Nano Science and Technology Institute

R&D Profile: InGaAs/GaAs Quantum Dots under Effective and Ab Initio Treatments: Comparison and Results, B. Vlahovic, North Carolina Central University, US

The Computational and Theoretical NanoScience group at North Carolina Central University develops effective numerical models and methods for accurate simulations of electronic and optical properties of nanostructures to aid in the experimental design of nanomaterials with properties tailored for specific device applications.

Research Overview Courtesy of Branislav Vlahovic, who is the Research Leader of the CREST Computational & Theoretical NanoScience group at the North Carolina Central University (NCCU) in Durham, NC, USA. The research team includes I.Filikhin, I.Bondarev, V.M.Suslov, Y.Tang, M.Wu and B.Vlahovic.

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Typical calculations of the optoelectronic properties of semiconductor and carbon nanostructures. Top panel shows: (a)calculated energies and effective masses of the electrons occupying s-, p-, and d-orbitals, (b)Coulomb shifts of the transition energies for positively (X+) and negatively (X–) charged trions and biexcitons (XX) as functions of the exciton recombination energy (solid lines – simulations, dashed lines – root-mean-square fits of experimental data), (c) cross sections of the single electron/hole probability distributions in different orbital states in the InAs/GaAs quantum dot. Bottom panel shows (left to right): surface plasmon density of states, dispersion of the coupled surface exciton-plasmon excitations, and exciton absorption lineshapes as the exciton energy is tuned to the nearest plasmon resonance of the (11,0) carbon nanotube (dimensionless frequency is defined as ħ[Frequency]/2γ0 with γ0=2.7 eV being the carbon nearest neighbor overlap integral).

THE EFFECTIVE POTENTIAL METHOD
The effective potential method has been developed by the NCCU group to calculate the properties of realistic semiconductor quantum dot nanostructures with the explicit consideration of quantum dot size, shape, and material composition. The method is based on the single sub-band approach with the energy dependent electron effective mass. In this approach, the confined states of carriers are formed by the band gap offset potential. Additional effective potential is introduced to account for cumulative band gap deformations due to strain and piezoelectric effects inside the quantum dot nanostructure. The magnitude of the effective potential is selected in such a way as to reproduce experimental data for a given nanomaterial. Additionally, an analog of the Kane formula is implemented in the model to take into account the non-parabolicity of the conduction band. The resulting nonlinear Schrödinger equation is solved by means of the iterative procedure with the adjusted effective electron mass and non-parabolicity parameter, where in each iteration step the Schrödinger equation is numerically linearized and solved by the finite element method.[1]

At present, simulations based on this approach are performed for the InGaAs/GaAs quantum dots and quantum rings of different sizes and configurations under different external conditions. The obtained results show that residual strain and conduction band non-parabolicity effects greatly affect the device related properties of semiconductor quantum dots. The results are in good agreement with available experimental data, closely matching energy level and effective mass data extracted from capacitance–voltage experiments. The method also allows one to accurately simulate spin-orbital coupling effects for the electrons in excited states (Figure, top panel), as well as the presence of admixtures, such as Ga. Our calculations of the Coulomb shifts of the exciton complexes (positively and negatively charged trions, biexcitons) in the InGaAs/GaAs quantum dots with 22%-25% Ga fraction match very well both capacitance-voltage and photoluminescence measurements. To best reproduce the experimental data, Ga fraction in the InGaAs/GaAs quantum dots should not exceed 25%.

Commonly used numerical approaches, such as the 8-band kp-theory, density functional theory, or atomistic pseudopotential technique, take into account inter-band interactions, strain and piezoelectric effects in quantum dots in an ab initio manner. Such methods are very computationally intensive and time-consuming. The main advantage of our method is that the high accuracy of calculations is obtained at a very low computational cost – calculations can typically be completed using a 3 GHz PC with 1 GB of memory in less than 20 minutes. Our effective potential method satisfactorily reproduces the results of ab initio simulations, thus offering an independent evaluation of the electronic confinement effects calculated within ab initio models. For example, we find that the atomistic pseudopotential model overestimates the strength of the electronic confinement in quantum dots, producing the stronger confinement for electrons and heavy holes than that obtained within the 8-band kp-theory.

OTHER RESEARCH RESULTS
Accurate simulations of electronic and optical properties of nanomaterials are the main research interest and the focus of the Computational and Theoretical NanoScience Research Group at NCCU. Theoretical models provide fundamental understanding of underlied physics and aid in the design of nanostructures with properties tailored for specific device applications. Our group has investigated exciton-phonon coupling and related exciton dephasing mechanisms affecting the optical response of semiconductor quantum dot heterostructures, developed the formalism to quantize an electromagnetic field in quasi-one-dimensional absorbing nanostructures (carbon nanotubes), and rigorously simulated a variety of near-field quantum electromagnetic phenomena, such as atomic spontaneous decay dynamics, atom-nanotube van der Waals coupling and inter-nanotube van der Waals interactions, light absorption and entanglement of atomic states close to carbon nanotubes, as well as exciton-plasmon interactions on the nanotube surface (Figure, bottom panel), with a specific goal to aid in the design of tunable optoelectronic device applications with semiconductor and carbon nanomaterials.[2]

REFERENCES
[1] I.Filikhin, V.M.Suslov, and B.Vlahovic, Modeling of InAs/GaAs quantum ring capacitance spectroscopy in the nonparabolic approximation, Physical Review B 73, 205332 (2006).

[2] I.V.Bondarev, Surface electromagnetic phenomena in pristine and atomically doped carbon nanotubes, Journal of Computational and Theoretical Nanoscience, special issue on ”Technology Trends and Theory of Nanoscale Devices for Quantum Applications”, ASP, USA (to appear in October, 2009).

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