中文摘要
　　異質薄膜組成之自捲曲薄板結構可廣泛應用在機械、光電、生醫等領域的微元件，如微光學量測系統中的鏡面可藉由自捲薄板定位其仰角，以免除人工架設的繁瑣；而以自捲薄板組裝適宜尺寸之微型籠狀元件攫取細胞或微生物，可避免傳統微鑷鉗致動器抓取不當造成之破壞。若能有效預測而掌握自捲薄板的曲率與外型，將對設計研發微元件大有裨益。目前，薄板自捲曲的作動機制尚不明確，以往分析對於內部因素諸如晶格常數變化量、介面差排發生、不匹配應變等因素著墨不多。建構一套整體性理論，以利自捲曲薄板在微元件上的應用，乃刻不容緩的要務。薄板自捲曲組裝微元件的研究，傳統多以實作為導向並搭配經驗公式進行探討，耗時且不經濟，缺乏一套完整的模擬分析與設計程序。因此，建立系統性的理論模型、模擬方法，以及設計流程，為一極具研究價值的要務。

　　本研究首先根據自組裝微元件的尺度與功能，建構出考量尺寸、材料等控制變因的設計方針，並規劃薄板內應力估算方法與電腦模擬的流程。接著推估不匹配參數、臨界層厚度等控制因素，建立不匹配應變理論，並考慮製程高溫，推算薄板殘留應力分佈值，包含晶格錯位應力與溫差造成的殘留熱應力。另外在加入薄膜缺陷殘留應力的考慮，整合為自捲薄板內建殘留應力估算模型。再來以估算的殘留應力為負載條件，並考量自捲薄板的幾何非線性變形，建立有限元素模型之電腦化模擬系統，求得薄板變形曲率，並且比對模擬結果與文獻資料以及探討誤差來源。驗證理論模型與電腦化模擬系統的正確性與可行性後，深入分析製程溫度與晶格錯位各控制變因之間的影響程度，和自捲薄板尺寸、材料組合對其彎曲變形之關係。了解各參數與曲率間的定量關係後，有助於調整薄板彎曲程度。最後提出微元件設計流程，以進行在微鏡面仰角定位與特定微攫取元件結構之設計的應用。

　　經由本文的研究中可發現，晶格錯位造成的殘留應力佔有總應力極大的比例，藉由溫度的設定，可有效調控晶格錯位的相關影響參數，進而掌握薄板自捲曲率的微量變化。另外，不同材料組合成的薄板，由於其晶格常數大相逕庭，可搭配出不同的晶格錯位程度，亦可有效控制自捲薄板的彎曲程度。在薄板的尺寸設計方面，本研究發現長寬的影響甚微，而薄板厚度與薄膜厚度比的設定，對薄板曲率的影響甚鉅，可藉此設計出不同彎曲程度的彎曲結構。藉由此理論模型與模擬系統的提出，可提供設計上一個有效的指引。藉由微鏡面仰角定位與微攫取元件結構設計的兩項應用，證實本文理論模型與設計流程可有效率地求得符合設計需求的控制參數，也驗證本文所提理論模型與設計流程具有實用性。

Abstract
　　Multilayer structures are widely used in microelectronics, optics, and other engineering areas. Recently developed three-dimensional micro- and nanostructures take advantages of self-scrolling phenomenon of multilayer epitaxial with lattice mismatch. Some typical devices are fabricated in an integrated procedure by combining the deposition and the forming processes. In order not to use the method of trial and error, a method that can predict the final shape of self-scrolling structures is usually preferred. Both analytical and numerical solutions are generally used. However, these solutions obtained by traditional methods have limited applicability only for narrow strip structures. The required precision is in general not good enough for small scales. For this reason, the goal of this work is to develop a theoretical model comprising all inner factors, and to build a computerized simulation system for small scale structures. By using the derived model, the influence of various geometrical factors, fabricating temperatures, and different materials of the self-scrolling sheet on system responses can be precisely predicted.

　　In the model formulation process, the lattice variations for various temperature settings are taken into consideration. The degree of lattice mismatch between hetero-materials inside the sheet by misfit strain is evaluated. In addition, the value of critical layer thickness is estimated and used to revise the misfit strain. The outer, inner, and thermal residual stresses are computed and fed into a stress computing process. Afterward, the finite element model is constructed and the load conditions are given to perform stress computation. The comprehensive model for predicting the curvature of self-scrolling sheet is finally derived. The computed results obtained by using the proposed simulation system are utilized to compare with experimental data in literature. It is found that the results of the present model agree well with those given in the literature.

　　Once the accuracy of the computer simulation system ensured, the influence of various system parameters and curvature magnitudes caused by various sheet dimensions and materials are studied. Major factors that affect the curvature include sheet thickness, material types, and temperature settings are investigated. A design procedure based on the aforementioned study between the inner factors and self-scrolling curvatures are proposed and used for design study. A design example is given to illustrate that the procedure presented in this thesis can be used by the designer for the estimation of the scrolling type and curvature of a designated sheet characteristic. The method can also be used to provide a clear direction for further design studies.

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