REVIEW 2D Materials www.advtheorysimul.com Computational Understanding of the Growth of 2D Materials Junfeng Gao, Ziwei Xu, Shuai Chen, Madurai S. Bharathi, and Yong-Wei Zhang* Over the last two decades, remarkable progress has been made in use of computational methods for understanding 2D materials growth. The aim of this Review is to provide an overview of several state-of-the-art computational methods for the modelling and simulation of 2D materials growth. First, the current status of 2D materials, and their major growth methods are addressed. Next, the applications of the ab initio method in 2D materials growth is discussed, focusing on reaction of precursors, diffusion of adatoms, energetics and kinetics of growth fronts, and effects of substrates. Then, the applications of the molecular dynamics approach in 2D materials growth is discussed, with emphasis on the growth of graphene on various substrates and the growth of boron nitride and silicene. Furthermore, the applications of the kinetic Monte Carlo method in 2D materials growth are discussed. The parametrization of the method and its application in dimer distribution, and nonlinear edge growth of graphene are discussed. Subsequently, the applications of the phase-field method in 2D materials growth are discussed, focusing on the growth rate and morphological evolution of 2D domains. Finally, perspectives and conclusions are presented. 1. Introduction 1.1. Current Status of 2D Materials Research Since graphene was first exfoliated from graphite in 2004, [1] it has opened the door for a brand new scientific arena: 2D materials. As a result, many 2D materials have been exfoli- ated and/or synthesized by different techniques, and their struc- tures, physical properties, and applications have been inves- tigated both theoretically and experimentally. [2–46] These stud- ies have revealed many fascinating, often exotic properties of 2D materials and demonstrated their various potential applica- tions, in electronics, [1–7] optoelectronics, [8,9] sensor, [10–13] energy storage, [14–16] surface catalysis, [17,18] biology, [19,20] etc. Besides graphene, there exist other elemental 2D materi- als of Group IV, such as silicene, [5,21–26] germanene, [23,27–30] Dr. J. Gao, Dr. S. Chen, Dr. M. S. Bharathi, Prof. Y.-W. Zhang Institute of High Performance Computing A*STAR, Singapore 138632, Singapore E-mail: zhangyw@ihpc.a-star.edu.sg Dr. Z. Xu School of Materials Science & Engineering Jiangsu University Zhenjiang 212013, China The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adts.201800085 DOI: 10.1002/adts.201800085 stanene. [30–35] These Group IV monolay- ers also possess a Dirac cone and honey- combed lattice, similar to graphene. Dif- ferent from the perfect planar structure of graphene, they exhibit a slightly buckled structure. From C to Sn element, the ef- fect of spin-orbital coupling (SOC) becomes increasingly stronger. As a result, a bigger nontrivial SOC gap in their Dirac cone is in- duced. This is especially true for heavy el- ements in Group IV. For example, it was reported that a nontrivial SOC gap of intrin- sic stanene was over 30 meV. In particular, for surface halogenated stanene, it was over 300 meV, which was large enough even for making quantum spin Hall (QSH) devices at the room temperature. [31,32] Besides these Group IV elemental 2D materials, semiconducting Group V elemental 2D materials, such as phos- phorene, [7,36,37] arsenene, [3,38] and anti- monene, [3,38–42] have also attracted great attention recently. For example, phospho- rene is a direct bandgap semiconductor possessing a ultra-high carrier mobility and a high on/off ratio. Therefore, phosphorene is suitable for fast nanoelectronics and optoelectronics. [43,44] In addition, borophene, which is a mono- layer of boron atoms in Group III, [45,46] is a metallic 2D elemen- tal material. [47,48] It was revealed that although 2D borophene had several phases with similar free energies, [45,46] suitable substrates might be able to mediate their relative stabilities. [49–51] Besides, theoretical studies also indicated that borophene might pos- sess Dirac Fermions [52] and exhibit superconductivity [53] at low temperatures. In addition to elemental 2D materials, compound 2D materi- als have also been studied extensively. Perhaps, the most studied family of compound 2D materials is transition metal dichalco- genides (TMDCs), [4,6] which are a group of semiconductors with a bandgap of around 2.0 eV, a large on/off ratio of up to 10 6 , and a reasonably good carrier mobility of about 100–200 cm 2 V −1 s −1 at room temperature. [54–56] Generally, there are two common phases for TMDCs, that is, 2H and 1T (1T ′ ) phases. Taking MoS 2 , for example, 2H MoS 2 monolayer is a semiconductor with a bandgap of 1.6 eV, while 1T’ MoS 2 monolayer is metallic. [57,58] A 2H-1T ′ phase transition of MoS 2 can be achieved by apply- ing strain and/or charge doping. [2,59,60] Therefore, it is possible to construct a sharp 2H-1T ′ metal-semiconductor interface with Ohm contact, [2] which is extremely beneficial for 2D integrated circuits. The family of 2D materials is still growing fast. Various new growth and synthesis techniques are being developed. Adv. Theory Simul. 2018, 1, 1800085 C  2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1800085 (1 of 29)