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Neubert M.,Leibniz Institute For Kristallzuchtung | Winkler J.,TU Dresden
Journal of Crystal Growth | Year: 2012

This contribution continues an article series [1,2] about the nonlinear model-based control of the Czochralski crystal growth process. The key idea of the presented approach is to use a sophisticated combination of nonlinear model-based and conventional (linear) PI controllers for tracking of both, crystal radius and growth rate. Using heater power and pulling speed as manipulated variables several controller structures are possible. The present part tries to systematize the properties of the materials to be grown in order to get unambiguous decision criteria for a most profitable choice of the controller structure. For this purpose a material specific constant M called interface mobility and a more process specific constant S called system response number are introduced. While the first one summarizes important material properties like thermal conductivity and latent heat the latter one characterizes the process by evaluating the average axial thermal gradients at the phase boundary and the actual growth rate at which the crystal is grown. Furthermore these characteristic numbers are useful for establishing a scheduling strategy for the PI controller parameters in order to improve the controller performance. Finally, both numbers give a better understanding of the general thermal system dynamics of the Czochralski technique. © 2012 Elsevier B.V.

Neubert M.,Leibniz Institute For Kristallzuchtung | Winkler J.,TU Dresden
Journal of Crystal Growth | Year: 2014

The paper proposes a model-based feedforward control for the Czochralski crystal growth process. It completes the system for nonlinear model-based control presented by the authors in previous publications. From a system theoretical point of view such a feedforward control requires a dynamic lumped parameter model of the hydrodynamical-geometrical as well as of the thermal subsystem of the process. For the heater feedforward control one lacks the latter one with the necessary accuracy. A static approach circumventing this problem is presented here, based on a mathematical description regarding the most important qualitative dependencies between relative changes of manipulated and controlled variables during growth. In combination with feedback control, high precision tracking of the most important system variables, crystal diameter and crystal growth rate, is ensured. Additionally, a comprehensive discussion of the dependencies of the heater feedforward control on technological parameters, growth regimes and crystal shapes is given. © 2014 Elsevier B.V.

Winkler J.,TU Dresden | Neubert M.,Leibniz Institute For Kristallzuchtung | Rudolph J.,Saarland University
Journal of Crystal Growth | Year: 2010

In this contribution a nonlinear observer for reconstruction of not directly measured quantities in Czochralski and liquid encapsulated Czochralski crystal growth is derived. The observer can be used in control systems which require knowledge of the crystal radius, of the crystal slope angle, and of the crystal growth rate. Using a nonlinear lumped parameter model these quantities are reconstructed from the weight gain signal which is usually available in growth plants. In contrast to existing solutions found in the literature the nonlinear observer can be used throughout the whole process, especially when growing the conical parts in which the dynamics of the process is changing heavily. The capability of the observer as well as thorough investigations regarding its robustness are illustrated using simulations and experimental results. © 2010 Elsevier B.V. All rights reserved.

Winkler J.,TU Dresden | Neubert M.,Leibniz Institute For Kristallzuchtung | Rudolph J.,Saarland University
Acta Physica Polonica A | Year: 2013

On the occasion of the centennial of the invention of the Czochralski crystal growth process by the Polish scientist Jan Czochralski, a review of selected strategies for the automatic control of this process is given. This review provides a sketch of the fundamental challenges of controlling the Czochralski process and the basic concepts of feedback control. Both early and modern approaches to the control of the Czochralski process are described. The discussion focuses on questions related to feed-forward control, feedback control, and state estimation. The presented methods rely on simple mathematical process models in contrast to the finite element model-based approaches typically used in crystal growth process design and analysis. Such mathematical models motivate both the structure and parameters of the chosen controller. A comprehensive list of references to background literature on this topic completes this survey.

Cho Y.,Paul Drude Institute for Solid State Electronics | Cho Y.,TU Eindhoven | Brandt O.,Paul Drude Institute for Solid State Electronics | Korytov M.,Leibniz Institute For Kristallzuchtung | And 4 more authors.
Applied Physics Letters | Year: 2012

We study the impact of substrate temperature and layer thickness on the morphological and structural properties of InN films directly grown on O-face ZnO (0001̄) substrates by plasma-assisted molecular beam epitaxy. With increasing substrate temperature, an interfacial reaction between InN and ZnO takes place that eventually results in the formation of cubic In 2O 3 and voids. The properties of the InN films, however, are found to be unaffected by this reaction for substrate temperatures less than 550°C. In fact, both the morphological and the structural quality of InN improve with increasing substrate temperature in the range from 350 to 500°C. High quality films with low threading dislocation densities are demonstrated. © 2012 American Institute of Physics.

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