Theoretical Study of Auxeticity and Carrier Mobility in Phosphorene and related two-dimensional materials

Since the successfully mechanical exfoliation of two-dimensional (2D) forms of graphene from its three-dimensional counterpart graphite, many 2D materials have shown exceptional mechanical, electronic, and catalytic properties. The transistor is a widely applied electronic device in integrated circuits, computers, hybrid vehicles, energy, and communications. The carrier mobility is one of the most key parameters in the semiconductor-based field-effect transistor. With the development of computational and communicational industries, the aim of faster switching and higher integrated circuits requires transistors with higher carrier mobility working materials. On the other hand, a moderate ON/OFF (106~1010 ) ratio of a practical transistor requires the working material with an appropriate band gap. The Dirac cone structure of graphene has the gapless nature, and many other 2D materials such as transition metal dichalcogenides have insufficient carrier mobility and poor conductivity, all of these features limit the wide application in the 2D materials based field-effect transistor. In 2014, a novel 2D counterpart of black phosphorus was firstly exfoliated, which was named after “phosphorene”. In the next few years, phosphorene has been reported with high hole mobility, comparable to graphene and a moderate band gap. These facts imply the phosphorene a future candidate of the working material in the transistor. Aimed to find new appropriate 2D working materials for the transistors, we have implemented a systematically first-principles calculation on the phosphorene in different phases and phosphorene isostructures (same structure but consists of different elements). In Chapter 1, we introduce the background in the relevant fields including the introduction of the previously found 2D material and their electronic properties in terms of the working material in the transistors, the theoretical framework of the carrier mobility and its dominant key factors, the fundamental concepts and the general principles in the semiconductor transistors. In Chapter 2, we generally introduce the first-principles and the density functional theory – what we used in the calculation. As the systems we calculate are all 2D materials, the Van der Waals interaction plays a significant role, so the Van der Waals corrected correlation function must be considered. Besides, as the calculation of intrinsic carrier mobility is derived from the results of band structure calculation, the hybrid function has been implemented in the relevant calculation. Since most of the systems we study in the present thesis are artificial, especially for the phosphorene isostructures, we first start from the structural and mechanical properties. Meanwhile, the strain has been considered an efficient method for engineering carrier mobility. Thus we firstly study a strain related mechanical properties of the phosphorene and phosphorene isostructures such as Young’s modulus, Poisson’s ratio and many more. In Chapter 3, we discuss the auxetic phenomenon in δ-phosphorene and δ-phosphorene isostructures (with the so-called lifeboat appearance). Two-dimensional auxetic materials with negative Poisson’s ratio expand in response to a tensile strain in cross-section. Such counter-intuitive behaviours have been mainly ascribed to concave structures with ideal rigid ball-stick models. Here, based on first-principles calculations, we systematically analyze the mechanical behaviours of three life-boat structured 2D materials and report two new auxetic materials: δ-arsenic and δ-graphane. The calculated Poisson’s ratio values are correlated with Young’s modulus, cohesive energy, and valence shell electron pair repulsion of isostructures. Combining with previous research, we provide a self-consistent explanation of the origin of the 2D in-plane negative Poisson’s ratio and an algorithmic route to discover new auxetic materials by comparing the energy restored in bond rotation and stretch. In Chapter 4, we introduce a strain-enhanced carrier mobility in α-phosphorene. Carrier mobility is a key parameter for the operation of electronic devices as it determines the ON-state current and switching speed/frequency response of transistors. 2D α-phosphorene has been considered as a potential candidate for field-effect transistors due to its high mobility. In chapter 4, we propose to further enhance the carrier mobility of phosphorene and device performance via strain engineering. A systematic ab-initio investigation on the anisotropic electronic structure of few-layer phosphorene reveals that the monolayer under 7.5~10% strain along zigzag direction shows an exceptional carrier mobility of ~106 cm2V-1s-1, which is 10 times higher than the strain-free case. The simulated device performance shows that strain-engineered phosphorene-based field-effect transistors demonstrate a cut-off frequency of ~1.14 THz with a gate length of 1.0 micron and 112 THz with a sub-10 nm gate length. The exceptionally low deformation potential is proposed as the key determinant for the high carrier mobility in α-phosphorene. This is related to its unique corrugated two-dimensional structure. In Chapter 5, we present a systematic first-principles density functional theory study on ten α-phosphorene isostructures by calculating the three key parameters of the carrier mobility. An electron mobility in the armchair direction with a value comparable to α-phosphorene is found in α-PAs, α-PCH, and α-AsCH, due to the structure-caused low deformation potential. The highest carrier mobility is predicted in α-graphane because of a two-order-of-magnitude smaller deformation potential than other isostructures. The low deformation potential can be correlated to the separation of charge carriers from neighbouring unit cells. This study highlights a feasible route to generating high mobility materials through deformation potential engineering. In Chapter 6, we summarize the major results and the academic contribution in this present thesis and gives a prospective vision of the future low-dimensional material and possible developing trend of the transistors