Figure 1

Structure of Bi${}_{1-x}$Sb${}_x$. (a) shows the rhombohedral lattice structure of bulk bismuth, bulk antimony, and their alloys Bi${}_{1-x}$Sb${}_x$. There are two atoms in each unit cell. The $C_3$ symmetry trigonal axis, the $C_2$ symmetry binary axis, and the $C_1$ symmetry bisectrix axis form a Cartesian coordinate system in three-dimensional space. The trigonal-bisectrix plane forms a mirror symmetry plane. (b) shows different carrier pockets in the first Brillouin zone of bulk Bi${}_{1-x}$Sb${}_x$.Reuse & Permissions

Figure 2

Band-edge energies at different carrier pockets vs antimony composition $x$ for bulk Bi${}_{1-x}$Sb${}_x$ (Ref. 5). The semimetal (SM) phase regions, the indirect-semiconductor (ISC) phase regions, and direct-semiconductor (DSC) phase region are labeled. The symbols for the various bands are indicated by the color and symbols in the bar below the plot.Reuse & Permissions

Figure 3

Schemes of how different carrier pockets at the $T$ point (red), the three $L$ points (blue) and the six $H$ points (green) are projected onto the film plane for Bi${}_{1-x}$Sb${}_x$ thin films grown normal to (a) the trigonal axis, (b) the bisectrix axis, and (c) the binary axis. How the band edges for the different carrier pockets change with antimony composition $x$ are calculated for Bi${}_{1-x}$Sb${}_x$ thin films grown normal to (d) the trigonal axis, (e) the bisectrix axis, and (f) the binary axis, where 100-nm-thick film systems are chosen as an example. The cases for other film thicknesses can be calculated in a similar way.Reuse & Permissions

Figure 4

Phase diagrams as a function of antimony composition $x$ and film thickness $l$ for the Bi${}_{1-x}$Sb${}_x$ thin-film systems grown normal to (a) the trigonal axis, (b) the bisectrix axis, and (c) the binary axis. The SM phase regions, the ISC phase regions, and DSC phase regions are labeled for each case. Region 1 and region 2 in each phase diagram are the regions where the top of the valence band is located at an $L$ point; region 4 and region 5 in each phase diagram are the regions where the top of the valence band is located at an $H$ point. The band gap (band overlap) value as a function of film thickness and antimony composition are shown in (d), (e), and (f), corresponding to (a), (b), and (c), respectively, where a positive value stands for the band gap of a direct or indirect semiconductor, while a negative value stands for the band overlap of a semimetal. A zero value stands for a gapless state, which corresponds to a semimetal-semiconductor or semiconductor-semimetal phase transition.Reuse & Permissions