Graphene/hBN heterostructures can be considered as one of the basic building blocks for the next-generation optoelectronics mostly owing to the record-high electron mobilities. However, currently, the studies of the intrinsic optical properties of graphene are limited to the standard substrates (SiO2/Si, glass, quartz) despite the growing interest in graphene/hBN heterostructures. This can be attributed to a challenging task of the determination of hBN’s strongly anisotropic dielectric tensor in the total optical response. In this study, we overcome this issue through imaging spectroscopic ellipsometry utilizing simultaneous analysis of hBN’s optical response with and without graphene monolayers. Our technique allowed us to retrieve the optical constants of graphene from graphene/hBN heterostructures in a broad spectral range of 250–950 nm. Our results suggest that graphene’s absorption on hBN may exceed the one of graphene on SiO2/Si by about 60%.
Combination of hexagonal boron nitride (hBN) with graphene into van der Waals heterostructures attracted much attention at a recent time1,2,3,4. hBN is an insulator with a large bandgap that possesses a honeycomb crystal structure commensurate to the one of graphene, but with a slight mismatch of the lattice constants. When assembled into such heterostructures in its high-quality single-crystal form, it provides a suppression of external disorder in graphene and an enhancement of electron mobilities. Thus, it has been proven to be a supreme substrate5, encapsulating layer6,7, and tunneling barrier8,9 in graphene-based electronic devices. Likewise, hBN was also found to be an irreplaceable constituent in graphene-based optoelectronic devices, such as photodetectors10,11, DUV electroluminescent devices12, THz optoelectronic elements13,14, and even light bulbs15. From the standpoint of optical properties, it is known that the integration of hBN with graphene may boost an infrared spectral range absorption when assembled into oriented moiré heterostructures16,17. Several works18,19,20 also report on studies of the total optical response from graphene/hBN heterostructures. Nevertheless, the influence of hBN substrate or encapsulation on the intrinsic optical response of an almost transparent graphene21,22 in the visible spectral range yet remains undetermined.
At the same time, the optical properties of graphene on standard substrates, such as SiO2/Si, quartz, and a variety of glasses were thoroughly investigated by spectroscopic ellipsometry23,24,25,26,27,28,29. Despite the non-identical fitting approaches and graphene samples (exfoliated or chemical vapor deposited), all works agree on the universal value of the absorption, which is defined by the fine-structure constant α. Nonetheless, several works16,17,30 argue that this situation may change in the presence of hBN.
In this work, we present an experimental investigation of the optical properties of graphene on hBN substrates through the imaging spectroscopic ellipsometry technique. We demonstrate an emergence of anomalous optical constants from monolayer graphene on top of a thick hBN and compare our results with the ones on one of the standard substrates (SiO2/Si) from the literature and of our own. We also demonstrate a highly sensitive approach to the detailed analysis of ellipsometric parameters and optical response of graphene, which can potentially be easily extended to other two-dimensional materials.
Before the optical measurements, we confirmed the quality of our exfoliated graphene samples on SiO2/Si and hBN substrates by analyzing their structural properties. Figure 1a, b displays the schematics along with an optical image of one of our samples prepared on SiO2/Si substrate through standard mechanical exfoliation technique. The acquired Raman spectrum suggests that it is a monolayer with a relative intensity ratio of 2D to G peaks larger than 2 (see inset of Fig. 1b). Figure 1c shows the results of rigorous examination of the surface morphology of our samples by atomic force microscopy (AFM). The roughness histogram of our SiO2 substrates show a standard deviation of σSiO2 ~136 pm for a fitted Gaussian, which is slightly smaller, but in general consistent with the typical values reported elsewhere5,31. On the other hand, in the case of hBN substrates, we assemble another set of samples on transparent substrates (glass) through the dry-transfer technique utilizing polycarbonate (PC) films32,33. Figure 1d, e demonstrates the schematics and an optical image of one of the studied heterostructures. The inset of Fig. 1e demonstrates its Raman response proposing a composition of monolayer graphene with a thick hBN layer. Performed AFM scans reveal that our samples are free of nanoscale distortions or wrinkles of any kind (see Fig. 1f). A histogram of the roughness of the hBN layer shows a standard deviation of a fitted Gaussian measured to be σhBN ~37 pm, which is about three times smaller than for SiO2 substrates and is also consistent with the typical values reported elsewhere (see inset of Fig. 1f)5,31. A prompt comparison of standard derivations measured for our graphene monolayers on SiO2 and on hBN substrates confirms that those precisely nest on the surfaces of whatever they are placed on (see insets of Fig. 1c, f). Thus, in the case of hBN substrates, we obtain ultraflat graphene layers with atomic smoothness.
We used imaging spectroscopic ellipsometry technique to characterize the optical response of our graphene monolayers on both substrates. The schematics of our experimental setup is shown in Fig. 2a. The sensitivity of our technique allows us to study exfoliated and dry-transferred flakes in miniature regions of interest (10 μm2) within the same field of view34. For both types of substrates, we performed a step-by-step analysis of the optical responses from the samples with and without graphene layers included (see “Methods” for further details). In the case of graphene on hBN substrate, the measured and calculated ellipsometric parameters Ψ and Δ are shown in Fig. 2b, c, respectively. Those are in a good agreement as the ones for graphene on SiO2/Si (see Supplementary Fig. 1).
To obtain the dielectric function of graphene from the acquired ellipsometric spectra, we used the Drude–Lorentz oscillators model (see “Methods”), which considers the optical response of quasi-free electrons (Drude oscillator), and graphene’s van Hove singularity for π-to-π* interband transitions (Lorentz oscillator)23.
The determined real Re[ε] and imaginary Im[ε] parts of the dielectric function of graphene on both substrates are shown in Fig. 2d, e, respectively. Unexpectedly, both parts of dielectric function of our ultraflat graphene on hBN (sample 1) are noticeably higher than for SiO2 substrate (sample 2) in the whole interval of measured wavelengths. Additional investigations demonstrate a good repeatability (sample 3). To further validate our findings, we evaluated the transmittance spectrum of graphene/hBN heterostructure accounting for the acquired anomalous optical response of graphene and compared it to the measured one. Despite the observed excessive values of graphene’s dielectric function, the theoretical transmittance spectrum matches well with the experimentally observed one as it can be seen in Fig. 2f. In addition, to rule out the possibility that ambiguity of the used optical constants of hBN could have caused such an increment in graphene’s optical response, we separately verified the optical response from the thick hBN flake using the same micro-transmittance technique (see Supplementary Fig. 2).
In general, the optical responses from atomically thin layers are responsible for a very limited contribution compared to the substrate in the acquired ellipsometric spectra, which causes the accuracy of the measurements to fall. This comes to nearly an extreme case for monolayer graphene.
To enhance the sensitivity of our spectroscopic imaging technique, we assembled a specific configuration of layers giving rise to a larger difference in optical responses from the substrate with and without the graphene layer, and thus, to a higher sensitivity of ellipsometric parameters to graphene optical constants.
This is achieved in the vicinity of topological phase singularities, which arise owing to intersection of graphene optical constant’s dispersion with the substrate zero-reflection surface35. Here, we dry-transferred another graphene/hBN heterostructure on top of a thick 200 nm Au film to ensure an appropriate form of a cavity, shown in the schematics and the optical image in Fig. 3a, b, for the realization of topological phase singularity in the vicinity of ellipsometer’s best sensitivity (around ~500 nm). The thickness of our hBN flake is 152 nm, which leads to a topological phase singularity at a wavelength of 477 nm. The corresponding ellipsometric parameter maps are presented in Fig. 3c, d.
As expected, Fig. 3d shows a noticeable difference between graphene/hBN/Au and hBN/Au structures in Δ owing to constructed phase topology. As a result, at this point, we have an increased sensitivity to graphene’s optical response. Hence, this allows us to make a unique fit of the optical absorption of our graphene. Here, we calculated the difference between calculated and measured ellipsometry spectra with respect to graphene absorption in terms of mean squared error (MSE). Figure 3e shows the resulting dependence of MSE of our measurements. Surprisingly, it reaches a minimum at values that are larger than πα, where α is the fine-structure constant21,22, validating our high dielectric permittivity of graphene on hBN presented in Fig. 2d, e. This suggests that the typical values of absorption could therefore be mended for our ultraflat graphene on hBN substrate.
The corresponding dependences of measured ellipsometric parameters on the wavelength in the vicinity of our topological phase singularity are demonstrated in Fig. 3f, g for Ψ and Δ, respectively. Insets demonstrate the apparent variation between the parameters evaluated for monolayer graphene accounting for two types of substrates studied. Notably, the variation is evidently smaller for the case of a graphene layer placed on an hBN substrate.
Figure 4 demonstrates acquired dependencies of refractive indices, extinction coefficients, and the intrinsic absorbance of our exfoliated graphene samples on both types of substrates (SiO2/Si and hBN) in comparison with literature data24,26,27 (exfoliated graphene optical constants on a standard SiO2/Si substrate). Despite the non-identical fitting approaches, all works report on universal optical responses for the case of graphene on SiO2/Si, including our measurements.
On the other hand, graphene on hBN demonstrates substantially higher optical constants (Fig. 4a, b), compared to graphene on SiO2/Si. For instance, graphene’s refractive index and extinction coefficient is about 20 and 40% higher on hBN than on SiO2/Si, which may be of use for the enhancement of absorption in graphene-based photonic devices36,37. In the case of an excitonic peak at 270 nm, the obtained behavior can be explained by significant difference in static dielectric permittivities of SiO2 (εSiO2 ~3.8) and hBN (εhBN ~7)38, which strongly affects excitonic optical response39. However, the situation in the near-infrared range is more complicated since even high doping of graphene40 should not affect its absorption in these spectral intervals (see Supplementary Fig. 3 and Supplementary Note 1).
Nevertheless, angle-resolved photoemission spectroscopy studies30 show that substrates with high dielectric permittivities can substantially modify the fine-structure constants owing to emergence of electron–electron interactions. Indeed, our ab initio calculations suggest that even a slight change in the interlayer distance between graphene and hBN may significantly affect the intrinsic optical response (see Supplementary Fig. 4 and Supplementary Note 2). Other approaches also suggest notable growth of optical constants in graphene/van der Waals material heterostructures41,42,43,44. Nevertheless, further research is required to explain the physical mechanisms of such an increase in graphene’s absorption when placed on top of hBN substrate, and other van der Waals materials.
Integration of hBN and graphene into van der Waals heterostructures results in emergence of extraordinary electronic properties. Therefore, it is of fundamental and practical interest to study the influence of hBN on graphene’s optical properties. Our imaging spectroscopic ellipsometry measurements showed that hBN substrates could substantially enhance the absorption in graphene by ~60% in the broad spectral range (250–950 nm). Hence, those are more suitable than standard SiO2/Si substrates for a variety of photonic applications, where absorption plays a key role, such as photo detection, modulation, and sensing. We attribute this behavior to electron–electron interactions arising due to high static dielectric response of hBN. From a broader perspective, our studies reveal that the universal optical absorption of bare and pristine graphene can be reconstructed in the dielectric environment.
We performed O2 plasma-cleaning for all the types of substrates to enhance the adhesion with two-dimensional layers prior to exfoliation. Next, the substrates were heated up to 120 °C and the standard mechanical exfoliation from bulk graphite and hBN crystals was performed using commercial scotch tapes from “Nitto Denko Corporation”. To integrate graphene monolayers with hBN, we used a polymer-based modified dry-transfer technique32,33 established on utilization of double thin films; polydimethylsiloxane (PDMS) and polycarbonate (PC).
Imaging spectroscopic ellipsometry
To analyze the optical constants of graphene samples, we used commercial imaging spectroscopic ellipsometer Accurion nanofilm_ep4 in the nulling operational mode. In our imaging ellipsometer, the spot size is about 2 mm in diameter. The high resolution is achieved not by focusing the light as it is usually done in classical ellipsometers, but by recording the image on a camera as it is shown in Fig. 3c, d. As a result, here, each of the pixels record the ellipsometric parameters, and allow us to take into account only the pixels that correspond to our sample. To avoid backside reflections, we used beam cutter following the approach presented by Funke and colleagues45. Ellipsometry spectra were recorded for the spectral range from ultraviolet (250 nm) to near-infrared (950 nm) for the samples on both types of substrates. During the measurements, we simultaneously recorded the ellipsometric signals from bare substrate and substrate with graphene. It allows us to determine the precise optical model of the substrate to eliminate errors arising from slight inconsistencies between literature optical constants and real one for substrate material (Si, SiO2, glass, and hBN). Note that for the individual ellipsometric parameter analysis of our hBN substrates, we followed the algorithm described in Supplementary Note 2 of our recent work34. Afterward, we fitted graphene optical constants with Drude–Lorentz optical model23:
where ε is the dielectric permittivity of graphene, E is the photon energy in eV, ε1∞ is the offset of the real part of dielectric permittivity, which takes into account absorption peaks for higher than measured energy range, ℏ is the reduced Planck’s constant, ε0 is the vacuum dielectric constant, ρ is the resistivity in Ω cm, τ is the scattering time in second, A is the Lorentz oscillator strength, B is the Lorentz broadening parameter, and E0 is the Lorentz peak central energy. In accordance with AFM microscopy results (see Fig. 1c, f), which show negligible roughness, we do not account for the roughness of our samples.
Atomic force microscopy
The morphology of all our samples was examined by AFM (NT-MDT Ntegra II). All measurements were performed in a dry state at room temperature using HybriD mode. AFM images were acquired using silicon tips (ScanSens, ETALON, HA_NC) with an elastic constant of 3.5 N/m and a resonance frequency of 140 kHz. The areas of 1 μm2 with 400 pixels per line were obtained at a scanning rate of 0.2 Hz for all samples. The surface height distributions were extracted from areas of 0.2 μm2 using Gwyddion software.
The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.
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This work was supported by Russian Science Foundation project No. 21-79-00218 and Ministry of Science and Higher Education of the Russian Federation Agreement No. 075-15-2022-1150 (topological phase singularity studies). The ab initio calculations were performed using resources provided by to the Joint Supercomputer Center of the Russian Academy of Sciences.
The authors declare no competing interests.
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Toksumakov, A.N., Ermolaev, G.A., Tatmyshevskiy, M.K. et al. Anomalous optical response of graphene on hexagonal boron nitride substrates. Commun Phys 6, 13 (2023). https://doi.org/10.1038/s42005-023-01129-9