JPK Instruments NanoWizard
®
Handbook Version 2.2a
43
Correction factors
The rather simple assumptions in the basic thermal noise analysis cause a few
systematic errors in the measurements. There are various differences with the real
measurement system.
One source of error is that
the sensitivity measured by the force curve on a hard
surface is for a relatively large, static deflection of the tip. The cantilever bending
shape during dynamic fluctuations is rather different, and since the detection system
is primarily sensitive to
angular deflections it has a different sensitivity for the
measurements of the thermal noise. Correction factors have been calculated for
instance by Butt and Jaschke (Nanotechnology 1995) to take account of the
difference between z-deflection and angular
deflection for the different bending
modes of the cantilever.
Usually the first resonance of the cantilever is used, as this has the largest
amplitude, and therefore the best signal-to-
noise ratio for accurate measurements.
For very soft cantilevers in
liquid, however, the first resonance is at frequencies
around 1kHz where it is affected by low frequency problems and
environmental/acoustic noise. Therefore in this case the second resonance can
give more reliable results. The second and higher resonanc
relations between z-
deflection and angular deflection at the tip, and so different
correction factors are needed.
The correction factors given in the software (Butt and Jaschke, 0.817 for the first
mode, 0.251 for the second mode and 0.0
863 for the third mode) are only valid
when the laser spot is positioned at the tip of the cantilever. As the sensi
canti
lever changes with changing laser spot position, the correction factors change
as well. E.g. for the first mode, the corre
ction factor is increasing with the laser spot
approaching the cantilever base (where it is attached to the chip). The position of
the laser spot is also im
portant for the use of higher modes of the thermal noise
spectrum to calibrate the spring constant.
The Butt and Jaschke correction factors
correct for the discrepancy of the bending shape between the sensitivity
determination (static deflection) and thermal noise measurement. The bending
shape of the static deflection and the first mode of the thermal
relatively similar, whereas it is quite different for the second mode oscilla
tion, when
moving the laser spot position along the cantilever. The result is a drastic change of
the fitted spring constant. Especially when using higher modes t
o determine the
spring constant, the laser spot should be positioned close to the cantilever tip,
where the discrepancies between the different bending modes is rather low. Please
read the Butt and Jaschke paper for more information.
Used when first resonance frequency is too low
Example correction factors from Butt
and Jaschke, Nanotechnology
(1995)
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