INFICON XTC/3 Thin Film Deposition Controller Operating Manual - Manual (Page 201)

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XTC/3 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.
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.
8.1.3 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
equation [4] .
[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.
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
-------------------------
 
 
=