Electronic and optical properties of $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ nanowire superlattices

The electronic structure of $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ nanowire superlattices with radius $R=10\mathrm{nm}$ is computed using a semiempirical $s{p}^3{d}^5{s}^{*}$ tight-binding model, taking strains, piezoelectric fields, and image charge effects into account. The electron-hole interaction is also included in the calculation of the optical properties. Strain relaxation is efficient in nanowire heterostructures, but highly inhomogeneous in thin InAs layers with thickness $t⪡R$. It digs a well in the conduction band that traps the electron at the surface of the nanowire, which might lead to its capture by nearby defects. This well disappears in thicker InAs layers that are almost completely relaxed. The strains and piezoelectric field, however, separate the electron from the hole when increasing $t$, which strongly reduces the oscillator strength of the exciton.

Figure 1

The image charge potential $\Sigma \left(r\right)$ in a nanowire with radius $R=10\mathrm{nm}$.

Figure 2

The hydrostatic strain $\delta \Omega ∕\Omega$ in 4- and $16\text{−}\mathrm{nm}$-thick InAs layers. The dots are the $\mathrm{In}∕\mathrm{Ga}$ atoms in the $\left(yz\right)$ plane of the plot. The vertical, dash-dotted lines delimit the InAs layers. The spacing between isolevel curves is 1%, the white one being $\delta \Omega ∕\Omega =0$.

Figure 3

The shear strain ${\epsilon }_{yz}$ in a $4\text{−}\mathrm{nm}$-thick InAs layer. The spacing between isolevel curves is 1%, the white one being ${\epsilon }_{yz}=0$.

Figure 4

The variation $\Delta V∕V$ of the volume of the InAs layers with reference to the free-standing case, as a function of $t∕R$. Data for $R=16$ and $20\mathrm{nm}$ are represented.

Figure 5

The piezoelectric potential $V_p\left(\mathbf{r}\right)$ in 4- and $16\text{−}\mathrm{nm}$-thick InAs layers. The spacing between isolevel curves is $10\mathrm{mV}$, the white one being $V_p\left(\mathbf{r}\right)=0$.

Figure 6

The conduction band profile $E_c\left(\mathbf{r}\right)$ in a $4\text{−}\mathrm{nm}$-thick InAs layer. The energy is measured with respect to the conduction band edge of bulk, unstrained InAs. The spacing between isolevel curves is $50\mathrm{mV}$, the white one being $E_c\left(\mathbf{r}\right)=0$.

Figure 7

The square of the highest hole (H1) and lowest electron (E1) wave functions in a $4\text{−}\mathrm{nm}$-thick InAs layer. Their energies (with respect to the valence band edge of bulk InAs) are $E\left(\mathrm{H}1\right)=-0.011\mathrm{eV}$ and $E\left(\mathrm{E}1\right)=0.946\mathrm{eV}$.

Figure 8

The square of the highest hole (H1) and lowest electron (E1) wave functions in a $16\text{−}\mathrm{nm}$-thick InAs layer. Their energies are $E\left(\mathrm{H}1\right)=-0.007\mathrm{eV}$ and $E\left(\mathrm{E}1\right)=0.593\mathrm{eV}$.

Figure 9

The exciton energy $E_0$ and Coulomb interaction energy $W$ (inset) as a function of the thickness $t$ of the InAs layers.

Figure 10

The oscillator strength $F_x$ as a function of the thickness $t$ of the InAs layers.