Instytut Podstawowych Problemów Techniki

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The rocksalt structure of ZnO has a very promising bandgap for optoelectronic applications. Unfortunately, this high-pressure phase is unstable under ambient conditions. This paper presents experimental results for rocksalt-type ZnO/MgO superlattices and theoretical considerations of the critical thickness of MgxZn1−xO layers. The correlations between the layer/spacer thickness ratio, elastic strain, chemical composition, and critical thickness are analyzed. The Matthews and Blakeslee model is revisited to find analytic conditions for the critical layer thickness resulting in phase transition. Our analysis shows that due to the decrease in misfit stresses below some critical limit, the growth of multiple quantum wells composed of rocksalt ZnO layers and MgO spacers is possible only for very large layer/spacer thickness ratios.

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Strain-induced changes of ZnTe energy gap in ZnTe/ZnMgTe core/shell nanowires arising from lattice mismatch between the core and the shell semiconductor are studied by means of optical methods. It is shown that the increase of the Mg content in the shell, as well as the increase of the shell thickness result in an effective redshift of the near band edge photoluminescence from ZnTe nanowire cores, which reflects directly the decrease of energy gap under tensile strain conditions. The conclusions are supported by theoretical calculations in terms of the valence force field model. The observed change of ZnTe energy gap can be as large as 120 meV with respect to the unstrained conditions and can be tuned in a continuous manner by adjusting shell parameters, which open a path towards an effective band gap engineering in these structures.

Słowa kluczowe:

Nanowires, II-VI semiconductors, Magnesium, Band gap, Quantum effects

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A Nd:YAG laser operating at a wavelength of 266 or 355 nm is used to deposit a thin layer of copper on the (0 0 0 1)α-Al2O3 surface. The formation process is precisely controlled by identification of time distribution of two characteristics: energy and flux density of particles incident on the substrate. For this purpose, the Cu-plasma expansion is described by means of an analytical hydrodynamic model whose self-similar solutions are fitted to the experimental plasma images and time-of-flight spectra. The obtained nanocomposite is examined by the aberration-corrected high-resolution transmission electron microscopy (Cs-HRTEM) method. The results reveal that copper crystals assume one main orientation relative to the substrate (1 1 1)[2 −1 −1]Cu∥ (0 0 0 1)[−1 −1 2 0]α–Al2O3 and the formed interface has a specific microstructure. To reconstruct the phase boundary region, molecular dynamic (MD) and static (MS) simulations are carried out. The results show that strong bonding between copper and sapphire induces structural changes in the (1 1 1) Cu layer nearest the substrate and leads to formation of the system of partially dissociated dislocations in the next layer. In consequence, the Cu/α–Al2O3 interface becomes the semicoherent system. The lattice matching regions of the individual Cu layers are significantly lowered, which results in strong deformations along the closed packed planes. The reconstructed interface is used for Cs-HRTEM image simulation. A good accordance with the experimental results indicates that the MD model correctly maps the microstructure at the phase boundary of the synthesized nanocomposite.

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The zinc telluride (ZnTe) nanowires grown recently are covered with the ZnMgTe shell. As a result of addition of magnesium the ZnMgTe lattice is expanded with respect to pure ZnTe lattice. From the lattice mismatch between the ZnMgTe shell and ZnTe nanowire core the internal strain and stress are created. Depending on the shell thickness and the Mg content in the shell the optical emission exhibits a considerable energy shift. To estimate this effect, at least qualitatively, the elastic state of the nanowire is calculated.

An analysis of the state of strain and stress in the core-shell nanowire within linear elasticity, using an analogy with thermal stresses is presented, in the similar way as it is applied, e.g. in hygro-mechanics. The suitable system of the differential Lame-Navier’s type equations is derived, and its solution for the axially symmetric problem is given. The jump of stress at the core-shell boundary is determined.

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We present transmission electron microscopy (TEM) and x-ray quantitative studies of the indium distribution in InxGa1−xN/GaN multiple quantum wells (MQWs) with x = 0.1 and 0.18. The quantum wells were grown by low-pressure metalorganic chemical vapour deposition (LP-MOCVD) on a bulk, dislocation-free, mono-crystalline GaN substrate. By using the quantitative TEM methodology the absolute indium concentration was determined from the 0002 lattice fringe images by the strain measurement coupled with finite element (FE) simulations of surface relaxation of the TEM sample. In the x-ray diffraction (XRD) investigation, a new simulation program was applied to monitor the indium content and lateral composition gradients. We found a very high quality of the multiple quantum wells with lateral indium fluctuations no higher than ΔxL = 0.025. The individual wells have very similar indium concentration and widths over the whole multiple quantum well (MQW) stack. We also show that the formation of 'false clusters' is not a limiting factor in indium distribution measurements. We interpreted the 'false clusters' as small In-rich islands formed on a sample surface during electron-beam exposure.

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Chemical composition in a ternary alloy is examined using a quantitative high resolution transmission electron microscopy, finite element modelling of the thin foil relaxation phenomena and microscopy image simulation. The measurement of local lattice distortion on transmission electron microscopy images is a powerful tool for chemical composition determination. However, for the correct interpretation of the results, one needs to take into account the inhomogeneous relaxation of the sample and the strain averaging across the sample. The 3D finite element modelling of such phenomena have been performed as a function of chemical composition and geometry of an indium rich cluster in a MOCVD InxGa1−xN/GaN quantum well. Lattice distortion field measured on: experimental transmission electron microscopy image and simulated one, obtained on the basis of finite element simulation, are compared. This procedure allows an accurate determination of chemical composition in such heterostructures.

Słowa kluczowe:

Indium clusters, Vapour deposition, Transmissionelectron microscopy, Elasticity, Finite element method, Lattice distortion, Image simulation

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In this paper the field theory of dislocations is used in the finite element analysis of residual stresses in epitaxial layers. By digital processing of the HRTEM image of a GaAs/ZnTe/CdTe system the tensor maps of dislocation distribution are extracted. Such obtained maps are used as the input data to the finite element code. The mathematical foundations of this code are based on the compatibility equations for lattice distortions. The surface tension induced by misfit dislocations is considered here in terms of a 3D boundary-value problem for stress equilibrium in the interfacial zone. The numerical results show how strongly the surface tension depends on the nonlinear elastic behaviour of the crystal structure.

Słowa kluczowe:

Microscopy and microanalysis techniques, Nonlinear elasticity, Dislocation structure, Finite element analysis, Residual stresses, Layered structures

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The cover picture of this issue depicts indium composition fluctuations in InGaN/GaN multi quantum wells. The coded color strain distribution (left) was derived from finite element method calculations of the strain relaxation process and high‐resolution transmission electron microscopy (HRTEM) image simulations, superimposed on the HRTEM image of the quantum wells. The possible corresponding shape and εxx strain profiles in the indium rich clusters (right) hint at a concentration close to pure InN in their core. The paper by Pierre Ruterana et al. [1] was presented at the 5th International Symposium on Blue Laser and Light Emitting Diodes (ISBLLED‐2004), held in Gyeongju, Korea, 15–19 March 2004.

Słowa kluczowe:

HRTEM, quantum well, composition fluctuation, strain distribution

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A nonlinear finite element approach presented here is based on the constitutive equations for anisotropic hyperelatic materials. By digital image processing the elastic incompatibilities (lattice mismatch) are extracted from the HRTEM image of GaN epilayer. Such obtained tensorial field of dislocation distribution is used next as the input data to the FE code. This approach is developed to study the stress distribution associated with lattice defects in highly mismatched heterostructures applied as buffer layers for the optically active structures.

Słowa kluczowe:

Dislocations, Anisotropic Hyperelasticity, Residual Stresses

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Following the need to accurately understand the In composition fluctuations and their role on the optical properties of the GaN based heterostructures, an investigation of MOCVD InGaN/GaN quantum wells is carried out. To this end, quantitative High Resolution Transmission Electron Microscopy (HRTEM) is coupled with image simulation and Finite Element Method (FEM) for the thin foil relaxation modelling. The results show that the indium content can reach x = 1 in the clusters inside the core. In these MOCVD QWs, we attempt to connect the Quantum dot density, composition, and shape to the growth conditions, in order to help the engineering process of highly efficient devices.

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Zinc oxide has wurtzite structure (wz-ZnO) at ambient conditions. Due to the promising bandgap (4.0-7.8eV) we consider the misfit stress for the growth of rock salt rs-Zn$_x$Mg$_{1-x}$O layers on rock salt MgO. At the ambient conditions, a solid solution of ZnO in MgO is stable only up to 13%. Nevertheless, due to the misfit stress the range of chemical composition of thermodynamically stable layers can be extended. We consider a mechanism of the dislocation network formation at the interface rs-Zn$_x$Mg$_{1-x}$O/MgO. Based on the dislocation theory, many different analytic formulas for critical layer thickness have been derived, cf. Hu (1991), Brown (2002). The formulas concern the critical thickness of the layers which retain thermodynamically stable at atmospheric pressure. On the other hand, for thin layers which lose the stability earlier, before the stress relaxation, we can expect a lower critical thickness. We present a derivation of an analytic formula for the critical thickness of rs-Zn$_x$Mg$_{1-x}$O layers which lose the stability due to the rocksalt-wurtzite phase transition, cf. Lu et al. (2016). In the new formula the dependency of the onset elastic energy $E(sigma, x)$ of the rs$ ightarrow$wz phase transition is taken into account. In the general case this energy depends on the misfit stress and chemical composition.

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Recent investigations reveal that interface bonding strength is dependent on the relative orientation of crystallites of the both phases [2]. The experimental, theoretical and computational investigations confirm this observation in the case of Cu/Al2O3 system, [3], [4]. It is shown that the statistical distribution of the values of interface strength for different relative orientations of bonded phases should be included in the phenomenological model of the damage initiation in nanocomposites. The novelty of the presented study is the combination of different experimental techniques: HRTEM, EBSD and molecular dynamics simulations with phenomenological theory of damage development in nanocomposites due to debonding at the interphase boundary [5], [6], [7]. A class of new models with the yield condition determined by one of quadric surfaces, in particular paraboloid or ellipsoid one is considered and the comparison with popular Gurson approach is discussed, [8].

Słowa kluczowe:

nanocompistes, strength, interface, bonding, HRTEM, EBSD, molecular dynamics

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Słowa kluczowe:

III-V semiconductors, piezoelectricity, high resolution transmission electron microscopy, band edge structure

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