Review of flexible and transparent thin-film transistors based on zinc oxide and related materials^*

The properties of polymer substrates will affect material quality and carrier transportation behavior and limit maximum fabrication temperature, and thus are of great importance for the flexible transparent devices. As shown in Fig. 3, according to the servicing temperature or glass transition temperature (${T}_{{\rm{g}}}$), the polymer substrates can be categorized into three types: conventional polymers (${T}_{{\rm{g}}}\lt 100^\circ {\rm{C}}$), common high-temperature polymers ($100\le {T}_{{\rm{g}}}\lt 200^\circ {\rm{C}}$) and high-temperature polymers (${T}_{{\rm{g}}}\ge 200^\circ {\rm{C}}$).^[117] The most commonly used polymer substrates in the literature include polyimide (PI), polyarylate (PAR), polyethylene terephthalate (PET), PEN, polyethersulfone (PES), polycarbonate (PC), polyetheretherketone (PEEK), polydimethylsiloxane (PDMS), etc.

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In Table 2 listed are the basic properties of PI, PEN, and PET for each of the three kinds of polymer substrates which are currently widely used.

Table 2.  Basic properties of four commonly used flexible transparent substrates.

Material	${{\boldsymbol{T}}}_{{\bf{g}}}$/${\boldsymbol{^\circ }}{\bf{C}}$	CTE/(ppm ${\boldsymbol{\cdot }}{\boldsymbol{^\circ }}{\bf{C}}$ ${}^{{\boldsymbol{-}}{\bf{1}}}$)	${{\boldsymbol{\lambda }}}_{{\bf{c}}}$/nm	Chemical resistance	Surface roughness
PI	300	12	500	Good	Good
PEN	120	20	380	Good	Moderate
PET	80	33	300	Good	Moderate
PDMS	–120	301	200	Good	Poor

The PI substrate has the highest ${T}_{{\rm{g}}}$, smallest CTE and surface roughness among all of the flexible substrates. In addition, it also shows good chemical stability in acid, alkali and organic solvents. Although the cut-off wavelength (${\lambda }_{{\rm{c}}})$ is in the visible range, which means that the PI substrates have deep color and poor optical transmittance as can be seen in Fig. 4, the colorless and optically transparent polyimide (CPI) films have been developed recently^[117] and used in IGZO TFT fabrication.^[118] In the case that the cost is not a problem, the CPI substrates will be the best choice for flexible transparent electronics. The PET substrate has excellent optical transparency and short ${\lambda }_{{\rm{c}}}$ (Fig. 4), and is currently widely used as the protection layers in various liquid crystal displayers (LCDs), such as televisions, computers and cellphones. The major disadvantage of PET for its use in flexible transparent TFTs is its relatively low servicing temperature (${T}_{{\rm{g}}}\approx 80^\circ {\rm{C}}$), which may bring challenges to device fabrication, integration and operation. The PEN substrate has higher servicing temperature (${T}_{{\rm{g}}}\approx 120^\circ {\rm{C}}$) than PET, but, as a compromise, it appears slightly white color as can be seen in Fig. 4. The PDMS substrate was recently used in flexible TFTs.^{[27,61,81,92,119]} Besides the high optical transmittance and short ${\lambda }_{{\rm{c}}}$, PMDS also features small elastic modulus ($E\approx 5$ MPa), which makes PDMS the perfect substrate for the emerging stretchable electronics.^{[17,27,61,92,120–122]} It is worth noting that ultra-thin (25 ${\rm{\mu }}$m–100 ${\rm{\mu }}$m) flexible glass, such as Willow by Corning company,^[123] is also regarded as a promising flexible substrate for flexible transparent electronics with considering its higher servicing temperature ($\sim 500^\circ {\rm{C}}$), good resistance to scratch and higher optical transmittance. However, up to now, few researches on flexible glass have been reported in the literature.^[62,74]

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To reduce the surface roughness and gas permeability, and to increase the chemical resistance and adhesion to the film, a barrier layer or encapsulation is often involved onto the substrate.^[69,83,124] The commonly used encapsulation materials are Al₂O₃,^[125,126] Si₃N₄,^[58,127] and SiO₂,^[27,82] which are electrical insulating and easy to grow by chemical vapor deposition with perfect coverage ratio. Encapsulations of stacked layer have also been reported.^[67,69,91]

Whatever the substrate is, the device performance usually depends on channel layer, especially within 1 nm–2 nm from the interfacial layer. The electron mobility, electron concentration, density of state and interfacial charge would directly influence the field-effect mobility, on/off ratio, sub-threshold swing and turn-on voltage. In this part, we summarize the properties of ZnO channel layer that only appears in flexible transparent device.

As described in subSection 2.1, limited by the utilized flexible substrate, the processing temperature cannot exceed ${T}_{{\rm{g}}}$, which could be as low as 80 °C. At such a low synthesis temperature, the materials usually appear to be polycrystalline or amorphous. In conventional semiconductors, such as silicon whose conduction band minimum (CBM) and valence band maximum (VBM) are composed of anti-bonding (${\mathrm{sp}}^{3}{\sigma }^{* }$) and bonding (${\mathrm{sp}}^{3}\sigma$) states of Si sp³ orbitals and whose band gap is formed by splitting the ${\sigma }^{* }$–σ energy levels (Fig. 5(a)), the carrier transport properties depend critically on the chemical bonding direction (Fig. 5(b)). This is the reason for the degradation of electron mobility in amorphous silicon ($\mu \lt 2\,{\mathrm{cm}}^{2}\cdot {{\rm{V}}}^{-1}\cdot {{\rm{s}}}^{-1})$ compared with crystalline silicon ($\mu \approx 1500\,{\mathrm{cm}}^{2}\cdot {{\rm{V}}}^{-1}\cdot {{\rm{s}}}^{-1})$. In contrast to silicon, ZnO has very strong ionicity and electrons transfer from zinc to oxygen atoms. The electronic structure is formed by rasing the electronic level in zinc and lowering the electronic level in oxygen through the Madelung potential as shown in Fig. 5(c). As a result, the CBM in ZnO is primarily contributed to by the unoccupied spherically symmetric Zn 4s orbitals and the VBM is primarily determioned by the fully occupied axial symmetry O 2p orbitals.^[4,9,128] Owing to the s orbitals being contributed to CBM, the electron transport is not affected significantly by the chemical bond direction and crystal structure randomness. That is the reason why high electron mobility occurs in ZnO and relevant materials in their polycrystalline and even amorphous states, and also why ZnO and relevant materials are suitable for low temperature process, such as flexible transparent electronics on polymer substrates.

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To further extend the s orbital of ZnO and thus to achieve higher electron mobility, indium (In) and tin (Sn) are often added into ZnO, because In ${}^{3+}$ and Sn ${}^{2+}$ have more broad-spreading 5s orbitals than Zn ${}^{2+}$ 4s. Ternary alloys such as IZO^[52,129] and ZTO^[130,131] do show higher mobility than pure ZnO. However, due to the scarcity and toxicity, In is not suitable for the large demands in commercial applications as shown in Figs. 1(a) and 1(b) and the safety use in the healthcare or medical areas as shown in Figs. 1(c) and 1(d). Sn has been regarded as a more promising candidate for increasing the electron mobility in ZnO. At low process temperature, lots of point defects which may act as scattering centers and electron traps within the channel layer, are unavoidably induced into ZnO.^[132–134] To suppress the concentration of V_O, cations, which has a stronger bonding with oxygen, such as gallium (Ga), Sn, aluminum (Al), magnesium (Mg), hafnium (Hf), zirconium (Zr), and Si have been incorporated into ZnO. Quarternary alloys, for example, InGaZnO,^[2,4,135] InSnZnO,^[96,136] MgSnZnO,^[137] AlSnZnO,^[138,139] HfInZnO,^[140,141] ZrInZnO,^[142] and SiInZnO,^[143,144] have been reported to have improved their performances and stabilities.

As listed in Table 1, the most commonly used synthesis technique for growing ZnO channel layer on polymers is still sputtering because its simplicity and effectiveness. Another widely used technique is solution processing techniques, including spin-coating, ink-jet printing, chemical bath deposition, etc.^[19,95,115] Although these synthesis technics are important and widely used, there is not much difference in the device fabrication technique between rigid and flexible substrates, and they have been described in detail in many reviews.^{[11,12,18,19,21,113,114]} Therefore, they will not be discussed here.

On the other hand, roll-to-roll (R2R), sheet-to-sheet (S2S), and roll-to-sheet (R2S) printing technologies hold great promise and offer advantages over classic microfabrication.^[61,145] It allows extremely low manufacture cost, large fabrication area, fast printing speed on the order of meters per second,^[146] and fine feature size of sub-10 ${\rm{\mu }}$m.^[147] The above-mentioned unique advantages make it a perfect candidate for applications in cheap, portable, large-volume and disposable systems, such as radio-frequency identification (RFID) tags, flexible displays, and food packaging.^[148–150] Figure 6 shows the schemes of an R2R (Fig. 6(a)) and R2S (Fig. 6(b)) gravure printing system, which describes a typical flexible device fabrication procedure. In each of the R2R gravure printing units, one particular material based ink is selected to print the functional layers, i.e., buffer layers, electrodes, active layers, insulators, passivation, logos, etc. The cells are filled with inks from an ink reservoir and wiped using a doctor blade, afterthat, the inks are transferred from the roll to the flexible substrate. Patterns are defined by recessed cells that are engraved into a roll. After the transfer process, the individual aliquots of inks spread and dry to form the final pattern. After going through each gravure printing unit, multi-functional layers are formed, patterned and aligned to each other as shown in Fig. 6(c).

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As the name indicates, the transistor means transfer + resistor, which is essentially a variable resistor whose resistance is determined by the external electric field, which is generated by the gate voltage (${V}_{{\rm{g}}})$ within a metal–insulator–semiconductor (MIS) capacitor. Therefore, the quality of the bulk dielectric and interface of semiconductor/dielectrics is of the vital importance. Currently, there are three types of dielectric materials, that is, inorganic dielectric, organic dielectric, and organic dielectric/inorganic hybrid dielectric dielectric, which are commonly used in the flexible ZnO TFTs in the literature.

2.3.1. Inorganic dielectrics

Silicon dioxide (SiO₂) and silicon nitride (Si₃N₄) are two kinds of inorganic dielectric materials adopted in a-Si:H and poly-Si TFTs.^[24] However, the high deposition temperature above 300 °C for high-quality film by industrialized plasma enhanced chemical vapor deposition (PECVD) hinders their application to flexible substrates. Instead of SiO₂^[39] and Si₃N₄,^[77] high-k dielectrics are more widely used in flexible transparent ZnO TFTs, because they can be synthesized at low temperature by atomic layer deposition (ALD)^[151] or solution processes. We have deposited aluminum oxide (Al₂O₃), a typical high-k dielectric material, on rigid silicon, quartz, flexible PEN and PI substrates by ALD at low temperatures of 150 °C, 150 °C, 100 °C and 100 °C, respectively. The capacitance–voltage (C–V) measurements of ZnO/Al₂O₃/ITO MIS capacitors at a frequency of 50 kHz on different substrates are shown in Fig. 7. The Al₂O₃ insulators show comparable insulating performances on rigid quartz substrate and flexible PEN, PI substrates. The 50-nm-thick Al₂O₃ on PEN exhibits a capacitance density of $1.5\times {10}^{-7}\,{\rm{F}}/{\mathrm{cm}}^{2}$ and dielectric constant of 8.47, which is basically equivalent to the dielectric property of the Al₂O₃ film fabricated on quartz.

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2.3.2. Organic dielectrics

Inorganic dielectric, such as Al₂O₃, has exhibited low-temperature fabrication convenience and excellent device performance. However, mechanical failure may occur when the film is under tensile or compressive strain as shown in Fig. 8. Jen et al. reported that a 80-nm-thick ALD-grown Al₂O₃ film could only sustain a strain level of 0.52%.^[152] Xu et al. claimed the critical strain, a critical point at which the film becomes useless, for 200-nm-thick anodized Al₂O₃ film on PEN is 0.6%.^[66] If the thickness of the flexible substrate is 125 ${\rm{\mu }}$m, the critical bending radius is approximately 10 mm (See Section 3 for more details of mechanical bending), which is not suitable for some flexible, foldable or stretchable applications.

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Nevertheless, organic dielectric materials,^[153] such as poly(4-vinylphenol) (PVP), poly(methyl methacrylate) (PMMA) and polystyrene (PS), can sustain larger strain^[91] because the molecules in them are linked through van der Waals bond and/or hydrogen bond, and they are weakly interacting. In addition, polymer dielectrics can be formed by simple and low-cost processes, such as spin-coating and printing. The characteristics of these materials can be tuned by designing the molecular precursors and polymerization reaction conditions, which offer more application opportunities in a wide range of electronic devices. Figure 9 shows the chemical structures of typical polymeric gate dielectrics.

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Lai et al. fabricated ultra-flexible IGZO TFT on 125-${\rm{\mu }}$m-thick PET substrate with PVP used as polymeric gate dielectrics, on which device performance shows no degradation upon bending to strain $\varepsilon =1.5$%.^[43] Kim et al. also reported flexible IGZO TFT on PET substrate with PMMA as gate dielectrics.^[155] However, they did not perform the bending test evaluation. Up to now, the reports of flexible transparent ZnO TFTs with pristine polymeric gate dielectrics have been still quite limited.

The stable and efficient operation of flexible transparent ZnO TFTs under mechanical stress requires all of the components to work stably and reliably. Lai et al. proposed that the polymeric gate dielectrics can also reduce the stress in the IGZO channel layer.^[43] The Young's modulus for polymer material is around several GPa. However, it is more than 100 GPa for oxide based inorganic semiconductor. This large difference enables the stress to be mainly located at the polymer side, leaving the IGZO layer less stressed as shown in Fig. 10.

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2.3.3. Organic/inorganic hybrid dielectrics

Although polymeric dielectrics sustain greater strain than their inorganic counterparts and can relax the stress in the channel layer, they have some drawbacks as follows.

i) Polymers are usually soft, and thus deposition of channel layer may induce damages inside polymer layer or at the polymer/channel interface, which will significantly influence the transport behaviors of field-modulated electrons.

ii) The values of dielectric constant (k) of most polymers are relatively low (${\varepsilon }_{{\rm{r}}}=2.5$–2.6 for PVP), which would exhibit smaller capacitance at a given thickness than inorganic dielectric materials.

iii) The polymeric dielectrics are more hydrophobic than inorganic materials, which is undesirable for directly growing the channel semiconductors.

Besides utilizing stacked organic/inorganic hybrid dielectric gate,^[156] these problems could also be solved by introducing inorganic nanoparticles into polymer matrices to form polymer nanocomposites. Lai et al. fabricated a nanocomposite dielectrics by incorporating high-k Al₂O₃ nanoparticles into polymer PVP films as shown in Fig. 11.^[68] Al₂O₃ nanoparticles (size $\lt 50$ nm) was added into PVP/poly(melamine-co-formaldehyde) precursor at a concentration in a range from 0.25 wt% to 1.00 wt%. After being stirred overnight, the solution was spin-coated on silver (Ag) gate. The nanocomposite dielectric was then post-treated with hot plate and ultraviolet illumination. The capacitance of the pristine PVP was 14 nF/cm² corresponding to a dielectric constant of 3.9. After adding 0.25, 0.5-wt% and 1-wt% Al₂O₃ nanoparticles, the capacitance increased to 19, 20, and 22 nF/cm², and the corresponding dielectric constants increased to 6.1, 7.1, and 8.1. After that, the lead oxide (PbO), which is a high-k material with ${\varepsilon }_{{\rm{r}}}=200$,^[157] was introduced into PVP polymer, and the dielectric constant increased to 21.2.^[158] Along with the improved capacitance, the TFT with nanocomposite dielectrics could sustain the same strain as the device with pristine PVP dielectrics.^[43,68] This means that the nanocomposite dielectric inherits the merits from both inorganic high-k material and organic polymer material. In addition, the incorporation of high-k nanoparticles into polymeric dielectrics was believed to improve the robustness against the plasma damage in the following sputtering process.^[68] In general, organic materials are more hydrophobic than inorganic materials, which is undesirable for the direct growing inorganic semiconductor materials on the polymeric dielectrics.^[159,160] However, few researchers havefocused the effects of incorporated nanoparticles on the surface energy of nanocomposite dielectric.

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The gate and source/drain electrodes in flexible transparent ZnO TFTs should possess at least three characteristics: low conductive resistivity, high optical transmittance, and good mechanical stability. Yet the most widely used flexible transparent electrodes (FTEs) are transparent conductive oxides (TCOs), represented by ITO, FTO, AZO, GZO, IZO, ZTO, and IZTO, as they have wide bandgaps, low resistivities and can be deposited at low temperatures.^[161,162] However, the mechanical stability of TCO electrode is still a tough issue to be solved for achieving stable and reliable device operation.^[163–166]

Leterrier et al. investigated the effect of ITO thickness on the crack onset strain (COS), the critical strain at failure of the film.^[163] The evolution of film mechanical failure under uniaxial strain was recorded as shown in Fig. 12 as growing ITO film has some microdefects in the form of pin-holes (Fig. 12(a)). Upon reaching a strain of 1.28%, small cracks originating from the microdefects appeared (Fig. 12(b)). Further increasing the strain to 1.42%, the initial crack propagated from the sites to finite size (Fig. 12(c)) and the resistivity began to increase as shown in the onset region in Fig. 12(e). At higher strain levels, the finite cracks increased and the width spanned to the whole sample (Fig. 12(d)). As a result, the resistivity increased markedly as can be seen in Fig. 12(e). They found that the COS decreased with ITO thickness, which means that for a thicker ITO film the safe operating range could be even smaller.

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To seek for flexible transparent electrodes which can sustain higher mechanical strains, oxide–metal–oxide (OMO) stacked structure (Fig. 13(a)) has been proposed. The most commonly used metal materials are silver (Ag) and copper (Cu) because of their good ductilities and high conductivities. What is more, by optimizing the metal layer thickness, the figure of merit (FOM), which can comprehensively characterize the property of transparent electrode, can be improved.^[167] By insetting a thin Ag layer into the middle of double 30-nm-thick IZO layers,^[168–171] the IZO/Ag/IZO stacked electrode showed improved optical transmittance and conductive resistivity (Fig. 13(b)).^[171] Maximum improvement of FOM was obtained with a 12-nm-thick Ag layer (Fig. 13(c)). More importantly, the mechanical robustness was improved compared with a single ITO layer (Fig. 13(d)). Other reported stacked electrodes with improved electrical conductivity, optical transmittance and mechanical robustness involve ITO/Ag/ITO,^[172,173] IZTO/Ag/IZTO,^[174] GZO/Ag/GZO,^[175] IZO/Ag/IZO, ZTO/Ag/ZTO,^[176,177] IZO/Ag/IZO/Ag,^[170] and ITO/Cu/ITO.^[173]

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The random meshed Ag nanowire (Ag NW)^[178–182] electrode is another promising candidate for flexible transparent ZnO TFTs, as Ag forms ohmic contact with ZnO.^[104] The unique advantage of Ag nanowire electrodes is their mechanical robustness, because nano-materials can be bent to much smaller radii than conventional "3D" materials.^[183] Figure 14(a) shows the SEM image of random meshed Ag NWs on a flexible substrate^[182] and Figure 14(b) shows the resistance change as a function of mechanical strains.^[179] Compared with the small COS of ITO shown in Fig. 12, the Ag NW flexible transparent electrode processes much better mechanical robustness, with only 3.9 times increase of resistance under 15% tensile strain and almost no change under 15% compressive strain.

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The bending test systems reported in the literature are all laboratory-made and can be roughly classified as two types according to how devices are bent: 1) substrate wrapped around a rigid rod (Fig. 15(a)) and 2) arched up under side extrusion (Fig. 15(b)). In type 1, the probe tips contact well with the electrodes. However, the variation of bending radius is not convenient in this setup. On the contrary, in type 2, the bending radius can be tuned by varying the distance between the two splints. But the probe tips might contact poorly with the electrodes especially when the substrate is thin or soft.^[88] Thus, attaching flexible polymer substrate onto a flexible metal sheet might be a good choice to combine good contact and flexibility.

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In a simplified case (no Poisson ratio nor fabrication-induced strain), the strain (ε) within the film on bending substrate can be roughly obtained through Eq. (1), under the premise that the substrate is much thicker than the film, or Eq. (2), under the assumption of neglecting the difference in Young's modulus between substrate (${Y}_{{\rm{s}}})$ and film (${Y}_{{\rm{f}}})$. Both the two mechanical models simplified the calculation process and were suited well for many other cases.^[43,68,186]

$$\begin{eqnarray}&&\varepsilon =\displaystyle \frac{{d}_{{\rm{s}}}}{2R},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\varepsilon =\displaystyle \frac{{d}_{{\rm{s}}}+{d}_{{\rm{f}}}}{2R},\end{eqnarray} \tag{ 2 }$$

where ${d}_{{\rm{s}}}$ is the thickness of substrate, ${d}_{{\rm{f}}}$ the thickness of film, and R the bending radius.

For the case in which neither the premise nor the assumption holds, one could go to Eq. (3)^[187–189]

$$\begin{eqnarray}&&\varepsilon =\left(\displaystyle \frac{{d}_{{\rm{s}}}+{d}_{{\rm{f}}}}{2R}\right)\displaystyle \frac{(1+2\eta +\chi {\eta }^{2})}{(1+\eta )(1+\chi \eta )},\end{eqnarray} \tag{ 3 }$$

where $\eta ={d}_{{\rm{f}}}/{d}_{{\rm{s}}}$ and $\chi ={Y}_{{\rm{f}}}/{Y}_{{\rm{s}}}$.

The relationships between ε and ${d}_{{\rm{s}}}$, R, η, χ in Eq. (1) and Eq. (3), are visualized in Figs. 16(a) and 16(b) (setting ${d}_{{\rm{s}}}=100\,{\rm{\mu }}{\rm{m}}$ and $R=5$ mm). As can be seen in Fig. 16(a), at a fixed radius, the strain can be reduced by utilizing a thin substrate. At a fixed ${d}_{{\rm{s}}}$, the strain increases markedly with radius decreasing, and the critical failure radius increases with ${d}_{{\rm{s}}}$ increasing. Taking ${d}_{{\rm{f}}}$ and the difference between ${Y}_{{\rm{f}}}$ and ${Y}_{{\rm{s}}}$ into account, the strain could become smaller with η and χ increasing as can be seen in Fig. 16(b).

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For a given film (fixed ${d}_{{\rm{f}}}$ and ${Y}_{{\rm{f}}})$, besides using thinner and more elastic substrates described above, there are other ways to reduce the strains in functional films. By encapsulating the film and forming an encapsulation/film/substrate sandwiched structure, the strains in film can be further reduced.^[189] If the configuration meets

$$\begin{eqnarray}&&{Y}_{{\rm{s}}}{d}_{{\rm{s}}}^{2}={Y}_{{\rm{e}}}{d}_{{\rm{e}}}^{2},\end{eqnarray} \tag{ 4 }$$

where ${Y}_{{\rm{e}}}$ and ${d}_{{\rm{e}}}$ are the Young's modulus and thickness of the encapsulation layer, respectively, the film without any strain is right in the neutral surface. Consequently, the functional film will not fail to work until the substrate and encapsulation are ineffective. In this approach, Sekitani et al. fabricated ultra-flexible organic TFT with a sandwiched poly-chloro-paraxylylene/pentacene-TFT/PI structure^[190] and Kinkeldei et al. reported sandwiched PI/IGZO TFT/PI structure with a small bending radius of 125 ${\rm{\mu }}$m.^[40] Park et al. proposed that inserting a buffer layer between film and substrate can also reduce the film strain.^[191]

In practical applications, the flexible transparent ZnO TFTs might be bent into various forms, and thus the functional films would sustain various kinds of strains, such as tensile, compressive and twisting. Besides conventional electrical field, the mechanical stress field is also an important issue that must be included in the analysis of flexible electronics. For flexible IGZO TFT, the tensile strains parallel (Fig. 17(a)) and perpendicular (Fig. 17(b)) to the current flow have different effects on electrical performance.^[42] As shown in Fig. 17(c), saturation mobility (${\mu }_{\mathrm{sat}})$ is slightly affected by the strain parallel to the channel up to $\varepsilon =0.72$%, while ${\mu }_{\mathrm{sat}}$ begins to be degraded when $\varepsilon \gt 0.3 \%$ under a strain perpendicular to channel. The degradations of both on- and off- currents of flexible TFT under the perpendicular strain are explained as being due to the crack of brittle chromium (Cr) gate. The cracks disconnect the parts of gate, leaving some of the channel areas uncontrolled, thus making the off-current increased and the on-current reduced. Whereas, no crack occurs under the parallel strain when $\varepsilon \lt 0.72 \%$. Once ε exceeds 0.72%, the cracks become unstable and destroy the device permanently.

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Bending the TFTs outwards causes a tensile strain, while bending the TFTs inwards causes a compressive strain. Compared with the tensile strain, the compressive strain has a relatively small effect on the electrical performance.^[192–194] The influence of strain on the electron transport mobility can be described as follows:

$$\begin{eqnarray}&&\displaystyle \frac{{\mu }_{\mathrm{bent}}}{{\mu }_{0}}=1+m\varepsilon ,\end{eqnarray} \tag{ 5 }$$

where μ₀ and ${\mu }_{\mathrm{bent}}$ are the charge carrier mobilities respectively in flat and bent conditions, and m is an empirical proportionality constant which depends on the channel material.^[195] For IGZO, Petti et al.^[72] and Münzenrieder et al.^[194] found that the tensile and compressive strains could induce TFT parameters shifting towards opposite directions as shown in Fig. 18. Under a tensile strain, the field mobility and subthreshold swing are increased, and the threshold voltage is reduced; while under a compressive strain, the field mobility and subthreshold swing are reduced, and the threshold voltage is increased. The dependence of electrical performance on the strain types can be explained with the electrical structure change associated with crystal structure deformation.^[85,196]

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The maximum operation strain of flexible transparent ZnO TFT depends on the mechanical property of each of the functional layers. Devices with high robustness that can sustain high intense and repeated bending are always desirable. In Table 3 summarized is the state-of-art results about bending test of flexible transparent ZnO TFTs. Most of the polymer substrates listed in Table 3 are PI, PET, and PEN with thickness values ranging from 1 to several hundred microns. For either wrapped around rigid rods or arched up with two parallel plates, majority of the devices are bent with tensile strain parallel to the current flow (channel length direction). However, compressive strain or strain perpendicular to current flow should also been considered since they could have different influences on the flexible ZnO TFT performance.^[42,194] Generally, smaller bending radii are desirable, because it means more flexibilities and serviceabilities. Bending radius can vary in a large range from 25 ${\rm{\mu }}$m to 10 cm depending mainly on the thickness of the substrate. Strain is in inverse proportion to bending radius as shown in Eqs. (1)–(3), and is the normalized parameter to describe the mechanical state in functional layer whatever the substrate thickness is. Fatigue test concerns the stability and reliability of flexible device. Typically, the fatigue tests conduct 10² to 10⁶ times with respect to the stressing times.

Table 3.  Results of bending test of flexible transparent ZnO TFTs in the period from 2010 to 2016.

Substrate	Setup	Paral. or perp. to current flow	Compressive or tension	Bending degree		Bending times	Ref.	Year
				Radius/mm	Strain/%
50-${\rm{\mu }}$m PI	arch	–	tensile	10/5	0.56/1.06	–	Cherenack et al.[26]	2010
220-${\rm{\mu }}$m PET	–	paral.	–	40	0.28	–	Liu et al.[35]	2010
50-${\rm{\mu }}$m PI	arch	–	tensile	0.25	6.35	100	Song et al.[29]	2010
50-${\rm{\mu }}$m PI	arch	paral.	compressive	0.125	–	–	Kinkeldei et al.[40]	2011
50-${\rm{\mu }}$m PI	wrap	both	tensile	3.5	0.72	20000	Münzenrieder et al.[42]	2012
125-${\rm{\mu }}$m PEN	wrap	–	–	4	1.5	100	Lai et al.[43]	2012
125-${\rm{\mu }}$m PI	–	–	tensile	5	1.25	–	Kim et al.[45]	2012
50-${\rm{\mu }}$m PI	wrap	paral.	tensile	7	0.36	–	Yang et al.[51]	2013
50-${\rm{\mu }}$m PI	wrap	paral.	tensile	3.5	0.72	–	Münzenrieder et al.[58]	2013
50-${\rm{\mu }}$m PI	wrap	paral.	tensile	3.5	0.72	–	Münzenrieder et al.[59]	2013
50-${\rm{\mu }}$m PI	wrap	paral.	tensile	5	0.5	–	Zysset et al.[60]	2013
PET	arch	–	both	4	–	6	Ji et al.[47]	2013
PET	–	–	–	20	–	–	Zhou et al.[52]	2013
50-${\rm{\mu }}$ mPI	–	–	tensile	5	1	10000	Hong et al.[49]	2013
100-${\rm{\mu }}$m glass	–	perp.	–	70	–	100	Dai et al.[62]	2013
200-${\rm{\mu }}$m PET	arch	–	both	-4.2/4.3	–	10000	Kim et al.[48]	2013
50-${\rm{\mu }}$m PEN	arch	–	both	4	0.6	106	Xu et al.[66]	2014
120-${\rm{\mu }}$m PI	–	–	–	10	–	–	Wee et al.[64]	2014
125-${\rm{\mu }}$m PEN	wrap	perp.	tensile	4	1.56	100	Lai et al.[68]	2014
PES	–	–	both	18	0.55	–	Park et al.[63]	2014
1-${\rm{\mu }}$m parylene	wrap	paral.	tensile	0.05	0.4	–	Salvatore et al.[23]	2014
70-${\rm{\mu }}$m glass	wrap	perp.	tensile	40	0.09	–	Lee et al.[74]	2014
50-${\rm{\mu }}$m PI	wrap	paral.	tensile	4	0.4	–	Münzenrieder et al.[73]	2014
1-${\rm{\mu }}$m PI	wrap	both	compressive	0.025	–	–	Karnaushenko et al.[16]	2015
PC	–	–	–	20	–	100	Hsu et al.[86]	2015
10-${\rm{\mu }}$m PI	–	–	tensile	2.6	–	1000	Honda et al.[78]	2015
5-${\rm{\mu }}$m PI	wrap	paral.	tensile	3.5	0.07	50000	Li et al.[75]	2015
PET	wrap	paral.	tensile	10	–	1000	Liu et al.[76]	2015
25-${\rm{\mu }}$m PEN	–	both	tensile	2	0.75	4000	Tripathi et al.[85]	2015
125-${\rm{\mu }}$m PEN	arch	paral.	tensile	3.3	1.9	10000	Park et al.[83]	2015
50-${\rm{\mu }}$m PI	wrap	perp.	tensile	5	0.48	–	Petti et al.[84]	2015
17-${\rm{\mu }}$m PI	arch	both	tensile	1.5	3.5	10000	Park et al.[91]	2016
3-${\rm{\mu }}$m PI	wrap	–	tensile	0.15	–	–	Kim et al.[93]	2016
200-${\rm{\mu }}$m PES	both	paral.	tensile	12	0.8	2000	Oh et al.[94]	2016
500-${\rm{\mu }}$m PDMS	wrap	–	tensile	15	–	–	Jung et al.[92]	2016
20-${\rm{\mu }}$m PI	wrap	–	tensile	100	–	–	Zhang et al.[89]	2016
125-${\rm{\mu }}$m PEN	arch	paral.	tensile	8	0.78	–	Zhang et al.[88]	2016