Berechnung des dreidimensionalen Hochfrequenzfeldes beim Zonenschmelzen von Silizium

Special induction coils., of which the axial symmetry is essentially disturbed, are used in float zone melting of silicon, crystals. This gives rise to three-dimensional (3D) electromagnetic field problem. Since the induction coil is supplied with high-frequency current in the megacycle region, the numerical calculation of the current distribution and of the converted specific power in the system can be efficiently performed with the aid of the Boundary Element Method (BEM). Vector potentials of the magnetic induction and of the current are introduced in order to set up the integral equation that is to be solved. The splitting up of the surfaces of the system, consisting of induction coil and ingot (silicon), into individual surface current elements transforms this equation into a linear algebraic system of equations for the scalar stream function of the surface current. The solution is achieved with the aid of Gaussian elimination. Numerical results for a greatly simplified model set up show good agreement with the results obtained by measurements. The Pascal programme that has been developed is used for the necessary parameter studies required for the optimum design of the induction coil.