INFICON STM-2 USB Thin Film Rate/Thickness Monitor - Manual (Page 94)

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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
----------- = =