INFICON MDC-370 Thin Film Deposition Controller User Manual
Page 124
MDC-370 DEPOSITION CONTROLLER
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.
where:
τ
= Period of loaded crystal (sec.)
τ
q
= Period of uncoated crystal (sec.)
Note: Units of are cm/sec.
Note that 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:
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
(
)
TK
N
f
q
q
f
q
=
⋅
−
ρ
ρ
τ τ
TK
N
R
R
f
q
f
q
z
z
q
=
⋅ ⋅
⋅
−
ρ
ρ
τ
π
π
τ τ
τ
arctan
tan
(2)
(3)
THEORY OF OPERATION
10-2