Heavy-hole–light-hole exciton system in GaAs/AlGaAs quantum wells

Light-hole (lh) excitons (Xlhs) in quantum wells (QWs) are hardly studied compared with heavy-hole (hh) excitons (Xhhs), mainly due to the difficulties of their experimental observation. In this paper, a comprehensive study of both types of excitons in high-quality GaAs/AlGaAs QWs of different widths is performed. We focus on the energy positions of exciton resonances and the exciton-light interaction. The effect of mixing lhs and hhs in GaAs-based structures on these exciton characteristics is investigated. The corrections to the exciton energy due to mixing are only a fraction of millielectronvolts for wide QWs, in which the energy levels of Xhhs and Xlhs are close to each other. It is also experimentally found that the oscillator strength of Xlhs is $\sim 2.5$ times less than that of Xhhs. This value noticeably deviates from the 3:1 oscillator strength ratio known for optical transitions between free electron and hole states. This deviation originates from the different squeezing of the Xlh and Xhh wave functions due to distinct values of the effective masses of the Xlh and Xhh in the heterostructure. Mixing of hh and lh valence bands is not so important.

Figure 1

Reflectance spectrum of heterostructure T844 with the 20, 30, and 40 nm $\mathrm{GaAs}/{\mathrm{Al}}_{0.16}{\mathrm{Ga}}_{0.84}\mathrm{As}$ quantum wells (QWs; points) and its fit by Eqs. (2) and (3) (solid curve). Labels Xhh and Xlh mark the lowest quantum-confined exciton states of heavy-hole and light-hole excitons, respectively, in each QW. Dashed lines divide regions with Xhh and Xlh resonances for 40, 30, and 20 nm QWs.

Figure 2

Structure T846 with 22, 33, and 55 nm $\mathrm{GaAs}/{\mathrm{Al}}_{0.13}{\mathrm{Ga}}_{0.87}\mathrm{As}$ quantum wells (QWs). In addition to the main resonances Xhh1 and Xlh1, several, less intense resonances Xhhk are identified with the use of the microscopic modeling (Sec. 3a). Colors mark resonances belonging to different QWs: orange for the 55 nm QW, yellow for the 33 nm QW, and blue for the 22 nm QW.

Figure 3

Energies of the heavy-hole (Xhh) and light-hole (Xlh) excitons. Symbols are the experimental data taken from Figs. 1 and 2. Solid curves are the numerical calculations. $E_g=1519.4$ meV [31].

Figure 4

Differences of exciton energies as functions of the quantum well (QW) width. The value $dX=X_{\text{coupl}}-X_{\text{no}}$ is calculated as the difference between the exciton energy with coupling accounted and the energy of the uncoupled exciton state.

Figure 5

(a) Effect of exciton coupling on the Xhh and Xlh decay rates. (b) Ratio of the radiative decay rates for the Xhh and Xlh calculated in different approaches.

Figure 6

Cross-sections of the envelope wave functions of the (a) Xhh and (b) Xlh in a 40 nm quantum well (QW) in coordinates $z_{eh}=z_e-z_h$ and $x_{eh}=x_e-x_h$. Axis $x$ is directed along the QW layer. The center of mass of the excitons is in the middle of the QW. (c) Mean electron-hole distances in the $z$ and $x$ directions for the Xhh and Xlh for different QW widths.

Figure 7

(a) Radiative broadening constants $\hslash {\mathrm{\Gamma }}_0$ for the heavy-hole (Xhh) and light-hole (Xlh) excitons (the lowest quantum-confined states) as functions of the quantum well (QW) width. (b) Ratio of the radiative constants for the Xhh and Xlh. Solid lines are the microscopic modeling (simplified approach). Symbols are the experimental data. The data obtained for other structures with the 14 and 20 nm QWs are also shown.