Polar optical phonons in core–shell semiconductor nanowires

Abstract

We obtain the the long-wavelength polar optical vibrational modes of semiconductor core-shell nanowires by means of a phenomenological continuum model. A basis for the space of solutions is derived, and by applying the appropriate boundary conditions, the transcendental equations for the coupled and uncoupled modes are attained. Our results are applied to the study of the GaAs-GaP core-shell nanowire, for which we calculate numerically the polar optical modes, analyzing the role of strain in the vibrational properties of this nanosystem.

Hybrid longitudinal-transverse phonon polaritons

“…Our starting point in order to microscopically model the hybridisation of phonon polaritons with ZFLOs is to expand the theory describing ionic motion in a polar dielectric 34–36 to the retarded regime. In frequency-space the material displacement X obeys the equationwhere ϕ ( A ), is the electromagnetic scalar (vector) potential, the material high-frequency dielectric constant is ε ∞ , the transverse (longitudinal) optical phonon frequency at the Γ point is ω T ( ω L ), the material density is given by ρ , the phonon damping rate by γ , the transverse (longitudinal) phonon velocities in the limit of quadratic dispersion by β T ( β L ) and the polarizability α .…”

Continuum model for low-frequency phonons of boron nitride nanotubes

“…We choose the axis of the wire along the z direction of the cylindrical coordinates r z , , θ ( ). Although the continuum approach employed in this work has been reported elsewhere [14][15][16]13,17], for the sake of completeness we summarize here the main features of the model, particularizing for the tubular geometry.…”

Electron-phonon deformation potential interaction in core-shell Ge-Si and Si-Ge nanowires

“…We choose the axis of the wire along the z-direction of the cylindrical coordinates (r, θ, z). Although the continuum approach employed in this work has been reported elsewhere, 22,24,32 for the sake of completeness and further applications focusing on the electron-phonon DP Hamiltonian, we briefly recall the main features of the model, particularizing for non-polar media and cylindrical core-shell geometry. Considering a harmonic time-dependence for the oscillations, the equations of motion for the optical modes in a isotropic nonpolar media is given by 33…”

“…In these expressions, β L , β T describe the quadratic dis-persions of the LO-and TO-bulk phonon branches of the optical modes in the long-wave limit, respectively. Applying the Helmholtz's method of potentials, 24,32,34 one can find a general basis of solutions for the problem, namely…”

“…15,21 To this end, we employ a continuum approach, as has been done for other systems, 22 including core-shell nanowires of polar semiconductors. 23,24 As in the polar case, both core and shell components develop strain due to the different lattice constant between the two materials. We include this effect in our model, so that frequencies at the center of the Brillouin zone of the bulk material are shifted with respect to the unstrained case.…”