Intermediate bands in type-II silicon clathrate with Cu and Ag guest atoms

The unique host-guest structure of the type-II silicon (Si) clathrate offers tunable electronic structures by doping guest atoms or molecules to the ${\mathrm{Si}}_{28}$ cages. Here we investigate the possibility of inducing intermediate bands (IBs) by Cu and Ag atoms employing first-principles calculations based on the density functional theory. Our analyses reveal that one or two isolated Cu/Ag atoms around the cage center are required to obtain IBs useful for photovoltaics; however, further clustering is likely to occur, which removes IBs and converts these Si clathrates into metal. Specifically, the formation of Cu and Ag clusters is mainly determined by local thermodynamics and local kinetics, respectively. All the Cu-clathrate structures presenting IBs are not energetically favorable, making Cu inappropriate for IB solar cells, whereas clathrates with one or two Ag atoms inside the cage that have IBs are thermodynamically stable, but the subsequent aggregation to form 3Ag or 4Ag clusters will destroy IBs. Thus, preventing clustering is crucial to realize IBs in Si clathrates by doping noble-metal atoms.

Figure 1

The conventional unit cell of the type-II clathrate. ${\mathrm{Si}}_{28}$ cages form a cubic diamond network. Four groups of ${\mathrm{Si}}_{20}$ cages, four cages each, occupy the tetrahedral interstices.

Figure 2

(a) DFT and (b) $GW$ band structures of type-II clathrate. The red dashed lines indicate the Fermi level, which is set as energy zero.

Figure 3

The highest binding energy [Eq. (1)] per guest atom and the maximum of the magnitude of chemical potential [Eq. (2)] for adding one more guest atom into a ${\mathrm{Si}}_{28}$ cage are plotted with respect to the number of Cu (black) and Ag (green) guest atoms per conventional unit cell.

Figure 4

The relaxed configurations for up to four Cu atoms (deep blue) in a ${\mathrm{Si}}_{28}$ cage (golden) inside one conventional unit cell. (a) Pure clathrate; (b),(c) one Cu; (d),(e) two Cu atoms; (f)–(i) three Cu atoms; and (j)–(l) four Cu atoms. The dispersed phase is more stable thermodynamically than the cluster phase until the number of Cu atoms reaches four. See Table 2 for a comparison of total energies.

Figure 5

The kinetic barriers are extracted by spline fitting from seven-image NEB calculations. (a),(b) correspond to the barrier for Figs. 4$\to$4. Both Cu atoms intend to jump out of hexagon center. (c),(d) The barrier on how a 4Ag cluster begins to form. The barrier prevents the Ag atom in the adjacent cage from passing through the hexagon, but once it enters the cage, it will rush to form the cluster with straight lowering potential energy path.

Figure 6

Electronic band structures of all the configurations given in the same order as in Fig. 4. The red dotted lines denote the top valence bands of these guest-host systems, while the blue dashed lines indicate the Fermi levels. Here the special k points are $\mathrm{\Gamma }$ $(0,0,0),X$ $(0,0,0.5),Q$ $(0,0.5,0.5)$, and $L(0.5,0.5,0.5)$.

Figure 7

The relaxed configurations of Ag atoms (light blue) in the ${\mathrm{Si}}_{28}$ cages (golden) in a conventional unit cell. (a),(b) One Ag atom; (c),(d) two Ag atoms; (e),(f) three Ag atoms; and (g),(h) four Ag atoms; while (i) shows a satellite Ag atom in a neighboring cage of a 4Ag cluster.

Figure 8

Electronic band structures of all the configurations listed in the same order as in Fig. 7. The red dotted lines denote the top valence bands of these guest-host systems, while the blue dashed lines indicate the Fermi levels.

Figure 9

Electronic band structures for (a) the configuration plotted in Fig. 4 and (b) the configuration plotted in Fig. 7, using the HSE hybrid functional. Here the red dotted lines denote the top valence bands of these guest-host systems, while the blue dashed lines indicate the Fermi levels.