INFICON TM-400 Thin Film Deposition Monitor - Manual (Page 55)

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TM-350/400 Operating Manual
Chapter 8
Theory of Operation
8.1 Basic Measurement
The TM-350/400 uses a quartz crystal as the basic transducing element. The
quartz crystal itself is a flat circular plate approximately 0.55 in. (1.40 cm) in
diameter and 0.011-0.013 in. (28-33 mm) thick for 6 and 5 MHz. The crystal
thickness is inversely proportional to the crystal frequency. The crystal is excited
into mechanical motion by means of an external oscillator. The unloaded crystal
vibrates in the thickness shear mode at approximately the frequency of the
specified crystal. The frequency at which the quartz crystal oscillates is lowered by
the addition of material to its surface.
8.2 Film Thickness Calculation
Early investigators noted that if one assumed that the addition of material to the
surface produced the same effect as the addition of an equal mass of quartz, the
following equation could be used to relate the film thickness to the change in crystal
frequency.
[1]
where:
N
q
= Frequency constant for an “AT” cut quartz crystal vibrating in thickness
shear (Hz x cm).
N
q
= 1.668 x 105 Hz x cm.
P
q
= Density of quartz g/cm
3
.
f
q
= Resonant frequency of uncoated crystal.
f = Resonant frequency of loaded crystal.
Tk
f
= Film thickness.
f = Density of film g/cm3
This equation proved to be adequate in most cases, however, note that the
constant of proportionality is not actually constant because the equation contains
the crystal frequency, which of course changes as the film builds up. Because the
achievable frequency change was small enough, the change in scale factor fell
within acceptable limits.
TK
f
N
q
P
q
⋅
P
f
f
2
⋅
----------------- f
q
f
–
( )
=