Impact of oxidation-induced strain on microscopic processes related to oxidation reaction at the $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Si}\left(100\right)$ interface

The reaction of oxygen molecules at the $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Si}\left(100\right)$ interface in the presence of oxidation-induced strain is investigated using total-energy electronic-structure calculations within the density-functional theory. It is found that the calculated effective barrier height for the ${\mathrm{O}}_2$ reaction at the interface with strained oxide layers less than 2 monolayer (ML) thick is almost identical to that at the strain-released interface. On the other hand, it increases significantly when the strained oxide layer reaches 2 ML. This is because the energy of the ${\mathrm{O}}_2$ near the strained oxide layer in the 2 ML oxidized interface is higher than that in the strain-released region. Given our result that the oxidation-induced strain should become large enough to prevent the oxidation reaction and the knowledge that oxide formation with smooth interface is continuous, we conclude that there must be some strain-release mechanism that is present during silicon thermal oxidation.

Figure 1

(Color online) Geometries of an ${\mathrm{O}}_2$ molecule located at the 1 ML oxidized interfaces. White (empty) and red (filled) circles denote Si and host O atoms, respectively, while O atoms of ${\mathrm{O}}_2$ molecule are represented by green (shaded) circles. The ${\mathrm{O}}_2$ molecules and inserted O atoms are indicated by arrowheads. The barrier height for ${\mathrm{O}}_2$ migration $E_d$ (${\mathrm{O}}_2$ insertion into the Si substrate $E_r$) is obtained from the energy difference between ${\mathrm{A}}_1$ and ${\mathrm{B}}_1$ (${\mathrm{C}}_1$ and ${\mathrm{D}}_1$).

Figure 2

(Color online) Energy profile as a function of distance measured from the position of ${\mathrm{O}}_2$ located in the strain-released oxide layer in the 1 ML (squares), 1.5 ML (triangles), and 2 ML (circles) oxidized interfaces. The calculated results for the strain-released (solid diamonds) and 0.75 ML oxidized (open diamonds) interfaces (Refs. 4, 5) are also shown. The incorporation energy $E_i$ corresponds to the energy difference between the ${\mathrm{O}}_2$ in the oxide layer at the interface and the gas-phase ${\mathrm{O}}_2$.

Figure 3

(Color online) Geometries of an ${\mathrm{O}}_2$ molecule located in the 1.5 ML oxidized interfaces. The barrier height for ${\mathrm{O}}_2$ migration $E_d$ (${\mathrm{O}}_2$ insertion into the Si substrate $E_r$) is obtained from the energy difference between ${\mathrm{A}}_2$ and ${\mathrm{B}}_2$ (${\mathrm{C}}_2$ and ${\mathrm{D}}_2$). Same notations as in Fig. 1.

Figure 4

(Color online) Geometries of an ${\mathrm{O}}_2$ molecule located in the 2 ML oxide layer. The barrier height for ${\mathrm{O}}_2$ migration, $E_d$ (${\mathrm{O}}_2$ insertion into the Si substrate, $E_r$), is obtained from the energy difference between ${\mathrm{A}}_3$ and ${\mathrm{B}}_3$ (${\mathrm{C}}_3$ and ${\mathrm{D}}_3$). Same notations as in Fig. 1.

Figure 5

(Color online) Calculated barrier height for ${\mathrm{O}}_2$ diffusion near the interface [$E_d$ (circles)] and ${\mathrm{O}}_2$ insertion into the Si substrate [$E_r$ (diamonds)], energy difference between stable and metastable structures of ${\mathrm{O}}_2$ in the oxide layer of the interface [$\Delta E$ (triangles)], and effective barrier height for the reaction process taking account of the ${\mathrm{O}}_2$ transfer from a big void in bulk $\mathrm{Si}{\mathrm{O}}_2$ [$E_a$ (squares)] as a function of the oxide density. Open symbols represent the values obtained in previous studies (Refs. 4, 5, 7). The vertical dotted lines indicate the oxidized layers. Note that the result of Bongiorno and Pasquarello (Ref. 6) is not shown due to the uncertainty of the incorporation energy $E_i$ and oxide density (the density range is $2.3–2.4\mathrm{g}∕{\mathrm{cm}}^3$ in Ref. 39).