Size-Dependent Optical Properties of ${\mathrm{V}\mathrm{O}}_2$ Nanoparticle Arrays

The size effects on the optical properties of vanadium dioxide nanoparticles in ordered arrays have been studied. Contrary to previous ${\mathrm{V}\mathrm{O}}_2$ studies, we observe that the optical contrast between the semiconducting and metallic phases is dramatically enhanced in the visible region, presenting size-dependent optical resonances and size-dependent transition temperatures. The collective optical response as a function of temperature presents an enhanced scattering state during the evolving phase transition. The effects appear to arise because of the underlying ${\mathrm{V}\mathrm{O}}_2$ mesoscale optical properties, the heterogeneous nucleation behind the phase transition, and the incoherent coupling between the nanoparticles undergoing an order-disorder-order transition. Calculations that support these interpretations are presented.

Figure 1

(a) The dark-field confocal setup used to study the samples. ${\theta }_o=60°$. (b) and (c) Scanning electron micrographs of ${\mathrm{V}\mathrm{O}}_2$ arrays with the particle radii $r=26$, 35, 44, 49 nm and corresponding lattice constant $L=166$, 222, 278, 310 nm. Scale bar is 200 nm.

Figure 2

(a) Scattering spectrum from a ${\mathrm{V}\mathrm{O}}_2$ array ($r=44\mathrm{n}\mathrm{m}$) at $23°\mathrm{C}$ and $90°\mathrm{C}$ normalized to the lamp intensity. (b) Peak position and (c) relative scattered intensity vs particle size in the metallic and semiconducting states (filled and open circles, respectively).

Figure 3

(a) Temperature evolution of the scattered signal at $\lambda =600\mathrm{n}\mathrm{m}$. (b) Typical hysteresis loop of the scattered light with indicator points along the phase transition from the ${\mathrm{V}\mathrm{O}}_2$ nanoparticles in array. (c) Temperatures of indicator points during a cycle of the ${\mathrm{V}\mathrm{O}}_2$ semiconductor-to-metal phase transition as a function of size. Solid lines are only a guide for the eye.

Figure 4

Calculated optical properties of ${\mathrm{V}\mathrm{O}}_2$ nanoparticles. (a) Mie extinction and scattering effective cross sections for a $r=80\mathrm{n}\mathrm{m}$ nanoparticle. (b) Wavelength of resonance vs particle radius. (c) Scattering efficiency vs particle radius. (d) Collective scattered intensity (solid line) for a given probability function (dashed line) of the nanoparticles undergoing phase transition in the array. Notice the less steep cooling side in agreement with observations on Ref. 20.