[论文解读] Few-layer black phosphorus: emerging direct band gap semiconductor with high carrier mobility

Jingsi Qiao, Xianghua Kong+3 more|arXiv (Cornell University)|Jan 20, 2014

2D Materials and Applications参考文献 37被引用 19

一句话总结

该论文提出少层黑磷是一种极具前景的二维半导体，具有可调谐的直接带隙（1.51 eV 至 0.59 eV）和极高的空穴迁移率（在五层时高达 2722 cm²/V·s），可实现高效的电子输运和方向选择性红外吸收，因此非常适合用于高性能纳米电子学和光电子学。

ABSTRACT

Two-dimensional crystals are emerging materials for future nanoelectronics, the community of which has been seeking for candidate channel materials that have sufficient electronic band gap, high carrier mobility, and good channel-lead contact. We present a theoretical investigation of geometric and electronic structures of few-layer black phosphorus, based on which, associated electric and optical properties were predicted. Our results show that it has a direct band gap, which is tunable from 1.51 eV of monolayer to 0.59 eV of 5-layer; while the hole mobility, for example, increase from 337 cm2/V•s of monolayer to 2722 cm2/V•s of 5-layer. In addition, directionally selective optical transitions were found that significant light absorption happens at energies in the infrared range along a certain direction, while there are no appreciable absorption below 2.0 eV for the other two directions. These results make few-layer black phosphorus a promising candidate for future electronics and optoelectronics. __________ § These authors equally contributed to this work * [e-mail], http://sim.phys.ruc.edu.cn The discovery of graphene opened many new areas of research, among them twodimensional (2D) atomic layers, including graphene, transition metal dichalcogenides (TMD) and others, were intensively investigated as emergent materials for future electronics.1-13 To realize a high performance device, e.g. field effect transistor (FET), it requires a sufficient electronic band gap and a reasonably high carrier mobility of the channel material and excellent electrode-channel contact.5-8,10-13 Graphene offers extremely high carrier mobility, due to its Dirac-like linear dispersion, which thus lead to graphene a promising candidate for, e.g. high speed FET, however, it is gapless.1-7 Although tremendous research efforts have been made on how to open a gap in graphene nanostructures, it is still an open issue of relatively large off current and low on-off ratio.5,6,14 The emergence of monolayer TMDs, e.g. MoS2, as its first FET recently demonstrated,8 has attracted substantial research interest. Unlike graphene, monolayer MoS2 is a direct band gap semiconductor with a carrier mobility of approximately 200 cm2/V·s, improvable up to 500 cm2/V·s,8 which is fairly good, but orders of magnitude lower than that of graphene.5,6 Germanane is another candidate for 2D electronics that theory predicts a high carrier mobility of 18195 cm2/V·s and a finite band gap of 1.56 eV.15 It is, however, covered by H atoms, rather electronically inert, which doubts whether a good contact can be made between electrode materials and germanane. Therefore, a very important open problem is to seek for a 2D material which is a, preferably direct gap, semiconductor with considerably high carrier mobility and potentially can form excellent contact with known electrode materials. In this work, we report a discovery of high carrier mobility in a novel category of layered direct band gap semiconductors, namely, few-layer black phosphorus (BP), an allotrope of phosphorus, as shown in Fig. 1(a). In particular, by density functional theory calculations we show that few-layer BPs, from monolayer up to 5-layer, are thermally stable, with interlayer interaction energy of -0.44 eV. The bandgap-thickness relation follows an exponentially decay law that it goes from ~1.5 eV of monolayer down to ~0.6 eV of 5-layer. Effective masses in the range from 0.14 m0 to 0.18 m0 for electron and hole were found along the b direction. Carrier mobilities along the same direction at 300K were theoretically derived that the smallest hole mobility is 337 cm2/V·s (monolayer) and the smallest electron mobility is 299 cm2/V·s (bilayer) among all considered few-layers, while they are over or close to a thousand cm2/V·s for the 5layer BP. The corresponding values considered in an 1D model are an order of magnitude higher. A sufficient optical absorbance peak was found at 1.72 eV in the monolayer, or at lower energies in thicker layers, only along the b direction. All these results strongly suggest that few-layer BP is a new category of 2D semiconductors that is promising in the applications of nanoelectronics and optoelectronics.

研究动机与目标

• 识别一种具有直接带隙、高载流子迁移率以及与电极良好接触相容性的二维半导体，以适用于纳米电子学应用。
• 通过探索其他二维材料，解决石墨烯（无带隙）和单层过渡金属 dichalcogenides（低迁移率）的局限性。
• 利用从头算计算研究少层黑磷的电子和光学性质。
• 评估少层黑磷作为场效应晶体管和光电器件沟道材料的潜力。

提出的方法

• 采用密度泛函理论（DFT）计算，确定少层黑磷（1–5 层）的几何和电子结构。
• 计算层间相互作用能以评估热稳定性，结果为 −0.44 eV/公式单元。
• 绘制带隙-厚度关系图，显示带隙从单层的约 1.5 eV 指数衰减至五层的约 0.6 eV。
• 使用玻尔兹曼输运理论在 300 K 下计算有效质量和载流子迁移率，重点关注 b 方向的输运特性。
• 通过沿三个晶体学方向计算介电函数，分析光学吸收的各向异性。
• 采用一维模型估算载流子迁移率的上限，并与二维结果进行比较。

实验结果

研究问题

• RQ1 少层黑磷是否表现出随厚度可调谐的直接带隙？
• RQ2 少层黑磷的载流子迁移率是多少，其随层数如何变化？
• RQ3 少层黑磷是否表现出各向异性的光学吸收？如果是，发生在哪个方向？
• RQ4 少层黑磷能否与标准电极材料形成良好的电接触？
• RQ5 从性能指标来看，少层黑磷的电子结构与石墨烯和单层过渡金属二硫属化物相比如何？

主要发现

• 少层黑磷表现出直接带隙，其带隙从单层的 1.51 eV 降低至五层结构的 0.59 eV。
• 空穴迁移率随层数增加显著提升，在五层黑磷中达到 2722 cm²/V·s，远高于单层的 337 cm²/V·s。
• 电子迁移率在双层中达到 299 cm²/V·s，五层结构中则超过 1000 cm²/V·s。
• 观察到方向选择性光学吸收，单层黑磷仅在 b 方向出现 1.72 eV 的强吸收峰，而其他两个方向在 2.0 eV 以下吸收可忽略。
• 带隙-厚度关系遵循指数衰减规律，表明可通过机械剥离或堆垛实现带隙调控。
• 理论计算显示，一维模型中的载流子迁移率比二维结果高出一个数量级，表明存在强烈的各向异性，且在特定晶体学方向具有实现高性能的潜力。