INFICON STC-2002 Thin Film Deposition Controller Operating Manual - Manual (Page 263)

p STC-2002 DEPOSITION CONTROLLER y
SECTION 7.XX e page 261 of 276 ^
SECTION 7.0 Theory and Calibration
Measurement Theory
The STC-2002 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:
Equation 1:
( )
( )
( )
Af =
Nq Dq
Df Z Fc
ArcTan Z
Tan
Fq - Fc
Fq
•
• • •
•
• 















•

 

Π
Π
Where the terms used in the equation are defined as:
Af Film Thickness, in Angstroms (1a=10-10 Meters)
Nq Frequency Constant for AT Cut Crystal, 1.668 X 1013 Hz/Å
Dq Density of Quartz 2.648 gm/cm3
Π
The Constant Pi, 3.14159265358979324
Df Density Of Film Material in gm/cm3
Z Z-Factor of material, is the square root of the ratio [(Dq*uq)/(Df*uf)]. Dq and Df are the
densities as above 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.
Measuring Period
By measuring the period of the sensor oscillator signal and using a stable reference clock, an
extremely accurate frequency value for Fc is derived using advanced counter technology. Ten 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 eq1 or dealt strictly with the period type of measurement solution. The
thickness zero function stores as a base or offset 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
Rate computation is based on the rate of change of these thickness readings, updated ten times per
second, then filtered for display. Also available from the instrument is the raw measured frequency of the
sensor crystal.