First-Principles Prediction of Icosahedral Quantum Dots for Tetravalent Semiconductors

Despite the scientific importance of semiconductor quantum dots (QDs), little is known about their structure other than the bulk form. Here, we show that one can join segments of tetravalent semiconductors into a seamless icosahedron. Calculations for Si show that pristine icosahedral QDs are more stable than bulklike ones for diameter $d<5\mathrm{n}\mathrm{m}$. Hydrogenated icosahedral quantum dots (IQDs) could also be stable and more atomiclike with larger level spacing and fivefold orbital degeneracy due to the $I_h$ symmetry not possible in the bulk. Experimental feasibility toward synthesizing the IQDs in Si and diamond is also discussed.

Figure 1

(a) The IQD bonding network, (b) surface morphology, and (c) tetrahedron building block truncated from the bulk for $N=600$. (Red) apex atoms of the tetrahedrons form a dodecahedron, and (yellow) edge atoms form radial channels of pentagonal rings.

Figure 2

Quantum dot energy as a function of diameter: (a) small sizes from 1 to 3.5 nm, (b) medium sizes from 4 to 6.5 nm, and (c) large sizes from 21.5 to 23.5 nm. Blue circles are IQD, green hexagons are BQD-14, and red squares are BQD-26. Large solid points are direct calculations, whereas small open points are modeling results. Insets show the various QDs before structural relaxations.

Figure 3

Energy versus H chemical potential and ${\mathrm{H}}_2$ partial pressure at $T=300\mathrm{K}$ for BQD558 and IQD600.

Figure 4

(Top) Energy levels for hydrogenated QDs with respect to the valence band maximum (VBM) and conduction band minimum (CBM). (Bottom) Density of states (DOS) for BQD558 and IQD600, showing sharper peaks throughout the energy spectrum for the latter. The lighter gray (red) lines indicate bulk DOS.

Figure 5

Solid, dotted, and dashed curves are site-decomposed density of states for IQD600 normalized, respectively, to the number of atoms in the red, yellow, and blue regions in Fig. 1. Insets show the charge contours of the states indicated by the arrows.

Figure 6

Silicon IQD optical properties. (Bottom) Dielectric function, ${\epsilon }_2$. (Top) Band-edge states and transition matrix elements (squared) that give rise to the ${\epsilon }_2$ peaks in the plot. Symbols, $h$, $g$, $t$, and $a$ denote five-, four-, three-, and onefold orbital degeneracy, respectively, which is also indicated by the length of the (horizontal lines) energy level. Symbols $u\left(ngerade\right)$ and $g\left(erade\right)$ denote parity.