Ab initio characterization of transition-metal-doped Si nanocrystals

We investigate the influence of transition-metal doping on silicon nanocrystals by means of first-principles calculations within a supercell approach. We focus on the energetic stability of different doping sites and on electronic and magnetic properties of the most stable configurations. Remarkable differences concerning the magnetic moments and the electronic properties are found between iron and manganese and for inclusion of strong electron correlation. In addition, a self-purification effect, which hampers an incorporation of transition-metal atoms in small nanocrystals, is observed.

Figure 1

(Color online) Schematic stick-and-ball representation of the used Si NCs. The positions of different substitutional and interstitial doping sites are indicated.

Figure 2

(Color online) Schematic illustration of the influence of a Hubbard-type Coulomb repulsion $U$ on the DOS: (a) $U\approx 0$ and (b) $U>0$. Both majority- and minority-spin channel DOS are indicated.

Figure 3

(Color online) Relative formation energy of differently sized NCs with incorporation of one Mn (left panel) or Fe (right panel) atom versus the variation in the Si chemical potential $\Delta {\mu }_{\text{Si}}$ with respect to its bulk value. The corresponding doping sites are indicated.

Figure 4

(Color online) Energy barriers between the three subsurface doping positions in a ${\text{Si}}_{40}{\text{TMH}}_{60}$ NC: black for Mn dopants and red (dark gray) for Fe dopants. The insets show stick-and-ball models of the corresponding NC geometries.

Figure 5

(Color online) Relative formation energy $\Delta {\gamma }_f$ for the most stable substitutional (red) and interstitial (blue) doping sites. Solid lines illustrate the incorporation of Mn atoms and dashed lines Fe atoms.

Figure 6

(Color online) Energy-level diagram of a simple defect-molecule model with $T_d$ symmetry. The shaded regions correspond to Si states of the undoped system.

Figure 7

(Color online) Energy-level diagrams of a ${\text{Si}}_{82}{\text{MnH}}_{108}$ NC with $N=5$ for substitutional doping sites at different radial positions. The gray regions correspond to conduction and valence states of the bare (undoped) Si NCs. The horizontal black lines represent the energy levels of the doped Si NCs. The degeneracy of the $\text{TM}3d$ states ($e_g$—blue and $t_{2g}$—red) is illustrated by open (empty) and filled (occupied) circles. Results in (a) GGA and (b) $\text{GGA}+U$ $\left(U=3\text{eV}\right)$ are presented. The horizontal dotted line defines the Fermi level. Majority-spin (left) and minority-spin (right) channels are shown.

Figure 8

(Color online) As in Fig. 7 but Fe instead of Mn.

Figure 9

(Color online) Energy-level diagrams for the three substitutional subsurface doping sites ${\left(\text{sub}3\right)}_s$, ${\left(\text{sub}3\right)}_m$, and ${\left(\text{sub}3\right)}_i$ for a ${\text{Si}}_{40}{\text{MnH}}_{60}$ NC. The gray regions correspond to conduction and valence states of the bare (undoped) Si NCs. The black lines represent the energy levels of the doped Si NCs. The degeneracy of the $\text{TM}3d$ states ($e_g$—blue and $t_{2g}$—red) is illustrated by open (empty) and filled (occupied) circles. Results in (a) GGA and (b) $\text{GGA}+U$ $\left(U=3\text{eV}\right)$ are presented. The horizontal dotted line defines the Fermi level. Majority-spin (left) and minority-spin (right) channels are shown.

Figure 10

(Color online) As in Fig. 9 but Fe instead of Mn.

Figure 11

(Color online) Energy-level diagrams of TM-doped Si NCs within (a) GGA and (b)$\text{GGA}+U$. The gray regions correspond to conduction and valence states of the bare (undoped) Si NCs. The horizontal black lines represent the energy levels of the doped Si NCs. The degeneracy of the $\text{TM}3d$ states ($e_g$—blue and $t_{2g}$—red) is illustrated by open (empty) and filled (occupied) circles. The Fermi level is indicated as horizontal dotted line. The vacuum level is used as energy zero.