In electronics industry silicon wafers are the strategic raw material. They are produced from single silicon crystals which are grown from purified silicon melt mainly by the Czochralski (CZ) method. Also other semiconductor materials, e.g., germanium and gallium-arsenide, are grown by the CZ crystal growth. In CZ growth, a cylindrical crystal rod (for silicon, typically with a diameter of 4-8 inches) is pulled vertically from the melt in a heated crucible. The crystal rod and the crucible are usually rotated in opposite directions. Solid crystals are afterwards cut to form thin semiconductor wafers from which, e.g., integrated circuits, are produced.

In the Czochralski process, the couplings between different physical phenomena lead to quite a complicated behavior of the system. Inside the Czochralski furnace, heat is transferred by radiation, convection and conduction. Radiation dominates the overall heat transfer due to the high temperature environment. Heat transfer in the melt flow is dominated by convection. Forced, natural and, to a lesser extent thermocapillary, convection mechanisms drive the melt flow. In addition, chemical reactions take place during the process. For example, the silicon melt slowly dissolves the silica crucible, creating silicon monoxide.

High crystal quality requires control and optimization of the process. In particular, in large-scale crystal growth environment, melt flow is time-dependent, three dimensional and at least mildly turbulent. There are relatively large temporal fluctuations in the melt temperature and flow fields, also directly under the crystal. These result in inhomogeneous material properties, e.g., dopant and oxygen striations, as well as in an occasional loss of the single crystalline structure. Thus, melt flow plays an essential role in crystal quality.

Experimental measurements for temperature and velocity fields offer invaluable information from physical mechanisms. They are, however, very laborious to make and require construction of complicated experimental systems. Mathematical models and numerical simulations provide insight into the physical phenomena in the crystal growth, and reduce the economical investments required in the experimental work.