The mechanism of the visible luminescence in Si nanostructures is a matter of great interest. Lockwood et al. presented strong experimental evidence for the light emission due to quantum confinement in amorphous Si/SiO 2 superlattices in which silicon layers form two-dimensional quantum wells . Both the interface and the quantum confinement play a role in c-Si/SiO 2 superlattices according to Kanemitsu et al. . A recent theoretical study presents results according to which crystalline Si/SiO 2 superlattices show quantum confinement and a direct band gap . However, this investigation was performed by using fitted parameters within tight-binding methods. We have undertaken a systematic first-principles study concerning the electronic band structure of Si/SiO 2 superlattices.
We used a full-potential LMTO method [4]. The exchange±correlation potential had the (LDA-) form of Perdew and Zunger [5]. The structural model consists of successive layers of crystalline Si and b-crystobalite along the [001] direction: {Si} m {SiO 2 } n ((m, n)-lattice) (see Fig. 1a in Ref. [3]).
The same structural parameters as in Ref.
[3] were used (especially a Si = 5.43 # e). Because of the computational load the maximum value for m and n was 2. The basis set consisted of s, p and d partial waves with kinetic energies ± ±j 2 = ± ±0.01 and ± ±1.0 Ryd. Si 3s and 3p and O 2s and 2p states were treated as valence states. The charge density and potential were expanded in spherical harmonics up to angular momentum l max = 5. Calculations were performed by using 50 k-points in the Brillouin zone. Because of the low symmetry of the supercells the atoms were divided into very many inequivalent classes. This is an advantage especially when one considers layer structures.
Figure shows the band structure of the (1,1)-lattice. The most remarkable feature is the almost dispersionless nature of the lowest conduction bands in directions parallel to the z-axis of the reciprocal space. However, the conduction band minimum is in G±C and R±Z directions. In this respect our results differ from those of Ref. [3]. The band gap has a value of 0.87 eV which is considerably bigger than that of bulk Si, 0.54 eV (one should note that LDA underestimates band gaps). Change in the thickness of the SiO 2 -layer ((1,2)-lattice) has only small effects on the overall Rapid Research Notes R17 Fig. 1. The band structure of (1, 1)-superlattice along different symmetry directions of the tetragonal Brillouin zone