Excitonic effects in the photoinduced conduction intersubband transitions in undoped quantum wells

We study the effects of excitons and their optical excitation or radiative decay in the photoinduced conduction intersubband transitions of undoped quantum wells. We show that the excitonic effects, in general, can strongly influence these transitions by making their dipole moments strongly dependent on the hole subband dispersions and quantum well strain. This allows spinor mixing of a hole subband to significantly suppress a photoinduced intersubband transition when this subband is strongly nonparabolic and/or is about to crossover another subband. Compared to those happening in the absence of any interband transition, however, we show that when the photoinduced intersubband transitions are accompanied with the optical excitation or radiative decay of excitons (excitonic interband transitions) their electric dipole moments can suffer an additional suppression. We attribute this effect to the influence of the correlation between the electron and hole positions in the photoinduced intersubband transitions and the way it depends on the excitonic interband transitions. In all cases, however, our results suggest that ignoring the effects of excitons in the conduction intersubband transitions of undoped quantum wells, i.e., considering only electron wave functions, could lead to an unrealistic overestimation of their dipole moments.

Figure 1

(a) Schematic illustration of the square QW structures considered in this paper; (b) and (c) represent the PI ISTs associated with the excitons in the presence and absence of excitonic interband transitions, respectively. The one-sided arrows refer to the ISTs and the two-sided one to the optical excitation or radiative decay processes of the excitons.

Figure 2

Normalized dipole moments of the PI-ISTs associated with the transitions between the $1s$ states of the $\mathrm{e}1\text{−}\mathrm{hh}1$ and $\mathrm{e}2\text{−}\mathrm{hh}1$ excitons. Squares refer to the PI ISTs associated with nonactive $\mathrm{e}1\text{−}\mathrm{hh}1$ excitons $({\mu }_{\mathrm{hh}1}^{\mathrm{nact}}∕e)$ and triangles to those associated with excitons that are being optically excited or decaying radiatively $({\mu }_{\mathrm{hh}1}^{\mathrm{act}}∕e)$. The dots refer to the dipole moments associated with the $\mathrm{e}1\text{−}\mathrm{e}2$ transitions excluding any excitonic effect $({\mu }_{12}^{\mathrm{ele}}∕e)$.

Figure 3

Normalized dipole moments of the PI-ISTs associated with the transitions between the $1\mathrm{s}$ states of the $\mathrm{e}1\text{−}\mathrm{lh}1$ and $\mathrm{e}2\text{−}\mathrm{lh}1$ excitons. Here squares refer to ${\mu }_{\mathrm{lh}1}^{\mathrm{nact}}∕e$, and triangles to ${\mu }_{\mathrm{lh}1}^{\mathrm{act}}∕e$. All other specifications are similar to those in Fig. 2.

Figure 4

Dipole moment mixing factors of the $\mathrm{e}1\text{−}\mathrm{hh}1$ to $\mathrm{e}2\text{−}\mathrm{hh}1$ PI ISTs associated with active (a) and nonactive excitons (b) for $x=0.25$. Dots refer to $L=5\mathrm{nm}$ and circles to $L=11\mathrm{nm}$. $a$ refers to the lattice constant of the ${\mathrm{In}}_{0.75}{\mathrm{Ga}}_{0.25}\mathrm{As}$ QW.

Figure 5

Band structure of a 5 nm ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x\mathrm{As}$ QW structure with InP barrier for $x=0.25$ (a), 0.42 (b), 0.59 (c) and 0.75 (d).

Figure 6

Dipole moment mixing factors for a 5 nm ${\mathrm{In}}_{0.41}{\mathrm{Ga}}_{0.59}\mathrm{As}$ QW structure with InP barrier. (a) refers to the PI ISTs associated with the $\mathrm{e}1\text{−}\mathrm{hh}1$ excitons that are either optically excited or decaying radiatively and (b) refers to the case where these excitons are nonactive.

Figure 7

(a) Band structure of a 11 nm ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ QW structure with InP barrier. (b) and (c) refer, respectively, to $I_{2,\mathrm{hh}1}^{\nu }$ and $I_{2,\mathrm{lh}1}^{\nu }$.