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THz conductivities of indium-tin-oxide nanowhiskers as a graded-refractive-index structure

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Abstract

Indium-tin-oxide (ITO) nanowhiskers with attractive electrical and anti-reflection properties were prepared by the glancing-angle electron-beam evaporation technique. Structural and crystalline properties of such nanostructures were examined by scanning transmission electron microscopy and X-ray diffraction. Their frequency-dependent complex conductivities, refractive indices and absorption coefficients have been characterized with terahertz time-domain spectroscopy (THz-TDS), in which the nanowhiskers were considered as a graded-refractive-index (GRIN) structure instead of the usual thin film model. The electrical properties of ITO GRIN structures are analyzed and fitted well with Drude-Smith model in the 0.2~2.0 THz band. Our results indicate that the ITO nanowhiskers and its bottom layer atop the substrate exhibit longer carrier scattering times than ITO thin films. This signifies that ITO nanowhiskers have an excellent crystallinity with large grain size, consistent with X-ray data. Besides, we show a strong backscattering effect and fully carrier localization in the ITO nanowhiskers.

©2012 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1 The scanning electron microscopy images of the ITO nanowhiskers fabricated with different deposition times: (a) 16.5 minutes (b) 22 minutes. The corresponding cross-sectional images in (c) and (d) show an estimated height of 418 nm and 698 nm, respectively.
Fig. 2
Fig. 2 The reflectance spectra of the bare silicon wafer (black circles) and ITO nanowhiskers with thickness of 418 nm (blue triangles) and 698 nm (red cubes) in the wavelength range of 200~2600 nm.
Fig. 3
Fig. 3 The TEM characterizations of ITO Nano-whiskers. (a) The TEM images reveal the structures of trunks and branches. (b) The high-resolution image shows the lattice pattern, corresponding to a constant of 5.18Å, and the XRD diffraction pattern of the corresponding crystalline structure (inset). (c) The line-scan profile in an EDX analysis of a ITO trunk. The composition profiles of In and O show significant variation from the edge to center, while the Sn composition show little variation.
Fig. 4
Fig. 4 X-ray diffraction patterns for ITO nanowhiskers deposited on silicon. The blue solid line and red dashed line correspond to ITO nanowhiskers with thicknesses of 418 nm and 698 nm, respectively.
Fig. 5
Fig. 5 Sketch of the graded-refractive-index structure of ITO nanowhiskers.
Fig. 6
Fig. 6 (a) The real parts of the refractive indices of ITO nanowhiskers with thickness of 418 nm (blue circles) and 698 nm (red triangles). (b) The power absorption of ITO nanowhiskers with thickness of 418 nm (blue circles) and 698 nm (red triangles). The imaginary parts of the refractive indices of ITO nanowhiskers with thickness of 418 nm (blue circles) and 698 nm (red triangles) are shown in the inset.
Fig. 7
Fig. 7 (a) The real parts of conductivities of ITO nanowhiskers with thickness of 418 nm (blue circles) and 698 nm (red triangles). (b) The imaginary parts of the conductivities of ITO nanowhiskers with thickness of 418 nm (blue circles) and 698 nm (red triangles). The blue solid lines and red dashed lines are the corresponding fitting results based on the Drude-Smith model.

Equations (8)

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f ITO (z)=1 1 1+ e b( z z 0 ) ,
E Sub * ( ω )= E 0 * t Air,Sub * t Sub,Air * ×exp[ i(ω/c) n Air d ]exp[ i(ω/c) n Sub * L ],
E ITO * ( ω )= E 0 * t Air,1 * t 12 * t 23 * ... t (m-1)m * ... t N,Sub * ×exp[ i(ω/c)( n 1 * + n 2 * + n 3 * ...+ n m-1 * + n m * +... n N * )(d/N) ] × t Sub,Air * ×exp[ i(ω/c) n Sub * L ],
T Theo * ( ω )= E ITO * ( ω )/ E Sub * ( ω )= t Air,1 * t 12 * t 23 * ... t (m-1)m * ... t N,Sub * ×exp[ i(ω/c)( d/N )( n 1 * + n 2 * + n 3 * +...+ n (m-1) * + n m * +...+ n N * N n Air * ) ]/ t Air,Sub * .
( n N * ) 2 = ε * ( ω )= ε +i σ * ( ω ) ω ε 0 ,
σ * ( ω )= ε 0 ω p 2 τ 1iωτ ( 1+ γ 1iωτ ),
Re{ σ }= ε 0 ω p 2 τ[ ( 1+γ )+ ω 2 τ 2 ( 1γ ) ] ( 1+ ω 2 τ 2 ) 2 ,
Im{ σ }= ε 0 ω ω p 2 τ 2 ( 1+2γ+ ω 2 τ 2 ) ( 1+ ω 2 τ 2 ) 2 .
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