Transferable tight-binding model for strained group IV and III-V materials and heterostructures

It is critical to capture the effect due to strain and material interface for device level transistor modeling. We introduce a transferable $s{p}^3{d}^5{s}^{*}$ tight-binding model with nearest-neighbor interactions for arbitrarily strained group IV and III-V materials. The tight-binding model is parametrized with respect to hybrid functional (HSE06) calculations for varieties of strained systems. The tight-binding calculations of ultrasmall superlattices formed by group IV and group III-V materials show good agreement with the corresponding HSE06 calculations. The application of the tight-binding model to superlattices demonstrates that the transferable tight-binding model with nearest-neighbor interactions can be obtained for group IV and III-V materials.

Figure 1

Different definitions of materials at GaAs/AlAs interfaces. Regions of AlAs and GaAs materials are separated by the dashed line. In all presented definitions, the left parts are AlAs and the right parts are GaAs. In definition (a), the interface As atoms are defined as atoms in AlAs; in definition (b), the interface As atoms are defined as atoms in GaAs. In the case (c), the interface As atoms are defined as As atoms in an averaged material of AlAs and GaAs.

Figure 2

Contribution of $p$ orbitals to the top valence bands (a) and contribution of $s$ orbitals to the lowest conduction bands of InX (X = P, As, Sb). The $p$ orbitals of In and cation atoms contribute to the top valence bands. When the lattice constant changes 1%, the $p$-orbital contribution is changed by less than 0.0002. The $s$ orbitals of In and anion atoms contribute to the lowest conduction bands. When the lattice constant changes 1%, the $s$-orbital contribution is changed by less than 0.02.

Figure 3

Strained systems considered in this work. (a) Hydrostatic strain, (b) with two bond length changes, (c) diagonal strain with ${\varepsilon }_{xx}={\varepsilon }_{yy}=-0.5{\varepsilon }_{zz}$, (d) off-diagonal strain with ${\varepsilon }_{xy}\ne 0$.

Figure 4

Band structure of III-V materials with ETB and HSE06 calculations. Presented band structures of IV materials include Si (a) and Ge (b). ETB band structures are in good agreement with HSE06 results. The HSE06 bands are adjusted to match experimental results under room temperature.

Figure 5

Band structure of III-V materials with ETB and HSE06 calculation. Presented band structures of III-V materials include (a) AlP, (b) GaP, (c) InP, (d) AlAs, (e) GaAs, (f) InAs, (g) AlSb, (h) GaSb, (i) InSb. ETB band structures are in good agreement with HSE06 results.

Figure 6

Band structure of Si with different lattice constants. (a) Si with a lattice constant of 5.4 Å, (b) Si with a lattice constant of 5.8 Å, (c) direct and indirect band gaps of Si with different lattice constants. The lowest conduction band at the $\mathrm{\Gamma }$ point transits from $p$ bands to $s$ bands at about 5.8 Å. When the lattice constant is 5.4 Å, Si is an indirect gap semiconductor, and the X conduction valley is the lowest conduction valley. As the lattice constant increases, the band gap of the X valley $\left[E_g\left(X\right)\right]$ increases slightly, while the band gap of the L valleys $\left[E_g\left(L\right)\right]$ and the direct band gap $[E_{cs}\left(G\right)-E_v]$ decrease significantly.

Figure 7

Strain-induced band edge splitting of selected conduction bands and valence bands at $\mathrm{\Gamma },X$, and $L$ points of InAs. At the $\mathrm{\Gamma }$ point, the 6 topmost valence bands and 2 lowest conduction bands are shown. The 4 lowest conduction bands at $X$ points are shown. The lowest conduction band at $L$ points are included in the figures. The valence bands at $X$ and $L$ points are not shown as those points are of low energy. The ETB band edge splitting is in good agreement with the corresponding HSE06 results.

Figure 8

Atom structure of Si/Ge and XAs/YAs type superlattices. (a) Si/Ge superlattice with 4 layers in the unit cell; (b) Si/Ge superlattice with 8 layers in the unit cell. (c) XAs/YAs superlattice with 4 layers in the unit cell; (d) XAs/YAs superlattice with 8 layers in the unit cell. (e) AX/BY superlattice with 4 atoms in the unit cell; (f) AX/BY superlattice with 8 layers in the unit cell. The primitive unit cells are marked by dashed lines.

Figure 9

Band structures of Si/Ge superlattices by ETB and HSE06 calculations. Panels correspond to supercells which contain 4 atoms (a) and 8 atoms (b) and band gaps of Si/Ge superlattices versus number of atoms in the supercell (c).

Figure 10

Band structures of arsenide superlattices by ETB and HSE06 calculations. Presented band structures include band structures of superlattices of 001 AlAs/GaAs [(a), (d)], InAs/GaAs [(b), (e)], and InAs/AlAs [(c), (f)]. Upper figures correspond to supercells which contain 4 atoms [Fig. 8], while lower figures correspond to supercells with 8 atoms [Fig. 8].

Figure 11

Band gaps of III-V superlattices by ETB and HSE06 calculations. The presented band gaps include superlattices of (a) XP/YP, (b) XAs/YAs, and (c) XSb/YSb (X and Y stand for different cations, X, Y = Al, Ga, or In) and (d) AlX/AlY, (e) GaX/GaY, and (g) InX/InY (X and Y stand for different anions, X, Y = P, As, or Sb). The ETB band gaps of different superlattices show good agreement with HSE06 results, demonstrating the ETB parameters have good transferability.

Figure 12

Band structures of InAs/GaSb superlattices by ETB and HSE06 calculations. Present figures include band structures of 4-layer (a) and 8-layer (b) InAs/GaSb superlattices. Band gaps of AX/BY type superlattices are shown in (c); InAs/GaSb, InAs/AlSb, InP/GaAs, and InP/AlAs superlattices are considered.