Limitations in using kilohertz radio frequencies for float zone silicon crystals

Abstract

Radio frequency generators in the range 2–5 MHz (megahertz) are commonly used for growing silicon crystals by the float- zone process. Industry demand for larger diameter crystals requires that the power output capability of the rf generators be increased. As the power output of a generator is increased, however, corona forms; and the resultant arcs prove to be a serious problem. The voltage across a work coil delivering a power, Pmelt at a frequency, f, is shown to be Va=1K P12meltf34 where K is a constant that depends on the coil and rod geometry. Since corona formation is a result of a large coil voltage impressed across the relatively small gap between the coil and rod and between the coil terminals, substantially less corona should result from lowering the frequency of an rf generator to the 200–500 kHz range which is widely used in industrial processes. Theoretical consideration of melting characteristics at lower frequencies indicate that there are formidable difficulties associated with the use of kHz frequencies for float-zone refining. The increased electrical skin depth at lower frequencies does not allow the outer surface of the silicon rod to properly melt. A calculation of the temperatures and heat transfer in a surface inductively heated at various frequencies shows this to be true. Experiments were conducted to study the melting characteristics of silicon at both MHz and kHz frequencies and the results were found to be in agreement with theoretical predictions. The rods could not be zone refined at kHz frequencies because smooth melting of the outer skin was uncontrolled. The surface formed a shell with a thickness and other features that depended on the work coil shape and the generator frequency. Various methods were tried to alter the melting pattern but with limited success.