Electron paramagnetic resonance calculations for hydrogenated Si surfaces

Electron paramagnetic resonance (EPR) signatures, more specifically the elements of the electronic $g$ tensor, are calculated within density functional theory for hydrogenated Si(111), Si(001), Si(113), Si(114), $\mathrm{Si}\left(11\overline{2}\right)$, and Si(110) surfaces. Thereby both perturbation theory and a more sophisticated Berry phase technique are applied. Specific defects on different surface orientations are shown to reproduce the resonances at $\overline{g}=2.0043$ and $\overline{g}=2.0052$ measured for hydrogenated microcrystalline silicon: The latter value is argued here to originate from regions with low hydrogen coverage; the resonance at $\overline{g}=2.0043$ is shown to appear in positions with dihydride environment, where an H atom is directly bound to the silicon dangling-bond atoms. A third group of EPR signals with considerably larger $\overline{g}$ values between 2.006 and 2.009 is predicted for highly symmetric dangling bonds resembling single dangling-bond defects in silicon bulk material. As the exact value depends strongly on local strain, this type of defect can explain a less intense signal with large $g$ strain observed in microcrystalline as well as in amorphous material.

Figure 1

Microcrystal with different surface orientations. Besides low-index surfaces, stable high-index orientations $\left(11\overline{2}\right)$, (113), (114) are indicated. Other high-index surfaces tend to faceting into low-index terraces.

Figure 2

Hydrogenated Si(111):H surface with a single H vacancy. Left: atomic structure (Si large, H small) and isosurfaces of the magnetization density $m\left(\vec{r}\right)=n_{\uparrow }\left(\vec{r}\right)-n_{\downarrow }\left(\vec{r}\right)$. The main part $[m\left(\vec{r}\right)>0$ red, $m\left(\vec{r}\right)<0$ blue] is located at the unsaturated dangling bond Si atom. There are three fluctuations of $m\left(\vec{r}\right)$ along the zigzag bond directions into the crystal. Calculated current density difference ${\vec{j}}_{\uparrow }^{\left(1\right),\mu }\left(\vec{r}\right)-{\vec{j}}_{\downarrow }^{\left(1\right),\mu }\left(\vec{r}\right)$ (middle) and induced magnetic field ${\vec{B}}^{\left(1\right),\mu }\left(\vec{r}\right)$ (right), both for the external magnetic field aligned perpendicular to the displayed plane (see also text). To facilitate direct comparison, the magnetization density is indicated again by isolines.

Figure 3

Calculated $g$ tensor components (bottom) for various surface unit cells (indicated above) used to model the prototypical Si(111):H dangling-bond defect.

Figure 4

Si(111):H dangling-bond defect: $g$ tensor components calculated for strain. Whereas the component $g_{\left|\right|}$ parallel to the surface normal appears quite robust, the lateral components $g_{\perp }$ depend critically on the strain.

Figure 5

Band structures calculated for the Si(111):H $2\sqrt{3}\times 2\sqrt{3}$ surface, completely hydrogenated (top) and with a single db defect (bottom); spin up/down indicated in red/green. Transition energies entering the Green's function calculation are exemplarily indicated, see text. The gray background is the surface projected Si bulk band structure.

Figure 6

Side view of the clean Si(001)$c(4\times 2)$ surface shown along the dimer rows. The alternating buckling of the Si-Si dimers can be clearly seen.

Figure 7

Symbolic top view of $\mathrm{Si}\left(001\right)$:H surface supercells (left) and corresponding band structures (right), shown here for surfaces with low hydrogen coverage. The first Brillouin zone is depicted in the insert (top right). Energies are given with respect to the Fermi level; spin-up bands plotted in red, spin-down in green.

Figure 8

Symbolic top view of $\mathrm{Si}\left(001\right)$ surface supercells (left) and corresponding band structures (right), shown here for structures with high hydrogen coverage, cf. Fig. 7.

Figure 9

Structural models, magnetization densities (insets), and induced spin currents calculated for selected defect structures from Figs. 7 and 8: 1 (top), 6 (middle); besides 9, its symmetric ground state $9^{*}$ (bottom) is shown. For comparison and further details, see also Fig. 2 and text.

Figure 10

Top: Structure model for ideal Si(113):H. Possible H vacancy positions are marked. The dashed lines show low-index crystal orientations. Lower parts: geometries and magnetization density of H vacancies at Si(113):H. H2 and H3 provide rather specific dangling bonds (middle, left/right); H1 mimics the symmetric, tripod-like H vacancy at Si(111) (bottom, left), cf. Fig. 2. For further comparison, a respective view onto the dangling bond of Si(110):H with H vacancy [rotated by $\sphericalangle \left(\right[110],[113\left]\right)]$ is also given (bottom, right).

Figure 11

Structure models for Si(114):H monohydride (top, left) and dihydride (top, right) surfaces. Possible H vacancy positions are marked. In the lower part, the spin distribution is given for the $s{p}^2$ hybridized H2 (left) and the symmetric, bond-bridging $\mathrm{H}{2}^{*}$ configurations (right ), cf. Table 5.

Figure 12

Schematic views of the $\mathrm{Si}\left(11\overline{2}\right)$:H surface with possible vacancy positions indicated (top). In the lower part, the spin distribution is given for the $s{p}^2$ hybridized H2 (right) and the symmetric, bond-bridging $\mathrm{H}{2}^{*}$ configurations (left).