INFICON TM-400 Thin Film Deposition Monitor User Manual
Page 56
8 - 2
IP
N 17
88
0
0 Re
v.
B
TM-350/400 Operating Manual
Improvements in sensor crystals and oscillator circuits resulted in a significant
increase in achievable frequency shift. Low cost integrated digital circuits became
available allowing a significant increase in basic instrument accuracy. As a result
of the above two factors, the frequency squared term in the scale factor became a
significant limitation on the measurement accuracy.
If the period of oscillation is measured rather than the frequency, 1/period can be
substituted for frequency resulting in the following equation.
[2]
where:
t = Period of loaded crystal (sec.)
t
q
= Period of uncoated crystal (sec.)
NOTE: Units of are cm/sec.
NOTE: The constant of proportionality in this equation is constant. This
approach was demonstrated to be a significant improvement over
frequency measurement and was widely adopted.
The original assumption that the addition of a foreign material to the surface of the
crystal produced the same effect as that of the addition of an equal mass of quartz
was of course, questionable and indeed work with crystals heavily loaded with
certain materials showed significant and predictable deviation between the actual
measured film thickness and that predicted by equation 2. Analysis of the loaded
crystal as a one-dimensional composite resonator of quartz and the deposited film
led to the equation below:
[3]
where:
R
z
is referred to as the Acoustic Impedance Ratio and is obtained by dividing
the acoustic impedance of quartz by the acoustic impedance of the deposited
film.
This equation introduces another term into the relationship, which is the ratio of the
acoustic impedance of quartz to the acoustic impedance of the deposited film. The
acoustic impedance is that associated with the transmission of a shear wave in the
material. Note that if the acoustic impedance ratio is equal to one, quartz on quartz,
equation 3 reduces to equation 2.
Although the above equation still involves a number of simplifying assumptions, its
ability to accurately predict the film thickness of most commonly deposited
materials has been demonstrated.
TK
f
N
q
P
q
⋅
P
f
----------------- t t
q
–
(
)
=
TK
f
P
q
P
f
-----
⎝ ⎠
⎛ ⎞ N
q
t
πR
z
---------
⎝
⎠
⎛
⎞ arc
R
z
π
tan
t t
q
–
t
-----------
⎝
⎠
⎛
⎞
tan
⋅
⋅
⋅
=