# Bismuth antimonide

Bismuth antimonides, Bismuth-antimonys, or Bismuth-antimony alloys, (Bi$_{1−x}$Sb$_x$) are binary alloys of bismuth and antimony in various ratios.
Some, in particular Bi$_{0.9}$Sb$_{0.1}$, were the first experimentally-observed three-dimensional topological insulators, materials that have conducting surface states but have an insulating interior.
Various BiSb alloys also superconduct at low temperatures, are semiconductors, and are used in thermoelectric devices.
Bismuth antimonide itself (see box to right) is sometimes described as Bi$_2$Sb$_2$.

## Synthesis

Crystals of bismuth antimonides are synthesized by melting bismuth and antimony together under inert gas or vacuum. Zone melting is used to decrease the concentration of impurities. When synthesizing single crystals of bismuth antimonides, it is important that impurities are removed from the samples, as oxidation occurring at the impurities leads to polycrystalline growth.

## Properties
### Topological insulator

Pure bismuth is a semimetal, containing a small band gap, which leads to it having a relatively high conductivity (7.7×10$^5$ S/m at 20 °C). When the bismuth is doped with antimony, the conduction band decreases in energy and the valence band increases in energy. At an antimony concentration of 4%, the two bands intersect, forming a Dirac point (which is defined as a point where the conduction and valence bands intersect). Further increases in the concentration of antimony result in a band inversion, in which the energy of the valence band becomes greater than that of the conduction band at specific momenta. Between Sb concentrations of 7 and 22%, the bands no longer intersect, and the Bi$_{1−x}$Sb$_x$ becomes an inverted-band insulator. It is at these higher concentrations of Sb that the band gap in the surface states vanishes, and the material thus conducts at its surface.

### Superconductor

The highest temperatures at which Bi$_{0.4}$Sb$_{0.6}$, as a thin film of thicknesses 150–1350 Å, superconducts (the critical temperature T$_c$) is approximately 2 K. Single crystal Bi$_{0.935}$Sb$_{0.065}$ can superconduct at slightly higher temperatures, and at 4.2 K, its critical magnetic field B$_c$ (the maximum magnetic field that the superconductor can expel) of 1.6 T at 4.2 K.

### Semiconductor

Electron mobility is one important parameter describing semiconductors because it describes the rate at which electrons can travel through the semiconductor. At 40 K, electron mobility ranged from 4.9×10$^5$ cm$^2$/V·s at an antimony concentration of 0 to 2.4×10$^5$ cm$^2$/V·s at an antimony concentration of 7.2%. This is much greater than the electron mobility of other common semiconductors like silicon, which is 1400 cm$^2$/V·s at room temperature.
Another important parameter of Bi$_{1−x}$Sb$_x$ is the effective electron mass (EEM), a measure of the ratio of the acceleration of an electron to the force applied to an electron. The effective electron mass is 2×10$^{−3}$ m$_e$ for x = 0.11 and 9×10$^{−4}$ m$_e$ at x = 0.06. This is much less than the electron effective mass in many common semiconductors (1.09 in Si at 300 K, 0.55 in Ge, and 0.067 in GaAs). A low EEM is good for Thermophotovoltaic applications.

### Thermoelectric

Bismuth antimonides are used as the n-type legs in many thermoelectric devices below room temperature. The thermoelectric efficiency, given by its figure of merit z$_T$ = ⁠σS$^2$T/λ⁠, where S is the Seebeck coefficient, λ is the thermal conductivity, and σ is the electrical conductivity, describes the ratio of the energy provided by the thermoelectric to the heat absorbed by the device. At 80 K, the figure of merit (z$_T$) for Bi$_{1−x}$Sb$_x$ peaks at 6.5×10$^{−3}$ K$^{−1}$ when x = 0.15. Also, the Seebeck coefficient (the ratio of the potential difference between ends of a material to the temperature difference between the sides) at 80 K of Bi$_{0.9}$Sb$_{0.1}$ is −140 μV/K, much lower than the Seebeck coefficient of pure bismuth, −50 μV/K.