INFICON MDC-360C Thin Film Deposition Controller - Manual (Page 135)

MDC-360C DEPOSITION CONTROLLER
THEORY OF OPERATION 10-1
10. THEORY OF OPERATION
10.1 BASIC MEASUREMENT
The MDC-360C 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. (28-33mm) 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.
10.2 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.
where:
N
q
= Frequency constant for an “AT” cut quartz crystal vibrating in thickness
shear (Hz x cm).
N
q
= 1.668 x 10
5
Hz x cm.
U
q
= Density of quartz g/cm
3
.
f
q
= Resonant frequency of uncoated crystal.
f = Resonant frequency of loaded crystal.
Tk
f
= Film thickness.
U
f
= Density of film g/cm
3
.
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.
f f
f
N
TK
q
f
q q
f

º
º
2
U
U
(1)