage and strain inconsistency.
	Bending test dependent on electrical signals	Strain-sensitive functional layers; strain sensors	Real-time stress distribution visualization during deformation.	Potential significant deviation in measured strains due to various factors.
	Bending test independent of electrical signals	CCD camera, surface labeled grating method, photoelasticity, Moiré patterns, X-ray diffraction	Independent of electrical signals, preserving sample’s mechanical properties.	Only surface strain measurable, necessitating sample surface modifications.
Impact-induced damage	Drop hammer impact test	Impedance analyzer	Straightforward handling.	Integrated hammer-base setup may cause additional vibrations and impact.
	Ball drop test	Impedance analyzer	Straightforward handling.	Falling ball may cause irregular secondary impacts.

To assess the failure mechanism of flexible electronic devices under tensile loading, electromechanical test methods, such as uniaxial tensile or fragmentation testing, are used (Figure 5a). This method is employed for new material and deposition process investigations in flexible electronic device development [180,181], and also for flexible thin film device inspection [180–182]. In these tests, the film-substrate system undergoes strain, forming cracks perpendicular to the strain direction until crack spacing saturates [129]. The critical reliability parameter, crack onset strain (COS), is maintained below any mechanical strain experienced during fabrication or use. To rapidly and accurately measure characterization data like COS, tensile testing is often paired with in-situ monitoring techniques for crack detection and mechanical characterization. Common techniques include optical microscopy (OM) [183–185], atomic force microscope (AFM) [132,186,187], scanning electron microscope (SEM), and field emission scanning electron microscope (FESEM) [188–191]. In-situ X-ray diffraction (XRD) is also used to determine thin film deformation mechanisms [188,189,192,193]. Characterization of electrical properties is also crucial in tensile testing. Pre-established metal contacts can measure the resistance of the thin film structure [110,194–196]. Resistivity changes pre- and posttest help ascertain the impact on device performance or possible failure.

Figure 5. Characterization methods for strength failure. (a) SEM images of Mo films of varying thickness - (I) 500 nm, (II) 250 nm, (III) 70 nm, and (Ⅳ) 40 nm - on PI substrates after the application of a 12% strain. Adapted with permission. Copyright 2017, Elsevier BV [130]. (b) the falling ball test, employed to evaluate the reliability of pressure stress concentrations in flexible displays. Left, a fully supported sample backed by a solid steel block. Right, a partially supported sample propped on two rollers. Reproduced with permission. Copyright 2008, IEEE [176]. (c) static bending test of the CIF assembly, utilizing bending rods of varied radii. Adapted with permission. Copyright 2016, IEEE [177]. (d) three-point static bending test. Reproduced with permission. Copyright 2016, IEEE [177]. (e) the lab-made bending test machine and outer/inner bending test experiments. Reproduced with permission. Copyright 2014, Elsevier BV [178]. (f) optical device for strain measurement on the surface of a curved film. Adapted with permission. Copyright 2021, Wiley-VCH Verlag [179].

Several bending experiments and monitoring techniques have been devised to evaluate the electromechanical performance of flexible devices under bending deformation. One such method, the rod bending test (Figure 5c), mounts flexible devices on cylindrical fixtures with different radii to calculate strain; concurrent in-situ electrical property tests are also performed [152,153,197]. Ji-Hye Kim et al. expanded on this with a three-point bending test (Figure 5d) to quantify the load and bending radius at the fragment fracture in chip-in-flex (CIF) [177]. Yang et al. employed a custom bending test apparatus (Figure 5e) to evaluate flexible devices bidirectionally. Starting with a flat-clamped sample, the decreasing bending radius was achieved by moving the fixtures closer. The outer bending (‘Λ’) induces tensile stresses on the film, while the inner bending (‘V’) results in compressive stresses [178]. Common techniques for monitoring the bending properties of flexible device layers include the direct encapsulation of strain-sensitive functional layers with the aid of existing bending devices [198–200], and the installation of flexible strain sensors on device surfaces [201]. However, strain measurements can be significantly skewed by neutral axis shifts, interlayer interface sliding, and the effects of strain sensors or strain-sensitive layers [202]. Hence, the use of alternative methods to observe the curvature and surface strain of curved films is vital in the research and development of flexible device. Kohei Kuwahara et al. evaluated the curvature at the bent film’s center using a charge-coupled device (CCD) camera to capture the film shape profile [184,185]. Norihisa Akamatsu et al. employed a surface marking grating method for quantitative evaluation of flexible materials’ surface radius (Figure 5F) [203,204]. Various other non-electrical methods for measuring curvature and surface strain have been reported, including photoelasticity, Moiré patterns, and X-ray diffraction [179,205,206]. Most tests focus on surface strains, with neutral mechanical plane (NMP) or neutral axis (NA) position control typically relying on theoretical methods. Notably, Masayuki Kishino et al. first experimentally quantified the internal strain distribution of bent PDMS films using a cholesteric liquid crystal elastomer (CLCE) as an internal strain sensor, determining the NMP position [207].

There are fewer studies on mechanical characterization tests for flexible electronic devices’ impact resistance. Yanan Wang et al. proposed an effective method for designing mechanically shock-tolerable (MST) e-skins, utilizing a drop hammer impact tester to evaluate the samples’ mechanical impact resistance. For control, the base itself was subjected to direct drop hammer impacts [161]. Alternatively, Quayle Chen et al. tested flexible displays’ drop resistance with a ball drop test. Two extreme support conditions were considered: ‘full support,’ where a solid steel block supports the sample, and ‘partial support,’ where two rollers support it (Figure 5b). A steel ball is dropped from a fixed height above the sample, creating an impact load and causing stress concentration on its surface. The drop height is altered until the sample is destroyed. To enhance drop point precision, a magnetically controlled system is typically employed to minimize experimenter interference [176].

4. Interfacial failure

The integration of semiconductor or metal conductors with a flexible substrate results in unique characteristics. Notably, the substrate, being a flexible material, has a significantly lower modulus of elasticity than the rigid functional layer. Consequently, the soft interface between the film and substrate introduces novel attributes of structural damage. Park et al. [208] observed a system consisting of single-crystal silicon strips and rods supported by plastic sheets through a compression bending experiment, during which one end of the substrate was fixed, and the other end of the substrate was compressed to cause upward buckling instability of the substrate until failure occurred between the thin film structure and the flexible substrate. The results indicated a variation in damage patterns based on film thickness. With a thin film, bending-induced failure was dominant, characterized by strain values surpassing the failure threshold due to bending, causing film fracture. A thicker film altered the damage mode to interface slipping, which prevented cracking even under high loads. Further increasing film thickness led to delamination as the dominant mode, starting at the strip edge and progressing to the center with increased bending, leading to eventual film detachment.

4.1. Interfacial slipping

Interface slipping, observable through in-situ tests, evolves gradually as tensile strain increases, as shown in Figure 6a [209]. In devices under tensile strain, this slipping commonly precedes material fracture. Park et al.‘s findings suggest that interfacial slip, although difficult to observe, poses a greater risk than material fracture in practical applications [208]. In the context of linear-elastic fracture mechanics (LEFM), the stress intensity factor, $K_{\mathrm{I}\mathrm{I}}$, of sliding mode (mode II crack) governs the interfacial slip damage [24,212,213].

Figure 6. Interfacial failure mechanisms alongside their characterization methods. (a) in situ SEM images capturing the progressive sliding at the interface of a horseshoe-shaped copper interconnect deposited on PDMS, stretched sequentially to 30%, 50%, and 100%. Adapted with permission. Copyright 2011, IOP Publishing [209]. (b) delamination between PI layers of prototype stretchable interconnect. (1) SEM image of a bonded sample where PI has been printed once on the top and bottom layers of encapsulated silver, following cooling from curing temperature to ambient temperature. (2) SEM image of a delaminated sample with PI printed three times on the top and bottom layers of encapsulated silver, following cooling from curing temperature to ambient temperature. (3) optical image of a printed interconnect, showcasing variable silver width and PI thickness after cooling from curing temperature to room temperature. Adapted with permission. Copyright 2021, Elsevier BV [210]. (c) the 3M tape adhesion test on the Cu/PET interface, following plasma treatments for durations of 0 min (left) and 7 min (Right). Reproduced with permission. Copyright 2017, Elsevier BV [44]. (d) Scotch tape adhesion test for an al feature on a magazine paper substrate. Reproduced with permission. Copyright 2012, American chemical Society [211]. (e) a peel test device integrated with a camera for examining the local geometry of the delamination front. Adapted with permission. Copyright 2010, IOP Publishing [209]. (f) schematic illustration of T-peel test on Cu/PET flexible substrate. Adapted with permission. Copyright 2017, Elsevier BV [44]. (g) schematic illustration of the laser-induced interplanar sputtering (LIIS) process, employed to facilitate the delamination of PI film from its substrate. Adapted with permission. Copyright 2020, American chemical Society [45].

Longchao Dai et al. [214] leveraged fracture mechanics to develop a slip model resistant to delamination damage. Noting the strain energy discrepancy in the structure ahead and behind crack tips [24], they expressed the energy release rate at the film-substrate interface as:

(5) $\begin{array}{c}G=\frac{1}{2{\bar{E}}_s}\frac{N_x^2}{h_s}\left[{\mathrm{\Delta }}_1-12\cdot \frac{w_0}{h_s}\frac{{\mathrm{\Delta }}_0}{{\mathrm{\Delta }}_3\left(1+t\mathrm{\Sigma }\right)}\right],\end{array}$(5)

where $N_x$ represents the internal force aligned with the film structure direction, and $w_0$ denotes the bulking amplitude [208]. Oher parameters (${\mathrm{\Delta }}_0,{\mathrm{\Delta }}_1,{\mathrm{\Delta }}_3,\mathrm{\Sigma }$) aredefined in terms of $t={\bar{E}}_f/{\bar{E}}_s$ (the moduli ratio of the films to the substrate), and $\eta =h_f/h_s$ (the thickness ratio of the films to the substrate). They further defined the stress intensity factor for mode II cracks as:

(6) $\begin{array}{c}{K}_{\mathrm{I}\mathrm{I}}=\sqrt{\frac{G{E}_{\ast }}{1-{\beta }^2}}\left|sin\psi \right|,\end{array}$(6)

where $\beta$ is the Dundurs’ parameter, $1/E_{\ast }=1/2\left(1/{\bar{E}}_s+1/{\bar{E}}_f\right)$, and $\psi$ is the phase angle, influenced by material parameters and structural geometry [213]. By substituting the observed $w_0$ into these equations, they obtained the critical energy release rate and the critical interfacial toughness $K_{\mathrm{I}\mathrm{I}\mathrm{C}}$. Subsequently, they analyzed the stress state near the crack tip for different film thicknesses during interfacial slip crack expansion. Using the simulated phase angle, they derived the stress intensity factor at the crack tip, which was then compared with the corresponding interfacial toughness.

On this basis, Chen Hang et al. deduced several qualitative conclusions through theoretical modeling and experiments. With an increasing applied load, the film initially slips to dissipate some deformation energy. As the sliding portion expands, the remaining deformation energy surpasses the critical threshold, triggering delamination. This shift from slip to delamination corresponds to the total release of the film’s deformation energy due to delamination [215]. Slip failure, which causes tangential displacement between the film and the substrate, is akin to mode II cracking, while film delamination resembles mode I cracking, where the crack opens. Different crack modes yield distinct stress intensity factors [216]. Therefore, for such flexible devices, which consist of brittle functional layers on flexible substrates and undergo finite deformation, the distinct dimensions and failure modes introduce difficulties and uncertainties concerning interfacial toughness. To address these uncertainties, Hang et al. proposed a slip zone model. By integrating the ideal elastic-plastic cohesive constitutive relation with strength theory, they quantitatively clarified the interfacial slipping failure mechanism in such flexible thin film structures with varying dimensions. They linked failure modes to stress thresholds at the interface, demonstrating that interfacial sliding happens when maximum shear stress equals the interface’s shear strength, and delamination occurs when maximum peeling stress meets the interface’s tensile strength [41].

Interfacial sliding signifies that flexible electronic device failure is not solely governed by the inorganic electronic material’s fracture strain. Rather, it’s also shaped by interfacial shear stresses prompting slip behavior, and these stresses typically peak near the free edge of the functional layer, a finding corroborated by Qian Zhao et al’s experiments [217].

4.2. Interfacial delamination

In thin film structures bending experiments, interfacial delamination is precipitated by interfacial normal stress or peeling stress [208]. Delamination occurs when this stress surpasses the interface’s tensile strength [218,219]. A common issue in IC chip-integrated flexible devices is interfacial delamination, triggered by bending and problems in bonding brittle structures with flexible substrates. To tackle this, Ying Chen et al. proposed an interfacial crack model-based theoretical model describing the delamination between IC chips and flexible substrates [220]. The model considers the flexible substrate as a support beam, with its bendability denoted by a critical curvature, determined by the interface strength between the IC chip and substrate. The energy release rate of the model is given by:

(7) $\begin{array}{c}G=\frac{c_1{M}^2}{16I{h}^3},\end{array}$(7)

where $M$ represents the interface’s equivalent bending moment; $h$ is the IC chip’s thickness; and $c_1$ and $I$ depend on the material and geometry of the elastic layers. The interfacial toughness is determined by the critical bending deformation, defined as:

(8) $\begin{array}{c}{G}_c=\frac{c_1{\left(1-C_3\right)}^2{\omega }_{\mathrm{m}\mathrm{a}\mathrm{x}}^2{\bar{E}}_1^2{I}_1^2}{16I{h}^3},\end{array}$(8)

where $C_3$ is a material and geometry dependent dimensionless constant, ${\bar{E}}_1$ and $I_1$ denote the plane-strain modulus and the moment of inertia per unit width of the IC chip, ${\omega }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the critical curvature. Failure occurs when the energy release rate surpasses the interfacial toughness [220]. Interface failures in IC chips integrated with flexible devices also often manifest at solder joints between chips and flexible circuits, jeopardizing circuit integrity and causing device failure. Liquid metals (LMs), which remain liquid at room temperature and exhibit metallic conductivity, offer potential solutions to these failures. LMs serve as stretchable, deformable conductors, surpassing the constraints of conducting polymers and or deterministic structures [221]. The utilization of liquid metals in flexible electronics is not unprecedented, having been employed in designs including stretchable wires, reconfigurable antennas, and self-healing circuits [222]. Ozutemiz et al. expanded liquid metal application to connect IC chips with LM-coated traces. They employed an innovative HCl vapor treatment to solder LM-coated trace terminals to microelectronic circuitry metal pins, enhancing conductivity and interface reproducibility [223]. Furthermore, Kim et al. innovated a room-temperature, stretchable soldering technique harnessing liquid metal properties to firmly link rigid chips and flexible connectors. This novel solder, a liquid metal-silver nanowire composite, demonstrated impressive conductivity and stretchability, maintaining its properties even when elongated by over 6 mm, ensuring minimal contact resistance [224].

For structures comprising flexible substrates and rigid islands, the stretch-induced interfacial delamination is controlled by the peak energy release rate, similar to flexible electronic integrated chips’ bending-induced delamination [225]. It is a major failure mode in interconnect design [226]. Under tension, interface delamination in a fully encapsulated structure can accelerate cohesive interconnect fractures, resulting in open or short circuits [227–229]. To comprehend the cohesive failure mechanisms of interconnected wires, O van der Sluis et al. established a 3D numerical model illustrating the stretching-induced delamination process, utilizing cohesion zone cells to mimic the interface behavior [230,231]. The experimental findings of delamination locations during structural loading are well-aligned with the numerically calculated processes [209].

Interfacial delamination can be a significant issue during not only the use but also the fabrication of devices, particularly during thermal processing. The mismatch in the coefficient of thermal expansion between brittle films and flexible substrates during thermal processing generates substantial compressive stresses, which can lead to instability and possible interfacial delamination. Moon et al. [232] conducted experiments that emphasized the role of initial interface defects in initiating delamination behavior.

Wrinkling is another potential instability in these structures, which can subsequently lead to delamination [233–235]. Utilizing the analytical solution of wrinkles and finite element analysis, Haixia Mei et al. formulated an approximate formula to estimate the normal traction at the interface under compressive loading and predict the onset of wrinkle-induced delamination. An additional study explored the influence of preexisting delamination on the critical strain at the buckling instability onset using finite element eigenvalue analysis [236]. This research demonstrated a smooth transition from wrinkle to delamination under increasing compressive loading. The behavior of buckling-induced delamination due to the two-point bending of the film structure was studied experimentally and numerically. O. van der Sluis et al. proposed a model to estimate the interfacial toughness that disregards the elastic energy released from the substrate and the plastic dissipation within it [198]. They integrated the substrate’s elastoplastic characteristics with the brittle structure’s post-energy-release straightening behavior to elucidate the interfacial delamination, subsequently deriving the work of separation and interfacial strength.

Thermal forces can also instigate wrinkling and delamination of elastic films attached to thick flexible substrates (Figure 6b) [210]. Sanjay Goyal et al. analyzed interface delamination caused by thin film buckling and wrinkling using an energy minimization principle. They developed a bilinear traction-separation law to describe temperature- related instability and failure onset [237]. Identifying the two critical temperature offsets for wrinkling and delamination onset enables the derivation of the cohesive stiffness and strength. Thermal-induced peeling stress exceeding the cohesive stiffness leads to wrinkles, and surpassing the cohesive strength causes delamination.

Vapor can also trigger interfacial delamination. Polyimide, a commonly used substrate material in flexible electronics, is highly hygroscopic, and its interfacial bond strength with other materials is influenced by its water absorption [238]. During high-temperature thermal processing, absorbed moisture may evaporate at the material interface, potentially causing delamination [239–241]. Jacob Brenneman et al. developed a nonlinear fracture model, using vapor pressure as the delamination driving force to simulate interface delamination induced by water evaporation in high-temperature environments. Their experimental findings reveal that the energy release rate is regulated by the moisture content, rather than the brittle film thickness or initial crack width [210].

4.3. Characterization methods and experiments for interfacial failure

The methods, procedures, and instruments for interfacial failure characterization are outlined in Table 2.

Table 2. Characterization methods of interfacial failure.

Failure modes	Test procedures	Measuring Instruments	Advantage	Disadvantage
Interfacial slipping	Bending test	SEM	Integration with in-situ observation techniques.	Provide only qualitative sample surface data.
Interfacial delamination	Fragmentation testing	OM, AFM, SEM, etc.	Real-time stress distribution capture during deformation.	Strains can show significant deviations due to factors like neutral axis movement or effects of flexible strain sensors.
	Peel-off test	SEM	Direct calculation of peeling force.	Tear risk in brittle layer due to high stress.
	Tape test	Tape	Suitable for unfixable brittle materials.	Only qualitatively assess interface adhesion performance, determining only if the test interface’s adhesion force is less than the tape’s adhesion force.
	Laser-induced heating technique	SEM, XPS	Usable for large area testing in production.	Inapplicable for interfaces between two materials with similar thermal expansion coefficients.

The interface integrity in flexible electronics is upheld by interfacial forces such as van der Waals, electrostatic, or chemical bonds [242]. Experimentally, interface bonding behavior can be gauged via interfacial force and toughness measurements. The former measures maximum force per unit area normal to the separating materials while the latter quantifies the work needed for material separation [243].

Concerning interfacial sliding, the key metric is the experimentally determined slipping toughness. Standard rigid film tests like indentation or three/four-point bending can yield inaccurate results due to large deformations of the soft substrate. Dai et al. utilized fracture mechanics to analyze the slip mechanism of soft interfaces and determined interfacial toughness [214]. Subsequently, Huang et al. developed a method for measuring interfacial slipping toughness using a specially designed bending load on a silicon strip on a PDMS substrate and in-situ SEM monitoring of interface slip displacement [244].

Interfacial delamination involves more complex causes and mechanisms, leading to a variety of methods to measure interfacial forces or toughness. Fragmentation tests are useful for measuring interfacial forces in various thin film coating systems, including both inorganic and organic coatings [132,187,245]. These tests include stages of crack initiation, saturation, and depth-wise development. The final damage phase occurs when the differing Poisson’s ratios of materials induce interfacial delamination due to film buckling on the substrate [132]. Analytical models can then be used to calculate interfacial forces [246,247].

Scratch tests, extended by G. Covarel and X. Boddaert et al., can assess the interfacial bonding properties of organic thin film transistors (OTFTs) and ultrathin organic films on flexible substrates [248,249]. These tests involve a scratch indenter applying an increasing normal force to the film, initiating cracks that propagate toward the interface, and leading to delamination. Post-test, the critical load causing a certain failure mode is determined by observing the scratch trajectory using in-situ methods like optical microscopy [250].

The peel test, a method frequently used to gauge adhesive properties, employs a fixture to hold one end of a film, which is subsequently peeled from the substrate at a fixed angle (e.g. 90°) (Figure 6e,f) [44,209]. During peeling, a constant driving force or peel force is reached, which depends on factors such as film thickness, peel angle, material, and interface properties. This force can be determined as a function of the fixture displacement. In a steady-state stripping process, the relation between energy and force can be represented by [251]:

(9) $\begin{array}{c}{\mathrm{\Gamma }}_0+{\mathrm{\Gamma }}_{\mathrm{D}}=\frac{P_{\mathrm{f}}}{\omega }\left(1-cos\theta \right),\end{array}$(9)

Where ${\mathrm{\Gamma }}_0$ and ${\mathrm{\Gamma }}_{\mathrm{D}}$ denote energy dissipation due to interfacial fracture and other dissipation mechanisms respectively. $P_{\mathrm{f}}$ is the peel force, and $\theta$ and $\omega$ symbolize the peeling angle and the separation area length respectively. Often, film sides are trimmed prior to testing to yield a flat peel band and negate edge effects, changes in stiffness due to uneven film edge thickness [252].

A peel test variant, the transparent tape test (Figure 6c,d), is used when film-substrate adhesion is too weak for a regular peel test. The tape is applied to the film and peeled off, measuring the peel force. The maximum interfacial force that can be tested is less than the strength of the tape-bonded area. This method was utilized in experiments by Park et al. [44]and Licheng Tan et al. [54] to measure the peel force at various interfaces and has been executed on diverse flexible electronic devices [211,253–258].

Jin-Woo Park’s team developed a laser-induced heating method to assess the interfacial bonding strength between transparent conductive oxides (TCOs) and polymer substrates. This technique exploits the thermophysical property disparities between TCOs and transparent polymer substrates. By determining the critical pulse energy necessary for delamination and the temperature differential before and after irradiation, the interfacial bond strength is ascertained through thermal stress calculations [259–261]. This method offers a controlled and precise measurement of interfacial adhesion properties and facilitates delamination. Jing Bian et al. discovered that nano-cavities formed around the PI-glass interface during laser-induced heating, significantly diminishing interfacial adhesion. Theoretical computations demonstrate that the gas byproducts from PI thermal decomposition contribute to the hydrodynamic exfoliation of molten PI around the interface [45]. Furthermore, they found that a combination of laser flux and irradiation number control can precisely manage interface delamination behavior, paving the way for the fabrication of functional membrane structures. Figure 6g depicts the varied outcomes of Laser-induced Interfacial Spallation (LIIS) dependent on specific process parameters. In the case of incomplete separation, Polyimide (PI) films exhibit a degree of detachment yet largely remain adhered to the glass substrate. For nondestructive separation, ultrathin PI films are fully disengaged from the glass substrate without causing any damage. However, under destructive separation, after an intense LIIS process, the ultrathin PI films are discernibly wrinkled [45].

Bending tests are frequently employed to evaluate interfacial properties, especially in materials like metals and ceramics. For systems under bending loads, the presence of tensile and compressive stresses expedite the evolution of interface behavior. In instances where the film layer is brittle and conventional test methods, such as the peel test, risk damaging the film, a two-point bend test is utilized [258,259]. Based on earlier research on bending models for thin film structures, these induced stresses can compute interfacial properties like interfacial fracture energy [262,263]. However, this method does not consider preexisting residual stresses in the film and lacks precision in controlling the development of the desired interface occurrence [198].

5. Fatigue failure

External loads within the strength limit do not cause damage to the device within a short period, they may cause performance degradation or fatigue failure under long-term action. For example, as shown in Figure 7b, under cyclic bending deformation, the peak resistance baseline of the Ni-Cr-based flexible strain gauges shifted upward with the increase in the number of cycles. At the same time, the SEM images also indicated that cracks were generated at the unconstrained location [265]. It is necessary to estimate initial electrical performance and long-term stability of flexible electronic devices during mechanical deformation. So fatigue failure is one of the flexible electronic devices’ most common failure modes [266,267].

Figure 7. Fatigue failure mechanisms. (a) resistance changes of serpentine interconnects under cyclic loading with different tensile strains. Adapted with permission. Copyright 2021, Wiley-VCH Verlag [264]. (b) resistance change of flexible NiCr-based strain gauges under cyclic bending deformation. (1) resistance response illustrates an upward shift in the baseline correlating with increased peak resistance; (2) SEM images of cracks in an unconstrained position; (3) schematic illustration for the evolution of cracks, starting from initial unconstrained state, proceeding through opening during bending, and culminating in a state of partial closure after stress relief. Adapted with permission. Copyright 2022, Elsevier BV [265].

5.1. Mechanisms of fatigue failure

Several approaches focused on structural failure when investigating the fatigue behavior of polymer-loaded metal films. Wang et al. identified the onset of crack extrusion saturation at a certain cycle number ($N_{\mathrm{f}}$) as a key indicator of failure [268]. They discovered a notable correlation between Cu film thickness and the device’s fatigue endurance; thinner films demonstrated superior endurance. Other studies adopted different criteria for fatigue failure, such as marked changes in structural rigidity or the appearance of visible cracks [269,270].

Conversely, various studies highlighted that microstructural deformation in brittle materials (crack initiation and propagation) enhanced film resistance. X J Sun et al. posited that the critical fatigue life at microcrack nucleation (FLMN) is a more pertinent measure for polymer-supported metal films in flexible electronics than the life at structural instability [271]. Microcracks formed in the metal film during cyclic loading can significantly boost device resistance, prompting the use of electrical resistance measurements to characterize FLMN.

To determine device lifespan, Byoung-Joon Kim et al. employed in-situ resistance measurements to track the evolution of mechanical fatigue damage in metal films on flexible substrates. They defined a 5% cyclical resistance increase from the initial value as the fatigue lifespan, observing that fatigue life diminishes with heightened applied strain [46,272]. In Low Cycle Fatigue (LCF) scenarios, the material experiences plastic strain that aligns with the Coffin-Manson equation:

(10) $\begin{array}{c}\frac{\mathrm{\Delta }\epsilon }{2}={\epsilon }_{\mathrm{f}}{\left(2N_{\mathrm{f}}\right)}^c,\end{array}$(10)

where $\mathrm{\Delta }\epsilon /2$, ${\epsilon }_{\mathrm{f}}$, $c$, $N_{\mathrm{f}}$ denote strain amplitude, fatigue ductility coefficient, fatigue ductility exponent, and number of cycles to failure.

In High Cycle Fatigue (HCF) conditions, the S-N curve (stress-life method) is applicable, formulated as follows [273]:

(11) $\begin{array}{c}\frac{\mathrm{\Delta }\sigma }{2}={\sigma }_{\mathrm{f}}{\left(2N_{\mathrm{f}}\right)}^b,\end{array}$(11)

where $\mathrm{\Delta }\sigma /2$, ${\sigma }_{\mathrm{f}}$, $b$, $N_{\mathrm{f}}$ stand for stress amplitude, fatigue strength coefficient, fatigue strength exponent, and number of cycles to failure. As a result, resistance as a function of the number of load-unload cycles is an effective predictive criterion for fatigue life [274].

Fatigue failure in devices typically falls into two categories: tensile-induced and bending-induced fatigue (Figure 7a,b). Despite different categorizations, the underlying mechanisms are similar, and failure generally occurs in brittle materials [275–277]. Fatigue damage in such materials stems from repetitive mechanical deformation causing dislocation motion. Increased stress leads to dislocation accumulation, surface extrusions and intrusions, and ultimately stress concentration. The consequential local stress elevation at the damage site triggers crack evolution. High stress can expedite dislocation motion in the metal film, leading to earlier and more pronounced resistance increases under higher strains in certain fatigue tests [278].

The film’s thickness and microstructure dictate its mechanical and electrical properties. Numerous studies have determined that the film’s thickness and applied strain synergistically influence fatigue lifetime or crack development in films on flexible substrates [46,268,274]. Under conditions typical of HCF, which involve low strains, thinner films tend to have longer fatigue lifetimes. In contrast, under conditions typical of LCF, which involve high strains, thicker films exhibit superior fatigue endurance. The fatigue mechanism at low strain chiefly involves fatigue damage caused by dislocations. As the number and size of extrusions decrease with film thickness, dislocation interactions are suppressed at smaller film thicknesses, which in turn inhibits crack propagation and enhances fatigue lifetimes. For high-strain fatigue, thicker ductile films with larger grains outperform thinner brittle ones in terms of fatigue life [46,279].

The mechanical properties of flexible films made from doped nanomaterials like Ag nanoparticle-modified graphene nanosheets are significantly influenced by cyclic deformations. These films have been used in flexible electronic devices following tests for cyclic bending. An increase in resistance was recorded on the bending tensile and compression sides as the number of cycles increased. This resistance change in bending under tension samples is preliminarily attributed to metal bending cracks affecting electron transport. However, considerable contact resistance exists between nanoparticles under bending stress [280]. In comparing nanoparticles and nanowires with nanosheets, the latter established a unique electrical conductivity principle and superiority in point-to-point and wire-to-wire contacts due to their advantage in physical contact stability as electrode materials, attributed to their surface-to-surface mutual contact [281]. In a separate study, flexible, stretchable electrodes were developed using PDMS-Ag nanosheet composites by Chengwei Li et al. The complex cyclic tensile tests, contact point tunneling effect theoretical model, and finite element simulations illustrated the conductivity mechanisms of these flexible electrodes during stretching. The resistance alteration in the course of stretching resulted from changes both in contact and tunneling resistance amid incompletely connected Ag nanosheets. When the proportion of PDMS in the electrode was minimal, subpar stretchability was observed, attributed to the split in the conductive network under stress dominating resistance change. Conversely, a higher PDMS content led to an increased tunneling effect on resistance, progressively amplified with the decrease in Ag nanosheet density, presenting visibly when strain led to separation between many Ag nanosheets [282].

Fatigue failure also impacts the utilization of three-dimensional (3D) flexible electronic devices. These devices, during real-world operations, inevitably experience repeated out-of-plane compression [283], which can cause fatigue failure of the ribbon interconnect [27,284]. This failure mode mirrors the fatigue failure observed in films on flexible substrates, typically resulting from cyclic stress-induced microcracking or crack propagation. To evaluate the fatigue resistance of 3D ribbon flexible electronic devices, Xu Cheng et al. proposed a fatigue lifetime model for three-layer ribbon mesostructures (PI/Cu/PI) [42]. Their model is contingent on the peak Mises stress in the polymer layer and the fatigue limit of the material. They also proposed a fatigue-resistant design strategy by encouraging a shift from metal-dominated to polymer-dominated failure [283–285].

Besides impacting resistance in flexible electronics, fatigue failure also compromises the energy storage capacity of flexible devices. This degradation is evident in the diminishing electrical energy storage with increasing external load cycles. For instance, Li et al. observed a decline in the capacity retention of flexible zinc-manganese batteries to approximately 90% after 100 bending cycles [286]. Similarly, Liu et al. reported a reduction in the capacitance of a flexible supercapacitor to 88.4% after bending at 180°, followed by 10,000 electrochemical cycles, while a non-bending supercapacitor showed negligible changes in capacitance [287]. Cai et al. noted that a flexible cell’s capacity fell to 95% post 30 electrochemical cycles under sustained bending, highlighting bending deformation’s adverse effect on battery longevity and stability [288]. Bending-induced uneven stress distribution can cause the electrode sections in flexible batteries to crack, leading to the loss of active material, battery capacity, and even outright failure. Notably, while thin film batteries and supercapacitors exhibit minor thickness, the repercussions of bending stress become more pronounced in thicker electrode materials [289].

The fatigue behavior of flexible electronic devices also correlates with environmental temperature. Martynenko et al. studied polyimide substrates with copper circuits, finding that higher temperatures, counterintuitively, postponed device failure due to reduced stiff motion of conductors at elevated temperatures, minimizing copper trace cracks [290]. Alzoubi et al. examined temperature’s impact on sputtered copper films on PET substrates, revealing faster failures with increasing temperature, likely due to oxidation and dislocation thermal activation [267]. Chapel et al. investigated the combined effects of thermal stress and cyclic loading on epoxy resin-encapsulated flexible electronic devices. Brief high-temperature exposure fortified the encapsulation-substrate bond, enhancing device endurance under cyclic strain. However, extended exposure at these temperatures weakened the encapsulating material, escalating the likelihood of device interface delamination under similar strains [101].

It’s worth noting that not just elevated temperatures but also cyclical thermal stresses influence the endurance of flexible devices. As the demand grows for compact flexible electronic devices with greater power outputs, their rigid conductors undergo repetitive on/off currents. Over the device’s lifespan, such temperature variations from current-induced heating could expose the flexible connectors or thin-film structures to nearly 10,000 thermal cycles [291]. Conventional integrated circuits have seen extensive research on thermal cycling-induced failures. Shien Ri reported on the damage to thin aluminum films following high-cycle thermal testing, observing mound and void formations on the stressed films. Young-Bae Park explored microstructural effects on failure modes by inducing Joule heating cycles in copper thin films using alternating current (AC) [292]. Thermal cycling subjects a flexible film to alternating tensile and compressive stresses, resulting from thermal expansion property disparities between the film and the flexible substrate. With increased cycling, these recurring stresses can trigger the emergence of cracks, voids, and hillocks in the film, compromising electrical conductivity [291,293].

5.2. Characterization methods and experiments for fatigue failure

Mechanical testing evaluates the fatigue properties of flexible electronic devices, identifying performance changes during or after mechanical deformation via in-situ observation or electrical testing (Table 3).

Table 3. Characterization methods of fatigue failure.

Failure modes	Test procedures	Measuring Instruments	Advantage	Disadvantage
Fatigue failure	Uniaxial/biaxial cyclic tensile testing	Semiconductor analyzer、Displacement Sensors	Applies solely tensile stress on the sample,	Requires sample pre-stretching for buckling prevention during cyclic loading.
	Free arc bending test	Battery cycler, Conductivity meter, Impedance analyzer, etc.	Maximum stress concentration at the sample’s bending point.	May induce large stresses near clamping area, and fixture movement limitations hinder large bending deformations.
	Variable radius bending test	Conductivity meter, Impedance analyzer, LCR meter, etc.	Adaptable bending shape to target bending radius, avoiding stress concentration near fixtures.	Limited test location, precludes comprehensive device performance testing in one run
	Sliding plate test	Impedance analyzer, Digital multimeter, etc.	Stable fixture-sample connection due to separation of clamped and bent parts, capable of high-frequency cyclic tests on multiple samples simultaneously.	High initial strain potentially causing relatively stiff device rupture
	Variable angle test	Impedance analyzer, Digital multimeter, etc.	Allows alternate cyclic bending deformation in two different directions on the same sample	Test instrumentation is complex and imposes constraints on the device shape.
	Cyclic rubbing test	Impedance analyzer	Simple setup, suitable for assessing the protective efficiency of encapsulation layers.	Accumulated heat during friction cycles may damage device or skew testing results.

Cyclic tensile tests, using a vertical axial tension machine, are commonly applied to study fatigue behavior of films on flexible polymer substrates (Figure 8f). Laser displacement sensors or capacitive-type extensometers are employed to quantify tensile displacement. Since in-situ observation tools like SEM are not compatible with loading devices, resistance measurements monitor device performance during loading [101,274,297]. Samples are subjected to a defined prestrain prior to cyclic loading to prevent buckling and enhance device flexibility [274]. Post-stretching treatments, such as silicon block attachment, prevent crack closure and facilitate damage observation in subsequent in-situ analyses [274,275].

Figure 8. Characterization methods of fatigue failure. (a)-(e).Schematic illustrations and devices of the bending test method for fatigue endurance. (a) free arc bending test. Reproduced with permission. Copyright 2021, Elsevier BV [294]. (b) variable radius bending test. Reproduced with permission. Copyright 2017, Nature Publishing group [141]. (c) sliding plate test. Adapted with permission. Copyright 2013, Elsevier BV [46]. (d) variable angle test for unidirectional bending. Adapted with permission. Copyright 2016, IEEE [295]. (e) variable angle test for bidirectional bending. Reproduced with permission. Copyright 2011, IEEE [267]. (f) Biaxial cyclic tensile testing system. Adapted with permission. Copyright 2022, American chemical Society [296]. (g) schematic illustration of cyclic rubbing test. Adapted with permission. Copyright 2022, Nature Publishing group [115].

Bending fatigue tests for flexible electronic devices have been precisely classified and standardized [278], encompassing the free arc, variable radius, sliding plate, and variable angle tests (Figure 8). The free arc bending test (Figure 8a), extensively used for testing hard films on flexible substrates, employs two fixtures to induce a bending motion in the sample [294,298–301]. The design should prevent stress concentration at the sample holding area, instead focusing maximum stress at the sample’s bending point. Additionally, the method permits cyclic application of tensile and compressive loads to the film on the flexible substrate, achieved by forming the sample into a convex and concave shape, respectively, in two sequential bending cycles [178,302,303]. Electrical property tests can be conducted during or after bending, facilitated by fixture electrical contacts. This method, albeit simple and straightforward, is limited in applying large bending deformations.

The variable radius bending test (Figure 8b) has a similar basic concept but with a distinct experimental approach where the sample is bent between two guides to attain the desired bending radius [44,141,304,305]. This approach, avoiding stress concentration near the fixture, is suitable for fatigue testing of thin films and silver nanowire electrodes on polymer substrates.

The sliding plate test (Figure 8c), with a setup akin to the variable radius test, features different motion trajectories for the plates [46,306,307]. In this method, one plate remains fixed while the other undergoes repetitive linear motion parallel to the sample. This cyclic motion allows different sample sections to alternately experience bending and non-bending states. The clamping section is separate from the bending part, ensuring stable clamp-sample connection and enabling high-frequency testing of multiple samples.

The variable angle test (Figure 8d), widely used for fatigue testing of various structures on flexible substrates, has two proposed experimental setups [267,279,295,308–310]. In the first setup, the sample is horizontally positioned on the device, held at one end by a fixture and at the other by a movable arm. The movable arm executes a back and forth motion around an axis at variable angles to apply sample bending [21,308,310]. Conversely, in the second setup, the sample is vertically positioned with two small pins perpendicular to the sample inducing cyclic bending (Figure 8e) [267,279,309]. The lower roller mitigates vibrations from the balancing block motion, ensuring a smooth bending process. Given that bending deformation varies with each test, the selection of an appropriate bending test method is crucial to simulate specific test operating conditions.

Fatigue patterns in flexible electronic devices differ based on their fabrication and application, often necessitating custom-designed fatigue tests. For instance, Chapel et al. explored the effects of thermo-mechanical aging on flexible devices, incorporating cyclic tensile testing and a heating device in their investigation [101]. In order to study the stability of flexible pressure sensors under friction, Yuan Zhang et al. conducted a test where a sample was subjected to a pressure of 10 kPa against sandpaper and was slid for a distance of 2 mm over 10,000 cycles (Figure 8g). The sensor exhibited commendable fatigue resistance, with no substantial change in signal waveform or amplitude throughout the test [115].

6. Electrical failure

The reliability of flexible electronic devices hinges on both mechanical and electrical stability. Electrical failure, shaped by the magnitude and pattern of current, underlies decisions in component selection and circuit design. Two phenomena, electromigration and Joule heating, often jeopardize electrical reliability, potentially precipitating performance failures [293]. Electromigration typically accompanies the Joule heating effect, hastening device failure [311]. In addition, the Joule heating effect also induces thermal mismatches within multilayer structures, instigating unique thermo-mechanical behavior and electrical failure mechanisms [312]. Moreover, electrochemical failure is increasingly observed in flexible energy storage devices. Flexible batteries, subjected to charge/discharge cycles and external deformations, experience complex stresses, including diffusion-induced stress (DIS), bending, and tensile forces. Despite their electrochemical strengths, many electrode materials degrade under these conditions, elevating the risk of breakdown [313,314].

6.1. Electromigration failure

Electromigration is a prevalent effect in high current density circuits, where the high electron flux displaces atoms within the conduction path toward the anode. This displacement depletes atoms at the cathode, causing void formation, and aggregates atoms at the anode, resulting in mounds and protrusions (Figure 9a). Void growth can precipitate wire breakage and localized Joule heating, leading to a complete circuit breakdown [311,317]. With flexible electronic devices operating typically at current densities of 10³-10⁴ A/cm² [318,319], electromigration is a significant concern, especially given the trend toward miniaturization and increased functionality [320,321].

Figure 9. Electrical failure mechanisms and characterization methods. (a) microstructural illustrations of silver-printed interconnects pre-failure (I) and post open-circuit failure (II), along with a SEM image at the cathode (III). Adapted with permission. Copyright 2019, Springer Verlag [48]. (b) Electrothermal coupling failure mechanism of stretchable thin-film conductors: (I) SEM image of an initially planar electrode (inset) displaying random intrinsic nano-cracks on the electrode; (II) SEM image of the fracture region (inset) post failure, along with a SEM image presenting dispersed metal particles within the crack, induced by electrical discharge. Adapted with permission. Copyright 2022, American chemical Society [312]. (c) (1) TEM images of the lithiation process of spherical silicon particles: expansion and cracking of the outer layer of the particles occurs. Adapted with permission. Copyright 2012, American chemical Society [315]. (2) SEM images of nanowires in their initial and lithiated expanded states. Adapted with permission. Copyright 2015, Nature Publishing group [316]. (d) (1) schematic diagram of the experimental setup for IR measurement during electromigration tests. (2) schematic representation of a dog-bone pattern structure of Ag interconnects. (3) SEM image of the microstructure of as-sintered interconnects. Adapted with permission. Copyright 2019, Springer Verlag [48]. (e) schematic illustrations (1) and images (2) of the electrothermal coupling failure process of stretchable thin-film conductors. Adapted with permission. Copyright 2019, Springer Verlag [312].

Electromigration-induced failure life in metallic wires is typically predicted using Black’s equation:

(12) $\begin{array}{c}{t}_f=A_B{J}^{-n}exp\left(-\frac{E_a}{k_{B}T}\right),\end{array}$(12)

where $A_B$ is a constant, $J$ is the current density, $E_a$ is the activation energy, $k_B$ is Boltzmann’s constant, $T$ is the substrate temperature, and $n$ is the current-density exponent [318,322]. However, Black’s equation lacks accuracy when considering electromigration in conductors with porous structures, as it doesn’t fully account for microstructural effects.

Electromigration, governed by diffusion and significantly accelerated by high temperatures and fine microstructures, is especially prominent in printed circuits and thin films of flexible devices [323]. These devices feature extensive low-temperature diffusion paths, like grain boundaries and interfaces, enabling substantial mass transport. As film thickness decreases and thermal effects intensify, diffusion processes along surfaces and interfaces become increasingly significant [324]. In the comparison conducted by Kyung-Tae Jang and colleagues, printed Ag interconnects, with their porous microstructure, were observed to fail earlier due to electromigration, compared to vacuum-deposited Ag interconnects with a dense, void-free microstructure [325]. Zhao Zhao et al. suggested a prediction method for the failure life of Ag wires, specifically for electromigration failures in printed Ag wires. Their model derives the resistance variation ratio $R\left(t\right)$ over time [326]:

(13) $\begin{array}{c}R\left(t\right)=\gamma \cdot \frac{{\rho }_0{\left(1-f_V\right)}^{1-m}\cdot l}{A_{\mathrm{A}\mathrm{g}}}{\left(1-\frac{t}{t_f}\right)}^{-\mu },\end{array}$(13)

where $\gamma$ denotes a statistical variation factor, ${\rho }_0$ is a pre-factor proportional to the metal’s bulk resistivity, $f_V$ is the void fraction in the sample, $A_{\mathrm{A}\mathrm{g}}$ is the cross-sectional area of pure silver, $m$ is the percolation coefficient, $l$ is the length of the printed Ag sample, and $\mu$ is the percolation parameter, contingent on the applied current density and temperature [327].

6.2. Electrothermal failure

The Joule heating effect is significant, particularly in flexible components and printed electrodes which have relatively high resistance. Consider, for instance, printed silver wire interconnects that exhibit a notable electromigration (EM) effect. These printed structures have a higher resistivity due to their porous nature. Under different mechanisms, the heating effect prompts morphological changes in interconnect circuits. During early EM testing of printed silver wires, Joule heating, induced by high-density currents in regions of elevated resistance, may enhance further sintering of silver nanoparticles [323,328]. As high-density current action time extends, EM-induced silver atom mass transport results in fewer conductors on the cathode side. This reduction in the interconnection’s cross-sectional area leads to an increased current density, intensifying both electromigration and Joule heat generation [329]. As heat accumulates and temperature reaches a certain threshold, silver nanoparticles aggregate due to the Ostwald ripening process. The particles, initially uniformly distributed, gradually converge into silver islands, eventually leading to a circuit break [48]. Furthermore, thermal migration can have a detrimental effect on flexible interconnect circuits under high-density currents. This process involves atomic diffusion caused by the thermal gradient resulting from Joule heating [330]. Several factors may contribute to thermal migration in interconnected wires. Due to the small size of flexible electronics and uneven heat dissipation, the temperature increase under the Joule heating effect is non-uniform, generating temperature gradients [331]. Additionally, the cross-sectional wire size may vary due to printing process limitations, causing differential resistance and thermal effects, thus contributing to temperature gradients [332].

The combined effect of Joule heating and high-density currents creates a specific failure mode in flexible circuits, as studied by Yang Zhao et al (Figure 9b). Their work revealed that device failure is driven by the thermo-mechanical coupling process between metal films and flexible substrates. Inherent defects in the thin film conductor incite local resistance increases, thereby augmenting Joule heating. Due to differential thermal expansion coefficients, heat accumulation induces significant thermal stress and deformation in the flexible substrate. Their empirical evidence, depicted in Figure 9d, replicated the process of electro-thermal coupling failure: (I) The conductor, initially flat with minor defects, undergoes increased deformation upon application of a critical current, leading to a vicious cycle (II, III); (II) Subsequent conductor breakage results in Joule heat dissipation, and disconnection of membrane segments whilst mechanical deformation in the elastic matrix relaxes (IV); (III) Eventually, irreversible electrical failure occurs due to complete conductor fracture (V). They also observed that mechanical deformation exacerbates as current intensity advances from (Ⅵ) to (Ⅷ) [312].

6.3. Electrochemical failure

Electrodes, to which active materials are affixed, are pivotal to the performance of flexible electrochemical energy devices. Hence, they necessitate optimal flexibility, electrical conductivity, and strong adhesion to collectors [289]. Electrochemical failures in these flexible electrodes often arise from intricate stress fields within the batteries, either directly or indirectly [314]. During operational loads, the detachment of active materials from electrodes and the separation within the battery’s internal structure can result in a loss of electrical contact, considerably diminishing device performance [333]. Although mechanical failures from external deformations are discussed in preceding sections, it’s crucial to understand diffusion-induced stress (DIS). Independent of flexural effects, DIS is prevalent during the charging and discharging of flexible batteries. This process (Figure 9c), characterized by the cyclical lithiation and delithiation of Li+, leads to inconsistent Li+ concentration within the electrode due to volume changes, producing stress fields that directly impact the mechanical stability of electrode materials [334,335].

DIS inflicts multifaceted damage to electrode materials. It not only disrupts both electronic and ionic pathways, evidenced by internal cracks in active materials and severance of active particles from adhesives, but it also leads to delamination between the active layer and collector, elevating battery impedance. Additionally, cracks resulting from DIS expose the active material to the electrolyte, leading to decomposition and lithium ion consumption, thereby reducing battery capacity. In a typical flexible battery, the compounded effects of DIS and the stress from flexible deformations severely compromise electrode material integrity, curtail the electrodes’ lifespan, and can precipitate battery failure [336,337]. Consequently, numerous studies have been undertaken to understand the electrochemical cycling of flexible electrodes under such deformations, aiming to enhance durability and minimize electrochemical failures.

Liu et al. introduced an analytical model detailing the ratcheting behavior, or plastic strain accumulation, during lithium-ion battery cycling, highlighting the impact of interfacial shear traction on this behavior [338]. Extending this, Xu et al. examined flexible planar electrodes under bending during electrochemical cycling. They found that using flexible electrode materials with higher strain hardening rates and lower expansion coefficients can counteract strain accumulation and plastic deformation effects [314]. Shi et al. studied the impacts of both constant and cyclic bending on flexible thin-film electrodes during charge/discharge cycles. Their research indicated distinct cumulative strain reasons for each deformation type, emphasizing the importance of ion concentration values in cyclic bending [339,340]. Peng et al. analyzed the mechanical deformation’s influence on ion transport and potential in flexible solid-state lithium metal batteries, concluding that bending can cause high internal stresses, potentially damaging electrode materials and reducing battery efficacy [341].

6.4. Characterization methods and experiments for electrical failure

Electrical failure characterization methods, procedures, and instruments are summarized in Table 4. Electromigration (EM) behavior of flexible devices and wires is commonly investigated using the EM test. The test setup typically includes a power supply applying constant current and a voltmeter measuring sample resistance changes. To expedite the test and induce EM failure, heating equipment, such as ovens [48] or incandescent lamps [342] is often employed. The sample is exposed to a fixed current density from a DC power supply until its resistance reaches a predetermined value, marking the test termination. This resistance threshold, acting as a failure criterion, is usually selected based on the detection of an open circuit in the interconnect(Figure 9d). Post-test, in-situ observations are typically carried out to scrutinize the sample surface for cracks and breakages [343]. For certain flexible substrates prone to thermal decomposition, the test is conducted at room temperature, with the device placed on a copper plate to facilitate quick heat dissipation [319].

Table 4. Characterization methods of electrical failure.

Failure modes	Test procedures	Measuring Instruments	Advantage	Disadvantage
Electromigration failure	EM test	Impedance analyzer, Digital multimeter, SEM, etc.	Accelerated testing and induced electromigration failure through simultaneous heating.	Limited to qualitative surface condition data.
Electrothermal failure	Electrothermal test	Digital multimeter, SEM, etc.	Artificial mechanical load application during testing enhances crack visibility.	Overlap of test results with electromigration failures can obscure failure root cause.
Electrochemical failure	Electrochemical measurement	Battery system, Electrochemical workstation, Potentiostat SEM, EIS, etc.	Straightforward handling.	Cannot be conducted in situ. Lacks detailed chemical information for failure mechanism analysis.

For characterizing electrothermal failure, Yang Zhao et al. proposed a similar experimental approach(Figure 9e) [312]. A stretchable thin film conductor was connected to a power source through pads and a DC was applied. The current intensity was gradually raised until conductor failure. In-situ observation methods, such as optical microscopy, were used to monitor the failure progression and measure the critical current at failure. Mechanical stress was applied to the sample by altering the horizontal displacement of the conductive pads.

Characterization techniques for electrochemical failures typically emphasize the assessment of battery capacity and the cycle stability of related energy storage devices. Xin Cai et al. utilized the Land Battery System (LAND CT-2001A) with consistent charging/discharging currents for tests examining the electrochemical cycling of flexible batteries under continuous bending deformation. They subsequently conducted Electrochemical Impedance Spectroscopy (EIS) using an electrochemical workstation [288]. Xue et al. evaluated the influence of flexible gel coatings on both the electrochemical performance and fatigue failure of lithium battery diaphragms. They assessed the electrochemical stability of these flexible batteries through linear voltammetry scanning on an electrochemical workstation [344]. Kim et al. probed the cycling durability of flexible lithium-ion batteries by capturing the EIS spectra of different batteries at varying state-of-charge (SoCs) levels with a potentiostat. They also used field emission scanning electron microscopy (FE-SEM) to analyze components (cathode, anode, and spacer) from both new and fatigued batteries, offering detailed microscopic observations [345].

7. Summary and outlook

Flexible electronic devices present distinct advantages of flexibility, transparency, and miniaturization over conventional electronics. However, their distinctive properties also demand tailored mechanical and environmental standards to circumvent potential failure modes that manifest throughout their lifecycle. In many instances, device failures arise from minor defects accrued during fabrication that are later exacerbated by environmental factors and external loads during operation. This review thus comprehensively examines four salient failure modes – strength, interfacial, fatigue, and electrical failure (Table 5). The strength failure section details the crack formation/evolution process during deformation of brittle films on flexible substrates, as well as the unique failure mechanisms due to the mismatch of hygroscopic properties within multilayer structures. The interfacial failure section outlines failure mechanisms of interface slip and peel and underscores the necessity of measuring interfacial adhesion force or toughness to inform device interfaces’ bonding behavior. The fatigue failure section describes fatigue mechanisms impacting both short-term (resistance of metal films on flexible substrates) and long-term (crack evolution and polymer degradation) durability of flexible devices, while considering both micro and macro-level factors influencing failure. Lastly, the electrical failure section discusses two prevalent types of electrical failures – electromigration and electrothermal coupling failure – highlighting the dominant role of high-density currents and metal film microstructures in these failures.

Table 5. Comparison among the four failure modes.

Failure modes	Failure mechanism	Possible areas of failure	Refs.
Strength failure	Stiffer components in flexible devices can crack or fracture under extreme mechanical loads due to material limitations, resulting in device failure or degradation.	Functional components, Interconnection circuits, Conductive Electrodes, etc.	[42,43,66,109,114,116,121,122,125,142,147,151]
Interfacial failure	Interfaces between different materials experience slipping or delamination under complex stress environments.	Adhesion regions of functional components to polymers, Interfaces between packages and devices, Conductive pins for components and circuits, etc.	[22,41,198,208,209,214–216,220–223]
Fatigue failure	Long-term cyclic mechanical or thermal loads may cause fatigue cracks in functional elements and aging of elastic polymers, resulting in decreased electrical performance or failure.	Functional components, Interconnection circuits, Conductive Electrodes, Polymer substrates, encapsulation layers, etc.	[22,46,101,264,267–272,286,287]
Electrical failure	High current densities in miniaturized flexible device interconnects can lead to mass migration and heat dissipation, resulting in short circuits, interruptions, and reduced performance. External loading may further degrade the electrochemical performance of flexible energy storage devices.	Interconnection circuits, Conductive Electrodes, Flexible battery, etc.	[48,293,311–314,323,326,327,333–335,338]

Despite substantial progress in elucidating the failure mechanisms of flexible electronics, a considerable disparity still exists between the device’s mechanical-electrical performance, reliability, and the requirements of actual operating environments. Although current strength failure, interfacial failure, and fatigue failure experiments impose force loads while measuring electrical performance, theoretical models still define device failure via the occurrence of cracks, slips, and delaminations. These fail to provide a comprehensive portrayal of the device’s failure state. The deterioration of electrical performance, which ought to precede structural failure, should be a more meaningful criterion for assessing failure. Therefore, the integration of fracture mechanics, interface mechanics, solid-state physics, and advanced computational algorithms to develop multi-field and multi-scale theoretical and numerical models is of paramount importance. Establishing links between device deformation, defects, and changes in electrical performance represents a vital direction for research into the failure mechanisms of flexible electronics.

In terms of characterization techniques, current test scenarios are typically idealized. Complex and non-uniform strains, alongside temperature and humidity, cannot be concurrently applied to the device to simulate the coupling effect in operating environments, such as human skin during motion. Under these multi-field coupled complex load conditions, the material’s mechanical and electrical properties undergo significant changes, making the device more prone to failure. Therefore, developing multi-field coupled characterization equipment and methods is crucial for predicting and optimizing device reliability.

Moreover, regarding device waterproofing, most current flexible electronic devices employ methods such as underwater operation. These lack the rigorous testing methods and standards, such as steam testing, ingress protection testing, water pressure level testing, etc., traditionally used for electronic devices, thus severely affecting the device’s reliability under practical conditions. It is essential to develop systematic waterproofing testing methods and standards.

Regarding device fabrication techniques, the majority of flexible electronic devices utilize transfer printing and encapsulation technologies for the heterogeneous integration of multiple layers. This approach, while effective, presents challenges in maintaining high success rates and precise component placement. By developing and broadening the application scope of innovative packaging and transfer methods – such as laser-assisted packaging [346], liquid film transfer printing [347], laser-driven programmable non-contact transfer [348], and magnetically driven non-contact transfer printing [349]—the thermal and mechanical damage to the substrate during the packaging and transfer phases can be significantly mitigated. This, in turn, reduces the stress endured by components post-fabrication, thereby bolstering the overall reliability of the device.

Furthermore, the concept of ‘molecularly stretchable electronics’ is a promising avenue worth exploring [350]. It pertains to designing electronic devices at the molecular level, enabling the molecular structures of nonconductors and semiconductors to adapt to strain. The controlled copolymerization of electronically active monomers could potentially yield mechanically flexible forms of various components in flexible electronics.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are thankful for the support by the National Natural Science Foundation of China (NSFC) [Grant No. 11972325, 12272342, 12202398], and the Natural Science Foundation of Zhejiang Province (LGF20A020001).