Differentiating 180° and 90° switching of ferroelectric domains with three-dimensional piezoresponse force microscopy

Roelofs, Andreas; Böttger, U.; Waser, Rainer; Schlaphof, F.; Trogisch, S.; Eng, Lukas M.

doi:10.1063/1.1328049

Cited by 163 publications

(101 citation statements)

References 11 publications

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“…The presence of the electrostatic forces hypothesis is also supported by observations of nonpiezoelectric surfaces. 32 In contrast, the existence of a lateral PFM signal [33][34][35] and the absence of relaxation behavior in PFM contrast as opposed to SSPM contrast, 36,25 as well as numerous observations using both EFM-SSPM and PFM, 37,38 clearly point to a significant electromechanical contribution to PFM contrast. In order to resolve the controversy regarding the origins of PFM contrast, we analyze the contrast formation mechanism and relative magnitudes of electrostatic versus electromechanical contributions to PFM interactions for the model case of c ϩ , c Ϫ domains in tetragonal perovskite ferroelectrics.…”

Section: Introductionmentioning

confidence: 85%

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

2002

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In order to determine the origin of image contrast in piezoresponse force microscopy (PFM), analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong (classical) and weak (field-induced) indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct ''piezoresponse contrast mechanism maps'' that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in BaTiO 3 and the temperature dependence of the piezoresponse are compared with GinzburgDevonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed. In order to determine the origin of image contrast in piezoresponse force microscopy ͑PFM͒, analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong ͑classical͒ and weak ͑field-induced͒ indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct ''piezoresponse contrast mechanism maps'' that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in BaTiO 3 and the temperature dependence of the piezoresponse are compared with Ginzburg-Devonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed.

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Section: Introductionmentioning

confidence: 85%

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

2002

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“…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.…”

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confidence: 90%

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

Peter

Rüdiger

Waser

et al. 2005

Review of Scientific Instruments

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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

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“…Vertical PFM ͑VPFM͒ and lateral PFM ͑LPFM͒ imaging methods, used to detect out-of-plane and in-plane polarization components, respectively, have been described in detail elsewhere. [5][6][7][11][12][13][14][15][16][17][18] The modulation voltage ͑typically 0.6 Vrms at 10 kHz͒ was applied to the top electrode of the capacitor using a conduca͒ Author to whom correspondence should be addressed; electronic mail: alexei -gruverman@ncsu.edu tive PFM tip, which was also used to detect the piezoelectric response of the capacitor. Commercially available Pt-coated Si rectangular cantilevers ͑1.0-2.6 N/m force constant͒ have been used in this study.…”

Section: Methodsmentioning

confidence: 99%

Three-dimensional high-resolution reconstruction of polarization in ferroelectric capacitors by piezoresponse force microscopy

Rodriguez

Gruverman

Kingon

et al. 2004

Journal of Applied Physics

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Nemanich, R. J.; and Cross, J. S., "Three-dimensional high-resolution reconstruction of polarization in ferroelectric capacitors by piezoresponse force microscopy" (2004 A combination of vertical and lateral piezoresponse force microscopy ͑VPFM and LPFM, respectively͒ has been used to map the out-of-plane and in-plane polarization distribution, respectively, of ͑111͒-oriented Pb(Zr,Ti)O 3 -based ͑PZT͒ ferroelectric patterned and reactively-ion-etched capacitors. While VPFM and LPFM have previously been used to determine the orientation of the polarization vector in ferroelectric crystals and thin films, this is the first time the technique has been applied to determine the three-dimensional polarization distribution in thin-film capacitors and, as such, is of importance to the implementation of nonvolatile ferroelectric random access memory. Sequential VPFM and LPFM imaging have been performed in poled 1 ϫ1.5 m 2 PZT capacitors. Subsequent quantitative analysis of the obtained piezoresponse images allowed the three-dimensional reconstruction of the domain arrangement in the PZT layers of the capacitors. It has been found that the poled capacitors, which appear as uniformly polarized in VPFM, are in fact in a polydomain state as is detected by LPFM and contain 90°domain walls. Despite the polycrystallinity of the PZT layer, regions larger than the average PZT grain size are found to have the same polarization orientation. This technique has potential for clarifying the switching behavior and imprint mechanism in micro-and nanoscale ferroelectric capacitors.

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Differentiating 180° and 90° switching of ferroelectric domains with three-dimensional piezoresponse force microscopy

Abstract: Articles you may be interested inPiezoresponse force microscopy studies on the domain structures and local switching behavior of Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals

Cited by 163 publications

References 11 publications

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces

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

Three-dimensional high-resolution reconstruction of polarization in ferroelectric capacitors by piezoresponse force microscopy

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