NANO LETTERS
Nanoparticle Assemblies as Memristors Tae Hee Kim,*,† Eun Young Jang,† Nyun Jong Lee,† Deung Jang Choi,† Kyung-Jin Lee,‡ Jung-tak Jang,§ Jin-sil Choi,§ Seung Ho Moon,§ and Jinwoo Cheon*,§
2009 Vol. 9, No. 6 2229-2233
Department of Physics, Ewha Womans UniVersity, Seoul 120-750, Korea, Department of Materials Science and Engineering, Korea UniVersity, Seoul 136-713, Korea, and Department of Chemistry, Yonsei UniVersity, Seoul 120-749, Korea Received January 5, 2009; Revised Manuscript Received April 4, 2009
ABSTRACT Recently a memristor (Chua, L. O. IEEE Trans. Circuit Theory 1971, 18, 507), the fourth fundamental passive circuit element, has been demonstrated as thin film device operations (Strukov, D. B.; Snider, G. S.; Stewart, D. R.; Williams, R. S. Nature (London) 2008, 453, 80; Yang, J. J.; Pickett. M. D.; Li, X.; Ohlberg, D. A. A.; Stewart, D. R.; Williams, R. S. Nat. Nanotechnol. 2008, 3, 429). A new addition to the memristor family can be nanoparticle assemblies consisting of an infinite number of monodispersed, crystalline magnetite (Fe3O4) particles. Assembly of nanoparticles that have sizes below 10 nm, exhibits at room temperature a voltage-current hysteresis with an abrupt and large bipolar resistance switching (ROFF/RON ≈ 20). Interestingly, observed behavior could be interpreted by adopting an extended memristor model that combines both a timedependent resistance and a time-dependent capacitance. We also observed that such behavior is not restricted to magnetites; it is a general property of nanoparticle assemblies as it was consistently observed in different types of spinel structured nanoparticles with different sizes and compositions. Further investigation into this new nanoassembly system will be of importance to the realization of the next generation nanodevices with potential advantages of simpler and inexpensive device fabrications.
The recent reports on the use of memristors, a contraction of “memory resistors”, have opened up new possibilities in the development of computer systems that would have nonvolatile random access memory.1-3 The reason that memristors differs from other circuit elements is that it carries a memory of its past. On the basis of this unique characteristic of memristors, one would expect there to lead to the enhancement of emerging memory technologies that would minimize the time for boot-up processes and consequently energy consumption. Williams et al. were the first to demonstrate the realization of a memristor composed of a thin (5 nm) titanium dioxide film between Pt electrodes.2 The device uses neither magnetic flux, as the theoretical memristor model suggests, nor does it store charges, like a capacitor does. Instead the new memristor was found to achieve a resistance that is dependent on a time-varying current by using a chemical mechanism. When an electric field is applied, a charge-carrier drift arises on a nanometer scale caused by changing the boundary between the high-resistance layer of pure titanium dioxide and the low-resistance layer of titanium oxide via positively charged oxygen holes. The on and off states can be maintained much longer if the voltage does not exceed a specific threshold. * To whom correspondence should be addressed. E-mail: (T.H.K.)
[email protected]; (J.C.)
[email protected]. † Ewha Womans University. ‡ Korea University. § Yonsei University. 10.1021/nl900030n CCC: $40.75 Published on Web 05/01/2009
2009 American Chemical Society
The titanium dioxide based system, discovered by Williams et al., can serve as a general model for memristive electrical switching in nanoscale thin film oxide devices. Nevertheless, the underlying physical details of memristors are still being debated. Moreover, several issues, including the design strategies and requirements of new nanodevices that are based on the memristic concept, have not been fully answered. Another important question in this area is whether memristic systems are limited to thin film devices or if they can be comprised of different kinds of nanostructured systems including nanoparticles. According to its definition, memristance, in other words “time-dependent resistance”, could be described by any of a variety of time-varying functions of net charge. In this work, we have made an effort to understand our hysteretic switching characteristics of nanoparticle assembly in terms of time-dependent electric phenomena (see vide infra). Hence, a new extended model of memristor is proposed as one of possible interpretations for such electric behaviors of the nanoparticle assemblies. Single crystalline magnetite (Fe3O4) nanoparticles, having diameters of 7, 9, 12, and 15 nm with the well-controlled size monodispersity (σ ≈ 5%), were prepared by using a nonhydrolytic chemical method.4,5 (see Supporting Information, Figure S1). Owing to the fact that the synthesized nanoparticles were coated with organic molecular layers, which can strongly affect electronic transport behaviors, their surface ligands were carefully removed by using a chemical
Figure 1. (a) Schematics of the electric circuit with the nanoparticle assemblies. The details of pellet fabrication and measurements are given in the text and methods. (b) Transmission electron microscopy (TEM) and high resolution TEM (HR-TEM, inset) images of 7 nm sized Fe3O4 nanoparticles. (c) For Fe3O4 nanoparticle assemblies of D ) 7 nm, V-I characteristics measured at RT (295 K). Transition from low (RON) to high (ROFF) resistance with (ROFF/ RON ) ca. 20) occurred by applying dc current-bias sweeping toward positive (0 A f +20 × 10-9 A), numbered 1-2, 6, and toward negative current (+20 × 10-9 A f -20 × 10-9 A), numbered 3-5.
method employing washing with tetramethylammonium hydroxide solution to have clean and pristine inorganic surface.6,7 The nanoparticle assemblies in the form of the compact pellets (0.5 × 1 × 4 mm) were then made by coldpressing in a die under 160 Pa for 15 min. In order to avoid alteration of the surface properties of the nanoparticles, no heat-treatment step was used in the preparation of the pellets. The V-I characteristics of the nanoparticle assembly pellets were probed by using a conventional four-point dc method (Figure 1a). In the case of nanoparticles with a diameter (D) of 7 nm (Figure 1b), a new type of hysteresis is observed at room temperature (RT), as shown in Figure 1c. The bistable V-I characteristics, observed in the sample of D ) 7 nm, illustrate that the switching properties are directly related to the existence of hysteretic behavior as the current is swept in steps 1 to 6 (corresponding 0 f +Imax f 0 f -Imax f 0). As the current increases from 0 to +Imax, the switching between the low-resistance state (RON ≈ 2 × 107 Ω) and the high-resistance state (ROFF ≈ 4 × 108 Ω) occurs at I ) +16 × 10-9 A. In contrast, ohmic behavior is seen when the current decreases from +Imax to 0. The same behavior is observed when the current direction is reversed. This type of instantaneous switching from the low-resistance (i.e., on-state) to the high-resistance (i.e., off-state) occurs in a typical ROFF/RON ratio of 20:1. It is remarkable that when sweeps are carried out repeatedly, no damage or breakdown of the sample occurs. To the best of our knowledge, this is the first room temperature observation of reversible switching behavior in a nanoparticle system. It is interesting to observe that the V-I hysteresis behavior described above is dependent on the size of the nanoparticle. For example, the current induced hysteric behavior of nanoparticle assembly pellets of D ) 12 nm appears only at 2230
Figure 2. V-I characteristics of the Fe3O4 nanoparticle assemblies of D ) 12 nm at two different temperatures: (a) 210 K and (b) 295 K. The numbered arrows denote the steps of current sweeping. While resistive switching behavior is clearly seen at 210 K, tunneling behavior is observed at higher temperatures (e.g., 295 K). (c) Temperature-dependent resistivity of Fe3O4 nanoparticle assemblies of D ) 15, 12, and 9 nm. It is observed that F increases with decreasing T and log F is approximately proportional to 1/T.10 According to the results, resistive switching appears in the shaded region where F > 50 MΩ·cm. Because of the measurement limitation (Keithley 2182 nanovoltmeter), the resistivity of the D ) 7 nm nanoparticle assemblies was not obtainable.
lower temperatures. As the data in Figure 2a show, at 210 K the switching transition of the D ) 12 nm assembly appears at a current of (7 × 10-9 A. In contrast, at RT (295 K) this sample shows a typical tunneling conductance behavior (Figure 2b). On the basis of the results of temperature-dependent resistivity (F(T)) measurements for the magnetite nanoparticles with different diameters, it appears that the switching behavior dominates when F value is higher than ca. 50 MΩ·cm (the shaded area of Figure 2c). An increase of F is observed with decreasing D. It is likely that the increased resistivity of smaller particles is a result of “nanosize” effects associated with increased surface to volume ratios.8-10 Quite different nonlinear I-V characteristics from our results have been observed in many amorphous conductive-insulating composites.11-13 Several conduction mechanisms were suggested for the possible explanations of the nonlinear I-V characteristics in applying percolation theory: (i) The tunneling of single electrons between neighboring particles.11 (ii) A simple geometrical model based on the average gap decrease between neighboring particles with the decrease in the particle size.12 As the gap becomes sufficiently small, the electron can overcome the Coulomb charging energy and the onset of conduction occurs. (iii) The dielectric breakdown between neighboring particles.13 Unfortunately, according to our present knowledge, none of these mechanisms provides a sufficient explanation for our experimental results. Nano Lett., Vol. 9, No. 6, 2009
Although the underlying mechanism is not fully clear yet, we propose a possible scenario to explain the switching behavior of nanoparticle assemblies as followings. An explanation for the V-I hysteresis observed for nanoparticle assemblies is based on an extended model of the memristor. In this model, the nanoparticle assembly is simply represented by a one-dimensional repeating nanoparticle array of Fe3O4, which have doped and undoped charge carrier regions separated by a moving boundary.2 Since this system has almost infinitely alternating repetition of the conducting and insulating parts, the time-dependent capacitance C(t) as well as the time-dependent resistance R(t) is considered in the model. Another feature of this system is that it is comprised of two charge carriers, Fe3+ and Fe2+ ions, that have different mobilities in the nanoparticle lattices.14-17 This results in a different distribution of each carrier and thus an additional time-dependent capacitance ∆C(t) across the particle boundaries. In contrast, the initial memristor model proposed in ref 2 consists of a single type of charge carrier drifting in the insulator and requires consideration of only the time dependent resistance. The time-dependent change of w and associated change of voltage for the nanoparticle system in response to injection of an alternating current can be simulated by using the following model. In the model, time-dependent state variable w is the length of the doped region, bounded between zero and L which is the full length of grain boundary region.2 We consider an impedance Z () (R2 + X2C)1/2) where XC is the resistance caused by the capacitance. The voltage drop V(t) is then given by eq 1
(4)
Figure 3. Simulation of a memristive device that has both timedependent resistance (R) and capacitance (C). (a) The doped region (w)/grain boundary (L) as a function of time. (b) Current (red line) and voltage (blue line) as a function of time. The shaded areas indicate the low resistance state (RON) of the device when the charge saturation is established, labeled 1 and 4. The voltage remains almost constant while the current varies in a sinusoidal manner during that process. On the other hand, the other areas (labeled 3 and 6) are related to the high resistance state (ROFF) during the refresh charge process. (c) V-I hysteresis obtained from the simulation. Numbers of 1-6 are corresponding each other through out panels a-c. The applied current is i0 sin(ω0t). All the axes are dimensionless with current, voltage, and time expressed in units of i0 ) 120 × 10-9 A, V0 ) 1 V, and t0 ) 2π/ω0 ) 0.01 s. Other parameters are the following: RON ) 107 Ω, ROFF/RON ) 20, L ) 1 × 10-9 m, µ ) 10-10 cm2 s-1 V-1, χ ) 100, and CON ) εrε0A/L C·V-1, εr ) 50, A ) 10-7 cm2 where ε0 is the permittivity of vacuum.
where RON (ROFF) is the resistance of the doped (undoped) region, CON is the capacitance at w ) 0, µ is the average carrier mobility, and ∆C(t) is the additional capacitance caused by the different mobilities of the two carriers and proportional to the imbalanced charge accumulation ∆q () QFe2+ - QFe3+) around the undoped region. The ∆q is assumed to be proportional to the total charge q with a dimensionless proportion coefficient χ, which is material and geometry dependent. As the current direction is reversed, the phase of ∆q is shifted by π because the sign of charge accumulation also depends on the current direction. Figure 3a,b show the time-dependent changes of w and associated changes of voltage, obtained by simulation using above equations, when an alternating current is injected. The consistency between the results of V-I hysteresis modeling
and the experimental observations (Figure 1c) is clearly shown. The model shows that this unusual hysteresis originates from abrupt changes of w (Figure 3a,b). When i(t) ) 0 and w(t) ) L, the nanoparticle assembly is in the low resistance state. As the current becomes increasingly larger, more charge accumulates until it reaches a critical value. At that point, the boundary abruptly moves back to w ) 0 in order to relax the charge accumulation and then the resistance is high. It should be noted that the experimentally observed chirality of hysteresis in both bias polarities is counter-clockwise (Figure 3c), whereas the chirality in the previously studied memristor with only time-dependent resistance changes depends on the bias polarity.2,3 The difference in the chirality of hysteresis between the two
V(t) ) i(t)
R2(w, t) +
q(t) 1 [i(t)]2 C(w, t)
(
2
)
(1)
where i is the current and q is the charge. R(w,t) and C(w,t) are the resistance and the capacitance respectively, and they are given by the relationships in eqs 2-4 w(t) w(t) + ROFF 1 L L L C(w, t) ) (CON - ∆C(t)) L - w(t)
R(w, t) ) RON
w(t) )
(
(
∫
q(t)dt µ RONq(t) + L CON - ∆C(t)
Nano Lett., Vol. 9, No. 6, 2009
)
)
(2) (3)
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Figure 4. (a) TEM and HR-TEM (inset) images of 12 nm sized MnFe2O4 nanoparticles. (b) Hysteric resistive switching behavior was observed for a MnFe2O4 nanoparticle assemblies. Numbers 1-6 denote current sweeping steps.
systems can be explained only when the capacitance part in the model is properly taken into account. The nanoparticle system described above is unique in terms of the size of the monodispersity and the mild conditions required for preparing pristine nanoparticle surfaces. In previous work on magnetite nanoparticles for which ligand eliminations were performed using high temperature thermal treatment procedures, in contrast to our observations, either only tunneling behavior18-21 was shown or the resistive switching22 was found to appear only at very low temperatures below 120 K. In the latter case, the switching was explained as a bulk effect in the context of the Verwey transition,23-25 which is not the case in this work since the hysteresis was observed at much higher temperature (i.e., RT) than TV. An important question that arises in viewing our findings concerns whether memristic behavior is limited to magnetite nanoparticles or whether it is a general phenomenon associated with other kinds of nanoparticles. In this regard, we found that it is consistently observed for spinel structured nanoparticles with different compositions (MFe2O4, M ) Mn, Co, Ni) (see the Supporting Information, Figures S2 and S3). As seen in Figure 4, for example, for MnFe2O4 nanoparticles, an abrupt bipolar switching was again observed at 225 K. The observations presented above regarding the switching behavior of nanoparticle assemblies can serve as the framework for devising new applications to a wide range of electronic devices. Since the elucidation of fundamental mechanism for the observed switching behaviors still needs more studies, it should be noted that current interpretation of observed electrical behaviors of nanoparticle assemblies as of memristor is not conclusive and could be explained more accurately by using modified or different theories in the future. Nonetheless, the potential applicability of nanoparticles as a key material for nanodevice is fascinating not only for the existing device property enhancements but also for unveiling of novel device phenomena. Predictions of the high potential of nanodevices based on nanoparticle assemblies are supported by the tremendous versatility to tune the electrical behavior of nanoparticles by controlling their nanoscale characteristics such as size, composition, dimension, surface area, and chemical potential. Methods. MFe2O4 (M ) Mn, Fe, Co, Ni) nanoparticles were synthesized by using a modification of the known 2232
method.4,5 The size and composition of nanoparticles were further controlled by varying growth conditions including the amount of reactants. Organic ligands on the surface of nanoparticles were removed by incubation in a 1 M tetramethylammonium hydroxide (TMAOH) solution.6,7 After 15 min sonication in TMAOH solution, the nanoparticles were isolated by centrifugation and washed with hexane, acetone, and ethanol. Isolated nanoparticles were dried under vacuum at room temperature before nanoparticle assembly pellet preparation. A pellet of nanoparticle assemblies was prepared by following procedures described in the main text. TEM images of a pellet are given in the Supporting Information, Figure S4. Electrical property measurements were performed by using the circuit shown in Figure 1a. The 10 mm diameter gold wires as electrodes were attached using indium pressure onto pellets to allow four-point transport measurements. The V-I characteristics were measured by using conventional fourprobe configuration with a Keithley 2182 nanovoltmeter and a Keithley 6220 current source. The shape of the nanoparticle assembly pellets was rectangular, 4 mm long, 1 mm wide, and 0.5 mm thick. An electrode (for current injection) was made at each end of the pellet (using indium contact) so that current flow was as uniform as possible. The voltage drop across the sample was observed using two other electrodes attached to the surface. It should be noted that switching behaviors sensitively depends on the surface treatments of the nanoparticles as we observed reproducible data when samples were prepared appropriately. Acknowledgment. We thank J.-G. Kim and Y.-J. Kim for TEM analyses (KBSI-HVEM (JEM-ARM1300S)). This work was supported in part by the National Research Laboratory (R0A-2006-000-10255-0), BK21 and WCU program (2008-8-1955) (for J.C.), Korea Research Foundation Grant (KRF-2006-531-C00026) and the Korea Science and Engineering Foundation (KOSEF) through the Quantum Meta-Materials Research Center (for T.H.K.). The simulation work was supported by KOSEF through the National Research Laboratory (M10600000198-06J0000-19810) (for K.-J.L.). The Fundamental R&D Program for Core Technology of Materials funded by the Ministry of Commerce (for T.H.K. & K.-J.L.). Nano Lett., Vol. 9, No. 6, 2009
Supporting Information Available: TEM images of MFe2O4 () Mn, Fe, Co, Ni) nanoparticles and nanoparticle pellet and switching behaviors of spinel structured nanoparticles with different compositions (CoFe2O4 and NiFe2O4). This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Chua, L. O. IEEE Trans. Circuit Theory 1971, 18, 507. (2) Strukov, D. B.; Snider, G. S.; Stewart, D. R.; Williams, R. S. Nature (London) 2008, 453, 80. (3) Yang, J. J.; Pickett, M. D.; Li, X.; Ohlberg, D. A. A.; Stewart, D. R.; Williams, R. S. Nat. Nanotechnol. 2008, 3, 429. (4) Lee, J.-H.; Huh, Y.-M.; Jun, Y.-w.; Seo, J.-w.; Jang, J.-t.; Song, H.T.; Kim, S.; Cho, E.-J.; Yoon, H.-G.; Suh, J.-S.; Cheon, J. Nat. Med. 2007, 13, 95. (5) Jun, Y.-w.; Huh, Y.-M.; Choi, J.-s.; Lee, J.-H.; Song, H.-T.; Kim, S.; Yoon, S.; Kim, K.-S.; Shin, J.-S.; Suh, J.-S.; Cheon, J. J. Am. Chem. Soc. 2005, 127, 5732. (6) Salgueirin˜o-Maceria, V.; Liz-Marza´n, L. M.; Farle, M. Langmuir 2004, 20, 6946. (7) Massart, R. IEEE Trans. Magn. 1981, MAG-17, 1247. (8) Batlle, X.; Labarta, A. J. Phys. D: Appl. Phys. 2002, 35, R15–R42. (9) Kodama, R. H. J. Magn. Magn. Mater. 1999, 200, 359.
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