Enhanced Strength Through Nanotwinning in the Thermoelectric Semiconductor InSb

The conversion efficiency ($zT$) of thermoelectric (TE) materials has been enhanced over the last two decades, but their engineering applications are hindered by the poor mechanical properties, especially the low strength at working conditions. Here we used density functional theory (DFT) to show a strength enhancement in the TE semiconductor InSb arising from the twin boundaries (TBs). This strengthening effect leads to an 11% enhancement of the ideal shear strength in flawless crystalline InSb where this theoretical strength is considered as an upper bound on the attainable strength for a realistic material. DFT calculations reveal that the directional covalent bond rearrangements at the TB accommodating the structural mismatch lead to the anisotropic resistance against the deformation combined with the enhanced TB rigidity. This produces a strong stress response in the nanotwinned InSb. This work provides a fundamental insight for understanding the deformation mechanism of nanotwinned TE semiconductors, which is beneficial for developing reliable TE devices.

Figure 1

The shear-stress-shear-strain relationships and atomic structures for crystal and nanotwinned InSb. (a) Stress-strain relations for crystal InSb along various slip systems; (b) atomic structure for crystalline InSb along the $(111)⟨\overline{1}\overline{1}2⟩$ slip system. This cell contains $24\times \mathrm{In}$ and $24\times \mathrm{Sb}$ atoms, (c) atomic structure for crystalline InSb along the $(111)⟨11\overline{2}⟩$ slip system; and (d) nanotwinned InSb structure with the TB along the $\{111\}$ plane. This cell contains $48\times \mathrm{In}$ and $48\times \mathrm{Sb}$ atoms. The upper half consists of the $(111)⟨\overline{1}\overline{1}2⟩$ system of InSb [Fig. 1], and the lower half part consists of the $(111)⟨11\overline{2}⟩$ system of InSb [Fig. 1]. The twin spacing is 1.0 nm; (e) stress-strain relations for nanotwinned InSb, as well as the comparison with crystalline InSb along the most plausible slip system $(111)⟨11\overline{2}⟩$.

Figure 2

The structural deformation and bond-responding processes for crystalline InSb shear along the $(111)⟨11\overline{2}⟩$ and $(111)⟨\overline{1}\overline{1}2⟩$ slip systems. (a) Structure at 0.592 shear strain before failure in the $(111)⟨11\overline{2}⟩$ system. (b) Structure at failure strain of 0.605 in the $(111)⟨11\overline{2}⟩$ system. The dashed lines between In2 and Sb1 atoms represent their weak or nonbonding interactions. (c) The typical bond lengths ($\mathrm{In}1─\mathrm{Sb}1$ and $\mathrm{In}2─\mathrm{Sb}1$) and the bond angles ($\mathrm{In}3─\mathrm{Sb}1─\mathrm{In}2$ and $\mathrm{In}3─\mathrm{Sb}1─\mathrm{In}1$) with the increasing shear strain in the $(111)⟨11\overline{2}⟩$ system. The red dashed line in Fig. 2 represents the strain just before failure. (d) Structure at 0.300 shear strain corresponding to the ideal shear strength in the $(111)⟨\overline{1}\overline{1}2⟩$ system. (e) Structure at failure strain of 0.491 in the $(111)⟨\overline{1}\overline{1}2⟩$ system. (f) The average bond lengths ($\mathrm{In}1─\mathrm{Sb}1$ and $\mathrm{In}2─\mathrm{Sb}1$) and the bond angles ($\mathrm{In}3─\mathrm{Sb}1─\mathrm{In}2$ and $\mathrm{In}3─\mathrm{Sb}1─\mathrm{In}1$) with the increasing shear strain in the $(111)⟨\overline{1}\overline{1}2⟩$ system.

Figure 3

Structural changes of nanotwinned InSb. (a) Structure at 0.266 shear strain, which corresponds to the ideal shear strength. (b) Structure at 0.277 shear strain. The $\mathrm{In}2─\mathrm{Sb}1$ covalent bond breaks and a new $\mathrm{In}3─\mathrm{Sb}1$ bond forms, which moves the lower half part left by one “In-Sb hexagon.” (c) Structure at 0.438 shear strain before the structural rearrangement. (d) Structure at 0.448 shear strain. The $\mathrm{In}3─\mathrm{Sb}1$ covalent bond breaks and a new $\mathrm{In}4─\mathrm{Sb}1$ bond forms, which moves the lower half part left by one more “In-Sb hexagon”. (e) Structure at 0.623 shear strain before the structural failure. (f) Structure at failure strain of 0.634. The $\mathrm{In}4─\mathrm{Sb}1$ covalent bond breaks and a new $\mathrm{In}1─\mathrm{Sb}1$ bond forms, which again moves the lower half left by one more “In-Sb hexagon.” The $\mathrm{In}5─\mathrm{Sb}2$ bond in the TBs breaks while the $\mathrm{In}5─\mathrm{Sb}5$ bond forms, which totally releases the shear stress and results in the structural failure.

Figure 4

Stress responses and structural patterns of nanotwinned and flawless crystal InSb under biaxial shear deformation. The flawless crystal is sheared along the $(111)⟨11\overline{2}⟩$ slip system. (a) Shear-stress-shear-strain relations; (b) atomic structure at 0.311 strain for flawless crystal before the failure; (c) atomic structure at a failure strain of 0.323 for flawless crystal; (d) atomic structure at 0.177 strain for the nanotwinned InSb before the failure; and (e) the failure structure at 0.187 strain for the nanotwinned InSb.