The phase transition in VO2 probed using x-ray, visible and

infrared radiations

Suhas Kumar1, John Paul Strachan1, A. L. David Kilcoyne2, Tolek Tyliszczak2, Matthew D.

Pickett1, Charles Santori1, Gary Gibson1 and R. Stanley Williams1

1 Hewlett Packard Laboratories, 1501 Page Mill Road, Palo Alto, California, 94304, USA,2 Advanced Light source, Lawrence Berkeley National Laboratory, Berkeley, California, 94720,

USA

Supplemental Material

1. Reflectance of visible light

Figure S1: (a) Temperature dependent normalized reflectance (rN) from a thin film of VO2 for a range of visible wavelengths. (b) Wavelength-filtered and white light images of a metallic region of VO2 with a background of insulating region of VO2. Metallic region was created by driving a current between two electrodes deposited on the film, to cause a sufficient increase in joule-heating-induced temperature along the current path. Two filtered images were produced using filters that have a fairly narrow spectral response centered at the noted wavelengths [Sensors 13, 1523 (2013)]. This observation emphasizes that optical properties like absorption and reflection become very important in the choice of the probing wavelength. A choice of λ=470 nm (likely an isobestic point, as shown in (a) with a vertical dashed line) to study the phase transition will lead to the conclusion that there is no phase transition at all, as indicated in (b).

The significance of the observation presented in Figure S1 is to emphasize that a complete understanding of the spectral features accessed by the probing radiation is important. In experiments involving infrared or visible light, there have sometimes been arbitrary choice of wavelengths or range of wavelengths [Applied Physics Letters 88, 081902 (2006), Journal of Applied Physics 112, 103532 (2012)] while more complete studies involving spectroscopic and nanoscale imaging have revealed a detailed understanding of the phase transition phenomena

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[Science, 318, 1750 (2007)]. We emphasize that such an understanding is more important when using optical techniques as against x-ray techniques because most x-ray studies involve some capability of spectroscopy that can provide information on an intelligent choice of the probing wavelength (for example, the use of closely spaced π* and d||* energies used in this study). Moreover optical properties of the constituent phases and the intermediate phases become important because they also contribute to the optical response of the material.

2. Film growth and characterization

The films were grown using a metallic precursor oxidation process, as noted in the main text. Silicon chips with a 20 nm nitride layer on top were processed to etch away the silicon substrate to expose 20 nm of silicon nitride through a 50 µm x 50 µm window. 20 nm vanadium was deposited on top of these windows. This was then oxidized in a tube furnace at 400 C for 1.5 hours at a pressure of 200 mTorr with an oxygen flow of 3-4 sccm. The resulting film was polycrystalline and was characterized by multiple techniques including atomic force microscopy, x-ray photoemission spectroscopy, energy dispersive x-ray spectroscopy and Raman spectroscopy. These told us that the stoichiometry is about 1:2.1 (V:O) and also that the as-grown film had features of the monoclinic crystal structure (Figure S2).

Figure S2: Various techniques used to characterize the as-grown films. (a) Atomic force microscopy, (b) X-ray photoemission spectroscopy, (c) Energy dispersive x-ray spectroscopy and (d) Raman spectroscopy. These clearly showed that the composition of the films were close to 1:2 (V:O) while the as-grown films showed most of the Raman-active modes of monoclinic VO2.

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3. Sources of radiation

For the infrared and visible light experiments, we used a Cary ultraviolet, visible light and near infrared spectrophotometer in transmission mode with the same sample of VO2. We monitored resistance of the sample using low bias (<0.1 V) right before and right after the optical measurement was performed at every temperature. Thus, there was no joule heating effect in the optical measurements. The two resistance readings were averaged and also found to be identical, implying that the optical measurement did not create an irreversible change in the material. A similar resistance measuring scheme was used for x-ray measurements. The resistance-temperature curves obtained from different experiments were found to be identical to one another, indicating the stability of the film and also of the stage heating setup. Thus, the resistance measurement served as a calibration in case of possible errors in the measured temperatures. X-rays were produced from the synchrotron at the Advanced Light Source at Lawrence Berkeley National Laboratory in Berkeley, CA on end-stations 11.0.2 and 5.3.2.2, designed for soft x-ray spectromicroscopy with a spatial resolution of ~25 nm and spectral resolution of <70 meV.

4. Mie scattering calculation

Mie scattering calculation using http://omlc.ogi.edu/calc/mie_calc.html

1) First, we attempt to validate the simulator using gold nanoparticles as test case

Gold, 80nm, in water

Table SI: Refractive index data from http://refractiveindex.info (The minus signs on k are required by the Mie calculator as a convention)

wavelength (µm)

n k extinction cross section (µm2)

extinction efficiency

0.500 0.86 -1.85 0.0173 3.430.550 0.42 -2.35 0.0336 6.680.600 0.24 -2.92 0.0174 3.450.650 0.18 -3.42 0.0062 1.24

The results seem close enough to those in Fig. 1c of Jain et al., J. Phys. Chem. B 110, 7238, (2006).

2) Vanadium Dioxide

We crudely estimate the refractive index from Figs. 6-9 of Verleur et al, Phys. Rev. 172, 788 (1968) (using 1000 A film curves). We take the complex square root of the dielectric constant to get the complex refractive index (n and k).

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Table SII: Below transition temperature (300K)energy (eV)

εr εi n k

1.0 10 -3 3.20 -0.471.5 8 -3 2.88 -0.522.0 9 -2 3.02 -0.33 2.5 10 -4 3.22 -0.62

Table SIII: Above transition temperature (355K)energy (eV)

εr εi n k

1.0 -2 -7.5

1.70 -2.21

1.5 2 -3 1.67 -0.902.0 5 -

2.5 2.30 -0.54

2.5 7 -4.5

2.77 -0.81

Table SIV: Let's consider 100nm particles of metallic VO2 surrounded by insulating VO2. (We use 100nm based on a rough estimate from the x-ray images and from Kumar et. al., Adv. Mater. 26, 7505 (2014)). The Mie scattering calculator does not allow the surrounding medium to be absorptive. As a best approximation, we will use the real part of the medium refractive index given above.Energy (eV)

wavelength (µm)

n (medium)

n k extinction cross section (µm2)

extinction efficiency

1.0 1.24 3.20 1.70

-2.21 0.0104 1.32

1.5 0.83 2.88 1.67

-0.90 0.0059 0.75

2.0 0.62 3.02 2.30

-0.54 0.0051 0.65

2.5 0.50 3.22 2.77

-0.81 0.0081 1.03

Table SV: It is also interesting to see what happens in air:Energy (eV)

wavelength (µm)

n (medium)

n k extinction cross section (µm2)

extinction efficiency

1.0 1.24 1 1.7 -2.21 0.0037 0.47

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0 1.5 0.83 1 1.6

7 -0.90 0.0050 0.63

2.0 0.62 1 2.30

-0.54 0.0036 0.46

2.5 0.50 1 2.77

-0.81 0.0078 0.99

Table SVI: We try using constants at 1550nm from Sweatlock et al., Opt. Express 20, 8700 (2012).wavelength (µm)

n (medium) n k extinction cross section (µm2)

extinction efficiency

1.55 3.15 3.12 -4.88 0.023 2.921.55 1 3.12 -4.88 0.00085 0.11

Table SVII: We try using constants at 1550nm from Wang et al., Adv. Optical Mater. 2, 30 (2014).wavelength (µm)

n (medium) n k extinction cross section (µm2)

extinction efficiency

1.55 3.25 2.55 -2.44 0.0109 1.391.55 1 2.55 -2.44 0.0017 0.22

So far, the extinction efficiency (which is equal to the scattering cross section divided by the sphere's physical cross section) is in the range of ~0.5 to 3, with the upper value only possible using Sweatlock's numbers, which don't agree with the other papers. Even if we take 3 as an upper limit, it is unlikely that this can explain how a sparse array of particles in a thin sheet could cause such a large change in transmission. Also, we expect to see a wavelength dependence if plasmonic effects are important.

For Rayleigh scattering, the scattering cross section scales as (diameter)6, so the scattering cross section becomes much smaller than the physical cross section for very small particles. If the particles are far sub-wavelength, then even if we completely fill the volume with particles, the scattering is weak. Since the size of the particles in this case is about a tenth (or lesser) than the probing wavelength, we expect Rayleigh scattering to be negligible too. We do acknowledge that Rayleigh scattering might play a role in visible light transition characteristics, although fairly weak, as evidenced by the calculation above.

5. X-ray maps of the transition

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Figure S3: Greyscale maps of the data shown in Figures 2c-2d.

Figure S4 displays the maps in Figure S3 on a common color scale. In order to quantify the observation mentioned in the main text that the length scales involved in the structural transition are larger, we plot the 2-dimensional Fourier transform of the maps obtained in the intermediate temperatures (Figures S3i-S3l) with the smallest step being 10 nm. It can be seen that the Fourier transforms corresponding to the electronic transition occupy larger frequencies (i.e.: have a larger spread away from the center) while those corresponding to the structural transition mostly occupy lower frequencies (i.e.: have a smaller spread away from the center). This means that the length scales involved are larger in the structural transition compared to those in the electronic transition.

Figure S4 also displays the spectral positions used to obtain the maps along with the extreme spectra corresponding to the monoclinic insulator and the rutile metal (panels m and n). This clarifies the reason for the ‘bright’ and ‘dark’ regions in the two sets of maps obtained at two different energies to correspond to differences in the electronic state and the lattice structure, as indicated [Advanced Materials, 26, 7505 (2014)].

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Figure S4: (a)-(h) Colored x-ray maps of those shown in Figures S3. (i)-(l) 2-dimensional Fourier transform maps of the x-ray maps in (b), (f), (c) and (g), respectively. These quantitatively prove that the length scales are larger in the structural transition. (m)-(n) depicting the physical information in the maps made at different energies using O K-edge spectra.

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Figure S5: Horizontal and vertical line cuts of the x-ray map in Figure 2d at 320.8 K. The signal to noise ratio, clearly seen over the dark and bright patches, is about 3. Hence there will be a significant error if we use the maps to compute the phase fractions. However, the qualitative nature of the coexistence of multiple phases during the transitions and the relative changes in the length scales associated with the electronic and structural transitions are confirmed with similar direct measurements [Advanced Materials, 26, 7505 (2014)].

6. Peak fitting

Peak fitting was done using Peakfit software. Each of the peaks were Lorentzian+Gaussian in nature, to account for the 1) broadening of the linewidth due to the shorter core-hole lifetime in the higher energy states (Lorentzian) and 2) spectral width limited by the monochromator (Gaussian). The peaks were allowed to vary in width, amplitude and position in the two extreme spectra (at extreme temperatures, where the material is in a single phase). The intermediate spectra were fitted using a linear weighted sum of the extreme spectra, where the individual weights were taken as the phase fractions. Hence, the peaks were not allowed to vary in width or position for the intermediate spectra.

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Figure S6: Pictures of the x-ray setup at the synchrotron. (a) Picture of the holder with the sample mounted. The electrodes and wires for reading the resistance are seen, as is the heating coil attached to the holder. For a scale, the holes on the metallic holder in (a) are 3 mm in diameter. The holes allow for x-ray transmission. (b) Picture of the sample mounted in the chamber. The white circle indicates the position where the holder is placed.

7. Bruggeman Effective Medium Approximation (EMA)

The Bruggeman EMA equation is ∑i

δi(σ¿¿ i−σ e)/(σ i+ (n−1 ) σ e)=0¿, where δ is the phase

fraction of every individual phase, counted by i, σi is the conductivity of every individual phase, σe is the effective conductivity of the medium and n is a dimensional constant, set to 2. This was set to 2 because we are looking to study percolation effects over several micrometers in the two lateral dimensions while such effects along the thickness (40 nm) are relatively negligible. To calculate the resistance-phase fraction plot displayed in Figure 3a, we assumed that the phase fractions of the insulating and metallic phases add up to 1 and obtained the conductance values of the two components from the resistance-temperature plot in Figure 1b. The resistance of the metallic phase was taken to be 1.4 kΩ. The resistance of the insulating phase during heating was taken as the value of the resistance just before it deviates from the straight dashed line shown in Figure 1b, namely 6.75 kΩ and similarly, during cooling, it was taken to be 8.89 kΩ. The plot in Figure 3a was calculated by parametrically varying the phase fraction.

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8. Isolating the intermediate state by joule heating

528 529 530 531 532

d||*

X-ra

y ab

sorp

tion

(a.u

.)

Energy (eV)

*Rutile-metal

Monoclinic-metal

Monoclinic-insulator

Electrodes

350 µA

4 µm

X-ra

y in

tens

ity (a

.u.)

Figure S7: X-ray transmission map (inset) of the same device as the rest of this study with a large current forced between the electrodes (throughout this study, a small voltage (<0.1 V) was used to measure low-bias resistance). The differently colored region (or filament) between the electrodes indicates the region that underwent a phase transition due to high temperatures induced by joule heating. Spectra corresponding to the three different regions, as indicated (main panel). Inside and outside the filament, we find the extreme phases of VO2 that are well known, namely the high-temperature rutile metal and the low-temperature monoclinic insulator, respectively. At the edge of the filament, where the temperatures are expected to be in the vicinity of the transition temperature, we find a new phase which has the signatures of a metal (with π* band at a lower energy) with a monoclinic phase ordering (with the significant presence of the d||* band). This intermediate phase is expected because the current was increased from 0 to 350 µA and held constant at 350 µA while the x-ray spectromicrograph was obtained. Hence, the sample was heated (and not cooled), thereby justifying the presence of the monoclinic metal. The ring of disconnected material in the center was due to film damage upon high-current operation.

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