Strain distribution and electronic spectra of InAs/GaAs self-assembled dots: An eight-band study

Jiang, Hongtao; Singh, Jasprit

doi:10.1103/physrevb.56.4696

Cited by 323 publications

(192 citation statements)

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“…Since the pyramid shape symmetry group is a subgroup of the symmetry of the zincblende crystal lattice, it follows that the symmetry group of the model is the double C 4 group 17 . Two different approaches are used to calculate the strain distribution in quantum dots -the continuum mechanical 8,11 and the valence force field model 8,10 . When the strain distribution is incorporated in the k · p method, the continuum mechanical model preserves the C 4 symmetry, while the valence force field model, due to its atomistic nature, breaks it 8,10 .…”

Section: Introductionmentioning

confidence: 99%

“…Two different approaches are used to calculate the strain distribution in quantum dots -the continuum mechanical 8,11 and the valence force field model 8,10 . When the strain distribution is incorporated in the k · p method, the continuum mechanical model preserves the C 4 symmetry, while the valence force field model, due to its atomistic nature, breaks it 8,10 . Nevertheless, the comparisons of the two models have shown that they give similar results 8,18 .…”

Section: Introductionmentioning

confidence: 99%

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Symmetry ofk∙pHamiltonian in pyramidalInAs∕GaAsquantum dots: Application to the

et al. 2005

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A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the C 4 symmetry of the 8-band k · p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasi-angular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer's double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry ofk∙pHamiltonian in pyramidalInAs∕GaAsquantum dots: Application to the

et al. 2005

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“…4 As quantum dots were grown on a GaAs͑001͒ substrate by metalorganic chemical-vapor deposition using a horizontal reactor cell operating at 76 Torr. For the growth of In x Ga 1Ϫx As islands, (CH 3 ) 3 Ga 3 , (CH 3 ) 3 In, and AsH 3 were used as precursors.…”

mentioning

confidence: 99%

Transmission electron microscopy study ofInxGa1−xAsquantum dots on a GaAs(00

et al. 1999

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A transmission electron microscopy ͑TEM͒ investigation of the morphology of In x Ga 1Ϫx As quantum dots grown on a GaAs͑001͒ substrate has been carried out. The size and the shape of the quantum dots have been determined using bright-field images of cross-section TEM specimens and ͓001͔ on-zone bright-field images with imaging simulation from plan-view TEM specimens. The results suggest that the coherent quantum dots are lens shaped with base diameters of 25-40 nm and aspect ratios of height to diameter of 1:6 -1:4. ͓S0163-1829͑99͒00920-0͔Since Esaki and Tsu 1 proposed the idea of semiconductor heterostructures and successfully grew Al x Ga 1Ϫx As/GaAs superlattices nearly three decades ago, quantum semiconductor structures have received increasing attention due to their potential applications in electronic and optoelectronic devices and circuits. 2,3 In recent years, fabrication of lowdimensional quantum semiconductor structures, such as quantum wires and quantum dots, has become possible with the development of modern epitaxial techniques. Compared with bulk or quantum well systems, these low-dimensional quantum semiconductor structures have unique and superior optical properties for optoelectronic devices. For quantum dots, carriers are confined three dimensionally, leading to different optoelectronic properties from those in bulk materials, quantum wells, and quantum wires. Since the shape and size of quantum dots are critical parameters in determining their optoelectronic properties, 4-7 determination of these parameters is important. Several techniques have been used to estimate these parameters, such as atomic force microscopy ͑AFM͒, 8-14 scanning tunneling microscopy, 15-17 reflection high-energy electron diffraction, 18,19 and transmission electron microscopy ͑TEM͒. 20-24 Different shapes of quantum dots such as lens-shaped, 9,10,23 cone-shaped, 14,17 pyramids with different facets, 11,12,[18][19][20][21] and truncated pyramids 22 have been reported using the above techniques. Differences in the predicted values for quantum dot ground state and excited state emission, and in intersublevel energies will be obtained depending on what shapes and aspect ratios are assumed in the calculation. Calculations for both pyramid-shaped 25,26 and lens-shaped In x Ga 1Ϫx As/GaAs quantum dots 27 have been reported; however, an exact experimental determination of the shape of these islands is at present controversial. AFM has been the most commonly used technique for the shape and size study of uncapped quantum dots. However, the convolution of the AFM tip with the dot structure limits its ability to resolve the shape of very small quantum dots, 28,29 and especially of the dots with facets. Although TEM techniques have been used to study the shape and size of the dots, reliable information has not been obtained. In this study, a comprehensive TEM investigation of the shape and the size of uncapped In x Ga 1Ϫx As quantum dots grown on GaAs͑001͒ is carried out.The In 0.6 Ga 0.4 As quantum dots were grown on a GaAs͑001͒ ...

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“…The k · p model is the most popular one for treating electronic structures of semiconductor quantum wells or superlattices. However, when applied to complex structures such as self-assembled quantum wires [4][5][6][7][8][9] or quantum dots [13,18,19], the method becomes very cumbersome if one wish to implement the correct boundary conditions that take into account the differences in k · p band parameters for different materials involved. EBOM is free of this problem, since different material parameters are used at different atomic sites in a natural way.…”

Section: Theoretical Approachmentioning

confidence: 99%

“…By varying the parameters A valence force field (VFF) model [13][14][15] is used to find the equilibrium atomic positions in the self-assembled QWR structure by minimizing the lattice energy. The strain tensor at each atomic (In or Ga) site is then obtained by calculating the local distortion of chemical bonds.…”

Section: Model Structuresmentioning

confidence: 99%

Systematic study of Ga1−xInxAs self-assembled quantum wires with varying interfacial strain relaxation

Sun

Chang

2001

Journal of Applied Physics

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A systematic theoretical study of the electronic and optical properties of Ga 1−x In x As self-assembled quantum-wires (QWR's) made of short-period superlattices (SPS) with strain-induced lateral ordering is presented. The theory is based on the effective bond-orbital model (EBOM) combined with a valence-force field (VFF) model.Valence-band anisotropy, band mixing, and effects due to local strain distribution at the atomistic level are all taken into account. Several structure models with varying degrees of alloy mixing for lateral modulation are considered. A valence force field model is used to find the equilibrium atomic positions in the QWR structure by minimizing the lattice energy. The strain tensor at each atomic (In or Ga) site is then obtained and included in the calculation of electronic states and optical properties.It is found that different local arrangement of atoms leads to very different strain distribution, which in turn alters the optical properties. In particular, we found that in model structures with thick capping layer the electron and hole are confined in the Ga-rich region and the optical anisotropy can be reversed due to the variation of lateral alloying mixing, while for model structures with thin capping layer the electron and hole are confined in the In-rich region, and the optical anisotropy is much less sensitive to the lateral alloy mixing.

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Strain distribution and electronic spectra of InAs/GaAs self-assembled dots: An eight-band study

Cited by 323 publications

References 18 publications

Symmetry ofk∙pHamiltonian in pyramidalInAs∕GaAsquantum dots: Application to the

Symmetry ofk∙pHamiltonian in pyramidalInAs∕GaAsquantum dots: Application to the

Transmission electron microscopy study ofInxGa1−xAsquantum dots on a GaAs(00

Systematic study of Ga1−xInxAs self-assembled quantum wires with varying interfacial strain relaxation

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