The influence of shape and potential barrier on confinement energy levels in quantum dots

The influence of the shape of silicon quantum dots embedded in an amorphous silica matrix on the quantum confinement energy levels, as well as that of the Si / SiO 2 potential barrier, are studied. The energy levels are computed using both the infinite and finite rectangular quantum well models for spherical quantum dots and the infinite rectangular quantum well for prolate spheroidal quantum dots. The results are compared with each other and also with the experimental activation energies obtained from the temperature dependence of the dark current. These activation energies are identified with the differences between the quantum confinement energies, subject to the selection rules. The finite rectangular quantum well model takes into account the experimental value of the finite potential barrier and the matrix-to-dot electron mass ratio. The energy levels are smaller than those for the infinite rectangular quantum well case; they decrease when the potential barrier decreases and the mass ratio increases. Different aspects of the models are discussed. All the errors are less than about 4%. The spheroidal shape lifts the degeneracy on the magnetic quantum number. The energy levels can decrease or increase with eccentricity as a consequence of the different quantum confinement effects along the major and minor axes. The supplementary information on the magnetic quantum number is beneficial for optical applications.