Atomistic and multiband k.p approaches to model semiconductor quantum dots

Abstract:

The modeling of spectral properties of quantum dots (QDs) was the subject of many theoretical studies. The methods commonly used in such calculations can be divided into two classes. The first one contains multiband k · p models based on the continuous media approximation, and the second one involves various atomistic models.

We discuss the theoretical approaches for modeling of InAs/GaAs self-assembled quantum dots. We compare the results obtained from the 8-band k · p and the sp3d5s* tight-binding models, and show that discrepancies are primarily related to different treatment of strain in both methods. While the tight-binding Hamiltonian inherently accounts for strain nonlinearity via exponential factors, the standard k · p Bir-Pikus Hamiltonian is linear in strain tensor elements. Although the second-order scheme [1] was proposed, no parameters have been provided so far. In the present work, we find the values of the second-order deformation potentials [2], and calculate energy levels for electron and hole
confined in a QD [2, 3]. We show that in the case of the electron, the accuracy of the continuous k · p model can be greatly improved with the second-order strain model.

Importantly, the tight binding model can explicitly take atomic disorder into account. We have recently shown that such atomic disorder can have a strong effect on the radiative Auger effect in InGaAs/GaAs QDs [4]. While the optical spectrum of a quantum dot is typically dominated by the fundamental transition, the radiative Auger process results in additional red-shifted emission lines. These lines can be used to extract information on otherwise unreachable single-particle excitation energies in the QD spectrum [5]. We present measurements of such radiative Auger lines for a range of quantum dots. We show that the atomistic tight-binding model combined with the configuration-interaction approach accounts for the intensities of the Auger lines and the changes from quantum dot to quantum dot. We emphasize the role of symmetry breaking caused by the alloy disorder, which turned out to be essential for the strength of the radiative Auger lines.

The final part of the talk will be devoted to GeSn QDs modeled in the atomistic way. We systematically study the interplay of Sn-driven indirect-direct band-gap transition and the quantum confinement effect in systems of reduced dimensionality [6]. We demonstrate the regime of sizes and compositions, where the ground state in GeSn quantum dot is optically active.

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[2] K. Gawarecki and M. Zieliński, Phys. Rev. B 100, 155409 (2019).
[3] P. Podemski, A. Musiał, K. Gawarecki, A. Maryński, P. Gontar, A. Bercha, W. Trzeciakowski, N. Srocka, T. Heuser, D. Quandt, A. Strittmatter, S. Rodt, S. Reitzenstein, G. Sęk, Appl. Phys. Lett. 116, 023102 (2020)
[4] K. Gawarecki, C. Spinnler, L. Zhai, G. N. Nguyen, A. Ludwig, R. J. Warburton, M. C. Löbl, D. E. Reiter, P. Machnikowski, Phys. Rev. B 108 (2023) 235410.
[5] M. C. Löbl, C. Spinnler, A. Javadi, L. Zhai, G. N. Nguyen, J. Ritzmann, L. Midolo, P. Lodahl, A. D. Wieck, A. Ludwig, and R. J. Warburton, Nat. Nanotechnol. 15, 558 (2020).
[6] K. Gawarecki, J. Ziembicki, P. Scharoch, R. Kudrawiec, arXiv:2311.18682 (2023)