3 z-match technique – INFICON IQM-233 Thin Film Deposition Controller PCI-Express Card Operating Manual User Manual
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IQM-233 Operating Manual
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.
7.1.3 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
.
[4]
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 yield
theoretically correct results in a time frame that was practical for process control.
To achieve this new level of accuracy requires only that the user enter an additional
material parameter, Z, for the film being deposited. This equation has been tested
for a number of materials, and has been found to be valid for frequency shifts
equivalent to
F
f
= 0.4F
q
. Keep in mind that
was valid to only
0.02F
q
and
was valid only to
~0.05F
q
.
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
d
f
F
c
Z
------------------
arctan Z tan
F
q
F
c
–
F
q
-------------------------
=