@phdthesis{Volkmann2004, author = {Volkmann, Thorsten}, title = {Lattice gas models and simulations of epitaxial growth}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-13812}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2004}, abstract = {In this PhD thesis, we develop models for the numerical simulation of epitaxial crystal growth, as realized, e.g., in molecular beam epitaxy (MBE). The basic idea is to use a discrete lattice gas representation of the crystal structure, and to apply kinetic Monte Carlo (KMC) simulations for the description of the growth dynamics. The main advantage of the KMC approach is the possibility to account for atomistic details and at the same time cover MBE relevant time scales in the simulation. In chapter 1, we describe the principles of MBE, pointing out relevant physical processes and the influence of experimental control parameters. We discuss various methods used in the theoretical description of epitaxial growth. Subsequently, the underlying concepts of the KMC method and the lattice gas approach are presented. Important aspects concerning the design of a lattice gas model are considered, e.g. the solid-on-solid approximation or the choice of an appropriate lattice topology. A key element of any KMC simulation is the selection of allowed events and the evaluation of Arrhenius rates for thermally activated processes. We discuss simplifying schemes that are used to approximate the corresponding energy barriers if detailed knowledge about the barriers is not available. Finally, the efficient implementation of the MC kinetics using a rejection-free algorithm is described. In chapter 2, we present a solid-on-solid lattice gas model which aims at the description of II-VI(001) semiconductor surfaces like CdTe(001). The model accounts for the zincblende structure and the relevant surface reconstructions of Cd- and Te-terminated surfaces. Particles at the surface interact via anisotropic nearest and next nearest neighbor interactions, whereas interactions in the bulk are isotropic. The anisotropic surface interactions reflect known properties of CdTe(001) like the small energy difference between the c(2x2) and (2x1) vacancy structures of Cd-terminated surfaces. A key element of the model is the presence of additional Te atoms in a weakly bound Te* state, which is motivated by experimental observations of Te coverages exceeding one monolayer at low temperatures and high Te fluxes. The true mechanism of binding excess Te to the surface is still unclear. Here, we use a mean-field approach assuming a Te* reservoir with limited occupation. In chapter 3, we perform KMC simulations of atomic layer epitaxy (ALE) of CdTe(001). We study the self-regulation of the ALE growth rate and demonstrate how the interplay of the Te* reservoir occupation with the surface kinetics results in two different regimes: at high temperatures the growth rate is limited to one half layer of CdTe per ALE cycle, whereas at low enough temperatures each cycle adds a complete layer. The temperature where the transition between the two regimes occurs depends mainly on the particle fluxes. The temperature dependence of the growth rate and the flux dependence of the transition temperature are in good qualitative agreement with experimental results. Comparing the macroscopic activation energy for Te* desorption in our model with experimental values we find semiquantitative agreement. In chapter 4, we study the formation of nanostructures with alternating stripes during submonolayer heteroepitaxy of two different adsorbate species on a given substrate. We evaluate the influence of two mechanisms: kinetic segregation due to chemically induced diffusion barriers, and strain relaxation by alternating arrangement of the adsorbate species. KMC simulations of a simple cubic lattice gas with weak inter-species binding energy show that kinetic effects are sufficient to account for stripe formation during growth. The dependence of the stripe width on control parameters is investigated. We find an Arrhenius temperature dependence, in agreement with experimental investigations of phase separation in binary or ternary material systems. Canonical MC simulations show that the observed stripes are not stable under equilibrium conditions: the adsorbate species separate into very large domains. Off-lattice simulations which account for the lattice misfit of the involved particle species show that, under equilibrium conditions, the competition between binding and strain energy results in regular stripe patterns with a well-defined width depending on both misfit and binding energies. In KMC simulations, the stripe-formation and the experimentally reported ramification of adsorbate islands are reproduced. To clarify the origin of the island ramification, we investigate an enhanced lattice gas model whose parameters are fitted to match characteristic off-lattice diffusion barriers. The simulation results show that a satisfactory explanation of experimental observations within the lattice gas framework requires a detailed incorporation of long-range elastic interactions. In the appendix we discuss supplementary topics related to the lattice gas simulations in chapter 4.}, subject = {Kristallwachstum}, language = {en} } @phdthesis{Weber2008, author = {Weber, Sebastian}, title = {Simulation of self-assembled nanopatterns in binary alloys on the fcc(111) surface}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-27914}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2008}, abstract = {In this PhD thesis, we study the heteroepitaxial crystal growth by means of Monte Carlo simulations. Of particular interest in this work is the influence of the lattice mismatch of the adsorbates relative to the substrate on surface structures. In the framework of an off-lattice model, we consider one monolayer of adsorbate and investigate the emerging nanopatterns in equilibrium and their formation during growth. In chapter 1, a brief introduction is given, which describes the role of computer simulations in the field of the physics of condensed matter. Chapter 2 is devoted to some technical basics of experimental methods of molecular beam epitaxy and the theoretical description. Before a model for the simulation can be designed, it is necessary to make some considerations of the single processes which occur during epitaxial growth. For that purpose we look at an experimental setup and extract the main microscopic processes. Afterwards a brief overview of different theoretical concepts describing that physical procedures is given. In chapter 3, the model used in the simulations is presented. The aim is to investigate the growth of an fcc crystal in the [111] direction. In order to keep the simulation times within a feasible limit a simple pair potential, the Lennard-Jones potential, with continuous particle positions is used, which are necessary to describe effects resulting from the atomic mismatch in the crystal. Furthermore the detailed algorithm is introduced which is based on the idea to calculate the barrier of each diffusion event and to use the barriers in a rejection-free method. Chapter 4 is attended to the simulation of equilibrium. The influence of different parameters on the emerging structures in the first monolayer upon the surface, which is completely covered with two adsorbate materials, is studied. Especially the competition between binding energy and strain leads to very interesting pattern formations like islands or stripes. In chapter 5 the results of growth simulations are presented. At first, we introduce a model in order to realize off-lattice Kinetic Monte Carlo simulations. Since the costs in simulation time are enormous, some simplifications in the calculation of diffusion barriers are necessary and therefore the previous model is supplemented with some elements from the so-called ball and spring model. The next point is devoted to the calculation of energy barriers followed by the presentation of the growth simulations. Binary systems with only one sort of adsorbate are investigated as well as ternary systems with two different adsorbates. Finally, a comparison to the equilibrium simulations is drawn. Chapter 6 contains some concluding remarks and gives an outlook to possible further investigations.}, subject = {Kristallwachstum}, language = {en} } @article{FornariRapplMorelhaoetal.2016, author = {Fornari, C. I. and Rappl, P. H. O. and Morelhao, S. L. and Peixoto, T. R. F. and Bentmann, H. and Reinert, F. and Abramof, E.}, title = {Preservation of pristine Bi\(_2\)Te\(_3\) thin film topological insulator surface after ex situ mechanical removal of Te capping layer}, series = {APL Materials}, volume = {4}, journal = {APL Materials}, doi = {10.1063/1.4964610}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-164468}, pages = {106107}, year = {2016}, abstract = {Ex situ analyses on topological insulator films require protection against surface contamination during air exposure. This work reports on a technique that combines deposition of protective capping just after epitaxial growth and its mechanical removal inside ultra-high vacuum systems. This method was applied to Bi2Te3 films with thickness varying from 8 to 170 nm. Contrarily to other methods, this technique does not require any sputtering or thermal annealing setups installed inside the analyzing system and preserves both film thickness and surface characteristics. These results suggest that the technique presented here can be expanded to other topological insulator materials.}, language = {en} } @phdthesis{Trabel2019, author = {Trabel, Mirko}, title = {Growth and Characterization of Epitaxial Manganese Silicide Thin Films}, doi = {10.25972/OPUS-18472}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-184720}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2019}, abstract = {This thesis describes the growth and characterization of epitaxial MnSi thin films on Si substrates. The interest in this material system stems from the rich magnetic phase diagram resulting from the noncentrosymmetric B20 crystal structure. Here neighboring spins prefer a tilted relative arrangement in contrast to ferro- and antiferromagnets, which leads to a helical ground state where crystal and spin helix chirality are linked [IEM+85]. This link makes the characterization and control of the crystal chirality the main goal of this thesis. After a brief description of the material properties and applied methods, the thesis itself is divided into four main parts. In the first part the advancement of the MBE growth process of MnSi on Si\((111)\) substrate as well as the fundamental structural characterization are described. Here the improvement of the substrate interface by an adjusted substrate preparation process is demonstrated, which is the basis for well ordered flat MnSi layers. On this foundation the influence of Mn/Si flux ratio and substrate temperature on the MnSi layer growth is investigated via XRD and clear boundaries to identify the optimal growth conditions are determined. The nonstoichiometric phases outside of this optimal growth window are identified as HMS and Mn\(_5\)Si\(_3\). Additionally, a regime at high substrate temperatures and low Mn flux is discovered, where MnSi islands are growing incorporated in a Si layer, which could be interesting for further investigations as a size confinement can change the magnetic phase diagram [DBS+18]. XRD measurements demonstrate the homogeneity of the grown MnSi layers over most of the 3 inch wafer diameter and a small \(\omega\)-FWHM of about 0.02° demonstrates the high quality of the layers. XRD and TEM measurements also show that relaxation of the layers happens via misfit dislocations at the interface to the substrate. The second part of the thesis is concerned with the crystal chirality. Here azimuthal \(\phi\)-scans of asymmetric XRD reflections reveal twin domains with a \(\pm\)30° rotation to the substrate. These twin domains seem to consist of left and right-handed MnSi, which are connected by a mirror operation at the \((\bar{1}10)\) plane. For some of the asymmetric XRD reflections this results in different intensities for the different twin domains, which reveals that one of the domains is rotated +30° and the other is rotated -30°. From XRD and TEM measurements an equal volume fraction of both domains is deduced. Different mechanisms to suppress these twin domains are investigated and successfully achieved with the growth on chiral Si surfaces, namely Si\((321)\) and Si\((531)\). Azimuthal \(\phi\)-scans of asymmetric XRD reflections demonstrate a suppression of up to 92\%. The successful twin suppression is an important step in the use of MnSi for the proposed spintronics applications with skyrmions as information carriers, as discussed in the introduction. Because of this achievement, the third part of the thesis on the magnetic properties of the MnSi thin films is not only concerned with the principal behavior, but also with the difference between twinned and twin suppressed layers. Magnetometry measurements are used to demonstrate, that the MnSi layers behave principally as expected from the literature. The analysis of saturation and residual magnetization hints to the twin suppression on Si\((321)\) and Si\((531)\) substrates and further investigations with more samples can complete this picture. For comparable layers on Si\((111)\), Si\((321)\) and Si\((531)\) the Curie-Weiss temperature is identical within 1 K and the critical field within 0.1 T. Temperature dependent magnetoresistivity measurements also demonstrate the expected \(T^2\) behavior not only on Si\((111)\) but also on Si\((321)\) substrates. This demonstrates the successful growth of MnSi on Si\((321)\) and Si\((531)\) substrates. The latter measurements also reveal a residual resistivity of less then half for MnSi on Si\((321)\) in comparison to Si\((111)\). This can be explained with the reduced number of domain boundaries demonstrating the successful suppression of one of the twin domains. The homogeneity of the residual resistivity as well as the charge carrier density over a wide area of the Si\((111)\) wafer is also demonstrated with these measurements as well as Hall effect measurements. The fourth part shows the AMR and PHE of MnSi depending on the angle between in plane current and magnetic field direction with respect to the crystal direction. This was proposed as a tool to identify skyrmions [YKT+15]. The influence of the higher C\(_{3\mathrm{v}}\) symmetry of the twinned system instead of the C\(_3\) symmetry of a B20 single crystal is demonstrated. The difference could serve as a useful additional tool to prove the twin suppression on the chiral substrates. But this is only possible for rotations with specific symmetry surfaces and not for the studied unsymmetrical Si\((321)\) surface. Measurements for MnSi layers on Si\((111)\) above the critical magnetic field demonstrate the attenuation of AMR and PHE parameters for increasing resistivity, as expected from literature [WC67]. Even if a direct comparison to the parameters on Si\((321)\) is not possible, the higher values of the parameters on Si\((321)\) can be explained considering the reduced charge carrier scattering from domain boundaries. Below the critical magnetic field, which would be the region where a skyrmion lattice could be expected, magnetic hysteresis complicates the analysis. Only one phase transition at the critical magnetic field can be clearly observed, which leaves the existence of a skyrmion lattice in thin epitaxial MnSi layers open. The best method to solve this question seems to be a more direct approach in the form of Lorentz-TEM, which was also successfully used to visualize the skyrmion lattice for thin plates of bulk MnSi [TYY+12]. For the detection of in plane skyrmions, lamellas would have to be prepared for a side view, which seems in principle possible. The demonstrated successful twin suppression for MnSi on Si\((321)\) and Si\((531)\) substrates may also be applied to other material systems. Suppressing the twinning in FeGe on Si\((111)\) would lead to a single chirality skyrmion lattice near room temperature [HC12]. This could bring the application of skyrmions as information carriers in spintronics within reach. Glossary: MBE Molecular Beam Epitaxy XRD X-Ray Diffraction HMS Higher Manganese Silicide FWHM Full Width Half Maximum TEM Tunneling Electron Microscopy AMR Anisotropic MagnetoResistance PHE Planar Hall Effect Bibliography: [IEM+85] M. Ishida, Y. Endoh, S. Mitsuda, Y. Ishikawa, and M. Tanaka. Crystal Chirality and Helicity of the Helical Spin Density Wave in MnSi. II. Polarized Neutron Diffraction. Journal of the Physical Society of Japan, 54(8):2975, 1985. [DBS+18] B. Das, B. Balasubramanian, R. Skomski, P. Mukherjee, S. R. Valloppilly, G. C. Hadjipanayis, and D. J. Sellmyer. Effect of size confinement on skyrmionic properties of MnSi nanomagnets. Nanoscale, 10(20):9504, 2018. [YKT+15] T. Yokouchi, N. Kanazawa, A. Tsukazaki, Y. Kozuka, A. Kikkawa, Y. Taguchi, M. Kawasaki, M. Ichikawa, F. Kagawa, and Y. Tokura. Formation of In-plane Skyrmions in Epitaxial MnSi Thin Films as Revealed by Planar Hall Effect. Journal of the Physical Society of Japan, 84(10):104708, 2015. [WC67] R. H. Walden and R. F. Cotellessa. Magnetoresistance of Nickel-Copper Single-Crystal Thin Films. Journal of Applied Physics, 38(3):1335, 1967. [TYY+12] A. Tonomura, X. Yu, K. Yanagisawa, T. Matsuda, Y. Onose, N. Kanazawa, H. S. Park, and Y. Tokura. Real-Space Observation of Skyrmion Lattice in Helimagnet MnSi Thin Samples. Nano Letters, 12(3):1673, 2012. [HC12] S. X. Huang and C. L. Chien. Extended Skyrmion Phase in Epitaxial FeGe(111) Thin Films. Physical Review Letters, 108(26):267201, 2012.}, subject = {Molekularstrahlepitaxie}, language = {en} }