Structural properties of monolayer and single- and multi-walled zigzag nanotubes of boron phosphide: a...

In this contribution, we investigate the stability of boron phosphide in various low dimensional forms ranging from the 3D bulk, the 2D slab model to the 1D single- and multi-walled zigzag nanotubes. A variety of energetic and geometric parameters including relaxation, cohesive and formation energies, polarisability, piezoelectric and elastic tensors components, and equilibrium lattice parameters have been reported. All arrangements are confirmed to exhibit a relatively wide band gap with properties dependent of geometric parameters. A connection between the 2D phonon modes and those of the 1D zigzag nanotubes has been established. Comparisons between IR and Raman of the single- and multi-walled nanotubes reveal that symmetry reduction leads to more active modes. By contrast, we found that angles and bond lengths only slightly deviate from those of the 1D single-walled nanotubes. By increasing the number of walls, the low frequency phonon modes become softer and shift toward lower wavelengths while high frequency phonon modes become harder with a blue shift owing to possible mechanical distortions that could occur between walls. These outcomes are expected to guide and motivate both experimentalists and theorists to design and optimize new emerging low dimensional inorganic materials for next generation nanodevices.

All computational modeling has been performed based on the density functional theory methodology with the B3LYP hybrid functional as implemented in the CRYSTAL23 program. The electronic wave-functions of the periodic 3D, 2D and 1D boron phosphide ground state are expressed with Bloch functions which are constructed as linear combination of Gaussian local type functions. Let us recall that the mode frequencies at the center of the Brillouin zone are obtained from the diagonalization of the mass-weighted Hessian matrix of the second derivatives of the total energy per cell with respect to atomic displacements. Therefore, IR and Raman spectra of all arrangements are simulated using the Coupled Perturbed Hartree-Fock or Kohn-Sham CPHF/KS approach.