Inficon IC6, Operating Manual

Page: 322 / 342

16 - 10
IP
N 07
4-
50
5-
P1
E
IC6 Operating Manual
assignment refer to the number of phase reversals in the wave motion along the
three axes of the crystal. The above-referenced papers by Wilson and Tiersten &
Smythe are examinations of modal properties, relating the various properties of the
radius of curvature to the placement of the anharmonics relative to the
fundamental.
As material is deposited upon one face of a crystal, the entire spectrum of
resonances shifts to lower frequencies. The three above mentioned modes are
observed to have slightly different mass sensitivity and hence undergo slightly
different frequency shifts. It is this difference that is used to estimate the Z-Ratio of
the material. Using the modal equations and the observed frequencies of the
modes [100] and [102], one can calculate the ratio of two elastic constants C
66
and
C
55
. Both of these elastic constants relate to shear motion. The essential element
of Wajid’s theory is the following equation:
[5]
where M is the aerial mass density (film mass to quartz mass ratio per unit area)
and Z is the Z-Ratio. It is a fortunate coincidence that the combination MZ also
appears in the Lu-Lewis
equation [4] , which can be used to extract an estimate of
the effective Z-Ratio from the equations below:
[6]
or
[7]
Where, F
q
and F
c
denote uncoated and coated crystal frequencies in the
fundamental mode (mode [100]). Due to the multi-valued nature of the
mathematical functions involved, the value of Z-Ratio extracted in this manner is
not always a positive definite quantity. This is hardly of any consequence however,
because M is uniquely determined with the estimated Z and the measured
frequency shift. Thus, thickness and rate of deposition are subsequently calculated
from the knowledge of M.
11
One must be aware of the limitations of this technique. Since the estimate for
Z-Ratio is dependent on the frequency shifts of the two modes, any spurious shift
due to excessive mechanical or thermal stress on the crystal will lead to errors.
11.U.S. Patent No. 5,112,642 (May 12, 1992) International Patents Pending.
C
55
C
66
  
coated
C
55
C
66
  
uncoated
--------------------------------------------
1
1 MZ +
 
-----------------------

MZ

F
c
F
q
-----
 
 
Z +

F
c
F
q
-----
 
 
tan tan 0 =
Z
MZ

F
c
F
q
-----
 
 
tan

F
c
F
q
-----
 
 
tan
--------------------------------- – =