Hydrogen/nitrogen/oxygen defect complexes in silicon from computational searches

Point-defect complexes in crystalline silicon composed of hydrogen, nitrogen, and oxygen atoms are studied within density-functional theory. Ab initio random structure searching is used to find low-energy defect structures. We find new lowest-energy structures for several defects: the triple-oxygen defect, $\left\{3{\text{O}}_{\text{i}}\right\}$, triple oxygen with a nitrogen atom, $\left\{{\text{N}}_{\text{i}},3{\text{O}}_{\text{i}}\right\}$, triple nitrogen with an oxygen atom, $\left\{3{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$, double hydrogen and an oxygen atom, $\left\{2{\text{H}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$, double hydrogen and oxygen atoms, $\left\{2{\text{H}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ and four hydrogen/nitrogen/oxygen complexes, $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$, $\left\{2{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$, $\left\{{\text{H}}_{\text{i}},2{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$, and $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$. We find that some defects form analogous structures when an oxygen atom is replaced by a NH group, for example, $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ and $\left\{3{\text{O}}_{\text{i}}\right\}$, and $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}}\right\}$ and $\left\{{\text{O}}_{\text{i}}\right\}$. We compare defect formation energies obtained using different oxygen chemical potentials and investigate the relative abundances of the defects.

Figure 1

(Color online) The $\left\{3{\text{O}}_{\text{i}}\right\}$ defect is composed of three buckled-bond-centered oxygen atoms each bonded to a single fourfold coordinated silicon atom. Silicon atoms are shown in yellow (light gray) and oxygen atoms in red (dark gray).

Figure 2

(Color online) The first metastable H/N defect, $\left\{2{\text{H}}_{\text{i}},{\text{N}}_{\text{s}}\right\}$, contains a threefold-coordinated nitrogen atom close to a lattice site. One of the hydrogen atoms is bonded directly to the nitrogen atom and points toward a neighboring threefold-coordinated silicon atom. The remaining hydrogen atom terminates a dangling bond on another neighboring silicon atom. The silicon atoms are shown in yellow (light gray), the nitrogen in blue (black), and the hydrogen atoms in white.

Figure 3

(Color online) The $\left\{{\text{N}}_{\text{i}},3{\text{O}}_{\text{i}}\right\}$ defect contains a four-atom ring consisting of a nitrogen atom, an oxygen atom, and two silicon atoms. The two other oxygen atoms are in buckled-bond-centered positions. Note that the structure contains an overcoordinated oxygen atom with three bonds. The silicon atoms are shown in yellow (light gray), the nitrogen in blue (black), and the oxygen atoms in red (dark gray).

Figure 4

(Color online) The lowest-energy $\left\{3{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defect consists of a four-atom ring of two nitrogen atoms and two silicon atoms adjacent to another four-atom ring of an oxygen atom, a nitrogen atom, and two silicon atoms. Note that the structure contains an overcoordinated oxygen atom with three bonds. The silicon atoms are in yellow (light gray), the nitrogen atoms in blue (black), and the oxygen atom in red (dark gray).

Figure 5

(Color online) The $\left\{2{\text{H}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defect is composed of a buckled-bond-centered oxygen atom adjacent to a distorted ${\left\{{\text{H}}_2\right\}}^{\ast }$ defect. The silicon atoms are shown in yellow (light gray), the oxygen atom in red (dark gray), and the hydrogen atoms in white. This defect has a negative formation energy showing that the ${\left\{{\text{H}}_2\right\}}^{\ast }$ defect (Ref. 44) is stabilized by the presence of oxygen.

Figure 6

(Color online) The $\left\{2{\text{H}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ defect is composed of two adjacent $\left\{{\text{H}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defects. The silicon atoms are shown in yellow (light gray), the oxygen atom in red (dark gray), and the hydrogen atoms in white.

Figure 7

(Color online) The $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defect contains a nitrogen and silicon atom sharing a lattice site with the dangling silicon bond terminated by the hydrogen atom. A nearest-neighbor silicon atom of the nitrogen atom is bonded to a buckled-bond-centered oxygen atom. The silicon atoms are shown in yellow (light gray), the oxygen in red (dark gray), the nitrogen in blue (black), and the hydrogen in white.

Figure 8

(Color online) The $\left\{2{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defect is similar to the $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defect but with the nitrogen atom acquiring the extra hydrogen atom making it overcoordinated with four bonds. This defect has the highest formation energy of all the H/N/O defects studied and is therefore unlikely to form. The silicon atoms are shown in yellow (light gray), the oxygen in red (dark gray), the nitrogen in blue (black), and the hydrogen atoms in white.

Figure 9

(Color online) The $\left\{{\text{H}}_{\text{i}},2{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ defect contains a four-atom ring of two nitrogen atoms and two silicon atoms. One of the nitrogen atoms is overcoordinated and is bonded to the hydrogen atom. A nearest-neighbor silicon atom to this nitrogen atom is also bonded to a buckled-bond-centered oxygen atom. The silicon atoms are shown in yellow (light gray), the oxygen in red (dark gray), the nitrogen in blue (black), and the hydrogen in white.

Figure 10

(Color online) The $\left\{{\text{H}}_{\text{i}},{\text{N}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ defect is very similar to the $\left\{3{\text{O}}_{\text{i}}\right\}$ defect but with one of the oxygen atoms replaced by a NH group. The silicon atoms are shown in yellow (light gray), the oxygen in red (dark gray), the nitrogen in blue (black), and the hydrogen in white.

Figure 11

(Color online) Relative concentrations of H/N/O defects in silicon as a function of the nitrogen concentration. At low nitrogen concentrations $\left(\text{H}:\text{N}:\text{O}=1:<0.5:1\right)$, the predominant defect is $\left\{2{\text{H}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$. As the nitrogen concentration increases the concentration of $\left\{2{\text{H}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ decreases, with $\left\{2{\text{N}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ and molecular hydrogen being formed. As the nitrogen concentration increases above unity, the concentration of $\left\{2{\text{N}}_{\text{i}},2{\text{O}}_{\text{i}}\right\}$ declines and $\left\{2{\text{N}}_{\text{i}},{\text{O}}_{\text{i}}\right\}$ begins to form. At nitrogen concentrations larger than 2, the additional nitrogen atoms form $\left\{2{\text{N}}_{\text{i}}\right\}$ defects.

Figure 12

(Color online) Relative concentrations of H/N/O defects in silicon as a function of the oxygen concentration. The behavior is complex in this case, although the general trend is simply that the more stable defects containing larger numbers of oxygen atoms are favored at higher oxygen concentrations.

Figure 13

(Color online) Relative concentrations of H/N/O defects in silicon as a function of the hydrogen concentration. Increasing the hydrogen concentration simply generates more interstitial hydrogen molecules.