Modelling of properties of point defects and their clusters in dislocationfree single crystal germanium
Piotr Śpiewak
Abstract
Dislocationfree germanium crystals, used to produce substrates for optoelectronic and electronic applications can be grown by the Czochralski crystal growth technique. In order to widen their applicability it is important to minimize defects on the surface of germanium substrates. At least part of these defects originate from grownin defects formed during the crystal growth process. Based upon analogies with the problem of defects in Czochralskigrown silicon crystals, the current understanding is that these microdefects are the result of aggregation of point defects which are formed at the crystal/melt boundary during the solidification process. In order to gain a better control of the crystal growth process and to minimize the distribution and/or size of grownin microdefects, it is essential to understand the mechanisms responsible for their formation. In sharp contrast to silicon there is little literature available on the formation of grownin defects in germanium. In these circumstances, the objectives of the presented Thesis were as follows: • to buildup a physical model which gives insight into the formation of grownin defects in Czochralskigrown germanium crystals, and its experimental verification, • to develop a method and software code which can be used to describe and predict the distribution of the microdefects in terms of the crystal growth process parameters (in particular the temperature distribution in the growing crystal and the pulling rate). The analyses presented in this thesis are based on a combination of atomistic, for computing materials properties, and mesoscale simulations, for computing the distribution of microdefects in crystals during their growth from the melt. For the development of the model, it was necessary to obtain satisfactory estimates of certain physical material properties. As measurements of these properties are currently hardly possible, they were estimated from ab initio and molecular dynamics calculations. However, widely used electronicstructure methods, based on local and semilocal densityfunctional calculations, give in the case of Ge a vanishing band gap. To overcome this deficiency higher level electronicstructure methods were used, such as the LDA+U approach and the screened hybrid functional HSE06. Based on the detailed analyse of the point defects dynamics and selfdiffusion data for silicon and germanium, a simplification of the mathematical description of microdefect formation in germanium was possible. It was shown that the selfdiffusion coefficient in germanium is dominated by vacancy diffusion and that the contribution of selfinterstitials is negligible. This allowed the exclusion of selfinterstitials from the defect dynamics model. Taking into account the twodimensionality requirement and the computational efficiency, the model based on classical nucleation theory was adapted for Ge. The mathematical model for aggregation was implemented in the Germanium Defect Code (GeDeC), developed in the frame of the present study, by using the finite volume method (FVM). The temperature dependent diffusion coefficient and thermal equilibrium concentration of vacancies were estimated based on published experimental data and from atomistic simulations. The obtained values were used as input for the aggregation software after adjustments based on experimental data. The distributions of microdefects in growing crystals have been simulated using GeDeC. The predicted histograms of microdefects distributions were compared to measured pit distribution on polished wafers. The good agreement observed between simulations and experiments suggests that the pits observed on germanium wafer surfaces originate from voids formed by vacancy clustering and vacancy diffusion controls cluster growth during the cooling of the crystal. The numerical simulations developed in this thesis relate technological process parameters with microdefect formation in crystalline germanium. From a technological point of view, these results provide a useful tool for quantitative predictions, which can be used to optimise the Ge crystal pulling technology. The use of the simulation techniques proposed here, may result in the reduction of expensive and time consuming trialanderror experiments currently needed for developing new technologies of crystal growth.Diploma type  Doctor of Philosophy  
Author 
Piotr Śpiewak (FMSE)
Piotr Śpiewak
 
Title in English  Modelling of properties of point defects and their clusters in dislocationfree single crystal germanium  
Language  en angielski  
Certifying Unit  Faculty of Materials Science and Engineering (FMSE)  
Discipline  material sciences and engineering / (technology domain) / (technological sciences)  
Defense Date  29012010  
Supervisor 
Krzysztof Kurzydłowski (FMSE / DMD)
Krzysztof Kurzydłowski
 
Internal reviewers 
Krzysztof Zdunek (FMSE / DSE)
Krzysztof Zdunek
 
External reviewers 
Adam Kiejna
Adam Kiejna
 
Pages  152  
Keywords in English  xxx  
Abstract in English  Dislocationfree germanium crystals, used to produce substrates for optoelectronic and electronic applications can be grown by the Czochralski crystal growth technique. In order to widen their applicability it is important to minimize defects on the surface of germanium substrates. At least part of these defects originate from grownin defects formed during the crystal growth process. Based upon analogies with the problem of defects in Czochralskigrown silicon crystals, the current understanding is that these microdefects are the result of aggregation of point defects which are formed at the crystal/melt boundary during the solidification process. In order to gain a better control of the crystal growth process and to minimize the distribution and/or size of grownin microdefects, it is essential to understand the mechanisms responsible for their formation. In sharp contrast to silicon there is little literature available on the formation of grownin defects in germanium. In these circumstances, the objectives of the presented Thesis were as follows: • to buildup a physical model which gives insight into the formation of grownin defects in Czochralskigrown germanium crystals, and its experimental verification, • to develop a method and software code which can be used to describe and predict the distribution of the microdefects in terms of the crystal growth process parameters (in particular the temperature distribution in the growing crystal and the pulling rate). The analyses presented in this thesis are based on a combination of atomistic, for computing materials properties, and mesoscale simulations, for computing the distribution of microdefects in crystals during their growth from the melt. For the development of the model, it was necessary to obtain satisfactory estimates of certain physical material properties. As measurements of these properties are currently hardly possible, they were estimated from ab initio and molecular dynamics calculations. However, widely used electronicstructure methods, based on local and semilocal densityfunctional calculations, give in the case of Ge a vanishing band gap. To overcome this deficiency higher level electronicstructure methods were used, such as the LDA+U approach and the screened hybrid functional HSE06. Based on the detailed analyse of the point defects dynamics and selfdiffusion data for silicon and germanium, a simplification of the mathematical description of microdefect formation in germanium was possible. It was shown that the selfdiffusion coefficient in germanium is dominated by vacancy diffusion and that the contribution of selfinterstitials is negligible. This allowed the exclusion of selfinterstitials from the defect dynamics model. Taking into account the twodimensionality requirement and the computational efficiency, the model based on classical nucleation theory was adapted for Ge. The mathematical model for aggregation was implemented in the Germanium Defect Code (GeDeC), developed in the frame of the present study, by using the finite volume method (FVM). The temperature dependent diffusion coefficient and thermal equilibrium concentration of vacancies were estimated based on published experimental data and from atomistic simulations. The obtained values were used as input for the aggregation software after adjustments based on experimental data. The distributions of microdefects in growing crystals have been simulated using GeDeC. The predicted histograms of microdefects distributions were compared to measured pit distribution on polished wafers. The good agreement observed between simulations and experiments suggests that the pits observed on germanium wafer surfaces originate from voids formed by vacancy clustering and vacancy diffusion controls cluster growth during the cooling of the crystal. The numerical simulations developed in this thesis relate technological process parameters with microdefect formation in crystalline germanium. From a technological point of view, these results provide a useful tool for quantitative predictions, which can be used to optimise the Ge crystal pulling technology. The use of the simulation techniques proposed here, may result in the reduction of expensive and time consuming trialanderror experiments currently needed for developing new technologies of crystal growth.  
Thesis file 

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