Phosphorene as a Postgraphene Material for Straintronics: Features of Electronic Structure and Dynamical X-ray Diffraction

The object of theoretical study is black phosphorene as an alternative to currently known quasi-two-dimensional materials of the post-graphene-discovery period due to its excellent electronic properties, particularly a direct band gap that can be tuned through thickness and strain. For a phosphorene monolayer of realistic sizes (with millions of P atoms), the effect of uniaxial tensile strain on the band gap is simulated within the tight-binding model. The numerical technique takes into consideration the strain-induced dependence of hopping integrals on the bond length and the resulting lateral (transversal) or out-of-plane deformation response to the applied longitudinal (uniaxial) or shear strain. If the in-plane (out-of-plane) Poisson’s ratio is not a constant but a function depending nonlinearly (nonmonotonically) on the stretching, the band gap value behaves nonlinearly (nonmonotonically) versus the strain. To study the dynamical (multiple) diffraction of the plane X-ray waves in the phosphorene–silver substrate system, we use the triple-axis diffractometry method for the case of Bragg diffraction geometry. The necessity of taking into account the variability of the lattice parameters as well as the strain- and direction-dependent Poisson’s ratio in calculating the complex structural factors and Fourier components of polarizability is substantiated. As shown, the alteration of the number of layers of phosphorene in the phosphorene–silver substrate system, as well as the introduction of strain, leads to a significant change in the diffraction profiles that makes it possible to determine the characteristics using the X-ray diffraction method.