Lateral confinement and band mixing in ultrathin semiconductor quantum wells with steplike interfaces

We study theoretically the effects of lateral confinement on the electronic structure of strained ultrathin $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ (001) quantum wells (QWs) with one-dimensional (wirelike) interface islands. We develop a theoretical approach allowing the efficient computational treatment of a large class of one-dimensional structures within the framework of the surface Green’s-function matching formalism. Using the semiempirical $s{p}^{3}s*$ nearest-neighbor tight-binding model, we calculate the energies, spatial distributions, and orbital character of electronic states for islands oriented along the ⟨010⟩ and ⟨110⟩ directions. The presence of the interface steps gives rise to localized states and leads to a band-gap reduction and an increase of the splitting between heavy holes (HH) and light holes (LH). We observe significant changes in the orbital character of both localized and extended (QW) states, namely a large anisotropy of the in-plane $p$ components in all subbands and an increase of the $p_z$ contribution to HH states. The valence-band structure depends strongly on the wire orientation. In ⟨110⟩-oriented islands, the HH-LH mixing is significantly enhanced by the lateral potential, whereas in ⟨010⟩ structures there is no evidence for such enhancement. The observed effects influence the optical properties of the structures and may cause optical anisotropy, relax some of the selection rules, and enhance the oscillator strengths for both interband and intersubband transitions.

Figure 1

A schematic plot of the structures under study. The QW interfaces are shown with a solid line, and principal layers are plotted with a dashed line. $A$ and $B$ denote principal layers containing QWs with different thicknesses. The structures are periodic in the direction perpendicular to the plot.

Figure 2

Principal layer representation of the structures from Fig. 1. Each symbol represents a principal layer. $A$ and $B$ are the domains containing narrower (wider) QWs, respectively. The two interface domains and the four interface layers are shown with the corresponding notation.

Figure 3

(Color online) Dependence of the conduction-band bound state energies on the wire width $L_{\mathrm{WR}}$ for ⟨010⟩ and ⟨110⟩ wire orientations. The energy of the conduction-band ground states of the 2 and $3\mathrm{ML}$ QWs is shown with horizontal lines at $1.333\mathrm{eV}$ and $1.286\mathrm{eV}$, respectively.

Figure 4

Spatial distribution of the conduction-band states in ⟨110⟩ wires: (a) first localized state, (b) second localized state, (c) extended state, and (d) quasilocalized state. The $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ interfaces are shown with a solid line; the wire widths and the energies of the states are shown next to each figure. The intensity scale is linear, the DOS of the extended states (c) and (d) is multiplied by 8 in order to achieve a contrast level comparable to that of the bound states (a) and (b).

Figure 5

(Color online) Contributions of the $s$, $p_{\perp }$, and $p_{\Vert }$ orbitals to the conduction-band local DOS in the principal layers adjacent to the interface terraces. Lines connect symbols corresponding to states with the same index (first, second, etc.) and wire orientation, but different wire widths. The energy of the $2\mathrm{ML}$ QW conduction- band edge $\left(1.333\mathrm{eV}\right)$ is shown with a vertical line.

Figure 6

(Color online) Dependence of the valence-band states energies on the wire width $L_{\mathrm{WR}}$ for ⟨010⟩ and ⟨110⟩ wire orientations. The energies of the HH and LH ground states of the 2 and $3\mathrm{ML}$ QWs are shown with horizontal lines and the four energy regions are marked with numbers at the right side of the graph (see the text for explanation).

Figure 7

(Color online) Orbital contributions to the local DOS of the HH states at the principal layers adjacent to the interface terraces: (a) $p_{\perp }$ and $p_{\Vert }$ orbitals, (b) $p_z$ orbital. Symbols corresponding to states with the same index (first, second, etc.) and wire orientation, but different wire widths, are connected with lines. The energy of the HH band edge of the $2\mathrm{ML}$ QW $\left(0.118\mathrm{eV}\right)$ is shown with a vertical line.

Figure 8

Valence-band local density of states in the InAs layer for ⟨010⟩ (right) and ⟨110⟩ (left) wires. The wires start from monolayer index 1. The intensity scale is linear. The DOS is normalized to the unit area of the wire cross section.

Figure 9

Variation of the local DOS in the InAs layer for the first LH state for ⟨110⟩ (a) and ⟨010⟩ (b) wires. The curves are shifted horizontally for clarity; the zero of each curve is shown with a horizontal line on the left-hand side of the graphs. The wire widths are shown at the right side of the graphs in monolayers (ML for ⟨010⟩ and $\sqrt{2}\mathrm{ML}$ for ⟨110⟩). The vertical dashed line shows the left interface of the wire.

Figure 10

Schematic plot of (001) $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ QWs grown on misoriented substrates. The $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}$ interfaces are shown with a solid line. The principal layers corresponding to the three different domains $A^{\prime }$, $B$, and $A$ are shown with a dashed line.