A New Approach for Feedback Control of Radius and Growth Rate in Czochralski (Cz) Processes Exemplarily Studied on LEC-InP

Abstract

Automatic control of Cz-processes plays an important role in mass production of mono crystalline material with respect e.g. to yield. Usually, in industrial scale, precise radius control can successfully be established using accumulated experiences over a large amount of growth runs together with PID algorithms at least in the cylindrical part of the crystal. However, with diameter up-scaling and the strong demand for increasing crystal quality new aspects like diameter control in the conical parts of the crystals and control of growth rate arise. As well, improvement of radius control even in the cylindrical part is essential. Thus, it is time to reconsider the problem of robust control of the Czochralski process. Our aim is to develop a robust controller which can be used i) without much experience concerning the thermal properties of the process; ii) to grow different crystal geometries without reparameterization; iii) for faster process set up, and iv) for high reproducibility, quality and yield. A new solution for the estimation of the system variables “radius” and “growth angle” by means of a nonlinear observer (“soft sensor”) is presented. With such a model based observer both variables can be reconstructed from the weighing cell signal much more accurately and less noisy as with classical numerical differentiation. Additionally, the observer is a prerequisite for sufficiently smooth reconstruction of the growth rate. The proposed new control scheme is partially based on a lumped parameter mathematical model of the process and allows us to control shape and growth rate of the crystal. It consists of two coupled loops providing the pull rate and temperature signals as the controls. The geometrical part of the Czochralski process is represented by the well known lumped parameter model of the capillary part of the system, which is quite accurate. This is not the case for the thermal part. Thus, for this part, a PID controller is applied. First experimental results confirm the capabilities of the proposed algorithms: • For 2-inch InP crystal growth the radius reference could be closely tracked within a range of 1-2% even in the conical parts. • The whole crystal shape (cylinder and conical parts) could be controlled using one set of control parameters only. • Within the same inner assemblies of the growth plant it is easily possible to grow crystals with differing geometry using the same parameter sets in the controller. • Crystal shape shows a high reproducibility. • Growth rate could be kept at its desired value for two hours using a single loop controller with a precision of less than 10%. The presented new control algorithm is believed to be of general character. It should be possible to adapt it quite directly to other types of Czochralski techniques, like LEC; low temperature gradient methods; growth from melt and solutions; materials like metals, semiconductors, oxides, halogenides, etc.