Strain effects on pyramidal InAs/GaAs quantum dot (original) (raw)
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A finite element study of the stress and strain fields of InAs quantum dots embedded in GaAs
Semiconductor Science and Technology, 2002
We report on a stress and strain analysis, using the finite element method, of the heterosystem of InAs quantum dots embedded in GaAs. The methodology of using the finite element method to simulate the lattice mismatch is discussed and a three-dimensional (3D) model of the heterostructure shows the 3D stress distribution in the InAs islands embedded in a matrix of GaAs substrate and cap layer. The initial shape of the InAs islands is pyramidal. The stress and strain distribution calculated corresponds well with the strain induced by the lattice mismatch. Factors such as the height of the spacer layer and the height of the island are found to play an important role in the stress and strain distribution. With the island having the shape of a truncated pyramid, the stress and strain distribution deviates from that of a full pyramidal island showing the effects that a change of shape in the islands has on the stress field. The stress distribution contributes to the driving force for the mechanism of surface diffusion in molecular beam epitaxy. The effects of anisotropy on the strain distribution are also studied.
InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonons, and electronic structure
Physical Review B, 1995
The strain distribution in and around pyramidal InAs/GaAs quantum dots (QD's) on a thin wetting layer fabricated recently with molecular-beam epitaxy, is simulated numerically. For comparison analytical solutions for the strain distribution in and around a pseudomorphic slab, cylinder, and sphere are given for isotropic materials, representing a guideline for the understanding of strain distribution in two-, one-, and zero-dimensional pseudomorphic nanostructures. For the pyramidal dots we find that the hydrostatic strain is mostly confined in the QD; in contrast part of the anisotropic strain is from the QD into the barrier. The optical-phonon energies in the QD are estimated and agree perfectly with recent experimental findings. From the variation of the strain tensor the local band-gap modification is calculated. Piezoelectric effects are additionally taken into account. The threedimensional effective-mass single-particle Schrodinger equation is solved for electrons and holes using the realistic confinement potentials. Since the QD s are in the strong confinement regime, the Coulomb interaction can be treated as a perturbation. The thus obtained electronic structure agrees with luminescence data. Additionally A1As barriers are considered.
Strain in inhomogeneous InAs/GaAs quantum dot structures
Journal of Physics: Conference Series, 2012
Most Non-destructive experimental approaches for the determination of indium concentration profiles give information about average indium concentration profiles only. Due to this, there is a need to extrapolate the indium concentration profiles in a way that takes into account the geometry of the quantum dots. We here present two extrapolation approaches. In the first approach we assume that the indium concentration profile is constant in the direction perpendicular to the measurement plane, while in the second approach we take into account the symmetry of the structure. Both approaches are compared to a profile with a constant indium concentration inside the dot.
Quantitative strain analysis of InAs/GaAs quantum dot materials
Scientific reports, 2017
Geometric phase analysis has been applied to high resolution aberration corrected (scanning) transmission electron microscopy images of InAs/GaAs quantum dot (QD) materials. We show quantitatively how the lattice mismatch induced strain varies on the atomic scale and tetragonally distorts the lattice in a wide region that extends several nm into the GaAs spacer layer below and above the QDs. Finally, we show how V-shaped dislocations originating at the QD/GaAs interface efficiently remove most of the lattice mismatch induced tetragonal distortions in and around the QD.
Two-step strain analysis of self-assembled InAs/GaAs quantum dots
Semiconductor Science and Technology, 2006
Strain effects on optical properties of self-assembled InAs/GaAs quantum dots grown by epitaxy are investigated. Since a capping layer is added after the self-assembly process of the quantum dots, it might be reasonable to assume that the capping layer neither experiences nor affects the induced deformation of quantum dots during the self-assembly process. A new two-step model is proposed to analyse the three-dimensional induced strain fields of quantum dots. The model is based on the theory of linear elasticity and takes into account the sequence of the fabrication process of quantum dots. In the first step, the heterostructure system of quantum dots without the capping layer is considered. The mismatch of lattice constants between the wetting layer and the substrate is the driving source for the induced elastic strain. The strain field obtained in the first step is then treated as an initial strain for the whole heterostructure system, with the capping layer, in the second step. The strain from the two-step analysis is then incorporated into a steady-state effective-mass Schrödinger equation. The energy levels as well as the wavefunctions of both the electron and the hole are calculated. The numerical results show that the strain field from this new two-step model is significantly different from models where the sequence of the fabrication process is completely omitted. The calculated optical wavelength from this new model agrees well with previous experimental photoluminescence data from other studies. It seems reasonable to conclude that the proposed two-step strain analysis is crucial for future optical analysis and applications.
Strain distributions in group IV and III-V semiconductor quantum dots
2013
A theoretical model was developed using Green's function with an anisotropic elastic tensor to study the strain distribution in and around three dimensional semiconductor pyramidal quantum dots formed from group IV and III-V material systems namely, Ge on Si, InAs on GaAs and InP on AlP. A larger positive strain in normal direction which tends to zero beyond 6nm was observed for all three types while the strains parallel to the substrate were negative. For all the three types of quantum dots hydrostatic strain and biaxial strain along x and z directions were not linear but described a curve with a maximum positive value near the base of the quantum dot. The hydrostatic strain in x-direction is mostly confined within the quantum dot and practically goes to zero outside the edges of the quantum dot. For all the three types, the maximum hydrostatic and biaxial strains occur in x-direction around 1nm and around 2nm in z-direction. The negative strain in x-direction although realtively weak penetrate more deeper to the substrate than hydrostatic strain.The group IV substrate gave larger hydrostatic and biaxial strains than the group III-V semiconductor combinations and InAs /GaAs was the most stable. The results indicated that the movements of atoms due to the lattice mismatch were strong for group III-V.
Elastic stress and emission nonhomogeneity in asymmetric InAs quantum dot in a well structures
physica status solidi (c), 2011
Photoluminescence (PL) and X-ray diffraction (XRD) have been studied in InAs quantum dots (QDs) embedded in asymmetric GaAs/In x Ga 1-x As/In 0.15 Ga 1-0.15 As/GaAs quantum wells (dot-in-a-well, DWELL) with the parameter x=0.10-0.25. The parameter x increasing in the capping layer is accompanied by the non monotonous variation of InAs QD parameters. The PL intensity increases and the PL peak shifts to low energy in structures with x=0.15. On the contrary the structures with x=0.20 and 0.25 are characterized by lower PL intensities and PL peak positions shifted to higher energy. The method of X-ray diffraction has been applied with the aim to study the variation of elastic strain in asymmetric DWELL structures. It was shown that the minimum of elastic strain corresponds to DWELL with x=0.15. In DWELLs with x=0.20 and 0.25 the level of compressive strain increases. The reasons of strain variation are discussed as well.
Applied Physics Letters, 2000
We report on the matrix-dependent strain effect in self-assembled InAs quantum-dot heterostructures using photoluminescence measurements. A series of samples were prepared to examine the effect of quantum dot position with respect to the so-called strain-reducing layer ͑SRL͒. Since the SRL reduces the residual hydrostatic strain in the quantum dots, long emission wavelength of 1.34 m is observed for the InAs quantum dots with an In 0.16 Ga 0.84 As SRL. The dependence of the emission wavelength on the thickness of the cap layer on SRL also indicates the importance of the role of matrix in the strain relaxation process of the dots. Using In 0.16 Al 0.84 As instead of In 0.16 Ga 0.84 As as the SRL, a blueshift in wavelength is observed because the elastic stiffness of In 0.16 Al 0.84 As is higher than that of In 0.16 Ga 0.84 As and less strain is removed from the dots with In 0.16 Al 0.84 As SRL.
We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots QD's within the empirical sp 3 s* tight-binding ETB model with interactions up to second nearest neighbors and spin-orbit coupling. Results for the model system of capped pyramid-shaped InAs QD's in GaAs, with supercells containing 10 5 atoms are presented and compared with previous empirical pseudopotential results. The good agreement shows that ETB is a reliable alternative for an atomistic treatment. The strain is incorporated through the atomistic valence-force field model. The ETB treatment allows for the effects of bond length and bond angle deviations from the ideal InAs and GaAs zinc-blende structure to be selectively removed from the electronic-structure calculation, giving quantitative information on the importance of strain effects on the bound-state energies and on the physical origin of the spatial elongation of the wave functions. Effects of dot-dot coupling have also been examined to determine the relative weight of both strain field and wave-function overlap.