Comparison of in-plane and out-of-plane optical amplification in AFM measurements

Abstract

The in-plane image of piezoresponse force microscopy ͑PFM͒ generally exhibits a higher resolution and less noise than the out-of-plane image. Geometrical considerations indicate that the optical in-plane amplification is Ϸ40 times larger than the out-of-plane amplification. We experimentally confirm this explanation in a dedicated setup. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1878153͔ Ferroelectric materials have been successfully characterized and manipulated on the micro-and nanometer scale by piezoresponse force microscopy ͑PFM͒ in recent years. [1][2][3][4][5][6][7] In this method a conducting tip is brought into contact with the sample and an ac voltage is applied to the tip. The in-plane and out-of-plane response of the piezoelectric material is optically detected as a deflection of the cantilever. In many cases the in-plane signal, as first conducted on thin films by Roelofs et al.,8 is substantially larger than the out-of-plane signal ͑usually more than one order of magnitude͒ and therefore shows more details and less noise. Taking the field distribution, the morphology and the piezoelectric coefficients ͑given for PbTiO 3 and BaTiO 3 in Table I͒ into account the out-of-plane piezoresponse should be larger than the in-plane response. 9 An example of the difference of in-plane and outof-plane PFM is given in Fig. 1 where the piezoresponse of nanograins prepared by chemical solution deposition 2 is shown.The most common detection method for the deflection of the cantilever is by measuring the position of a reflected laser beam on a photosensitive detector. The out-of-plane position is given by ͓͑a + b͒ − ͑c + d͔͒ / ͑a + b + c + d͒. This so-called optical lever arm method is presented in Fig. 2. The "lever amplification:"L is a factor of about one thousand. 10 Using the same method for detecting the in-plane deflection of the cantilever ͑tor-sion͒ the two left and two right quadrants of the photodiode have to be regarded as one, i.e. ͓͑a + c͒ − ͑b + d͔͒ / ͑a + b + c + d͒. The simplified movement of the tip is shown in Fig. 3.We assume that the apex of the tip moves a lateral distance ␦ whereas the middle of the base of the tip remains stationary. In the out-of-plane case the laser is deflected vertically, in the in-plane case horizontally. This is accounted for by the fact that the left and right quadrants of the photodiode are regarded as one unit instead of the bottom and top quadrants. From Fig. 3 it follows for small ␣:where h is the height of the tip plus the thickness of the cantilever. The change of the irradiated area of the left and right parts of the photodiode is then a linear function of the displacement:With this equation the amplification factor can be determined:The ratio R between these in-plane and

Piezoelectricity in collagen type II fibrils measured by scanning probe microscopy

“…In fact, determination of the slope and linear fit error shows that the average shear coefficient for type I (2.2 6 0.5 a.u., n ¼ 5) is approximately 68% higher than that of type II (0.7 6 0.2 a.u., n ¼ 10). When the piezoelectric signals are calibrated via geometric scaling, 42 the measured shear coefficient for type I is in the same range as reported previously. 12 The increase in piezoelectric signal for type I cannot be attributed to tip wear, etc., as type II was investigated prior to type I using the same tip.…”

Dynamic behaviour in piezoresponse force microscopy

“…Given that typically H << L, this implies that the "vertical" PFM signal is more sensitive to the longitudinal surface displacement than to the vertical surface displacement. This is also the case for amplification between flexural and torsional modes, as noted by Peter et al 33 .…”

“…However, this approach is rather tedious. An alternative approach includes the use of a shear wave oscillator 33 in different orientations with respect to the cantilever axis to calibrate longitudinal and lateral contributions to PFM . However, the oscillators themselves are typically characterized by complex intrinsic dynamic behavior with a number of vertical and shear modes, which will be coupled with cantilever response.…”

“…Ref. [33]), the complete electromechanical response vector can be measured, an approach referred to as Vector PFM . 12 Transduction of surface vibrations to the tip is significantly different for vertical and in-plane components.…”

Area fraction quantification of ferroelectric domain orientations in BaTiO3 using piezoresponse force microscopy

“…10 However, in order to determine the domain directions the signals must be comparable. Kalinin et al 8 proposed a method for correcting the intensities using the ratio between VPFM and LPFM measured in a known a-c domain structure ͑for example, in BaTiO 3 ͒.…”