LETTER pubs.acs.org/NanoLett
Electromechanical Actuation and Current-Induced Metastable States in Suspended Single-Crystalline VO2 Nanoplatelets Alexander Tselev,*,† John D. Budai,† Evgheni Strelcov,‡ Jonathan Z. Tischler,† Andrei Kolmakov,‡ and Sergei V. Kalinin† † ‡
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Physics Department, Southern Illinois University Carbondale, Carbondale, Illinois 62901, United States
bS Supporting Information ABSTRACT: Current-induced electromechanical actuation enabled by the metalinsulator transition in VO2 nanoplatelets is demonstrated. The Joule heating by a sufficient current flowing through suspended nanoplatelets results in formation of heterophase domain patterns and is accompanied by nanoplatelet deformation. The actuation action can be achieved in a wide temperature range below the bulk phase transition temperature (68 C). The observed current-sustained heterophase domain structures should be interpreted as distinct metastable states in free-standing and end-clamped VO2 samples. We analyze the main prerequisites for the realization of a current-controlled actuator based on the proposed concept. KEYWORDS: Vanadium dioxide, metalinsulator transition, actuator, heterophase domains, Joule heating
D
evelopment and manufacture of functional nanoscale devices and systems ranging from smart dust sensors to nanoscale robots requires a technology for generating and controlling mechanical motion on the nanoscale. The existing approaches for electromechanical actuation include piezoelectric, electrostatic, magnetic, and electrothermal actuators,1,2 as well as “artificial muscles” based on carbon nanotube aerogels and ionically active polymers.3,4 Fast response speeds and simple electrical control favor actuators based on piezoelectric phenomena. However, relatively small effective deformations and large footprints are characteristic for devices of this type. Electrothermal bimorph and quasi-bimorph actuators utilizing differential thermal expansion have the smallest footprint among nanoactuator classes extending to ∼103 mm3.1,5 However, the use of operational temperatures in excess of 600 C is necessary for a large displacement range, which leads to undesirably large thermal gradients, power consumption, and thermal-cross talk. This also limits the choice of the materials in the systems where such actuators can be implemented.1 Here, we investigate the viability of electrothermal actuation utilizing the reversible metalinsulator transition (MIT) (alternatively referred to as metalsemiconductor transition) in vanadium dioxide to produce the actuator action at operational temperatures below 100 C. The MIT in vanadium dioxide occurs in close proximity to ambient temperature (Tc = 68 C in pure VO26) and can be further reduced by doping.7,8 The phase transition results in several orders of magnitude change of electrical conductivity and is accompanied by a change of the lattice structure from tetragonal (rutile type, R) in metallic phases to a lower-symmetry r 2011 American Chemical Society
monoclinic in semiconducting phases. Depending on doping or stress, two possible monoclinic structures M1 and M2 or a triclinic structure T can be realized.912 The MIT is associated with spontaneous expansion of ∼1% along the tetragonal cR axis of the higher-temperature metallic phase and a ∼0.5% contraction perpendicular to this direction.9,13,14 This strong coupling between conductivity and lattice strain generally suggests a significant potential of the material for a broad range of electromechanical and piezoresistive phenomena. This is particularly important for quasi-1D single-crystalline VO2 nanostructures, where significant extension (contraction) of the length can be realized. Thermally controlled bilayer actuators based on the structural transition in VO2 thin films deposited on Si microcantilevers15 and wafers16 were previously demonstrated. However, the polycrystalline nature of thin films does not allow utilization of the full potential of the structural transformation because of the anisotropic character of the spontaneous strain. Cao et al. in ref 17 achieved significantly larger bending curvatures with thermally controlled bilayer cantilevers based on single-crystalline VO2 nanobeams. The nanobeams were grown with the tetragonal cR axis along the length, and the authors used a Cr layer deposited on one surface of a VO2 nanobeam to form a bilayer structure. In this article, we demonstrate that the large ∼1% difference in the lattice parameters of metal and semiconductor phases of VO2 can be employed to generate electrically controlled mechanical Received: February 10, 2011 Revised: June 28, 2011 Published: June 29, 2011 3065
dx.doi.org/10.1021/nl200493k | Nano Lett. 2011, 11, 3065–3073
Nano Letters motion. The concept proposed here ultimately employs coupling of both electronic and structural aspects of the MIT in VO2 to achieve actuator action, in contrast to previous reports where only the thermally activated structural component of the transition was used. In most actuator applications, electrical control provides greater switching speeds and flexibility compared with thermal control. The motion generation concept we explore is based on the observation first documented in 1976 by Fisher,18 who reported on the formation and behavior of metallic and semiconducting domains when a current exceeding the switching threshold passes through single crystalline needles of VO2. He noticed that with increasing current, growth and motion of metallic domains are accompanied by a shape change of the entire sample. Due to recent progress in material synthesis, highquality single-crystalline nanoscale beams and platelets of VO2 of dimensions significantly smaller than those used in Fisher’s work have become available.1921 The micrometer-scale dimensions of VO2 nanobeams and nanoplatelets allow them both to sustain large strains while maintaining material integrity22 (in contrast to bulk samples of macroscopic dimensions) and to make them potentially suitable for use in micro- and nanoscale electromechanical systems. Here we show that Joule heating leads to formation of metalsemiconductor domains in suspended VO2 nanoplatelets carrying an electrical current. The metal and semiconductor domains are self-organized in chains providing a path for the current flow. This results in nanoplatelet bending depending on the current strength, which can be used for electrically controlled actuator action. We find that with similar device sizes, achievable displacements are comparable to those characteristic for the existing electrothermal actuator designs, while operational temperatures are well below 100 C. The actuation action as presented here can be achieved in a wide temperature range, including room temperature. From a broader scientific perspective, the observed currentsustained heterophase domain structures can be considered as distinct metastable states of free-standing and end-clamped samples as compared to fully clamped nanobeams and nanoplatelets. The existence of these metastable states should be taken into account in the interpretation of experimental observations with nanobeams of a smaller size carrying an electric current. Phase Transition Behavior in Suspended Nanoplatelets. Single-crystalline VO2 nanoplatelets for our experiment were grown on Si/SiO2 substrates by a vapor transport method.19,23 The nanoplatelets grow as rectangular cross-section, high aspect ratio elongated single crystals with longitudinal direction coinciding with the tetragonal c axis (cR) of the higher-temperature metallic phase and with the upper surface parallel to the tetragonal (110)R lattice plane.19,21 The test device configuration is depicted in Figure 1. To suspend nanoplatelets between electrical contacts and above a substrate, their ends were immersed into liquid metal droplets of the low-melting point GaInSn eutectic. This method of electrical contact formation is similar to that used earlier for VO2 nanowire thermistor gas sensors24 as well as to that used in refs 18 and 25. The width of the nanoplatelets used in the experiments was between 10 and 30 μm and the thickness is between 0.5 and 2 μm. We choose relatively large-sized single-crystalline nanoplatelets, where domain patterns can be readily studied under an optical microscope. Using polarized light optical microscopy allows us to distinguish between orientational (twin) domains of the monoclinic semiconducting phases M1 and M2 as well as to distinguish between
LETTER
Figure 1. Schematic of the test device configuration. (a) and (b) illustrate the motion generation concept. At a substrate temperature Ts below the phase transition temperature Tc: (a) due to Joule heating at a circuit driving voltage Vd = V1, a nanoplatelet is fully metallic and perfectly straight; (b) with a reduced driving voltage V2 < V1, flow of the current through the nanoplatelet causes its deformation associated with formation of metallic and semiconducting domains. (c) Fully semiconducting nanoplatelet may buckle due to Euler instability.
Figure 2. Five resistance-vs-temperature hysteresis loops obtained with a low driving voltage (Vd = 0.8 V) for the nanoplatelet shown in the inset of Figure 3.
the semiconducting and metallic, R (rutile), phases at the same time.12 In addition, synchrotron Laue microdiffraction with a spatial resolution of ∼0.5 μm was used to quantitatively identify local domain structures and orientations.26 The liquid contacts, where the nanoplatelets are suspended above the substrate, provide paths for the current flow without creating significant mechanical force, which allows nearly external-force-free deformations of the nanoplatelets during temperature changes and phase transitions. Due to high viscosity, surface tension, and partial oxidation of the alloy components of the eutectic liquid drops, some amount of mechanical interaction between nanoplatelets and the contacts is still present even in the newly made devices. The force from the contacts can cause buckling of thinner nanoplatelets perpendicular to their thickness below the transition temperature as depicted in Figure 1c (see also Figure 4c) as a result of the ∼1% lattice expansion in the longitudinal direction upon transition into the semiconducting phase. However, the mechanical reaction of the liquid drops is insufficient to sustain a strain-induced coexistence of metallic and semiconducting phases at the phase transition (in contrast to refs 14 and 20). Thus, the configuration with liquid contacts ensures that single-crystalline nanoplatelets behave as single-domain particles during thermal cycling. In this case, we observed extremely abrupt metalsemiconductor phase transitions on cooling and heating with a transition width as small as 0.001 C as illustrated in Figure 2 for one of the devices. The resistance 3066
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters
LETTER
Figure 3. (a, b) A Laue diffraction pattern and a stereographic projection derived from it, identifying the low-temperature M1 phase. (c, d) Same as (a) and (b) for the high-temperature R phase. Unindexed peaks in the Laue patterns are from the Si substrate. Inset shows a polarized light image of the nanoplatelet, for which the Laue patterns were obtained. The image was taken at room temperature with the nanoplatelet in the M1 phase. The nanoplatelet orientation approximately corresponds to that in the X-ray diffraction setup. Scale bar in the inset is 50 μm.
change on the phase transition is from 3 to 5 orders of magnitude for all devices studied. The resistance versus temperature curve in Figure 2 was measured by applying a driving voltage Vd = 0.8 V across the circuit consisting of the device and a series limiting resistor Rs (Figure 1). The current produced by this voltage is sufficiently small and does not interfere with the thermal phase transition, which was confirmed by measuring the resistance versus temperature curves for a set of voltages below 1 V as well as by observing the structural transition with synchrotron X-ray microdiffraction, both with and without an electric current. The Laue diffraction patterns shown in Figure 3 for this particular nanoplatelet unambiguously identified the low-temperature and hightemperature phases as monoclinic (M1) and rutile (R), respectively. Moreover, in situ X-ray measurements at low currents showed that the resistive and the structural transitions occurred abruptly and simultaneously, at least within the 0.5 s time resolution set by the X-ray exposures. The width of the phase transitions versus temperature was determined during slow— about 0.005 C/s—change of the sample temperature. The small widths of the transitions are direct indicators of a negligibly small mechanical interaction between the liquid electrodes and the nanoplatelets. Taking into account the sharpness of the transitions, the observed hysteresis is ascribed to supercooling and superheating (compare transition temperatures in Figure 2 with Tc = 65.7 ( 0.2 C found in ref 14). The hysteresis loops in Figure 2 reflect typical phase transition behavior. The transitions on heating occurred at temperatures scattered in a smaller interval than
transitions on cooling with the width of the hysteresis varying from ∼3 to ∼5 C for different samples. With duration of time (several weeks in ambient), oxidation of the eutectic (mainly due to accumulation of Ga2O327) leads to solidification of the drops, which is reflected in the appearance of steps at the MIT in the resistance versus temperature curves as a result of the heterophase domain formation caused by strain, analogously to substrateclamped nanobeams.20 Nevertheless, the phenomena described below were observed both with liquid and with solidified eutectic drops. Self-Organized Domain Patterns in the Presence of Currents. To demonstrate generation of mechanical motion in the suspended current-carrying nanoplatelets, the experiment is started at a substrate temperature of 70 C, when the nanoplatelets are fully in the metallic phase. Voltages ranging from 10 to 30 V were applied to the circuit of a nanoplatelet and the limiting resistor Rs = 5 kΩ. In the fully metallic state, the device resistance— including contact resistance at the interface between nanoplatelets and liquid electrodes—is typically in the range from about 100 to 200 Ω, and therefore, current is largely determined by the applied voltage and the limiting resistor Rs. Due to Joule heating, the nanoplatelets remain fully in the metallic state on cooling down to a substrate temperature Ts < Tc (varying from device to device) as is illustrated by an example in Figure 4a. If the current is larger than a certain value depending on the nanoplatelet dimensions, instead of being fully transformed into the semiconducting state on cooling, the nanoplatelets abruptly 3067
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters
LETTER
Figure 6. A schematic illustrating development of triangular semiconducting domains across a nanoplatelet from the metallic state. Figure 4. Polarized light optical images of a VO2 nanoplatelet with the driving voltage of 10 V across the circuit: (a) at a substrate temperature Ts = 60 C, the nanoplatelet is fully in the metallic state; (b) at Ts = 44 C, the nanoplatelet is in the mixed state; and (c) it is fully transformed into the insulating phase at Ts = 25 C. In (c), the nanoplatelet is buckled up. The bright and dark domains visible in (c) correspond to different orientational domains of the M1 phase. The R, M1, and M2 phases indicated in the images were identified by X-ray microdiffraction and correlate with the contrast in the optical images. The nanoplatelet length between electrodes is 180 μm, and its width is 8 μm.
Figure 5. Plots of device resistance, current, and dissipated power as functions of substrate temperature for the device shown in Figure 4. The circuit driving voltage Vd = 10 V. The data were recorded on cooling.
break into alternating domains of semiconducting and metallic phases as is shown in Figure 4b. The domains and domain boundaries may move until the pattern is stabilized (see movies in the Supporting Information). Due to lattice expansion in the cR direction upon transformation into the semiconducting phase, this transition is accompanied by deformation of the nanoplatelet as is visible in Figure 4b. On further cooling, after several abrupt rearrangements of domains with appearance of new semiconducting domains, the nanoplatelet eventually is fully transformed into the semiconducting phase (Figure 4c). We observed similar behavior in all nanoplatelets (about 15) that were investigated with large currents. (See also movies in Supporting Information.)
Figure 5 shows the plots of device resistance, current, and dissipated power as functions of substrate temperature for the device shown in Figure 4. The dissipated power was calculated as P = IV, where I is the current and V is voltage drop across the device. The sharp steps on the plots correspond to nucleation of new domains and corresponding change of domain patterns. Along smooth segments of the curves, the geometry of domain patterns remained stable, while small shifts of domain boundaries were observed. As indicated in Figure 4b, we observe two types of domain pattern topologies stabilized by the electrical current (close to those reported in ref 18 and our prior work24). The first type is alternating metallic and semiconducting triangular domains similar to those appearing in nanobeams bent in an arc shape by an externally applied force as observed in ref 22. The structure of the second type consists of stripelike metallic domains surrounding triangular semiconducting domains in a zigzag fashion. In this case, the bending direction follows the domain structure, and the overall bending is significantly smaller than for the first type. Notably, X-ray microdiffraction and optical studies show that the semiconducting domains in the heterophase structure are predominantly in the monoclinic M2 phase apparently due to the tensile stress in these domains, similar to the observation in ref 11 for nanobeams bent by an external force. These observations can be explained as follows. We note that below the critical temperature the metallic phase in the system (Figure 6a) is unstable, and a semiconducting domain can nucleate and grow (Figure 6b). Generally, the appearance of a semiconducting domain, where the current density drops to near zero, results in local cooling of this volume of the material. Since the lattice constant in the lateral direction is larger for the semiconducting phase, the nanoplatelet will bend to accommodate the semiconducting domain as illustrated in Figure 6b. This deformation leads to compressive strain at the opposite edge of the nanoplatelet. At the same time, the increase of the current density around the semiconducting domain causes an increase of the Joule heating and local temperature at the constriction for the current flow in the metallic phase. Both the compressive strain and the local temperature increase favor stabilization of the metallic phase,14,22 which effectively slows further growth of 3068
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters
Figure 7. (a) Cycling of the nanoplatelet between straight and bent by stepping the driving voltage Vd from 10 to 4 V and back (Ts = 64 C). (b) Optical image of thin heterophase domains in the buckled portion of the nanoplatelet (Vd = 10 V, Ts = 41 C). Scale bar in (a) is 20 μm.
the semiconducting domain near the compressed edge of the nanoplatelet. Eventually, a semiconducting domain of a triangular shape forms (Figure 6c). With several triangular semiconducting domains nucleated in the system, the metallic and semiconducting domains are selfarranged in a stable pattern of alternating domains. Neighboring metallic domains of triangular or parallelogram shape partially overlap at vertexes with a continuous path for the current flow, or a gap of semiconducting phase can form between the vertexes so that the semiconducting domain spreads across the whole nanoplatelet width similar to ref 18. The whole structure is selfstabilized by the uneven temperature distribution with temperature maxima at the narrow junctions between metal domains and by the inhomogeneous strain across the deformed nanoplatelet. On further lowering the substrate temperature or current strength, the growth of the semiconducting domain continues until the Joule heating drops to a negligible value, and the nanoplatelet completes the transition into the semiconducting state. Current-Induced Actuation in Suspended VO2 Nanoplatelets. It immediately follows that the mixed phase state is metastable since any event breaking the continuity of the current path leads to transformation of the whole nanoplatelet into the semiconducting phase, when the substrate temperature is below Tc. On the other hand, it is clear that with increase of the current trough the nanoplatelet in the mixed phase state should lead to increase of the temperature due to Joule heating, which can trigger the transformation of the whole nanoplatelet volume between the electrodes into the metallic state with the corresponding change in its shape. When the voltage is stepped back down, the nanoplatelet can be returned to the mixed phase state. This switching can be repeated multiple times. As an illustrative experiment (see Supporting Information for a movie of the experiment), we preheat the nanoplatelet shown in Figure 4 above the transition temperature, and then apply a voltage of Vd = 4 V across the circuit, which results in a circuit current of about 0.8 mA (with a device resistance close to 90 Ω). After the sample is cooled down to a temperature of about Ts = 64 C, a domain of semiconducting phase appears at the growth defect at the edge of the nanoplatelet as is seen in Figure 7a, and the nanoplatelet bends both at the domain site and in the vicinity of the contacts. After application of Vd = 10 V across the circuit, the semiconducting domain disappears, and the nanoplatelet straightens. Stepping the voltage between 10 and 4 V, we repeatedly change the shape of the nanoplatelet from straight to bent and back. (Currents through the nanoplatelet in these regimes are 1.8 and 0.7 mA with device resistances of 450 and 890 Ω, respectively. As
LETTER
discussed below, the device resistance in this case is determined by the contact resistance due to presence of semiconducting domains at the electrodes.) With increase of the current flow through the nanoplatelet, the substrate temperature can be lowered down to room temperature while keeping the nanoplatelet in the metallic state. We have found that nanoplatelets with thicknesses below 1 μm are prone to buckling along the thickness direction at lower substrate temperatures. However, with thicker nanoplatelets—with a thickness close to 2 μm—we were able to achieve the bistable current-controlled behavior at a substrate temperature of Ts = 28 C using voltages of Vd = 12 V and Vd = 30 V for stabilization of mixed and metallic states, respectively. As is evident, the nanoplatelet bending driven by the formation of the heterophase domain patterns can be potentially employed to produce actuator action. To estimate the maximally achievable motion amplitude, we assume formation of a periodic structure of alternating triangular metallic and semiconducting domains along the whole length of the nanoplatelet between the contacts as sketched in Figure 1b. Since the circular arcs along the outer and inner edges of the maximally bent nanobeam fully consist of the semiconducting and metallic phases, respectively, the beam width w and radius of curvature R of the inner (metallic) edge of the beam are related as w=R ¼ δcR =cR
ð1Þ
where δcR/cR is the relative change of the lattice parameter in the longitudinal direction. To estimate possible maximum transverse displacement of the beam center point due to development of the triangular domain structure, we can use an approximate relation j δx ¼ R 1 cos 2 w LðδcR =cR Þ L2 ðδcR =cR Þ ð2Þ 1 cos ¼ ≈ ðδcR =cR Þ 2w 8w where δx is the transverse displacement, L is the length of the nanobeam, and j = L/R , 1 is the angular length of the arc made by the curved beam. For δcR/cR = 102, w = 1 μm, and L = 100 μm, this yields δx = 12.5 μm, which is comparable with the displacement achievable with the quasi-bimorph electrothermal actuators of similar dimensions.5 (More accurately, δcR/cR ∼ 1 102 for the R f M1 transition and ∼1.7 102 for the R f M2 transition based on the lattice plane spacing values along the long axis of the nanoplatelet R(001) ≈ 2.849 Å, M1(201) ≈ 2.877 Å (ref 13), and M2(020) ≈ 2.898 Å (ref 9) for R, M1, and M2 phases, respectively). As was shown by Cao et al.22 on single-crystalline VO2 nanobeams bent by an external force, the strain energy (and, consequently, stress) in the coexistence regime with triangular domains is relieved almost everywhere except near the vertices of the domains. In this state, nanoplatelets are expected to exhibit a behavior close to superplasticity with an external force leading to redistribution of domains rather than to increase of stress similar to nanobeam observations in ref 28. This means that upon transition from straight (metallic state) to curved (mixed-phase) state, little mechanical work can be done by the nanoplatelet. However, upon heating with increased current, a significant amount of work can be done at the cost of the strain energy accumulated in the curved nanoplatelet fully transformed back into the straightened metallic state. As follows from eq 1, the curvature of an unclamped bent nanoplatelet consisting of triangular insulating and metallic 3069
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters
LETTER
domains is k ¼ 1=R ¼ ðδcR =cR Þ=w
ð3Þ
This parameter determines the amount of work as well as force, which can be produced by a curved nanoplatelet. It is of interest to compare this value with the maximal curvature, which can be achieved in a narrow bimorph beam. As follows from Timoshenko’s theory of a narrow bimetal uniformly heated strip thermostat29 (see also eq 2 in ref 15 or eq 1 in ref 17), for a given strain ε (difference in relative expansions of the layers), the maximal curvature attainable by a bimorph strip of a total thickness w is kmax ¼ 3=2ðε=wÞ
ð4Þ
which is achieved at t1/t2 = (E2/E1)1/2, where t1 and t2 are thicknesses of the layers (t1 + t2 = w) with Young’s moduli E1 and E2, respectively. If one of the layers in the bimorph strip is a single-crystalline VO2 nanoplatelet with its cR axis parallel to the length, the meaning of ε is the spontaneous strain at the MIT along cR: ε = δcR/cR. Comparing eqs 3 and 4, we conclude that for a given total thickness, the theoretical maximal achievable curvature is larger by a factor of 3/2 for a bimorph structure than in the current-driven actuator considered in the present work. However, a single-material structure can be of advantage in situations, when fabrication of a bilayer structure is problematic or undesirable. We note that the metastable state in the system with heterophase domain patterns can be reached from the metallic state with flowing current either by lowering the substrate temperature or by lowering the current at constant Ts < Tc. The exact shape of the nanoplatelets in the metastable state is determined by the history of the domain structure formation and generally is stochastic as is governed by the random events of semiconducting domain nucleation. However, it can be engineered by introducing predetermined defects, where the nucleation barrier is reduced. The possibility of this is evidenced by the observation of the repeating semiconducting domain nucleation at the defect site in the nanoplatelet shown in Figure 7a. The possible ways to engineer the domain formation patterns may include removing material, e.g., using focused ion beam milling at predefined locations on the nanoplatelet to create domain nucleation sites, or deposition of a thin layer of an insulating material in order to change thermal and mechanical conditions along one of the nanoplatelet edges. As an alternative to substrate cooling from above Tc as was used in the above experiments, similar domain structures can be generated at temperatures below Tc by applying a sufficiently high voltage to the nanoplatelet.24,25 However, the domain patterns formed in such a way are more random with less possibility for reproducible control. Instead, application of the current can be used to drive the nanoplatelets metallic as an alternative to the substrate heating with a following decrease of the current to achieve the mixed state. The observed shape instability may occur along both short and long cross-sectional dimensions of nanoplatelets depending on the nanoplatelet shape and thermal/current cycling history. In thinner nanoplatelets, buckling with the heterophase domains crossing the thickness rather than the width of the nanoplatelet is readily observed. Figure 7b shows a higher magnification image of the same nanoplatelet as shown in Figure 4b at a lower temperature. The alternating bright and dark stripes are domains of the metallic and semiconducting phases crossing the thickness
of the nanoplatelet. The current flows at the bottom surface within this portion of the nanoplatelet, and the nanoplatelet is curved up. In the adjacent dark portion, the metallic domain and the current flow are along the upper surface. Accordingly, the nanoplatelet is curved down. Notably, the period of the structure of the alternating heterophase domains in the bright part is about 1.4 μm suggesting from simple geometrical considerations that the nanoplatelet thickness is about 0.7 μm (the angle between the domain wall and the longitudinal cR axis is ∼45). We note that it also suggests that the current-stabilized domain patterns can be formed in nanobeams of smaller dimensions than those of the nanoplatelets used in our experiments. In particular, similar domain structures may explain observations of ref 30 as an alternative to formation of metallic M2 phase induced by charge carrier injection in nanobeams clamped by contact pads on a substrate. The authors of ref 30 used Raman spectroscopy for phase identification. However, a mixture of R and M2 phases will be identified as the M2 phase since the Raman scattering of the R phase is significantly weaker than that of the M2 phase.12,30,31 Analysis and Numerical Modeling. To obtain more quantitative insight into the observed phenomena, we have performed a simple analysis of the stability factors of the Joule-heatingstabilized triangular domain patterns. In the steady state, heat generation and heat loss are in equilibrium. For a long nanoplatelet, far away from contacts, the main heat source in the metastable mixed state with triangular metal and semiconducting domains is narrow junctions between vertices of metallic domains with the rest of the nanoplatelet contributing a negligibly small amount of heat and with the main heat loss taking place due to heat conduction to the substrate through the air and to contacts (analogous to refs 32 and 33). We consider here that the nanoplatelet is oriented with its width parallel to the substrate. The number of the metal domain junctions n per nanoplatelet unit length is inversely proportional to the nanoplatelet width: n w1. Therefore, for an estimate, one can write for the heat loss per junction: qout w2(T Ts)/lair where T is the local temperature at the nanoplatelet surface facing the substrate, Ts is the substrate temperature, and lair is the nanoplateletsubstrate distance. In turn, the Joule heat generation per junction qin is: qin = I2Rj, where I is the current through the nanoplatelet and Rj is the resistance of the junction. Rj is determined by the geometry of the junction, and it can be “self-tuned” by shifts of the heterophase domain walls so that a steady state with qin = qout is reached, which provides a stabilization mechanism for the heterophase domain pattern. It follows then that the exact geometry of the junction is dependent on external parameters determining qout and on the properties of the electrical circuit determining I. The MIT is a first-order phase transition with thermal hysteresis resulting from supercooling and superheating of phases, which is controlled by phase nucleation and growth kinetics. As noted by Fisher,18 in the steady state, a semiconducting domain is stable if the temperature across it is nowhere higher than the temperature of the M f R transition in the hysteresis loop. In turn, temperature across a metallic domain should not drop below the R f M transition temperature. Both temperatures are not constant over the sample but depend on the local stress due to alteration of the critical temperature of the transition.11 Therefore, a full comprehensive treatment of the mixed state development and stabilization would require a self-consistent analysis of domain formation and growth in inhomogeneous fields of stress, temperature, and heat exchange, which is a 3070
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters
Figure 8. (a) Geometry of the FEA model (top) and temperature distribution along a structure of triangular metallic and semiconducting domains obtained with the FEA simulations (bottom). The color scale covers the temperature range from 63 to 73 C to highlight details of the temperature distribution in the nanoplatelet between contacts. The temperature in the contact region in the model is changing in a larger range from 44 to 256 C. The temperatures below 63 C and above 73 C are out of the color scale and correspond to heavily dark blue or heavily dark red colors, respectively. (b) A schematic showing orientation of {111}R-type walls between metallic and semiconducting domains in a nanoplatelet. (c) Same for {021}R-type walls; here the orientation of the tetragonal rutile unit cell is shown with the (021)R plane within it.
complex task. As an initial treatment, we performed numerical simulations of the temperature distribution in a static structure of triangular metallic and insulating domains. The model was constructed to mimic the nanoplatelet in the state imaged in Figure 4b, ignoring the small deformation of the nanoplatelet and Peltier effect at the domain boundaries18 with a slight overlap of metallic triangle domains at vertices. As illustrated in Figure 8a (top), the nanoplatelet is represented by a 3D rectangular bar consisting of right triangles of semiconducting and metallic phase and carrying an electric current flowing between two terminals at its ends. To model the domain overlap, a thin strip of the metallic phase was assumed to extend across the bases of the metallic phase triangles along the whole length of the heterophase portion of the model as shown in Figure 8a (top). Varying the width of the strip, we were able to alter the junction resistance. The main goals of the modeling were to estimate the temperature variations along the nanoplatelet, values of the Rj as well as contact resistance in the mixed state, and general trends in temperature distribution as a function of the heat loss distribution. The simulations were performed using the Joule heating module of the COMSOL v.4.1 multiphysics finite elements analysis (FEA) package. The portions of the nanoplatelet at the ends, which are covered by electrodes and serve as current terminals, were supposed to be in the semiconducting phase. The input parameters of the model and their sources are indicated in Table 1. The air gap between the substrate and the nanoplatelet lair was measured with an uncertainty (1 μm by consecutively focusing an optical microscope with a small (about 1 μm) depthof-field objective on the substrate and on the upper surface of the
LETTER
nanoplatelet. Electrical conductivity of the metallic (R) phase was determined by measuring resistance of three other nanoplatelets right before and after the MIT using a four-point configuration with two thin voltage probe electrodes made of the liquid alloy across the length. These measurements were also used to determine the contact resistance in the metallic state. The measurement yielded values of the conductivity of the R phase in the range σR = 4.6 105 to 7.3 105 S/m and contact resistances in the range Rc = 540 Ω per contact with Ohmic behavior. For data in Figure 5, we assumed Rc = 12 Ω (taking into account variations of the total device resistance from heating cycle to heating cycle with the lowest one being 66 Ω) and derived σR = 5.7 105 S/m as listed in Table 1. The conductivity of the M2 phase was determined by measuring the resistance of the sample in the fully M1 phase close to the transition temperature at a small driving voltage Vd = 0.8 V (the contribution of the contact resistance is below 10% of the total resistance and can be ignored for the semiconducting phase for the purpose of these calculations). The derived conductivity of the M1 phase was then reduced by a factor of 3 following the result of ref 11, where the M2 resistivity was found to be 3 times greater than that of M1. Further details of the modeling are provided in the Supporting Information. The modeling yielded a resistance of ∼21 Ω per junction between adjacent metallic domains with the width of the edge metal-phase strip of 300 nm. We note that the measured resistance of the nanoplatelet is ∼1120 Ω, which is about 900 Ω larger than the aggregate resistance of all junctions visible in optical images indicating that the resistance of the nanoplatelet is overwhelmingly determined by the resistance at contacts with Rc ≈ 450 Ω. Therefore, most of the Joule heat is also generated at the contacts to compensate for the larger heat loss due to a significantly larger thermal conduction to the substrate through the electrode material than through air. The simulated temperature distribution along the nanoplatelet surface is shown in Figure 8a (bottom). The color scale covers the temperature range from 63 to 73 C (presumed hysteresis width). At the half-length of the nanoplatelet, the temperature at the metal domain junctions is close to 73 C and is about 66 C at the opposite edge. The temperature noticeably drops toward the ends. The temperature is maximal at the metal domain junction with electrodes and reaches 256 C at the electrode hot spots according to the simulations, while it becomes less than 75 C a few micrometers away from the hot spots. It can be speculated, however, that such a high temperature is a result of simplification of the electrode geometry in the model and the maximal temperature in the experiment is lower. It is worth noting that the extrapolation of the linear, lower temperature portion of the dissipated power vs temperature plot in Figure 5 toward higher temperatures yields T = 84 C at P = 0 W, which can be assumed to be close to the true temperature at the contact hot spots. The modeling shows that the properly tuned thermal balance is a key factor for a successful realization of an actuator. In fact, in our devices, the temperature near the contacts (where it is lower) determines the stability of the mixed state. Ideally, the heat loss to the contacts should be reduced to a negligible value to maximize the achievable lateral displacement and stability of the deformed shape of the nanoplatelet. The modeling also reveals (data not shown) that with increased transfer of the heat loss through the air (e.g., at smaller values of lair or Ts), the temperature gradient across the nanoplatelet width increases so that the temperature at the semiconducting 3071
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters
LETTER
Table 1. Major Input Parameters Used in the FEA Model parameter
value (source)
parameter
value (source) 5.7 105 S/m
length (L)
128 μm
electric conductivity of the metal phase (σR)
(experiment, see text)
width (w)
8 μm (Figure 4)
electric conductivity of
6.4 S/m
the insulating phase, M2 (σM)
(experiment, see text)
thickness (h)
0.7 μm (see text)
thermal conductivity of
6 W/(m K)a
nanoplatelet
9 μm (see text)
thermal conductivity of
substrate air gap (lair) substrate temperature (Ts)
44 C
the insulating phase (kM) device current (I)
1.57 mA (Figure 5)
heat transfer coefficient for the
7340/4580/17000 W/(m2 K)
Added as a note: heat transfer coefficient
5 106 W/(m2 K) (a result of this model,
the metal phase (kR)
a
substrate-facing/upper/side
(numerical calculations,
surfaces (h)
see Supporting Information)
3.7 W/(m K)a
for the surfaces within electrodes (hc)
see Supporting Information)
Reference 34.
edge significantly drops. In this case, a structure of connected metallic domains can still remain at the opposite edge with reduced size of metallic triangular domain. This situation can be observed in movie 2 in the Supporting Information. Since the range of the stability of the mixed state is strongly dependent on the properties of the junctions between metallic domains, it is of importance to understand details of their behavior. Concerning this point, it is worth noting that in a few cases we observed in optical images that a gap of semiconducting phase formed between triangular metallic domains so that the semiconducting domain spread across the whole nanoplatelet width. However, the resistance of such a gap determined using conductivity of the semiconducting phase would be >30 kΩ per micrometer of its width, which is significantly larger than the resistance of the whole nanoplatelet of a few kiloohms in the mixed state as was observed in the experiments. This discrepancy can be explained by the presence of the conducting channel on the bottom side of the nanoplatelet facing the substrate due to domain wall tilts with respect to the nanoplatelet surface. Indeed, in the optical images, the angle between domain boundaries and the longitudinal direction of the nanoplatelet is between 45 and 49. Taking into account that the upper surface of the nanoplatelet is a {110}R plane, the apparent intersection between domain walls and the upper surface of the nanoplatelet corresponds to a Æ112æR direction of the rutile tetragonal lattice, which is at approximately 48 relative to the cR axis (as can be deduced from the R-phase lattice parameters). On the basis of the observations alone, any lattice plane containing one of these directions can be considered as a plane of a domain wall. Panels b and c of Figure 8 show two such possibilities with overlapping metallic domains bounded by walls along {111}R planes or along {021}R planes. Note that in the latter case, the semiconducting domain spans the whole width of the crystal at the upper surface, while metallic domains overlap at the lower surface. Nevertheless, the observed details of the domain structure call for additional studies to clarify the observations. Summary and Perspectives. As we demonstrated here, sufficiently strong electrical current and resulting Joule heating lead to formation of metastable metalsemiconductor domain patterns in suspended VO2 nanoplatelets where domains are selforganized in topologies, which provide paths for the current flow and are sustained by the inhomogeneous temperature and strain distributions. This coexistence state results in nanoplatelet bending
depending on the current strength. We have shown that this phenomenon can be used for electrically controlled motion generation. Achievable displacements are comparable to those characteristic for existing electrothermal actuator designs, while operational temperatures are dramatically smaller. The actuation action can be realized over a wide temperature range, including substrates at room temperature. On the basis of our results, two major prerequisites should be fulfilled for realization of an actuator with use of the proposed concept. First, the domain structure should be controlled and stabilized by introducing domain nucleation sites and/or by deposition of thermal and mechanical control layers. Second, such an actuator should be designed with possibly reduced heat loss through the nanoplatelet ends to keep the thermal gradients along the nanoplatelets length close to zero. From a broader perspective, the observed current-sustained heterophase domain structures should be taken into account in the interpretation of experimental observations with smaller nanobeams, where these structures are difficult or impossible to access optically.
’ ASSOCIATED CONTENT
bS
Supporting Information. Methods used in numerical simulations of the temperature distribution, additional results of FEA simulations as well as movies showing heterophase domain dynamics versus varying temperature at a constant circuit driving voltage, versus varying driving voltage at a constant temperature, and repeatable current-controlled change of a VO2 nanoplatelet shape. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT Authors thank Nikolay Lavrik for fruitful discussions. Research at ORNL’s Center for Nanophase Materials Sciences was sponsored by the Division of Scientific User Facilities, Office of Basic Energy Sciences, U.S. DOE. The research at SIUC was supported through NSF ECCS-0925837 and SISGR-DOE ERKCM67. J.D.B. and J.Z.T. were supported by the Materials 3072
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
Nano Letters Sciences and Engineering Division, Office of Basic Energy Sciences, U.S. DOE. Use of the APS beamline 34-ID-E was supported by the Scientific User Facilities Division of BES, U.S. DOE.
LETTER
(33) Jungen, A.; Pfenninger, M.; Tonteling, M.; Stampfer, C.; Hierold, C. J. Micromech. Microeng. 2006, 16, 1633. (34) Oh, D.-W.; Ko, C.; Ramanathan, S.; Cahill, D. G. Appl. Phys. Lett. 2010, 96, 151906.
’ REFERENCES (1) Hubbard, N. B.; Culpepper, M. L.; Howell, L. L. Appl. Mech. Rev. 2006, 59, 324. (2) Bell, D. J.; Lu, T. J.; Fleck, N. A.; Spearing, S. M. J. Micromech. Microeng. 2005, 15, S153. (3) Aliev, A. E.; Oh, J.; Kozlov, M. E.; Kuznetsov, A. A.; Fang, S.; Fonseca, A. F.; Ovalle, R.; Lima, M. D.; Haque, M. H.; Gartstein, Y. N.; Zhang, M.; Zakhidov, A. A.; Baughman, R. H. Science 2009, 323, 1575. (4) Madden, J. D. Science 2007, 318, 1094. (5) Sahu, B.; Taylor, C. R.; Leang, K. K. J. Manuf. Sci. Eng. 2010, 132, 030917. (6) Morin, F. J. Phys. Rev. Lett. 1959, 3, 34. (7) Gu, Q.; Falk, A.; Wu, J.; Ouyang, L.; Park, H. Nano Lett. 2007, 7, 363. (8) Rakotoniaina, J. C.; Mokrani-Tamellin, R.; Gavarri, J. R.; Vacquier, G.; Casalot, A.; Calvarin, G. J. Solid State Chem. 1993, 103, 81. (9) Marezio, M.; McWhan, D. B.; Remeika, J. P.; Dernier, P. D. Phys. Rev. B 1972, 5, 2541. (10) Pouget, J. P.; Launois, H.; D’Haenens, J. P.; Merenda, P.; Rice, T. M. Phys. Rev. Lett. 1975, 35, 873. (11) Cao, J.; Gu, Y.; Fan, W.; Chen, L. Q.; Ogletree, D. F.; Chen, K.; Tamura, N.; Kunz, M.; Barrett, C.; Seidel, J.; Wu, J. Nano Lett. 2010, 10, 2667. (12) Tselev, A.; Luk’yanchuk, I. A.; Ivanov, I. N.; Budai, J. D.; Tischler, J. Z.; Strelcov, E.; Kolmakov, A.; Kalinin, S. V. Nano Lett. 2010, 10, 4409. (13) Kucharczyk, D.; Niklewski, T. J. Appl. Crystallogr. 1979, 12, 370. (14) Wei, J.; Wang, Z.; Chen, W.; Cobden, D. H. Nat. Nanotechnol. 2009, 4, 420. (15) Rua, A.; Fernandez, F. E.; Sepulveda, N. J. Appl. Phys. 2010, 107, 074506. (16) Viswanath, B.; Ko, C.; Ramanathan, S. Scr. Mater. 2011, 64, 490. (17) Cao, J.; Fan, W.; Zhou, Q.; Sheu, E.; Liu, A.; Barrett, C.; Wu, J. J. Appl. Phys. 2010, 108, 083538. (18) Fisher, B. J. Phys. C: Solid State Phys. 1976, 9, 1201. (19) Guiton, B. S.; Gu, Q.; Prieto, A. L.; Gudiksen, M. S.; Park, H. J. Am. Chem. Soc. 2005, 127, 498. (20) Wu, J.; Gu, Q.; Guiton, B. S.; de Leon, N. P.; Ouyang, L.; Park, H. Nano Lett. 2006, 6, 2313. (21) Tselev, A.; Strelcov, E.; Luk’yanchuk, I. A.; Budai, J. D.; Tischler, J. Z.; Ivanov, I. N.; Jones, K.; Proksch, R.; Kalinin, S. V.; Kolmakov, A. Nano Lett. 2010, 10, 2003. (22) Cao, J.; Ertekin, E.; Srinivasan, V.; Fan, W.; Huang, S.; Zheng, H.; Yim, J. W. L.; Khanal, D. R.; Ogletree, D. F.; Grossman, J. C.; Wu, J. Nat. Nanotechnol. 2009, 4, 732. (23) Strelcov, E.; Davydov, A. V.; Lanke, U.; Watts, C.; Kolmakov, A. ACS Nano 2011, 5, 3373. (24) Strelcov, E.; Lilach, Y.; Kolmakov, A. Nano Lett. 2009, 9, 2322. (25) Fisher, B. J. Phys. C: Solid State Phys. 1975, 8, 2072. (26) Budai, J. D.; Liu, W.; Tischler, J. Z.; Pan, Z. W.; Norton, D. P.; Larson, B. C.; Yang, W.; Ice, G. E. Thin Solid Films 2008, 516, 8013. (27) Morley, N. B.; Burris, J.; Cadwallader, L. C.; Nornberg, M. D. Rev. Sci. Instrum. 2008, 79, 056107. (28) Fan, W.; Huang, S.; Cao, J.; Ertekin, E.; Barrett, C.; Khanal, D. R.; Grossman, J. C.; Wu, J. Phys. Rev. B 2009, 80, 241105. (29) Timoshenko, S. J. Opt. Soc. Am. 1925, 11, 233. (30) Zhang, S.; Chou, J. Y.; Lauhon, L. J. Nano Lett. 2009, 9, 4527. (31) Marini, C.; Arcangeletti, E.; Di Castro, D.; Baldassare, L.; Perucchi, A.; Lupi, S.; Malavasi, L.; Boeri, L.; Pomjakushina, E.; Conder, K.; Postorino, P. Phys. Rev. B 2008, 77, 235111. (32) Venditti, R.; Lee, J. S. H.; Sun, Y.; Li, D. J. Micromech. Microeng. 2006, 16, 2067. 3073
dx.doi.org/10.1021/nl200493k |Nano Lett. 2011, 11, 3065–3073
