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Abstract
Atomic layers of hexagonal boron nitride (h-BN) crystal, primarily serving as atomically-smooth dielectric layers in two-dimensional (2D) electronics and structural materials in 2D nanoelectromechanical systems (NEMS), have recently emerged as a promising platform for nanoscale optics and photonics. Ultrawide bandgap (~5.9 eV) of h-BN promises ultraviolet (UV) and deep ultraviolet (DUV) responsivity; it can host defect states related to single photon generation. Meanwhile, it also gives rise to the visibility challenge of these atomically-thin crystals, because of the optical transparency in the visible range. In this work, we conduct a comprehensive study, synergizing numerical modeling and experimental efforts, to reveal the optical contrast signatures of h-BN on various substrates. We demonstrate that the visualization and thickness identification based on optical contrast are applicable to mechanically suspended h-BN crystals, without interference enhancement from the commonly used oxidized silicon (SiO2 on Si) wafer. The understanding and protocols developed here offer a non-contact, rapid thickness estimation method for h-BN thin films on suspended device platforms, where conventional contact methods such as scanning probes are incapable or cumbersome. The results and methods presented here also serve as valuable guidelines for engineering the h-BN platform towards 2D nanophotonic and optoelectronic applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Two-dimensional (2D) hexagonal boron nitride (h-BN) layers isolated from its bulk crystal inherit the ultrawide electronic bandgap (~5.9 eV) [1], excellent chemical and thermal stability [2,3]. It thus has been widely incorporated into van der Waals heterostructures as atomically smooth dielectric layers for enabling high-performance 2D electronic devices. The outstanding mechanical properties of h-BN, including a theoretical Young’s modulus as high as EY~780 GPa and a breaking strain limit up to ~22% [4,5], have also been exploited to develop robust resonant nanoelectromechanical systems (NEMS) [6,7].
Beyond the established works in electronics and mechanics, growing research efforts have been contributed to exploring the exotic optical and photonic characteristics of h-BN, following recent reports of hyperbolic phonon-polaritons and robust quantum emitters [8–10]. h-BN is a representative hyperbolic material: a crystal possessing the in-plane and out-of-plane components of the dielectric tensor having the opposite signs [11]. The hyperbolic nature of h-BN, along with strong phonon resonances, could lead to near-field optical imaging, guiding, and focusing applications over a broad spectral range in the technologically important infrared (IR) band. The wide bandgap of h-BN has been demonstrated beneficial to hosting optically active defect centers that strongly emit single photons even at room temperature [10,12,13]. Although the crystallographic and photophysical properties are still underinvestigated [14,15], these robust quantum emitters may hold solid potential for integrated on-chip quantum nanophotonics, optomechanics, cavity quantum electrodynamics (QED) and quantum sensing.
The investigation and device development of layered atomic crystals, including but not limited to h-BN, generally start with thickness identification, because their optical properties highly depend on the number of layers [10,16,17]. Especially for the flakes isolated by mechanical exfoliation and devices enabled by various layer transfer and stacking, it is critical to identify the ones with desired thickness out of a hatch of flakes. Optical reflectivity contrast has been demonstrated as a simple, fast, and noninvasive approach to providing quantitative thickness information of graphene [18,19], transition metal dichalcogenides (TMDCs) [20,21], and h-BN [22,23]. Most of these studies have focused on 2D crystals supported by oxidized Si substrates (e.g., 290 nm SiO2 on Si), which can produce interference to enhance the optical contrast [18,24]. However, atomically-thin h-BN exhibits little optical contrast, less than 1.5% for a monolayer, even with these optically engineered oxidized substrates, due to the ultrawide bandgap and zero opacity in the visible spectrum [22]. Moreover, the SiO2 on Si substrate is not an ideal platform for emerging photonic applications. Despite the wide bandgap and excellent dielectric properties, h-BN has a relatively small refractive index of n = 1.8. The thin oxidized layers of 90 to 300 nm are not adequate to prevent the light from leaking to the underlying bulk Si with a refractive index n = 4 in the visible range. Further, the detrimental interactions, such as nonradiative recombination, charge transfer, and excitonic transitions, between h-BN and substrates underneath can lead to spectral diffusion and blinking issues of emission [25,26].
Therefore, it is desirable and constructive to explore the light-matter interaction in h-BN crystals free from the conventional oxidized Si substrate. Here, we take the initiative to investigate the optical contrast signatures of h-BN on various substrates, including polydimethylsiloxane (PDMS) and bare Si. In synergy with the numerical modeling, experimental efforts have been made to scrutinize the optical contrast of h-BN on suspended device platform. By analyzing the red (R), green (G), and blue (B) values of optical microscopic images, we extend the capability of optical contrast methods for thickness characterization to suspended 2D materials. This work demonstrates a noninvasive approach to rapidly characterizing the thickness of h-BN in the scenarios and device platforms that conventional contact-mode measurements and scanning probes (e.g., atomic force microscopy (AFM)) become incapable or highly undesirable. The present results also provide criteria for better engineering the dielectric environment and device geometry to achieve high-performance photonic and optoelectronic components based on h-BN and other 2D materials beyond.
2. Materials and methods
In order to study the optical contrast of suspended h-BN thin layers, a suite of specially developed, completely dry exfoliation and transfer techniques are employed [27], as illustrated in Fig. 1(a). h-BN layers of a few nanometers thick are mechanically exfoliated from a high-quality bulk h-BN and pressed onto polydimethylsiloxane (PDMS) stamps. After exfoliation, we transfer the h-BN nanosheets, with controlled alignment, onto pre-defined device features (microtrenches and cavities) on Si or SiO2-on-Si substrates with the aid of a micromanipulator to achieve mechanically suspended structures.
Fig. 1 (a) Real color and inverted color microscopy images of a h-BN flake, and schematic illustration of PDMS assisted dry transferring of h-BN crystals onto pre-patterned device platform. The color difference comes from the thickness variation of the flake. (b)-(d) Schematic diagrams of multi-reflection model for h-BN on PDMS, bare Si, 290 nm SiO2/Si and corresponding color contour plots of the optical contrast as a function of both h-BN thickness and excitation wavelength calculated by the Fresnel equations. The schematic light path is simplified without refraction for the nearly normal incident condition.
The patterned Si substrate starts with a 4-inch Si-on-insulator (SOI) wafer consisting of a 12-µm Si top layer and a 2-µm SiO2 layer. Standard photolithography and deep reactive ion etching (DRIE) are utilized to pattern the SOI wafer with a spatial resolution of 1 µm. After buffered oxide etching (BOE) to remove the oxide layer underneath, the Si wafer is released in critical point dryer (CPD) to prevent stiction. As-fabricated Si substrate contains arrays of holes with diameters of 4–5 µm and a narrow microtrench with a width of 2 µm, and the entire patterned Si structure is suspended with an air gap of ~2 µm. The gap between the transferred h-BN and the etched surface of the bottom substrate is ~12 µm and ~14 µm before and after releasing. Similarly, the drumhead substrates are made from a Si substrate with a 290 nm thermally grown SiO2 layer. Standard contact lithography is applied to define the circular hole patterns on photoresist coated SiO2. The unprotected SiO2 is completely removed and the underlying Si is also partially etched by using reactive ion etching (RIE), resulting in an air gap measured to be 2080 nm.
The dry transfer techniques applied here enable the fabrication of pristine suspended h-BN free from wet chemistry contamination compared with the conventional wet transfer methods [28,29]. In addition, after all the device fabrication and transfer steps, we conduct high-temperature annealing up to 850 °C to further minimize the potential chemical contaminations and enhance the adhesion between h-BN and the patterned substrates.
The optical contrast modeling is performed using a program developed in MATLAB environment based on the Fresnel equations. The detailed calculation follows the guidelines presented in our previous work and other previous reports [6,30]. The contrast spectrum C(λ) of h-BN on SiO2/Si substrate has been described with Eqs. (1–4) under normal incident conditions [17]
In the above equations, R stands for the reflected light intensity and r represents the relative indices of refraction at each interface; n0, n1, n2 and n3 are the refractive indices of air, h-BN, SiO2 and Si; d1 = N × d and d2 are the thicknesses of h-BN and SiO2, respectively. We use the thickness d = 0.33 nm for the monolayer h-BN, and N is the number of layers. For h-BN, only the real part of the refractive index (n1 = 1.8) is taken into consideration; but for SiO2 and Si, wavelength dependent complex refractive indices are applied for calculation [31,32].
To further evaluate the optical contrast directly from the optical microscopic images, we employ the method reported in [33]. The average contrast of RGB channels are obtained by integrating the R(λ) values over 590 nm–720 nm (R), 520 nm–590 nm (G), and 435 nm–520 nm (B), following the wavelength ranges of the Bayer RGB filter in the commercial charge-coupled device (CCD) and then applying to the Eq. (1). The modeling results of the aforementioned steps are exemplified in Fig. 2. The contrast spectrum and integrated RGB values for the substrates other than SiO2/Si are derived from the general equations with similar manners, by substituting the refractive index n0 with the value of PDMS, Si or air for the suspended cases, respectively.
Fig. 2 Typical modeling results of h-BN supported on a SiO2/Si substrate. (a) Reflectance spectra of 1–10 layers of h-BN calculated from Eq. (2). (b) Contrast spectra of 1–10 layers of h-BN calculated from Eq. (1). (c) Integrated contrast spectra of 1–1000 layers of h-BN over RGB channels and zoom-in spectra for 1–10 layers. (d)–(f) The dependence of optical contrast on the dielectric SiO2 layer thickness and air gap thickness under different sample configurations. The thickness of h-BN is set as 15 nm (45 layers) for (d), 30 nm (91 layers) for (e), and 188 nm (570 layers) for (f).
The experimental contrast values are attained based on the optical microscopic images captured by an Olympus MX50 microscope equipped with a 50× objective and a 5MP CCD. Since the images are captured under the reflection mode, the intensity of each pixel I, scaled using 256 gray levels (0 means darkest and 255 means brightest), is directly proportional to the reflected light intensity. The color images are split into R, G, and B channels by following the Bayer filter ranges mentioned above via a built-in function in open-source software ImageJ, and single-channel images are exemplified as Fig. 3(a), 3(b), 5(a) and 5(e). The gray values over areas of interest are also read out by ImageJ and supplied to the following equations to calculate the contrasts for individual color channel.
Fig. 3 Optical microscopy images (splitting channels) of a h-BN flake on (a) PDMS and transferred onto (b) the patterned SiO2/Si substrate. (c) Gray values measured from each channel along the orange dashed line in (a) & (b). (d) Atomic force microscopy trace of the flake on SiO2/Si along an identical line as the orange dashed line. (e) Measured optical contrast traces of each channel derived from SiO2/Si data shown in (c). (f) The theoretical and experimental optical contrast of h-BN on PDMS and SiO2/Si. The red triangles, green circles, and blue squares with error bars mark the measured optical contrast values averaged over the h-BN region highlighted in (c) & (e) for channel R, G, B, respectively. The SiO2 thickness of 287 nm is used for the theoretical calculation, giving a better match. The black dashed line indicates the thickness of 15 nm (45 layers) position in the contrast spectra. The scale bar represents 10 µm.
It is worth mentioning that the optical contrast calculated for each color channel is a relative intensity (reflection) ratio between the interested h-BN region and substrate within a single microscopic image. The effects from wavelength-dependent intensity distribution of the light source and wavelength-dependent responsivity of the CCD can be minimized. However, the dispersion from the optical path and sample geometry may have contributions to the deviation of the measured contrast values, which will be elaborated in the section below.
3. Results and discussions
For lack of optical absorption in the visible spectral region, the optical contrast of h-BN originates mainly from the changes in the optical path. Figure 1 unambiguously reveals the effects of the dielectric environment on the optical contrast of h-BN. For the thermally oxidized Si substrate, the 290 nm SiO2 engages in multiple reflections with the incident light, producing interferences that lead to enhancement or attenuation of the light outcoupling. Hence, both positive, negative, and zero optical contrast can be observed in the spectra (Fig. 1(d)). On the contrary, for h-BN on PDMS or bulk Si, optical contrast only presents negative or positive values (Fig. 1(b) & 1(c)), relying on the sign of the relative refractive indices r2.
When the number of h-BN layers is lower than ~200 (Fig. 1(b)–(c), middle panel), the absolute values of optical contrast rise as the number of layer N increases for the ones on PDMS and bare Si. However, as the number of layers exceeds ~300 (Fig. 1(b)–(d), bottom panel), optical contrast periodically oscillates for all these three configurations studied in Fig. 1, suggesting the interference from h-BN itself starts to play a role. For example, the h-BN flakes on SiO2/Si with number of layers of 700 (231 nm) share similar optical contrast as the ones of 200 layers (66 nm) at 550 nm excitation (Fig. 1(d)). It indicates the thickness determined from optical contrast measurement with monochromatic or narrow band light sources may seriously deviate from the real value. Therefore, in this study, we implement the measurement based on white-light microscopy images and utilize all the three channels, which can give an exclusive combination of RGB contrast values for each thickness (Fig. 2(c)).
Figure 3 shows a typical h-BN flake on PDMS stamp and then transferred onto the patterned SiO2/Si substrate with circular holes. The reflected light is significantly intensified by the interferometric cavity formed with the SiO2 layer, as the numerical modeling predicted (Fig. 3(c)). The thickness of this flake has been confirmed by atomic force microscopy (AFM) measurement as 15 nm. Comparing the experimental measurement and theoretical calculation (Fig. 3(e) & 3(f)), we can see the optical contrast values match well for certain color channels, depending on the substrate and interference configuration. For the PDMS substrate, green and red channels present good agreement; while for the SiO2/Si substrate, the blue and red channels exhibit less deviation from the theoretical calculation. The aforementioned dispersion effects induced by the optical components within the light path and the thickness and flatness variations of the substrate may play roles here. Figure 2(d) illustrates the optical contrast dependence on the thickness of SiO2 layer. It is clear that the green channel will suffer more deviation, if the SiO2 layer thickness is slightly different from the standard 290 nm. With the same h-BN thickness and sample configuration, the absolute optical contrast of green channel for a 280-nm thick SiO2 is half the value of a 290-nm one.
For suspended h-BN, thickness dependent optical contrast is summarized in Fig. 4. Two different contrast values have been evaluated, as illustrated in Fig. 4(a) and 4(b). In configuration (a), the contrast value is deduced from the difference between suspended and suspended h-BN (Fig. 4(e) & 4(f)); while, in configuration (b), the contrast is derived from the difference between suspended h-BN and surrounding air gap (Fig. 4(c) & 4(d)). For configuration (b), regardless of the Si or SiO2/Si substrate, the optical contrast oscillates between −1 to 1. On the other hand, extremely large negative contrast values can be obtained from configuration (a).
Fig. 4 Schematic diagrams of multi-reflection model and optical microscopy images of h-BN suspended over patterned (a) SiO2/Si and (b) Si substrates. (c)–(d) Optical contrast plots of suspended h-BN in configuration (b). (e)–(f) Optical contrast plots of suspended h-BN in configuration (a). The schematic light path is simplified without refraction for the nearly normal incident condition. The scale bar represents 20 µm.
The experimental results of suspended h-BN are presented in Fig. 5. Both supported and suspended areas show clear optical contrast, but with opposite sign for each channel. For the flake suspended over a SiO2/Si drumhead cavity with a thickness of 30 nm confirmed by AFM, the optical contrast from the supported region agrees well with the theoretical calculation; however, the value measured from the suspended region shows discrepancy in the red channel (Fig. 5(b)–5(d)). Based on the calculation, the optical contrast of the red channel indeed exhibits higher dependence on the thickness of the air gap for h-BN suspended over SiO2/Si substrate, as shown in Fig. 2(e). Moreover, the chemical etching process of microholes and microtrenches employed here cannot guarantee optical flatness of the bottom surface. The surface roughness and the resulting scattering effects also lead to mismatch between the measurement and calculation, of which the impact can hardly be quantitatively evaluated and compensated.
Fig. 5 Optical microscopy images (splitting channels) of h-BN flakes suspended over patterned (a) SiO2/Si and (e) Si substrates. Measured contrast traces of (b) & (f) supported areas and (c) & (g) suspended areas along the orange dashed lines in optical images. (d) and (h) Calculated contrast plots with solid lines (solid symbols) for supported cases and dashed lines (open symbols) for suspended cases. The red triangles, green circles, and blue squares with error bars mark the measured contrast values averaged over the h-BN region highlighted in (b)–(c) & (f)–(g) for channel R, G, and B, respectively. The SiO2 thickness of 287 nm is used for the theoretical calculation, giving a better match than using the nominal 290 nm. The black dashed lines indicate the thickness of 30 nm (91 layers) position in (d) and 188 nm (570 layers) position in (h). The scale bar represents 10 µm.
By employing the method developed above, the thickness of the h-BN suspended on patterned Si substrate shown in Fig. 5(e) can also be estimated as ~188 nm, based on the optical contrast values derived from Fig. 5(f)–5(h). Again, the deviation presented can be explained by the thickness variation of air gap shown in Fig. 2(f), the contrast values in blue and green channels oscillate more intensively with the thickness. The geometry parameters, such as dielectric layer and air gap thickness, extracted from scanning electron microscopy measurement would be helpful to achieve a more accurate estimation of the h-BN thickness.
4. Conclusions
In summary, by combining numerical modeling and experimental measurement, we have performed optical contrast characterization of both substrate-supported and mechanically suspended h-BN thin layers on different device-oriented substrates and platforms beyond the commonly used SiO2-on-Si substrate. The present results demonstrate the capability of optical contrast measurement in thickness identification of h-BN on suspended device platform, which is often challenging and unsuitable for AFM measurement. The effects of surrounding dielectric environment on the light coupling of h-BN investigated here would also provide useful insights for future design and development of h-BN photonic structures and devices.
Funding
National Science Foundation (EFMA #1641099).
Acknowledgments
We thank the financial support from the National Science Foundation via the EFRI ACQUIRE program (Grant: EFMA #1641099) and its Supplemental Funding through the Research Experience and Mentoring (REM) program.
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