Quantum dots and tunnel barriers in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures: Electronic and optical properties

We compute the structural and electronic properties of ⟨111⟩-oriented $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures using Keating’s valence force field and a tight-binding model. We focus on the optical properties (exciton energies and polarization) of InAs quantum dots embedded in InP nanowires and on the height of InP and InAsP tunnel barriers embedded in InAs nanowires. We show that InAs quantum dots exhibit bright optical transitions, at variance with the highly mismatched $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ nanowire heterostructures. The polarization of the photons is perpendicular to the nanowire for thin InAs layers but rotates parallel to the nanowire for thick enough ones, as a result of the increasing light-hole character of the exciton. As for tunnel barriers, we show that the residual strains can significantly reduce the conduction band discontinuity in thin InAsP layers. This must be taken into account in the design of nanowire tunneling devices.

Figure 1

(Color online) The strain ratio ${\rho }_{\text{strain}}$ as a function of $t_{\mathrm{In}\mathrm{As}}∕R$ in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ and $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures. The dashed line is Eq. (2).

Figure 2

(Color online) The piezoelectric potential in an $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ quantum well $(t_{\mathrm{In}\mathrm{As}}=4\mathrm{nm})$ and along the axis of $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire (NW) heterostructures ($R=10\mathrm{nm}$, $t_{\mathrm{In}\mathrm{As}}=4$ and $16\mathrm{nm}$). The vertical dash-dotted lines delimit the InAs layers.

Figure 3

(Color online) Single-electron (a) and single-hole (b) energies in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures with radius $R=10\mathrm{nm}$. Circles (stars) are single-particle states with symmetry $E_{1∕2}$ $\left(E_{3∕2}\right)$. The lines are just guides to the eyes. The valence band structure down to $E\simeq -0.1\mathrm{eV}$ has been computed for $t_{\mathrm{In}\mathrm{As}}=4$, 8, 12, and $16\mathrm{nm}$.

Figure 4

(Color online) Isoprobability surfaces of selected electron wave functions in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures ($R=10\mathrm{nm}$, $t_{\mathrm{In}\mathrm{As}}=4$ and $16\mathrm{nm}$) (Refs. 57, 58). Only one quarter of the nanowire is shown for clarity. As atoms appear in dark gray (in red in the color online figure).

Figure 5

(Color online) Isoprobability surfaces of the ground-state hole wave function in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures ($R=10\mathrm{nm}$, $t_{\mathrm{In}\mathrm{As}}=4$ and $16\mathrm{nm}$). Only one quarter of the nanowire is shown for clarity. As atoms appear in dark gray (in red in the color online figure).

Figure 6

(Color online) Exciton energies $E_0$ in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures with radii $R=10$ and $R=16\mathrm{nm}$ and in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterostructures with radius $R=10\mathrm{nm}$. Inset: exciton Coulomb energies $W$.

Figure 7

(Color online) Perpendicular (a) and parallel (b) E1H1 oscillator strengths in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures with radii $R=10$ and $R=16\mathrm{nm}$ and in $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterostructures with radius $R=10\mathrm{nm}$.

Figure 8

(Color online) Oscillator strength spectrum (parallel and perpendicular polarizations) of $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures with $R=10\mathrm{nm}$ and $t_{\mathrm{In}\mathrm{As}}=4\mathrm{nm}$.

Figure 9

(Color online) Oscillator strength spectrum (parallel and perpendicular polarizations) of $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures with $R=10\mathrm{nm}$ and $t_{\mathrm{In}\mathrm{As}}=16\mathrm{nm}$.

Figure 10

(Color online) Polarization ratio as a function of the temperature $T$ for $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures with $R=10\mathrm{nm}$ and $t_{\mathrm{In}\mathrm{As}}=4$, 8, and $16\mathrm{nm}$, with [solid (red) line] and without [dotted (blue) line] local-field effects.

Figure 11

(Color online) Conduction band energy $E_c\left(\mathbf{r}\right)$ in an $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructure with $R=10\mathrm{nm}$ and $t_{\mathrm{In}\mathrm{P}}=4\mathrm{nm}$. $E_c$ is measured with respect to the conduction band edge of bulk unstrained InAs. The dots are the $\mathrm{As}∕\mathrm{P}$ atoms in the $\left(yz\right)$ plane of the plot. The vertical dash-dotted lines delimit the InP layer. The spacing between isolevel curves is $50\mathrm{meV}$, the white dashed line being $E_c=0$ and the white solid line $E_c=0.5\mathrm{eV}$.

Figure 12

(Color online) Effective potential $V_c\left(z\right)$ in an $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ NWHET with radius $R=10\mathrm{nm}$. The bulk and 2D barrier heights are reported in the figure. The vertical dotted lines delimit the $16\mathrm{nm}$ thick InP layer, and the arrows point to the small barrier that appears on each side in InAs.

Figure 13

(Color online) Conduction band barrier height ${\Delta }_c^{\mathrm{str}}$ in $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ nanowire heterostructures as a function of $t_{\mathrm{In}\mathrm{P}}∕R$. The bulk and 2D barrier heights are reported in the figure. The dashed line is Eq. (13).

Figure 14

(Color online) Normalized conduction band barrier height ${\Delta }_c^{\mathrm{str}}∕{\Delta }_c^{\text{bulk}}\left(x\right)$ in $\mathrm{In}\mathrm{As}∕\mathrm{In}{\mathrm{As}}_x{\mathrm{P}}_{1-x}$ nanowire heterostructures as a function of $t_{\mathrm{In}\mathrm{As}\mathrm{P}}∕R$ for various As mole fractions $x$ $(R=10\mathrm{nm})$. The bulk and 2D $(x=1)$ barrier heights are reported in the figure. The dashed line is Eq. (13).