Ab initio study of the diffusion and decomposition pathways of ${\text{SiH}}_x$ species on Si(100)

Diffusion and decomposition of ${\text{SiH}}_x$ species adsorbed on the clean Si(100) surface are processes of relevance for the growth of crystalline silicon by plasma-enhanced chemical vapor deposition. In this work, we report an extensive search of diffusion and decomposition pathways for ${\text{SiH}}_3$, ${\text{SiH}}_2$, and SiH by means of combined ab initio metadynamics simulations and optimization of minimum-energy reactions paths. We find that on the clean surface ${\text{SiH}}_3$ undergoes stepwise decompositions into Si and H adatoms according to ${\text{SiH}}_3\to {\text{SiH}}_2+\text{H}\to \text{SiH}+2\text{H}\to \text{Si}+3\text{H}$ with an overall reaction barrier of the order of 0.8 eV, consistent with the scenario inferred from secondary ion mass spectroscopy data. The lifetime of ${\text{SiH}}_3$ at room temperature calculated within transition state theory in the harmonic approximation is in agreement with experiments. The lifetime of ${\text{SiH}}_2$ turns out to be similar to that of ${\text{SiH}}_3$. Possible trap states for ${\text{SiH}}_2$ are proposed, based on energetics and by comparing calculated scanning tunneling microscope images with experimental data.

Figure 1

(Color online) Simulation supercell adopted in this work containing eight dimers, viewed along the [100] $\left(z\right)$ direction. The unit cell of the $c\left(2\times 4\right)$ reconstruction is marked with a dashed line. Throughout this paper, the up atoms of the buckled dimers are highlighted with a thicker border to serve as a reference, regardless of the actual buckling state in a given geometry.

Figure 2

(Color online) Trajectory of the $\left(x,y\right)$ coordinates of the silicon atom of the silyl during the metadynamics simulation, superimposed to our simulation box. A series of snapshots taken along the trajectory are reported below. Only the relevant part of the box, highlighted with a thick line, is drawn. Along the path one witnesses the intradimer diffusion, the decomposition into ${\text{SiH}}_2$ and eventually into SiH; a movie of the complete trajectory is available as additional material (Ref. 41).

Figure 3

(Color online) Synoptic scheme of the diffusion and decomposition pathways of ${\text{SiH}}_3$ on the clean Si(100) surface. The different configurations are labeled as ${\mathbf{3}}_{\alpha }^m$ where the number indicates that there are three H atoms of which $m$ are bound to the silicon adatom; $\alpha$ labels different configurations with the same $m$. Configurations ${\mathbf{3}}_{\alpha }^m$ and ${\mathbf{3}}_{{\alpha }^{\prime }}^m$ differ only because of the buckling state of the dimers. Energies (eV) with respect to a reference state $\left({\mathbf{3}}_a^3\right)$ are given for the local minima in rounded boxes. Energies of the transition states (with the same zero energy reference) are given above the arrows connecting two local minima. Energies corrected by ZPE and frequency prefactor (terahertz) in reaction rates (see text) are given in squared boxes for selected local minima and reactions. The reference of energy is again the state $\left({\mathbf{3}}_a^3\right)$ also with ZPE correction. Reaction energies are obtained as energy difference between the local minima, while activation energies for reactions are obtained as energy differences of transition and initial state.

Figure 4

(Color online) Synoptic scheme of decomposition pathways of ${\text{SiH}}_3$ in the presence of an additional adsorbed H atom. The different configurations are labeled as ${\mathbf{4}}_{\alpha }^m$ where the number indicates that there are four H atoms of which $m$ are bound to the silicon adatom; $\alpha$ labels different configurations with the same $m$. Energies (eV) of local minima and transition states are given. For all other notations see caption of Fig. 3. All the configurations are in a closed-shell state, but for ${\mathbf{4}}_c^2$ which is a diradical.

Figure 5

(Color online) Synoptic scheme of the diffusion and decomposition pathways of ${\text{SiH}}_2$ on the clean Si(100) surface. The different configurations are labeled as ${\mathbf{2}}_{\alpha }^m$ where the number indicates that there are two H atoms of which $m$ are bound to the silicon adatom; $\alpha$ labels different configurations with the same $m$. Energies (eV) of local minima and transition states are given. For all other notations see caption of Fig. 3. All the configurations are in a closed-shell state, but for ${\mathbf{2}}_b^1$ which is a diradical.

Figure 6

(Color online) Energy profile along the minimum-energy path for ${\beta }_2$ reaction of two ${\text{SiH}}_2$ groups, followed by the formation of a NRMH dimer. The structures of local minima and transition states are also sketched.

Figure 7

(Color online) Trajectory of the $\left(x,y\right)$ coordinates of the SiH silicon atom during the metadynamics simulation. A series of snapshots taken along the trajectory are reported below; only the relevant part of the simulation box is drawn. A movie of the complete trajectory is available as additional material (Ref. 41).

Figure 8

(Color online) Synoptic scheme of the diffusion and decomposition pathways of SiH on the clean Si(100) surface. The different configurations are labeled as ${\mathbf{1}}_{\alpha }^m$ where the number indicates that there is one H atom bound $\left(m=1\right)$ or unbound $\left(m=0\right)$ to the silicon adatom; $\alpha$ labels different configurations with the same $m$. Energies (eV) of local minima and transition states are given. For all other notations see caption of Fig. 3.

Figure 9

(Color online) Hydrogenated dimers obtained by barrierless reaction of two SiH fragments: (a) an “on-channel” dimer, obtained from ${\mathbf{1}}_c^1$ configuration, and b) an “on-row” dimer, obtained from ${\mathbf{1}}_a^1$ configuration.

Figure 10

(Color online) Simulated STM images of different metastable minima for ${\text{SiH}}_x$ radicals on Si(100) surface. Plots represent height profiles of the surface at a constant local density of states $\left(0.8\times {10}^{-5}\text{a}\text{.u}\text{.}\right)$, for $-1.5\text{V}$ (filled states) and 1.5 V (empty states) tip-sample biases. In the Tersoff-Hamann approximation, the plot corresponds to a constant-current image. All the structures but ${\mathbf{3}}_a^3$ exist in two symmetry-equivalent buckling states. The first two profiles correspond to frozen dimers, while in the last two we plot the average of the two equivalent configurations, which takes into account to a certain extent the dynamic average of the STM images to be expected in a room-temperature measurement. The profile for the clean surface is plotted as a reference, and the average height for the clean surface for each bias is taken as the zero height for the other images.