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The influences of thickness of spacing layer and the elastic anisotropy on the strain fields and band edges of InAs/GaAs conical shaped quantum dots
Chinese Physics B
Abstract
Based on the continuum elastic theory, this paper presents a finite element analysis to investigate the influences of elastic anisotropy and thickness of spacing layer on the strain field distribution and band edges (both conduction band and valence band) of the InAs/GaAs conical shaped quantum dots. To illustrate these effects, we give detailed comparisons with the circumstances of isolated and stacking quantum dot for both anisotropic and isotropic elastic characteristics. The results show that, in realistic materials design and theoretical predication performances of the optoelectronic devices, both the elastic anisotropy and thickness of the spacing layer of stacked quantum dot should be taken into consideration.
... On the other hand, introducing Sb into the CL gives rise to an important redshift with respect to the sample 1GaAs with QDs capped at the same rate (1 ML/s), but the reasons of these modifications to the recombination energies are not straightforward. First, compressive SRLs increase the biaxial strain component and decrease the hydrostatic one in InAs QDs, shrinking the bandgap energy of InAs QDs [22][23][24]. Second, the presence of Sb atoms during capping also hinders the QD decomposition, so we should expect taller and/or Inricher QDs [25]. Third, a type-II alignment appears for Sb compositions in the CL above 16%, with the electrons confined in the InAs QDs and holes confined in the GaAsSb SRL [26,27]. ...
In this work, two different strategies to preserve InAs/GaAs QDs against decomposition during the capping process have been compared structurally and optically. They are based on: (i) the control of the growth parameters of the capping layer (CL), such as growth rate, and (ii) the nature of the CL, such as the use of GaAsSb strain-reducing layers (SRL). For this, we have statistically determined the average size, composition and areal density in sample populations of dozens of QDs as well as the wetting layer features. Faster growth rates and the presence of Sb in the CL results in an increase of both average QD height as well as the In content but the thorough comparison among all the samples allowed us to draw the following important inferences. i) QD volume is a better parameter than QD height to assess QD decomposition and PL redshift; ii) higher QD volumes are not always linked to higher In contents and iii) a reduction in the QD density is observed in both strategies related to the increase of the average volume. The results are discussed in terms of the mechanisms that might operate during the capping process, such as surface coverage, intermixing or segregation.
... In such systems, an important role may play, in particular, effects of mechanical stress. This question has been studied in [10,11]. Thus, the authors based on the continuum elastic theory, present a finite element analysis to investigate the influences of the elastic anisotropy and thickness of spacing layer on the strain field distribution and band edges (both conduction band and valence band) of the InAs/GaAs conical shaped quantum dots. ...
In the framework of the adiabatic approximation, the energy states of electron as well as the direct light absorption are investigated in conical quantum dot. Analytical expressions for particle energy spectrum are obtained. The dependence of the absorption edge on geometrical parameters of conical quantum dot is obtained. Selection rules are revealed for transitions between levels with different quantum numbers. In particular, it is shown that for the radial quantum number transitions are allowed between the levels with the same quantum numbers, and any transitions between different levels are allowed for the principal quantum number.
... The strain distribution induced by HfO 2 is computed by the continuum elastic model. [8][9][10] The valence band structure is calculated by the 6 × 6 · method, in which the strain is included as a perturbation Hamiltonian. [11][12][13] The twodimensional Poisson-Schrödinger [14,15] self-consistent solver is developed to evaluate the confinement of the tri-gate on the hole density distribution on the transverse plane. ...
The strain impact on hole mobility in the GOI tri-gate pFETs is investigated by simulating the strained Ge with quantum confinement from band structure to electro-static distribution as well as the effective mobility. Lattice mismatch strain induced by HfO2 warps and reshapes the valence subbands, and reduces the hole effective masses. The maximum value of hole density is observed near the top corners of the channel. The hole density is decreased by the lattice mismatch strain. The phonon scattering rate is degraded by strain, which results in higher hole mobility.
... The FEM is our option to solve problems of the strain and the electronic ground state. Because of its flexibility in dealing with different structures, FEM has been widely used in calculating the strain field and the electronic structures of various heterostructures [22][23][24][25]. ...
The strain distribution and electronic structures of the InAs/GaAs quantum ring molecule are calculated via the finite element
method. In our model, three identical InAs quantum rings are aligned vertically and embedded in the cubic GaAs barrier. Considering
the band edge modification induced by the strain, the electronic ground state and the dependence of ground state energy on
geometric parameters of the quantum ring molecule are investigated. The change of localization of the wavefunction resulting
from the applied electric field along the growth direction is observed. The ground state energy decreases as the electric
field intensity increases in a parabolic-like mode. The electric field changes the monotonic dependence of the energy level
on the inter-ring distance into a non-monotonic one. However, the electric field has no effect on the relationships between
the energy level and other geometric parameters such as the inner radius and outer radius.
Keywordsstrain distribution-electronic structure-quantum ring molecule-applied electric field
... Taking into account the effects of strain-induced potential and piezoelectric potential, the wave functions of the electron and hole will become asymmetry and be hard to be described with analytic expressions. [7][8][9] But the problems can be resolved with numerical methods such as finite element method, and finite difference method. ...
Under the framework of the Hartree approximation, the ground state exciton binding energy and the interband transition energy are calculated by solving the coupled Schrodinger equations taking into account the coulomb interaction. The self-consistent effective confining potentials are obtained using a fast three-dimensional Fourier transform in every step of the reduced Schrodinger equations. The exciton binding energy increases at first, and then goes through the process of the decline with the increment of the size of conical InAs/GaAs quantum dot. The ground-state exciton oscillator strength becomes larger when the size of the quantum dots increases. It indicates that the radiative lifetime of the exciton will become shorter. The temperature will affect the interband transition energy, but the exciton binding energy is almost temperature-independent.
In the framework of effective mass envelope function, by solving the single-band Schrdinger equation, the ground state energy level of two-dimensional InAs/GaAs quantum ring is calculated both in the absence and the presence of the magnetic field to analyze the electronic structure of quantum ring nano-materials. The relationships between the energy level and the inner radius, outer radius, average radius and width of the ring are analyzed. It is indicated that the magnetic field perpendicular to the plane of the quantum ring will evidently increase the ground state energy. Moreover, the magnetic field makes the dependence of the energy level on outer radius of the ring weaker, i.e. the level will keep in changeless if the outer radius exceeds a critical value.
The optical properties of quantum dots have a close relationship with the size fluctuation, density, strain filed distribution of the dots and the spacer layer thickness. InAs/GaAs quantum dot with GaNXAs1-X strain compensation layers (SCL) is theoretically investigated for improving the crystal quality. The reduction effects of the spacer thickness are discussed quantitatively. The influence of the location and the N concentration of the GaNXAs1-X SCL on compensation of the strain formed on quantum dots (QDs) and the system is also discussed. The reduction effect of SCL on strain of system is analyzed and the vertical alignment probability between the adjacent layers is calculated. Our results can provide a theoretical basis for finding the optimal properties of SCL to realize the high quality multi-QD layer.
The effects of strain and surface roughness scattering on the quasi-ballistic hole transport in a strained gate-all-around germanium nanowire p-channel field-effect transistor (pFET) are investigated in this work. The valence subbands are shifted up and warped more parabolically by the influence of HfO2 due to the lattice mismatch. However, the boundary force only shifts the subbands downwards and has little effect on the reshaping of bands. Strain induced by HfO2 increases both the hole mobility and ON-current (I ON), but has little effect on the hole mobility. The I ON is degraded by the surface roughness scattering in both strained and unstrained devices.
We modify the anisotropic phase-field crystal model (APFC), and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model. The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme, thereby, allowing us to work on a large system and for a long time. The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed. In particular, we investigate the morphological evolution in heteroepitaxial growth of our model. A new formation mechanism of misfit dislocations caused by vacancy trapping is found. The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions, and it could significantly change the growth orientation of epitaxial layers.
The morphologies of quantum dots and distributions of stresses in and around quantum dots
structures have a significant effect on photoelectric properties and electronic
structures. Optical and electronic devices of different efficiencies based on quantum dots
can be manufactured by choosing self-assembly of different materials to control epitaxial
growth. In this article we investigate the equilibrium morphologies and the strain
distributions of self-assembled pyramidal semiconductor quantum dots in Stranski-Krastanov
growth mode based on the finite element method of the anisotropic theory of elasticity. We
also give the equilibrium morphologies and the distribution of the stress and the strain,
the hydrostatic strain and the biaxial strain for different lattice mismatched quantum
dots. The results can serve as a basis for interpretation of experiments.
Electronic structures of the artificial molecule comprising two truncated pyramidal quantum dots vertically coupled and embedded in the matrix are theoretically analysed via the finite element method. When the quantum dots are completely aligned, the electron energy levels decrease with the horizontally applied electric field. However, energy levels may have the maxima at non-zero electric field if the dots are staggered by a distance of several nanometers in the same direction of the electric field. In addition to shifting the energy levels, the electric field can also manipulate the electron wavefunctions confined in the quantum dots, in company with the non-perfect alignment.
The equilibrium composition in strained quantum dot is the result of both elastic relaxation and chemical mixing effects, which have a direct relationship to the optical and electronic properties of the quantum-dot-based device. Using the method of moving asymptotes and finite element tools, an efficient technique has been developed to compute the composition profile by minimising the Gibbs free energy in self-assembled alloy quantum dot. In this paper, the composition of dome-shaped GexSi1-x/Si quantum dot is optimized, and the contribution of the different energy to equilibrium composition is discussed. The effect of composition on the critical size for shape transition of pyramid-shaped GeSi quantum dot is also studied.
Molecular dynamics simulations using a Coulomb–Buckingham potential have been used to investigate the process of wurtzite GaN films growth, including the appearance of films in early stage, regulation of growth, structure of the surface and the dynamic features. The simulations show that the N atoms and Ga atoms are absorbed on the lattice of substrate and take on a distinct sandwich structure. Time evolution of the mean square displacements and diffusion coefficient of the deposited atoms are observed, the results show that the clusters will become stable with the increase of time steps and the atoms reach the initial stable state after 25ps; N atoms reach the equilibrium positions more quickly than Ga atoms. It is proved by radial distribution function and the ratio of vacancy of every deposited layer that the crystalline characters of the films will become better as the time steps increase and weaker from bottom to top.
This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings. The strain distribution calculations are based on the continuum elastic theory. An ideal three-dimensional circular quantum ring model is adopted in this work. The electron and heavy-hole energy levels of the InAs/GaAs quantum rings are calculated by solving the three-dimensional effective mass Schrödinger equation including the deformation potential and piezoelectric potential up to the second order induced by the strain. The calculated results show the importance of strain and piezoelectric effects, and these effects should be taken into consideration in analysis of the optoelectronic characteristics of strain quantum rings.
Depositions of Si, Ge and C atoms onto a preliminary Si (001) substrate at different temperatures are investigated by using the molecular dynamics method. The mechanism of atomic self-assembling occurring locally on the flat terraces between steps is suggested. Diffusion and arrangement patterns of adatoms at different temperatures are observed. At 900 K, the deposited atoms are more likely to form dimers in the perpendicular [110] direction due to the more favourable movement along the perpendicular [110] direction. C adatoms are more likely to break or reconstruct the dimers on the substrate surface and have larger diffusion distances than Ge and Si adatoms. Exchange between C adatoms and substrate atoms are obvious and the epitaxial thickness is small. Total potential energies of adatoms and substrate atoms involved in the simulation cell are computed. When a newly arrived adatom reaches the stable position, the potential energy of the system will decrease and the curves turns into a ladder-like shape. It is found that C adatoms can lead to more reduction of the system energy and the potential energy of the system will increase as temperature increases.
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.
The elastic fields in the self-organized quantum dot (QD) structures are investigated in details by three-dimensional finite element analysis for an array of lens shaped QDs. Emphasis is placed on the effect of elastic anisotropy of the materials with the anisotropy ratio A ranging from 0.25 to 4.0 for both the QDs and the matrix. It is found that the elastic anisotropy strongly influences the distributions of strain, stress, and strain energy density in the QD structures. It is shown that the elastic interactions among the buried QDs play crucial role in the formation of the satellite energy minima at the cap layer surface, while the materials anisotropy and the cap layer thickness also play important roles. By changing the elastic anisotropy ratio and the cap layer thickness, substantially different distributions of strain energy minima on the cap layer surface are obtained, which may result in various QD ordering phenomena such as vertical alignment, partial alignment, or complete misalignment. Based on the calculation results, a phase diagram is constructed to show the effect of material anisotropy and cap layer thickness on the vertical correlation of QDs.
Nanoheteroepitaxy is a fundamentally new epitaxial approach that utilizes three-dimensional stress relief mechanisms available to nanoscale heterostructures to eliminate defects provided the island diameter is below a critical value 2lc. Analysis shows that 2lc∼(15–30)× the critical thickness hc. In the case of GaAs on Si (∼4% misfit), 2lc∼40 nm. In material systems such as GaN on Si (∼20% misfit), where the misfit is much larger and interfacial defects are unavoidable, the nanoheteroepitaxial structure is shown to reduce the formation and propagation of threading defects. Nanostructured substrate parameters that impact growth are discussed and interferometric lithography is introduced as a method for fabrication of large-area substrates for nanoheteroepitaxy. Si nanoisland diameters as small as 20 nm are demonstrated. Scanning and transmission electron microscopy data of GaN grown on Si (via organometallic vapor phase epitaxy) shows reduced threading defects in nanostructured samples compared to growth on planar substrates. Photoluminescence intensity data of nanostructured samples is enhanced by ∼100× as compared to planar-growth samples. © 2000 American Vacuum Society.
We report atomistic simulations of InxGa1-xAs/GaAs quantum dots (QDs) with nonuniform composition. The Tersoff potential is used to model the atomic interactions of an inhomogeneous system of 400 000 atoms and to obtain dynamic relaxation through energy minimization. From the relaxed atomistic model, the bond deformations are analyzed in order to predict the strain maps. The same technique is also employed to model the strain relaxation of a cleaved QD, allowing us to study the loss of planarity of the cleavage surface and to compare this with experimental scanning tunneling microscopy results. We confirm that an inverted pyramidlike In composition is likely to generate the topographical maps previously reported.
The present work demonstrates via numerical analysis that the presence of a thin InGaAs ternary layer around InAs quantum dots (QDs) reinforces the in-plane (epsilon(rr)) and vertical (epsilon(zz)) strain components of InAs quantum dots as compared to the QDs embedded directly in GaAs matrix, contrary to the general belief of strain relief. It has been further shown that such reinforced epsilon(rr) and epsilon(zz) states yields a decreased band-gap energy, i.e., the experimentally observed redshift in the literature. (c) 2006 American Institute of Physics.
We present a complete study both by experiments and by model calculations of quantum dot strain engineering, by which a few optical properties of quantum dot nanostructures can be tailored using the strain of quantum dots as a parameter. This approach can be used to redshift beyond 1.31 µm and, possibly, towards 1.55 µm the room-temperature light emission of InAs quantum dots embedded in InGaAs confining layers grown on GaAs substrates. We show that by controlling simultaneously the lower confining layer thickness and the confining layers’ composition, the energy gap of the quantum dot material and the band discontinuities in the quantum dot nanostructure can be predetermined and then the light emission can be tuned in the spectral region of interest. The availability of two degrees of freedom allows for the control of two parameters, which are the emission energy and the emission efficiency at room temperature. The InAs/InGaAs structures were grown by the combined use of molecular beam epitaxy and atomic layer molecular beam epitaxy; their properties were studied by photoluminescence and photoreflectance spectroscopies and by atomic force microscopy; in particular, by means of photoreflectance not only the spectral features related to quantum dots were studied but also those of confining and wetting layers. The proposed approach has been used to redshift the room-temperature light emission wavelength up to 1.44 µm. The optical results were analyzed by a simple effective-mass model that also offers a rationale for
engineering the properties of structures for efficient long-wavelength operation.
A systematic investigation is made on the influence of the longitudinal and transverse period distributions of quantum dots on the elastic strain field. The results showed that the effects of the longitudinal period and transverse period on the strain field are just opposite along the direction of center-axis of the quantum dots, and under proper conditions, both effects can be eliminated. The results demonstrate that in calculating the effect of the strain field on the electronic structure, one must take into account the quantum dots period distribution, and it is inadequate to use the isolated quantum dot model in simulating the strain field.
The performance of a two-way quantum-key-distribution (QKD) system are analyzed using the differential-phase-shift keying (DPSK) protocol. The comparison is based on the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984, the Bennett-Brassard-Mermin 1992, and the coherent differential-phase-shift keying protocols. We discussed the security of DPSK protocol against any type of individual photon splitting attack and concluded that the simple and efficient DPSK protocol allows for more than 200km of secure communication distance with high communication rates.
The performance of various quantum-key-distribution (QKD) systems is analyzed using 1.55 μm up-conversion single-photon detector. The dependence of quantum efficiency and dark count rate change on the pump power was also discussed. The comparison is based on the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984, the Bennett-Brassard-Mermin 1992, and the coherent differential-phase-shift keying protocols. We show that the up-conversion detector allows for higher communication rate and longer communication distance than the commonly used InGaAs/InP APD for all three QKD protocols, and the properties of quantum key distribution system can be greatly improved by this detector.
Kinetic Monte Carlo simulations are applied to study the growth of self-assembled vertical ordering InAs quantum dot superlattice on GaAs substrate. The study is focused on the influences of flux and interruption time at the initial stage when the first sub-monolayer is forming on the wetting layer. We demonstrate that uniform sized and regularly ordered island arrays can be obtained by controlling flux and interruption time, by means of studying the surface morphology, average island size, island size distribution and the standard deviation of island size distribution comprehensively. The size and order of island arrays will greatly affect the location and size of quantum dots in subsequent three-dimensional growth.
The performance of various quantum-key-distribution (QKD) systems is analyzed using 1.55μm up-conversion single-photon detector. The dependence of quantum efficiency and dark count rate change on the pump power was also discussed. The comparison is based on the secure communication rate as a function of distance for three QKD protocols: The Bennett-Brassard 1984, the Bennett-Brassard-Mermin 1992, and the coherent differential-phase-shift keying protocols. We show that the up-conversion detector allows for higher communication rate and longer communication distance than the commonly used InGaAs/InP APD for all three QKD protocols, and the properties of quantum key distribution system can be greatly improved by this detector.
A systematic investigation is made on the influence of the longitudinal and transverse period distributions of quantum dots on the elastic strain field. The results showed that the effects of the longitudinal period and transverse period on the strain field are just opposite along the direction of center-axis of the quantum dots, and under proper conditions, both effects can be eliminated. The results demonstrate that in calculating the effect of the strain field on the electronic structure, one must take into account the quantum dots period distribution, and it is inadequate to use the isolated quantum dot model in simulating the strain field.
The photoluminescence of self-assembled InAs/GaAs quantum dots, which are 7.3 nm in height and 78 nm in base size, was investigated at 15 K under hydrostatic pressures up to 9 GPa. The emissions from both the ground and the first excited states in large InAs dots were observed. The pressure coefficients of the two emissions are 69 and 72 meV/GPa respectively, which are lower than those of small InAs/GaAs dots. The analysis based on nonlinear elasticity theory reveals that the small pressure coefficients mainly result from the changes of the misfit strain and the elastic constants with pressure. The pressure experiments suggest that the excited state emissions originate from the optical transitions between the first excited electron states and the first excited hole states.
Photoluminescence of some low-dimensional semiconductor structures has been investigated under pressure. The measured pressure coefficients of In0.55Al0.45As/Al0.5 Ga0.5As quantum dots with average diameter of 26, 52 and 62 nm are 82, 94 and 98 meV/GPa respectively. It indicates that these quantum dots are type-I dots. On the other hand, the measured pressure coefficient for quantum dots with 7 nm in size is -17 meV/GPa, indicating the type-II character. The measured pressure coefficient for Mn emission in ZnS:Mn nanoparticles is -34.6 meV/GPa, in agreement with the predication of the crystal field theory. However, the DA emission is nearly independent on pressure, indicating that this emission is related to the surface defects in ZnS host. The measured pressure coefficient of Cu emission in ZnS:Cu nanoparticles is 63.2 meV/GPa. It implies that the acceptor level introduced by Cu ions has some character of shallow level. The measured pressure coefficient of Eu emission in ZnS:Eu nanoparticles is 24.1 meV/GPa, in contrast to the predication of the crystal field theory. It may be due to the strong interaction between the excited state of Eu ions and the conduction band of ZnS host.
The performance of a two-way quantum-key-distribution (QKD) system are analyzed using the differential-phase-shift keying (DPSK) protocol. The comparison is based on the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984, the Bennett-Brassard-Mermin 1992, and the coherent differential-phase-shift keying protocols. We discussed the security of DPSK protocol against any type of individual photon splitting attack and concluded that the simple and efficient DPSK protocol allows for more than 200 km of secure communication distance with high communication rates.
Kinetic Monte Carlo simulations are applied to study the growth of self-assembled vertical ordering InAs quantum dot superlattice on GaAs substrate. The study is focused on the influences of flux and interruption time at the initial stage when the first sub-monolayer is forming on the wetting layer. We demonstrate that uniform sized and regularly ordered island arrays can be obtained by controlling flux and interruption time, by means of studying the surface morphology, average island size, island size distribution and the standard deviation of island size distribution comprehensively. The size and order of island arrays will greatly affect the location and size of quantum dots in subsequent three-dimensional growth.
Finite-element calculations are used to study strain fields in vertically aligned InAs islands in GaAs. Such strain fields are found to be quite different from those of uncovered islands and nearly insensitive to the position of the island in the stacking. The driving force for vertically self-organized growth is known to be the interacting strain fields induced by the islands. The calculation of strain fields by the finite-element method makes it possible to model the correlations between adjacent InAs layers. A kinetic approach based on the effect of strain on surface diffusion is first proposed. A thermodynamic model is then analyzed to predict local island nucleation probabilities. Pairing probabilities of correlation between stacked islands, first calculated in the case of the InAs/GaAs system, are extended to the case of III-V semiconductors with a cubic crystalline structure. They are shown to be essentially dependent both on the ratio between the spacer layer thickness and the island height and on the lattice mismatch between islands and spacer layers.
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.
Three-dimensional stacking of semiconductor nano-islands in multilayers or superlattice structures provides a powerful tool for controlling the properties of self-assembled quantum dots. These stackings can be caused by several different mechanisms based on: (i) elastic interactions due to the strain fields of the buried dots; (ii) morphological interactions due to nonplanarized spacer topographies; or (iii) interactions based on chemical composition modulations within the spacer material. All three interactions may give rise to a vertical dot alignment in columns as well as to oblique or staggered dot stackings, depending on the details of the interaction mechanisms. For the interlayer correlations mediated by the elastic strain fields, the elastic anisotropy and surface orientation, but also the dot sizes and spacer layer thicknesses play a crucial role. As a result, transitions between different types of dot stackings can be induced as a function of spacer layer thicknesses and growth parameters. The large range of parameters involved in interlayer correlation formation may allow the controlled synthesis of new types of ordered structures with novel properties. To cite this article: G. Springholz, C. R. Physique 6 (2005).
An atomistic model of an InxGa1−xAs/GaAs quantum dot with nonuniform composition is investigated. An empirical interatomic potential, the Tersoff potential, is used to obtain dynamic relaxation through energy minimisation. Bond deformations are analysed in order to predict the components of the strain tensor with resolution on the atomic scale, revealing the nature of the lattice distortion in both the dot pyramid and the capping layer. The piezoelectric charges are then computed directly from the off diagonal components of the strain, revealing a wider distribution of the dipoles compared to those previously reported by other groups.
The minimum energy configurations of the atomic structure of a Ge island on a Si(001) substrate are calculated by using the conjugate gradient minimization of the potential energy of the system. The island is assumed to be covered or uncovered by a Si layer and assumed to be of pyramidal shape with the sidewalls of {110} or {105} facets; the base length of the island ranges from 5.43 to 10.9 nm. Two empirical potentials, the Keating and Stillinger–Weber potentials, are used. At the interfaces between the regions occupied by the atoms of different species, the potential parameters for such bondings are properly adopted. The strain profiles along the three selected paths within the structure and along the cap surface are calculated. While the profiles of the normal strain component ϵxx obtained by the two potentials are in good agreement with each other except within the substrate and at the edges of the island in the uncovered structures, the two profiles of the normal strain component ϵzz show a considerable difference in their magnitude, and the use of the Stillinger–Weber potential is recommended for the islands of the small sizes below 10 nm. The validity of the valence force field model with the Keating potential for such small islands is questionable although this model is widely recognized to be applicable to the calculation of strains in the quantum dot structures. The strain relaxation in the uncovered island is discussed through the comparison with that in the covered island. The strain profile along the cap surface explains vertical self-organization of stacked dots. © 2001 American Institute of Physics.
The finite element method is applied to strain-induced islands. The distribution of the elastic energy in the island and the substrate is determined as a function of the island aspect ratio and inter-island distance. When the height-over-base ratio increases, the total elastic energy density decreases and the relative contribution of the substrate increases. When the inter-island distance decreases, the elastic energy density increases and the relative contribution of the substrate decreases. The influence of the aspect ratio on the relaxation rate is amplified for short inter-island distances. © 1998 American Institute of Physics.
Self-organized quantum dots pattern depends strongly on the elastic strain energy of the substrate. It is well-known experimentally that for the elastic substrate with a high degree of anisotropy, the epitaxially grown island patterns are different for different growth orientations. In this paper, by incorporating the anisotropic strain energy field into a kinetic Monte Carlo algorithm for adatom diffusion, we show that the self-organized island pattern on the surface of an anisotropic substrate is closely correlated to the elastic energy distribution on the surface. The anisotropic substrates studied are GaAs with different growth orientations (001), (111), and (113). An isotropic substrate Iso (001), reduced from GaAs, is also investigated for the purpose of comparison. The island patterns on these substrates with and without elastic strain energy are presented. Besides the effect of substrate anisotropy, different growth parameters, including temperature, coverage, and interruption time, are further investigated to identify the optimal growth values. It is observed that the strain energy field in the substrate is the key factor that controls the island pattern, and that the latter is closely correlated to the substrate orientation (anisotropy). Our simulated patterns are also in qualitative agreement with recent experimental growth results.
We report on our study of the effects of interdot coupling on the properties of quantum dot infrared photodetectors. The main effect we address here is the splitting of the optical absorption of coupled quantum dots due to electron hopping between the dots. The splitting depends on the size of the dots and the interdot distance and it can be observed only for small dots, less than 20 nm. The system is studied numerically within the effective mass approximation. (c) 2006 American Institute of Physics.
The influence of wetting-layer states on quantum-dot states and vice versa is analysed numerically for electrons in the conduction band in the general case with arbitrary kinetic energy in the plane of the quantum-well wetting layer. Since the analysed quantum dot is embedded in a barrier material with different properties, the effective mass approximation methodology leads to a Schrödinger model with discontinuous coefficients. This complicates the analysis and, in addition, requires a special attention to the formulation of boundary conditions for the entire structure, consisting of the quantum dot with wetting layer embedded in a barrier material. In the present paper, the complete model is formulated and solved numerically via a variational approach based on finite element approximations and Arnoldi iterations. By analysing different geometrical configurations, we demonstrate that the ground eigenstate of the entire structure can be considerably affected by the presence of the wetting layer. The dependency demonstrated between eigenstates of the 'pure' quantum dots and the quantum-well wetting layers indicates that a conventional analysis of quantum-dot structures without accounting for wetting layers may not be sufficient for an adequate characterization of quantum dots as active regions in future electronic and optical devices.
A systematic investigation about the strain distributions around the InAs/GaAs quantum dots using the finite element method is presented. A special attention is paid to influence of an In0.2Ga0.8 As strain reducing layer. The numerical results show that the horizontal- and vertical-strain components and the biaxial strain are reinforced in the InAs quantum dot due to the strain-reducing layer. However, the hydrostatic strain in the quantum dot is reduced. In the framework of eight-band k p theory, we study the band edge modifications due to the presence of a strain reducing layer. The results demonstrate that the strain reducing layer yields the decreasing band gap, i.e., the redshift phenomenon is observed in experiments. Our calculated results show that degree of the redshift will increase with the increasing thickness of the strain-reducing layer. The calculated results can explain the experimental results in the literature, and further confirm that the long wavelength emission used for optical fibre communication is realizable by adjusting the dependent parameters. However, based on the calculated electronic and heavy-hole wave function distributions, we find that the intensity of photoluminescence will exhibits some variations with the increasing thickness of the strain-reducing layer.
This paper presents a finite element method of calculating strain distributions in and around the self-organized GaN/AIN hexagonal quantum dots. The model is based on the continuum elastic theory, which is capable of treating a quantum dot with an arbitrary shape. A truncated hexagonal pyramid shaped quantum dot is adopted in this paper. The electronic energy levels of the GaN/AIN system are calculated by solving a three-dimension effective mass Shrödinger equation including a strain modified confinement potential and polarization effects. The calculations support the previous results published in the literature.
We gave an analysis about the wavelength-division multiplexing isolation filter consisted of two concatenated long period fiber grating (LPFG), and the numerical simulation was performed by transfer matrix method. The key factors in design this high performance filter was proposed. Based on the key factors, flat transmission spectrum of the LPFG in range of 80 nm was obtained by the particle swarm optimization algorithm. The simulation results demonstrate that such type of isolation filters have equal frequency spacing, high isolation, and neglectable dispersion in the pass band, and the channel spacing can be tuned by tuning the fiber length between the two concatenated LPGs.
A theory for describing nonequilibrium dynamics in a semiconductor quantum-dot laser is presented. This theory is applied to a microcavity laser with a gain region consisting of an inhomogeneous distribution of quantum dots, a quantum-well wetting layer, and injection pumped bulk regions. Numerical results are presented and the effects of spectral hole burning, plasma heating, and many-body effects are analyzed.
- H Shin
- J B Kim
- Y H Yoo
Shin H Kim J B and Yoo Y H 2006 J. Appl. Phys. 99
023521
- W C Weng
- W K Stephan
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