隨著微流體技術的進步，介電濕潤晶片已廣泛應用於各種生化實驗。具有非規則電極的玻璃基底介電濕潤晶片已經被提出，它允許更可靠的液滴操作且支持光學傳感器應用在生化實驗中。此外，在介電濕潤晶片中可以利用非規則電極（如叉指狀電極）來精確控制液滴體積，並且特定形狀的電極對於某些應用是必須的。然而，由於玻璃基板上製造多層互連的技術壁壘，電極和導線位在同一層基板中，使得在有限繞線資源的條件下，非規則電極的引腳選擇是非常重大的挑戰。在本文中，我們提出了一種名為NR-Router的基於最小成本流的繞線算法，該算法為具有非規則電極的單層介電濕潤晶片提供高效和穩定的繞線工具。據我們所知，NR-Router是第一個可以在具有非規則電極的單層介電濕潤晶片中準確佈線的算法。我們構建了一個最小成本流算法來生成最佳繞線路徑，接著提出輕量模型有效處理流量。NR-Router 實現了100%的可繞線性，同時在更短的運行時間內最大限度地減少了線長，並通過調整設計參數生成可直接投入製造的文件。實驗結果證明了我們提出的算法的穩定性和效率。

With the advances in microfluidics, electrowetting-on-dielectric (EWOD) chips have widely been applied to various laboratory procedures. Glass-based EWOD chips with non-regular electrodes are proposed, which allow more reliable droplet operations and facilitating integration of optical sensors for many biochemical applications. Besides, non-regular electrode designs (e.g., interdigitated electrodes) are utilized in EWOD chips to precisely control droplet volume, and electrodes with a specific shape become necessary for certain applications. However, due to the technical barriers of fabricating multi-layer interconnection on the glass substrate (e.g., unreliable process and high cost), both control electrodes and wires are fabricated with a single-layer configuration, which poses significant challenges to pin selection for non-regular electrodes under the limited routing resource. In this thesis, we propose a minimum cost flow-based routing algorithm called NR-Router that features efficient and robust routing for single-layer EWOD chips with non-regular electrodes, which overcomes the challenges mentioned above. NR-Router is the first algorithm that can accurately route in single-layer EWOD chips with non-regular electrodes to the best of our knowledge. We construct a minimum cost flow algorithm to generate optimal routing paths followed by a light-weight model to handle flow capacity. NR-Router achieves 100% routability while minimizing wirelength at shorter run time, and generates mask files feasible for manufacturing via adjustments of design parameters. Experimental results demonstrate the robustness and efficiency of our proposed algorithm.

[1]  H.­H. Shen, S.­K. Fan, C.­J. Kim, and D.­J. Yao, ”EWOD microfluidic systems for biomedical applications,” Microfluidics and Nanofluidics, vol. 16, pp. 965­987 (2014). 

[2]  W.­C. Nelson and C.­J. Kim, ”Droplet Actuation by Electrowetting­on­Dielectric (EWOD): A Review,” Journal of Adhesion Science and Technology, vol. 26, pp. 1747­ 1771 (2012). 

[3]  E.Samiei,M.Tabrizian,andM.Hoorfar,”Areviewofdigitalmicrofluidicsasportable platforms for lab­on a­chip applications,” Lab on a Chip, 10.1039/C6LC00387G vol. 16, pp. 2376­2396 (2016). 

[4]  M.­G. Pollack, R.­B. Fair, and A.­D. Shenderov, ”Electrowetting­based actuation of liquid droplets for microfluidic applications,” Applied Physics Letters, vol. 77, pp. 1725­1726 (2000). 

[5]  J. Chen, Y. Yu, J. Li, Y. Lai, and J. Zhou, ”Size­variable droplet actuation by interdig­ itated electrowetting electrode,” Applied Physics Letters, vol. 101, p. 234102 (2012). 

[6]  J.BerthierandC.Peponnet,”Amodelforthedeterminationofthedimensionsofdents for jagged electrodes in electrowetting on dielectric microsystems,” Biomicrofluidics, 2006, vol. 1, p. 014104 (2006). 

[7]  L. Malic, T. Veres, and M. Tabrizian, ”Nanostructured digital microfluidics for en­ hanced surface plasmon resonance imaging,” Biosensors and Bioelectronics, vol. 26, pp. 2053­2059 (2011). 

[8]  N.­Y.­J.­B. Nikapitiya, S.­M. You, and H. Moon, ”Droplet dispensing and splitting by electrowetting on dielectric digital microfluidics,” IEEE MEMS, 2014, pp. 955­958, (2014). 

[9]  N.­Y.­J.­B. Nikapitiya, M.­M. Nahar, and H. Moon, ”Accurate, consistent, and fast droplet splitting and dispensing in electrowetting on dielectric digital microfluidics,” Micro and Nano Systems Letters, vol. 5, p. 24 (2017). 

[10] X. Xu, L. Sun, L. Chen, Z. Zhou, J. Xiao, and Y. Zhang, ”Electrowetting on dielec­ tric device with crescent electrodes for reliable and low­voltage droplet manipulation,” Biomicrofluidics, vol. 8, p. 064107 (2014).
[11] P. Y.­Keng, S. Chen, H. Ding, S. Sadeghi, G.­J. Shah, A. Dooraghi, M.­E. Phelps, N. Satyamurthy, A.­F. Chatziioannou, C.­J. Kim and R.­M. van Dam, ”Micro­chemical synthesis of molecular probes on an electronic microfluidic device,” Proc. Natl Acad Sci USA, vol. 109, pp. 690­5 (2012).
[12] J.Li,S.Chen,andC.­J.Kim,”Low­costandlow­topographyfabricationofmultilayer interconnections for microfluidic devices,” Journal of Micromechanics and Microengi­ neering, vol. 30, pp. 077001 (2020).
[13] T.­W.Huang,S.­Y.Yeh,andT.­Y.Ho,“Anetwork­flowbasedpin­countawarerout­ ing algorithm for broadcast­addressing ewod chips,”IEEE Transactions on CAD, vol. 30, no. 12, pp. 1786–1799, (2011).
[14] P.­H. Yuh, C.­L. Yang, and Y.­W. Chang, “Bioroute: A network­flow­based routing algorithm for the synthesis of digital microfluidic biochips,”IEEE Transactions on CAD, vol. 27, no. 11, pp. 1928–1941, (2008).
[15] K. Chakrabarty and T. Xu, “Droplet­trace­based array partitioning and a pin assign­ ment algorithm for the automated design of digital microfluidic biochips,”Proc. of CODES+ISSS, pp. 112–117, (2006).
[16] Q. Wang, Z. Li, H. Cheong, O.­S. Kwon, H. Yao, T.­Y. Ho, K. Shin, B. Li, U. Schlichtmann, and Y. Cai, “Control­fluidic codesign for paper­based digital microflu­ idic biochips,”Proc. of ICCAD, pp. 1–8, (2016).
[17] D. Grissom, P. Brisk, “A Field­Programmable Pin­Constrained Digital Microfluidic Biochip,”Proc. IEEE/ACM DAC, pp. 46, (2013)
[18] T.Yan,andM.­D.Wong,“Acorrectnetworkflowmodelforescaperouting,”Proc. of DAC, pp. 332–335, (2009)
[19] W.­T.Chan,F.­Y.Chin,andH.­F.Ting,“Afasteralgorithmforfindingdisjointpaths in grids,”Proc. of ISAAC, pp. 393–402, (1999)
[20] J.­W. Fang, and Y.­W. Chang, “Area­i/o flip­chip routing for chip­ package co­ design,”Proc. of ICCAD, pp. 518–522, (2008)
[21] “Or­tools,”https://developers.google.com/optimization/.