Rendering Ti3C2Tx (MXene) monolayers visible

ABSTRACT Herein we report on how to render Ti3C2Tx (MXene) monolayers deposited on SiO2/Si wafers, with different SiO2 thicknesses, visible. Inputting the effective thickness of a Ti3C2Tx monolayer (1 ± 0.2 nm) measured by atomic force microscopy, and its refractive index into a Fresnel-law-based simulation software, we show that the optical contrast of Ti3C2Tx monolayers deposited on SiO2/Si wafers depends on the SiO2 thickness, number of MXene layers, and the light’s wavelength. The highest contrast was found for SiO2 thicknesses around 220 nm. Simulations for other substrates, namely, Al2O3/Si, HfO2/Si, Si3N4/Si and Al2O3/Al, are presented as supplementary information. GRAPHICAL ABSTRACT IMPACT STATEMENT The experimental and simulated color contrasts between Ti3C2Tx (MXene) monoflakes deposited on SiO2 of various thicknesses—under an optical microscope—were obtained for the first time.

MXenes-early transition metal carbides and/or nitrides, that are produced by the selective etching of the A layers from the MAX phases-represent the newest, and potentially largest, 2D family of solids [12][13][14][15]. The MAX phases, in turn, are a large ( > 70) family of layered ternary transition metal carbides, where M is an early transition metal, A is an A-group element (mostly groups 13 and 14), and X is C or/and N [16]. Because during etching, the A-group element layers such as Al and Ga are replaced by -O, -OH, and -F terminations [17,18], the proper designation of the resulting 2D material is Figure 1. (a) AFM scan of a Ti 3 C 2 T x monolayer on a 285 nm thick SiO 2 substrate. Average height between flake and substrate is 1.8 ± 0.3 nm. AFM measurements of the folded corner are more reliable as they are less influenced by instrumental offsets and other artifacts. These measurements show a reproducible step of 1 ± 0.2 nm, which is the value assumed herein. Small bright regions in (a) are residues from the MXene dispersion; (b) visible spectrum unfiltered OM images of same flake-located in the center of the dotted frame-in which the folded MXene corner appears slightly darker. (c) Ellipsometric measurements of the real, n, and imaginary, k, parts of the refractive indices of Ti 3 C 2 T x as a function of wavelength in the visible region, reproduced from Ref. [27].
were measured [27]. Since as discussed below, n and k are important input parameters in our modeling, it is important to briefly explain how they were measured and why it is justifiable to use these values here. First, both single flakes and films were spincast from nominally identical colloidal solutions. Second, given that n and k are typically functions of film thickness, it would have been ideal if the values used herein were those measured on monolayered films. However, since currently such films do not exist, we chose instead to use the n and k values (Figure 1(c)), measured ellipsometrically on a 75 nm thick spincoated Ti 3 C 2 T x film. The details can be found in supplementary information of Ref. [27].
As far as we are aware, that information has yet to be exploited to render MXenes visible under an optical microscope (OM), in the same way that, for example, Blake et al. [35] and others [36][37][38][39], rendered single graphene layers visible. The same was done for single layers of transition metal dichalcogenides [40], BN [41], and other 2D systems [42]. The capability to quickly and accurately distinguish single from multiple flakes is a crucial requisite first step for using MXenes in microelectronic devices. To be able to do so rapidly and accurately with nothing more sophisticated than an OM is therefore important. The purpose of this work is to delineate the conditions under which Ti 3 C 2 T x monolayers, deposited on oxidized Si wafers, would be visible under an OM. To that effect, we measured the thicknesses of various flakes-deposited on substrates with varying SiO 2 thicknesses-using atomic force microscopy (AFM). We then combined these results, with the refractive indices of Ti 3 C 2 T x [27], to predict the best conditions to visualize Ti 3 C 2 T x monoflakes in an OM for a variety of substrates.
The Ti 3 C 2 T x flakes were produced by selective etching of Al from Ti 3 AlC 2 . The details can be found elsewhere [34]. To deposit single Ti 3 C 2 T x flakes, they were first dispersed in water-with a concentration of ≈ 1 to 2 mg/ml-and spincoated on Si wafers. For the latter, a drop was placed on the substrate and the spincoater was accelerated from 0 to 6000 rpm in 1 s and held at that speed for 60 s. The substrates were then inspected under an OM. Flakes, presumed to be monolayers, were scanned by tapping mode AFM. The difference in height between the monolayers and the Si substrate was measured to be 1.8 ± 0.3 nm, which overestimates the real thickness because of anomalies related to the measuring conditions of the AFM [43], instrument offset [44], and other artifacts [45,46], as well as the possible presence of adsorbates on top of the flakes in addition to surface terminations. The same is true of graphene where control experiments on monolayered graphene flakes revealed them to be offset by about ≈ 0.6 nm under the same experimental and environmental conditions. To solve this problem, the 2D community has concluded that folded regions give the most reliable measurements of thickness (see, e.g. [47]). Measurements on folded flakes here provided a reproducible thickness of 1 ± 0.2 nm, for a Ti 3 C 2 T x monolayer, in agreement with the SiO 2 -MXene step height (1.8 ± 0.3 nm) reduced by the determined offset of ≈ 0.6 nm. It is important to note that, based on X-ray diffraction measurements, half the c-axis lattice parameter of Ti 3 C 2 T x is ≈ 1 nm [12]. Therefore, all such flakes were deemed single-layered. Figure 1(a) shows the AFM scan for a monolayer MXene flake deposited on a Si wafer with a nominally 300 nm thick SiO 2 layer. In the AFM scan shown in Figure 1(a), small particulates are imaged both on the MXene and substrate. These particulates are most probably small oxide particles that form during MXene production and need further investigation. The largest of these particles are detectable under an OM and have been avoided when selecting regions for colorimetric evaluations. An OM micrograph taken using the whole range of visible light is shown in Figure 1 Figure 1(c) shows the functional dependencies of n and k of Ti 3 C 2 T x , on wavelength, λ, in the visible range (380-780 nm), which is the region of interest for this work. These values are taken from Ref. [27] and are reproduced here because the colorimetric simulations are based on them. Interestingly, we note that the average values of n and k in this region (2.6 and 1.3) are comparable to those of graphene in the same spectral window [48,49].
Similar to what was done for other 2D systems [35,40], we model our MXene sample as a stacked structure (Figure 2(a)) composed of air (layer 0, with refractive index n 0 ), MXene (layer 1, with thickness d 1 and refractive index n 1 ), SiO 2 (layer 2, with thickness d 2 and refractive index n 2 [50,51], and Si (layer 3, with refractive index n 3 [52]. Under these conditions, the MXene reflectivity is given by [53]: where r 1 = (n 0 − n 1 )/(n 0 + n 1 ), r 2 = (n 1 − n 2 )/(n 1 + n 2 ), and r 3 = (n 2 − n 3 )/(n 2 + n 3 ) are the relative changes in the index of refraction and φ i = 2π n i d i /λ are the phase shifts in the various regions of the optical path for a given λ. Similarly, the substrate without MXene has a reflectivity expressed by R Sub = |(r 2 e iφ 2 + r 3 e −iφ 2 )/(e iφ 2 + r 2 r 3 e −iφ 2 )| 2 , where r 2 = (n 0 − n 2 )/ (n 0 + n 2 ). The absolute contrast for a MXene monolayer for a given λ is defined as: When this equation is plotted for a single Ti 3 C 2 T x layer as a function of SiO 2 thickness and λ (Figure 2(b)), three regions of high contrast are found. These represent the optimal experimental conditions for the identification of single Ti 3 C 2 T x layers on SiO 2 . They roughly follow the relation 2 · d SiO 2 · n SiO 2 = (m + 1/2)λ, with m = 0, 1, 2, corresponding to the optical path being a half-integer times the wavelength. This formula indicates that these Fabry-Perot-type resonances come from standing waves in the SiO 2 and reflection at an open end (antinode) on the MXene-SiO 2 interface side and reflection at a fixed end (node) on the Si-SiO 2 interface side. Figure 3(a-c) show the contrast between 1 (bottom curve) to 5 (top curve) layers of Ti 3 C 2 T x as a function of SiO 2 thickness for monochromatic blue, green, and red light, respectively. Note that the position of the absolute contrast maxima for each λ is independent of the number of MXene layers.  Since these results pertain to a single λ, they are not of much use in an OM without filters, where all frequencies need to be taken into account. In that case, the colorimetric CIE 1931 XYZ [54] space should be calculated for visible wavelengths as: wherex(λ),ȳ(λ), andz(λ) are the CIE 1931 matching functions, respectively (See Ref. [54] for selected colorimetric tables), R(λ) is the reflectivity of the system, S(λ) is the spectrum of the incident light source, that depends on the type of illumination and P is the total illumination power. The incident light source used here is an incandescent tungsten-filament light with a temperature of 2856 K, the most common source of light in OMs and thus illuminant A is used. It is described by a Planck's distribution law (shown in the supplementary information (SI)) and tabulated in Ref. [54]. Once the CIE 1931 XYZ color space is calculated, it is transformed to the CIELab color space which offers a more perceptual uniformity [39,54], by operating the transformations [39]: where X n , Y n , and Flakes were illuminated by a standard W-lamp, without filters under the same experimental and environmental conditions (clean room controlled temperature and humidity). The luminosity of these pictures was adjusted in order to have a consistent color balance between experiment and simulations [38]. The experimentally measured CIELab total color differences are in quite good agreement with the calculations.
Lastly, we use the total color difference, TCD, defined as as the colorimetric distance between two colors. Figure 4(a) shows the calculated color contrast between bare and Ti 3 C 2 T x covered substrates as a function of the number of monolayers-up to 50-and the thickness of the SiO 2 , observed under a W-lamp (Illuminant A), delineating the experimental conditions for which the contrast would be largest. Here again there are combinations of the number of layers and SiO 2 thicknesses that result in bands of high contrast. When the same results are plotted as a function of the number of MXene layers-for three different SiO 2 thicknesses, 100, 200, and 300 nm (Figure 4(b))-the contrast curves have maxima between 8 and 12 layers before decreasing. Interestingly, there is second peak-at around 60 layers for the thickest SiO 2 substrates-possibly a Fabry-Perot resonance in the MXene layer.
Since herein we were particularly interested in identifying single flakes, Figure 5(a) plots the color contrast for the latter as a function of SiO 2 thickness. These results predict that a SiO 2 thickness of 222 nm provides the highest contrast. To test this prediction, we deposited single MXene layers on SiO 2 /Si substrates of different thicknesses. The latter were prepared by etching standard Si wafers-with 285 nm thick, thermally grown SiO 2 (Crys-Tec, Berlin, Germany)-in buffered HF (20%) for 15, 30, 60, 90, and 120 s, which resulted in SiO 2 thicknesses of 223, 170, 134, 127, and 87 nm, respectively. To determine the SiO 2 thicknesses, a set of wafers-with a 285 nm thick thermal oxide-were etched, as above, with part of the wafer masked. A profilometer was then used to measure the step height between the etched and un-etched regions yielding the SiO 2 thickness. These measurements were confirmed by a colorimetric comparison between the color of SiO 2 of the etched samples and the calculated ones for the measured thicknesses. To complete the set, a 90 nm thick SiO 2 layer thermally grown on Si (CrysTec Berlin, Germany) was also used.
When the TCD simulations (solid line in Figure 5(a)) and the experimental results (data points with error bars in Figure 5(a)) are compared, it is obvious that the agreement is quite good. The images were taken with a camera (Canon EOS 500D), attached to an OM (Zeiss Axiotech) with a 100 X objective and a numerical aperture of 0.75. The results ( Figure 5(b-h)) are shown after luminosity balancing (full procedure for balancing and comparison between theory and experiments is discussed in the SI). The experimental results confirm that the best contrast is achieved with a SiO 2 thickness of 223 nm, where TCD peaks at ≈ 12 ( Figure 5(c)) in excellent agreement with our theoretical predictions (12.3 at 222 nm). Interestingly, the second highest peak of visibility is calculated to be around 280 nm with a TCD of 11.8 (confirmed by a measured value of 11.5 at 285 nm). This thickness would allow good visibility for both MXene and graphene. It is worth noting that the thickness of every flake shown in Figure 5(b-h) was measured by AFM before observing them in the OM. Only single flakes were imaged in the OM and used.
In conclusion, making use of Fresnel's theory, we delineate the conditions under which MXene mono-and, in principle, multilayers can be rendered visible under an OM-using a W-lamp-after deposition on Si wafers with various SiO 2 thicknesses. Our simulations predict that SiO 2 thicknesses of 222 and 280 nm should result in the best contrast as observed experimentally. This work establishes a framework for detecting single MXene flakes on Si and other substrates. Colorimetric results on other substrates, such as Al 2 O 3 /Si, HfO 2 /Si, Si 3 N 4 /Si and Al 2 O 3 /Al, with other illuminants (D65), present a shift of the maxima of contrast, but are similar in general to those on silica. For further details about these results and details of our methodology refer to the SI.

Funding
This work was funded by Ceramics Division of NSF (DMR-1310245) and Swedish Foundation for Strategic Research (Synergy Grant FUNCASE).