二維鐵電薄膜之晶域分佈模擬

Abstract

由於鐵電材料具有許多特殊的材料性質，近年來成為熱門的研究題材，也被廣泛地應用於感測器、致動器以及傳動元件上。而這些特殊性質是源自於材料內部微結構作演化達成秩序性排列所導致的宏觀反應。因此，為了正確的模擬材料行為並有效地利用這些材料性質，瞭解材料微結構演化機制成為首要的基本工作。本論文藉由能量之描述，建立可用於模擬二維鐵電薄膜微晶域演化的新式相場法數學模型。 穩定態的鐵電微結構其實是系統總能量演化至最低態時的晶域分佈。欲求得此分佈我們需要一套具多變量且適用於各種邊界條件下之微結構模擬的架構，來描述系統在降低能量項的過程中，驅動微結構聚結化、細微化、選擇與校列等相互抗衡的機制。不同於傳統相場法，新式相場法引入「多階層狀結構」的觀念，選擇區域的層狀體積分率作為場變數，來表示晶域的組成狀況。如此一來，系統的能量基態結構便可以用解析的數學式描寫。

過去研究團隊所處理的薄膜問題略可視為薄膜表面之模擬，變數在平面兩軸向上具有無限域之週期性質；相較於過去的研究，我們用不同的視角切入薄膜問題，以薄膜之縱向面作為探討與模擬的研究課題，即是考慮到薄膜上下邊界面所帶造成的影響。 此次研究為使用新式相場法模擬二維鐵電薄膜在正方晶態中所構成的穩定微結構。在薄膜厚度較大的設定下，模擬結果呈現滿足諧和條件且如同非薄膜時的晶域分佈。再以不滿足諧和條件之晶格排列狀況作能量計算，並與 COMSOL軟體之計算結果作比較，驗證理論與模擬程式的正確性。最後，我們調變薄膜厚度與各項參數，由模擬結果來討論薄膜厚度對諧和條件滿足性的影響及其原因。

Because ferroelectric materials having many unique features, they have been widely studied and utilized in micro-devices as sensors, actuators and transducers. However, these unique features and behaviors originate from the evolution and arrangement of the underlying microstructures. Therefore, it is essential to investigate the rule of evolution before simulating and taking advantage of these materials. A novel phase-field model for studying and simulating the 2-D domain pattern of ferroelectric materials based on energy arguments is developed in this thesis. A steady state ferroelectric microstructure is a result as the formation and evolution of microscopic domain patterns in ferroelectrics. This in turn calls for a multivariant framework suitable for microstructure simulation under various boundary conditions to describe the coarsening, refinement, selection, and alignment of microstructure. A different choice of field variables in novel phase-field model, local volume fraction of laminates, is introduced to represent domain configurations by using multirank laminates. As a result, the energy-well structure can be expressed explicitly in a unified fashion. Finally, we observe the domain patterns obtained in simulations by changing the thickness and parameters, and discuss the effect of thickness on compatibility. The variants in the film problem that our team dealt in the past are periodic and infinite in axials. Considering the effect of free boundary is the main subject this time. The framework is applied to domain simulation in two-dimensional ferroelectric thin films in tetragonal phase assuming that polarization is close to one of their ground states. The compatible domain patterns obtained in simulations with thick film and are similar to bulk. And then, we compare the computed energy under non-compatible domain with COMSOL to make sure the accuracy.