Mechanical simulation for the bending process of the AMOLED panel pad

Panel pad bending is a critical process to improve the screen-to-body ratio of an active-matrix organic light-emitting diode (AMOLED) panel. The failure analysis of the metal wirings is the key to ensure the reliability of signal transmission when the pad be bent to the back of the panel. In the present work, the sub-modeling technique combined with the periodic boundary condition was used to simulate the stress distribution of the bending area of the pad. The progressive failure of bent metal wirings was investigated by the extended finite element method. It is proved to be rational to prevent the wirings damage if the interlayer dielectric is replaced by an organic layer. In order to reduce stress of metal wirings, it is a measure to replace the original ultraviolet (UV) curable adhesive with a higher-modulus UV adhesive. The simulated results also show that rectangular perforations can avoid the stress concentration caused by the holes compared with circular perforations. For better stress distribution of metal wirings, it is necessary to increase the lengths of the rectangular holes and decrease the widths of that to a certain extent, which is helpful for restraining crack propagation by means of low-stress zones and holes.


Introduction
Recently, full-screen or full-view mobile phones with a good view experience have become the mainstream products in the current consumer market. Due to the high requirement of continuously increasing the screento-body ratio, new challenges are presented for the display design [1][2][3]. Both for the organic light-emitting diode (OLED) display and the liquid crystal display (LCD), the narrow borders of top and side parts can be achieved through shaped cutting and circuit design, respectively [4,5]. However, the pad portion, which is electrically connected to an integrated circuit (IC) chip or a printed circuit board, should be foldable to the back of the panel to narrow down the bottom border [6,7]. OLED is expected to be a dominant part of the panel display for its attracting features such as ultrathin structure, vivid color, light weight, high color-rendering index, and high power-conversion efficiency [8][9][10][11][12][13]. More specifically, thanks to the high flexibility, the flexible active-matrix organic light-emitting diode (AMOLED) can reduce the CONTACT  bottom bezel and has gained more attention for their application in smart phones [14].
During the bending process in which the AMOLED pad portion is bent to the back of the panel, a large tensile stress is applied to the conductive metal wirings which are located on the flexible substrate [7]. If signal lines are broken under the action of external stress, driving transistors will remain in conducting state, thus a bright line is formed in the display area. Patterned perforations in metal wirings have been experimentally proved to be an effective method to improve the process yield [15]. However, even with circular-patterned perforations in the metal wirings, the wirings may still be damaged after pad bending. More reasonable structural design of pad bending area and better-patterned perforation of metal wirings are worthy of further research to avoid wirings damage. Numerical simulation is generally used to obtain the stress distribution and crack propagation in microelectronic devices [16][17][18][19]. The previous researches mostly focus on the bending stress of a flexible OLED panel in the display area [20][21][22][23][24][25][26]. However, the bending radius of the panel pad ( < 0.5 mm) is much smaller than the display area, which indicates that the bending area of the pad portion has higher risk of damage. Currently, the stress of the bending area of pad is rarely reported, and the failure of the bending area of pad also requires further research. This information is not only important to find a rational explanation of the perforation design, but also provides available suggestions for optimizing the structure of the bending area of panel pad.
In this work, the unit cell model including a metal wiring in the bending area of the pad is simulated by the finite element method (FEM). Based on the unit cell, the sub-modeling technique is applied to research the local stress near the holes in a metal wiring. Then extended finite element method (XFEM) [27][28][29][30][31][32][33][34] is used to predict the failure of the bent metal wiring, which is an effective way to simulate the difference in crack propagation before and after the metal wiring is perforated and the interlayer dielectric (ILD) is replaced. Then the changes of the strain-neutral surface before and after replacing the ILD and UV adhesive are further studied. Furthermore, the effects of the hole shapes and sizes on the stress distribution of the bending area of the pad are analyzed. Finally, the inhibitory effects of rectangular holes on the cracks in metal wirings are explored.

Structure
The panel pad is the terminal portion of an AMOLED display device, and it should be foldable to the back of the panel to narrow down the bottom border, as shown in Figure 1(a). The structure of the display area, pad, and bending area is shown in Figure 1(b), and the bending direction is perpendicular to the pad wirings, the detailed structure of which can be seen in the next section.

Periodic boundary condition
The bending area of pad portion is composed of a polyimide (PI) substrate, ILD, metal conductive wirings, an organic planarization (PLN) layer, and an ultraviolet (UV) curable adhesive covering the surface. The parallelequidistantly arranged wirings are deposited on the ILD surface by the ion sputtering process. The wiring distribution in the bending portion has remarkable periodicity (see Figure 2(a)), and a single wiring together with the surrounding materials (UV adhesive is hidden) constitutes the unit cell model (see Figure 2(b)). Here x k is the width of the unit cell, which also represents the characteristic width of the single-wiring model. For a periodic boundary, the displacement field of surface pair needs to satisfy the following equation [35] u j+ − u j− =ε k x k (1) where u is displacement, and the superscripts j+ and j− represent the positive and negative directions perpendicular to periodic boundary surfaces, respectively;ε k is the effective strain of unit cell; x k is the width of the unit cell. Equation (1) is realized by enforcing multi-point constraints on the corresponding nodes of the unit cell through Python script on the Abaqus platform.

Failure mechanism of ILD and wirings
The material in the bending area of the pad portion can be divided into metallic, organic, and inorganic materials. Whereas, the ILD is the only inorganic component.
Since the ILD is brittle, cracks penetrate the wirings even though the wirings are perforated, which has been confirmed by optical microscope (see Figure 3). In order to improve the bending performance, the ILD can be alternatively removed by the etching process. As a result of the above facts, this paper only considers the failure mechanism for inorganic ILD and metal wirings. The failure mechanism consists of two ingredients: a damage initiation criterion and a damage evolution law. Crack initiation criteria are available based on Abaqus built-in models.
If the maximum principal stress/strain criterion is satisfied, the newly introduced crack is always orthogonal to the maximum principal stress/strain direction. The direction of crack extension has to be specified if any other built-in crack initiation criteria are used. Since metal wirings are isotropic materials and most cracks propagating through the wirings belong to the mode I cracks, the maximum principal stress criterion is specified to ensure that the crack propagation path is solutiondependent.
The maximum principal stress criterion can be represented as where σ 0 max is the maximum allowable principal stress; the symbol represents the Macaulay bracket with the usual interpretation (i.e. σ max = 0 if σ max < 0 and σ max = σ max if σ max ≥ 0), which signifies that damage is assumed to initiate when the criterion f reaches a value of one and the damage evolution law is specified in terms of equivalent plastic displacement.

Extended finite element method
The XFEM, a developed form of the FEM, is a numerical simulation for solving discontinuous problems. In order to simulate fractures in the ILD and metal wirings, the XFEM is adopted, thus an additional set of freedom degrees, called the enrichment functions, is introduced to the nodes of the elements intersected by the crack. The displacement vector function u(x) with the partition of enrichment functions can be written as where N I (x) and u I are shape functions and displacement vector for the usual nodes, respectively, as shown in Figure 4. C are the nodes through which the crack interior passes, and C A are the nodes of crack-tip elements. One nodal enriched degree of freedom vector a I associated with the discontinuous jump function H(x) represents the displacement jump across the crack surfaces; another freedom vector b a I associated with elastic asymptotic crack-tip functions ϕ a (x) can capture the singularity around the crack tip [29].
With the additional degree of freedom to describe the physical interface, the simulation of crack propagation by XFEM is independent of the model geometrics. The crack propagation path is not sensitive to the mesh division, and the wiring failure in the bending process can be easily observed.

Finite element model
The geometry of the unit cell model is shown in Figure 2(b). It should be noted that the UV adhesive is omitted from the schematic, but it is indeed taken into account in the finite element model. Here x k is 15 μm, and the wiring width d w is 9 μm. The thicknesses of PI substrate, ILD, metal wiring, PLN, and UV adhesive are 15, 1.5, 0.75, 4.5, and 50 μm, respectively. Each component has at least three layers of grids, and the model after the pad is bent is shown in Figure 5. The model is loaded by applying a fixed boundary condition to one end, and a rotational displacement to the opposite end. L f is the length of the fixed side and L b is the length of the bended side. The length of the deformed zone is π * r, and the bending area of the panel pad forms a semicircle of radius r under the bending load. Here the radius r is 0.3 mm, L f and L b are both 0.2 mm.  The constitutive model is an important aspect to simulate the stress and crack propagation of the bending area of the pad. Without affecting the comparability of simulation results, all the materials except metal wirings are regarded as linearly elastic. The elastic parameters of the components are shown in Table 1, and the properties of these materials are determined by nanoindentation in a Hysitron TI-750 TriboIndenter. Due to the yield strain of metal is much smaller than that of polymer, the elastic-plastic constitutive model is adopted for the metal wirings, and the stress-strain curve is shown in Figure 6. It should be noted that the properties of Ti-Al-Ti metal wirings are obtained by volume average method, and the Poisson's ratio is 0.3. The failure properties of metal wirings and ILD are shown in Table 2.

Simplification of finite element model
Due to the excessive computational complexity of the original model, the global-to-local method is utilized based on the unit cell model. The unit cell model is referred to as the global model and the so-called submodel is its local part with a refined mesh. The global solution is interpolated onto the sub-model boundary to  obtain an accurate, detailed solution in a local region. There are three cases of the mesh model for comparison. The first case is a global model which has eleven metal wirings, as shown in Figure 7(a,d). The second case is a unit cell model which only has a single wiring, as shown in Figure 7(b,e). The third case is a sub-model based on the unit cell, as shown in Figure 7(c,f). It can be found that three models have uniform stress distributions. The maximal stress error between the eleven-wiring model and sub-model only amounts to 4.46% (see Table 3). Therefore, the global-to-local model based on the unit cell can be accepted in the engineering applications.

Effects of ILD on cracks in metal wirings
It can be seen from Figure 7 and Table 3 that the stress of the ILD after bending is extremely large, which is much greater than its failure strength. Thus, the ILD will generate cracks during the bending process. An initial crack is assumed in the ILD film of the XFEM model. This crack propagates to the adjacent wiring interface and continues to expand during the bending process. Finally, the crack tip penetrates the wiring and leads to the circuit break (see Figure 8(a)). In the figure, some layers such as UV adhesive and PLN are hidden. Even if openings are made in wirings, the crack can expand along the brittle ILD film and bypass the opening area. The wiring fracture also occurs on the other side of the hole (see Figure 8(b)), and circuit break is still inevitable. Therefore, considering the fracture mechanism, it is suggested to replace ILD by PLN. ILD can be alternatively removed by the etching process. After the ILD is replaced, the hole can inhibit the crack propagation (see Figure 8(c)). The crack tip reaches the perforated position and does not continue to expand.

Adjustment of neutral plane
After replacing ILD by PLN, the holes in the metal wirings can inhibit the crack propagation. However, replacing ILD will cause the movement of strain-neutral plane and the change of wiring stress in the model. This section selects the straight wiring as the first studying object and examines the Mises stress and longitudinal strain in the bending area of the pad. Figure 9 shows the stress distribution of straight wirings in three different models. One default model was built as described in Section 3.1, and the other models replaced the ILD by PLN. The wiring stress is 156.7 MPa in the original model (see Figure 9(a)), while the stress is found up to 186.7 MPa in the model without ILD (see Figure 9(b)). Stress comparison shows that the default structure with ILD seems to be more beneficial to protect wirings from damage. This is because stress distribution depends on the component stiffness. In the original structure, according to the strain distribution in Figure 9(d), the ILD with the highest modulus is responsible for a major part of the tensile stress under the bending load. If the ILD is replaced by soft PLN, the neutral plane of the model will shift downward, which makes the metal wirings subject to greater tensile stress. In order to reduce stress, it is a measure to replace the original UV adhesive with a higher-modulus (480 MPa) UV adhesive. The neutral plane of the model is moved upward (see Figure 9(d)), and the stress is reduced to 153.6 MPa (see Figure 9(c)). The high-modulus UV adhesive is used in the subsequent discussion.

Effects of holes on the stress distribution of the bending area of the pad
Openings in the wirings are often present in the design of the panel pad and a plurality of holes is evenly located along the wiring centerline. In the process of photomask revision, the distance between adjacent holes is difficult to change, but the hole size can be adjusted at a low cost. This section examines the influence of hole shape and size on the Mises stress surrounding an opening position. It should be noted that ILD is replaced in the models presented in this and the next sections. The distance between the adjacent hole centers is assumed to be the same, which is 7 μm. Figure 10 shows the stress contour maps for different hole shapes. In the figure, other layers except the metal wirings are hidden for facilitating observation. The diameter of the circular hole and the side length of the rectangular hole are both 3 μm. In the metal wirings, the low-stress zones are formed on the upper and lower sides of the holes due to less constraints. The stress concentrations on the left and right sides of the circular holes are attributed to the reduction of local stiffness (see Figure 10(b)), while the rectangular holes have no obvious stress concentration zones due to the uniform wiring width (see Figure 10(c)). Hence, the rectangular hole scheme is suggested that can not only restrain crack propagation by means of low-stress zones and holes, but also avoid the stress concentration caused by holes.
After the rectangular hole scheme is determined, the effect of the hole size on the stress distribution of the metal wiring needs to be analyzed. In the length direction (y-axis) and width direction (z-axis) of the metal wiring, the rectangular hole sizes of 2, 3, and 4 μm are designed respectively, and then nine holes of different sizes can be formed, as shown in Figure 11. In the figure, other layers except the metal wirings are hidden for facilitating observation. In the width direction of the metal wiring, as the hole width decreases gradually, the distance from the edge of the metal wiring to the hole position becomes larger, which is beneficial to avoid the fracture  of the metal wiring and to ensure the electrical conductivity of the metal wiring (see Figure 11(a-c)). In the length direction of the metal wiring, as the hole length increases gradually, the stress of the metal wiring between the two holes decreases gradually. For example, when the hole width is 2 μm, the Mises stress corresponding to the hole length 2 μm is 149.1 MPa (see Figure 11(c)), the Mises stress corresponding to the hole length 3 μm is 146.5 MPa (see Figure 11(f)), and the Mises stress corresponding to the hole length 4 μm is 135.6 MPa (see Figure 11(i)). Thus, the hole size of Figure 11(i) is optimal. Combined with the above calculation results, in order to avoid the fracture of the metal wiring, it is necessary to increase the lengths of the rectangular holes and reduce the widths of that to a certain extent.

Effects of rectangular holes on crack propagation in metal wirings
In the manufacturing process of metal wirings, a small amount of inter-microcracks is still inevitably after full annealing treatment. During the pad portion is bent to the back of the panel, the high stress and energy at the crack tip can be released as the crack propagates to a hole. In order to analyze the inhibition effect of rectangular holes on cracks, two cracks were prefabricated in the metal wiring, and the tips of crack 1 and crack 2 were aligned with the center of one hole and the middle of two holes, respectively. When the crack 1 reaches the opening position, the crack propagation is terminated (see Figure 12(a)). In the figure, other layers except the metal wirings are hidden for easy observation. When the crack 2 reaches the low-stress zone between the two holes, the crack propagation is also terminated (see Figure 12(b)). Therefore, the rectangular holes can effectively prevent or reduce the damage of cracks. By contrast, the crack in the original straight-metal wiring will continue to expand until the metal wiring is completely broken (see Figure 12(c)). It should be noted here that the ILD of the model in Figure 12(c) is replaced by PLN, which is different from that in Figure 8(a).
From the results of crack propagation, the wiring with rectangular holes (with a length of 4 μm and a width of 2 μm) can avoid penetrating cracks. A penetrating crack leads to the circuit break, which is an unserviceable condition. By contrast, the increase in impedance due to partial wiring breakage is acceptable. On the premise that the limitation on wirings width is lifted, a more reasonable representation to prevent crack growth can be obtained if two staggered rows of holes are arranged in metal wirings.

Conclusions
The sub-modeling technique is combined with the unit cell model as well as the eleven-wiring global model to simulate the local stress in the bending area of the AMOLED panel pad. Then XFEM is used to explore the crack propagation of the bending area of the panel pad in the bending process. Due to the brittle ILD, even if openings are made in wirings, the crack can expand along the ILD film and destroy the wirings.  If the ILD is replaced by PLN, the cracks will be inhibited at the holes; hence, ILD etching process has been widely used in OLED industry. However, replacing ILD by PLN will lead to increased stress in the metal wirings. By using a higher-modulus UV adhesive, the position of strain-neutral plane in the model can be adjusted, thereby reducing the stress in the wirings.
In the metal wirings, the low-stress zones are formed between the two holes of the rectangular holes or the circular holes. There are stress concentrations on both sides of circular hole, while the rectangular holes have no obvious stress concentration. According to the calculation results of rectangular holes of different sizes, in order to avoid the fracture of the metal wirings, it is necessary to increase the lengths of the rectangular holes and reduce the widths of that to a certain extent.
The rectangular hole scheme is suggested that can not only avoid the stress concentration caused by holes, but also restrain crack propagation by means of low-stress zones and holes. When the crack aligned with the center of one hole reaches the opening position, high stress and energy at the crack tip can be released, and the crack propagation is terminated. When the crack aligned with the middle of two holes reaches the low-stress zone, the crack propagation is also terminated.

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

Funding
This work was supported by the Science and Technology Unveiling Program of Hubei Province (2020BED014).