Proton-Induced Fixed Positive Charge at the $\mathrm{Si}(100)\mathrm{\text{−}}{\mathrm{SiO}}_2$ Interface

Positively charged defects induced by protons at the $\mathrm{Si}(100)\mathrm{\text{−}}{\mathrm{SiO}}_2$ interface are studied through density-functional calculations and realistic interface models. Protons generally preserve the bonding network, but cause the spontaneous breaking of strained bonds leading to threefold-coordinated $\mathrm{Si}(3{)}^{+}$ and $\mathrm{O}(3{)}^{+}$. Defect energies fall within a band of $\sim 0.5\mathrm{eV}$, which is stabilized by $\sim 0.3\mathrm{eV}$ at the interface. Only the $\mathrm{O}(3{)}^{+}$ at $\sim 1\mathrm{eV}$ lower energies stand out as deep defects. This description is consistent with several experimental observations and supports the $\mathrm{O}(3{)}^{+}$ as the origin of the fixed positive charge generated during silicon oxidation, in accord with a previous suggestion inferred from electrical data.

Figure 1

Atomic representation of typical ${\mathrm{H}}^{+}$-related defects at the $\mathrm{Si}\mathrm{\text{−}}{\mathrm{SiO}}_2$ interface: $\mathrm{Si}\mathrm{\text{−}}{\mathrm{H}}^{+}\mathrm{\text{−}}\mathrm{Si}$ (left column) and $\mathrm{Si}\mathrm{\text{−}}{\mathrm{OH}}^{+}\mathrm{\text{−}}\mathrm{Si}$ (right column) and their evolution to atomic structures involving threefold-coordinated Si [$\mathrm{Si}(3{)}^{+}$, second row] and O [$\mathrm{O}(3{)}^{+}$, third row] atoms.

Figure 2

Formation energy of ${\mathrm{H}}^{+}$-induced defects vs position with respect to the $\mathrm{Si}(100)\mathrm{\text{−}}{\mathrm{SiO}}_2$ interface. The shaded area encloses typical energies of defects which do not involve bond breaking (closed symbols): $\mathrm{Si}\mathrm{\text{−}}{\mathrm{H}}^{+}\mathrm{\text{−}}\mathrm{Si}$ (squares) and $\mathrm{Si}\mathrm{\text{−}}{\mathrm{OH}}^{+}\mathrm{\text{−}}\mathrm{Si}$ (circles). Open symbols refer to defects involving bond breaking, giving $\mathrm{Si}(3{)}^{+}$ [with either Si-H (squares) or Si-O-H (circles) bonds] and $\mathrm{O}(3{)}^{+}$ defects (diamonds). The lower case letters in the legend refer to panels in Fig. 1.

Figure 3

Defect formation energy vs (a) Si-Si bond length prior to ${\mathrm{H}}^{+}$ insertion at the bond center and (b) Si-O bond length prior to ${\mathrm{H}}^{+}$ attachment to the bridging O atom. The lines correspond to linear regressions of the formation energies of non-bond-breaking defects (closed symbols). The notation is the same as in Fig. 2.

Figure 4

(a) Defect formation energy vs Fermi level in the Si band gap for the lowest-energy proton-induced defects of each kind found in Fig. 2. (b) Charge density distribution of an extra electron at the interface in the presence of an $\mathrm{O}(3{)}^{+}$. The positions of the center of charge of the extra electron and of the $\mathrm{O}(3{)}^{+}$ are indicated by arrows.