Identification of Hexagonal Boron Nitride Thickness on SiO₂/Si Substrates by Colorimetry and Contrast

Abstract

Hexagonal boron nitride (hBN) is a layered material with a wide variety of excellent properties for emergent applications in quantum photonics using atomically thin materials. For example, it hosts single-photon emitters that operate up to room-temperature, it can be exploited for atomically flat tunnel barriers, and it can be used to form high finesse photonic nanocavities. Moreover, it is an ideal encapsulating dielectric for two-dimensional (2D) materials and heterostructures, with highly beneficial effects on their electronic and optical properties. Depending on the use case, the thickness of hBN is a critical parameter and needs to be carefully controlled from the monolayer to hundreds of layers. This calls for quick and non-invasive methods to unambiguously identify the thickness of exfoliated flakes. Here, we show that the apparent color of hBN flakes on different SiO₂/Si substrates can be made to be highly indicative of the flake thickness, providing a simple method to infer the hBN thickness. Using experimental determination of the colour of hBN flakes and calculating the optical contrast, we derived the optimal substrates for the most reliable hBN thickness identification for flakes with thickness ranging from a few layers towards bulk-like hBN. Our results offer a practical guide for the determination of hBN flake thickness for widespread applications using 2D materials and heterostructures.

1. Introduction

Hexagonal boron nitride (hBN) is a wide-bandgap van der Waals material [1,2] that features a remarkable chemical inertness [3,4], making it an ideal capping or encapsulating material for two-dimensional (2D) crystals [5,6,7,8,9,10,11,12]. In fact, hBN is currently widely used to protect air-sensitive 2D materials from oxidation and deterioration effects [13,14,15]. The use of hBN as a substrate or as a capping material has also been shown to have marked beneficial effects on the charge carrier mobility of 2D materials [5,14,16,17], or on their light emission properties, leading to a significant narrowing of the exciton linewidth towards the homogeneous limit [8,9,18]. The top and bottom hBN encapsulation flakes may also form a microcavity-like structure that enables control of the radiative lifetime of excitons in 2D semiconductors through the Purcell effect by simply tuning the thickness of the hBN [19]. hBN can even have structural stabilization effects on mechanically-deformed 2D materials, as in the case of 2D-material bubbles for which hBN capping prevents their deflation when reducing the pressure of the substance trapped inside, e.g., when reducing temperature [20,21]. This has enabled the achievement of remarkably high strains even at cryogenic temperatures, providing a means to generate quantum emission in WS₂ [20]. hBN has also attracted wide interest for its intrinsic properties, such as its remarkable mechanical robustness [22,23,24,25], which was exploited for the realization of high-quality mechanical resonators [26], or its capability to sustain the propagation of hyperbolic phonon polaritons [27,28,29]. Moreover, hBN hosts color centers [30,31,32,33,34,35]—discrete states lying in the middle of the bandgap formed by crystal vacancies or impurities— that are optically active even at room-temperature and whose zero-phonon line spans a wide range from near-IR [31,36,37] up to UV [32]. These properties are made even more relevant by the fact that the hBN crystal itself can be patterned to form photonic cavities with an extremely high quality factor that Purcell-enhances its quantum emission [37], or the emission of other 2D materials deposited on it [38]. Boron vacancies and carbon-related defects in hBN have also been shown to act as spin defects that can be optically read-out and manipulated, representing an ideal platform for quantum sensing [35,39,40,41,42].

Depending on the use case, hBN layers with different thicknesses are employed. For example, single or few layers are used when hBN acts as a gate dielectric [5,43] or as a spacer in 2D devices [44,45]; flakes with variable thicknesses, from monolayer up to tens of layers, are used as tunneling barriers between 2D materials in transistor and diode devices [46,47,48,49]; flakes with thicknesses of tens of layers are used when hBN is employed to encapsulate other van der Waals materials and heterostructures [18]; and bulk hBN layers with thicknesses of hundreds of nm are selected for the realization of photonic cavities [37]. The remarkable versatility of hBN calls for quick and non-invasive methods to identify the layer thickness.

Optical methods have indeed shown to be very effective for identifying monolayers or few-layer-thick flakes of van der Waals materials such as graphene and transition metal dichalcogenides (TMDs) [50,51,52,53,54,55,56,57]. From very early studies, it was immediately clear that optical interference effects are of utmost relevance to determine the thicknesses of atomically thin materials [58]. For atomically thin flakes with just one or a few layers, cavity effects are indeed essential to make them visible using conventional light microscopy. SiO₂/Si substrates were quickly shown to facilitate the observation of thin layers of 2D materials with sufficient optical contrast, thanks to Fabry–Pérot effects involving the 2D material and the SiO₂ film. Specific thicknesses of SiO₂ were thus identified as being optimal for graphene and monolayer TMDs, since they maximize the optical contrast in the visible range [50,55].

Similar studies were conducted for hBN. For instance, Anzai et al. [59] identified a color scale in the visible range for hBN flakes from a few nm to hundreds of nm on 90 nm SiO₂/Si substrates, and experimentally and theoretically determined the optical contrast. Krečmarová et al. [60] experimentally and theoretically characterized the optical contrast for different wavelengths, from blue to red, of thin hBN flakes on 290 nm SiO₂/Si substrates. Nguyen et al. [61] and Wang et al. [62] probed the visibility of thin hBN on Si and SiO₂/Si substrates coated with polymers. Gorbachev et al. [63] studied the visibility of mono- to few-layer-thick hBN on SiO₂/Si substrates with thicknesses of 290 nm and 90 nm and calculated the wavelength-dependent optical contrast for hBN monolayer as a function of SiO₂ thickness. Zhang et al. [64] showed that red-light-filtered imaging can be used to quantify the number of layers of thin hBN flakes on 90 nm SiO₂/Si substrates. Puebla et al. [55] acquired images of a multilayered hBN flake which was picked up and transferred on several SiO₂/Si substrates with different SiO₂ thicknesses, establishing, for each of them, a color scale for hBN in the $0-100$ nm range. While these studies provide very valuable information in a specific parameter space, there are still gaps, and, furthermore, a comprehensive overview and practical guide is still missing. Here, we systematically probe the hBN color and contrast experimentally for a wide range of hBN thicknesses, from a few layers to bulk-like crystals, and on three different SiO₂/Si substrates. Our results, combined with those of previous works, allow us to identify the best substrates for the observation of hBN flakes with desired thicknesses from the monolayer limit to $\simeq 200$ nm. Our work thus provides a complete overview of the visibility of hBN flakes on SiO₂/Si substrates, which can be used in a predictive manner to facilitate the observation of hBN flakes with desired thicknesses.

2. Materials and Methods

Optical images of about 120 mechanically exfoliated hBN flakes on SiO₂/Si substrates with SiO₂ thicknesses of 70 nm, 150 nm, and 280 nm were acquired using an Olympus BX53M optical microscope (Olympus, Shinjuku City, Tokyo, Japan). The images were all recorded using white light illumination (color temperature 5700 K) with fixed intensity, in order to have the same substrate color for all the flakes on substrates with the same thickness. A microscope objective (LMPLANFLN by Olympus, Shinjuku City, Tokyo, Japan) with a 50× magnification and numerical aperture NA = 0.50 was used to acquire the optical images. Indeed, previous works have shown that the optical contrast of 2D materials is not remarkably affected by the presence of beam components away from normal incidence for NA $\lesssim 0.55$, while variations in the optical contrast were observed for higher NA [56,65]. We have also verified the effect of NA on the hBN contrast and found consistent results. The 50× magnification and NA = 0.5 of our objective thus provided relatively high resolution and, at the same time, allowed us to measure the optical contrast under conditions for which the normal incidence approximation remains valid. This ensures that the measured contrast is similar to that obtained with objectives with lower NA, as are typically used to search for 2D flakes. To obtain information on the thickness of the hBN flakes, the same flakes were measured by atomic force microscopy (AFM) in tapping mode using a Brucker Dimension Icon XR AFM (Brucker, Billerica, MA, USA). The thickness of our hBN flakes ranged from 1.6 nm to 313 nm for the 70 nm substrate, from 0.3 nm to 326 nm for the 150 nm substrate, and from 1.6 nm to 197 nm for the 280 nm substrate. For the color analysis of the flakes, a numerical code (in Python, 3.12.7 version) was used to extract the red/green/blue (RGB) values from the images. More specifically, the program allows the user to open the images and manually draw a rectangle to select a region with a given color; the program then extracts the RGB intensity values for all pixels in the selected region and calculates the average values. It should be noticed that, in the RGB color notation, the RGB intensity is a dimensionless quantity that spans from 0 to 255 (each color being represented by 8 bits). The average RGB values that we estimate for our flakes/substrates are typically characterized by a standard deviation of about 2. The average RGB values obtained as a function of the hBN thicknesses measured by AFM were then interpolated and used to calculate the thickness-dependent optical contrast, as discussed in more detail below.

3. Results and Discussion

Figure 1 shows typical optical micrographs of hBN flakes with similar thicknesses of ≈135 nm on the three different SiO₂/Si substrates with SiO₂ thicknesses of 70 nm (top), 150 nm (middle), and 280 nm (bottom). From these images, the corresponding RGB images were extracted numerically. As shown in panel (a), the region of the hBN flake with 132.9 nm thickness shows a pink color on the 70 nm substrate. A hBN flake with similar thickness (134.8 nm) on the 280 nm substrate shows a similar magenta color. In contrast, a 136.0 nm thick hBN flake deposited on the 150 nm substrate shows a very different greenish color. A clear color contrast difference between the flakes on the different substrates can also be noticed by looking separately at the RGB channels and at the gray-scale images. Panel (b) analogously shows color, RGB and gray images for thin flakes of about 6 nm on the three different substrates, revealing a clear color and contrast difference depending on the substrate.

These exemplifying images reveal the major role played by the substrate in determining the color and contrast of the hBN flakes, calling for the need to define an optimal parameter space for the identification of specific hBN layer thicknesses.

For the present work, a similar color and thickness analysis was performed for about 120 hBN flakes, thus allowing us to establish a correspondence between the RGB values and the hBN layer thicknesses. The RGB color scales, the gray-scale, and RGB/gray intensity values vs hBN thicknesses obtained for the three different substrates are shown in Figure 2.

While numerical software programs to simulate the color of thin films on substrates were developed [66,67,68], we found discrepancies between the simulated colors and our experimental data. These might be due to the high sensitivity of numerical [66,67,68] and analytical [50,59] methods to input parameters, such as the refractive indices of the material and substrate. Our experimental data in Figure 2 might serve as a benchmark for the future optimization of such methods.

The RGB/gray values feature oscillating behaviors as a function of hBN thickness that are strongly color- and substrate-dependent. While the three RGB channels separately provide information on the RGB contrast, white-light sources are typically used in optical microscopes to identify 2D flakes. To obtain an overall understanding of the magnitude of the optical contrast in an image acquired with white light, it can be useful to merge the information obtained using the RGB channels into a single, gray-scale variable: luminance. Here, luminance describes the brightness of the gray-scale image. Following the BT.601 standard, the luminance, ${\mathrm{I}}_{\mathrm{L}}$, can be calculated using [69]

$${\mathrm{I}}_{\mathrm{L}}=0.299·\mathrm{R}+0.587·\mathrm{G}+0.114·\mathrm{B},$$

(1)

where the coefficients that multiply the RGB channels reflect the human perception of brightness for different colors.

The use of luminance allows for a simple methodology to obtain quantitative information on color images through a single variable, or can be also useful to analyze images acquired with microscopes equipped with black-and-white cameras.

Starting from the RGB/gray intensity values, we can calculate the corresponding contrast. The optical contrast for a specific wavelength $\lambda$ is defined as

$$\mathrm{C}(\mathrm{t},\tilde{\mathrm{n}},\lambda )={\displaystyle \frac{{\mathrm{I}}_{\mathrm{sub}}\left(\lambda \right)-{\mathrm{I}}_{\mathrm{flake}}(\mathrm{t},\tilde{\mathrm{n}},\lambda )}{{\mathrm{I}}_{\mathrm{sub}}\left(\lambda \right)}},$$

(2)

where I is the reflected light intensity and where the dependence from the complex refractive index of the material $\tilde{\mathrm{n}}$ and its thickness t are made explicit. ${\mathrm{I}}_{\mathrm{sub}}$ and ${\mathrm{I}}_{\mathrm{flake}}$ further depend on the refractive indexes of SiO₂ and Si and on SiO₂ thickness. ${\mathrm{I}}_{\mathrm{sub}}\left(\lambda \right)$ and ${\mathrm{I}}_{\mathrm{flake}}(\mathrm{t},\tilde{\mathrm{n}},\lambda )$ can be computed as discussed in ref. [50]. However, this only allows for a direct comparison with experiments if the optical images are acquired under illumination at a specific wavelength, while a more complex theoretical framework is needed to calculate the RGB color values under white-light illumination [59].

Here, we similarly define the contrast ${\mathrm{C}}_{\mathrm{X}}$ as

$${\mathrm{C}}_{\mathrm{X}}\left(\mathrm{t}\right)={\displaystyle \frac{{\mathrm{I}}_{\mathrm{X}},\mathrm{sub}-{\mathrm{I}}_{\mathrm{X}},\mathrm{flake}\left(\mathrm{t}\right)}{{\mathrm{I}}_{\mathrm{X}},\mathrm{sub}}},$$

(3)

where X = R, G, B, L (L is the luminance, representing the gray-scale). Experimental values of ${\mathrm{C}}_{\mathrm{X}}\left(\mathrm{t}\right)$ can be obtained from the intensity values provided in Figure 2, where the intensity of the substrate corresponds to hBN thickness t $=0$ (${\mathrm{I}}_{\mathrm{X}},\mathrm{sub}={\mathrm{I}}_{\mathrm{X}},\mathrm{flake}(\mathrm{t}=0)$). A comparison between the RGB and gray-scale contrast obtained for the three SiO₂/Si substrates with SiO₂ thicknesses of 70 nm, 150 nm, and 280 nm is presented in Figure 3.

We performed a similar analysis for substrates with SiO₂ thicknesses of 90 nm, 215 nm, 271 nm, and 297 nm, starting from data available in the literature. In particular, (i) we considered the RGB values measured by Anzai et al. for hBN flakes on SiO₂/Si substrates with SiO₂ thicknesses of 90 nm, as reported in Supplementary Table S1 of Ref. [59], and (ii) we determined the RGB values by analyzing the optical micrographs shown by Puebla et al. in Figure 15d–f of Ref. [55] for substrates with SiO₂ thicknesses of 215 nm, 271 nm and 297 nm. In both cases, the RGB values were interpolated, and the optical contrast was then calculated using Equation (3). The combined analysis of our experimental data and of those available in the literature allows us to explore the phase-space of hBN and SiO₂ thicknesses in order to identify the most suitable substrate for a desired target hBN thickness. This analysis is summarized in Figure 4a for RGB and gray-scale contrasts as 2D plots displaying the contrast magnitude vs hBN thicknesses for the considered substrates.

While the absolute contrast provides information on the visibility of flakes of a given thickness, for thin flakes, it is often needed to be able to discern contrast variations to determine the number of layers. In that case, both the absolute value and the variance of the contrast are of importance. The latter can be quantified by the derivative of the contrast with respect to the hBN thickness t:

$${\mathrm{D}}_{\mathrm{X}}={\displaystyle \frac{{\mathrm{dC}}_{\mathrm{X}}}{\mathrm{dt}}},$$

(4)

where X = R, G, B, or L. The contrast derivative obtained from RGB and gray-scale data for all substrates is displayed in Figure 4b. Inspecting Figure 4a,b reveals that the choice of the most suitable substrate for the identification of hBN depends on the desired thickness.

Figure 5 provides a zoomed-in overview of the plots of Figure 4 in the thin limit range, from 0.3 to 30 nm.

From the plots in Figure 4 and Figure 5 the following conclusions can be drawn, as also summarized in

Table 1. Summary of the most suited substrates for the observation of hBN flakes. For every hBN thickness range, the substrate giving the highest contrast and derivative is displayed. The substrates in the last column are also good and represent the second-choice substrates. The substrates within brackets are characterized by a relatively high contrast, but a relatively low derivative.

hBN Thickness	Optimum SiO2 Thickness	Second Choice SiO2 Thickness
0–10 nm	70 nm	280 nm
10–40 nm	90 nm	297 nm
40–50 nm	271 nm	70 nm, 280 nm, (90 nm, 297 nm)
50–65 nm	280 nm	(90 nm, 297 nm)
65–100 nm	297 nm	(90 nm, 271 nm, 70 nm)
100–115 nm	70 nm	(90 nm, 280 nm)
115–128 nm	90 nm	280 nm
128–137 nm	70 nm	150 nm, 280 nm, (90 nm)
137–141 nm	150 nm	280 nm, (90 nm)
141–150 nm	90 nm	(280 nm)
150–155 nm	(90 nm)	(280 nm)
155–180 nm	90 nm	(280 nm)
180–200 nm	70 nm	(90 nm, 280 nm)

: the substrate with a 70 nm SiO₂ thickness is the one that shows the highest contrast and contrast derivative in the range of 0–10 nm, thus representing the most suitable candidate for the exfoliation and identification of thin flakes with a specific layer number. The 280 nm substrate is also a relatively good one for thin flakes. In the range of 10–40 nm, the substrates with SiO₂ thicknesses of 90 nm and 297 nm are good candidates, as they show both a high contrast and a high-contrast derivative. Increasing the hBN thickness into the range of 40–50 nm, a SiO₂ thickness of 271 nm is suggested, followed by thicknesses of 70 nm and 280 nm; while substrates with 280 nm and 297 nm SiO₂ thicknesses are suitable in the 50–65 nm range and in the 65–100 nm range, respectively. The 150 nm substrate could also represent an option, but only in the 80–95 nm range. If the determination of the exact thickness is not crucial, however, the 90 nm substrate shows the highest contrast across the entire range of 10–100 nm, followed by the 297 nm substrate. Above 100 nm, the 90 nm SiO₂ is generally the most suitable substrate featuring a sizable contrast, followed by the 280 nm one. However, their derivative is not always high. More specific information on the 100–200 nm range can be found in Table 1.

A comparison between the experimental results and the calculated optical contrast suggests that the use of a proper substrate leading to a high-contrast derivative allows for the identification of hBN thicknesses with very high precision of just a couple of layers (while a much larger uncertainty up to tens of layers is obtained when the derivative is small).

This overview shows how the choice of the substrate can be engineered based on the specific hBN thickness needed, and an overall knowledge of the color and contrast behavior of hBN flakes as a function of thickness can be crucial for the efficient and reliable identification of hBN flakes for specific target applications.

It should be noticed that while very thin hBN flakes are generally more difficult to see than, e.g., graphene or TMD ones, their observation can still be made possible through an optimized choice of the substrate. Figure 6a shows the simulated color (and RGB/gray images) for thin hBN flakes with the shape of a star and with hBN thicknesses ranging from 1 to 10 layers on a 70 nm SiO₂/Si substrate (representing the best substrate for this hBN thickness range). Even monolayer flakes can be observed in the color and gray images, albeit rather faintly. Furthermore, even though the color is similar for all thicknesses, a clear intensity progression can be seen, with the intensity values decreasing in steps of 1–2 for R, ∼2 for G, and 0–1 for B. This results in the contrast progression displayed in Figure 6b. Such a progression suggests that the thickness of thin hBN flakes could be inferred just based on their color, with a relatively high precision of just 2/3 layers.

4. Conclusions

In this work, we systematically investigated the colorimetry and optical contrast of hBN flakes on three different SiO₂/Si substrates with varying SiO₂ thicknesses. By analyzing optical images together with AFM height profiles from about 120 flakes, we determined how the RGB channels and gray-scale intensity change as a function of hBN thickness, and we calculated the optical contrast and respective derivatives. This allowed us to explore the phase space of hBN thickness and SiO₂ thickness, and to make a direct comparison between the contrast obtained for different substrates as a function of the hBN thickness. Our results can be used as a practical guide when exfoliating hBN flakes to immediately identify the most suitable substrates for their identification depending on the desired target thickness.