INFICON STM-100/MF Thin Film Deposition Monitor - Manual (Page 48)

Calibration and Theory
Measurement Theory
The STM-100 / MF uses the resonant frequency of an exposed quartz crystal
to sense the mass of deposited films attached to its surface. There is a known
relationship between the mass of such a film and the measured frequency of
the sensor crystal. Knowing the frequency change due to accumulated mass,
film thickness is determined by the following equation:
( )
( )
( )
Af =
Nq Dq
Df Z Fc
ArcTan Z Tan
Fq - Fc
Fq
(1) (2)
•
• • •





 • •
•












Π
Π
Where The Terms Used In The Equation Are Defined As:
Af Film Thickness, In Angstroms (1Å=10
-10
Meters)
Nq Frequency Constant For At Cut Crystal, 1.668 X 10
13
Hz-Ång
Dq Density Of Quartz 2.648 gm/cm
3
Π
The Constant Pi, 3.14159265358979324
Df Density Of Film Material In gm/cm
3
Z Z-Factor of material, is the square root of the ratio [(dq·uq)÷(df·uf)].
Dq and df are the density and uq and uf are the shear moduli of
quartz and the film, respectively. These values are available in
several materials handbooks.
Fq Frequency of sensor crystal prior to depositing film material on it.
This value is a manufacturing controlled constant.
Fc Frequency Of Loaded Sensor Crystal.
By measuring the period of approximately 1.2 million cycles of the sensor
oscillator signal and using a stable vhf reference clock, an extremely accurate
frequency value for fc is derived. Four times per second, a new value is
determined and used to update the above equation. The mathematics is
computed using IEEE double precision floating point format, ensuring the most
accurate results obtainable from the exact equation, even over wide extremes
of the Z-Factor and density parameters used in thin-film deposition. Use of the
tangent and arctangent functions to compute the film thickness to the
resolution of the floating point numeric format (56 bits of resolution) ensures
maximum accuracy. Previous solutions incorporated approximations to
Equation 1 or dealt strictly with the period type of measurement solution. The
thickness zero function stores as a base or offset of the current sensor
frequency and film thickness information, which is then continuously subtracted
from the later updated readings, yielding a deposited film thickness value
based on accumulated material since the latest zero function was performed.
Rate computation is based on the rate of change of these thickness
readings, updated four times per second, then filtered for display. Also
available from the instrument is the raw measured frequency of the sensor
crystal.
SECTION 4.1
Equation 1:
Measuring Period
Rate Computation
Page 4 - 1 Calibration and Theory