Inficon SQC-310

8 - 1
PN 074-550-P1D
IQM-233 Operating Manual
Chapter 8
Measurement Theory
8.1 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 is 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 1950s 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 g/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
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
KF
d
f
----------------
=