Yumin Liu

THE STRAIN DISTRIBUTIONS AND CARRIER'S CONFINING POTENTIALS OF SELF-ORGANIZED InAs/GaAs QUANTUM DOT

On the basis of the finite element approach, we systematically investigated the strain field distribution of conical-shaped InAs/GaAs self-organized quantum dot using the two-dimensional axis-symmetric model. The normal strain, the hydrostatic strain and the biaxial strain components along the center axis path of the quantum dots are analyzed. The dependence of these strain components on volume, height-over-base ratio and cap layer (covered by cap layer or uncovered quantum dot) is investigated for the quantum grown on the (001) substrate. The dependence of the carriers confining potentials on the three circumstances discussed above is also calculated in the framework of eight-band k (.) p theory. The numerical results are in good agreement with the experimental data of published literature.

Dependence of elastic strain field on the self-organized ordering of quantum dot superlattices

A systematic investigation of the strain distribution of self-organized, lens-shaped quantum dot in the case of growth direction on (001) substrate was presented. The three-dimensional finite element analysis for an array of dots was used for the strain calculation. The dependence of the strain energy density distribution on the thickness of the capping layer was investigated in detail when the elastic characteristics of the matrix material were anisotropic. It is shown that the elastic anisotropic greatly influences the stress, strain, and strain energy density in the quantum dot structures. The anisotropic ratio of the matrix material and the combination with different thicknesses of the capping layer, may lead to different strain energy density minimum locations on the capping layer surface, which can result in various vertical ordering phenomena for the next layer of quantum dots, i.e. partial alignment, random alignment, and complete alignment.

Valence band structures of InAs/GaAs quantum rings using the Fourier transform method

The valence band structures of strained InAs/GaAs quantum rings are calculated, with the four-band k ? p model, in the framework of effective-mass envelope function theory. When determining the Hamiltonian matrix elements, we develop the Fourier transform method instead of the widely used analytical integral method. Using Fourier transform, we have investigated the energy levels as functions of the geometrical parameters of the rings and compared our results with those obtained by the analytical integral method. The results show that the energy levels in the quantum rings change dramatically with the inner radius, outer radius, average radius, width, height of the ring and the distance between two adjacent rings. Our method can be adopted in low-dimensional structures with arbitrary shape. Our results are consistent with those in the literature and should be helpful for studying and fabricating optoelectronic devices.

Investigation of the dependence of volume, cap layer, and aspect ratio on the strain distribution and electronic structure of self-organized InAs/GaAs quantum dot

We systematically investigated the strain field distribution of conical-shaped InAs/GaAs self-organized quantum dot using the two-dimension axis-symmetry model. The normal strain, the hydrostatic and biaxial components along the center axis path of the quantum dots was analyzed. The dependence of these strain components on volume, height-over ratio and cap layer (covered by cap layer or uncovered quantum dot) are investigated for the quantum grown on the (001) substrate. The dependence of the carriers confining potentials and electronic effective mass on the three circumstances discussed above is also calculated in the framework of eight-band k • p theory. The numerical results are in good agreements with the experiment data in published literature.

Full-vector analysis of photonic crystal fiber and 2D plane photonic crystals waveguides by finite difference method

An important class of optical waveguides are those refractive index profile is not continuous, such as Bragg fiber, photonic crystal fiber and 2-D photonic crystal waveguides. These microstructure fibers and waveguides become more and more important in the future optical devices for their novel and spurious optical characteristics. To give a full understand of these devices, the exact mode fields solver is very critical. In this paper, we use the full-vector finite difference approach free of spurious modes to solve mode field characteristics of the photonic crystal and 2-D plane photonic crystal waveguides. The photonic band structures within an irreducible Brillouin zone are investigated for both in plane and out plane propagation. The out of plane propagation can be used for the photonic crystal fiber. The coupled difference equations are in terms of the transverse magnetic filed components. Based on the appropriate transparent boundary conditions, a unique set of couple five-point difference equation are developed, and an efficient numerical technique to solve the deterministic equations by the Eispark in Matlab. For the in plane propagation, the guides mode are either TE or TM modes, the difference equations are uncoupled. Using the appropriate period boundary condition and combined with the transparent boundary condition, we derived the five point difference equations that can be used for the 2-D plane photonic crystal waveguides. Based on these finite difference equations, we analyzed the optical mode field characteristics of the crystal fiber and the plane optical crystal waveguides. The filling materials either dielectric or air are also analyzed. Good agreements are obtained compared the numerical results with the experiment data and the published literature. The mode fields solver can also be used for the other waveguides such as Bragg fibers.

Determination on wave function of quantum structures using finite-difference time domain

With the interest in quantum structures, there is a need to have a flexible method that can help us to determine eigenfunctions for these structures. In this article, we present a method that accomplishes this by using the simulation of the Schrödinger equation based on finite-difference time-domain (FDTD). We choose one-and two-dimensional finite square well potential, and one-and two-dimensional harmonic oscillator potential as examples. Giving the initial condition, we determine the eigenfrequencies through a Fourier transform of the time domain data collected at the center point in the problem space. Another simulation implements a discrete Fourier transform at the eigenfrequencies at every point in the problem space, hence, the eigenfunctions can be constructed.

The couple electronic state of the stack quantum dots by axial symmetrical finite element analysis

Semiconductor quantum dots have been of major interest in recent years. This has largely been simulated by progress in quantum dot growth technology, whereby self-organized quantum dots array can be fabricated by MBE and MOCVD facilities using Stranski Krastanow growth mode. Quantum does material has achieved broad applications in optoelectronic devices and quantum information fields because of the unique 3D electron confinement. However, a good understanding about the electronic, excitonic and optoelectronics properties of the quantum materials are very important in fabrication nanostructure devices based on quantum dots. Based on the 1-band effective-mass theory, a finite element numerical technique is developed to calculate the electronic structure of truncated conical shaped InAs GaAs vertical aligned quantum dot molecular, including the wetting layer. Using the axis-symmetry model, the 3D effective-mass Schrödinger equation with step potential barrier can be reduced to a 2D problem by separating variable technique, which greatly reduced the calculation cost. Form the calculated results, we found that the coupling effects is obviously when the separation distance is in the range of the less than 10nm. The wave functions will exhibits large probability in the region between the quantum dots. In order to consider the effect of the distance between the two layers of quantum dots on the electronic state coupling, we calculated the results when the distance is 6nm, 11nm, 14nm and 17nm. The ground state, the second excited and the highest excited state will lower its energy with decreasing the distance between the quantum dots, but the second excited state will increase its energy. With increasing the distance between the two quantum dots, the coupling effect will become weaker, and for the ground state, the wave function distribution will tend to localized only in one of the quantum dot, the energy become something degenerate. The calculated results show that the ground state and the first excited state are degenerate. With decreasing of the distance, the degenerate states are broken, and the energy levels are separated. In our simulations, the strain effects are ignored. In the future woks, strain should be taken in to account as an easy way. The calculated results can help us to examine optoelectronic properties of the semiconductor nanostructure based on multi sheet of quantum dots with wetting layers.

Full-Vector Finite Element Analysis of Birefringence Properties in rectangle Lattice photonic crystal with circular and elliptical holes

Photonic crystal fibers (PCFs) have attracted much interests recently mainly because of their unique properties. Based on the light confinement mechanisms, the photonic crystal fibers can be divided into tow classes: the index-guiding PCFs and the photonic bandgap (PBG) PCFs. The former, with multiple air holes periodically arranged around the core, possess numerous unusual properties, such as structure controllable chromatic dispersion, large mode areas, birefringence and stronger optical nonlinenarity.Based on the full vector, semi vector or even the approximate-scalar model, Lots of methods have been used to design the PCFs, such as the effective index approach, the localized function expansion method, the plane wave expansion method, the multipole method, the beam propagation method, the finite difference method, the finite difference time domain method, and the finite element method. Each of theses method mentioned above are accurate and efficient for ideal PCF, however, for the real fabricated PCFs, the geometry structure may not perfect, induced the base mode degeneracy may be destructive, and posses birefringence properties. Sometime the birefringence properties is necessary for special usefulness, such as polarization mode dispersion (PMD) compensation, and PCFs based polarized optical devices. In this paper, a full vector finite element is applied to investigate the mode birefringence, mainly focus on the rectangle lattice PCFs with elliptical or circular holes. It has been demonstrated from the calculated results that high birefringence to the order of 0.01 can be achieved by decreasing both the pitch and the x and y ratio of the elliptical hole. To increase the birefringence of the circular holes rectangle lattice, reduction of the width and height ratio of the lattice is necessary. Based on the simulation results, we conclude that both single polarization transmission and high birefringence polarization maintaining can be achieved by using the proposed structure with suitable parameters respectively. The available high birefringence at relative high frequency regime in the fibers and also the sufficiently broad single mode region would make the fabrication of highly birefringent photonic crystal fibers with novel properties possible.

The strain energy density distribution of the capping layer surface for InAs/GaAs quantum dot along different growth directions

In this paper, we calculated the strain distribution of low dimension structure using the elastic continuum model. The strain energy density distribution on the different thickness of capping layer surface for the self-organized InAs/GaAs quantum dots system is investigated by the numerical finite element method. The influence of the different growth directions on the strain energy density distributions can be found from the calculated results. The results can explain some experiment results, such as the ordering array of the quantum dots supper-lattices. So the growth direction and spacing thickness can be regarded as another control parameters for strain engineering self-organized semiconductor quantum materials. As a comparison, the strain distributions of other low-dimension self-organized materials are also calculated.

The Electronic Structure of Truncated-Conical Shaped InAs/GaAs Quantum Dot With Wetting Layers

Semiconductor quantum dots have been of major interest in recent years. This has largely been simulated by progress in quantum dot growth technology, whereby self-organized quantum dots array can be achieved using Stranski-Krastanow growth mode. Quantum does material has achieved broad applications in optoelectronic devices and quantum information fields because of the unique 3-D electron confinement. Based on the 1-band effective-mass theory, a finite element technique is developed to calculate the electronic structure of conical shaped InAs/GaAs quantum dot, including the wetting layer. Using the axis-symmetry model, the 3-D effective-mass Schrodinger equation with step potential barrier can be reduced to a 2-D problem by separating variable, which greatly reduced the calculation cost. Based on the result, we found, compared without wetting layer, the wetting layer can influence the electron level. This may attribute to the increase of the confining potential width rather than the potential height. The presented finite element code can be further used to analysis the transverse or vertical coupled quantum dot molecule.Copyright