Multiband theory of multi-exciton complexes in self-assembled quantum dots

We report on a multiband microscopic theory of many-exciton complexes in self-assembled quantum dots. The single particle states are obtained by three methods: single-band effective-mass approximation, the multiband $\mathbf{k}\bullet \mathbf{p}$ method, and the tight-binding method. The electronic structure calculations are coupled with strain calculations via Bir-Pikus Hamiltonian. The many-body wave functions of $N$ electrons and $N$ valence holes are expanded in the basis of Slater determinants. The Coulomb matrix elements are evaluated using statically screened interaction for the three different sets of single particle states and the correlated $N$-exciton states are obtained by the configuration interaction method. The theory is applied to the excitonic recombination spectrum in InAs/GaAs self-assembled quantum dots. The results of the single-band effective-mass approximation are successfully compared with those obtained by using the of $\mathbf{k}\bullet \mathbf{p}$ and tight-binding methods.

Figure 1

Band structure of ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$ described by the eight-band $\mathbf{k}\bullet \mathbf{p}$ method (dotted lines), the tight-bindinglike effective bond-orbital method (solid lines), and the empirical $s{p}^3{s}^{*}$ tight-binding method (dashed lines).

Figure 2

Two-dimensional plot of the density of first six electron (first row) and hole (second row) wave functions calculated by the multiband $\mathbf{k}\bullet \mathbf{p}$ method.

Figure 3

Calculated energy levels of the ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$/GaAs self-assembled quantum dot by the eight-band $\mathbf{k}\bullet \mathbf{p}$ (KP) method and EBOM. Also shown are the energy levels fitted for the effective-mass approximation (EMA).

Figure 4

Addition energy spectra $\mu \left(N\right)=E_g\left(N\right)-E_g\left(N-1\right)$, calculated by the single-band effective-mass approximation (triangular dots), the multiband $\mathbf{k}\bullet \mathbf{p}$ method (circular dots) and EBOM (square dots) for the ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$/GaAs disklike quantum dot.

Figure 5

Excitonic emission spectra calculated by the single-band effective-mass method.

Figure 6

Excitonic emission spectra calculated by the multiband $\mathbf{k}\bullet \mathbf{p}$ method.

Figure 7

Excitonic emission spectra calculated by EBOM.

Figure 8

Emission spectra from three-exciton complex calculated by different methods.