以第一原理方法計算二硫化鉬過渡金屬摻雜與黑磷鈧金屬電極電子結構之研究

First-Principle Calculations of the Electronic Structure of Two-Dimensional Materials: Doping Engineering of Molybdenum Disulfide and Scandium Contact of Black Phosphorus

蔡易珈(Yi-Chia Tsai)

指導教授 ： 李義明

國立交通大學/電機學院/電信工程系所/碩士(2018年)

摘要

半導體產業經過超過半世紀的發展，積體電路元件已發展到5 奈米的技術層級，更複雜與多樣的電路與系統可以被設計與製造在同一矽晶片中。隨著大數據與人工智慧應用技術的潮流，對於晶片運算速度的需求日與俱增。利用製程微縮而提升運算效能的做法受到「摩爾定律」（Moore’s Law）與量子力學的限制。雖然製程微縮持續挑戰其微縮極限，創新材料因擁有更好的材料特性而逐漸成為學界、業界逐漸重視的課題。其中，低維度材料的應用更是全球矚目的焦點。
二維材料的研究萌芽於2004 年單層二維材料石墨烯(Graphene)。然而，因為石墨烯沒有能隙，因此限制了它在半導體領域的運用。2011 年單層過渡金屬二硫屬化物(Transition Metal Dichalcogenide) 與2014 年多層黑磷(Black Phosphorus)電晶體的研究吸引更多的研究目光。研究如何將二維材料應用在下世代積體電路元件至今仍是半導體技術重要的發展方向之一。其中一項重要課題是如何透過摻雜原子調整二維材料的半導體特性，特別是應用到光電領域的二硫化鉬(Molybdenum Disulfide)。在傳統矽晶圓的架構下，週期表上的三、五族元素如硼與砷分別用來作為p 型與n 型半導體的摻雜物。然而二維材料不同於塊材尺寸的矽晶圓，二維材料的表面積與體積的比例較高使得表面效應非常顯著，此外二硫化鉬的元素組成為硫與鉬原子，因此合適的摻雜原子與摻雜濃度是目前急迫了解的議題。
本論文在密度泛函理論的架構下透過Blocked Davidson 迭代法求解科恩－沈吕九方程式(Kohn–Sham equation)並且結合了經驗推導的凡得瓦爾力修正去正確描述原子間的交互作用力與材料的電子結構。實務上我們運用VASP 第一原理技術軟體進行各種電子交換能的精準度測試並進行原子的鬆弛與能階的計算。
本論文透過第一原理研究不同過渡金屬的摻雜對單層二硫化鉬電特性的影響。我們首先透過比對實驗結果校估模擬參數與模式的選擇。我們透過量化電子轉移深入探討摻雜原子如何調變單層二硫化鉬的表面真空位勢、電子親和力、功函數、費米能階。同時我們也討論不同摻雜原子在各摻雜濃度下對費米能階調變的影響並歸納出屬於單層二硫化鉬的n 型與p 型摻雜物。
另外一項迫切的研究課題是電極材料的選擇，其中黑磷雖然擁有極高的載子遷移率，但是作為電晶體應用時，顯著的接觸電阻使得黑磷優異的材料特性無法被有效發揮。然而，顯著的接觸電阻並不只有在黑磷電晶體上觀察到，在一維材料(如：奈米碳管)與其他總類的二維材料(如：二硫化鉬)皆被廣為研究。做為二維材料的新成員，黑磷電晶體的相關研究正在如火如荼的產開。其中國外學者使用鈧金屬做為黑磷電晶體的電極並透過實驗的方式量測到較高的驅動電流，但是背後的物理尚不明確。
本論文首先採用創新的混和交換能計算法提升計算的精確度並與實驗校估以提升模擬的可信度。基於黑磷的結構與電特性皆準確的計算成果下，我們建構金屬與三層黑磷的接面探討電極材料與黑磷表面的鍵結行為與表面鍵結對它層黑磷電特性的影響。探討層面涵蓋接面位勢、接面電子濃度、鍵結後接面電子轉換、能態密度分布，並總結使用鈧金屬電極在黑磷電晶體有較優異性能的因素。
綜合以上所述，本論文主要探討過渡金屬摻雜對單層二硫化鉬電特性的調變和金屬電極對黑磷的電特性影響。此研究成果可作為下世代電晶體的製造與發展之參考，並可供半導體工業界研發相關之製程技術。

關鍵字

第一原理 ； 二維材料 ； 黑磷 ； 二硫化鉬 ； 接觸電阻 ； 過渡金屬摻雜

並列摘要

The semiconductor industry has undergone a huge development over the past fifty years. The technology node has finally scaled down to five nanometer which allows designers to devise more complicated and diverse functions and systems in the same silicon chip. Driven by the big data and artificial intelligence technology, the need for high-performance logic circuit is growing astronomically. However, miniaturization which was used to boost the performance of transistors is limited by Moore's law and quantum mechanics. Although industry is still trying to challenge the limitation of miniaturization, advanced alternative materials equipping with superb material property has gaining importance from both academia and industry. Among them, the applications of low-dimensional materials are the cynosure of all eyes.

People's interest in two-dimensional burgeoned since graphene was exfoliated from graphite in 2004. However, the zero-gap property of graphene limits its potential in logic design. The invention of monolayer transition metal dichalcogenide transistor in 2011 and few-layer black phosphorus transistor in 2014 grab more attention. However, researching how to implement two-dimensional materials in next-generation integrated circuit is still an important topic of semiconductor industry. One of the emerging topics is how to modulate the electronic property of two-dimensional by doping engineering, especially for molybdenum disulfide because it is promising for optoelectronics. In the traditional silicon technology, the elements in group III and V, such as boron and arsenic, are frequently used as dopants for p-type and n-type semiconductor. However, distinct from the bulk size of silicon, the surface effect is significant in two-dimensional materials due to higher surface/volume ratio. Also, because molybdenum disulfide is constructed by molybdenum and sulfur elements, therefore it is an urgent task to find out the proper dopants and doping levels that lead to n-type or p-type property.

In this thesis, we apply blocked Davidson iteration to solve Kohn-Sham equation. We also integrate the model with empirical van der Waals correction to describe the interaction among atoms and calculate the electronic structure. In practical, we exploit VASP first-principles technical software for the test of exchange-correlation functionals, the atomic relaxation, and the calculation of energy levels.

Based on the methodology, we investigate the impact of transition metal dopants on the electronic property of monolayer molybdenum disulfide using first-principles calculation. Firstly, we verify and calibrate the parameters and models by comparing with experimental measurement. We discuss how the dopants modulate the vacuum potential, electron affinity, work function, and Fermi energy of monolayer molybdenum disulfide by analyzing charge transfer. Meanwhile, we consider the effect of doping level on the Fermi energy for each dopant and categorize the proper dopant and doping level for n-type and p-type monolayer molybdenum disulfide.

The other urgent task is to explore the proper electrode materials for black phosphorus. Although black phosphorus has a high carrier mobility, but the high contact resistance keeps black phosphorus from fully wield its excellent material property. The significant contact resistance was also observed in one-dimensional materials, such as carbon nanotube, and other kinds of two-dimensional materials, such as molybdenum disulfide, however, they had already been well-studied. Black phosphorus, on the contrary, is the youngest member in the two-dimensional family, thus the corresponding research are still progressing. It worth noting that an international researcher used scandium as contact material and measured a high performance, but lacks a theoretical explanation.

In this thesis, we first propose the revolutionary hybrid exchange-correlation functional to lift the computational accuracy and boost the reliability by calibrating with experiments. Based on the accuracy in atomic and electronic structures, we construct the interface between contact materials and trilayer black phosphorus to analyze the interfacial binding behavior and the impact of binding on the other layers of trilayer black phosphorus. We analyze the performance of contact material from the insight of interfacial potential, charge density, charge transfer, and density of states. Finally, we conclude that why scandium electrode leads to superior performance.

In short, this thesis mainly focuses on how the transition metal dopants modulate the electronic property of monolayer molybdenum disulfide and the impact of contact materials on the electronic property of black phosphorus. The results of this thesis can be a valuable reference for the development of next-generation transistor and can provide contemporary semiconductor industry to develop and improve the innovative technology.

並列關鍵字

First-Principle Calculation ； 2D Materials ； Black Phosphorus ； Molybdenum Disulfide ； Contact Resistance ； Transition-Metal Doping

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