[Paper Review] Biexciton recombination rates in self-assembled quantum dots

Michael Wimmer, Selvakumar V. Nair+1 more|University of Regensburg Publication Server (University of Regensburg)|Dec 23, 2005

Semiconductor Quantum Structures and Devices1 references4 citations

TL;DR

This paper develops a Feynman path-integral Monte Carlo method to calculate radiative recombination rates of biexcitons in self-assembled quantum dots, accounting for many-body correlations and thermal effects. It finds that typical dots lie in the strong-to-intermediate confinement regime, predicting a relative biexciton decay rate ΓXX/ΓX ≈ 1.5–2, which explains experimental observations and shows that configuration interaction methods with uncorrelated basis sets fail for absolute rates despite capturing trends.

ABSTRACT

The radiative recombination rates of interacting electron-hole pairs in a quantum dot are strongly affected by quantum correlations among electrons and holes in the dot. Recent measurements of the biexciton recombination rate in single self-assembled quantum dots have found values spanning from two times the single exciton recombination rate to values well below the exciton decay rate. In this paper, a Feynman path-integral formulation is developed to calculate recombination rates including thermal and many-body effects. Using real-space Monte Carlo integration, the path-integral expressions for realistic three-dimensional models of InGaAs/GaAs, CdSe/ZnSe, and InP/InGaP dots are evaluated, including anisotropic effective masses. Depending on size, radiative rates of typical dots lie in the regime between strong and intermediate confinement. The results compare favorably to recent experiments and calculations on related dot systems. Configuration interaction calculations using uncorrelated basis sets are found to be severely limited in calculating decay rates.

Motivation & Objective

• To develop a microscopic many-body method for calculating radiative recombination rates in self-assembled quantum dots.
• To resolve discrepancies in experimental measurements of biexciton decay rates relative to single exciton rates.
• To assess the limitations of configuration interaction (CI) methods using uncorrelated single-particle basis sets in predicting absolute decay rates.
• To determine the confinement regime (strong to intermediate) in which typical quantum dots operate based on correlation effects.
• To provide a reliable theoretical framework for interpreting time-resolved photoluminescence experiments on single quantum dots.

Proposed method

• A Feynman path-integral formulation is used to include thermal and many-body effects in recombination rate calculations.
• Real-space Monte Carlo integration is applied to evaluate path-integral expressions for realistic 3D models of InGaAs/GaAs, CdSe/ZnSe, and InP/InGaP quantum dots.
• The method incorporates anisotropic effective masses and treats electron-hole correlations beyond mean-field approximations.
• The approach is applied to lens-shaped self-assembled quantum dots with realistic potential profiles and material parameters.
• Results are compared with experimental data and with configuration interaction (CI) calculations using uncorrelated basis sets.
• The formalism naturally includes thermal distributions of carriers and is extendable to indirect bandgap semiconductors.

Experimental results

Research questions

• RQ1 What is the correct theoretical description of biexciton recombination rates in self-assembled quantum dots, accounting for electron-hole correlations and thermal effects?
• RQ2 Why do experimental measurements of ΓXX/ΓX vary so widely, from 0.33 to 2, and can this be explained by intrinsic dot properties?
• RQ3 To what extent do configuration interaction methods with uncorrelated basis sets fail in predicting absolute recombination rates, despite capturing qualitative trends?
• RQ4 In which confinement regime—strong, intermediate, or weak—do typical self-assembled quantum dots operate, based on recombination dynamics?
• RQ5 How do many-body correlations and the coherence volume of the many-particle wave function influence the relative biexciton decay rate?

Key findings

• The path-integral Monte Carlo method successfully calculates recombination rates in realistic 3D quantum dot models with anisotropic effective masses and many-body correlations.
• Typical self-assembled quantum dots operate in the strong-to-intermediate confinement regime, where Coulomb correlations become significant.
• The relative biexciton decay rate ΓXX/ΓX is predicted to lie in the range of 1.5 to 2, consistent with many experimental observations.
• Configuration interaction methods using uncorrelated basis sets severely underestimate absolute decay rates, even with large basis sets (e.g., 44 states), though they reproduce qualitative trends.
• The cancellation of errors in CI calculations leads to a relative decay rate close to the path-integral result, despite poor absolute accuracy.
• The observed low relative decay rates (e.g., ΓXX/ΓX ≈ 0.33) in some experiments cannot be explained by weak confinement, but rather require strong correlation effects.