Quantum confinement in Si and Ge nanostructures: effect of crystallinity

Abstract

We look at the relationship between the preparation method of Si and Ge nanostructures (NSs) and the structural, electronic, and optical properties in terms of quantum confinement (QC). QC in NSs causes a blue shift of the gap energy with decreasing NS dimension. Directly measuring the effect of QC is complicated by additional parameters, such as stress, interface and defect states. In addition, differences in NS preparation lead to differences in the relevant parameter set. A relatively simple model of QC, using a ‘particle-in-a-box’-type perturbation to the effective mass theory, was applied to Si and Ge quantum wells, wires and dots across a variety of preparation methods. The choice of the model was made in order to distinguish contributions that are solely due to the effects of QC, where the only varied experimental parameter was the crystallinity. It was found that the hole becomes de-localized in the case of amorphous materials, which leads to stronger confinement effects. The origin of this result was partly attributed to differences in the effective mass between the amorphous and crystalline NS as well as between the electron and hole. Corrections to our QC model take into account a position dependent effective mass. This term includes an inverse length scale dependent on the displacement from the origin. Thus, when the deBroglie wavelength or the Bohr radius of the carriers is on the order of the dimension of the NS the carriers ‘feel’ the confinement potential altering their effective mass. Furthermore, it was found that certain interface states (Si-O-Si) act to pin the hole state, thus reducing the oscillator strength.