三維可拉伸微電子學,透過PμSL面投影微立體光刻技術實現

突破傳統製造限制:利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置

          可拉伸且柔性的電子裝置與人體皮膚保形或植入生物組織中,引起了人們對健康監測和醫療領域新興應用的極大興趣。儘管已經設計和製造了各種可拉伸材料和結構,但大多數僅限於互連和主動組件的二維 (2D) 佈局。在這裡,透過使用基於面投影微立體光刻(PμSL) 的三維(3D) 列印,我們引入了microArch® 微米3D列印機,以突破製造極限,擁有2μm的高分辨率實現以前無法實現的3D幾何形狀。在印刷微結構上塗上薄金膜後,3D導電結構具有優異的拉伸性 (∼130%)、順應性和穩定的導電性(100% 拉伸應變時電阻變化 <5%)。這種製造流程還可進一步應用於直接創建複雜主動組件的複雜3D互連網絡,如此處的可拉伸電容式壓力感測器陣列所示。所提出的方案為複雜、整合的3D柔性電子系統提供了簡單、便利且可擴展的製造路線。

1. 三種不同3D結構設計的有限元素分析(Finite element analyses of three different 3D structure designs)

           U 型結構包含由垂直線連接的半圓,而馬蹄形結構則由與其垂直翻轉對應部分相連的弧線組成。 這三種設計的幾何參數,包括厚度(t)、寬度(w)、高度(a)和波長(λ)(圖S1a)保持相同以進行比較。 特別地,為了讓三個 3D 結構在基板上有良好的附著力,在底部添加了短線段 (l = ~ 0.07λ) 以連接晶胞。

由於彎曲主導的變形,所有三種結構的表面都出現較高的拉伸/壓縮應變值,但遠低於聚合物材料的失效應變(~5%,見圖 S2d)。 如圖 2a 所示,正弦結構的拉伸載荷導致頂部區域下表面處出現急劇的應力集中。 相較之下,雖然U形和馬蹄形設計在同一位置也具有最大應變,但分佈範圍更廣,並且在相應的上表面和底線段附近的區域也可以找到相當高的值(圖2b、c) 。 綜上所述,馬蹄形設計優於其他兩種,將正弦設計的最大應變降低了53%,U形設計的最大應變降低了13%,顯示出最強的適應大拉伸應變的能力。 同時,三種結構也能夠承受軸向壓縮變形(20%,圖S2(a-c)),其中馬蹄形結構仍然是最佳設計,儘管與拉伸相比差異較小。

U-shaped structure contains semicircles connected by vertical lines whereas horseshoe- shaped structure is made up of an arc jointed to its vertical-flipped counterpart. The geometrical parameters of these three designs including thickness (t), width (w), height (a), and wavelength (λ) (Figure S1a) are kept the same for comparison. Specially, to allow three 3D structures to have a good attachment on substrate, short line segments (l = ~ 0.07λ) are added on the bottom to connect unit cells.
Due to bending-dominated deformation, higher values of tensile/compressive strains all occur at the surface for all three structures, but well below the failure strain of the polymer materials (~5%, see Figure S2d). As shown in Figure 2a, tensile loading of the sinusoidal structures causes sharp stress concentrations at the lower surface of the top region. By contrast, although both U-shaped and horseshoe-shaped design also possess the maximum strain at the same location, it is broader distributed and comparable high values can be found as well at the corresponding upper surface and the regions next to bottom line segments (Figure 2b, c). In conclusion, the horseshoe-shaped design outperforms the other two by reducing the maximum strain of sinusoidal design by 53% and U-shaped design by 13%, showing the strongest ability to accommodate large stretching strains. Meanwhile, the three structures are also able to bear axial compression deformation (20%, Figure S2(a-c)), under which horseshoe-shaped structure is still the optimal design among others despite the smaller difference than being stretched.

2. 馬蹄形結構的拉伸性分析(Stretchability analyses of horseshoe-shaped structure)

          為了進一步探討3D 馬蹄形結構的拉伸性和幾何參數(包括弧角(θ)、半徑(R) 和寬度(w))之間的關係(圖S1a),我們採用了Widlund 等人工作中的分析模型。1. 注意事項與有限元素分析不同的是,模型沒有考慮附加的線段部分。 不同設計的拉伸性透過εmax/εapp 進行評估,其中εmax 是在施加總單軸應變εapp 下結構上的最大應變,因為較小的εmax/εapp 代表基於εmax 達到固有失效應變的失效準則的更大拉伸性材料。 基於 Winkler 曲梁 (CB) 理論,蛇形帶的 εmax/εapp 推導為

To further explore the relationship between stretchability and geometrical parameters of 3D horseshoe-shaped structure including arc angle (θ), radius (R), and width (w) (Figure S1a), we adopted the analytical model from the work by Widlund et al 1. Note that the additional line segment parts are not considered in this model, which is different from the finite element analysis. The stretchability of different designs is evaluated by εmax/εapp, where εmax is the maximum strain on the structure under the applied overall uniaxial strain εapp, since smaller εmax/εapp represents greater stretchability based on failure criterion of εmax reaching the intrinsic failure strain of the materials. Building on the Winkler curved beam (CB) theories, εmax/εapp of serpentine-shaped ribbons is deduced as

利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:馬蹄形結構的拉伸性分析

       (1)對於我們的馬蹄形結構,幾何參數參數 L 取為零。 由於 t 對 εmax/εapp 幾乎沒有影響,因此我們假設 t/w=1。 因此,方程式簡化為

Where the geometrical parameters parameter L is taken as zero for our horseshoe- shaped structure. Since t almost has no impact on εmax/εapp, we assume t/w=1. Thus, the equation is simplified as

利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:馬蹄形結構的拉伸性分析

      (2)然後可以得到無量綱參數w/R和弧角θ對εmax/εapp的影響,如圖S1b中的等值線圖所示,其中εmax/εapp的大小透過色標來解釋。 顯然,這兩個參數的影響在感興趣的範圍內都是單調的:較小的w/R和較大的θ都會導致較小的εmax/εapp。 這是因為較小的 w/R 代表更細長的結構,由於彎曲引起的應變而具有減小的 εmax/εapp ,而較大的 θ 結構可以透過增強的旋轉貢獻來適應更大的施加應變。 除右下角一小部分區域外,εmax/εapp的值均小於1,這表示採用相應幾何參數的馬蹄形結構有利於降低材料的固有應變。 考慮到較大的θ也會導致相鄰兩個圓弧的幾何重疊以及3D列印過程中的困難,我們採用θ=42o。 在這個固定的弧角下,將 w/R 從 1 減少到 0.1(由等值線圖上的兩個白點表示),εmax/εapp 可以從 0.39 進一步顯著減小到 0.02。 結果表明,改變w/R提供了改變εmax/εapp的有效途徑,並且根據製造限制將w/R的下限設定為0.1進行研究。 
等值線圖上所涵蓋的紅點座標為 (0.17, 42o),它表示與我們的 FEA 模型以及後續列印樣本相同的形狀,得出 εmax/εapp =0.039。 此計算值與 FEA 結果 0.036 吻合良好,驗證了所提出的分析模型可以在感興趣的範圍內準確預測 εmax/εapp。 FEA模型中的額外線段和解析方法的小變形假設同時導致FEA結果比解析解小。 總之,對於固定的 R,θ=42o 的 3D 馬蹄形結構的拉伸性主要受寬度 w 控制,採用 w=0.17R 的窄設計預計可將拉伸性比直結構提高 28 倍。

Then the effect of dimensionless parameters w/R and arc angle θ on εmax/εapp can be obtained as shown by the contour plot in Figure S1b, in which the magnitude of εmax/εapp is explained by color scale. Obviously, the effects of the two parameters are all monotonic within the range of interest: the smaller w/R and the larger θ would all contribute to a smaller εmax/εapp. This is because that smaller w/R represents more slender structures with reduced εmax/εapp due to the bending-induced strain whereas larger θ structures could accommodate larger applied strain through enhanced rotational contribution. Apart from only a small region at the lower right corner, the values of εmax/εapp are all lower than 1, meaning that adopting the horseshoe-shaped structure of corresponding geometrical parameters is useful in reducing the intrinsic strains of the material. Considering that large θ would also cause geometric overlap of two neighboring arcs and difficulties in 3D printing process, we adopt θ = 42o. At this fixed arc angle, εmax/εapp can be further significantly reduced from 0.39 to 0.02 by decreasing w/R from 1 to 0.1 (denoted by two white dots on the contour plot). The result indicts that changing w/R offers an effective route to alter εmax/εapp and the lower limit of w/R is set as 0.1 to study according to the fabrication constrains. 
The red dot overlaid on the contour plot with the coordinate (0.17, 42o), which represents the same shape with our FEA models as well as the subsequent printed samples, yields εmax/εapp =0.039. This calculated value agrees well with the FEA results of 0.036, validating that the proposed analytical model can accurately predict εmax/εapp within the range of interest. The additional line segments in FEA model and small deformation assumption of analytical approach concurrently causes the smaller FEA results than the analytical solution. In conclusion, for a fixed R, stretchability of 3D horseshoe-shaped structures with θ=42o is mainly governed by width w and adopting the narrow design of w=0.17R is expected to improve stretchability by 28 times than its straight counterpart.

參考文獻 REFERENCES
(1) Widlund,T.;Yang,S.X.;Hsu,Y.Y.;Lu,N.S.,StretchabilityandComplianceof Freestanding Serpentine-Shaped Ribbons. Int J Solids Struct 2014, 51 (23-24), 4026- 4037.

Supplementary Figures

利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置,馬蹄形結構的晶胞以及幾何參數的圖示
Figure S1. (a). 馬蹄形結構的晶胞以及幾何參數的圖示。A unit cell of the horseshoe-shaped structure with illustration of the geometrical parameters. (b). 作為馬蹄形結構的 w/R 和弧角 θ 函數的Ɛmax/Ɛapp 等高線圖。Contour plot of Ɛmax/Ɛapp as a function of w/R and arc angle θ of the horseshoe-shaped struct
利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置,有限元素分析所得的正弦結構、U形結構和馬蹄形結構
Figure S2. 有限元素分析所得的(a)正弦結構、(b)U形結構和(c)馬蹄形結構在20%壓縮應變下的最大主應變分佈比較。插圖對應於頂部區域下表面的放大視圖。 (d). 3D列印聚合物材料的應力-應變曲線。 Comparison of max principal strain distribution between (a) sinusoidal structure, (b) U-shaped structure, and (c) horseshoe-shaped structure under 20% compression strain resulted by finite element analyses. The insets correspond to the magnified views of the lower surface of top region. (d). The stress-strain curve of the 3D-printed polymer materials.
利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:3D 和 2D 馬蹄形結構佔用面積的比較;電容式壓力感測器陣列島橋設計的整體拉伸性(斷裂應變)示意圖
Figure S3. (a) 3D 和 2D 馬蹄形結構佔用面積的比較,(b) 電容式壓力感測器陣列島橋設計的整體拉伸性(斷裂應變)示意圖。 Schematic illustration of (a) comparison of occupied area between 3D and 2D horseshoe-shaped structures, (b) overall stretchability (fracture strain) of the island- bridge design of capacitive pressure sensor arrays.
利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:不同厚度的Ag或Au薄膜塗覆的3D馬蹄形微結構導體;碳奈米管塗層的 3D 馬蹄形微結構的光學影像
Figure S4.(a)不同厚度的Ag或Au薄膜塗覆的3D馬蹄形微結構導體(長1cm,寬150μm)的電阻。 (b)碳奈米管塗層的 3D 馬蹄形微結構的光學影像。 (a). Resistance of 3D horseshoe-shaped microstructure conductor (1cm long, 150 μm wide) coated by Ag or Au films with different thickness. (b). Optical image of 3D horseshoe-shaped microstructures coated by CNTs.
利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:機械測試設定
Figure S5. 機械測試設定(a)定製手動擔架,輔以尺進行單調拉伸測試。 (b)Microtest 安裝在 SEM 上進行原位拉伸測試。 Mechanical testing setups. (a). Customized manual stretcher assisted with a ruler for monotonic tensile test. (b). Microtest mounted on SEM for in-situ tensile test.
利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:實現不同的電路佈局
Figure S6. 實現不同的電路佈局 (a)惠斯登電橋。 (b)達美連接。 Realization of different circuit layouts. (a). Wheatstone bridge. (b). Delta connection.
利用高分辨率 PμSL 3D 列印技術創建可拉伸、高導電性電子裝置:單一感測器電極和感測器電極陣列的光學影像
Figure S7. (a)單一感測器電極和(b)感測器電極陣列的光學影像,(c)單一感測器電極表面微結構的俯視圖 SEM 影像。 Optical images of (a) a single sensor electrode, and (b) a sensor electrode array, (c) SEM image of surface microstructures of a single sensor electrode from top view.

補充表 Supplementary Table
Table S1.  3D馬蹄形微結構塗層的電阻。Resistance of 3D horseshoe-shaped microstructures coated with different

materials

Coating materials
Ag nanowires
CNTs
Graphene
Resistance (1 cm long, 140 μm wide)
50.8 Ω
26.3 kΩ
12.8 MΩ

參考文獻:Three-Dimensional Stretchable Microelectronics by Projection Microstereolithography (PμSL)
原文連結: https://pubs.acs.org/doi/10.1021/acsami.0c20162

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