Introduction

Two-dimensional (2D) nanosheets with atomic or molecular thickness have been emerging as a new frontier of materials science owing to their unique properties. Inspired by the intriguing properties of graphene, many efforts have been devoted to synthesizing 2D nanosheets of various inorganic materials, including transition-metal dichalcogenides (TMDCs)1,2, metal oxides3,4 and hydroxides3,5, as well as primarily investigating their unique electronic structures and physical properties1,6,7. Among the types of inorganic nanosheets, oxide nanosheets are important and fascinating research targets because of the virtually infinite varieties of layered oxide materials with interesting functional properties, including high-κ ferroelectricity, superconductivity and magnetism8. A variety of oxide nanosheets (such as Ti1-δO2, Ti1-xCoxO2, MnO2 and perovskites) have been synthesized by delaminating layered precursors into molecular single sheets via a soft-chemical process3.

These oxide nanosheets have distinct differences and advantages compared with graphene and other inorganic nanosheets because of their potential uses as insulators, semiconductors, conductors and even ferromagnets, depending on their composition and structure. Most oxide nanosheets synthesized to date are d0 transition metal oxides (with Ti4+, Nb5+, Ta5+, W6+) with wide-gap semiconducting or insulating nature7. Current research on oxide nanosheets has thus focused on their use as semiconducting or dielectric nanoblocks in energy, environmental and electronic applications. Regarding the fundamental study and practical applications of oxide nanosheets, thickness information and sufficient characterization range is particularly important, but still challenging. Localized techniques such as atomic force microscopy (AFM) or transmission electron microscopy (TEM) are commonly used to measure the thickness of oxide nanosheets6,9. However, these techniques are time-consuming and unsuitable for rapid measurement over a large area. In the cases of graphene and TMDCs, mono- and few-layer forms are identified by their optical contrasts and Raman signatures10,11,12,13. Little is known about these characteristics for oxide nanosheets. Developing a general and effective thickness characterization scheme is highly desirable in the 2D scientific community because it enables the facile fabrication of monolayer devices based on oxide nanosheets.

Here, we report the optical properties of mono- and few-layer titania nanosheets (Ti1-δO2) obtained by solution-based exfoliation of a layered titanate14,15. Because of their zero opacity (the band gap is 4 eV), Ti1-δO2 nanosheets exhibit a low degree of optical contrast, even if interference enhancement using oxidized Si wafers is employed. We show that the use of thinner SiO2 (100 nm) offers optimum visualization conditions with a contrast of 5% per layer and this contrast level is sufficient to detect the monolayers under a microscope. To show the versatility of our optical technique, we have extended our research to other oxide nanosheets (Ca2Nb3O10, Ca2NaNb4O13, RuO2, MnO2) and heterostructures (RuO2/Ti0.87O2, MnO2/Ti0.87O2).

Results and Discussion

Optical properties of titania nanosheets

Titania nanosheet Ti1-δO2 (δ ≈ 0.09)14,15, the initially developed model system of oxide nanosheets, was chosen as the specimen (Fig. 1a,b). Ti1-δO2 nanosheets are a new class of nanometer-sized titanium oxide prepared by delaminating a layered titanate into single molecular sheets. Elemental Ti1-δO2 nanosheets are characterized by a 2D structure; the thickness is 0.75 nm, corresponding to two edge-shared TiO6 octahedra16. The compositions of the exfoliated 2D nanosheets slightly deviate from the stoichiometry of TiO2, with a general formula of Ti1-δδO2δ− (where □ represents vacancies) depending on the starting layered compounds14,15,17. Theoretical and experimental investigations have demonstrated that Ti0.87O2 nanosheets act as a high-κ dielectric and its multilayer films exhibit a high dielectric constant (εr) of 125 at thicknesses as low as 10 nm18,19.

Figure 1
figure 1

Structure and optical properties of Ti1−δO2 nanosheet.

(a) Structural model of Ti1-δO2 nanosheet. Ti atom is coordinated with six oxygen atoms and resulting TiO6 octahedra are joined via edge-sharing to produce the 2D lattice. Its thickness is 0.75 nm, being consisted of two edge-shared TiO6 octahedra. (b) AFM image of Ti0.87O2 nanosheet on an oxidized Si substrate. A tapping-mode AFM in vacuum condition was used to evaluate the morphology of the nanosheet. (c) Absorbance spectrum for a monolayer film of Ti0.87O2 nanosheets on a quartz glass substrate. Inset shows a photograph. (d) Spectral function of the refractive index (n) and extinction coefficient (k) of Ti0.87O2 nanosheet.

Because of their unique 2D structure and high-κ dielectric nature, Ti0.87O2 nanosheets exhibit some distinctive optical properties in comparison with their bulk counterparts20. As shown in Fig. 1c, a sharp absorption peak centered at 265 nm was observed for Ti0.87O2 nanosheets. An analysis of the square root of the absorption edge [i.e., (αhν)0.5] against photon energy () provides the information to estimate a band gap energy (Eg) of 3.85 eV, considerably larger than those of bulk anatase, rutile and the layered parent titanate20. We also note that Ti0.87O2 nanosheets possess a high transmittance (>99%), higher than those of graphene (98%)21 and MoS2 (95%)22. Fig. 1d depicts the spectral function of the refractive index (n) and extinction coefficient (k) of a Ti0.87O2 nanosheet. Ti0.87O2 nanosheet possessed a higher n (>2) and nearly a zero extinction coefficient (k), which agree well with the high permittivity value19 and previous studies on Ti0.91O2 case23. Due to its zero opacity (the band gap is 4 eV), Ti0.87O2 nanosheet exhibited a low degree of optical contrast, even when employing interference enhancement using oxidized Si wafers. For the standard oxide thickness of 500 nm of SiO2, Ti0.87O2 showed a white-light contrast of <1.5%, which precludes identification using conventional optical microscopy (Supplementary Fig. S1).

Thickness identification of titania nanosheets by optical microscopy

To model the optical contrast of Ti0.87O2 nanosheets, we employed an analysis based on the Fresnel law, which has been proven to be valid for graphene10. In our simulation, we used a matrix formalism of interference in a multilayer system, where the light incident from the air is assumed to be normal to the Ti0.87O2/SiO2/Si structure (Fig. 2a). The reflected light intensity can be expressed as

Figure 2
figure 2

Calculated optical contrast of monolayer Ti0.87O2 nanosheets.

(a) Sample geometry used for our analyses. (b) Calculated optical contrast of Ti0.87O2 nanosheets as a function of the wavelength of light and SiO2 thickness.

where the subindexes 0, 1, 2 and 3 refer to the medium (air), Ti0.87O2 nanosheet, SiO2 and Si, respectively. λ is the wavelength of the inspection light. r1 = (n0 − n1)/(n0 + n1),r2 = (n1 − n2)/(n1 + n2), r3 = (n2 − n3)/(n2 + n3) are the relative indexes of refraction at the top of the nanosheet surface, the interface between the nanosheet and SiO2 and between the SiO2 and the Si substrate, respectively. ni is the refractive index of a given medium. ϕi = 2πnidi/λ is the phase shift due to the light passing through a given medium, where di is the thickness of the medium i. The optical contrast of the system can be defined as

where R0 and R and are the intensities of reflected light from the SiO2/Si substrate and the nanosheets, respectively. We used spectroscopic ellipsometry data for 5-layer films of Ti0.87O2 nanosheets and found k  0 and n  2.1. Assuming that the optical properties of monolayers change little with respect to 5-layer films, we obtain the dependences shown in Fig. 2b. The developed theory allows us to predict the SiO2 thickness at which the optical contrast for monolayer Ti0.87O2 nanosheets would be maximal; here, a contrast peak is predicted at a thickness of 100 nm. In this case, the contrast remains relatively strong (>5%) over a wide range of visible wavelengths (400–550 nm). Moreover, the contrast changes from negative to positive when crossing from the blue-light to the red-light region of the spectrum, going through zero in the green-light region.

This prediction has been confirmed experimentally by imaging monolayer Ti0.87O2 nanosheets on a 100 nm SiO2/Si substrate (Fig. 3a).We also investigated the optical contrast of monolayer Ti0.87O2 nanosheets on SiO2/Si substrates with different SiO2 thicknesses (90 and 285 nm) (Supplementary Fig. S2). Several observations can be made from these data. The contrast for Ti0.87O2 nanosheets can be both negative and positive depending on the wavelength, with a zero crossing in between. A contrast of zero means that the nanosheet is invisible at that wavelength, i.e., it has the same reflectivity as the substrate. The negative contrast was stronger, with a peak observed at 450 nm, while the positive contrast appeared at >550 nm. On the bottom panels (Fig. 3b), we show optical images of Ti0.87O2 nanosheets taken at selected wavelengths centered at 400, 450, 500, 550, 600 and 700 nm. To acquire the image, we have taken optical micrographs using illumination through narrow bandpass filters (with a width of ±5 nm). Clearly, Ti0.87O2 nanosheets showed greater reflectivity than the substrate at 450 nm (i.e., negative contrast) and lesser reflectivity than the substrate at 600 nm (i.e., positive contrast). The 550-nm image corresponds to the wavelength showing zero contrast. Comparing the observed and calculated values, the theory accurately reproduces the observed contrast (Fig. 3a), including its reversal at 550 nm. We note that the optical contrast at 450 nm reaches 5% per layer and this contrast level is comparable to those of graphene and TMDCs10,11,12,13.

Figure 3
figure 3

Optical identification of Ti0.87O2 nanosheets.

(a) Optical contrast of monolayer Ti0.87O2 nanosheets on a 100 nm SiO2/Si substrate (blue circle: experimental value, pink line: theoretical prediction). (b) Optical images of Ti0.87O2 nanosheets were taken at selected wavelengths centered at 400, 450, 500, 550, 600 and 700 nm.

The optical contrast also depends on the number of layers (N) of Ti0.87O2 nanosheets. From a similar analysis as the one presented in Fig. 2, we investigated the layer dependence of the optical contrast for Ti0.87O2 nanosheets on a 100 nm SiO2/Si substrate (Fig. 4a, Supplementary Fig. S3). This calculation suggests that the use of the 450-nm light is suitable for monitoring the layer dependence in Ti0.87O2 nanosheets. In Fig. 4b, we show the optical image taken with the 450-nm light, which is near the negative peak. The AFM image (Fig. 4c) revealed different thicknesses ranging from 1 to 4 layers. From the line profiles at the selected area (Fig. 4d), the optical contrast increased in integer steps (by a factor of N for N layers of Ti0.87O2 nanosheets), a trend consistent with the theoretical prediction (Fig. 4e). In this study, we evaluated thicknesses up to 4 layers. A trend of a linear increase of the optical contrast is persistent up to N ≈ 15. These results imply that the contrast observation at a single wavelength (450 nm) can be used for rapid and reliable characterization of the thickness of Ti0.87O2 nanosheets. We also note that the typical acquisition time for an optical image is 500 ms, much shorter than that of AFM, which is on the order of 10 min.

Figure 4
figure 4

Thickness identification of Ti0.87O2 nanosheets by optical microscopy.

(a) Calculated optical contrast of Ti0.87O2 nanosheets as a function of the wavelength of light and number of layers (N). (b) Optical image for Ti0.87O2 nanosheets on a 100 nm SiO2/Si substrate. Image was taken with the 450-nm light, which is near the negative peak. (c) AFM image taken from the same film as (b). This image clearly revealed different thicknesses ranging from 1 to 4 layers. (d) A line profile at the selected area in (b). The trace shows step-like changes in the contrast for 1, 2, 3 and 4 layers. (e) Comparison between the observed (blue circle) and theoretically predicted (pink line) optical contrast for Ti0.87O2 nanosheets. A trend of a linear increase of the optical contrast is persistent up to N ≈ 15.

Optical identification in 2D oxide nanosheets and their architectures

Through a systematic study of the optical reflectivity of Ti0.87O2 nanosheets on SiO2/Si substrates, we show that the use of thinner SiO2 (100 nm) offers optimum visualization, with an optical contrast of >5%. A particular feature of the Ti0.87O2 nanosheets is that the contrast is a nonmonotonic function of λ and changes its sign at ≈550 nm; the nanosheets are brighter than the substrate at short wavelengths and darker at long ones. These features are different from those of graphene and TMDCs, in which the contrast is either positive or negative10,11,12,13. We note that the nonmonotonic optical response is common to 2D nanosheets with wide-gap semiconducting or insulating nature, including h-BN, Ca2Nb3O10 and Ca2NaNb4O13. A particular feature of these materials is zero opacity, causing a nearly zero extinction coefficient (k). Actually, perovskite nanosheets (Ca2Nb3O10, Ca2NaNb4O13) with higher εr (>200)7 also showed a nonmonotonic response of the optical contrast; the nanosheets were brighter than the substrate at short wavelengths and darker at long ones (Fig. 5). The optical contrast also depends on the number of layers (N) of perovskite nanosheets, a situation being similar to that of Ti0.87O2 nanosheets (Fig. 4, Supplementary Fig. S5). The calculation on the thickness dependence suggests that the use of the 450-nm light is suitable for monitoring the layer dependence in Ca2Nb3O10 nanosheets; a trend of a linear increase of the optical contrast is persistent up to N ≈ 12. Despite their high-κ nature (i.e., higher n), these nanosheets afforded higher optical contrast compared to Ti0.87O2 nanosheets, reaching 10%. This is probably due to both the reduced band gap (Eg 3.4 eV) and slightly larger thicknesses (1.8 nm for Ca2Nb3O10, 2.2 nm for Ca2NaNb4O13). In this context, h-BN nanosheets possess a large band gap (5 eV), causing a rather low contrast (<2.5%)24,25; it is still much harder to detect h-BN than graphene and oxide nanosheets.

Figure 5
figure 5

Optical identification of perovskite nanosheets.

(a) Calculated optical contrast of Ca2Nb3O10 nanosheets as a function of the wavelength of light and SiO2 thickness. (b,c) Optical images for Ca2Nb3O10 and Ca2NaNb4O13 nanosheets on a 100 nm SiO2/Si substrate. Images were taken at selected wavelengths centered at (1) 450 nm, (2) 550 nm and (3) 600 nm. Insets in (b-1) and (c-1) present the line profiles of multilayer parts.

Our optical identification method will facilitate the thickness-dependent study of various 2D oxide nanosheets and their architectures. An attractive aspect is that oxide nanosheets can be organized into various nanoarchitectures by applying a solution-based layer-by-layer assembly method23. Sophisticated functionalities or nanodevices can be designed through the selection of nanosheets and combining materials6,7,26,27,28,29,30,31. Fig. 6 shows a practical application of this imaging method; we extend our research to heterostructures such as RuO2/Ti0.87O2 and MnO2/Ti0.87O2. These structures are basic components of nanocapacitors30 and photo conversion devices27. In this study, we prepared hetero-assembled structures on SiO2/Si substrates by a drop-casting method. Through a systematic study of the optical reflectivity of RuO2/Ti0.87O2 and MnO2/Ti0.87O2 on SiO2/Si substrates, we show that the use of thinner SiO2 (90 nm) and shorter wavelength light (λ = 470 nm) offers optimum visualization; RuO2 and MnO2 cause the positive contrast at 470 nm, while Ti0.87O2 the negative contrast (Supplementary Fig. S5, S6). RuO2 and MnO2 are either metallic or semi-metallic, causing a strong positive contrast (5  10%) with respect to Ti0.87O2 and SiO2/Si substrate. We also emphasize that our technique offers rapid thickness identification with a sufficient characterization range (even on the sub mm scale). These results imply the versatility of our optical technique for the rapid and reliable characterization of various 2D oxide nanosheets and their architectures.

Figure 6
figure 6

Optical identification of nanosheet heterostructures [RuO2/Ti0.87O2 and MnO2/Ti0.87O2].

(a,b) Calculated optical contrast of monolayer RuO2/Ti0.87O2 and MnO2/Ti0.87O2 on a 90 nm SiO2/Si substrate. The use of thinner SiO2 (90 nm) offers optimum visualization; here, RuO2 and MnO2 cause the positive contrast, while Ti0.87O2 the negative contrast (Supplementary Fig. S5, S6). RuO2 and MnO2 are either metallic or semi-metallic, causing a strong negative contrast with respect to Ti0.87O2 and SiO2/Si substrate. (c,d) Optical images for RuO2/Ti0.87O2 and MnO2/Ti0.87O2 on a 90 nm SiO2/Si substrate. Images were taken with the 470-nm light, which is near the maximal contrast for Ti0.87O2 nanosheets.

Methods

2D Oxide Nanosheets

A colloidal suspension of Ti0.87O2 nanosheets with a lateral dimension of 5–10 μm was prepared by delaminating a layered titanate (K0.8Ti1.73Li0.27O4) according to previously reported procedures14,15,17. Ti0.87O2 nanosheets were deposited on SiO2/Si substrates (SiO2 thicknesses: 90, 100, 285 and 300 nm) by a modified Langmuir-Blodgett (LB) technique32 (Supplementary Fig. S7). In usual LB experiments, densely packed monolayer films were obtained with an optimized surface pressure (15 mN/m). In this study, films having dispersed nanosheets were obtained by controlling the surface pressure (3 mN/m). The as-fabricated films were irradiated by UV/white light from a Xe lamp (4 mW/cm2) for 48 h to decompose the tetrabutylammonium ions used in the exfoliation process. Repeated LB deposition yielded multilayer structures. The main data were obtained from Ti0.87O2 nanosheets with different thicknesses ranging from 1 to 4 layers. Complementary data were obtained from perovskite nanosheets (Ca2Nb3O10, Ca2NaNb4O13), RuO2, MnO2 and heterostructures (RuO2/Ti0.87O2, MnO2/Ti0.87O2). The films with dispersed nanosheets were prepared by a drop-casting method. The synthesis and characterization of these nanosheets were described elsewhere30,33,34,35.

Optical Microscopy of 2D Nanosheets

Optical images of 2D oxide nanosheets were obtained by a bright-field optical microscope (Olympus, BX51 with a 100×, 0.9 NA objective lens). Monochromatic images were acquired using illumination through narrow bandpass filters (with a width of ±5 nm). A CCD camera head (Nikon, DS-1) with a digital camera control unit was used to capture color optical images of the 2D nanosheets at the resolution of 1280 × 960 pixels. The typical acquisition time was 500 ms; in low-contrast cases, acquisition times were varied between 100 ms and 30 s to avoid overexposure. The color optical images were processed by Image-J software (version 1.48, National Institutes of Health, USA). For color images (RGB images), the contrast value of each pixel (CV) was calculated using the following equation:

where CVR, CVG and CVB are the R, G and B values per pixel, respectively (0–255, corresponding to darkest to brightest). The contrast levels of the R, G and B channels were extracted and converted to a gray-scale image, where 0 is black and 255 is white.

To model the optical contrast of oxide nanosheets, we employed an analysis based on the Fresnel law, which has been proven to be valid for graphene10. In our simulation, we used a matrix formalism of interference in a multilayer system (Fig. 2a). We used spectroscopic ellipsometry data for 5-layer films of oxide nanosheets. Ellipsometric measurements were performed by a spectroscopic ellipsometer (J.A. Woollam Japan, M-2000).

Thickness Measurements by AFM

An AFM (SII Nanotech, E-Sweep) was used to confirm the number of layers of 2D oxide nanosheets by measuring the film thickness with tapping mode in air.

Additional Information

How to cite this article: Kim, H.-J. et al. Hunting for Monolayer Oxide Nanosheets and Their Architectures. Sci. Rep. 6, 19402; doi: 10.1038/srep19402 (2016).