Polarization imprint and size effects in mesoscopic ferroelectric structures

Alexe, Marin; Harnagea, Cătălin; Hesse, D.; Gösele, U.

doi:10.1063/1.1385184

Cited by 174 publications

(113 citation statements)

References 21 publications

(15 reference statements)

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“…͑14a͒ and ͑14b͒ for the prolate domain with l ӷ r, namely, Ϸ 0.1-1 m from the formulaes R d = ͱ 11 0 k B T / ͑e 2 n d ͒ ͑T is absolute temperature and k B is Boltzmann's constant͒, using permittivity 11 = 70 obtained from independent dielectric measurements and carrier concentration n d ϳ 10 14 -10 16 cm −3 extracted from the conductivity measurements of the same bismuth ferrite ͑BFO͒ films at room temperature. 89 Note that in most cases, the bias required for nucleation is of the order of 5 -20 V. Similar hysteresis loops are observed for other ferroelectric materials, including PZT, 44 strontium-bismuth titanate ͑SBT͒, 37,45 etc.…”

Section: Shown Insupporting

confidence: 59%

“…[36][37][38][39][40][41] Recently, PFM spectroscopy has been extended to an imaging mode using an algorithm for fast ͑100-300 ms͒ hysteresis loop measurements developed by Jesse et al 42 The progress in experimental studies has stimulated a parallel development of theoretical models to relate PFM hysteresis loop parameters and materials properties. A number of such models are based on the interpretation of phenomenological characteristics of PFS hysteresis loops similar to macroscopic P-E loops, such as slope, imprint bias, coercive bias, remanent response, and work of switching, 43,44 as illustrated in Fig. 1.…”

Section: Current Results On Nanoscale Polarization Dynamicsmentioning

confidence: 99%

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Piezoresponse force spectroscopy of ferroelectric-semiconductor materials

Morozovska

Svechnikov

Eliseev

et al. 2007

Journal of Applied Physics

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Section: Shown Insupporting

confidence: 59%

Section: Current Results On Nanoscale Polarization Dynamicsmentioning

confidence: 99%

Piezoresponse force spectroscopy of ferroelectric-semiconductor materials

Morozovska

Svechnikov

Eliseev

et al. 2007

Journal of Applied Physics

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“…Among the accomplishments of the PFM approach is an insight into spatial variability issues of ferroelectric capacitors. [8][9][10][11][12] In addition, the role of mechanical stress in the spatial inhomogeneity of switching behavior in ferroelectric capacitors has recently been emphasized by PFM. 10,11 To better understand a nanoscale mechanism of switching in polycrystalline films it would be helpful to reconstruct the three-dimensional domain arrangement at the subgrain level.…”

Section: Introductionmentioning

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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“…͓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.…”

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confidence: 99%

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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Polarization imprint and size effects in mesoscopic ferroelectric structures

Cited by 174 publications

References 21 publications

Piezoresponse force spectroscopy of ferroelectric-semiconductor materials

Piezoresponse force spectroscopy of ferroelectric-semiconductor materials

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

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

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