First-principles study of group III impurity doped PbSe: Bulk and nanowire

Fully relativistic calculations are used to perform a systematic study on the energetic stability, and electronic properties of group III (Al, Ga, In, and Tl) impurities in the cation-site (Pb) of PbSe: bulk and nanowire (NW). Our results show that group III impurities have lower formation energies in the NW than in the bulk. The impurities are site-dependent in the nanowires: they are more stable on the surface of the NW as compared to the core. In the bulk, Al and In are donor levels, while Ga and Tl are acceptor impurities. For the NW, the same trend is obtained for Al and Tl, whereas Ga and In are deep donors. A two-level model based on the interaction between the impurity states and the host crystalline field explains the electronic properties of group III impurity doped PbSe bulk and NW. This model agrees with the projected density of states and helps us to understand the unexpected $n$-type character of some group III impurity doped PbSe.

Figure 1

Cross-section (a) and lateral (b) views of the PbSe NW (2.3 nm in diameter) in the RS structure and aligned along the [001] direction. Small green spheres represent Se atoms and large gray spheres represent Pb atoms. The labels A to J indicate the sites where the impurities will be incorporated.

Figure 2

Schematic two-level model for a group III impurity in the Pb site of PbSe. ${\varepsilon }_I$ and ${\varepsilon }_H$ are the impurity ion $X$ and host Se states, respectively. $E_{\mathrm{HDS}}$ and $E_{\mathrm{DDS}}$ are the bonding and antibonding impurity states, respectively, resulting from the repulsion $R$ with respect to the $\overline{\varepsilon }$ average energy (see text).

Figure 3

Schematic diagram of the calculated band structure and impurity levels $E_{\mathrm{HDS}}$ and $E_{\mathrm{DDS}}$ of group III doped bulk PbSe.

Figure 4

Calculated electronic band structure and DOS for PbSe NWs doped with group III impurities in the cation (Pb) site. From left to right, we have Al, Ga, In, and Tl. The upper part presents the results without the inclusion of SO interactions, while the botton presents the results with SO interactions. The horizontal dash-dotted lines represent the Fermi level, and the red lines are the impurity states. The PDOS for the impurities, Pb, and Se atoms are represented by solid (magenta), dashed (blue), and dotted (green) lines, respectively.

Figure 5

Schematic diagram of the calculated band structure and impurity levels $E_{\mathrm{HDS}}$ and $E_{\mathrm{DDS}}$ of group III doped PbSe NW.

Figure 6

Calculated electronic charge density; (a)–(c) of HOMOs at the $X$ point for Al${}_{\mathrm{Pb}}$, Ga${}_{\mathrm{Pb}}$, and In${}_{\mathrm{Pb}}$, respectively, and (d) LUMO at the $\Gamma$ point for Tl${}_{\mathrm{Pb}}$.