Optical polarization in columnar InAs/GaAs quantum dots: 8-bandk⋅pcalculations

Abstract

We have theoretically studied the optical polarization in columnar InAs/GaAs quantum dots (QDs), in which the self-assembled QDs are vertically stacked with no interdot spacing. The model structure of the columnar QDs consists of truncated-cone-shaped InAs QDs with the stacking-layer numbers (SLNs) of 1, 3, 5, 7, and 9. We used the valence-force-field model to calculate the strain distribution. We find that the biaxial strain in the middle layers of the columnar QDs decreases with increasing SLN and becomes negative for $\text{SLN}=9$. This is due to the condition that the vertical lattice constant of InAs in these layers has to match that of the side GaAs. By using the strain-dependent 8-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory for the electronic states, we calculated the transverse-electric (TE)- and transverse-magnetic (TM)-mode intensities for the electron-hole transitions. The piezoelectric effect is included in the calculations. For $\text{SLN}=1$ and 3, only the TE-mode transition occurs. With increasing SLN beyond 3, the TM-mode intensity increases while the TE-mode one decreases. Consequently, when SLN changes from 7 to 9, the dominant polarization character changes from the TE mode to the TM mode. This dominant polarization change is attributed to the increase of the light-hole character in the wave function of the ground hole state, which is the consequence of the negative biaxial strain in the middle layers for $\text{SLN}=9$. The change in the optical polarization calculated in this study is in good agreement with the photoluminescence experiment reported by Kita et al. [Jpn. J. Appl. Phys., Part 2 41, L1143 (2002)].