Anisotropic reflectivity of black phosphorus in the far-infrared region

Black phosphorus, which is the most stable allotropic modification of phosphorus, is a semiconductor with a narrow-band gap of 0.3 eV [1]. The crystal is composed of puckered layers of atoms and belongs to an orthorhombic crystal structure (D2h1e). The structure of the puckered layer is schematically shown in Fig. la with a cartesian coordinate. According to its crystal symmetry, two infrared active phonon modes, i.e. B1u and B3u modes, are predicted to exist at the F point of the Brillouin zone [2]. Although black phosphorus possesses no permanent dipole moment because four atoms in the primitive unit cell are the same, it has been pointed out by a theoretical work [2] that an effective dipole moment will be induced by the atomic displacement according to each infrared active mode. The induced dipole moment due to the B3u mode is directed along the z-axis of the crystal and that due to the B1u mode along the x-axis. The lattice vibration according to the B1u mode is drawn in Fig. 1b. The B3u phonon mode was observed at 470 cm−1 by infrared absorption [3, 4] and reflection measurements [5] and the direction of its induced dipole moment was confirmed to lie in the direction of the z-axis of the crystal. Up to now, on the other hand, a quantitative measurement on the B1u mode has not been done. Sugai and Shirotani [53 made first a reflection measurement at the room temperature in the far-infrared region and observed a sharp peak which was assigned to the B1u phonon mode. However, a quantitative analysis was not given because of the difficulty of a precise measurement of the reflectivity on a small solid specimen in this region.