The studies about the electronic structures of Si3N4 and Si crystalline quantum dots by the tight-binding approximation and the recursion method are presented, in which spherical clusters with high symmetry and optimized surface are used as models of the quantum dots. The variations of the positions of the top of valence band and the bottom of conduction band following the size change of guantum dot are given. The local and average densities of state (DOS) of the central atom in 328-atom Si3N4 quantum dot and 323-atom Si quantum dot have been calculated, and the relations between DOS and spectral structures have been discussed. From the discussions, it is concluded that local DOS of central atom can give good descriptions of optical spectra of quantum dots. which has been proved by experimental results.