INFICON STM-2XM 2-Channel Rate/Thickness Monitor - Manual (Page 138)

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STM-2XM Operating Manual
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/monitors 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.
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 [2] was valid to only 0.02F
q
and equation [3] 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
-------------------------
 
 
=