Computer simulation of growth and photo-induced phenomena
The thesis consists of three main parts: i) kinetic Monte Carlo simulation of step-bunching on crystalline surface during growth, ii) molecular dynamics simulation of growth of amorphous semiconductors, iii) tight-binding molecular dynamics investi-gation of photo-induced phenomena in amorphous Sele...
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|Summary:||The thesis consists of three main parts: i) kinetic Monte Carlo simulation of step-bunching on crystalline surface during growth, ii) molecular dynamics simulation of growth of amorphous semiconductors, iii) tight-binding molecular dynamics investi-gation of photo-induced phenomena in amorphous Selenium. In Chapter 2 I have investigated the influence of immobile impurities on epi-taxial growth for the first time using two dimensional kinetic Monte Carlo simula-tions, more specifically how immobile impurities cause step-bunching. I have im-plemented a kinetic Monte Carlo code which is capable to simulate the deposition of about one million atoms in the relevant parameter regime. I have instigated systems with two, three and eight steps. Systems with two steps showed three different type of behavior corresponding to the type of impurities. Systems show step-pairing if I co-deposit impurities which cause extra potential barriers on the surface, i.e. impuri-ties which hinder diffusion locally. If impurities do not effect the potential barrier for hopping of adatoms on the flat surface then the time development of the terrace sizes follow random walk behavior and do not show either any sign of step-pairing nor any tendency to equalize distances between steps. By co-depositing impurities which en-hance local diffusion I observed terrace size-equalization after the deposition of ten monolayers. More complicated situation arises in the case of three steps. The time development of the terrace sizes even in the absence of impurities shows a more complex behavior due to the coupling between velocities of neighboring steps through shared terrace. That is the reason why oscillations of terrace sizes can be observed even in the case of no impurities. Impurities can either enhance or suppress the oscillations but they do not cause stable step-pairing any more, as this was the case when considering only two steps. Step-pairing can be observed in the case of three-steps, but step-pairs remain only bound for the time needed to depozit about one monolayer. In the case of eight-steps I investigated the interaction between steps. By applying impurities which enhance local diffusion it is possible to equalize the terrace sizes in the case of systems with eight steps. No step-bunching has been ob-served when I co-deposited impurities which suppress local diffusion, only step-pairs have been clearly observed which were stable only for the deposition time of about two monolayers. Step pair formation and dissolution shows wave like behavior. Simulation results suggests that although impurities effect the growth dynamics sub-stantially, but no step-bunching takes place as the direct consequence of the presence of impurities in the system. It may happen however that larger step-bunches form under certain conditions due to complex behavior of the system if the system size and number of deposited impurities becomes macroscopically large. The situation is expected in that case to be similar to traffic jams on highways. In Chapter 3 I investigated the growth of amorphous semiconductors using molecular dynamics simulation. Chapter 3 has three main sections where I discuss results (Section 3.3, Section 3.4 and Section 3.5). In Section 3.3 I present results on molecular dynamics simulation of prepara-tion methods of amorphous Selenium using classical empirical potential to describe interatomic interactions. Classical empirical potentials enable the simulations of large systems (1000-2000 atoms) and long time scales (1-2 ns) on a single processor. I have compared structures grown at different bombarding energies (0.1 eV, 1 eV and 10 eV) keeping all other parameters unchanged: substrate temperature is 100 K, injection rate is one atom in every 300 fs. I have observed strong dependence of the densities on the bombarding energies. The density increases with bombarding en-ergy: 3.21 g/cm3 (0.1 eV), 3.73 g/cm3 (1 eV) and 4.34 (10 eV) g/cm3. I have noticed that number of backscattered atoms increases with decreasing bombarding energy. Kinetics of the growth is different depending on bombarding energy. In the case of 0.1 eV bombarding energy a porous structure is built up with voids. These voids be-come filled up by atoms in a later stage of the bombardment. On the other hand, in the case of 1 eV bombarding energy there is no difference between early and late stages of growth. I also compared different preparation techniques: growth versus rapid quenching. The rapid quenched sample was more homogeneous than its grown counterpart, this can be explained by the smaller number of voids present in the rapid quenched sample. I compared physical properties of the prepared amorphous samples with diffraction measurements both on amorphous samples and on large number of Selenium containing molecules. The simulation produced a too narrow first neighbor peak when compared to diffraction measurements on amorphous samples. Agree-ment with structure of molecules was on the other hand remarkable, both with re-spect to bond length and to bond angle distributions. In Section 3.4 I have compared amorphous Selenium structures grown using three different type of interatomic potentials with various accuracy to determine when it is necessary to use the more accurate but more CPU intensive method. The three applied potentials were: a classical empirical potential (CLASS), a tight-binding model without Hubbard-term (TB-NOHUB) and a self-consistent tight-binding model with Hubbard-term (TB-HUB). The Hubbard term helps to avoid any large charge transfer. I analysed the structural properties of the obtained amorphous networks: significant differences were found in the radial distribution functions, bond angles, dihedral angles and coordination defects. Furthermore, I have presented sta-tistics based on a large number of diffraction measurements on molecules containing Selenium fragments. I observed an increase in bond length with decreasing bond an-gle. Only model TB-HUB did not reproduce this experimental result. Overall, model TB-HUB is the most realistic amorphous Selenium network. Model TB-NOHUB is unacceptable due to it is high number of coordination defects. In Section 3.5 I describe the results after I have implemented a recently pro-posed tight-binding model for Silicon (Lenosky model) in the ATOMDEP program package. This new model should perform much better than previous versions. My motivation was to produce good quality structural models of amorphous Silicon and I was also motivated by the fact that – to my knowledge – the potential has not been tested so far for disordered structures. I have prepared an amorphous Silicon sample using the same procedure and physical parameters that have been used by K. Kohary who has applied a different tight-binding description developed by Kwon et al. My aim was to compare the two structural models and decide which tight-binding model is more appropriate to provide good amorphous Silicon structures. I have compared densities, bond lengths, bond angles, number of coordination defects, number of tri-angles and squares. The most decisive difference can be seen in the description of coordination defects. The Kwon model produces six-fold and two-fold coordinated defects while the Lenosky model not. I have also examined the compatibility of both tight-binding models with the Wooten-Winer-Weaire amorphous Silicon structural model which has 100 % four-fold coordinated atoms. I have relaxed the Wooten-Winer-Weaire model containing 216 atoms at T=0 K with both tight-binding models and calculated the number of coordination defects in the models. The two tight- binding models produced opposite results: the Lenosky model introduced three-fold coordinated defects, while the Kwon model five and six-fold coordinated defects. Overall, I conclude that the Lenosky model provides better description for amor-phous Silicon, the most important reason for this is that the Lenosky model does not produce six-fold coordinated defects in the amorphous structure. Such defects should be present only in liquid phase. In Chapter 4 I present results on tight-binding molecular dynamics simulation of photo-induced phenomena in amorphous Selenium. In isolated eight-member Se-lenium ring and in isolated Selenium chain I have observed bond-breaking after transferring one electron from the highest occupied molecular orbital to the lowest unoccupied molecular orbital. Following this finding I simulated the behavior of a 162 atom amorphous Selenium network under photo-excitation. In that calculations I assumed that electron-hole interaction can be neglected because the energy scale of the potential fluctuations due to disorder is larger than the typical energy of electron-hole coupling. Therefore I handled electrons and holes separately and I simulated electron creation and hole creation in separate runs. Based on the simulation results I have proposed a new explanation for the photo-induced volume changes in chalco-genide glasses. I have found that covalent bond breaking occurs in the networks with excited electrons, whereas holes contribute to the formation of inter-chain bonds. In the ideal situation both processes are reversible. The interplay between photo-induced bond breaking and inter-chain bond formation leads to either volume expan-sion or shrinkage. Therefore, both the expansion and the contraction of chalcogenide glasses can be described in this frame, supported by molecular dynamics simulations. I also considered the non-ideal case, where only a part of the processes is irreversible and the total expansion includes reversible and irreversible changes. The microscopic explanation of the macroscopic photo-induced volume change is consistent with the first in-situ surface height measurements. By showing that tight-binding molecular dynamics simulations are capable to predict and explain physical processes on the atomic level I have pioneered one way for future simulations on photo-induced phenomena.|