1 Ferroelectrics, 291: 27 35, 2003 Copyright c Taylor & Francis Inc. ISSN: print / online DOI: / New Approach to Analysis of the Switching Current Data in Ferroelectric Thin Films V. YA. SHUR, I. S. BATURIN, E. I. SHISHKIN, and M. V. BELOUSOVA Inst. Phys. & Appl. Math., Ural State University, Ekaterinburg, Russia (Received September 15, 2002) A new approach to analysis of the switching current allows to extract distribution function of the threshold field from the current data recorded during conventional hysteresis loop measurements. Quasi-static switching (domain kinetics in slow-increasing field) in spatially inhomogeneous ferroelectric was investigated by computer simulation. Domain arising ( nucleation ) and growth was considered under the assumption that the threshold field for appearance of isolated nuclei is essentially higher than for nuclei at the domain wall. The obtained complicated relation between switching current shape and the threshold field distribution function essentially differs from predictions of Preisach approach. The new method has been successively used for analysis of the switching current data measured during cycling in PLZT thin films. Keywords: Switching current; thin films; Preisach approach; internal bias field INTRODUCTION Polarization reversal is widely used in memory devices based on ferroelectric thin films . Therefore the knowledge of the domain kinetics in electric field is very important. It is well known that in situ domain visualization in thin films is very difficult so the recording of the charge and current during polarization reversal ( switching ) is the most popular experimental technique. Two types of field pulses have been used usually for such investigations: (a) rectangular pulses (Merz technique ) and (b) triangular ones (observation of hysteresis and current loops) . In turn two approaches have been used for analysis of the experimental data: (a) the kinetic approach [4 7] and (b) the quasi-static one [8 11]. Application of both approaches is restricted. The first approach cannot be applied for real spatially nonuniform films, while the second one completely neglects the domain growth. In this paper we propose the new approach for analysis of switching current data in spatially nonuniform ferroelectrics obtained during quasi-static switching taking into account the domain growth. Finally we demonstrate some /27
2 28/ V. YA. SHUR et al. preliminary results of its application for extracting the evolution of the bias field distribution function during fatigue in thin films. KINETIC APPROACH The most popular method for measurements of the switching current has been proposed by Merz . The switching current is recorded under the action of rectangular pulses of electric field (Fig. 1(a)). Kinetic approach is applied for analysis of the current data. It is supposed that the current shape is determined by domain kinetics (nucleation and growth) thus it is possible to use the Kolmogorov-Avrami formulas suggested for describing the crystallization of metals [4, 5]. Ishibashi and Takagi  have applied this approach for ferroelectrics. It can be used for complete switching by single rectangular pulse in uniform infinite ferroelectric. Modification of K-A formula for finite size media has been proposed in . For realization of the Merz method the switching field has to be constant during the whole switching process. This condition is never realized during fast switching in thin ferroelectric films due to rise time comparable with switching one (Fig. 1(b)). Moreover the kinetic approach can be used only for absolutely uniform media, which is far from the real situation in thin films. Therefore it is impossible to use kinetic approach for the quantitative analysis of switching current data recorded during rectangular pulse measurements in thin films. Figure 1. Merz technique. (a) Scheme of switching current measurement by rectangular pulses and (b) typical switching current and applied voltage pulse in thin films. Rise time comparable with switching one.
3 NEW APPROACH TO ANALYSIS OF THE SWITCHING CURRENT DATA /29 QUASI-STATIC APPROACH: NUCLEATION ONLY MODEL In addition to kinetic approach quasi-static approaches were also suggested and used for slow switching when the voltage rise time is smaller than the local switching time. This condition is typical for conventional hysteresis measurements. Usually in such measurements the increasing field (triangular pulses) of low frequency (from 1 to 1000 Hz) is used. Current loops are essentially more sensitive to switching conditions and therefore more useful for mathematical analysis than polarization ones. The quasi-static approach has been proposed by Preisach for explanation of the hysteresis loop shape in ferromagnets  and later has been applied for ferroelectrics by Turik . Recent years some applications of Preisach approach in ferroelectric thin films were made[10, 11]. According to quasi-static approach the uniform ferroelectric should be switched momentary. However all real ferroelectrics are nonuniform and such situation does not realize on practice. There are several types of nonuniformity: nonuniform distribution of the field components Ez in polycrystalline ferroelectrics (ceramics and thin films) due to the random orientation of polar axes in grains spatially nonuniform field in thin films due to variation of the thickness nonuniform threshold field or random field in all real ferroelectrics due to nonuniform distribution of structural defects spatially nonuniform internal bias field formed during cycling, which leads to fatigue effect [12 15]. According to Preisach quasi-static approach each small part of nonuniform ferroelectric is characterized by the local value of threshold field and is switched when the switching field has reached this value. Thus the switching current shape is determined by distribution function of threshold field (Fig. 2). Hence Preisach approach corresponds to nucleation only model. At the same time it is well known that the input of domain growth (domain wall motion) in switching current is very significant. NUCLEATION AND GROWTH MODEL We have modified the quasi-static approach taking in consideration both nucleation and growth stages of switching process at each step of applied
4 30/ V. YA. SHUR et al. Figure 2. (a) Distribution function of threshold field and (b) corresponding switching current according to Preisach approach (nucleation only model). field. The domain kinetics in ferroelectric with spatially inhomogeneous threshold field under the action of slow increasing field has been studied by computer simulation. In such case the polarization reversal has been considered as a switching in step-by-step increasing external field (Fig. 3). E ex (n) = n δe (1) where n is the step number. It was assumed that switching at each field-step occurs through formation of isolated nuclei and subsequent nucleation at the walls (Fig. 4). The isolated nuclei appear in all points, where the external field exceeds the threshold value E th n, while threshold field for nucleation at the existing wall E th gr is essentially lower where E 0. E th n = E th gr + E (2) Figure 3. Step by step increasing of switching field.
5 NEW APPROACH TO ANALYSIS OF THE SWITCHING CURRENT DATA /31 Figure 4. Switching kinetics through isolated nucleation and growth during single field step. Domain configurations (a) before the considered step, (b) after isolated nucleation and (c) after following domain growth. - Previously switched area - area switched by isolated nucleation and - area switched by domain growth. The sum area of the regions A(n) switched at each step (duration δ?t) determines the switching current j(n) = 2Ps A(n)/δt at corresponding external field E(n). Similarly to the Preisach model we suppose that duration of each step is long enough for switching in all regions, where local field E loc exceeds the local threshold one E th. For spatially nonuniform threshold field E th the switching is obtained in all regions, in which E loc (n) = E ex (n) + E rd + E b > E th (3) where E rd residual depolarization field produced by bound charges and partially compensated by external screening, E b internal bias field. Two mechanisms of domain switching at each step are considered. Nucleation (arising of new domains) is obtained in all points over the whole area where E loc > E th n. The domain growth (nucleation at the wall) proceeds at all points neighboring to the domain boundaries, where E loc > E th gr. The Gaussian distribution function of threshold field with dispersion w has been chosen. The simulated currents for different values of E/w (where w is the dispersion of the Gaussian distribution of E th ) are shown at (Fig. 5(a)). The dependence of the current on field/time is proportional to the threshold and/or internal bias field distribution function for E = 0 only, which is corresponding to the Preisach model. Otherwise the relation between current shape and distribution function is more complicated when E 0. The results of simulations obtained within nucleation and growth model differ significantly from the Preisach approximation and correlate with the experimental ones (Fig. 5(a)). It must be pointed out that the input of domain growth in switching current leads to strong dependence of the current shape
6 32/ V. YA. SHUR et al. Figure 5. (a) Time dependence of switching current simulated according to proposed approach with different value of E th /w and (b) simulated dependence of current maximum on E th /w value fitted by equation (4). on E. The following dependence of the current maximum on E/w was obtained by simulation (Fig. 5(b)) j max ( E/w) = j max (0) + j[exp(a E/w) 1] (4) where j and a are constants. The current can be divided in two stages. At the first stage the current shape is determined by domain growth, while at the final stage it coincides with the threshold field distribution function. Transition to the final stage is obtained when the whole unswitched area is bordered with the switched one. Such behavior allows us to reveal the parameters of the threshold field distribution function by fitting of the final stage of the current data by Gaussian with integral equal to the switched charge (Fig. 6). Figure 6. Fitting by Gaussian function of the final stage of switching current simulated for different value of E th /w.
7 NEW APPROACH TO ANALYSIS OF THE SWITCHING CURRENT DATA /33 Figure 7. Fitting by Gaussian function of the final stage of experimental switching currents recorded during cycling in PLZT thin films. The proposed approach has been applied for analysis of the experimental current data in sol-gel PLZT 5/40/60 thin films (Fig. 7). The experimental procedure has been described elsewhere [12, 14]. The shape of experimental currents measured during switching by bipolar triangular pulses is very similar to simulated one (Fig. 7). Recently it was shown that this model is also applicable for describing the fatigue effect [12 15]. The evolution of the parameters of the distribution function extracted by fitting of experimental data measured during fatigue is shown at (Fig. 8). It is seen that slow decrease of the dispersion is obtained Figure 8. Change of the switching current parameters during cycling. P r remnant polarization, J max maximum value of the switching current and w dispersion of the Gaussian distribution function of internal bias field extracted by current fitting.
8 34/ V. YA. SHUR et al. up to 10 5 cycles, which corresponds to the rejuvenation ( wake-up ) stage and correlates with increase of the switching charge. While decreasing of the switching charge at the fatigue stage is followed by essential increasing of the Gaussian dispersion. Such behavior one-to-one correlates with predictions of our recently proposed model of fatigue effect as a result of kinetic imprint . CONCLUSION We have shown how the information about the distribution function of the threshold fields and the spatial correlation function can be extracted from the switching current data measured in triangular pulses at low frequencies. The proposed approach has been applied for analysis of the experimental currents in PLZT thin films measured during fatigue cycling. Our investigations revealed that the proposed method opens the possibilities for quantitative characterization of the ferroelectric films produced by different technologies and can be used for detail investigation of the fatigue effect kinetics. ACKNOWLEDGMENTS The authors are grateful to T. Schneller for providing PLZT thin film and to E. Rumyantsev for helpful discussions. The research was made possible in part by Programs Basic Research in Russian Universities (Grant?? ) and Priority Research in High School. Electronics (Grant No ), by Grant No of the Russian Foundation of Basic Research, by Grant No of RFBR-DFG, by Award No. REC-005 of CRDF. REFERENCES  J. F. Scott, Ferroelectric Memories (Springer, Berlin, Heidelberg, 2000).  W. J. Merz, J. Appl. Phys. 27, 938 (1956).  E. Fatuzzo and W. J. Merz, Ferroelectricity (North-Holland Publishing Com., Amsterdam, 1967), p  A. N. Kolmogorov, Izv. Acad. Nauk USSR., Ser Math. 3, 355 (1937).  M. Avrami, J. Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941).  Y. Ishibashi and Y. Takagi, J. Phys. Soc. Jap. 31, 506 (1971).  V. Ya. Shur, E. L. Rumyantsev, and S. D. Makarov, J. Appl. Phys. 84, 445 (1998).
9 NEW APPROACH TO ANALYSIS OF THE SWITCHING CURRENT DATA /35  F. Preisach, Z. Phys. 94, 277 (1935).  A. V. Turik, Sov. Phys. Solid State 5, 885 (1963).  G. Robert, D. Damjanovic, and N. Setter, Appl. Phys. Lett. 77, 4413 (2000).  A. T. Bartic, D. J. Wouters, H. E. Maes, J. T. Rickes, and R. M. Waser, J. Appl. Phys. 89, 3420 (2001).  V. Ya. Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, and I. S. Baturin, J. Appl. Phys. 90, 6312 (2001).  V. Ya. Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, I. S. Baturin, M. Ozgul, and C. A. Randall, Integrated Ferroelectrics 33, 117 (2001).  V. Ya. Shur, E. V. Nikolaeva, E. I. Shishkin, I. S. Baturin, D. Bolten, O. Lohse, and R. Waser, MRS Sym. Proc. 655, CC (2001).  V. Ya. Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, and I. S. Baturin, Phys. Solid State 44, 2145 (2002).
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