Quantum Confinement of Si Nanosphere with Radius Smaller than 1.2nm

We calculate the density of states, the squared optical matrix element along the x direction, and the band gap of Si nanosphere with radius r smaller than 1.2nm using the method of linear combination of atomic orbitals. It is shown that the quantum confinement effect of Si nanocrystals exists obviously, fulfilling E =1.92 + 0.23/r^1.8, but the band gap exhibits fluctuation with nanocrystal size, which is caused by the dangling bonds of atoms in outer layers. The obtained result indicates that the surface chemical bonds have larger influence on the energy band structure of Si nanosphere when its radius is smaller than 1.2nm.