Density functional theory study on the B doping and B/P codoping of Si nanocrystals embedded in $\mathrm{Si}{\mathrm{O}}_2$

Doping silicon nanocrystals (Si NCs) embedded in silicon dioxide ($\mathrm{Si}{\mathrm{O}}_2$) with boron (B) and phosphorus (P) is a promising way of tuning the properties of Si NCs. Here we take advantage of density functional theory to investigate the dependence of the structural and electronic properties of Si NCs embedded in $\mathrm{Si}{\mathrm{O}}_2$ on the doping of B and P. The locations and energy-level schemes are examined for singularly B-doped or B/P-codoped Si NCs embedded in $\mathrm{Si}{\mathrm{O}}_2$ with a perfect or defective Si/$\mathrm{Si}{\mathrm{O}}_2$ interface at which a Si dangling bond exists. A dangling bond plays an important role in the doping of Si NCs with B or B/P. The doping behavior of B in Si NCs embedded in $\mathrm{Si}{\mathrm{O}}_2$ vastly differs from that of P. The electronic structure of a B/P-codoped Si NC largely depends on the distribution of the dopants in the NC.

Figure 1

Model of an optimized 1.4-nm Si NC embedded in $\mathrm{Si}{\mathrm{O}}_2$ with an (a) perfect Si/$\mathrm{Si}{\mathrm{O}}_2$ interface ($\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2, \mathrm{S}{\mathrm{i}}_{123}{\mathrm{H}}_{100}{\mathrm{O}}_{96}$) or (b) defective Si/$\mathrm{Si}{\mathrm{O}}_2$ interface at which a Si dangling bond exists ($\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2, \mathrm{S}{\mathrm{i}}_{123}{\mathrm{H}}_{101}{\mathrm{O}}_{95}$). Si, H, and O atoms are denoted by green, gray, and red balls, respectively. A Si atom initially with a dangling bond at the Si/$\mathrm{Si}{\mathrm{O}}_2$ interface is highlighted by an orange ball. A substitutional or passivating B atom is indicated by a violet ball. B1, B2, B3 (B3′), B4 (B4′), and B5 (B5′) result from moving a substitutional B atom along the path of 1 → 2 → 3 (3′) → 4 (4′) → 5 (5′). When a B atom replaces a Si atom connected to one, two, or three H atoms at the surface, it is denoted as ${\mathrm{B}}_a,{\mathrm{B}}_b$, or ${\mathrm{B}}_c$, respectively. As a B atom passivates a Si dangling bond at the Si/$\mathrm{Si}{\mathrm{O}}_2$ interface, it is denoted as ${\mathrm{B}}_{db}$.

Figure 2

Formation energy of B in (a) $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ or (b) $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$ as a B atom substitutionally moves from the center to the surface. The solid lines are used to guide the eye. The vertical dashed lines indicate the regions of the core, Si/$\mathrm{Si}{\mathrm{O}}_2$ interface, and surface.

Figure 3

Energy-level diagrams for undoped and B-doped (a) $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ or (b) $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$ at the ground state. Filled (empty) circles indicate that energy levels are occupied (unoccupied) by electrons. Spin-up (spin-down) states of defect energy levels induced by a B atom or dangling bond are indicated by up (down) arrows.

Figure 4

(a) Distribution of the isosurface for the electron density of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for undoped or ${\mathrm{B}}_b$-doped $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$. Those of the highest occupied deep energy-level (HODE) and the lowest unoccupied deep energy-level (LUDE) for B3′- or B5-doped $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ are also shown. (b) Distribution of the isosurface for the electron density of the HODE and LUDE for undoped, $\mathrm{B}{3}^{\prime }-,\mathrm{B}5-$, or ${\mathrm{B}}_{db}$-doped $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$.

Figure 5

Model of a (a) $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ codoped with P3 and B3′ or (b) $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$ codoped with ${\mathrm{P}}_{db}$ and B5. Si, H, O, B, and P atoms are denoted by green, gray, red, violet, and blue balls, respectively.

Figure 6

Formation energies of B/P dopants in (a) $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ or (b) $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$.

Figure 7

Energy-level diagrams for undoped and B/P-codoped (a) $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ or (b) $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$ at the ground state. Filled (empty) circles indicate that energy levels are occupied (unoccupied) by electrons. Spin-up (spin-down) states of defect energy levels are indicated by up (down) arrows. The highest occupied deep energy-level (HODE) and lowest unoccupied deep energy-level (LUDE) are indicated by red bars.

Figure 8

(a) Distribution of isosurface for the electron density of the HODE and LUDE for P1-B3′ or P3-B3′ codoped $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$. Those of the HOMO and LUMO for {P3-B3′} codoped $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$ are also shown. (b) Distribution of the isosurface for the electron density of the HODE and LUDE for ${\mathrm{P}}_{db}-\mathrm{B}3$ or ${\mathrm{P}}_{db}-\mathrm{B}5$ codoped $\mathrm{Si}{@}_{db}\mathrm{Si}{\mathrm{O}}_2$.

Figure 9

HODE-LUDE, LUDE-LUMO, and HODE-HOMO gaps for P1-B3′, P3-B3′, or P3′-B1 codoped $\mathrm{Si}@\mathrm{Si}{\mathrm{O}}_2$. The solid line is used to guide the eye.