Modeling of Quantum Dots with the Finite Element Method

Mantashian, Grigor A.; Mantashyan, Paytsar; Hayrapetyan, D. B.

doi:10.3390/computation11010005

Cited by 16 publications

(11 citation statements)

References 76 publications

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“…Structures employing QDs as the intermediate band include InAs/GaAs, GaAs/AlGaAs, and InAs/AlGaAs [27][28][29][30]. QDs with pyramidal, spherical, and cylindrical shapes have demonstrated improved light absorption and efficiency [31][32][33]. Among these, cylindrical QDs exhibit less sensitivity to incident light angles than other dot shapes, resulting in minimal changes and higher absorption rates [2,34].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Investigation and Improvement of Characteristics of InAs/GaAs Quantum Dot Intermediate Band Solar Cells by Optimizing Quantum Dot Dimensions

Farhadipour,

Olyaee,

Kosarian

2024

Symmetry

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Quantum dot (QD)-based solar cells have been the focus of extensive research. One of the critical challenges in this field is optimizing the size and placement of QDs within the cells to enhance light absorption and overall efficiency. This paper theoretically investigates InAs/GaAs QD intermediate band solar cells (QD-IBSC) employing cylindrical QDs. The goal is to explore factors affecting light absorption and efficiency in QD-IBSC, such as the positioning of QDs, their dimensions, and the spacing (pitch) between the centers of adjacent dots. Achieving optimal values to enhance cell efficiency involves modifying and optimizing these QD parameters. This study involves an analysis of more than 500 frequency points to optimize parameters and evaluate efficiency under three distinct conditions: output power optimization, short-circuit current optimization, and generation rate optimization. The results indicate that optimizing the short-circuit current leads to the highest efficiency compared to the other conditions. Under optimized conditions, the efficiency and current density increase to 34.3% and 38.42 mA/cm², respectively, representing a remarkable improvement of 15% and 22% compared to the reference cell.

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Section: Introductionmentioning

confidence: 99%

Theoretical Investigation and Improvement of Characteristics of InAs/GaAs Quantum Dot Intermediate Band Solar Cells by Optimizing Quantum Dot Dimensions

Farhadipour,

Olyaee,

Kosarian

2024

Symmetry

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“…One of the powerful numerical methods for calculating the electronic structure of QDs is the finite element method (FEM), a method for solving equations that approximates continuous quantities as a collection of discrete quantities at regular intervals to form a grid or mesh [33][34][35][36]. FEM is one of the most effective numerical tools that may be utilized for this aim.…”

Section: Introductionmentioning

confidence: 99%

“…This approach allows us to solve the eigenvalue problem quickly and efficiently for QDs with complex morphological and potential profiles without needing a supercomputer or computing cluster. The authors of [33] utilized FEM to calculate the first twenty-six probability densities and energy values for the following GaAs structures: rectangular, spherical, cylindrical, ellipsoidal, spheroidal, and conical QDs, as well as quantum rings, nanotadpoles, and nanostars. The authors' numerical calculations were compared to the exact analytical solutions, and a good divergence was found.…”

Section: Introductionmentioning

confidence: 99%

Optical Properties of Conical Quantum Dot: Exciton-Related Raman Scattering, Interband Absorption and Photoluminescence

et al. 2023

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The current work used the effective mass approximation conjoined with the finite element method to study the exciton states in a conical GaAs quantum dot. In particular, the dependence of the exciton energy on the geometrical parameters of a conical quantum dot has been studied. Once the one-particle eigenvalue equations have been solved, both for electrons and holes, the available information on energies and wave functions is used as input to calculate exciton energy and the effective band gap of the system. The lifetime of an exciton in a conical quantum dot has been estimated and shown to be in the range of nanoseconds. In addition, exciton-related Raman scattering, interband light absorption and photoluminescence in conical GaAs quantum dots have been calculated. It has been shown that with a decrease in the size of the quantum dot, the absorption peak has a blue shift, which is more pronounced for quantum dots of smaller sizes. Furthermore, the interband optical absorption and photoluminescence spectra have been revealed for different sizes of GaAs quantum dot.

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“…Additionally, the authors used FEM to study the diffusion effects on the potential depth of spherical CdSe/CdS quantum dots and obtained results consistent with experimental data. Overall, FEM allows for a detailed analysis of the electronic properties of QDs with complex geometries, providing valuable insights for the design and optimization of QDbased devices 52 .…”

Section: Introductionmentioning

confidence: 99%

The contribution of edge number on the optical properties in ZnO pyramidal quantum dots

Mantashyan

2023

Quantum Optics and Photon Counting 2023

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Considerable advances in the growth process of quantum dots with non-trivial geometries have been obtained. These advances lead to countless applications in quantum optics, quantum information, and biophysics. However, the theoretical investigation of these objects is complex and analytically impossible in most cases. The investigation of pyramidal or conical quantum dots with a comparable height-to-base ratio is one of those problems. That is why the numerical finite element method in the framework of the envelope function approximation has been used to obtain the eigenvalues and eigenfunctions for ZnO pyramidal and conical quantum dots. The mesh domains required for the finite element method calculation were pyramidal domains with bases ranging from an equilateral triangle to an equilateral decagon. Cones were used for the approximation of the mesh objects for pyramidal quantum dots with a larger number of edges. Different head radius to height ratios (½, 1, 2, 3, 4) were considered. The optical transition energies were shown to decrease with the increase in the number of faces. The optical transition strengths were shown to exhibit the opposite behavior. The interband absorption curves generally exhibit a redshift with the increase in the number of edges.

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Modeling of Quantum Dots with the Finite Element Method

Cited by 16 publications

References 76 publications

Theoretical Investigation and Improvement of Characteristics of InAs/GaAs Quantum Dot Intermediate Band Solar Cells by Optimizing Quantum Dot Dimensions

Theoretical Investigation and Improvement of Characteristics of InAs/GaAs Quantum Dot Intermediate Band Solar Cells by Optimizing Quantum Dot Dimensions

Optical Properties of Conical Quantum Dot: Exciton-Related Raman Scattering, Interband Absorption and Photoluminescence

The contribution of edge number on the optical properties in ZnO pyramidal quantum dots

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