Zone melting

Process details

The principle is that the segregation coefficient k (the ratio at equilibrium of an impurity in the solid phase to that in the liquid phase) is usually less than one. Therefore, at the solid/liquid boundary, the impurity atoms will diffuse to the liquid region. Thus, by passing a crystal boule through a thin section of furnace very slowly, such that only a small region of the boule is molten at any time, the impurities will be segregated at the end of the crystal. Because of the lack of impurities in the leftover regions which solidify, the boule can grow as a perfect single crystal if a seed crystal is placed at the base to initiate a chosen direction of crystal growth. When high purity is required, such as in semiconductor industry, the impure end of the boule is cut off, and the refining is repeated.

In zone refining, solutes are segregated at one end of the ingot in order to purify the remainder, or to concentrate the impurities. In zone leveling, the objective is to distribute solute evenly throughout the purified material, which may be sought in the form of a single crystal. For example, in the preparation of a transistor or diode semiconductor, an ingot of germanium is first purified by zone refining. Then a small amount of antimony is placed in the molten zone, which is passed through the pure germanium. With the proper choice of rate of heating and other variables, the antimony can be spread evenly through the germanium. This technique is also used for the preparation of silicon for use in integrated circuits ("chips").

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.

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.

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.

${\displaystyle k_O}$: 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

${\displaystyle dI=(C_O-k_O{C}_L)dx}$

${\displaystyle C_L=I/L}$

${\displaystyle {\int }_0^{x}dx={\int }_{I_O}^I\frac{dI}{C_O-\frac{k_{O}I}{L}}}$

${\displaystyle I_O=C_{O}L}$

${\displaystyle C_S=k_{O}I/L}$

${\displaystyle C_S(x)=C_O\left(1-(1-k_O)e^{-\frac{k_{O}x}{L}}\right)}$