探究在過渡金屬二硫族化物層厚度和堆疊的影響，提供電子特性與可調性上之新洞見，並指引出新穎的研究和應用方向。本論文對一層至十層的二硫族化鋯薄膜之層相依的穩定性和電子特性進行了全面性的第一原理研究。研究結果顯示，在二硫族化鋯的塊材和薄膜中最穩定結構皆為 1T 堆疊結構。1T 二硫化鋯和二硒化鋯薄膜是絕緣體，從單層至十層的能隙是逐漸減少，然而 1T 二碲化鋯薄膜及塊材則皆是半金屬。最後，我們發現在無應變的二層和受應變的三層 1T 二硫化鋯薄膜中存在凡霍夫奇異點。由於厚度相依性和應變，這些結果展示了二維材料其可調整的電子特性。

Probing the effects of layer thickness and stacking on transition metal dichalcogenides (TMD) offers novel insights on their electronic properties and tunability which leads to a new avenue of research and applications. A comprehensive first-principles study on layer-dependent stabilities and electronic properties of ZrX2 (X=S, Se, Te) thin films from 1 layer to 10 layers is performed in this thesis. Result shows that both ZrX2 bulk and thin films adopt 1T allotrope as the most stable structures. Furthermore, 1T ZrS2 and ZrSe2 thin films are insulators and their band gaps decreased as the number of layers is increased to 10 layers, while 1T ZrTe2 thin films and bulk are semi-metallic. Lastly, we discovered existence of van Hove singularities in unstrained 2-layer and strained 3-layer 1T ZrS2 thin films. These results showcase the tunable electronic properties of two-dimensional materials due to thickness dependence and strain.

論文審定書 i
Acknowledgements ii
摘要 iii
Abstract iv
List of Figures vii
List of Tables x
Chapter 1 1
Introduction 1
Chapter 2 5
Computational Methods 5
2.1 Vienna Ab-initio Simulation Package (VASP) 5
2.2 Electronic Band Structure 6
2.3 Electronic Density of States 7
2.4 Formation Energy 8
2.5 Lattice Strain 9
2.6 Spin-orbit Interaction 10
2.7 External Electric Field 11
2.8 Hybrid Functional Calculations 11
Chapter 3 12
Results and Discussion 12
3.1 Atomic Structures of Bulk and Layered ZrX2 12
3.2 Stability of ZrX2 Allotropes 17
3.3 Band Structure of Bulk ZrS2 20
3.4 Band Structure of Bulk ZrSe2 21
3.5 Band Structure of Bulk ZrTe2 23
3.6 Robust Dirac Fermion on Bulk ZrTe2 25
3.7 Band Structures of Layered ZrS2 27
3.8 Band Structures of Layered ZrSe2 29
3.9 Band Structures of Layered ZrTe2 31
3.10 van Hove Singularities for Select ZrX2 34
Chapter 4 39
Conclusion 39
References 41
Appendix 54
Supplementary Materials 54

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