Extraordinary Dynamic Mechanical Response of Vanadium Dioxide

Letter pubs.acs.org/NanoLett

Extraordinary Dynamic Mechanical Response of Vanadium Dioxide Nanowires around the Insulator to Metal Phase Transition Aaron Holsteen,† In Soo Kim,† and Lincoln J. Lauhon* Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *

ABSTRACT: Nanomechanical resonators provide a compelling platform to investigate and exploit phase transitions coupled to mechanical degrees of freedom because resonator frequencies and quality factors are exquisitely sensitive to changes in state, particularly for discontinuous changes accompanying a first-order phase transition. Correlated scanning fiber-optic interferometry and dual-beam Raman spectroscopy were used to investigate mechanical fluctuations of vanadium dioxide (VO2) nanowires across the first order insulator to metal transition. Unusually large and controllable changes in resonator frequency were observed due to the influences of domain wall motion and anomalous phonon softening on the effective modulus. In addition, extraordinary static and dynamic displacements were generated by local strain gradients, suggesting new classes of sensors and nanoelectromechanical devices with programmable discrete outputs as a function of continuous inputs. KEYWORDS: VO2, nanowire, NEMS, sensing, fiber-optic interferometry, phase transition

T

lattice, as microscopic changes in lattice structure should be manifest in the resonance frequency, amplitude, and quality factor. For example, the bending of c-axis-oriented VO2 nanowires should be particularly sensitive to the change in modulus from the M1 to the R phase. In sensors, one might exploit the modulus difference to modify the mechanical response through (1) introduction of defects,27,28 (2) creation of mixed domain states,28 and (3) controlled propagation of domain walls. As we show here, understanding these aspects of the phase transition could lead to new classes of tunable sensors with a discrete and programmable frequency response with temperature. Singly clamped nanomechanical resonators (Figure 1) are fabricated from individual single crystal VO2 nanowires oriented along the [001]R direction with (1̅10)R and (1̅1̅0)R side facets.29 The heights and widths of these rectangular nanowires are smaller than the characteristic domain size, and interfacial strain present in previous studies30,31 is absent here. Vertical nanowire displacement was monitored via a polarization-dependent scanning fiber-coupled interferometer based on the design of Nichol et al.32 (Figure 1a), and a spectrum analyzer was used to record the thermally induced vertical motion (perpendicular to the growth axes [100]M1 and [001]R) across a band of frequencies centered on the fundamental mode (Figure 1b). Because the nanowire displacement was measured perpendicular to the growth axis, the values of Young’s moduli are dominated by displacements normal to the (100)M1 and

he downscaling of nanomechanical resonators while controlling quality factors1,2 has created new opportunities for sensing3−6 and pushed the limits of force and mass detection into the quantum regime.7,8 A thorough understanding of damping mechanisms including viscous ambient damping,9 clamping losses,10 thermoelastic damping,11 and material losses12 have been essential to improved performance. While bottom up nanostructures such as carbon nanotubes have useful characteristics such as increased resonant frequencies and quality factors,3,13−15 functional nanomaterials that undergo phase transitions in which mechanical and electronic degrees of freedom are coupled16,17 could lead to new sensing modalities.6,18,19 Here we investigate the influence of the insulator to metal transition on mechanical fluctuations in vanadium dioxide (VO2) nanowire resonators. We observe unusually large and controllable changes in resonator frequency approaching and moving across the phase transition due to the combined influences of domain wall motion and phonon softening, pointing the way to new classes of sensors and nanoelectromechanical devices. VO2 undergoes a first order phase transformation from a monoclinic (M1) insulator to a tetragonal (R) metal upon heating above 68 °C (341 K)20 that has been characterized by optical microscopy,21 Raman spectroscopy,22 and X-ray diffraction.23−25 Across the phase transition, the c-axis (a-axis) contracts (expands) by ∼1% (∼0.6%) and develops a pronounced elastic anisotropy with the largest increase in modulus along the rutile c-axis.26 In the vicinity of the transition, a pronounced phonon softening is also observed.26 A nanowire nanomechanical resonator provides a compelling platform to investigate static and dynamic properties of the © 2014 American Chemical Society

Received: December 17, 2013 Revised: February 24, 2014 Published: March 5, 2014 1898

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Figure 1. Interferometric detection of nanowire motion. (a) Schematic of fiber-optic interferometer. (b) Normalized displacement amplitude versus frequency at temperatures of 303, 313, 323, and 333 K, bottom to top, for the fundamental bending mode. (c,d) End-view and topview, respectively, of nanowire in a scanning electron microscope.

(001)R planes. The nanowire substrate was mounted on a ceramic heater to investigate the influence of the thermally driven insulator to metal transition on the nanowire resonant frequency, displacement amplitude, and quality factor, each of which were extracted from the spectra. Measurements were conducted in vacuum (∼10−5 Torr) to minimize extrinsic damping (Supporting Information Figure S1). A VO2 nanowire (#9) was heated and cooled through the transition temperature while the resonant frequency and quality factor were measured (Figure 2). Raman spectroscopy (Figure 2b) and video imaging (Supporting Information Video 1) were performed concurrently, but separately from the interferometry, to confirm that the nanowire transforms from the room temperature M1 phase (region I) to the high-temperature R phase (region III). The Young’s moduli of the M1 and R phases were initially estimated as 146 ± 8 and 202 ± 10 GPa, respectively, by applying the Euler-Bernoulli equation for a rectangular beam33 f=

β 2t 4πl 2

E 3ρ

Figure 2. Influence of insulator to metal transition on nanowire resonance. (a) Schematics of nanowire resonator in low-temperature M1 phase (I), high-temperature R phase (III), and intermediate temperature mixed domain state (II). (b) Raman spectra that are the basis of the phase assignments in (a). (c) Experimental resonant frequency of fundamental bending mode and dissipation as a function of substrate temperature. Filled (open) circles indicate increasing (decreasing) temperature. Points at which simulations were conducted to extract elastic moduli and domain structures are indicated with open triangles.

range of tunable resonant frequencies controlled by domain structure. Between 62 and 80 °C in Figure 2c (Region II), the nanowire exhibits discrete changes in resonant frequency upon heating (cooling) due to the advance (retreat) of the rutile phase from the substrate toward the end of the nanowire, as illustrated schematically in Figure 2a. In contrast, as-grown singly clamped nanowires transform spontaneously and completely from M1 to R at ∼92 °C substrate temperature in air (Supporting Information Video 2). The M1 and R phases coexist in the nominally strain-free beam because the nanowire in Figure 2 was laser annealed in vacuum (250 μW, λ = 1547 nm, spot size ∼2.1 μm) ∼34 μm from the base, creating local defects that pin the advancing rutile domain28 and stabilize a mixed domain state between 62 and 80 °C (Figure 2, region II). Using the domain structure observed by optical microscopy to identify the discontinuous manner in which the domain wall advances (Supporting Information Figure S2), the continuous changes in resonant frequency in regions I and III, and the discrete changes in region II, were reproduced by the COMSOL model (Figure 2c, open triangles). While the pinning sites were not controlled in this experiment, intentional engineering of domain wall-pinning defects coupled with doping to modify the phase transition temperature35,36 could be used to create highly tunable temperature sensitive nanomechanical resonators. In this context, it is also important to identify sources of dissipation in both the single phase and mixed domain states (Figure 2c). Dissipation, which influences a resonator’s spectral purity and sensitivity to an externally applied forces,2 arises from a

(1)

where t = 586 nm, l = 40.6 μm, the density ρ = 4670 kg/m , the factor β = 1.8751 for singly clamped beams, and f is the resonant frequency. Using COMSOL finite element analysis (FEA) with a more accurate cross-section determined from scanning electron microscopy (Figure 1c) and a linear elastic model, the Young’s moduli were determined more accurately as 151 ± 2 and 218 ± 3 GPa for the M1 and R phases, respectively. These values are consistent with a prior report for the M130 phase in a thin-film coated cantilever, but not the R34 phase in a nanowire cantilever. However, our measurement avoids artifacts introduced by interfacial strain, which changes across the transition, as well as grain boundaries. In addition, the extracted moduli are dominated by displacements along the [001]R (c-axis) oriented nanowire, which enables us to clearly resolve a large change in modulus from M1 to R. The effect, which is diminished or absent in polycrystalline samples, arises from the anisotropic speed of sound in single crystalline tetragonal VO2.26 This suggests that VO2 nanomechanical resonators could be engineered to have an extraordinarily large 3

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combination of (i) viscous ambient damping,9 (ii) clamping losses,10 (iii) thermoelastic damping,11 (iv) material losses due to the relaxation of defects,12 and (v) electronic dissipation such as ohmic losses due to induced charge motion in a capacitively coupled environment.37 In addition, domain wall motion in a material undergoing a first order structural phase transition also leads to dissipation.38,39 To model the dissipation in the terminal phases (regions I and III), thermal profiles were simulated (see Supporting Information) in COMSOL and used as inputs for a mechanical model incorporating (1) clamping losses and thermoelastic damping using known bulk materials constants and the elastic moduli determined here, and (2) an empirically determined structural loss factor arising from internal degrees of freedom, likely associated with defects and/or mobile charge (Figure 3). The

is due in part to anomalous phonon softening of the M1 phase as identified in the discussion of Figure 4.

Figure 4. Influence of IMT driven by local laser heating on nanowire resonator. (a) Schematics of nanowire resonator in low temperature M1 phase (I), mixed M1 and M2 domains (II), and mixed M1 and R domains (III). Small amounts of the M2 phase exist between the M1 and R phases in region III, but not in region III′. (b) Raman spectra that are the basis of the phase assignments in (a). (c) Experimental resonant frequency of fundamental bending mode and dissipation as a function of incident laser power at 1.55 μm wavelength. Points at which simulations were conducted to extract elastic moduli and domain structures are indicated with open triangles. Filled (open) symbols indicate increasing (decreasing) power.

Figure 3. Modeling of nanowire resonator quality factor. The experimental dependence of the quality factor Q on temperature and domain structure is shown by the black line. Regions I, II, and III are as indicated in Figure 2. Open symbols show finite element simulations of Q including clamping losses (diamonds), clamping losses and thermoelastic damping (squares), and clamping, thermoelastic, and structural losses (triangles).

Dramatically, the introduction of a domain wall (region II) results in significant decrease in Q (Figures 2c and 3). The dissipation associated with domain wall motion during a firstorder phase transition has been measured in VO239 and described by a phenomenological model38 in which an equation of motion is solved considering both an oscillatory driving force and resistive drag forces; acoustic wave emission at the phase boundary produces loss. In VO2, oxygen vacancies strongly influence this dissipation,40 presumably through interactions between the domain walls and the vacancy configurations. It is likely that the local vacuum laser annealing of our nanowires created spatially varying oxygen vacancy configurations that are responsible for the observed domain wall pinning. Therefore, the dissipation has a complex dependence on the position of the domain wall. Furthermore, anomalous phonon softening also contributes substantially to the dissipation in the mixed phase region (see below) with its own temperature dependence. Therefore, quantitative modeling and extraction of the domain wall dissipation in region II was determined to be infeasible with this type of sample. The phase transformation exhibits strikingly distinct characteristics when the same nanowire is driven through the insulator to metal transition by localized laser heating below the damage threshold. With increasing laser power, the M1 phase

temperature dependent quality factor QTot in regions I and III is described by −1 −1 −1 −1 QTot (T ) = Q PML (T ) + QTE (T ) + Q SL (T )

(2)

Perfectly matched layer conditions were used to calculate the dissipation due to clamping Q−1 PML(T), and distinct structural loss factors were established empirically for the M1 and R −1 phases: Q−1 SL,M1(T) and QSL,R(T), respectively. As seen in Figure 3, clamping losses and thermoelastic damping alone do not account for the quality factor of the single phase regions; additional internal dissipation is present and is accounted for with the structural loss factor. Using the Q−1 SL,M1(T) for the nanowire (#9) analyzed in Figures 2 and 3, the temperaturedependent quality factors for four other nanowires of different aspect ratios were accurately predicted (Supporting Information Table 1), indicating that the structural loss arises from bulk dissipation and is not dominated by the nanowire surface. Such losses might be reduced by modifying the synthesis conditions to, for example, achieve better stoichiometry. In regions I and III, the monotonic decrease in Qtot with temperature is reproduced by the simulation, which is a result of increasing thermoelastic damping. The higher rate of decrease in region I 1900

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As in the substrate heating experiment, the presence of a domain wall (Figure 4, regions II, III, III′) increases the rate of mechanical dissipation relative to the single phase region (Figure 4, region I). However, with laser heating we observe an even greater increase in dissipation prior to the nucleation of the M2 phase due to the anomalous increase in lattice anharmonicity near the phase transition.26 The increasing anharmonicity causes little change in lattice constant but a strong decrease in the speed of sound along the along [001]R direction,26 which coincides with long axis of the nanowire in our geometry. This axis sustains the largest displacements in the fundamental bending mode, facilitating the observation of anomalous phonon softening and the associated enhanced dissipation through monitoring of this mode. We note that this additional source of dissipation can account for the deviation between experiments and simulations in region I of Figure 4c (though the effect is diminished in the substrate heating experiments as a result of more gradual strain gradients). We therefore recognize that phonon softening also contributes, together with domain wall motion, to dissipation in the mixed phase region II. While the analysis above provides a quantitative description of the mechanical behaviors of these novel nanomechanical resonators, two features arose in the static and dynamic measurements that motivate further investigation of the potential to engineer unusual mechanical properties. First, video monitoring of the nanowire position under local laser illumination reveals large axial and transverse displacements of the nanowire beyond the point of illumination that are associated with the laser induced phase transition (Supporting Information Figure S7). This behavior appears to be analogous to the superelastic response observed in VO2 nanowires undergoing flexural bending.34 Intriguingly, spontaneous increases in measured amplitude of several orders of magnitude were occasionally observed in the two-phase region when the fiber-optic was used both for heating and displacement detection. While our experimental apparatus did not enable video monitoring simultaneous with the high-frequency nanomechanical displacement detection, we speculate that this behavior originates from oscillations of the phase boundary. The stability of the local M2 phase induced by optical excitation is highly sensitive to minute axial strains associated with both the thermomechanical flexural modes and optical trapping forces. If the domain wall is angled with respect to the NW axis,17 then slight kinking of the NW will occur due to the changing lattice parameters associated with the phase transformation,23 which could in turn influence the amplitude of fluctuations. This unusual mechanical behavior could be engineered to enhance the sensitivity of a VO2 nanomechanical resonator to an external perturbation, suggesting an important new direction for nanomechanical resonators beyond the pursuit of ultrahigh quality factors.

exhibits substantial phonon softening, manifest in the large decrease in f1 and increase in dissipation Q−1 (Figure 4, region I′) immediately prior to nucleation of an M2 domain directly beneath the laser focal point (Figure 4, region II). The observed softening and dissipation are due in part to anomalously large lattice anharmonicities approaching the phase transition26 as discussed in the next paragraph, but simulations indicate that tensile strain generated by the temperature gradient in the excitation region also plays a role (Supporting Information Figure S3). The local tensile strain also stabilizes an M2 domain in region II, providing access to the mechanical characteristics of this metastable phase. Consistent with this claim, as the point of excitation approaches the substrate, the local temperature gradient and therefore strain gradient becomes steeper, which lowers the barrier for the nucleation of M2.41 The tensile strain is also associated with an increased temperature of transition to the R phase,41 and the increase in the transition temperature (∼3 K) from the simulated temperature profile is consistent with the presence of tensile strain (though the simulated temperatures could not be validated by direct probing of the nanowire temperature). However, negligible propagation of the M2 domain (in either direction) was observed upon increasing power because the position of the steepest temperature gradient does not shift toward the substrate and there is no large temperature gradient induced toward the tip past the excitation point (Supporting Information Figure S4). Thus, with increasing laser power, the M2 region transforms completely to R (Figure 4, region III), leading to a mixed M1 + R domain state as observed with substrate heating of the defective nanowire; the stabilization of this configuration is dominated by local increase in temperature. The transformation of the tip of the nanowire to the R phase occurred at a laser power that was sensitive to the position of the laser focus as well as the nanowire dimensions. Thus, while it is clear that the local heating geometry plays some role in delaying the transformation of the tip to the R phase, the lack of a direct experimental measurement of the tip temperature precluded a quantitative analysis. Upon cooling, the rutile portion transforms directly to the M1 phase (Figure 4, region III′). In this case, absence of the metastable M2 phase can be explained by a decrease in local strain. Interestingly, the M2 phase transforms back to M1 directly if no rutile domain is nucleated (Supporting Information Figure S5). The Young’s modulus of the M2 phase was estimated using temperature-dependent finite element analysis with input from laser power-dependent domain structure measured with dual-beam Raman spectroscopy (Supporting Information Figure S6). Our estimate of 106 ± 4 GPa is in agreement with a measurement of 102 ± 3 GPa for Cr-doped polycrystalline VO2 coated Si cantilevers30 but differs from the value of 156 ± 10 GPa derived from stress− strain measurements on doubly clamped nanowires in a specialized transmission electron microscopy stage.42 However, the same work reports a modulus of 128 ± 10 GPa for the M1 phase, which is significantly less than expected. Furthermore, the authors note that the presence of residual M1 phase, which was not assumed in the extraction of the M2 modulus, could contribute significantly to the uncertainties. Uncertainties in domain size influence the present analysis as well but appear to be insufficient to account for the differences in the estimated M2 modulus. Further work is needed to reconcile the differences between the static and dynamic measurements.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

S Supporting Information *

Supplementary figures and videos illustrating domain structure evolution, additional simulated temperature profiles, and details of the simulation. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. 1901

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Author Contributions

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†

A.H. and I.S.K. contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Camille and Henry Dreyfus Foundation (A.H.). I.S.K. acknowledges the support from a Northwestern University Ryan Fellowship and partial support of DOE-BES through DE-FG02-07ER46401.

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