Appendix A
Material Properties
The equation governing all quartz crystal thin film monitors and controllers is:
T f
.
.
N q D q
.
.
.
π
D m F c Z
atan .
Z tan
.
π
F q F c
F q
where the constant terms for the quartz crystal are:
AT crystal constant:
Density of Quartz:
D q
.
2.648
gm
cm
3
For example, a material and sensor frequency change of:
Density of material:
D m
.
2.700
gm
cm
3
Z-Factor of material:
Z
1.00
Starting Frequency:
F q
.
6000000
Hz
Ending Frequency:
F c
.
5999995
Hz
Yields a Thickness (in Angstroms) of:
=
.
T f m
10
2.272
Z-Factor 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:
Z-Factor = Z
q
/ Z
m
For example, the acoustic impedance of gold is Z=23.18, so:
Gold Z-Factor = 8.83 / 23.18 = .381
N q
.
.
1.668 10
13
Hz
m
10