Anisotropic strain in SmSe and SmTe: Implications for electronic transport

Mixed valence rare-earth samarium compounds $\mathrm{Sm}X$ ($X=\text{Se,Te}$) have been recently proposed as candidate materials for use in high-speed, low-power digital switches driven by stress induced changes of resistivity. At room temperature these materials exhibit a pressure driven insulator-to-metal transition with resistivity decreasing by up to seven orders of magnitude over a small pressure range. Thus, the application of only a few GPa's to the piezoresistor ($\mathrm{Sm}X$) allows the switching device to perform complex logic. Here we study from first principles the electronic properties of these compounds under uniaxial strain and discuss the implications for carrier transport. Based on changes in the band structure and a model we show that the piezoresistive response is mostly governed by the reduction of band gap with strain. Furthermore, the piezoresistive reponse becomes optimal when the Fermi level is pinned near the localized valence band. The piezoresistive effect under uniaxial strain, which must be taken into account in thin films and other systems with reduced dimensionality, is also studied. Under uniaxial strain we find that the piezoresistive response can be substantially larger than in the isotropic case. Analysis of the complex band structure of SmSe yields a tunneling length of the order of 1 nm. This suggest that the conduction mechanism governing the piezoresistive effect in bulk, i.e., thermal promotion of electrons, should still be dominant in few-nanometer-thick films.

Figure 1

Crystal and band structure of rock-salt SmSe: (a) Crystal structure. (b) Energy surfaces of conduction (top) and valence bands (bottom) at 0.25 eV above and below the band edge, respectively. (c) Band structure of SmSe near the Fermi level ($E_F=0$). Color indicates projections of Bloch states onto localized atomic orbitals of Sm (left) and Se (right) with different angular momentum (from top to bottom): $L=0$ (purple), 1 (green), 2 (red), and 3 (blue).

Figure 2

Band structure of rock-salt SmTe near the Fermi level ($E_F=0$). Color indicates projections of Bloch states onto localized atomic orbitals of Sm (left) and Te (right) with different angular momentum (color code as Fig. 1).

Figure 3

Changes in the electronic properties with hydrostatic strain. Indirect (circles) and optical (squares) band gaps as a function of the (isotropic) volume change: (a) SmSe; (b) SmTe. Effective masses of bands near the Fermi level: light holes (diamonds), heavy holes (squares), and electrons (circles) as a function of the (isotropic) volume change: (c) SmSe; (d) SmTe.

Figure 4

Band gap reduction under uniaxial strain in $\mathrm{Sm}X$. (Top row) 3D Brillouin zone of the rock-salt crystal structure $Fm\overline{3}m$ turns into one with lower symmetries under uniaxial strain: body centered tetragonal ${\mathrm{BCT}}_2$ ([001]), body-centered orthorhombic ORCI ([011]), and rhombohedral RHL ([111]). In the first two cases, degeneracy at symmetry points where the conduction band edge resides is lifted. The center and bottom rows indicate change of the indirect (solid symbols) and optical (open symbols) band gap as a function of the volume change for SmSe and SmTe, respectively. Each column corresponds to the strain case indicated in the top row. For comparison we also show the results for isotropic strain (dashed lines). The top of the valence bands resides in all cases at the $\Gamma$ symmetry point; bottoms of the conduction band are located at the $X$ symmetry point for the FCC, at $X$ and $Z$ for the ${\mathrm{BCT}}_2$, at $T$ and $Z$ for the ORCI, and at $F$ for the RHL.

Figure 5

Effective mass dependence of conduction band under uniaxial strain in: SmSe (top row) and SmTe (bottom row). Uniaxial strain is applied along the [001] (left, not broken vertical axis), [011] (center) and [111] right. The effective mass along the strain direction (open symbols) can be significantly different than the effective mass (solid symbol) depending on the strain direction. For comparison we also show the results for isotropic strain (dashed lines).

Figure 6

Complex band structure (CBS) of SmSe near the Fermi level at symmetry points of the 2D Brillouin zone. Real and imaginary band structures are plotted along the positive and negative wave vector axis, respectively. (Bands appear to have direct band gaps due to band folding and superposition.) We use as energy reference the middle of the indirect band gap (dotted line). Unstrained crystal for transport along different directions: (a) [001], (b) [011], and (c) [111]. The energy level at which tunneling is minimized (i.e., imaginary wave vectors are largest) resides below the middle of the gap (dashed line). Bottom row: CBS along the [001] direction under 4% compressive strain: (d) hydrostatic and (e) uniaxial. The unstrained band structure is also plotted for reference (gray).