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The successful and continuous improvement of modern semiconductor devices depends significantly on the ability to observe and describe the material properties as precisely as possible, in order for that understanding to serve as a basis for new developments. Complex semiconductor devices, such as
multijunction solar cells  and laser devices [3, 4], consist of multilayer structures and a combination of multinary material systems. Not only are the geometrical parameters of the system important to characterize, but the chemical composition also plays a crucial role in the functionality of the device. The STEM offers an effective combination of lateral resolution, i.e., sub-angstrom, and quantitative methods to gain insight into the material. Complementary simulations are essential to gain quantitative information from the investigated sample structure. In the course of this thesis, a workflow was developed to precisely model a real-world electron microscope sample. This included accounting for the most important experimental influences on efficient multislice simulations. An implementation of Kirkland’s commonly-used multislice algorithm was realized in the STEMsalabim software package  and explained in chapter 4.1. The software was specifically adapted and optimized for HPC clusters with a multi-CPU architecture. This enables the user to simulate samples with large lateral dimensions and perform important parameter sweeps within a reasonable timeframe. The mixture of different semiconductor material systems in multilayer structures can induce stress at
the interfaces where the magnitude is connected to the lattice mismatch of the two compounds. With very thin TEM samples, the stress is relaxed via elastic surface relaxation. The surface of the samples deforms elastically and the atomic lattice planes from the material bend from their resting positions. The resulting bent lattice planes provoke the electrons to de-channel, influencing the collected STEM ADF intensity. The effect itself, in addition to its influence on the STEM HAADF, is presented and explained in chapter 4.2. The simulation study modeled sample structures of GaP/GaAs/GaP with varied geometrical parameters and relaxed the structures by a FE algorithm. Multislice simulations were then performed with the relaxed supercells as input. It could be demonstrated that the mean square displacement of the atomic lattice planes is directly connected to the STEM ADF intensity. This enables computationally demanding multislice simulations to be exchanged with cheap FE simulations to still obtain an effective overview of the effect of surface relaxation. The simulation method was then adapted and applied to an experimental sample of GaP/Ga(As,P)/GaP. The simulated structure quantitatively matched with the experimental findings. This emphasizes the quality and precision of the FE simulations.
With the knowledge that the intensity of multislice simulations demonstrates a very good agreement with experimental intensities, a known method for composition determination was extended to achieve high lateral resolution and single-atom accuracy. The basis was to compare the experimental intensities to a simulated composition set, and determine the best match. The accuracy of the method was investigated in detail, and it was determined that a perfect agreement can only be achieved with very thin TEM samples. This is due to the way in which the intensities from materials with substitute elements are created. The statistical distribution of substitute atoms in the material leads to a spread in intensities for a given composition, due to the different possible Z-height configurations for this atomic column . Since the simulation set inherits the statistical nature of the height distribution of the substitute atoms by design, the effect on the STEM intensity is taken into account. The simulation study demonstrated that on average, the statistical composition errors eventually cancel out, and thus the
mean error of composition is symmetrically distributed around zero. Furthermore, the application of the method to three technologically important samples, namely (Ga,In)As, Ga(P,As) and SiGe, demonstrated a very good agreement with the widely-used HRXRD technology. The extended intensity method also provided a greatly improved 2D resolution of one atomic column. Furthermore, it is also possible to apply the extended method to determine unknown semiconductor
compositions via STEM intensity in multinary semiconductors. This was illustrated with a Ga(N,As,P) model system in , and with (Ga,In)(As,Bi)/GaAs and (Ga,In)(As,Bi)/InP in . The enhanced method makes use of the increased STEM intensity, in lower angular regions, generated by the lattice distortion due to N atoms in the lattice. This allows conclusions to be drawn about the N-content of the material. The higher angle intensity is mainly sensitive to the As content, and hence the individual chemical compositions can be determined individually. In summary, a comprehensive workflow has been developed and presented that includes experimental influences such as elastic surface relaxation, a finite source size and amorphous materials. All of this combined makes it possible to quantitatively investigate experimental STEM images via multislice simulations. An advantage of this technique is that no additional methods need to be used, and only STEM HAADF images and simulations are necessary. Some general improvements for future work are discussed in the following paragraphs. Firstly, the
simulation of amorphous materials could be prevented if the residual amorphous materials on the experimental samples could be decreased significantly. This would drastically improve the general quality of the experimental images . The speed of the calculations within the STEMsalabim software package could be improved by adapting the code to run on graphical processing units (GPU). A GPU is optimized for graphics problems, and consists of thousands of smaller efficient cores that are designed to handle multiple tasks simultaneously. The very large number of Fourier transformations that occur during a multislice simulation could be conducted on GPUs . Simulated STEM intensities exhibit a significant discrepancy in low angular regions in relation to
experimental data , and there are some indications that this may be due to inelastic scattering events . Currently, only elastic scattering events are taken into account by STEMsalabim. Techniques that take the inelastic effects into account have already been presented [88, 120], and could improve
the quality of the simulations with regard to angular intensity distribution. A further improvement would be the use of a pixelated detector that records the complete angular intensity distribution of every scan point, rather than the cumulative incoherent sum. If the angular intensity distribution could be present for every scan point of the experimental data, improved fitting methods could be applied to each pixel. This would increase the precision of simulation-based fitting
methods greatly [121-123]. The statistical distribution of substitute atoms in the multislice simulations leads to a spread in intensities for a given composition of an atom, due to the different possible Z-height configurations for this atomic column. Therefore, a mean intensity value was assigned, along with an associated width of the intensity distribution. The width of this intensity distribution determined the minimum uncertainty associated with any composition determination, and is primarily influenced by atomic column thickness, due to the increasing number of possible atomic configurations. Every method that relies on comparing
simulated intensities to experimental images is sensitive to the assumed or calculated sample thickness. Especially when the goal is to achieve single-atom accuracy, a falsely assumed sample thickness can have a significant effect. With the use of a pixelated detector, position averaged convergent beam
electron diffraction (PACBED) patterns could be evaluated, and PACBEDs could be easily recorded at every scan position, thus creating a very precise thickness map of the sample .