A Chemical Bond Theory of Quantum Size Effects of Semiconductor Clusters

Size dependence effects in semiconductor clusters have been a subject of extensive studies for the last two decades. However, it is still difficult to employ the existing theoretical models to give reliable results of energies for clusters in the whole nanometer region. Here we offer a new theoretical method for the quantum size effects based on the idea that the energy gap shift of the cluster arises from the sum of the surface effect shift and quantum effect shift parts. We express the effects through algebraic relations rather than through variational solutions of the wave equation, without the use of any special adjustable parameter. Results reveal for the first time that the shape of the energy gap shift curve is dominated by the surface energy shift. Our method can also predict quantitatively the size dependence of dielectric constant. The new theoretical findings in the ultrasmall (<1 nm) anatase TiO2 and the silicon clusters cannot be explained using previous theories.