Interconnection effects on the electronic and optical properties of Ge nanostructures: A semi-empirical approach

A supercell model is applied to a semi-empirical sp3s⁎sp3s⁎ tight-binding (TB) approach to calculate the electronic band gap and imaginary part of the dielectric function of two Ge nanostructures—ordered arrays of pores and stand-alone nanowires—and one example of their interconnections. The pores are modeled by removing columns of Ge atoms in the [0 0 1] direction. The results of the variation band gap are compared with those obtained by TB-sp3, TB-sp3d5s⁎TB-sp3d5s⁎, density functional theory (DFT), and experimental data. The imaginary part of the dielectric function is calculated by including both intra-atomic and inter-atomic dipole matrices using (for both) the interconnected and free standing (chessboard-like) models for the Ge skeleton. The calculation shows that although the intra-atomic matrix elements are small in magnitude a quantitative treatment of the optical absorption spectrum of Ge nanostructures may not be possible without the inclusion of these matrix elements. Finally, the calculations confirm that also ordered porous germanium (PGe) show a clear quantum confinement signature, even though the wave functions could in principle behave like delocalized Bloch states.

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► Study of the interconnection between nanowires present in real samples of o-PGe.
► We use a supercell model within a semi-empirical sp3s⁎sp3s⁎ tight-binding (TB).
► Band-gap scales linearly with the porosity index.
► The ϵ2ϵ2 is calculated by including intra-atomic and inter-atomic dipole matrices.
► The supercell model emphasizes the interconnection of the system.