以第一原理計算探討二氧化鋯之鐵電與反鐵電性質之物理機制

Abstract

本論文以基於密度泛函理論之第一原理計算方法研究二氧化鋯之鐵電與反鐵電生成機制。論文的第一部分比較了導致鐵電性之極化正交晶相（空間群：Pca21）與反鐵電性的非極化四方晶相（空間群：P42/nmc）之間的熱力學穩定度。研究結果顯示兩者之極化與非極化構型不必然與晶胞之正交與四方形狀有關。本論文將在薄膜被基材限制時、由非極化相變至極化相之現象視為定體積之熱力學過程。透過聲子頻譜計算，兩相之振動自由能隨溫度之變化可用於尋找穩定極化與非極化相之晶胞特徵。可以得知兩相皆有常溫下穩定之晶胞尺寸範圍。兩相穩定度隨溫度的變化亦可解釋文獻所認為導致反鐵電性質的電場誘發相變。第二部分探討了動力學抑制熱力學較穩定之單斜晶相（空間群：P21/c）與反極化（antipolar）排列之正交晶相（空間群：Pbca）的效應。若只考慮熱力學穩定度，極化相即使晶格限制下也並非最穩相，然而晶格限制亦改變了各相之間的相變能障，使得具鐵電性之極化即使並非最穩相也得以形成並持續穩定存在。最後，本研究針對薄膜之自由表面對相穩定度的影響進行討論，結果表明僅以薄膜之表面效應並不足以解釋實驗所觀察之鐵電與反鐵電性質隨厚度之變化。相對地，晶格之束縛效應可從熱力學與動力學上解釋二氧化鋯薄膜隨厚度之性質變化並作出與 實驗結果相符之預測。

In this thesis, we explore the physical origin of ferroelectricity and antiferroelectricity in zirconium oxide (ZrO2) using first-principles calculation based on density function theory (DFT). In the first part, the relative stability between ferroelectric phase (orthorhombic phase, space group: Pca21) and antiferroelectric phase (tetragonal phase, space group: P42/nmc) is investigated. It is found that their polar and nonpolar configurations may not necessarily coupled to the shape of the cell. When the lattice of the thin film is confined by the substrate, phase transformation between polar and nonpolar phase can be described as a constant-volume thermodynamic process. Calculation of vibrational Helmholtz free energy obtained from phonon spectra is conducted to characterize the dimensions of lattice favoring stable ferroelectric and antiferroelectric behvaior is investigated. Antiferroelectircity is explained by thermodynamic stability between the polar and nonpolar phase under a fixed lattice and field-driven phase transformation under application of electric field. The second part focuses on the kinetic suppression of monoclinic phase (space group: P21/c) and the antipolar orthorhombic phase (space group: Pbca). It is shown that polar phase is never thermodynamically stable even with lattice confinement. Nevertheless, the change in energy barrier under confinement leads to the formation of polar phase with comparably long lifetime. At the end, the effect of free surface of thin film is discussed and found that the presence of free surface alone cannot result in the thickness-dependent ferroelectricity and antiferroelectricity. The confinement of lattice, on the other hand, successfully elucidates the thickness-dependence of properties of ZrO2 using in thermodynamics and kinetics and is consistent to the experimetal findings.