Optical anisotropies of asymmetric double GaAs (001) quantum wells

In the present work, we were able to identify and characterize a source of in-plane optical anisotropies (IOAs) occurring in asymmetric double quantum wells (DQWs), namely a reduction of the symmetry from $D_{2d}$ to $C_{2v}$ as imposed by asymmetry along the growth direction. We report on reflectance anisotropy spectroscopy (RAS) of double GaAs quantum well structures coupled by a thin ($<2$ nm) tunneling barrier. Two groups of DQW systems were studied: one where both QWs have the same thickness (symmetric DQW) and another where they have different thicknesses (asymmetric DQW). RAS measures the IOAs arising from the intermixing of the heavy and light holes in the valence band when the symmetry of the DQW system is lowered from $D_{2d}$ to $C_{2v}$. If the DQW is symmetric, residual IOAs stem from the asymmetry of the QW interfaces, e.g., that associated with Ga segregation into the AlGaAs layer during the epitaxial growth process. In the case of an asymmetric DQW with QWs with different thicknesses, the AlGaAs layers (that are sources of anisotropies) are not distributed symmetrically at both sides of the tunneling barrier. Thus the system loses its inversion symmetry, yielding an increase in the RAS strength. The RAS line shapes were compared with reflectance spectra in order to assess the heavy- and light-hole mixing induced by the symmetry breakdown. The energies of the optical transitions were calculated by numerically solving the one-dimensional Schrödinger equation using a finite-difference method. Our results are useful for interpretation of the transitions occurring in both symmetric and asymmetric DQWs.

Figure 1

Monochromatic light coming from a tungsten lamp is focused onto the (001) surface of the DQW structures. The angle of incidence is approximately $4^{\circ }$. RAS spectra were obtained by taking the difference between the reflectance for ${\widehat{e}}_1$ and ${\widehat{e}}_2$ light polarizations. The experiments were performed at 30 K. Thicknesses $d_1$ and $d_2$ for the samples used in this work are listed in Table 1.

Figure 2

Probability density functions (left panel) and confinement energies (right panel) for (a) sample S1 (symmetric DQW) and (b) sample A2 (asymmetric DQW).

Figure 3

RAS spectra for the (a),(b) asymmetric and (c) symmetric DQWs. The dashed vertical line indicates the expected energy of the excitonic transition of the GaAs substrate. Above this energy, the optical transitions come from the DQWs. The inset shows the PL spectra measured for each sample. Two peaks can be identified in each spectrum, a larger one associated with the transition $e1$-hh1 and a much smaller one associated with the $e1$-lh1 [for spectrum (b) this peak is observed as a shoulder]. The energies obtained from the PL spectra are indicated by the arrows in the RAS spectra. Note that the structures associated with $e1$-hh1 and $e1$-lh1 increase their strength when the DWQs become more asymmetric. The RAS spectra were measured at 30 K.

Figure 4

Reflection anisotropy (RAS, open and closed circles) and differential reflection (DR, solid line) spectra for asymmetric DQWs A2 and A3, grown on an AlGaAs $n$-type and $p$-type layer, respectively. Note that while the heavy-hole transitions ($e1$-hh1 and $e2$-hh2) in the RAS and DR spectra have the same concavity, for the light-hole transitions ($e1$-lh1 and $e2$-lh2) the concavities are opposite, and DR spectra show the highest level transitions. The bottom arrows point to the experimental transitions for the two first levels, whereas the top arrows show the calculated energies to three energy levels. The RAS and DR spectra were measured at 30 K.