Confinement, surface, and chemisorption effects on the optical properties of Si quantum wires

We have used the empirical pseudopotential method to study the electronic and optical properties of [001] Si quantum wires with (110)--(1\ifmmode\bar\else\textasciimacron\fi{}10) square cross sections ranging from 4\ifmmode\times\else\texttimes\fi{}4 to 14\ifmmode\times\else\texttimes\fi{}14 monolayers (7.7\ifmmode\times\else\texttimes\fi{}7.7 to 26.9\ifmmode\times\else\texttimes\fi{}26.9 \AA{}, respectively). We present energy levels, band gaps, oscillator-strength, and charge-density distributions. To understand the electronic structure of these systems we calculate their properties in a stepwise process, considering (1) wires with a free surface but without hydrogen and (2) wires with hydrogen chemisorption on the surface. We find that (i) in both cases, the band gap between bulklike states increases as the wire size is reduced (due to quantum confinement). However, (ii) hydrogen chemisorption acts to reduce the gap. (iii) Whereas the low-energy states near the valence-band minimum are effective-mass-like, the near-band-gap states with or without H on the surface can be decisively non-effective-mass-like. The lowest conduction states are pseudodirect, not direct. (iv) The calculated energy dependence of the transition lifetimes is too strong to explain the observed low-energy ``slow'' emission band in porous Si purely in terms of transitions in an ideal wire. However, an alternative model, which introduces a mixture of wires and boxes, can account for the experimental slope.