Dependence of the electronic structure of self-assembled (In,Ga)As∕GaAs quantum dots on height and composition

Abstract

While electronic and spectroscopic properties of self-assembled In1−xGaxAs/GaAs dots depend on their shape, height and alloy compositions, these characteristics are often not known accurately from experiment. This creates a difficulty in comparing measured electronic and spectroscopic properties with calculated ones. Since simplified theoretical models (effective mass, k·p, parabolic models) do not fully convey the effects of shape, size and composition on the electronic and spectroscopic properties, we offer to bridge the gap by providing accurately calculated results as a function of the dot height and composition. Prominent features of our results are the following. (i) Regardless of height and composition, the confined electron energy levels form shells of nearly degenerate states with a predominant orbital "s", "p", · · · character. In contrast, the confined hole energy levels form shells only in flat dots and near the highest hole level (HOMO). (ii) In alloy dots, the electrons' "s-p" splitting depends weakly on height, while the "p-p" splitting depends non-monotonically-due to alloy fluctuations. In pure, non-alloyed InAs/GaAs dots, both these splittings depend weakly on height. Further, the "s-p" splitting is larger while the "p-p" has nearly the same magnitude. For holes levels in alloy dots, the "s-p" splitting decreases with increasing height (the splitting in tall dots being about 4 times smaller than in flat dots), whereas the "p-p" splitting remains nearly unchaged. Shallow, pure non-alloyed dots have a "s-p" splitting of nearly the same magnitude, whereas the "p-p" splitting is about three times larger. (iii) As height increases, the "s" and "p" character of the wavefunction of the HOMO becomes mixed, and so does the heavy-and light-hole character. (iv) In alloy dots, regardless of height, the wavefunction of low-lying hole states are localized inside the dot. Remarkably, in non-alloyed InAs/GaAs dots these states become localized at the interface as height increases. The localized states are nearly degenerate and polarized along [110] and [110]. This localization is driven by the peculiarities of the biaxial strain present in the nanostructure.

Carrier relaxation mechanisms in self-assembled(In,Ga)As∕GaAsquantum dots: EfficientNarvaez1, Bester2, Zunger3 2006Phys. Rev. BSelf Cite

“…Therefore, inter-shell relaxation via single-phonon emission due to electron-phonon coupling (within the Born-Oppenheimer adiabatic approximation) is expected to be ineffective-20,21 the phonon-bottleneck effect-because energy cannot be conserved in the inter-shell relaxation process. Finally, hole states do not form shells, with exception of flat dots 22 (height of about 20Å), and the splitting between hole states is about 1-20 meV, thus comparable to acoustic phonon frequencies. Given these general characteristics, the main electron-and hole-relaxation channels within the dot are:…”

Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements

“…As the size of the QD is decreased, the electron will penetrate deeper into the barrier than the hole, thus reducing the overlap. 24 The detailed understanding of how the size affects the overlap between the electron and hole wavefunctions is crucial in order to optimally tailor QDs for efficient coupling to light. The observed energy dependence of the oscillator strength is compared to a simple effective-mass QD model.…”

Multiple charging ofInAs∕GaAsquantum dots by electrons or holes: Addition energies and ground-state configurations

“…For even taller QDs (e.g., height/base > 5/25 nm), the large biaxial strain will develop a "hole trap" at the InAs/GaAs interface, which lead to the hole localization on the interface of the dots. 31,43 In these cases, where the hole (envelope) wave functions are totally different from those predicted by 2D-EMA model, the relationship between Coulomb and exchange energies are, accordingly, very different from those of 2D-EMA model.…”

“…For example, as shown in Ref. 43, for a InGaAs/GaAs alloy dot, with 25.2 nm in base and 2 nm in height, s level has 90% S character, while both p 1 and p 2 levels have 84% P character. When the height of the dot increases to 7.5 nm (with fixed base size), the leading angular momentum characters for these three levels are 84% S, 78% P and 75 % P respectively.…”