Optical Emission Properties of Silicon Quantum Dots

The combination of novel physical properties and technological applications has led to an enormous growth in the study of the optoelectronic properties of semiconductor nanoclusters over the last decade. In the nanometer size range, quantum confinement effects significantly alter the optoelectronic properties from those of the bulk material. As the size of a cluster is decreased, the optical gap increases and the dipole oscillator strength increases. Many of the size dependent optical properties of various semiconductor nanoclusters have been measured and characterized using a variety of methods. In addition, theoretical calculations have supplemented the experimental measurements by calculating ideal absorption gaps and spectra.

Despite the diversity of calculations of the absorption gap, often referred to as the optical gap or band gap, it is actually the emission energy that is most often measured and usually more relevant for technological applications. In general, the absorption gap is larger than the emission gap, i.e. light absorbed by clusters is red-shifted to longer wavelengths on emission (see figures to right and below). This red shift is reffered to as the Stokes shift and its origin, magnitude and size dependence is a notable source of controversy, especially for silicon nanoclusters. The figure on the right shows a silicon quantum dot which absorbs blue light and then re-emits red light due to a Stokes shift.

We have calculated both the absorption and emission energies of a range of prototype silicon nanoclusters using density
functional theory (DFT) to determine atomic geometries and single-particle gaps, and quantum Monte Carlo (QMC) to calculate optical gaps. To determine the size dependence of the Stokes shift in each class of nanoclusters, we studied clusters with diameters up to 1.8 nm. We studied crystalline silicon nanostructures with purely hydrogen terminated surfaces, nanoclusters with reconstructed surfaces, and nanoclusters with surfaces partially passivated with
oxygen in two different geometries. We demonstrate that while two structures may exhibit a very similar absorption gap, they may exhibit significantly different Stokes shifts and hence, different emission energies. Combined, these
results help explain several existing differences among measured values of the absorption, emission and Stokes shift energies.

The HOMO and LUMO orbitals of four of the clusters we studied are shown in the left hand figure. All of the clusters are ~1 nm in size. Figure (a) shows that in a nanocluster with pure hydrogen passivation and no reconstruction of the surface the HOMO and LUMO are delocalized throughout the core of the nanocluster. Figure (b) shows that the HOMO and LUMO are localized around the surface of the cluster when the surface of the clusters is reconstructed. Figure (c) shows a single oxygen atom placed in a Si-O-Si bridged position on the surface of an otherwise unreconstructed cluster. The HOMO and LUMO charge densities are partially drawn towards the surface with most charge still existing in the core of the cluster. Finally, figure(d) shows that the placement of a single oxygen atom in a Si=O double bonded position on the surface of an otherwise unreconstructed cluster almost completely localizes both the HOMO and LUMO on the Si=O double bond at the surface of the cluster.

The structural changes resulting from the creation of an exciton in each cluster are shown in the right hand column of the figure by arrows proportional to the vector displacement of the atoms. The RMS displacement of atoms in the completely hydrogenated structures, e.g. Si35H36, is ~0.3 A for 1~nm structures and decreases quickly to <0.1 A as the cluster size increases to around 2~nm. In these clusters, Figure (a) shows that the change in charge density resulting from the HOMO to LUMO exitation is distributed relatively evenly throughout the cluster and hence all atoms in the cluster experience forces of approximately equal magnitude. This is confirmed by the similar magnitude of the vector displacements plotted in the right column of figure(a). These displacements show that the excited state structural relaxation of hydrogenated clusters corresponds to a change in shape from a spherical to elliptical
geometry where the top and bottom atoms move towards the center and the left and right atoms move outwards. This shape change is consistent with the change in symmetry predicted by exciting from the triply degenerate p-like HOMO to a non-degenerate s-like LUMO. As the size of these clusters increases, the relative change in charge density around each atom due to the excitation of a single electron decreases inversely proportionally to the number of atoms in the
cluster and hence the RMS displacements also decrease.

The clusters with reconstructed surfaces, e.g. Si29H24 (Fig(b)) and the clusters with Si-O-Si bridged oxygen
on the surface, e.g. Si29H34O (Fig.(c)) show smaller RMS displacements than the completely hydrogenated clusters.
In these reconstructed clusters, the charge density change associated with the HOMO-LUMO excitation is localized on the surface of the cluster and therefore the reconstructed surface atoms experience the greatest force. However, the additional Si-Si or Si-O-Si bonds produced by the reconstruction of the surface restrict the movement of these surface atoms, resulting in the significantly lower observed RMS displacements and in the smaller magnitude of the vector displacements plotted in the right column of Figs.(b) and (c). As for the hydrogenated clusters, as the size of the reconstructed clusters increases, the charge density change due to the excitation of a single electron from the HOMO to LUMO is distributed over a larger area and hence the force on each individual surface atoms again decreases with size as confirmed by the decreasing RMS displacements of the larger reconstructed clusters.

In the clusters with oxygen double bonded to the surface, e.g. Si35H34O (Fig.d), the RMS displacement is slightly larger. However, in this class of clusters, considering the RMS displacement is somewhat misleading as almost all the atomic
relaxation is concentrated on the double bonded oxygen atom. The displacement vectors plotted in Fig.(d) show that the double bonded oxygen atom rotates around the cluster by over 42~degrees when excited into the triplet state. This focus of the Stokes shift relaxation on the double bonded oxygen atom results from the localization of the HOMO and LUMO orbitals on the double bond as shown in Fig.(d).~ In these clusters the Stokes shift is relatively independent of the size of the cluster as the relaxation mechanism is localized on a single bond on the surface.

For more information contact: Andrew Williamson

References:

A. Puzder, A. J. Williamson , J.C. Grossman and G. Galli, Optical Emission of Silicon nanoclusters, J. Amer. Chem. Soc. 125 , 2786 (2003) .