a r X i v :c o n d -m a t /0610167v 1 [c o n d -m a t .m t r l -s c i ] 5 O c t 2006
Crosstalk Correction in Atomic Force Microscopy
Hoﬀmann,T.Jungk,and E.Soergel ∗Institute of Physics,University of Bonn,Wegelerstraße 8,53115Bonn,Germany
Commercial atomic force microscopes usually use a four-segmented photodiode to detect the mo-tion of the cantilever via laser beam deﬂection.This read-out technique enables to measure bending and torsion of the cantilever separately.A slight angle between the orientation of the photodiode and the plane of the readout beam,however,causes false signals in both readout channels,so-called crosstalk,that may lead to misinterpretation of the acquired data.We demonstrate this fault with images recorded in contact mode on ferroelectric crystals and present an electronic circuit to compensate for it,thereby enabling crosstalk-free imaging.
The atomic force microscope (AFM)has become a standard tool for determining the surface properties on the nanometer scale not only in physics but also in all life sciences.This is mainly due to its high versatility as it can detect various surface properties such as topog-raphy as well as e.g.frictional,electrostatic or magnetic interaction between tip and sample (see e.g.).This feature of the AFM is even more attractive since those surface properties can be detected simultaneously by us-ing an appropriate setup.Unfortunately an unambigu-ous separation of the diﬀerent read-out channels is not generally assured,leading to crosstalk.Although com-mercially available AFM’s are generally equipped with a powerful software for operation and subsequent image processing,a correction for crosstalk is not provided.In this contribution,we address the problem of crosstalk be-tween the read-out channels for bending and torsion of the cantilever.
Figure 1shows the notations used.The forces sensed by the tip can be out of plane (i)and in plane (ii)of the surface to be investigated.Whereas (i)leads to a bend-ing of the cantilever,(ii)results either in torsion or in buckling,depending on the orientation of the force with respect to the axis of the cantilever.Note that
FIG.1:(a)Forces acting on the tip.F bend :bending of the cantilever due to forces out of plane,F buck and F tor :buckling and torsion of the cantilever due to forces in plane with the surface.(b)Readout with the position sensitive detector,left:vertical signal (bending &buckling),right:lateral signal (torsion).
I n p u t
C r o s s t a l k -c o m p e n s a t e d o u t p u t
FIG.3:Schematics of the electronic circuit used for crosstalk compensation.P V and P L :potentiometer for vertical and lateral crosstalk correction respectively.Σ:summing up of the signals.
for every AFM.In addition,to achieve a perfect align-ment,it would be necessary to rotate the PSD thereby avoiding an angular mismatch αbetween the axis of the PSD and the plane of the read-out laser beam (Fig.2).The latter is given by the incoming laser beam and the one reﬂected from the cantilever.Although this problem is described in the literature ,a rotation of the PSD is in general not possible.In case of a misalignment by the angle αthe correct vertical and lateral signals for bend-ing and torsion (V and L )are falsiﬁed to the measured signals (V m and L m )via the rotation matrix as
V m L m =
cos αsin α−sin αcos α .(1)To correct for this misalignment we realized an elec-tronic circuit depicted in Fig.3,thereby adding sepa-rately to every readout channel a component from the
other channel with the adequate amplitude,adjustable via potentiometers.The crosstalk-corrected signals V c and L c can thus be calculated by
V c L c
= V m L m
1−x x 1
of the vertical and the lateral signal amplitudes(V m and L m)of the excited cantilever is required.Furthermore, their relative phase relation must be known to identify the sign of the necessary rotation.These signal param-eters,however,are not accessible in general.(ii)For crosstalk compensation via software both images(lateral and vertical)are necessary since image processing takes only place after recording.(iii)This implies that a real-time monitoring of the data during image acquisition is not possible.(iv)Finally,a software based solution lim-its the possibilities to record freely chosen input signals (e.g.the outputs of two lock-in ampliﬁers as demon-strated in the above presented example).Note that the drawbacks as described above could be solved by the manufacturer with a software compensation during data acquisition and additional hardware modiﬁcations of the control unit.
In this contribution we have demonstrated the eﬀect of a misalignment of the optical detection unit on the recording of bending and torsion signals with AFM.We have furthermore proposed an electronic circuit to com-pensate for false signals caused by this type of crosstalk which can be incorporated to every AFM if the outputs of the position sensitive detector are directly accessible.
Financial support of the DFG research unit557and of the Deutsche Telekom AG is gratefully acknowledged.
E.Meyer,H.J.Hug,and R.Bennewitz”Scanning Probe
Microscopy:The Lab on a Tip”,Springer(2003)
Lee,and S.-I.Park Rev.Sci.Instr.74,4378,(2003). S.Jeon,Y.Braiman,and T.Thundat Rev.Sci.Instr.75,
4841,(2004).R.Piner and R.S.Ruoﬀ,Rev.Sci.Instr.73,3392,(2002).
T.Jungk,A.Hoﬀmann,and E.Soergel Appl.Phys.Lett.
to be published(2006).
T.Jungk,et al to be published
T.Jungk,A.Hoﬀmann,and E.Soergel Appl.Phys.Lett.