First-principles study of $n$- and $p$-doped silicon nanoclusters

We report on an ab initio study of the structural and electronic properties of B- and P-doped Si nanoclusters. The neutral impurities formation energies are calculated. We show that they are higher in smaller nanoclusters and that this is not related to the structural relaxation around the impurity. Their dependence on the impurity position within the nanocluster is also discussed. Finally, we have calculated the B and P activation energies showing the existence of a nearly linear scaling with the nanocluster inverse radius. Interestingly, no significant variation of the activation energy on the impurity species is found and the cluster relaxation gives a minor contribution to it.

Figure 1

The $\mathrm{B}\text{−}\mathrm{Si}$ bond length as a function of the cluster inverse radius. The lines are guides for the eyes. The two sets of data correspond to the longer (circles) and the three shorter (squares) bonds. The impurity is at the cluster center.

Figure 2

Formation energy of the neutral impurities at the cluster center, as calculated from Eq. (1), as a function of the inverse nanocluster radius. Both (a) B- and (b) P-doped nanoclusters are considered. The three sets of data correspond to total energies in Eq. (1) calculated for three different geometries: (i) both doped and undoped nanoclusters have not been relaxed, filled squares; (ii) only the undoped cluster has been relaxed, empty circles; (iii) both clusters have been relaxed, empty triangles. The zero inverse radius corresponds to bulk Si. The lines are linear fits of the corresponding set of data (see the text).

Figure 3

(Color online) Formation energies for neutral impurities as a function of the impurity position within the cluster (b). The impurity is moved along two different paths toward the surface, as shown in (a). The lines are guides for the eyes.

Figure 4

Impurity activation energy, as a function of the inverse nanocluster radius. Both B- (filled squares) and P-doped (open circles) Si-nc are considered. The zero inverse radius corresponds to bulk Si. The solid line is a linear fit of the data for the B-doped clusters. The impurity is at the cluster center.