Theoretical overview of black phosphorus

In this chapter, we discuss the electronic and optoelectronic properties of few-layer BP, a layered semiconductor that can be exfoliated from bulk black phosphorus (BP), the most stable allotrope of phosphorus [1, 2, 3]. Just like graphite, this elemental layered material is composed of layers of atoms organized in a stable linked-rings structure, where the layers are held together by weak van der Waals forces, which facilitates its exfoliation into few-layers form from its bulk parent. However, the atomic rings in black-phosphorus layers exhibit a puckered structure, resulting in the opening of a gap in its electronic spectrum and yielding strongly anisotropic in-plane properties, such as angle-dependent electrical and thermal conductivities, as well as excitonic polarization. Moreover, the observed high carrier mobilities of ≈1000cm²/Vs along its light effective mass direction makes it promising for electronic applications [4, 5, 6, 8]. In fact, the unique crystal structure and anisotropic properties of bulk BP has drawn attention to this material for decades, from the 1950s to the 1980s [2]. Interest on this material has been renewed since 2014, when its exfoliation into few-layers was first demonstrated [4, 5, 6, 7, 8], allowing for its fabrication as an atomically thin semiconductor, whose optical band gap and electronic properties are controllable by the number of layers. For instance, the optical band gap of BP is found to range from 0.3 eV, in bulk BP, to ≈1.6eV, in monolayer BP [1, 2, 7, 9, 10], making it a promising material for optoelectronics across a wide spectrum [11, 12, 13, 14, 15]. In what follows, we discuss the theory of the electronic band structure, the optical, electronic, thermal and mechanical properties of monolayer to few-layer black-phosphorus. Crystal and Electronic Band Structures The crystal structure of bulk BP is shown in Fig. 21.1(a) along with the first Brillouin zone schemes of bulk and monolayer BP in Fig. 21.1(b), where high-symmetry points are highlighted. Their two main in-plane directions, namely, zig-zag and armchair, are labeled. Bulk and monolayer BP have a base-centered orthorhombic [Cmce space group (No. 64)] and simple orthorhombic [Pmna space group (No. 53)] crystal structures [16], respectively, both with four P atoms per primitive cell.