Inficon XTC/3, Operating Manual, Page: 187 / 210

7 - 3
XTC/3 Operating Manual
7.4 Laboratory Determination of Z-Ratio
A list of Z-values for materials commonly used is available in the Material Library.
For other materials, Z can be calculated from the following formula:
[3]
[4]
where:
d
f
= density (g/cm
3
) of deposited film
µ
f
= shear modulus (dynes/cm
2
) of deposited film
d
q
= density of quartz (crystal) (2.649 g/cm
3
)
µ
q
= shear modulus of quartz (crystal) (3.32 x 10
11
dynes/cm
2
)
The densities and shear moduli of many materials can be found in a number of
handbooks.
Laboratory results indicate that Z-values of materials in thin film form are very close
to the bulk values. However, for high stress producing materials, Z-values of thin
films are slightly smaller than those of the bulk materials. For applications that
require more precise calibration, the following direct method is suggested:
1
Establish the correct density value as described in section 7.2 on page 7-1 .
2
Install a new crystal and record its starting frequency F
co
. It will be necessary
to send the S13 command to get this information (refer to Chapter 5, Remote
Communications ).
3
Make a deposition on a test substrate such that the percent crystal life display
will read approximately 50%, or near the end of crystal life for the particular
material, whichever is smaller.
4
Stop the deposition and record the ending crystal frequency F
c
using the S13
command.
5
Remove the test substrate and measure the film thickness with either a multiple
beam interferometer or a stylus-type profilometer.
6
Using the density value from step 1 and the recorded values for F
co
and F
c
,
adjust the Z-Ratio value in thickness equation [5] to bring the calculated
thickness value into agreement with the actual thickness. If the calculated value
Z
d
q

q
d
f

f
------------
 
 
 
1
2
---
=
Z 9.378 10
5
d
f

f
 
-
1
2
---

=