The electronic structure and the band gap of nano-sized Si particles: competition between quantum confinemen and surface reconstruction

The electronic structure and especially the band gap of Sin clusters (n = 3–45 atoms) is studied by photoelectron spectroscopy. Contrary to expectations of quantum conf nement, almost all clusters studied here have a band gap smaller than that of crystalline Si or even display a continuous (metallic) density of states. We attribute this to covalent bond formation analogous to the reconstructions observed on single-crystal surfaces. Additionally, for Si30 and Si33 a gap size of 0.6 eV (0.4 eV) is observed, supporting the prediction of stable, spherically symmetric structures of these particular clusters. PACS: 71.20.Tx; 73.20.Dx; 36.40.-c Quantum conf nement in nanostructures fabricated from Si, such as thin f lms or porous Si, results in a renormalization of the band gap [1]. Energy gap values more than triple the size of crystalline Si have been reported for these systems [2, 3]. Moreover, the changes in the electronic structure caused by quantum conf nement have also resulted in optical activity of these modif ed structures, a phenomenon very much sought after by developers of optoelectronics but prevented in bulk Si by an indirect band gap. Calculations for small Si quantum dots and Si nanostructures containing typically 1000 atoms are also predicting a considerable opening of the band gap up to an energy of 4 eV [4]. In contrast to this result, cluster calculations of small Si clusters containing fewer than 10 atoms show that this trend does not continue in the size range of very small particles [5, 6]. The onset of the calculated absorption spectra of Si clusters containing fewer than 10 atoms is typically at values around 2 eV [6]. For only slightly larger clusters in the size range between 10–20 atoms classical ‘force f eld’ calculations predict that these clusters are either found in ‘metallic’ or ‘covalent’ structures, as characterized by their bond angles [7]. All of these have an energy gap smaller than or of similar size to bulk-crystalline Si. Additionally for some of the Si−n clusters, especially n = 33, 39, and 45, very interesting spherical-shaped structures have been proposed to exist by calculations [8]. These spherical structures are quite similar to the fullerenes formed by carbon atoms, even though they are not hollow structures. Again, these structures should exhibit a special stability and, in addition to that, largely degenerate electronic states due to their high symmetry. On the experimental side the picture is similarly confusing. Early photoemission spectra of small Si−n clusters (n = 3−12) reveal very broad features with an almost continuous density of states, with the exception of Si4 , Si − 6 , and Si10, which all exhibit a gap of approximately 1 eV [9, 10]. High-resolution studies, where the vibrational f nestructure was resolved for Sin clusters for n = 3−7, confirme these results of the band gap [11]. Furthermore, in an experiment probing the optical absorption of clusters, the quite unexpected result was reported that all Sin clusters for n = 18−40 exhibit a very similar, almost featureless absorption spectrum [12]. Recently, mobility measurements have been carried out for Si cluster cations concentrating on the intermediate size range between n = 10 and 26 and compared with calculations [13]. However, even these careful and extensive studies could not give any def nite answers about the Si cluster structures in this size range. This leaves Si7 as the largest cluster with a well-conf rmed structure, a pentagonal bi-pyramid, which also seems to persist upon isolation of these clusters in a matrix [14].