Transmission electron microscopy of InGaNAs nanostructures using ab-initio structure factors for strain-relaxed supercells

Abstract

This thesis reports on theoretical, methodical and experimental studies concerning scattering and structural properties of In(x)Ga(1−x)N(y)As(1−y) using transmission electron microscopy (TEM). First, theoretical concepts to describe electron scattering at real crystals including the effects of bonding and static atomic displacements (SAD) are considered. The approach of modified atomic scattering amplitudes (MASA), which uses density functional theory (DFT) to model bonding in an atomistic manner, is exploited to calculate compositiondependent MASA for InGaNAs. Valence force field (VFF) calculations are applied to determine SAD caused by atom size effects. Huang scattering caused by SAD is shown to pile up in the vicinity of Bragg peaks, contrary to the smooth background caused by thermal diffuse scattering (TDS). In simulation studies it is demonstrated that Huang scattering leads to significant attenuation of Bragg beam amplitudes, for which additional absorptive form factors can be defined that are added as an imaginary part to atomic scattering amplitudes (ASA). The reliability of VFF strain relaxation is verified by full DFT calculations of residual forces for supercells with 216 atoms. It is found that atomic forces after VFF relaxation do not exceed 10mRy/Bohr, which translates to a maximum error of 2.58 pm for SAD. Furthermore, results for composition-dependent structure factors calculated by full DFT and atomistic models are compared. This confirms that SAD affect structure factor amplitudes and phases drastically and exhibits that the MASA approach in combination with SAD obtained by VFF meets the full DFT results most accurately. Thus it is possible to account for both bonding and SAD in large supercells containing 106 atoms by modelling bonding via MASA and calculating SAD by VFF. Second, structure factors for GaAs and InAs are measured by parallel and convergent beam electron diffraction (PBED and CBED) to verify the MASA approach. The PBED method was implemented in Bloch wave routines embedded in a least-squares refinement that allows for a refinement of structure factors, Debye-Waller factors, specimen thickness and -orientation. The method is based on extraction of integrated Bragg intensities from electron spot diffraction patterns. Errors in PBED are estimated from the application to simulated diffraction patterns with TDS background, and rules for the recognition of reasonable initial refinement conditions are derived. Then, PBED is applied to the measurement of the 200 structure factors of GaAs and InAs. Conversion to X-ray structure factors yields X(GaAs, 200) = −6.366 ± 0.015 and X(InAs, 200) = 53.687 ± 0.110, respectively. By CBED, X(GaAs, 200) = −6.350 ± 0.015 is measured. All results agree with each other and with expectations from the MASA concept inside the error margins, whereas isolated atom ASA must be rejected. Additionally, Debye-Waller factors for GaAs have been refined to B(Ga) = 0.275 ± 0.003 A² and B(As) = 0.242 ± 0.003 A² at 99K using PBED. Third, above theoretical scattering data is used in composition measurements in InGaNAs solar cell and laser structures via TEM lattice fringe imaging. Lattice strain and chemically sensitive 200 fringe contrast are measured from a single image and compared with simulations based on elasticity theory and the Bloch wave approach. First, a two-beam lattice fringe image formed by beams 000 and 200 is used to investigate the effect of bonding and SAD on composition quantification in In(0.08)Ga(0.92)N(0.03)As(0.97). In particular, neglect of bonding results in a relative error of 25% for the In content, whereas SAD have small impact. Second, a three-beam imaging technique is developed that utilises beams 000, 200 and 220, for which an L-shaped objective aperture was inserted into an FEI Titan 80/300 microscope. By decomposition of the image into 220 and 020 fringe images, artefacts due to nonlinear imaging are circumvented. Imaging conditions that minimise errors induced by inaccurately known specimen thickness are derived. Bloch wave simulations of reference 200 fringe contrast include structure factors adapted for chemical bonding, SAD, and diffuse losses due to SAD and TDS. As a main application, the threebeam method is applied to In(0.28)Ga(0.72)N(0.025)As(0.975) before and after thermal annealing. Dissolution of In-rich islands and N-rich clusters and formation of a homogeneously thick quantum well with nearly constant stoichiometry is found. The increase by a factor of 20 and blue-shift of 60meV of the photoluminescence peak are finally interpreted by means of the TEM results.