Stress relaxation in highly strained InAs/GaAs structures as studied by finite element analysis and transmission electron microscopy

Benabbas, T.; François, P.; Androussi, Y.; Lefebvre, Alain

doi:10.1063/1.363193

Cited by 110 publications

(52 citation statements)

References 31 publications

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“…Rosenauer et al [3] determined the composition profile of In x Ga 12x As QDs using high resolution TEM and FEA. Benabbas et al [5] applied FEA to generate strain fields of InAs͞GaAs QDs, and they calculated two-beam dynamical electron diffraction contrast images to study their shape.…”

mentioning

confidence: 99%

Indium Segregation and Enrichment in CoherentInxGa1−xAs/GaAsQua

et al. 1999

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Significant differences in the image features of In x Ga 12x As quantum dots (QDs) grown on (001) and vicinal (001) GaAs were seen in [001] on-zone bright-field transmission electron microscope images. Simulated images were obtained by modeling the strain field distribution of the QDs with finite element analysis and then using this model in dynamical electron diffraction contrast simulations. Comparison of the experimental images and the simulated images shows that (i) In segregation exists in the QDs and (ii) the average In content of the QDs is higher than the average In content of the film. [S0031-9007(99)09460-0] PACS numbers: 81.05.Ea, 61.14. Lj, 61.16.Bg, 68.35.Dv The composition, shape, and size of quantum dots (QDs) are essential parameters in determining their optoelectronic properties [1]. Many techniques have been used to study these parameters [2,3]. Among them, transmission electron microscopy (TEM) has been one of the most frequently used. It is well known that, under the usual dynamical two-beam or on-zone axis multibeam imaging conditions, the TEM diffraction contrast image arises largely from the strain field, which is sensitive to the composition, shape, size, and elastic constants of both the substrate and the QD. Consequently, it should be possible to obtain information about the composition, shape, and size of QDs from such images. However, to correctly interpret diffraction contrast images, image simulations are essential [2].Obtaining the strain field distribution within and around the QDs is necessary for image simulations. Finite element analysis (FEA) methods have been widely and successfully used to study the strain field of nanometer-size semiconductor QDs and applied to TEM investigations. For example, Christiansen et al. [4] used FEA to obtain the displacement field of Ge(Si) islands grown on Si. Using convergent beam electron diffraction, their study showed that the displacement field obtained in this way is correct. Rosenauer et al. [3] determined the composition profile of In x Ga 12x As QDs using high resolution TEM and FEA. Benabbas et al.[5] applied FEA to generate strain fields of InAs͞GaAs QDs, and they calculated two-beam dynamical electron diffraction contrast images to study their shape.In this study, we use three dimensional anisotropic FEA to generate strain field distributions of In x Ga 12x As QDs grown on (001) GaAs. We then use these strain field distributions in multibeam dynamical electron diffraction calculations to produce contrast simulations of [001] on-zone bright-field TEM images. An earlier study [6] showed that the [001] on-zone bright-field imaging can be used to estimate the size of the unburied QDs. Here, we show that indium composition plays a role in defining the boundary of the TEM image and in determining several of the image features. Both electron diffraction patterns and comparison of the simulated and experimental images show that the composition of the dots is different from the composition of the thin film alloy from which the QDs formed....

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confidence: 99%

Indium Segregation and Enrichment in CoherentInxGa1−xAs/GaAsQua

et al. 1999

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“…Actual strain simulations for the In x Ga 1Àx NQ W s were performed by a thermoelastic method accommodated within ANSYS. 13,14 The piezoelectric polarization tensor was then calculated by the "E-first" route preferred by Christmas et al 29 Finally, by introducing the piezoelectric potential into the one-dimensional Schrödinger equation, and neglecting the inbuilt p-n junction field and carrier screening effects, the optical transition energy of the QW was calculated with MATLAB software. In later discussion, the calculated transition energies are compared with the measured QW emission energies directly, i.e., the Stokes shift was assumed to be constant.…”

Section: Methodsmentioning

confidence: 99%

“…10, the finite element method (FEM), embodying macroscopic elastic theory, was used. Analogous FEM calculations have proved effective in simulating semiconductor nanostructures including self-organized GaN/AlN quantum dots, 13 InAs quantum dots 14 and nanocolumnar GaN/AlGaN disks. 15 However, in choosing boundary conditions, previous authors have usually just considered the local environment of the QWs while neglecting the influence from other layers.…”

Section: Introductionmentioning

confidence: 99%

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

Xie

Chen

Edwards

et al. 2012

Journal of Applied Physics

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This version is available at https://strathprints.strath.ac.uk/40400/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the A size-dependent strain relaxation and its effects on the optical properties of InGaN/GaN multiple quantum wells (QWs) in micro-pillars have been investigated through a combination of high spatial resolution cathodoluminescence (CL) hyperspectral imaging and numerical modeling. The pillars have diameters (d) ranging from 2 to 150 lm and were fabricated from a III-nitride light-emitting diode (LED) structure optimized for yellow-green emission at $560 nm. The CL mapping enables us to investigate strain relaxation in these pillars on a sub-micron scale and to confirm for the first time that a narrow ( 2 lm) edge blue-shift occurs even for the large InGaN/GaN pillars (d > 10 lm). The observed maximum blue-shift at the pillar edge exceeds 7 nm with respect to the pillar centre for the pillars with diameters in the 2-16 lm range. For the smallest pillar (d ¼ 2 lm), the total blue-shift at the edge is 17.5 nm including an 8.2 nm "global" blue-shift at the pillar centre in comparison with the unetched wafer. By using a finite element method with a boundary condition taking account of a strained GaN buffer layer which was neglected in previous simulation works, the strain distribution in the QWs of these pillars was simulated as a function of pillar diameter. The blue-shift in the QWs emission wavelength was then calculated from the strain-dependent changes in piezoelectric field, and the consequent modification of transition energy in the QWs. The simulation and experimental results agree well, confirming the necessity for considering the strained buffer layer in the strain simulation. These results provide not only significant insights into the mechanism of strain relaxation in these micro-pillars but also practical guidance for design of micro/nano LEDs.

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“…The calculation of the spatial strain distribution in a QD structure requires the solution of a three-dimensional problem in elasticity theory, for a generally nontrivial quantum dot shape. This is often achieved by using finite-difference or atomistic techniques, 2,6,16 which require considerable computational effort. An analytical method was recently presented to calculate the Fourier transform of the strain distribution, 17 which we use here to directly determine the strain-dependent terms in the Hamiltonian matrix.…”

Section: ͑22͒mentioning

confidence: 99%

Theoretical analysis of electron-hole alignment in InAs-GaAs quantum dots

2000

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We present a theoretical analysis of the mean electron and hole positions in self-assembled InAs-GaAs quantum-dot structures. Because of the asymmetric dot shape, the electron center of mass should be displaced with respect to the hole center of mass in such dots, giving rise to a built-in dipole moment. Theoretical calculations on ideal pyramidal dots predict the electron to be localized above the hole, contrary to the results of recent Stark-effect spectroscopy. We use an efficient plane-wave envelope-function technique to determine the ground-state electronic structure of a range of dot models. In this technique, the Hamiltonian matrix elements due to all components of the potential are determined using simple analytical expressions. We demonstrate that the experimental data are consistent with a truncated dot shape and graded composition profile, with indium aggregation at the top surface of the dot.

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Stress relaxation in highly strained InAs/GaAs structures as studied by finite element analysis and transmission electron microscopy

Cited by 110 publications

References 31 publications

Indium Segregation and Enrichment in CoherentInxGa1−xAs/GaAsQua

Indium Segregation and Enrichment in CoherentInxGa1−xAs/GaAsQua

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

Theoretical analysis of electron-hole alignment in InAs-GaAs quantum dots

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