Hunting for Monolayer Oxide Nanosheets and Their Architectures

In two-dimensional materials, thickness identification with a sufficient characterization range is essential to fundamental study and practical applications. Here, we report a universal optical method for rapid and reliable identification of single- to quindecuple-layers in oxide nanosheets (Ti0.87O2, Ca2Nb3O10, Ca2NaNb4O13). Because of their wide bandgap nature (Eg = ∼4 eV) and zero opacity, most oxide nanosheets exhibit a weak white-light contrast (<1.5%), which precludes optical identification. 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 conditions with a contrast of >5%; the contrast is a nonmonotonic function of wavelength and changes its sign at ≈550 nm; the nanosheets are brighter than the substrate at short wavelengths and darker at long ones. Such a nonmonotonic optical response is common to semiconducting oxide nanosheets, including Ca2Nb3O10 and Ca2NaNb4O13. The optical contrast differences between the substrates and nanosheets with different numbers of layers were collected, serving as a standard reference from which the number of layers can be determined by optical microscopy. Our method will facilitate the thickness-dependent study of various oxide nanosheets and their architectures, as well as expedite research toward practical applications.

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 SiO 2 (∼ 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 (Ca 2 Nb 3 O 10 , Ca 2 NaNb 4 O 13 , RuO 2 , MnO 2 ) and heterostructures (RuO 2 /Ti 0.87 O 2 , MnO 2 /Ti 0.87 O 2 ).

Results and Discussion
Optical properties of titania nanosheets. Titania nanosheet Ti 1-δ O 2 (δ ≈ 0.09) 14,15 , the initially developed model system of oxide nanosheets, was chosen as the specimen (Fig. 1a,b). Ti 1-δ O 2 nanosheets are a new class of nanometer-sized titanium oxide prepared by delaminating a layered titanate into single molecular sheets. Elemental Ti 1-δ O 2 nanosheets are characterized by a 2D structure; the thickness is ∼ 0.75 nm, corresponding to two edge-shared TiO 6 octahedra 16 . The compositions of the exfoliated 2D nanosheets slightly deviate from the stoichiometry of TiO 2 , with a general formula of Ti 1-δ □ δ O 2 δ− (where □ represents vacancies) depending on the starting layered compounds 14,15,17 . Theoretical and experimental investigations have demonstrated that Ti 0.87 O 2 nanosheets act as a high-κ dielectric, and its multilayer films exhibit a high dielectric constant (ε r ) of ∼ 125 at thicknesses as low as 10 nm 18,19 .
Because of their unique 2D structure and high-κ dielectric nature, Ti 0.87 O 2 nanosheets exhibit some distinctive optical properties in comparison with their bulk counterparts 20 . As shown in Fig. 1c, a sharp absorption peak centered at ∼ 265 nm was observed for Ti 0.87 O 2 nanosheets. An analysis of the square root of the absorption edge [i.e., (αhν) 0.5 ] against photon energy (hν) provides the information to estimate a band gap energy (E g ) of 3.85 eV, considerably larger than those of bulk anatase, rutile, and the layered parent titanate 20 . We also note that Ti 0.87 O 2 nanosheets possess a high transmittance (> 99%), higher than those of graphene (∼ 98%) 21 and MoS 2 (∼ 95%) 22 . Fig. 1d depicts the spectral function of the refractive index (n) and extinction coefficient (k) of a Ti 0.87 O 2 nanosheet. Ti 0.87 O 2 nanosheet possessed a higher n (> 2) and nearly a zero extinction coefficient (k), which agree well with the high permittivity value 19 and previous studies on Ti 0.91 O 2 case 23 . Due to its zero opacity (the band gap is ∼ 4 eV), Ti 0.87 O 2 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 SiO 2 , Ti 0.87 O 2 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 Ti 0.87 O 2 nanosheets, we employed an analysis based on the Fresnel law, which has been proven to be valid for graphene 10 . 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 Ti 0.87 O 2 /SiO 2 /Si structure (Fig. 2a). The reflected light intensity can be expressed as where the subindexes 0, 1, 2, and 3 refer to the medium (air), Ti 0.87 O 2 nanosheet, SiO 2 , and Si, respectively. λ is the wavelength of the inspection light. r 1 = (n 0 − n 1 )/(n 0 + n 1 ),r 2 = (n 1 − n 2 )/(n 1 + n 2 ), r 3 = (n 2 − n 3 )/(n 2 + n 3 ) are the relative indexes of refraction at the top of the nanosheet surface, the interface between the nanosheet and SiO 2 and between the SiO 2 and the Si substrate, respectively. n i is the refractive index of a given medium. φ i = 2πn i d i /λ is the phase shift due to the light passing through a given medium, where d i is the thickness of the medium i. The optical contrast of the system can be defined as where R 0 and R and are the intensities of reflected light from the SiO 2 /Si substrate and the nanosheets, respectively. We used spectroscopic ellipsometry data for 5-layer films of Ti 0.87 O 2 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 SiO 2 thickness at which the optical contrast for monolayer Ti 0.87 O 2 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 Ti 0.87 O 2 nanosheets on a 100 nm SiO 2 /Si substrate (Fig. 3a).We also investigated the optical contrast of monolayer Ti 0.87 O 2 nanosheets on SiO 2 /Si substrates with different SiO 2 thicknesses (90 and 285 nm) ( Supplementary Fig. S2). Several observations can be made from these data. The contrast for Ti 0.87 O 2 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 Ti 0.87 O 2 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, Ti 0.87 O 2 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 TMDCs [10][11][12][13] .
The optical contrast also depends on the number of layers (N) of Ti 0.87 O 2 nanosheets. From a similar analysis as the one presented in Fig. 2, we investigated the layer dependence of the optical contrast for Ti 0.87 O 2 nanosheets on a 100 nm SiO 2 /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 Ti 0.87 O 2 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 Ti 0.87 O 2 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 Ti 0.87 O 2 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.
Optical identification in 2D oxide nanosheets and their architectures. Through a systematic study of the optical reflectivity of Ti 0.87 O 2 nanosheets on SiO 2 /Si substrates, we show that the use of thinner SiO 2 (∼ 100 nm) offers optimum visualization, with an optical contrast of > 5%. A particular feature of the Ti 0.87 O 2 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 negative [10][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, Ca 2 Nb 3 O 10 , and Ca 2 NaNb 4 O 13 . A particular feature of these materials is zero opacity, causing a nearly zero extinction coefficient (k). Actually, perovskite nanosheets (Ca 2 Nb 3 O 10 , Ca 2 NaNb 4 O 13 ) with higher ε r (> 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 Ti 0.87 O 2 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 Ca 2 Nb 3 O 10 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 Ti 0.87 O 2 nanosheets, reaching ∼ 10%. This is probably due to both the reduced band gap (E g ∼ 3.4 eV) and slightly larger thicknesses (1.8 nm for Ca 2 Nb 3 O 10 , 2.2 nm for Ca 2 NaNb 4 O 13 ). 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.
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 method 23 . Sophisticated functionalities or nanodevices can be designed through the selection of nanosheets and combining materials 6,7,26-31 . Fig. 6 shows a practical  30 and photo conversion devices 27 . In this study, we prepared hetero-assembled structures on SiO 2 /Si substrates by a drop-casting method. Through a systematic  Supplementary Fig. S5, S6). RuO 2 and MnO 2 are either metallic or semi-metallic, causing a strong positive contrast (5 ∼ 10%) with respect to Ti 0.87 O 2 and SiO 2 /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.  (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/cm 2 ) 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 Ti 0.87 O 2 nanosheets with different thicknesses ranging from 1 to 4 layers. Complementary data were obtained from perovskite nanosheets (Ca 2 Nb 3 O 10 , Ca 2 NaNb 4 O 13 ), RuO 2 , MnO 2 , and heterostructures (RuO 2 /Ti 0.87 O 2 , MnO 2 /Ti 0.87 O 2 ). The films with dispersed nanosheets were prepared by a drop-casting method. The synthesis and characterization of these nanosheets were described elsewhere 30,33-35 . 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 (C V ) was calculated using the following equation:

2D
where C VR , C VG , and C VB 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 graphene 10 . 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.