Few-layer black phosphorus: emerging direct band gap semiconductor with high carrier mobility

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 * wji@ruc.edu. cn, 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.