INFICON XTC/C Thin Film Deposition Controller - Manual (Page 140)

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XTC/C - XTC/2 Operating Manual
accumulates cycles from the reference oscillator until m counts are
accumulated in the first. Since the frequency of the reference is stable and
known, the time to accumulate the m counts is known to an accuracy equal to
± 2/F
r
where F
r
is the reference oscillator’s frequency. The monitor crystal’s
period is (n/F
r
)/m where n is the number of counts in the second accumulator.
The precision of the measurement is determined by the speed of the reference
clock and the length of the gate time (which is set by the size of m). Increasing
one or both of these leads to improved measurement precision.
Having a high frequency reference oscillator is important for rapid
measurements (which require short gating times), low deposition rates and low
density materials. All of these require high time precision to resolve the small,
mass induced frequency shifts between measurements. When the change of a
monitor crystal’s frequency between measurements is small, that is, on the
same order of size as the measurement precision, it is not possible to establish
quality rate control. The uncertainty of the measurement injects more noise into
the control loop, which can be counteracted only by longer time constants. Long
time constants cause the correction of rate errors to be very slow, resulting in
relatively long term deviations from the desired rate. These deviations may not
be important for some simple films, but can cause unacceptable errors in the
production of critical films such as optical filters or very thin layered
superlattices grown at low rates. In many cases the desired properties of these
films can be lost if the layer to layer reproducibility exceeds one, or two,
percent. Ultimately, the practical stability and frequency of the reference
oscillator limits the precision of measurement for conventional instrumentation.
5.5.4 Z-Match Technique
After learning of fundamental work by Miller and Bolef
5
, which rigorously
treated the resonating quartz and deposited film system as a one-dimensional
continuous acoustic resonator, Lu and Lewis
6
developed the simplifying
Z-Match equation in 1972. Advances in electronics taking place at the same
time, namely the micro-processor, made it practical to solve the Z-Match
equation in “real-time”. Most deposition process controllers sold today use this
sophisticated equation that takes into account the acoustic properties of the
resonating quartz and film system as shown in
equation [8] .
[8]
where Z=(d
q
u
q
/d
f
u
f
)
1/2
is the acoustic impedance ratio and u
q
and u
f
are the
shear moduli of the quartz and film, respectively. Finally, there was a
fundamental understanding of the frequency-to-thickness conversion that could
5.J. G. Miller and D. I. Bolef, J. Appl. Phys. 39, 5815, 4589 (1968)
6.C. Lu and O. Lewis, J Appl. Phys. 43, 4385 (1972)
T
f
N
at
d
q
πd
f
F
c
Z
------------------
⎝ ⎠
⎛ ⎞
arctan Z tan
π F
q
F
c
–
( )
F
q
---------------------------
⎝ ⎠
⎛ ⎞
=