G. Jurczak

HOLZ lines splitting on SiGe/Si relaxed samples: Analytical solutions for the kinematical equation

Sample thinning for TEM observation introduces large changes with respect to the initial strain state of the bulk sample and particularly relaxation via the free surfaces which leads to HOLZ lines splitting in the CBED pattern. This phenomenon has been simulated owing to extensive calculations either in the kinematical or the dynamical framework of electron diffraction mainly using displacement fields resulting from finite element modelling of the sample relaxation. HOLZ line splitting is well reproduced and numerical fits can be used to compare experimental and calculated curves. This paper proposes new analytical solutions for the kinematical equation of electron diffraction. Simple mathematical functions are used to approximate the deformation profiles. We showed that, under certain conditions, the rocking curve profile can be analytically calculated, thus providing some clue to separate different contributions to the rocking curves against deformation profile. These simplified analytical expressions are used to extract the maximum amplitude displacement within the sample with about 10% accuracy. This accuracy can even be improved to 1% with a short adjustment routine. The influence of the shape of the displacement profile on the rocking curves is demonstrated.

Strong electric field and nonuniformity effects in GaN∕AlN quantum dots revealed by high pressure studies

The photoluminescence (PL) from GaN quantum dots (QDs) embedded in AlN has been investigated under hydrostatic pressure. The measured pressure coefficient of emitted light energy [dEE∕dP] shows a negative value, in contrast with the positive pressure coefficient of the GaN band gap. We also observed that increasing pressure leads to a significant decrease of the light emission intensity and an asymmetric broadening of the PL band. All these effects are related to the pressure-induced increase of the built-in electric field. A comparison is made between experimental results and the proposed theoretical model which describes the pressure behavior of nitride QDs.

Finite Element Simulation of Residual Stresses in Epitaxial Layers

A nonlinear finite element approach presented here is based on the constitutive equations for anisotropic hyperelastic 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.

An analytical approach of the HOLZ lines splitting on relaxed samples

For many years, Convergent Beam Electron Diffraction (CBED) has been intensively used for lattice parameter determination because of the extremely high sensitivity of High Order Laue Zone (HOLZ) lines position to small lattice parameter changes. But, for highly stressed systems, the sample thinning down to electron transparency induces a relaxation. In such cases, HOLZ lines are splitted due to an inhomogeneous variation of lattice parameter (Figure 1.a). Conventional measurement of lattice parameter using quasi-kinematical approach of HOLZ lines shift is then impossible and new models have to be developed. Recently, several approaches have been proposed in order to reproduce the experimental profile of split HOLZ lines also called “rocking curves” I g(s), and deduce the stress distribution in the sample [1, 2, 3, 4]. But, several questions are still open and relation between the rocking curve features and the atomic displacement profile is not completely understood.

Effects of Nonlinear Elasticity in Nitride Semiconductors and their Nanostructures

We theoretically investigate the effects of the nonlinear elasticity on the electronic structure of strained nitride InGaN/GaN and AlGaN/GaN quantum wells and GaN/AlN quantum dots. In these systems, the elastic stiffness tensor in the optically active regions is significantly modified by the presence of the built‐in hydrostatic pressure. In the present studies, we take into account the pressure dependence of elastic stiffness tensor. We show that this effect leads to (i) decrease of the volumetric strain and (ii) increase of the polarization‐induced built‐in electric field in the QWs and QDs. Consequently, the interband transition energies in the nanostructures decrease when the nonlinear elasticity effects are considered.

Modeling of elastic, piezoelectric and optical properties of vertically correlated GaN/AlN quantum dots

We theoretically investigate elastic, piezoelectric and optical properties of wurtzite GaN/AlN quantum dots, having hexagonal pyramid-shape, stacked in a multilayer. We show that the strain existing in quantum dots and barriers depends significantly on the distance between the dots i.e. on the width of AlN barriers. For typical QDs, having the base diameter of 19.5nm, the drop of the electrostatic potential in the quantum dot region slightly decreases with decreasing of the barrier width. This decrease is however much smaller for QDs than for superlattice of GaN/AlGaN quantum wells, with thickness similar to the height of QDs. Consequently, the band-to-band transition energies in the vertically correlated GaN/AlN QDs show unexpected, rather weak dependence on the width of AlN barriers. Increasing the QD base diameter leads to stronger decreasing dependence of the band-to-band transition energies vs. the width of AlN barriers, similar to that observed for superlattieces of QWs.