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引用次数: 9
摘要
石墨烯中的电荷输运对于新一代纳米级电子器件的设计至关重要。一个合理的模型是用价带和导带电子的半经典玻尔兹曼方程表示的。如Romano et al. (J. Comput.)理论物理。, 2015),不连续伽辽金方法是解决这些方程数值积分问题的可行方法,即使还设计了适当包含泡利原理的有效DSMC。用确定性方法得到的解的优点之一当然是没有统计噪声。这一事实对于马约拉纳等人证明的低磁场迁移率的准确估计至关重要。工业,2016)在恒定电场下悬浮石墨烯片中单极电荷传输的情况下。漂移-扩散方程是CAD中最常用的电荷输运模型,迁移率表达式对于漂移-扩散方程是必不可少的。这里是马约拉纳等人的分析。Industry, 2016)通过两种方式得到改进:包括价带和导带中的电荷输运;通过考虑氧化物作为石墨烯片的衬底的存在。获得了新的迁移率模型,特别是对低场迁移率进行了相应的改进。
Improved mobility models for charge transport in graphene
Abstract Charge transport in graphene is crucial for the design of a new generation of nanoscale electron devices. A reasonable model is represented by the semiclassical Boltzmann equations for electrons in the valence and conduction bands. As shown by Romano et al. (J. Comput. Phys., 2015), the discontinuous Galerkin methods are a viable way to tackle the problem of the numerical integration of these equations, even if efficient DSMC with a proper inclusion of the Pauli principle have been also devised. One of the advantages of the solutions obtained with deterministic approach is of course the absence of statistical noise. This fact is crucial for an accurate estimation of the low field mobility as proved by Majorana et al. (J. Math. Industry, 2016) in the case of a unipolar charge transport in a suspended graphene sheet under a constant electric field. The mobility expressions are essential for the drift-diffusion equations which constitute the most adopted models for charge transport in CAD. Here the analysis by Majorana et al. (J. Math. Industry, 2016) is improved in two ways: by including the charge transport both in the valence and conduction bands; by taking into account the presence of an oxide as substrate for the graphene sheet. New models of mobility are obtained and, in particular, relevant improvements of the low field mobility are achieved.
期刊介绍:
Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.