INFICON STM-2XM 2-Channel Rate/Thickness Monitor - Manual (Page 136)

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STM-2XM Operating Manual
Since there is currently no way to separate the frequency change caused by added
mass (which is negative), or even the frequency changes caused by temperature
gradients across the crystal or film induced stresses, it is essential to minimize
these temperature-induced changes. It is only in this way that small changes in
mass can be measured accurately.
Figure 8-3 Thickness shear displacement
8.1.2 Period Measurement Technique
Although instruments using equation [2] were very useful, it was soon noted that
they had a limited range of accuracy, typically holding accuracy for DF less than
0.02 F
q
. In 1961, it was recognized by Behrndt 4 that:
[3]
where T
c
and T
q
are the periods of oscillation of the crystal with film (composite)
and the bare crystal, respectively.
The period measurement technique was the outgrowth of two factors:
 the digital implementation of time measurement, and
 the recognition of the mathematically rigorous formulation of the proportionality
between the thickness of the crystal, I
q
, and the period of oscillation, T
q
= 1/F
q
.
displacement node
X
X
X
2
1
3
E
4.K. H. Behrndt, J. Vac. Sci. Technol. 8, 622 (1961)
M
f
M
q
-------
T
c
T
q
–  
T
q
----------------------
F   
F
c
----------- = =