ULTRAPURIFICATION B Y DISTILLATION W .
R . W I L C O X 1
Par& Semiconductors, Inc., Lawndale, Calif.
With the recent progress in the science of the solid state, it has become increasingly essential to use materials of exceedingly high purity. Fractional distillation shows great promise as an effective technique for preparing ultrapure materials. The special equations necessary to design such a batch distillation are derived. They are much simpler than the usual batch distillation equations, because the quantity of the second component is very small in ultrapurification.
H
purity has become increasingly necessary for progress of solid-state materials. in the science and application .. A recent conference was devoted entirely to the subject of ultrapurification of semiconductor materials ( 7 ) . These efforts originally stemmed from the fact that apparently insignificant amounts of certain impurities produced unexpectedly large electrical effects. For example, one part in 1010 of gold in silicon is easily detected by its effect in reducing carrier lifetime. About a thousandth of a monolayer of copper is detectable on the surface of germanium, simply by the change caused in the resistivity at room temperature upon heating the crystal. Many techniques have been employed to approach these stringent purity requirements. T h e ancient workhorse of industrial and laboratory separations, fractional distillation, has also been employed occasionally, but clearly not to the extent possible. The equations necessary to design a simple batch distillation for ultrapurification are derived in this paper. Basically, distillation is the selective vaporization of a mixture of liquids, so that the vapor's composition differs from that of the liquid. In the most elementary form of distillation, the liquid is partially vaporized and the vapor condensed. T h e efficiency of the process is multiplied by contact of the vapor with condensate flowing in the opposite direction in a column. Various types of trays and packings are employed to make this contact more effective. Ultrapurification poses special problems for the materials of construction of the distillation system. Very pure and especially very inert and insoluble materials must be used-for example, quartz would be advisable for distillation of silicon compounds. Column packing could be made from quartz tubing. The whole apparatus could then he easily cleaned using hydrofluoric acid IGH
Derivation of Equations
Because the quantity of each impurity is small, interactions between them can safely be ignored. Hence, the following derivations are for binary mixtures only-i.e., the behavior of each impurity is considered independent. The usual batch distillation operation is shown schematically in Figure 1. The relation among the overhead composition, x,: the boiler composition. Y,,. a t any instant of time: and the number of theoretical plates is given by the Lelvis equation (2: 6). 1
Present address, Aerospace Corp., El Segundo. Calif.
A constant reflux ratio, D ' 0 , is assumed. The molar concentration. y n , in the vapor a t any point is related to that in the liquid, x,, by an equilibrium expression, such as
If 3 and x are for the impurity concentration in a very pure material, Equation 2 reduces to
y =
(3)
cy%
The fractional error in this approximation is X ( L Y - 1). For example, with LY = 1.5. the error would be only 1% for a 2y0 impurity content. which is much higher than would normally be encountered in purifications of this type. Substituting Equation 3 into Equation 1 we obtain
(4)
Rearranging, we obtain XL =
(5)
YXn
This equation gives the relation between the instantaneous values for concentration in the boiler and in the condenser. T o relate these concentrations to the initial concentration, x ~ , in~ the , boiler feed we use the following modified form of the Rayleigh equation (7) :
I t is assumed that the effect of column holdup is negligible. In practice holdup operates to reduce the effectiveness of the separation. Substituting Equation 5 into Equation 6 we obtain
(7) L / L , is the fraction of the feed that remains in the boiler. It is usually desired in such a'purification to reduce the amount of impurity by a given factor. LVe call this factor the purification, P, which equals the initial impurity concentration divided by the product impurity concentration VOL. 3
NO.
1
FEBRUARY
1964
81
Case A. a > 1 . For a > 1 the impurity is more volatile and, hence, the residue in the boiler is the purified fraction. T h e purification is
P =
( y ) (L,) =
L
This gives
(Y - ' ) Y
Case A. a
>
1
Case B.
withdrawn and all of the condensate is returned to the column. This may be calculated by means of the Fenske equation (4)
Problem. T h e vapor pressure of the impurity is twice that of the material to be purified. I t is desired to reduce the amount of impurity to oile hundredth, while sacrificing half of the liquid supplied. Find a reasonable column size and reflux ratio. Solution. a P
=
2
=
100
(LIL,)= 0.5 From Equation 15 the minimum number of trays, N , is given by
But so
In a
or
xg
=
as
XL
(13) In
Substituting this into Equation 6, we obtain as the maximum possible separation
-
In 2 =
Case A. a
>
1
Case B. a
