Photoelectron spectra calculations of $\mathrm{N}@{\mathrm{C}}_{60}$ molecules on a crystalline Si surface

The shapes of the angular distributions of electrons photoejected from the $1s$ level of atomic N encapsulated within a fullerene cage have been calculated for $\mathrm{N}\mathrm{@}{\mathrm{C}}_{60}$ adsorbed on a Si (100) crystal surface. Two possible schemes of experimental arrangements have been considered. The first involves the measurement of the photoelectron spectra as a function of the polar angle for fixed azimuthal angle. The second scheme studies the dependence of the spectra on the azimuthal angle. It is shown that in both types of experiments the shape of the photoelectron angular distribution is extremely sensitive to both the molecular location on the crystal surface and the orientation of the molecular axis of the fullerene cage relative to crystallographic directions. Therefore, the study of photoelectron spectra can, in principle, be used for diagnostics of the position of the fullerenelike molecule on a crystal surface.

Figure 1

Geometry of the positions of the N atom, 6 C atoms (28-29-30-31-32-33) of the ${\mathrm{C}}_{60}$ cage and 13 Si atoms for the $\mathrm{N}\mathrm{@}{\mathrm{C}}_{60}$ molecule on the (100) crystal surface. The N atom is located at point $A$. Distances $a$ and $d$ are the lattice constant and the bond length of the ${\mathrm{C}}_{60}$ hexagon, respectively. The azimuthal angles ${\phi }_e$, ${\phi }_k$, and ${\phi }_j$ are measured from the $X$ axis toward the $Y$ axis, counterclockwise, viewing the surface from point $A$.

Figure 2

(Color online) Structural function $S\left({\vartheta }_k\right)$ for photoelectron emission in the plane $XZ$. The dashed line corresponds to data for the free N atom near the Si crystal surface at point $A$, and the solid line is $S\left({\vartheta }_k\right)$ for $\mathrm{N}\mathrm{@}{\mathrm{C}}_{60}$ at point $A$.

Figure 3

Structural function $S\left(\mathbf{k}\right)$ as a function of polar angle ${\vartheta }_k$ for the $\mathrm{N}\mathrm{@}{\mathrm{C}}_{60}+\left(\mathrm{Si}\text{surface}\right)$ system when the N atom is located at the first point of adsorption (see Fig. 1 and text). Each of the figures corresponds to a fixed azimuthal angle ${\phi }_k$, shown in the upper left corner of each figure.

Figure 4

(Color online) Structural function $S\left(\mathbf{k}\right)$ as a function of polar angle ${\vartheta }_k$ for the second point of the $\mathrm{N}\mathrm{@}{\mathrm{C}}_{60}$ molecule adsorption (see Fig. 1 and text). The vectors $\mathbf{\kappa }$ and $\mathbf{e}$ are situated in the $XZ$ plane. The solid line corresponds to $S\left(\mathbf{k}\right)$ for the fixed azimuthal angle ${\phi }_k$ and the dashed line to $S\left(\mathbf{k}\right)$ for angle $2\pi \text{−}{\phi }_k$. The angle ${\phi }_k$ is shown in the upper left corner of the figure.

Figure 5

(Color online) Structural function $S\left(\mathbf{k}\right)$ as a function of polar angle ${\vartheta }_k$ for the third adsorption point (see Fig. 1 and text). The vectors $\mathbf{\kappa }$ and $\mathbf{e}$ are situated in the $YZ$ plane. The solid line corresponds to $S\left(\mathbf{k}\right)$ for the fixed azimuthal angle ${\phi }_k$ and the dashed line to $S\left(\mathbf{k}\right)$ for angle $\pi \text{−}{\phi }_k$. The angle ${\phi }_k$ is shown in the upper left corner of the figure.

Figure 6

(Color online) Structural function $S\left(\mathbf{k}\right)$ as a function of azimuthal angle ${\phi }_k$ at fixed polar angle ${\vartheta }_k=60°$ for the different adsorption points (see Fig. 1 and text). Dashed, dotted, and dash-dotted curves correspond to the molecule rotated around the $Z$ axis as described in the text.