INFICON Guardian EIES Controller - Manual (Page 129)

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Guardian Co-Deposition Controller Operating Manual
6.3 Theory of QCM Measurements
As material is deposited on a quartz crystal, its frequency decreases. The
frequency change correlates to a thickness, using the QCM equation:
[4]
AT crystal constant: [5]
Density of quartz: [6]
6.3.1 Density
Material density tables (in gm/cc) are commonly available in an Appendix to this
Operating Manual, chemical handbooks, and on the Internet. If you cannot find the
density of your material, it can be calculated empirically using this method:
1. Place your substrate adjacent to a new quartz sensor.
2. Set QCM Density to an approximate value; Z-Ratio =1; Tooling =100.
3. Deposit approximately 1000 to 5000 Å of material.
4. Use a profilometer or interferometer to measure the substrate's film thickness.
5. The actual density value is calculated by:
[7]
6.3.2 Z-Ratio or Z-Factor
Z-Ratio is used to match the acoustic impedance of the deposited material (Z
m
) to
that of the base quartz material (Z
q
=8.83) of the sensor crystal:
[8]
For example, the acoustic impedance of gold is Z=23.18, so:
[9]
T
f
N
q
D
q

 D
m
F
c
Z   
---------------------------------- Z
 F
q
F
c
–   
F
q
------------------------------ tan  atan  =
N
q
1.668
5
10 Hz-Cm  =
D
q
2.648
gm
cm
3
----------  =
Density
Actual
Density
Approx
Thickness
QCM
Thickness
Actual
------------------------------------------  =
Z-Ratio
Z
q
Z
m
------- =
Gold Z-Ratio
8.83
23.18
------------- .381 = =