Organic Electronics 14 (2013) 3399–3405

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Organic Electronics

journal homepage: www.elsevier .com/locate /orgel

Multi-bit organic ferroelectric memory

1566-1199/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.orgel.2013.09.006

⇑ Corresponding author.E-mail address: m.kemerink@tue.nl (M. Kemerink).

Vsevolod Khikhlovskyi a,b, Andrey V. Gorbunov a, Albert J.J.M. van Breemen b, René A.J. Janssen a,Gerwin H. Gelinck b, Martijn Kemerink a,⇑a Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsb Holst Centre, TNO-The Dutch Organization for Applied Scientific Research, High Tech Campus 31, 5656 AE Eindhoven, The Netherlands

a r t i c l e i n f o

Article history:Received 4 July 2013Received in revised form 29 August 2013Accepted 4 September 2013Available online 19 September 2013

Keywords:Multi-bit memoryFerroelectric polymerDipole switching theory (DST)P(VDF-TrFE)

a b s t r a c t

Storage of multiple bits per element is a promising alternative to miniaturization forincreasing the information data density in memories. Here we introduce a multi-bitorganic ferroelectric-based non-volatile memory with binary readout from a simple capac-itor structure. The functioning of our multi-bit concept is quite generally applicable anddepends on the following properties for the data storage medium: (a) The data storagemedium effectively consists of microscopic switching elements (‘hysterons’). (b) The posi-tive and negative coercive fields of each hysteron are equal in magnitude. (c) The distribu-tion of hysteron coercive fields has substantial width. We show that the organicferroelectric copolymer P(VDF-TrFE) meets these requirements. All basic properties ofour device were measured and modeled in the framework of the dipole switching theory(DST). As a first example we show the possibility to independently program and subse-quently read out the lower, middle and upper parts of the hysteron distribution function,yielding a 3-bit memory in a single capacitor structure. All measured devices show goodstate reproducibility, high endurance and potentially great scalability.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

There is a great ongoing search for novel non-volatilememory technologies. Systems investigated include phasechanging materials [1], filamentary conductivity switchingoxides [2,3] and various ‘ferroic’ systems like ferromag-netic, ferroelectric and multi-ferroic materials [4–10]. Ofthese the organic ferroelectric random access memory(FeRAM) is a promising element for printable, large area,low-cost electronic circuits. A major concern in FeRAM isthe limited minimum feature size that can be reached ingeneral and with low-cost, large-area technology in partic-ular. Potentially this problem can be mitigated by usingmultiple discrete states in a single memory element.Recently a number of multi-bit memory elements wereproposed [11,12] but these either require undesired

additional device structuring or suffer from non-binaryreadout signals.

Here we propose a non-volatile multi-bit organic ferro-electric-based memory with binary readout from a simplecapacitor structure. The operational principle behind ourmulti-bit device is quite general, with the applicability ofthe dipole switching theory (DST) as only constraint[13,14]. The DST considers ferroelectric material as a col-lection of micro dipoles (hysterons) described by a specificPreisach distribution function [15]. We show experimen-tally that the organic ferroelectric copolymer P(VDF-TrFE)meets all the requirements to be described by the DST.On this basis we demonstrate a non-volatile 3-bit datastorage element. We show the possibility to independentlyprogram and subsequently read out the lower, middle andupper parts of the hysteron distribution function. Thisshows that a simple capacitor structure based on thisorganic ferroelectric material can be used as multi-bitlow-cost memory element.

Fig. 2. Schematic representation of the signals used for measuring innerand saturated ferroelectric hysteresis loops and corresponding schematiccurrent responses. The amplitude Vmax of the preparation signal is chosento be well above the coercive voltage of the ferroelectric capacitor.Different probing signals have the same ramping speeds but differentamplitudes for measuring inner ferroelectric hysteresis loops. Red solidcurves represent schematic current responses measured with the probingsignals ‘‘1’’ and ‘‘2’’. The shaded area corresponds to the switching currentassociated with the reversal of the ferroelectric polarization. Dotted anddashed black lines represent currents due to leakage and displacement,respectively. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

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2. Results and discussion

The devices investigated here were simple metal-insu-lator-metal capacitors with Au electrodes and the organicferroelectric P(VDF-TrFE) as insulator. The material is com-mercially available and known for its robustness and goodretention [16,17]. Fabrication and measurement detailscan be found in the experimental section. First, the generalferroelectric properties of the P(VDF-TrFE) capacitor werecharacterized. Fig. 1 shows a series of ferroelectric (dis-placement charge) hysteresis loops using sinusoidal inputvoltage with different amplitudes at a frequency of50 Hz. The inner loops correspond to the partially switchedpolarization whereas the saturated loop is related to thecompletely switched ferroelectric. From the saturated loopthe remnant polarization (Pr) and coercive voltage (Vc) areestimated to be 70 mC/m2 and 13.5 V respectively. It has tobe noticed that the Pr and the Vc cannot be accuratelydetermined from such measurements due to the presenceof displacement and leakage currents.

In order to obtain the pure ferroelectric polarization ofthe P(VDF-TrFE) capacitor the displacement contributionand the leakage current should be suppressed and ex-cluded. A proper and simple way of doing this is by usingthe double-wave method (DWM), which is a powerful toolfor accurately measuring ferroelectric hysteresis loops[18,19]. The concept of the DWM is based on the idea thatthe polarization state of a ferroelectric can be probed byflipping its polarization and detecting the correspondingswitching charges. In the DWM a sequence of pulses is ap-plied to a ferroelectric capacitor and the correspondingcurrents are measured. The DWM relies on the chargeextraction associated with the switching of the ferroelec-tric polarization. Fig. 2 shows a typical input signal usedin the DWM-based experiments for measuring inner andsaturated ferroelectric hysteresis loops together with thecorresponding schematic current responses. The prepara-tion part of the signal is used for constructing the desiredpolarization state of the ferroelectric. The probing part isused for studying the prepared ferroelectric polarization.To probe the ferroelectric polarization a triangular pulse,

Fig. 1. Displacement charge versus applied voltage hysteresis loop of a200 nm thick Au/P(VDF-TrFE)/Au capacitor at a frequency of 50 Hz.

labeled ‘‘1’’ in Fig. 2, is applied and the correspondingswitching current is read out. Contributions from displace-ment and the leakage currents can be determined with asecond probing pulse – ‘‘2’’ in Fig. 2. As this pulse is equalin size and slope to the first, no polarization switching oc-curs, whereas displacement and leakage currents are thesame. Red solid curves, labeled ‘‘1’’ and ‘‘2’’ in Fig. 2, repre-sent the corresponding schematic current responses. Theshaded area corresponds to the current associated withthe switching of the ferroelectric polarization. Dotted anddashed black lines represent current responses due to theleakage and the displacement contribution, respectively.Thus using the response to the second pulse all unwantedresponses can be subtracted from the response to the firstpulse, giving solely the voltage-dependent switching re-sponse of the ferroelectric. Moreover the displacement cur-rent can upfront be significantly suppressed by doing slowmeasurements – the so-called quasi-static regime of theDWM. In addition the preparation part of the signal canbe changed as well as the probing one, giving the possibil-ity to study different switching properties of a ferroelectricmaterial. The DWM provides a simple and a powerful toolfor detailed study of ferroelectrics.

It should be noted that the DWM originates from the so-called PUND (Positive ‘‘Up’’ Negative ‘‘Down’’) approach[20,21]. The basic idea behind both methods is similar andcan be summarized as flipping the polarization state of theferroelectric and detecting both the switching (i.e. associ-ated with the ferroelectric polarization) and the nonswitch-ing currents (i.e. displacement and leakage current).However, the PUND approach is usually associated withstep-like voltage pulses. It often serves for transient-type

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measurements or for determining a total polarization of theferroelectric material. At the same time the DWM uses con-tinuous transients, for instance linearly increasing/decreas-ing voltages, giving rise to much lower displacementcurrents. Hence it is more suitable for the quasi-static re-gime in which we are interested here.

The solid curves in Fig. 3a represent a series of ferro-electric hysteresis loops measured on the P(VDF-TrFE)capacitor using the quasi-static approach of the DWM ex-plained above. Since the displacement contribution andthe leakage current were always negligible and completelyexcluded from the data, all measured values correspond tothe pure ferroelectric polarization of the capacitor. This isin line with a fact that P(VDF-TrFE) is known to be anexcellent insulator (resistivity <1010 Ohm�m. In additionno signs of moving ionic or parasitic electronic chargeswere observed. The remnant saturated polarization (Pr)and coercive voltage (Vc) are determined to be 60 mC/m2

and 9.2 V (Ec = 4.6 � 107 V/m) respectively. As in the previ-ous case the inner loops describe the partially switchedferroelectric polarization. The difference between hystere-sis loops and related parameters shown in Fig. 1 and Fig. 3ais due to the displacement and leakage contributions dis-cussed above and due to the frequency dependence ofthe switching properties of the ferroelectric [22]. The fre-quency dependence of the P(VDF-TrFE) hysteresis curvesof our devices is shown in Fig. S1.

The analysis of the measured ferroelectric hysteresisloops shown in Fig. 3a was done according to the dipoleswitching theory (DST) [13,14]. In contrast to behavioralmodels like Miller’s concept [23], the DST is a practicaland accurate physical model based on the Preisach theoryfor extrinsically switching ferroelectrics [15]. It includesthe possibility of consistently modeling inner and satu-rated loops and it is capable of taking into account historydependent effects. Similarly to the Preisach theory the DSTconsiders a ferroelectric material as a collection of microdipoles (hysterons) where each hysteron has two normal-ized spontaneous polarization states and correspondingcoercive fields U0, V0 (Fig. 4a). Each hysteron behaves as aperfect ferroelectric – its polarization can be flipped byapplication of a well-defined electric field, yielding rectan-gular ‘microscopic’ polarization loops. An aggregation ofhysterons typically leads to a distribution of coercive fields.

Fig. 3. (a) Solid lines: ferroelectric polarization charge P versus applied voltage V hcapacitor. Dashed lines represent the corresponding calculated ferroelectric hferroelectric hysteresis loops taken from (a) and plotted from the same starting p(right axis).

A 2D projection of this Preisach distribution function isrepresented by the Preisach plane shown in Fig. 4b. Theshaded triangular area corresponds to all possible typesof hysterons present in a ferroelectric material. However,in contrast to the general case considered in Preisach the-ory the DST hysterons possess symmetric coercive fields±U0. In this case the distribution function is confined to alimited part of the Preisach plane, namely the dashed lineshown in Fig. 4b. Alternatively the DST hysteron distribu-tion function can be represented by a 2D plot as shownin Fig. 4c. Each point on the curve represents the relativedensity q of hysterons having a coercive field U0. E.g. theshaded area in Fig. 4c corresponds to hysterons havingcoercive fields in the range of ±[U0, U0 + DU].

In terms of the Preisach model the inner loops in Fig. 3acorrespond to a partially filled hysteron distribution func-tion. Fig. 3b shows ascending hysteresis loops taken fromFig. 3a and plotted from the same level together with thehysteron distribution function used in the DST simulations.An important finding in Fig. 3b is that all measured innerloops follow the same ascending curve. This means thatthe hysteron distribution function can be gradually filled.An important concern regarding the applicability of theDST model to our system is related to the average domainsize in the P(VDF-TrFE) material. This is because the appli-cability of Preisach-type models demands that the do-mains are small compared to the size of the device. In(unpublished) previous work we used scanning probes tolocally pole and switch ferroelectric P(VDF-TrFE) film. Indi-vidual domains with an average size much smaller than100 nm were observed, which is in line with previously re-ported values [24,25]. That is orders of magnitude smallerthan the size of the devices investigated here. In otherwords, the organic ferroelectric copolymer P(VDF-TrFE)seems to meet all the requirements to be described interms of the DST mentioned above.

A next step was to study in detail the hysteron distribu-tion function of the P(VDF-TrFE) ferroelectric capacitor. Todo this the saturated hysteresis loop was fitted in theframework of the DST. Details regarding the implementa-tion of the DST are given in the Supporting Information.The dashed black curve in Fig. 3a demonstrates theexcellent quality of the resulting fit; the correspondinghysteron distribution function is shown in Fig. 3b. The

ysteresis loops measurements of a 200 nm thick P(VDF-TrFE) ferroelectricysteresis loops on basis of the dipole switching theory. (b) Ascendingoint (left axis). Hysteron distribution function used in the DTS simulations

Fig. 4. Basic concepts of the Preisach model and the dipole switching theory (DST). (a) Polarization hysteresis loop of a single Preisach hysteron. (b)Schematic representation of the Preisach plane. The dashed line corresponds to the DST case where V0 = �U0. (c) Schematic representation of the hysterondistribution along the dashed line in (b), i.e. in the DST case. The shaded area shows hysterons having coercive fields in the range [U0, U0 + DU]. (d)Schematic representation of the broadening effect discussed in the text. The solid and dashed distributions represent the actually flipped hysterons uponfull and partial switching the ferroelectric capacitor, respectively. The vertical solid line corresponds to the maximum applied voltage used for partialswitching. The dark and light shaded areas respectively represent hysterons that, in comparison to the situation without broadening, are and are notswitched.

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obtained hysteron distribution function was subsequentlyused for simulating the inner hysteresis loops withoutany further parameter adjustments. The dashed curves inFig. 3a show the corresponding predicted inner polariza-tion loops of the P(VDF-TrFE) capacitor. Although the over-all agreement is quite good, some systematic differencesarise, especially at intermediate applied voltages wherethe measured inner loops show larger values for the satu-rated polarization as compared to the simulated loops. Thisis most likely due to the broadening effect explained inFig. 4d: there is some fraction of hysterons with coercivefields above the maximum applied field that is stillswitched, as well as some (smaller) fraction of hysteronswith coercive fields below the maximum applied field thatare not switched. In Fig. 4d solid and dashed curves repre-sent the switching charges measured upon fully and par-tially inverting the polarization of a ferroelectriccapacitor, respectively. The solid line indicates the maxi-mum applied voltage V0 used for partial switching. Shadedlight and shaded dark areas represent hysterons that arenot switched respectively additionally switched due tothe broadening effect. This means that upon partial polingthe broadening effect significantly changes the shape andthe integral of the actual hysteron distribution function.Assuming a more or less constant shape of the broadeningfunction the largest difference between measured andsimulated loops is expected for inner loops close to themaximum of the hysteron distribution function. This is in-

deed observed, as seen in the 3rd curve, counted from thesmallest loop, of Fig. 3a. Since the DST does not account forany broadening effects we can conclude that the calculateddata is in a good agreement with the experimental results.

A next step was to study in more detail the partial fillingand reading of the hysteron distribution function of theP(VDF-TrFE) ferroelectric capacitor. To do that a specificpolarization state of the ferroelectric was prepared andsubsequently probed. Again the quasi-static approach ofthe DWM was used. Fig. 5a, b shows the filling and probingof the hysteron distribution function of the P(VDF-TrFE)ferroelectric capacitor. Colored solid curves are the switch-ing current of the ferroelectric capacitor as prepared by thesignals shown in the left insets. The first pulse of the prep-aration signal was used for erasing previous memory ef-fects and preparing a fully up (a) or down (b) polarizedferroelectric capacitor. The second pulse of the preparationsignal created the desired polarization state of the ferro-electric. The right insets give a schematic representationof the expected hysteron distribution functions as pre-pared by the corresponding preparation signals. Positiveand negative signs represent the two possible orientationsof hysterons: up or down. Colored vertical dashed linescorrespond to the amplitude of the variable second pulseof the preparation signal shown in the left insets.

To probe the created polarization state of the ferroelec-tric capacitor two probing triangular pulses (Fig. 2) wereused. In order to probe the state of the entire hysteron dis-

Fig. 6. 3-bit data storage in a single 200 nm thick Au/P(VDF-TrFE)/Auferroelectric capacitor. Left insets: preparation signals. Right insets:schematic representations of the corresponding hysteron distributionfunctions. Colored vertical dashed lines represent the amplitudes of thelast two pulses of the preparation signals shown on the left insets. Thereadout voltages are positive such that ‘down’ hysterons give a currentresponse. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

Fig. 5. Filling and probing a distribution function of a 200 nm thick Au/P(VDF-TrFE)/Au ferroelectric capacitor. Colored solid curves describe the switchingof the ferroelectric capacitor with the distribution function filled with negatively oriented hysterons from the left (a) and right side (b). Left insets:corresponding preparations signals. Right insets: schematic representation of the resulting hysteron distribution functions. Colored dashed lines indicatethe amplitudes of the variable 2nd part of the preparation signals shown in the left insets. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

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tribution the amplitude of the probing pulses was chosento be higher than the coercive voltage of the ferroelectriccapacitor. The sign of the readout pulse was such that hys-terons switched in the second preparation pulse are readout, i.e. are switched again and give rise to a current re-sponse. It is important to stress that in this probing schemehysterons with a polarization state that corresponds to thefirst preparation pulse do not give a current response.Black solid curves correspond to the switching of a fullypolarized ferroelectric capacitor, i.e. the largest amplitudeof the second polarization pulse. The measured signals inFig. 5a, b show that hysterons with low and high coercivefields can be poled in opposite directions: the readout peakgrows with the (magnitude of the) second preparationpulse, and, importantly, maintains its shape with a maxi-mum shifting to the higher (panel a) or lower voltage (pa-nel b). This means that the hysteron distribution functioncan indeed be gradually filled as described in the right-sideinsets of Fig. 5. It should also be noted that the currenttraces in Fig. 5 extend beyond the dashed lines, i.e. themagnitude of the second preparation pulse. This is anothermanifestation of the broadening effect discussed at Figs. 3and 4.

The important consequence of the data in Fig. 5 is thatthe polarization of any ferroelectric material that followsthe DST can contain more information than just ‘up’ or‘down’. A well-known consequence is that the total polar-ization state of ferroelectrics can be continuously tunedbetween full polarization in up and down directions. Thisunderlies the multi-level memory demonstrated in Ref.[12]. However, the mean of a distribution does not containthe full information. In particular, we shall demonstratebelow that the possibility to tailor the distribution functioncan be used to store multi-bit information in a single mem-ory element.

Fig. 6 demonstrates 3-bit data storage realized in a sin-gle P(VDF-TrFE) ferroelectric capacitor. The figure displaysthe most demanding polarization states ‘‘010’’ and ‘‘101’’with black and red solid curves respectively. The left andright insets describe the preparation signals and aschematic representation of the corresponding hysterondistribution functions. Colored dashed lines correspond

to the amplitudes of the last two pulses of the preparationsignals shown in the left inset. Like in Fig. 5 the first pulseof the preparation signal fully polarized the ferroelectriccapacitor. The second and the third pulses subsequentlycreated the desired polarization state of the ferroelectricas sketched in the right insets. As before two triangularprobing pulses were used for reading out the created polar-ization states of the ferroelectric. Clearly ‘‘010’’ and ‘‘101’’preparation pulses give rise to well distinguishable peaksand valleys at the anticipated positions: the data storageis binary. Hence three bits of information can be storedin such single memory element.

Although the same ramping speed in the readout pulseswas used in Figs. 5 and 6, the current signal in the latterwas much reduced. The reason is the broadening effect dis-cussed before. Especially in the ‘‘101’’ response (red line) itis clear that the middle part of the distribution function not

3404 V. Khikhlovskyi et al. / Organic Electronics 14 (2013) 3399–3405

completely separates the outer two. Since the probingscheme measures, at each point in the distribution func-tion, the difference between the up and down fractions,this leads to the observed signal reduction. As a conse-quence, the ‘‘010’’ state cannot be obtained unambiguouslyby subtraction of the ‘‘101’’ state from the ‘‘111’’ state inour device. The latter corresponds to the fully switched fer-roelectric polarization shown by the black lines in Fig. 5 aand b. In passing we also note that the lowest peaks inFig. 5 (green in panel a and red in b) correspond to the‘‘100’’ and ‘‘001’’ signals.

Finally, we should address some practical aspects ofthese devices. First, these devices were not optimized inany way. Au and P(VDF-TrFE) were taken for ease of fabri-cation and availability. However, P(VDF-TrFE) is known forits excellent retention and great environmental stability.All programmed signals were stable over at least severaltens of hours suggesting that the hysteron distributionfunction is time stable. Moreover all measured devicesshowed good state reproducibility, as may be expectedfrom the simple processing, and therefore may be expectedto have a potentially great scalability.

In summary, we have introduced multi-bit data storagewith binary readout from a simple capacitor structure. Theworking principle of our multi-bit device is completelygeneral and only demands the applicability of the dipoleswitching theory (DST). The DST considers ferroelectricmaterial as a collection of micro dipoles (hysterons) de-scribed by a specific Preisach distribution function. Weshowed experimentally that the organic ferroelectriccopolymer P(VDF-TrFE) meets all the requirements to bedescribed in terms of the DST. All basic ferroelectric prop-erties together with the hysteron distribution function ofP(VDF-TrFE) ferroelectric capacitors were studied usingthe quasi-static double-wave method. In addition, ferro-electric properties of the device were modeled in theframework of the DST. Finally, we demonstrate a 3-bit datastorage element. As a first example we show the possibilityto independently program and subsequently read out thelower, middle and upper parts of the hysteron distributionfunction, yielding a 3-bit memory in a single capacitorstructure. All measured devices show good state reproduc-ibility, high endurance and potentially great scalability.Hence we expect that our findings will be interesting forthe realization of multi-bit organic ferroelectric-basedmemories for low-cost large area electronics.

3. Materials and methods

Poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) (Mw = 220 kDa, 2.3 < D < 2.8 with a 77/23 VDF/TrFEratio) was supplied by Solvay Specialty Polymers. Deviceswere made by spin-coating a 200 nm thick film of P(VDF-TrFE) ferroelectric polymer on top of glass substrates withpatterned gold electrodes: 1.2 � 1.2 mm2, 700 � 700 lm2,400 � 400 lm2, 250 � 250 lm2. After spin coating, thefilms were annealed for 1 h at 135 �C followed by the depo-sition of the top Au electrode. Using surface profilometrythe layer thickness of the P(VDF-TrFE) was determined tobe �200 nm. P–V characteristics and the properties of the

hysteron distribution function were measured using anAgilent function generator 33120A (source) and an exter-nal voltage amplifier and a Keithley picoammeter 6485(sense).

Acknowledgements

The authors thank Rui Wang and Francisco G. Rodriguezfor their contribution to the device fabrication. Theresearch leading to these results has received funding fromthe European Community’s Seventh FrameworkProgramme (FP7/2007-2013) under Grant Agreement No.248092 of the MOMA project.

Appendix A. Supplementary material

Supplementary data associated with this article can befound, in the online version, at http://dx.doi.org/10.1016/j.orgel.2013.09.006.

References

[1] H.-S.P. Wong, S. Raoux, S. Kim, J. Liang, J.P. Reifenberg, B. Rajendran,M. Asheghi, K.E. Goodson, Phase change memory, Proc. IEEE 98(2010) 2201.

[2] F. Verbakel, S.C.J. Meskers, R.A.J. Janssen, H.L. Gomes, M. Cölle, M.Büchel, D.M. de Leeuw, Reproducible resistive switching innonvolatile organic memories, Appl. Phys. Lett. 91 (2007) 192103.

[3] M. Cölle, M. Büchel, D.M. de Leeuw, Switching and filamentaryconduction in non-volatile organic memories, Org. Electron. 7 (2006)305–312.

[4] Q.-D. Ling, D.-J. Liaw, C. Zhu, D.S.-H. Chan, E.-T. Kang, K.-G. Neoh,Polymer electronic memories: materials, devices and mechanisms,Prog. Polym. Sci. 33 (2008) 917–978.

[5] P. Heremans, G.H. Gelinck, R. Müller, K.-J. Baeg, D.-Y. Kim, Y.-Y. Noh,Polymer and organic nonvolatile memory devices, Chem. Mater. 23(2011) 341–358.

[6] B.H. Park, B.S. Kang, S.D. Bu, T.W. Noh, J. Lee, W. Jo, Lanthanum-substituted bismuth titanate for use in non-volatile memories,Nature 401 (1999) 682.

[7] I. Jung, J.Y. Son, A nonvolatile memory device made of a graphemenanoribbon and a multiferroic BiFeO3 gate dielectric layer, Carbon 50(2012) 3854–3858.

[8] I. Stolichnov, S.W.E. Riester, H.J. Trodahl, N. Setter, A.W. Rushforth,K.W. Edmonds, R.P. Campion, C.T. Foxon, B.L. Gallagher, T. Jungwirth,Non-volatile ferroelectric control of ferromagnetism in (Ga, Mn)As,Nat. Mater. 7 (2008) 464.

[9] T. Kawahara, K. Ito, R. Takemura, H. Ohno, Spin-transfer torque RAMtechnology: review and prospect, Microelectron. Reliab. 52 (2012)613–627.

[10] R.C. Sousa, I.L. Prejbeanu, Non-volatile magnetic random accessmemories (MRAM), C. R. Phys. 6 (2005) 1013–1021.

[11] A.K. Tripathi, A.J.J.M. van Breemen, J. Chen, Q. Gao, M.G. Ivan, K.Reimann, E.R. Meinders, G.H. Gelinck, Multilevel information storagein ferroelectric polymer memories, Adv. Mater. 23 (2011) 4146–4151.

[12] D. Lee, S.M. Yang, T.H. Kim, B.C. Jeon, Y.S. Kim, J.-G. Yoon, H.N. Lee,S.H. Baek, C.B. Eom, T.W. Noh, Multilevel data storage memory usingdeterministic polarization control, Adv. Mater. 24 (2012) 402–406.

[13] L. Wang, J. Yu, Y. Wang, G. Peng, F. Liu, J. Gao, Modeling ferroelectriccapacitors based on the dipole switching theory, J. Appl. Phys. 101(2007) 104505.

[14] F. Yang, M.H. Tang, Y.C. Zhou, X.J. Zheng, F. Liu, J.X. Tang, J.J. Zhang, J.Zhang, C.Q. Sun, A model for the polarization hysteresis loops of theperovskite-type ferroelectric thin films, Appl. Phys. Lett. 91 (2007)142902.

[15] C.H. Tsang, C.K. Wong, F.G. Shin, Modeling saturated andunsaturated ferroelectric hysteresis loops: an analytical approach,J. Appl. Phys. 98 (2005) 084103.

[16] Y.J. Park, J. Chang, S.J. Kang, C. Park, Polarization retention of thinferroelectricya capacitors, Appl. Phys. Lett. 95 (2009) 102902.

[17] K.-H. Kim, Properties of ferroelectric VDF-TrFE copolymer capacitorsdirectly deposited on Si wafers, J. Korean Phys. Soc. 52 (2008) 88–91.

V. Khikhlovskyi et al. / Organic Electronics 14 (2013) 3399–3405 3405

[18] M. Fukunaga, Y. Noda, Improvement of the double-wave method forferroelectric hysteresis loops and its application to multiferroicEuMn2O5, J. Korean Phys. Soc. 55 (2009) 888–892.

[19] M. Fukunaga, Y. Noda, New technique for measuring ferroelectricand antiferroelectric hysteresis loops, J. Phys. Soc. Jpn. 77 (2008)064706.

[20] J.F. Scott, L. Kammerdiner, M. Parris, S. Traynor, V. Ottenbacher, A.Shawabkeh, W.F.J. Oliver, Switching kinetics of lead zirconatetitanate submicron thinfilm memories, Appl. Phys. 64 (1988) 787.

[21] S.D. Traynor, T.D. Hadnagy, L. Kammerdiner, Capacitor testsimulation of retention and imprint characteristics for ferroelectricmemory operation, Integr. Ferroelectr. 16 (1997) 1-4. pp. 63–76.

[22] N. Tsutsumi, X. Bai, W. Sakai, Towards nonvolatile memory devicesbased on ferroelectric polymers, AIP Adv. 2 (2012) 012154.

[23] S.L. Miller, J.R. Schwank, R.D. Nasby, M.S. Rodgers, Modelingferroelectric capacitor switching with asymmetric nonperiodicinput signals and arbitrary initial conditions, J. Appl. Phys. 70(1991) 2849.

[24] B.J. Rodriguez, S. Jesse, S.V. Kalinin, J. Kim, S. Ducharme, V.M. Fridkin,Nanoscale polarization manipulation and imaging of ferroelectricLangmuir–Blodgett polymer films, Appl. Phys. Lett. 90 (2007)122904.

[25] P. Sharma, T. Nakajima, S. Okamura, A. Gruverman, Effect of disorderpotential on domain switching behavior in polymer ferroelectricfilms, Nanotechnology 24 (2013) 015706.