
transport and growth rates by a factor of approximately 10
4
at 1000
C and 10
2
at 1200
C.
Most vapor growth is done in quartz ampoules and the typical upper limit for use of quartz
is in the 1200–1300
C range. Experimental measurements by ZN Technology of the
transport rate of ZnO using PVT have typically resulted in rates lower than 1 10
6
mol
cm
2
h
1
which is too low to be practical for crystal growth. In these experiments, a
buffer gas of helium at a pressure of 370 Torr was used with a temperature differential
between the charge and the seed of 50
C. Even this low rate may have been
enhanced by residua l moisture or other impurities in the growth charge and system that
may have acted as transporting agents and increased the transport rate beyond that of
sublimation only.
The SCVT method provides the potential for much higher transport rates of ZnO at
significantly lower temperatures. In this method, the transporting agent reacts with the
source material causing a decrease in the partial pressure of the transporting agent and
production of high vapor pressure products. The vapor products formed by the reaction
then flow towards the growing crystal where the reverse reaction takes place. At the growth
interface, the reverse reaction releases the transporting agent causing an increase in the
transporting agent’s partial pressure at that point. Th erefore, the pressure differentials of
the transporting agent and the crystal forming products force the net fluxes of the zinc and
oxygen cont aining vapors to be from source to crystal while that of the transporting agent
is in the opposite direction. This counter flow of gases does not normally exist in PVT and
results in a slightly more complex flow system inside the ampoule.
Although not the only possibility, the transporting agent chosen for ZnO is hydrogen.
The reversible chemical reactio n of hydrogen with ZnO proceeds as:
ZnOðsÞþH
2
ðgÞ$ZnðvÞþH
2
OðvÞð7:1Þ
At the source (polycrystalline charge) end, the reaction proceeds from left to right (see
Figure 7.1) resulting in vaporization of the solid ZnO through usage of the hydrogen. At
the growth end, the reaction proceeds in the opposite direction with solid ZnO formed and
molecular hydrogen released. Transport rates of 5 10
4
mol cm
2
h
1
were achieved by
ZN Technology using a 20% mixture of hydrogen in helium.
While it would be possible to use pure hydrogen to increase the transport rate, growth of
high quality crys tals often requires reduced growth rates. To control the growth rate, the
SCVT growth of ZnO has been conducted with a mixture of inert gas and hydrogen. This
not only reduces the hydrogen partial pressure, a controlling factor in the transport rate, but
also provides a medium through which the vapors must diffuse to reach the growing
crystal. If conditions are set such that the transport rate is limited by the diffusion of the
vapors from one end of the ampoule to the other, independent control of the growth rate
and growth temperature can be achieved resulting in improved reproducibility and long
term stability of the system.
Faktor et al . developed a one-dimensional model for vapor transport and applied it to
crystal growth of CdS by PVT.
[11]
In their analysis, they used a combination of drift and
diffusion to describe the flux of a vapor per unit cross-sectional area given by:
J
vap
¼
U
RT
p
vap
D
RT
d
dx
p
vap
ð7:2Þ
Transport Theory and Comparison with Growth Data 173