Diffusion and desorption of $\mathrm{Si}{\mathrm{H}}_3$ on hydrogenated $\mathrm{H}:\mathrm{Si}\left(100\right)\text{−}(2\times 1)$ from first principles

We have studied diffusion pathways of a silyl radical adsorbed on the hydrogenated $\mathrm{Si}\left(100\right)\text{−}(2\times 1)$ surface by density-functional theory. The process is of interest for the growth of crystalline silicon by plasma-enhanced chemical vapor deposition. Preliminary searches for migration mechanisms have been performed using metadynamics simulations. Local minima and transition states have been further refined by using the nudged-elastic-band method. Barriers for diffusion from plausible adsorption sites as low as $0.2\mathrm{eV}$ have been found, but trap states have also been spotted, leading to a more stable configuration, with escape barriers of $0.7\mathrm{eV}$. Diffusion among weakly bound physisorbed states is also possible with very low activation barriers $(<50\mathrm{meV})$. However, desorption mechanisms (either as $\mathrm{Si}{\mathrm{H}}_3$ or as $\mathrm{Si}{\mathrm{H}}_4$) from physisorbed or more strongly bound adsorption configurations turn out to have activation energies similar to diffusion barriers. Kinetic Monte Carlo simulations based on ab initio activation energies show that the silyl radical diffuses at most by a few lattice spacing before desorbing at temperatures in the range $300–1000\mathrm{K}$.

Figure 1

(Color online) The slab model of the $\mathrm{H}:\mathrm{Si}\left(100\right)\text{−}(2\times 1)$ surface, (a) top and (b) side views.

Figure 2

Minimum energy path obtained by NEB optimization for the migration from the minimum (a) to the minimum (b) of Fig. 4. The energy profile with respect to a suitably defined reaction coordinate $q$ is reported. Path A is optimized with the $\Gamma$ point only. Path B corresponds to the total energies obtained with one special $k$ point in the surface BZ for the geometries of path A. Path C has been fully optimized by using one special $k$ point.

Figure 3

(Color online) Four snapshots from the metadynamics trajectory of silyl diffusion on $\mathrm{H}:\mathrm{Si}\left(100\right)\text{−}(2\times 1)$: (a) $t=0\mathrm{ps}$, (b) $t=2.1\mathrm{ps}$, (c) $t=3.5\mathrm{ps}$, and (d) $t=10\mathrm{ps}$.

Figure 4

(Color online) Sketches of ten different local minima for $\mathrm{Si}{\mathrm{H}}_3$ adsorbed on $\mathrm{H}:\mathrm{Si}\left(100\right)\text{−}(2\times 1)$ surface. Side views of (a) and (i) structures are also reported at the bottom to illustrate the difference in geometry between strongly bound and physisorbed minima. Structures (e) and (g) are not perfectly symmetric with respect to the dimer plane, so that two corresponding mirror structures exist; this small asymmetry is due to the balance between the interaction of the $\mathrm{Si}{\mathrm{H}}_3$ hydrogen atoms with the surface hydrides, and the barrier for interconversion between the mirror configurations is likely to be very low. For what concerns diffusion, the two mirror images can be regarded as a single, symmetric structure.

Figure 5

(Color online) Spin polarization $[m\left(\mathbf{r}\right)={\rho }_{\uparrow }\left(\mathbf{r}\right)-{\rho }_{\downarrow }\left(\mathbf{r}\right)]$ for the four configurations, (a), (b), (f), and (j) of Fig. 4, is shown in the four corresponding panels. Isosurfaces at $m=\pm {10}^{-3}\mathrm{a.u.}$ are reported, with colors depending on the spin sign. In the three structures, $\int d^3\mathbf{r}\mid m\left(\mathbf{r}\right)\mid$ is approximately $1.2$, corresponding to the unpaired electron introduced by the silyl, plus some polarization effects. Structure (a) shows the most pronounced spin delocalization, with the unpaired electron shared between the silyl silicon and two surface silicon atoms.

Figure 6

(Color online) A synoptic scheme of the different migration mechanisms we have considered. The energy of local minima and transition states (in eV) are reported with reference to the desorbed $\mathrm{Si}{\mathrm{H}}_3$ (zero of energy). Activation energies for jumps in both directions can be obtained as energy differences. Transition-state energies for desorption from the physisorbed states, either as silyl or as silane, are also reported (large arrows).

Figure 7

(Color online) Diffusion pathways for a $\mathrm{Si}{\mathrm{H}}_3$ radical; (a) parallel to the dimer row and (b) perpendicular to the dimer row. Energies of transition states and intermediate minima (in eV) are given. The zero of energy corresponds to the desorbed $\mathrm{Si}{\mathrm{H}}_3$.

Figure 8

(Color online) Two paths leading to the trap state (f) from the local minimum (b). The zero of energy (eV) corresponds to the desorbed $\mathrm{Si}{\mathrm{H}}_3$.

Figure 9

(Color online) A path for diffusion between two equivalent (a) sites, passing through physisorbed state (i). Energies (eV) of minima and transition states are given. The zero of energy corresponds to the desorbed $\mathrm{Si}{\mathrm{H}}_3$. See Fig. 4 for sketches of the two structures viewed along $\left[0\overline{1}1\right]$.

Figure 10

(Color online) Simplified scheme that accounts for most of the features of the complex reactions scheme of Fig. 6; the activation energies have to be considered just qualitative estimates, because of both the limited accuracy of DFT calculations and the fact that each of the barriers in this figure correspond to different pathways with slightly different activation energies (cf. Fig. 6). For simplicity, we label as “chemisorbed” (here and in Table ) the bound states of $\mathrm{Si}{\mathrm{H}}_3$ with adsorption energy in the range $0.15–0.35\mathrm{eV}$.

Figure 11

Distribution of resident times $t$ of the silyl on the surface (before desorption). The initial configuration is always site (a) (see text). The results are averaged over ${10}^6$ independent KMC runs. The distribution is shown with a logarithmic scale on abscissa $[h\left(x\right),x={\log }_{10}t]$. Panels (a) and (b) correspond to simulations at $T=500\mathrm{K}$ and $T=1000\mathrm{K}$, respectively. Curve A corresponds to the full reaction scheme, with the energies given in Fig. 6. Curve B corresponds to the complete scheme, where, for each simulation, energies for the minima and the transition states have been randomized (see text). Curves C and D correspond to the simplified model, with parameters given in Table and or with randomized energies (see text), respectively.

Figure 12

Maximum distance along $\left[0\overline{1}1\right]$ reached by the silyl before desorption as a function of temperature. The results are averaged over ${10}^6$ independent KMC runs. Curve A corresponds to the full reaction scheme, with the energies given in Fig. 6. Curve B corresponds to the complete scheme with randomized activation energies (see text). Curves C and D correspond to the simplified model, with parameters given in Table and with randomized energies (see text), respectively. Distances are given in units of the lattice spacing along $\left[0\overline{1}1\right]$ $(a_y=3.84\mathrm{\AA })$.

Figure 13

Comparison of KMC simulations performed on the simplified model and constant prefactors (continuous curve A) and with prefactors chosen according to harmonic transition-state theory predictions (dotted curve B, cf. Table ). In both cases, averages are performed over ${10}^6$ independent KMC runs, with activation barriers randomized as described in the text. (a) Distribution of resident times of the silyl on the surface at $500\mathrm{K}$ (cf. Fig. 11). (b) Maximum distance along $\left[0\overline{1}1\right]$ reached by the silyl before desorption as a function of temperature (cf. Fig. 12). Distances are given in units of the lattice spacing along $\left[0\overline{1}1\right]$ $(a_y=3.84\mathrm{\AA })$.