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.
Under the proviso that the existing tight-binding (TB) and effective mass (EM) theoretical models provide a good description of the Ge dot energy gap versus dot diameter, this work investigates the effect of nanoparticle size and the size distribution on the near infrared PL spectrum obtained from self-assembled Ge dots grown on a thin layer of TiO2 or SiO2 on Si. For the as-grown samples, the dot PL emission occupies a wide near-infrared band between 0.8 and 1 eV. The PL efficiency versus dot size for four samples was obtained in three steps. Firstly, the PL spectrum was converted to an intensity plot versus dot diameter rather than energy by taking the PL emission from each dot to occur at the dot bandgap calculated using the TB or EM model. Secondly, a numerical form for the physical size distribution of that sample was obtained by performing a least-squares fit of a Gaussian to the dot size distribution measured by atomic force microscopy or transmission electron microscopy. Finally, the PL efficiency versus dot size was calculated using the fitted Gaussian dot size distribution to normalize the PL intensity distribution obtained in the first step. Although the absolute intensities of the PL from the samples vary, the calculated curves are all well-fitted by straight lines on a log-log plot with essentially the same slope for all samples, which indicates that under weak confinement there is a universal power-law increase in PL efficiency with decreasing dot size.