Band alignment switching and the interaction between neighboring silicon nanocrystals embedded in a SiC matrix

We present results from density functional theory study of the electronic properties of silicon nanocrystals (Si NCs) embedded in a silicon carbide (SiC) matrix, considering different combinations of various NCs and host matrix sizes. We show that the NC and the host matrix form a type-II band alignment, with the states at the top of the valence band being in the Si NC and the states at the bottom of the conduction band in the host matrix. Moreover, this band alignment can be interchanged with introducing oxygen at the interface. This interchange in the band alignment has a rather weak influence on the absorption of the system. We demonstrate that the charge densities of some valence band states can overlap with the charge densities of the neighboring NCs. We also demonstrate that this leakage of states is significant when the distance between the neighboring NCs is less than $\sim 1.6\mathrm{nm}$.

Figure 1

Ball and stick models of (a) 1.5 nm, (b) 2.0 nm, and (c) 2.5 nm Si NCs, embedded in $8\times 8\times 8$ SiC (model A). The Si atoms from the NCs are shown in red, and the Si and C atoms from the matrix are shown in tan and gray, respectively.

Figure 2

DOS of models A, B, C, and D, as a function of the size of the SiC matrix, for 1.5 nm NCs (left panel), and of the NC size for $8\times 8\times 8$ matrix (right panel). The Fermi level is at 0 eV.

Figure 3

PDOS of (a) model A, (b) model B, (c) model C, and (d) model D, and the corresponding projections of the charge densities on the $x-y$ plane. The PDOS of the core, interface, and matrix regions are shown in blue, red, and green, respectively.

Figure 4

PDOS of model D with $7\times 7\times 7$ matrix with (a) 1.5 nm and (b) 2.0 nm Si NCs. The PDOS of the core, interface, and matrix regions are shown in blue, red, and green, respectively.

Figure 5

Absorption indices of Si NCs embedded in (a) $6\times 6\times 6$ SiC matrix and (b) $7\times 7\times 7$ SiC matrix, and different models. The absorption indices of models A, B, C, and D with 1.5 nm NCs are shown in orange, green, blue, and red, respectively. The absorption indices of models C and D with 2.0 nm NCs are shown in violet and yellow, respectively. The absorption indices of hydrogenated 1.5 nm Si NC and pure SiC are shown in black and purple, respectively.

Figure 6

(a) Schematic representation of the WF amplitudes of electrons in a periodic potential well, with two different shapes of the potential barrier. Projections of the charge densities on the $x-y$ plane, for two adjacent cells of models with (b) 1.5 nm NCs in different size matrix and (c) $8\times 8\times 8$ matrix with NCs with different size. The surface-to-surface distances between NCs in neighboring cells are given on the right side of each panel. The energy intervals, for which states the charge densities are calculated, of model A and model C are $-0.5$ to $-0.3$ eV and $-0.7$ to $-0.5$ eV, respectively. (d) Average charge densities in a series of $\left\{100\right\}$ planes along the [100] direction, of models A (left part) and C (right part) with 1.5 nm NCs, corresponding to the same charge densities shown in (b).