Electron states and luminescence transition in porous silicon

The theoretical analysis of two different Si wires of size 5×4 and 3×4, simulating porous Si, has been performed through the linear-muffin-tin-orbitals method in the atomic sphere approximation. All the atomic core energies were self-consistently computed and used to directly compare the energies of the quantum wires and that of the crystalline Si, by aligning the 2p core level of a Si atom located at the center of the wire to that corresponding to crystalline Si. The optical properties of the wires have been computed by evaluating the imaginary part of the dielectric function. The main results are (i) the opening of the gap is asymmetric; 1/3 of the widening is in the valence band, while 2/3 in the conduction band; (ii) the near band-gap states originate mainly from Si atoms located at the center of the wire; (iii) the imaginary part of the dielectric function shows a low-energy structure, strongly anisotropic, that follows the blueshift for the gap and is identified as responsible of the luminescence transition; (iv) the spatial localization of the valence- and conduction-band states participating in the luminescence transition shows that all the Si atoms of the wire are collectively involved.