Modeling multifrequency eddy current sensor interactions during vertical Bridgman growth of semiconductors

Abstract

Electromagnetic finite element modeling methods have been used to analyze the responses of two ͑''absolute'' and ''differential''͒ eddy current sensor designs for measuring liquid-solid interface location and curvature during the vertical Bridgman growth of a wide variety of semiconducting materials. The multifrequency impedance changes due to perturbations of the interface's location and shape are shown to increase as the liquid/solid electrical conductivity ratio increases. Of the materials studied, GaAs is found best suited for eddy current sensing. However, the calculations indicate that even for CdTe with the lowest conductivity ratio studied, the impedance changes are still sufficient to detect the interface's position and curvature. The optimum frequency for eddy current sensing is found to increase as the material system's conductivity decreases. The analysis reveals that for a given material system, high frequency measurements are more heavily weighted by the interfacial location while lower frequency data more equally sample the interface curvature and location. This observation suggests a physical basis for potentially measuring both parameters during vertical Bridgman growth.