The crystal weighing technique of the automatic control of diameter in Czochralski growth process is widely used for years. Already in the one of the first publications on the method the certain troubles in application of it to control of diameter of semiconductor crystals were observed, and the cause of instability of control system for semiconductor materials was qualitatively explained [1]. If the melt is denser then material solid, then the apparent weight shows an anomalous time dependence and dependence of on crystal radius, which cause positive feedback in the servo-loop and lead to instability. The similar effect takes place if melts do not completely wet solid. The problem increases with decreasing pulling rate.

Later weighing signal behavior was investigated in many works. To overcome the problem it is necessary to provide a low noisy differentiation of weighing signal, to use effective algorithms of control object identification and to apply control units, which provide control actions both on the temperature and the pulling rate [2-6]. The recent example of sophisticated approach to the problem is the article series about nonlinear model-based control of the LEC Czochralski process [7].

Meanwhile a simple effective approach, free from problems with anomalous behavior, was realized for the melt-level technique of automatic Czochralski crystal growth [8]. For measuring a crystal diameter the stepped crystal pulling in combination with stepped feeding of raw material was performed. After rapid lifting the crystal holder at a small distance the melt level drop in the crucible was measured and fixed. From these two values and the crucible diameter a current diameter or more exactly cross-sectional area of crystal can be calculated. Then the feeding system restored the melt level to its initial value and the cycle was repeated. This approach can easily be extended to the case of weighing the crystal or the crucible of melt. 

The essential development of the method presented in the report is the following. Under computer control small value periodical seesaw shifts are affecting the steady motion of the crystal holder. Buoyancy forces deviate as the crystal periodically moves across the melt level. Thus the weighting sensor generates buoyancy forces modulated signal. Neglecting the surface tension terms the growing crystal actual cross-sectional area is computed via the weighting modulated signal and the seesaw shifts of the crystal holder using the well-known formulas for buoyancy forces. 

Automatic feeding of the raw material during crystal growth does not needed at this case.  The magnitude of shift is established to be small enough and measuring cycle time to be short enough to prevent noticeable modulation of growth rate. It also should be noted measuring cycle time is much less than characteristic relaxation times of the processes that determine the dynamics of crystal growth. This is important factor in providing dynamical stability of the control system.

The method was checked on the growth of germanium crystal at low thermal gradients ~1 K/cm and at growth rate as low as 2 mm/h. It was found that the simple PI control law provides good system stability and dynamics. 

The main advantage of weighing control with modulation of movement of the pulling rod is the possibility to provide good performance of diameter control of CZ growth process using simple control laws for materials with “anomalous” behavior of weight signal. That is correct for the wide range of crystallization rates and also for LEC CZ.

Another essential advantage is radical lowering of the requirements to zero drift of weighing cell. Besides effect of evaporation on the control system is eliminated with the method under consideration. 

Corrections related to the effect of the meniscus on the results of measurement of the diameter of the crystal are discussed.

[1] W. Bardsley, G.W. Green, C.H. Holliday, D.T.J. Hurle. J. Cryst. Growth 16 (1972) 277.

[2] W. Bardsley, D.T.J. Hurle, G.C. Joyce. J. Cryst. Growth 40 (1977) 13.

[3] M. A. Gevelber, G. Stephanopoulos. J. Cr. Growth 84 (1987) 647

[4 ] G. Satunkin, A. Leonov. J. Cryst. Growth 102 (1990) 592.

[5] N.V. Abrosimov, V.N. Kurlov, S. N. Rossolenko. Prog. Cryst. Growth and Charact. of Materials 46 (2003) 1.

[6] G. Satunkin. Progress in Cryst. Growth and Charact. of Materials 56 (2010) 1.

[7] J. Winkler, M. Neubert, J. Rudolph. J. Cryst. Growth 312 (2010) 1005; ibid 312 (2010) 1019; M. Neubert, J. Rudolph. Ibid 360 (2012) 3.

[8] L.G. Eidelman, V.I. Goriletsky, V.G. Protsenko et al. J. Cryst. Growth, 128, (1993) 1059. 

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