Near-field spectroscopy of silicon dioxide thin films

L. M. Zhang, G. O. Andreev, Z. Fei, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. Castro-Neto, D. N. Basov, and M. M. Fogler

Phys. Rev. B 85, 075419 – Published 21 February 2012

Abstract

We analyze the results of scanning near-field infrared spectroscopy performed on thin films of a-SiO $_{2}$ on Si substrate. The measured near-field signal exhibits surface-phonon resonances whose strength has a prominent thickness dependence in the range from 2 to $300 nm$ . These observations are compared with calculations in which the tip of the near-field infrared spectrometer is modeled either as a point dipole or an elongated spheroid. The latter model accounts for the antenna effect of the tip and gives a better agreement with the experiment. Possible applications of the near-field technique for depth profiling of layered nanostructures are discussed.

Received 19 October 2011

DOI:https://doi.org/10.1103/PhysRevB.85.075419

Authors & Affiliations

L. M. Zhang¹, G. O. Andreev², Z. Fei², A. S. McLeod², G. Dominguez³, M. Thiemens³, A. H. Castro-Neto⁴, D. N. Basov², and M. M. Fogler²

¹Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
²Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
³Department of Chemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
⁴Graphene Research Centre and Department of Physics, National University of Singapore, 2 Science Drive 3, 117542, Singapore

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Vol. 85, Iss. 7 — 15 February 2012

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Images

Figure 1
Schematics of an s-SNOM experiment. A scanned probe, modeled as a metallic spheroid of length $2 L$ and the apex curvature radius $a$ , is positioned distance $z_{tip}$ above the sample. The sample contains a film of thickness $d_{1}$ and dielectric function $ε_{1}$ on a substrate with dielectric function $ε_{2}$ . The system is illuminated by infrared field $E_{ext}$ at an angle of incidence $θ$ . Scattering of this radiation by the tip creates evanescent waves with in-plane momenta $q \sim 1 / a$ . The experiment measures the total radiating dipole $p$ of tip, which is determined by multiple reflections of the evanescent waves between the tip and sample. The reflections off the sample are characterized by the coefficient $r_{_{P}} (q, ω)$ .Reuse & Permissions
Figure 2
(a) Main panel: measured infrared near-field spectra for several SiO $_{2}$ film thicknesses. The quantity plotted is the absolute value $s_{3}$ of the third harmonic of the scattering amplitude normalized by that for the Si wafer. Inset i: a topographic AFM image of a region of an 18-nm sample. Inset ii: a near-field image of the same region acquired near the peak frequency $ω \approx 1130 {cm}^{- 1}$ . (b) Theoretical results for the spheroid model with $a = 30 nm$ and $L = 15 a$ . (c) Theoretical results for the point-dipole model with $a = 30 nm$ and $b = 0.75 a$ . (d) Measured approach curves for the 105-nm thick SiO $_{2}$ . Note that $z_{0}$ is determined up to an additive constant $\sim$ $1 nm$ (see text). (e) Calculated approach curve for the spheroid model. (f) The same for point-dipole model.Reuse & Permissions
Figure 3
(a) Dielectric function of bulk SiO $_{2}$ as a function of frequency from ellipsometry. (b) The real and (c) the imaginary parts of the near-field reflection coefficient $r_{_{P}} (q, ω)$ for several $q d_{1}$ . In all the panels three dashed lines indicate the transverse optical phonon frequency $ω_{_{TO}} \approx 1074 {cm}^{- 1}$ , the surface optical phonon frequency $ω_{_{SP}} \approx 1164 {cm}^{- 1}$ , and the longitudinal optical phonon frequency $ω_{_{LO}} \approx 1263 {cm}^{- 1}$ .Reuse & Permissions
Figure 4
(a) The absolute value and (b) the phase of the infinite-plane far-field factor computed as a function of frequency for the incidence angle $θ = 45^{\circ}$ . The black trace is for bulk Si substrate, the blue one is for bulk SiO $_{2}$ substrate, the green one is for $300 nm$ thick SiO $_{2}$ followed by bulk Si. The meaning of the dashed lines is the same as in Fig. 3. (c) Same as Fig. 2b but with the far-field factor included. (d) Same as Fig. 2c but with the far-field factor included.Reuse & Permissions
Figure 5
The thickness dependence of the $s_{3}$ peak for different tip models. The circles represent the point-dipole calculations, one for $a = 30 nm$ (blue) and the other for $a = 50 nm$ (green). The diamonds are for the spheroid model with $a = 30 nm$ and $L = 15 a$ , the same as in Fig. 2b. The black squares are derived from the experimental data shown in Fig. 2a after some smoothing over fluctuations.Reuse & Permissions

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