INFICON Cygnus Thin Film Deposition Controller - Manual (Page 199)

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Cygnus Operating Manual
Chapter 9
Measurement and Control Theory
9.1 Basics
The Quartz Crystal deposition monitor, or QCM, utilizes the piezoelectric sensitivity
of a quartz monitor crystal to added mass. The QCM uses this mass sensitivity to
control the deposition rate and final thickness of a vacuum deposition. When a
voltage is applied across the faces of a properly shaped piezoelectric crystal, the
crystal is distorted and changes shape in proportion to the applied voltage. At
certain discrete frequencies of applied voltage, a condition of very sharp
electro-mechanical resonance is encountered. When mass is added to the face of
a resonating quartz crystal, the frequency of these resonances are reduced. This
change in frequency is very repeatable and is precisely understood for specific
oscillating modes of quartz. This heuristically easy to understand phenomenon is
the basis of an indispensable measurement and process control tool that can easily
detect the addition of less than an atomic layer of an adhered foreign material.
In the late 1950’s it was noted by Sauerbrey 1,2 and Lostis 3 that the change in
frequency, F = F
q
-F
c
, of a quartz crystal with coated (or composite) and uncoated
frequencies, F
c
and F
q
respectively, is related to the change in mass from the
added material, M
f
, as follows:
[1]
where M
q
is the mass of the uncoated quartz crystal. Simple substitutions lead
to the equation that was used with the first “frequency measurement”
instruments:
[2]
where the film thickness, T
f
, is proportional (through K) to the frequency change,
F, and inversely proportional to the density of the film, d
f
. The constant, K =
N
at
d
q
/F
q
2
; where d
q
(= 2.649 gm/cm
3
) is the density of single crystal quartz and N
at
(=166100 Hz cm) is the frequency constant of AT cut quartz. A crystal with a
starting frequency of 6.0 MHz will display a reduction of its frequency by 2.27 Hz
when 1 angstrom of Aluminum (density of 2.77 gm/cm
3
) is added to its surface. In
this manner the thickness of a rigid adlayer is inferred from the precise
1.G. Z. Sauerbrey, Phys. Verhand .8, 193 (1957)
2.G. Z. Sauerbrey, Z. Phys. 155,206 (1959)
3.P. Lostis, Rev. Opt. 38,1 (1959)
M
f
M
q
-------
F   
F
q
----------- =
T
f
K F   
d
f
----------------
=