InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonons, and electronic structure (original) (raw)
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Strain effects on pyramidal InAs/GaAs quantum dot
Strain distribution in a pyramidal InAs/GaAs quantum dot is investigated. The strain field induced by mismatch of lattice constants in heterostructures is analyzed based on theories of linear elasticity and of thermal stress. The strain-induced potential is then incorporated in the steady state Schrödinger equation. Both the strain field and the solution of the steady state Schrödinger equation are found numerically with the aid of a finite element package-FEMLAB. Eigenenergy and the probability density function of conduction band of quantum dot are calculated. Results from two different models, namely anisotropic material model and isotropic material simplification, during the stage of strain analysis are also compared. Numerical results show eigenenergy and the degeneracy of low eigenenergy are affected by strains. On the other hand, the differences between anisotropic and isotropic materials are not large. Therefore, it is suitable to treat InAs/GaAs quantum dot as isotropic materials.
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.
Effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots
Physical Review B, 2004
The effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots grown on GaAs is investigated with an atomistic valence-force-field model and an empirical tight-binding model. By comparing a dot with and without a wetting layer, we find that the inclusion of the wetting layer weakens the strain inside the dot by only 1% relative change, while it reduces the energy gap between a confined electron and hole level by as much as 10%. The small change in the strain distribution indicates that strain relaxes only little through the thin wetting layer. The large reduction of the energy gap is attributed to the increase of the confining-potential width rather than the change of the potential height. First-order perturbation calculations or, alternatively, the addition of an InAs disk below the quantum dot confirm this conclusion. The effect of the wetting layer on the wave function is qualitatively different for the weakly confined electron state and the strongly confined hole state. The electron wave function shifts from the buffer to the wetting layer, while the hole shifts from the dot to the wetting layer.
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.
Materials, 2015
This work reports on theoretical and experimental investigation of the impact of InAs quantum dots (QDs) position with respect to InGaAs strain reducing layer (SRL). The investigated samples are grown by molecular beam epitaxy and characterized by photoluminescence spectroscopy (PL). The QDs optical transition energies have been calculated by solving the three dimensional Schrödinger equation using the finite element methods and taking into account the strain induced by the lattice mismatch. We have considered a lens shaped InAs QDs in a pure GaAs matrix and either with InGaAs strain reducing cap layer or underlying layer. The correlation between numerical calculation and PL measurements allowed us to track the mean buried QDs size evolution with respect to the surrounding matrix composition. The simulations reveal that the buried QDs' realistic size is less than that experimentally driven from atomic force microscopy observation. Furthermore, the average size is found to be slightly increased for InGaAs capped QDs and dramatically decreased for QDs with InGaAs under layer.
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.
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.
Strain-interactions between InAs/GaAs quantum dot layers
Thin Solid Films, 2004
InAs/GaAs quantum dot (QD) bilayer and trilayer structures have been grown on GaAs(001) substrates by molecular beam epitaxy and the properties of the uncapped QDs investigated using atomic force microscopy (AFM). The emphasis is on understanding the influence a variation of the thickness of the GaAs spacer layer (S) between the QD layers has on the morphological properties of the QDs in the up-most layer, which is grown at a significantly reduced temperature compared to the first QD layer. The size distribution of the QDs in the second layer is shown to be exceptionally narrow for a spacer thickness of 10 nm, with a large average QD size. Larger values of S lead to a much broader size distribution and the appearance of significantly smaller dots. Complete strain relief is only achieved upon deposition of f 50 nm GaAs in bilayer and f 60 nm in trilayer structures, a result that has important implications for multiple stacking of QD layers in device applications.