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Search Results: 1 - 10 of 167584 matches for " E. Soergel "
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Impact of Electrostatic Forces in Contact Mode Scanning Force Microscopy
F. Johann,á. Hoffmann,E. Soergel
Physics , 2010, DOI: 10.1103/PhysRevB.81.094109
Abstract: In this $\ll$ contribution we address the question to what extent surface charges affect contact-mode scanning force microscopy measurements. % We therefore designed samples where we could generate localized electric field distributions near the surface as and when required. % We performed a series of experiments where we varied the load of the tip, the stiffness of the cantilever and the hardness of the sample surface. % It turned out that only for soft cantilevers could an electrostatic interaction between tip and surface charges be detected, irrespective of the surface properties, i.\,e. basically regardless its hardness. % We explain these results through a model based on the alteration of the tip-sample potential by the additional electric field between charged tip and surface charges.
Consequences of the background in piezoresponse force microscopy on the imaging of ferroelectric domain structures
T. Jungk,A. Hoffmann,E. Soergel
Physics , 2005,
Abstract: The interpretation of ferroelectric domain images obtained with piezoresponse force microscopy (PFM) is discussed. The influences of an inherent experimental background on the domain contrast in PFM images (enhancement, nulling, inversion) as well as on the shape and the location of the domain boundaries are described. We present experimental results to evidence our analysis of the influence of the background on the domain contrast in PFM images.
Contrast Mechanisms for the Detection of Ferroelectric Domains with Scanning Force Microscopy
T. Jungk,A. Hoffmann,E. Soergel
Physics , 2008, DOI: 10.1088/1367-2630/11/3/033029
Abstract: We present a full analysis of the contrast mechanisms for the detection of ferroelectric domains on all faces of bulk single crystals using scanning force microscopy exemplified on hexagonally poled lithium niobate. The domain contrast can be attributed to three different mechanisms: i) the thickness change of the sample due to an out-of-plane piezoelectric response (standard piezoresponse force microscopy), ii) the lateral displacement of the sample surface due to an in-plane piezoresponse, and iii) the electrostatic tip-sample interaction at the domain boundaries caused by surface charges on the crystallographic y- and z-faces. A careful analysis of the movement of the cantilever with respect to its orientation relative to the crystallographic axes of the sample allows a clear attribution of the observed domain contrast to the driving forces respectively.
Detection mechanism for ferroelectric domain boundaries with lateral force microscopy
T. Jungk,A. Hoffmann,E. Soergel
Physics , 2006, DOI: 10.1063/1.2234303
Abstract: The contrast mechanism for the visualization of ferroelectric domain boundaries with lateral force microscopy is generally assumed to be caused by mechanical deformation of the sample due to the converse piezoelectric effect. We show, however, that electrostatic interactions between the charged tip and the electric fields arising from the surface polarization charges dominate the contrast mechanism. This explanation is sustained by quantitative analysis of the measured forces as well as by comparative measurements on different materials.
Influence of the inhomogeneous field at the tip on quantitative piezoresponse force microscopy
T. Jungk,A. Hoffmann,E. Soergel
Physics , 2006, DOI: 10.1007/s00339-006-3768-9
Abstract: Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relies on the converse piezoelectric effect: a voltage applied to the sample leads to mechanical deformations. In case of PFM one electrode is realized by the tip, therefore generating a strongly inhomogeneous electric field distribution inside the sample which reaches values up to $10^8 $V/m directly underneath the apex of the tip. Although often assumed, this high electric field does not lead to an enhancement of the piezoelectric deformation of the sample. On the contrary, internal clamping of the material reduces the observed deformation compared to the theoretically expected value which depends only on the voltage thus being independent of the exact field distribution.
Crosstalk Correction in Atomic Force Microscopy
A. Hoffmann,T. Jungk,E. Soergel
Physics , 2006, DOI: 10.1063/1.2424448
Abstract: Commercial atomic force microscopes usually use a four-segmented photodiode to detect the motion 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.
Limitations for the determination of piezoelectric constants with piezoresponse force microscopy
T. Jungk,A. Hoffmann.,E. Soergel
Physics , 2007, DOI: 10.1063/1.2827566
Abstract: At first sight piezoresponse force microscopy (PFM) seems an ideal technique for the determination of piezoelectric coefficients (PCs), thus making use of its ultra-high vertical resolution (<0.1 pm/V). Christman et al. \cite{Chr98} first used PFM for this purpose. Their measurements, however, yielded only reasonable results of unsatisfactory accuracy, amongst others caused by an incorrect calibration of the setup. In this contribution a reliable calibration procedure is given followed by a careful analysis of the encounted difficulties determining PCs with PFM. We point out different approaches for their solution and expose why, without an extensive effort, those difficulties can not be circumvented.
Impact of the tip radius on the lateral resolution in piezoresponse force microscopy
T. Jungk,A. Hoffmann,E. Soergel
Physics , 2007, DOI: 10.1088/1367-2630/10/1/013019
Abstract: We present a quantitative investigation of the impact of tip radius as well as sample type and thickness on the lateral resolution in piezoresponse force microscopy (PFM) investigating bulk single crystals. The observed linear dependence of the width of the domain wall on the tip radius as well as the independence of the lateral resolution on the specific crystal-type are validated by a simple theoretical model. Using a Ti-Pt-coated tip with a nominal radius of 15 nm the so far highest lateral resolution in bulk crystals of only 17 nm was obtained.
Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy
T. Jungk,A. Hoffmann,E. Soergel
Physics , 2005, DOI: 10.1063/1.2362984
Abstract: The contrast mechanism for ferroelectric domain imaging via piezoresponse force microscopy (PFM) is investigated. A novel analysis of PFM measurements is presented which takes into account the background caused by the experimental setup. This allows, for the first time, a quantitative, frequency independent analysis of the domain contrast which is in good agreement with the expected values for the piezoelectric deformation of the sample and satisfies the generally required features of PFM imaging.
Andersen Filtration and Hard Lefschetz
Wolfgang Soergel
Mathematics , 2006, DOI: 10.1007/s00039-007-0640-9
Abstract: On the space of homomorphisms from a Verma module to an indecomposable tilting module of the BGG-category O we define a natural filtration following Andersen and establish a formula expressing the dimensions of the filtration steps in terms of coefficients of Kazhdan-Lusztig polynomials.
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