First stages of silicon oxidation with the activation relaxation technique

Using the art nouveau method, we study the initial stages of silicon oxide formation. After validating the method's parameters with the characterization of point defects diffusion mechanisms in pure Stillinger-Weber silicon, which allows us to recover some known results and to detail vacancy and self-interstitial diffusion paths, the method is applied onto a system composed of an oxygen layer deposited on a silicon substrate. We observe the oxygen atoms as they move rapidly into the substrate. From these art nouveau simulations, we extract the energy barriers of elementary mechanisms involving oxygen atoms and leading to the formation of an amorphouslike silicon oxide. We show that the kinetics of formation can be understood in terms of the energy barriers between various coordination environments.

Figure 1

Top: Energy differences between the final and initial states for the (left) vacancy and (right) interstitial in crystalline silicon for accepted events. Bottom: Energy barriers (saddle minus initial state) for the same system.

Figure 2

Schematic of the energy barriers along the interstitial diffusion path. From EDI to EDI site (the most stable state), the DI site is a transitional configuration along the most probable energy barriers represented in the full line (ABCDE pathway). The CD'E pathway (dashed line) corresponds to less favorable events occurring from the DI to EDI site.

Figure 3

Profiles and top views of the system. (a) At the onset of the simulation, with the oxygen deposited on the surface. (b) At the end of one of the art nouveau simulations.

Figure 4

Evolution of (a) the total energy and (b) the number of SiO bonds as a function of event number averaged over the six independent trajectories. Inset: Total energy as a function of the number of SiO bonds.

Figure 5

Evolution of the interspecies coordination numbers around (a) O and (b) Si atoms averaged over six independent simulations as a function of art nouveau events.

Figure 6

(a) Locations of the Si and O centers of mass along the $z$ axis during the art simulations and (b) positions of Si and O atoms along the $z$ axis (broadened by a Gaussian with a standard deviation of 0.5 Å) before and after the art run averaged over six independent simulations.

Figure 7

(a) Distribution of energy differences between the initial and the final minima obtained during the art procedure for six independent runs. (b) Projected distributions of the barrier energies as a function of the asymmetry energy ($E_f-E_i$). The color coding indicates the probability as a function of barrier height.

Figure 8

Distribution of energy barriers during the reaction of oxygen atoms with the silicon substrate as a function of the bonding environment. (a) All barriers (in black) as well as the individual ones shown separated in (b) to (g).