Overview of black phosphorus

The band theory of graphite was first analyzed by Wallace in 1947 as a beginning for understanding the electronic properties of 3D graphite [1], but the feasible method of fabricating two-dimensional graphene remained unknown. In 2004, Novoselov et al. discovered a convenient way to fabricate 2D graphene with the thickness is decreased down to only single layer or few layers by using scotch tape to mechanically peel graphene thin flakes from bulk graphite crystal [2]. This exfoliation

method has aroused tremendous interests in the study of graphene and other two

dimensional materials such as hexagonal-boron nitride (h-BN), transition metal dichalcogenides (TMDCs) and black phosphorus (BP) [3, 4].

Although graphene has extremely high mobility due to its massless Dirac feature

fermions, which made graphene a possible candidate for field effect transistor(FET) applications [5, 6], the fact that pristine graphene’s lack of energy bandgap makes graphene-based FET too hard to be turned off [7], which implies that graphene is not suitable for FET applications. Therefore, many researchers have turned to other 2D materials such as molybdenum disulfide (MoS2), which is one kind of transition metal dichalcogenides (TMDCs) and has a large bandgap of 1.8eV [8]. In 2011, Radisavljevic et al. fabricated the first single layered molybdenum disulfide (MoS )

FET with a high drain current on/off ratio and low standby power loss [9]. However, the mobility of MoS2 or other TMDCs-based transistors are relatively low owing to the heavy effective mass of carriers and severe phonon scattering at room temperature [10, 11]. Besides, it also faces a problem of not compatible to modern CMOS

processes [12]. Recently, black phosphorus (BP), one of the 2D materials, has brought about much interests due to its better electrical properties such as proper bandgap and high mobility [13, 14].

Black phosphorus is the most thermodynamically stable allotrope of phosphorus at room temperature and pressure [15]. Bulk BP can be synthesized by heating white phosphorus or red phosphorus under high pressures (12,000 atmospheres) [16, 17].

The electronic properties and crystal structure of BP are very much like those of graphite with both being black and flaky, a conductor of electricity [18-20], and having puckered sheets of linked atoms. While black phosphorus is the most steady form among all allotropes of phosphorus, environmental vulnerability is still a crucial issue [21, 22].

Black phosphorus is a layered material in which individual atomic layers are stacked together by van der Waals force [23]. BP has an orthorhombic structure and is the least reactive allotrope of phosphorus, a result of its lattice of interlinked six-membered rings where each phosphorus atom is covalently bonded to three

adjacent phosphorus atoms to form a puckered honeycomb structure [19, 24, 25], as shown in Fig 1.1. In this figure, the x and y directions in BP structure correspond to

the armchair(AC) and zigzag(ZZ) direction, respectively. It should also be noted that

phonons, photons, and electrons in layered black phosphorus structure display rather anisotropic features within the plane of layers [26-28].

Fig. 1.2 (a) shows the primitive cell of black phosphorus in its honeycomb lattice.

Its primitive unit vector in reciprocal lattice can be obtained by using Fourier transform, as well as its Brillouin zone and high symmetry points, as shown in Fig.

1.2 (b).

2D Matererials, 2014, 1(2) 025001

Fig. 1.1 Schematic diagram of the crystalline structure of black phosphorus (a) 3D representation, (b) lateral view, (c) top view.

Crystal structure is obtained by density functional theory(DFT).

P.-L. Gong et al., arXiv:1507.03213.

Fig. 1.2 (a) Crystal structure of bulk BP marked with coordinate axes(x,y,z) and lattice vectors(a,b,c) (b) The first Brillouin zone and

some high symmetric points of bulk black phosphorus.

The band structure of black phosphorus is thickness dependent, which can be attributed to interlayer interactions. Fig. 1.3 (a) shows the calculated band structure of black phosphorus for monolayer, bilayer, trilayer and bulk by density functional

theory(DFT) [24]. The bandgap of monolayer black phosphorus(phosphorene) is predicted to be about 2.0eV at the Γ point of the first Brillouin zone [14]. It should be

noticed that as the layer number increases, the bandgap of BP remains direct at the Γ point of the first Brillouin zone for all thicknesses. Fig. 1.3 (b) shows the relationship between thickness and bandgap calculated with different ab initio methods [24, 29, 30]. Even though the magnitude of bandgap counts on which approximation method

increases [14]. This thickness dependent bandgap, which is due to the quantum confinement of the charge carriers in the out-of-plane direction [31], is stronger than that observed in those of the other 2D semiconductor materials. The band structure approximation of BP shows that BP has the needed bandgap for the field-effect transistor applications.

Moreover, although black phosphorus exhibits an intrinsic ambipolar behavior, the conduction type in few layered BP is hole-dominant for the following two reasons.

First, the activation energy for p-type BP is lower than that of n-type BP [14]. Second one is the higher degree of anisotropy of the hole effective mass [32].

(a)

(b)

2D Materials, 2014. 1(2): p. 025001.

Fig. 1.3 (a) Calculated band structures for monolayer, bilayer, trilayer

and bulk black phosphorus sheets at all high-symmetry points in the

Brillouin zone. The energy is scaled with respect to the Fermi energy

calculated with different approaches.

According to the in-plane anisotropic geometry of BP crystal, lots of its physical characteristics are also quite different in armchair(AC) and zigzag(ZZ) directions such as electronic, thermal, optical and mechanical properties [33, 34]. Some physical properties along AC and ZZ directions for few-layered BP are theoretically predicted, listed in Table. 1.1. Except for mono layer, the ratio of mobility along AC and ZZ directions are predicted to be about 2 for holes and 4 for electrons at room temperature [30]. The experimental ratio of hole mobility, the dominant transport carriers of BP, is about 1.5~1.8 [28, 35]. Thus, in order to achieve better performance for BP devices, the AC direction should be used as the current channel because of the higher mobility on this direction.

Table 1.1 Predicted carrier mobility. NL represents the number of layers, mx* and my* are carrier effective masses along AC and ZZ, respectively. μx_2D and μy_2D are

mobilities along AC and ZZ, respectively.