Electronic properties of silicon with ultrasmall germanium clusters

The electronic states of silicon with a periodic array of spherical germanium clusters are studied within the pseudopotential approach. The effects of quantum confinement in the energies and wave functions of the localized cluster states are analyzed. It is demonstrated that clusters up to 2.4 nm in size produce one localized s state whose energy monotonically shifts deep into the silicon band gap as the cluster size increases. The wave function of the cluster level corresponds to the single-valley approximation of the effective-mass method. In the approximation of an abruptly discontinuous potential at the heterointerface, the quantities calculated using the effective-mass method for clusters containing more than 200 Ge atoms are close to those obtained by the pseudopotential method. For smaller clusters, it is necessary to take into account the smooth potential at the interface.