Zone melting

Heaters

A variety of heaters can be used for zone melting, with their most important characteristic being the ability to form short molten zones that move slowly and uniformly through the ingot. Induction coils, ring-wound resistance heaters, or gas flames are common methods. Another method is to pass an electric current directly through the ingot while it is in a magnetic field, with the resulting magnetomotive force carefully set to be just equal to the weight in order to hold the liquid suspended. Optical heaters using high-powered halogen or xenon lamps are used extensively in research facilities particularly for the production of insulators, but their use in industry is limited by the relatively low power of the lamps, which limits the size of crystals produced by this method. Zone melting can be done as a batch process, or it can be done continuously, with fresh impure material being continually added at one end and purer material being removed from the other, with impure zone melt being removed at whatever rate is dictated by the impurity of the feed stock.^{[citation needed]}

Indirect-heating floating zone methods use an induction-heated tungsten ring to heat the ingot radiatively, and are useful when the ingot is of a high-resistivity semiconductor on which classical induction heating is ineffective.^{[citation needed]}

Mathematical expression of impurity concentration

When the liquid zone moves by a distance ${\displaystyle dx}$, the number of impurities in the liquid change. Impurities are incorporated in the melting liquid and freezing solid.^{[5][clarification needed]}

${\displaystyle k_{O}}$: segregation coefficient

${\displaystyle L}$: zone length

${\displaystyle C_{O}}$: initial uniform impurity concentration of the solidified rod

${\displaystyle C_{L}}$: concentration of impurities in the liquid melt per length

${\displaystyle I}$: number of impurities in the liquid

${\displaystyle I_{O}}$: number of impurities in zone when first formed at bottom

${\displaystyle C_{S}}$: concentration of impurities in the solid rod

The number of impurities in the liquid changes in accordance with the expression below during the movement ${\displaystyle dx}$ of the molten zone

${\displaystyle dI=(C_{O}-k_{O}C_{L})\,dx\;}$

${\displaystyle C_{L}=I/L\;}$

${\displaystyle \int _{0}^{x}dx=\int _{I_{O}}^{I}{\frac {dI}{C_{O}-{\frac {k_{O}I}{L}}}}}$

${\displaystyle I_{O}=C_{O}L\;}$

${\displaystyle C_{S}=k_{O}I/L\;}$

${\displaystyle C_{S}(x)=C_{O}\left(1-(1-k_{O})e^{-{\frac {k_{O}x}{L}}}\right)}$

Solar cells

In solar cells, float zone processing is particularly useful because the single-crystal silicon grown has desirable properties. The bulk charge carrier lifetime in float-zone silicon is the highest among various manufacturing processes. Float-zone carrier lifetimes are around 1000 microseconds compared to 20–200 microseconds with Czochralski method, and 1–30 microseconds with cast polycrystalline silicon. A longer bulk lifetime increases the efficiency of solar cells significantly.^{[citation needed]}

High-resistivity devices

It's used for production of float-zone silicon-based high-power semiconductor devices.^[6]: 364

Zone remelting

Another related process is zone remelting, in which two solutes are distributed through a pure metal. This is important in the manufacture of semiconductors, where two solutes of opposite conductivity type are used. For example, in germanium, pentavalent elements of group V such as antimony and arsenic produce negative (n-type) conduction and the trivalent elements of group III such as aluminium and boron produce positive (p-type) conduction. By melting a portion of such an ingot and slowly refreezing it, solutes in the molten region become distributed to form the desired n-p and p-n junctions.^{[citation needed]}