INFICON XTM/2 Thin Film Deposition Monitor - Manual (Page 99)

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XTM/2 Operating Manual
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
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 equation [6] was
valid to only 0.02F
q
and equation [7] was valid only to ~0.05F
q
.
5.5.5 Active Oscillator
All of the instrumentation developed to date has relied on the use of an active
oscillator circuit, generally the type schematically shown in
Figure 5-4 . This
circuit actively keeps the crystal in resonance, so that any type of period or
frequency measurement may be made. In this type of circuit, oscillation is
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
---------------------------
⎝ ⎠
⎛ ⎞
=