$p$-type ${\text{Bi}}_2{\text{Se}}_3$ for topological insulator and low-temperature thermoelectric applications

The growth and elementary properties of $p$-type ${\text{Bi}}_2{\text{Se}}_3$ single crystals are reported. Based on a hypothesis about the defect chemistry of ${\text{Bi}}_2{\text{Se}}_3$, the $p$-type behavior has been induced through low-level substitutions (1% or less) of Ca for Bi. Scanning tunneling microscopy is employed to image the defects and establish their charge. Tunneling and angle-resolved photoemission spectra show that the Fermi level has been lowered into the valence band by about 400 meV in ${\text{Bi}}_{1.98}{\text{Ca}}_{0.02}{\text{Se}}_3$ relative to the $n$-type material. $p$-type single crystals with $ab$-plane Seebeck coefficients of $+180\mu \text{V}/\text{K}$ at room temperature are reported. These crystals show an anomalous peak in the Seebeck coefficient at low temperatures, reaching $+120\mu \text{V}{\text{K}}^{-1}$ at 7 K, giving them a high thermoelectric power factor at low temperatures. In addition to its interesting thermoelectric properties, $p$-type ${\text{Bi}}_2{\text{Se}}_3$ is of substantial interest for studies of technologies and phenomena proposed for topological insulators.

Figure 1

(Color online) (a) Spatially averaged density of states $\left(dI/dV\right)$ measurements showing the shift of $E_F$ between $n$-type ${\text{Bi}}_2{\text{Se}}_3$ and $p$-type ${\text{Bi}}_{1.98}{\text{Ca}}_{0.02}{\text{Se}}_3$. (b) STM topography of the empty states of ${\text{Bi}}_2{\text{Se}}_3$ ($V_B=+1\text{V}$, and $I=10\text{pA}$) showing triangular-shaped defects observed at various intensities, indicating they are located in different layers beneath the surface. (c) Topography of the empty states of ${\text{Bi}}_{1.98}{\text{Ca}}_{0.02}{\text{Se}}_3$ ($V_{B=}+2.0\text{V}$ and $I=10\text{pA}$) showing clover-leaf-looking defects and a substantial reduction in the density of the triangular defects, which dominated the undoped samples. (d) Topography of the filled states over the same area as in (c) ($V_B=-1.0\text{V}$ and $I=10\text{pA}$). The area around the triangular defect near center shows a depression around it in the filled states, demonstrating it is positively charged. In contrast, the Ca-related defects exhibit an area of enhancement around them, indicating they are negatively charged. All STM topographies are $500\times 500{\text{Å}}^2$.

Figure 2

(Color online) (a) The valence-band structure of $n$-type ${\text{Bi}}_2{\text{Se}}_3$ measured by ARPES near the Fermi energy and the $\Gamma$ point of the Brillouin zone. The chemical potential (the Fermi level) is about 0.4 eV above the top of the valence band, about 0.3 eV above the surface Dirac point (Ref. 15). (b) The band structure of a Ca-doped ${\text{Bi}}_2{\text{Se}}_3$ crystal $\left({\text{Bi}}_{1.98}{\text{Ca}}_{0.02}{\text{Se}}_3\right)$ measured under similar conditions. The chemical potential is within 30 meV of the valence band. For (a) and (b), the $\Gamma$ point is 0.0 on the horizontal axes and the band dispersions are shown in the $\pm \text{M}$ directions. (c) The momentum-selective DOS near the $\Gamma$ point, compared for the $n$- and $p$-type crystals, covering a large binding energy range. A large shift of the chemical potential with Ca doping can be traced by considering the shift of DOS peaks in the valence band. The drop of the chemical potential by about 380 meV confirms the hole-doped nature of the Ca-doped samples.

Figure 3

(Color online) Temperature-dependent resistivity between 2 and 300 K in the $ab$ plane of single crystals of ${\text{Bi}}_2{\text{Se}}_3$ and Ca-doped variants. The stoichiometric material is $n$ type and the Ca-doped materials are all $p$ type. The upper inset shows the resistivities in the low temperature regime. The lower inset shows the Hall-effect data employed to determine the carrier concentrations for undoped ${\text{Bi}}_2{\text{Se}}_3$ and one Ca-doped crystal.

Figure 4

(Color online) Temperature-dependent Seebeck coefficients between 2 and 300 K in the $ab$ plane of single crystals of ${\text{Bi}}_2{\text{Se}}_3$ and Ca-doped variants. The inset shows the low temperature region for both pure and lightly Ca-doped ${\text{Bi}}_2{\text{Se}}_3$. The undoped ${\text{Bi}}_2{\text{Se}}_3$ is $n$ type, with a carrier concentration of $8\times {10}^{17}{\text{cm}}^{-3}$ and the Ca-doped material with $x=0.005$ is $p$ type with a carrier concentration of $1\times {10}^{19}{\text{cm}}^{-3}$.

Figure 5

(Color online) Temperature-dependent total thermal conductivities between 2 and 300 K in the $ab$ plane of single crystals of ${\text{Bi}}_2{\text{Se}}_3$ and Ca-doped variants. The inset shows the low temperature region for both pure and lightly Ca-doped ${\text{Bi}}_2{\text{Se}}_3$.

Figure 6

(Color online) Temperature-dependent thermoelectric power factor between 2 and 300 K in the $ab$ plane of single crystals of ${\text{Bi}}_2{\text{Se}}_3$ and Ca-doped variants. All materials show a peak at low temperatures but the peak in the $p$-type variant with 1% Ca-doping (${\text{Bi}}_{2-x}{\text{Ca}}_x{\text{Se}}_3$ with $x=0.02$) is particularly dramatic. The inset shows the thermoelectric figure of merit in the same temperature range.