References / Literature

1. Detailed introduction to the VCz-process and Czochralski-crystal growth in general
2. Publications dealing with the control of the Czochralski-process in general
3. Publications dealing with the dynamics of the meniscus region and its influence on the weighing signal
4. Introduction to heat transfer mechanism and modelling
5. Very few important publications dealing with modern control and observation theory

Detailed introduction to the VCz-process and Czochralski-crystal growth in general

1

P. Rudolph, M. Neubert, S. Arulkumaran, and M. Seifert.
Vapour pressure controlled Czochralski (VCz) growth -- a method to produce electronic materials with low dislocation density.
Crystal Research and Technology, 32:35-50, 1997.

2

P. Rudolph and M. Jurich.
Bulk growth of GaAs -- an overview.
Journal of Crystal Growth, 198:325-335, 1999.

In german:

3

M. Neubert and P. Rudolph.
Das VCz-Verfahren -- eine Technologie zum Ziehen defektarmer GaAs- und anderer III-V-Kristalle großer Durchmesser.
Mitteilungsblatt der DGKK, 69:11-16, 1999.

4

K.Th. Wilke and J. Bohm.
Kristallzüchtung.
VEB Deutscher Verlag der Wissenschaften (Berlin), 1988.

Publications dealing with the control of the Czochralski-process in general

5

M.A. Gevelber and G. Stephanopoulos.
Dynamics and control of the Czochralski process i.
Journal of Crystal Growth, 84:647-668, 1987.

6

M.A. Gevelber, G. Stephanopoulos, and M.J. Wargo.
Dynamics and control of the Czochralski process ii.
Journal of Crystal Growth, 91:199-217, 1988.

7

M.A. Gevelber.
Dynamics and control of the Czochralski process iii.
Journal of Crystal Growth, 139:271-285, 1994.

8

M.A. Gevelber.
Dynamics and control of the Czochralski process iv.
Journal of Crystal Growth, 139:286-301, 1994.

9

D.P. Looze, A. Farzin, and B. Bernstein.
Modelling and identification of the liquid encapsulated Czochralski GaAs process for control.
Journal of Crystal Growth, 148:79-95, 1995.

Consider the following articles which are very interesting and mathematicaly complex (but maybe less important for application):

10

G.A. Satunkin.
Mathematical modelling and control system design of Czochralski and liquid encapsulated Czochralski processes: the basic low order mathematical model.
Journal of Crystal Growth, 154:172-188, 1995.

11

P.K.C. Wang.
Feedback control of a heat diffusion system with time-dependent spatial domain.
Optimal Control Applications & Methods, 16:305-320, 1995.

Publications dealing with the dynamics of the meniscus region and its influence on the weighing signal

12

S.V. Tsivinskii.
Inzh. Fiz. Zh. Akad. Nauk. Bellorussk SSR 5, (1962), 59.

13

D.T.J. Hurle.
Analytic representation of the shape of the meniscus in Czochralski growth.
Journal of Crystal Growth, 63:13-17, 1983.

14

W. Bardsley, D.T. Hurle, and G.C. Joyce.
The weighing method of automatic Czochralski crystal growth.
Journal of Crystal Growth, 40:13-20, 1977.

15

T.H. Johansen.
Analysis of the weighing method applied to liquid encapsulated Czochralski growth.
Journal of Crystal Growth, 84:609-620, 1987.

16

T.H. Johansen.
On the theory of the weighing method for automatic crystal shape control on Czochralski growth.
Journal of Crystal Growth, 80:343-350, 1987.

Introduction into heat transfer mechanism and modelling

17

W.M. Rohsenow, J.P. Hartnett, and Y.I. Cho, editors.
Handbook of heat transfer.
McGraw-Hill (New York), 1998.

18

W. Miller, U. Rehse, and K. Böttcher.
Influence of melt convection on the interface during Czochralski crystal growth.
Solid-State Electronics, 44:825-830, 2000.

Very few important publications dealing with modern control and observation theory

19

M. Fliess, J. Levine, P. Martin, and P. Rouchon.
Flatness and defect of non-linear systems: introductory theory and examples.
International Journal of Control, 61:1327-1361, 1995.

20

M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph.
Controlling the transient of a chemical reactor: a distributed parameter approach.
In Proc. CESA'98 IMACS-IEEE, Hammamet, Tunesia, 1998.

21

D. Guillaume, P. Rouchon, and J. Rudolph.
Two simple observers for a class of polymerization reactors.
In Proc. of 4th European Control Conference, Brussels, Belgium, 1997.
Paper no. 849.

22

F.E. Thau.
Observing the state of non-linear dynamic systems.
International Journal of Control, 17:471-479, 1973.

In german:

23

R. Rothfuß, J. Rudolph, and M. Zeitz.
Flachheit: Ein neuer Zugang zur Steuerung und Regelung nichtlinearer Systeme.
at -- Automatisierungstechnik, 11:517-525, 1997.