Grazing-Incidence SEM Characterization of MoS₂ Nanosheet Coatings Prepared by Liquid-Phase Exfoliation

Highlights

What are the main findings?

• Grazing-incidence SEM strongly enhances surface-sensitive contrast in ultrathin MoS₂ coatings.
• Sobel-based edge analysis quantitatively confirms increased morphological information content.
• MoS₂ colloids predominantly contain mono- and few-layer nanosheets after settling.

What are the implications of the main findings?

• Simple stage tilting enables surface-sensitive SEM without hardware modification.
• Method provides reliable morphological assessment of ultrathin 2D coatings.
• Approach is applicable to other layered coatings and nanostructured films.

Abstract

Ultrathin two-dimensional (2D) coatings exhibit functional properties that are strongly defined by morphological features such as sheet edges, fracture sites, overlaps, folds, and local thickness variations, which are often difficult to resolve using conventional scanning electron microscopy (SEM) configurations. Here, we introduce a grazing-incidence SEM approach based on controlled sample tilting close to 90° for enhancing surface sensitivity and morphological feature detectability in ultrathin coatings. The method is proved on colloidal MoS₂ nanosheet coatings prepared by liquid-phase exfoliation. Optical absorption spectroscopy confirms the presence of mono- and few-layer MoS₂ nanosheets in the dispersion, confirming the ultrathin nature of the deposited coating. Compared to standard 0° imaging, grazing-incidence SEM reveals clearer boundaries and discontinuities. Quantitative Sobel-based image analysis supports these observations, showing an increase in edge density from 5.9% to 7.6% and in average gradient magnitude from 0.151 to 0.172 a.u. under grazing incidence, indicating a higher amount of retrievable morphological information. The proposed approach relies only on standard stage tilting and provides a broadly applicable framework for the surface-sensitive morphological characterization of ultrathin 2D coatings and thin films.

1. Introduction

Ultrathin coatings based on two-dimensional (2D) nanomaterials are increasingly used to enable advanced surface functionalities [1,2], including optical, electronic, catalytic, and protective properties [3]. In such systems, performance is often determined by morphological details, such as sheet edges, overlapping regions, folds, fractures, and local thickness variations, that are distributed over micrometric lateral dimensions while extending only a few atomic layers in the out-of-plane direction. In functional 2D coatings, electronic and optical properties are highly sensitive, not only to thickness and stacking order but also to interfacial proximity effects. In van der Waals heterostructures, coupling with adjacent layers or substrates can significantly modify the electronic band structure, spin–orbit interaction, and valley-dependent properties, thereby enabling emerging nanoelectronic and valleytronic functionalities [4].

Reliable access to this morphological information is therefore essential for understanding and optimizing the behavior of 2D coatings. However, imaging ultrathin and multiscale coatings remains particularly challenging [5]. Conventional scanning electron microscopy (SEM) geometries, while offering excellent depth of field and easiness of sample preparation, often lack sufficient surface sensitivity to discriminate nanoscale thickness variations and edge-related features in atomically thin layers [5,6]. As a result, critical morphological features may remain poorly discernible or ambiguous when standard normal-incidence SEM observations are adopted. This limitation is particularly relevant for ultrathin 2D coatings, where micrometric lateral dimensions coexist with nanometric thickness [7]. Under conventional SEM configurations, thickness-related cues and edge features may remain difficult to resolve, motivating alternative surface-sensitive observation strategies.

In this context, the development of alternative observation geometries capable of enhancing surface sensitivity is becoming increasingly relevant. A particularly promising approach is the use of grazing-incidence SEM, a technique inspired by natural visual strategies and optimized for highlighting tiny topographical and morphological features that are otherwise undetectable [8,9]. Such an approach is especially useful when dealing with ultrathin coatings, interfaces, or 2D nanostructures, where the interplay between micro- and nanoscale features strongly influences material performance.

By tilting the sample relative to the electron beam-detector axis, the interaction volume of primary electrons (PE) is confined closer to the surface, thus promoting near-surface secondary electron (SE) emission [10]. Since image quality is directly correlated with the number of SE reaching the detector, an increase in contrast upon tilting implies a higher SE yield (number of SE per PE). This enhancement arises from the geometry of electron–sample interaction, which can be optimized by adjusting the sample inclination within the limits imposed by the depth of field [11,12,13]. Beyond improving conventional imaging, this methodology can provide fundamental morphological insights into materials whose function relies on nanoscale organization, such as catalytic surfaces, functional coatings, or layered 2D systems like MoS₂. Its application thus bridges the gap between classical SEM imaging and advanced morphological analysis, offering a versatile tool for materials science and biomimetic engineering.

This geometry bears a conceptual analogy with natural visual strategies based on grazing observation, widely exploited by living organisms to enhance the perception of surface textures and edges [9]. Importantly, in SEM, this configuration does not operate through shadow formation, as in optical systems, but through the maximization of surface-sensitive electronic signals.

Beyond a simple increase in image brightness, grazing-incidence SEM has the potential to modify the type of morphological information that can be extracted from ultrathin coatings. Morphological features may become more readily detectable due to the enhanced sensitivity to surface-localized electron emission. This aspect is particularly relevant for 2D coatings, where the distinction between monolayer, few-layer, and multilayer regions is often crucial but difficult to establish using standard SEM configurations alone [14,15,16].

In this work, we propose grazing-incidence SEM as a surface-sensitive imaging strategy for the morphological analysis of ultrathin 2D coatings. We evaluate the impact of this geometry in terms of morphological feature detectability, supported by complementary image-analysis descriptors that capture edge-related information. Colloidal MoS₂ coatings are employed as a representative case study, owing to their layered structure and relevance in functional coatings. Optical absorption spectroscopy validation of the ultrathin nature of the deposited nanosheets, providing an independent assessment of the material structure. The methodology presented here is general and can be extended to a broad range of 2D coatings and thin-film systems, offering a simple and non-destructive route to enhanced surface-sensitive morphological characterization.

2. Materials and Methods

2.1. Preparation and Optical Characterization of MoS₂ Colloidal Suspensions

Owing to its layered structure, MoS₂ can be exfoliated by the combined action of mechanical shear and sonoacoustic energy to originate monolayer and/or few-layer nanosheets. Commercial powder of MoS₂ (98% by weight, average size of 4–5 µm, Werth-Metall, Grammetal, Germany) has been used as starting material for the preparation of colloidal suspensions. Morphology and size of the as-received powder have been investigated by SEM imaging at different magnifications (see Figure 1a,b). The chemical composition of this powder has been established by energy-dispersive X-ray spectroscopy (EDS, see Figure 1c). Accordingly, the MoS₂ grains have a layered structure and contain a small amount of copper and iron as impurities.

In the preparation of colloidal suspensions, the as-received MoS₂ powder underwent preventive mechanical treatment. This mechanical treatment was based on the application of shear stress to the basal planes of the micrometric lamellar crystals to convert them to small platelets. Internal coherency in these small crystalline platelets results much lower than in the starting micrometric lamellas, thus allowing their easy sonoacoustic exfoliation. In particular, the as-received powder was slightly pressed between two circularly moving surfaces of polytetrafluoroethylene (PTFE). While sandpaper has been previously reported for a similar purpose [10], PTFE was preferred here to minimize contamination. This mechanical pretreatment is of pivotal importance, as sonication alone does not effectively induce exfoliation.

Following mechanical pretreatment, the powder was dispersed in high-purity acetonitrile (CH₃CN, HPLC-grade, J.T. Baker, London, UK) [11] at an initial concentration of 5 g·L⁻¹. The mixture was magnetically stirred and subsequently sonicated (ultrasonic bath with built-in heating SONOREXT^M SUPER, Bandelin, Berlin, Germany) in order to convert the MoS₂ platelets to a mixture of monolayer and few-layer nanocrystals. Sonication was performed for 2 h, taking the liquid sample in a closed glass vial. A known volume of such stable suspension was further diluted by pure acetonitrile (1:10 by volume); then, it was sonicated under the same experimental conditions (sonication bath at room temperature) for 2 h and allowed to settle in a glass vial for a couple of weeks. The final supernatant concentration, separated by decanting, was 0.1 g·L⁻¹, as found by simple system weighting after solvent removal by evaporation.

The concentrated MoS₂ colloidal suspension was stable due to electrostatic repulsion between charged nanosheets. Dilution increased interparticle spacing and promoted sedimentation of larger particles. Therefore, to further purify the dispersion and selectively isolate few-layer crystals of MoS₂, the achieved colloidal suspension was diluted with additional pure acetonitrile and sonicated under identical conditions (see Figure 2a). Then, the diluted suspension was left to settle for a few weeks. After settling, the supernatant was carefully collected by decantation and used for subsequent analyses. The colloids were optically characterized by UV-Vis spectroscopy (PerkinElmer Lambda 850 spectrophotometer, Waltham, MA, USA) in order to establish the presence of MoS₂ monolayers.

2.2. Sample Preparation for SEM Analysis

Samples for SEM characterization were prepared by drop-casting small volumes of liquid supernatant onto clean glass substrates. The solvent (acetonitrile) was allowed to evaporate under ambient conditions, leaving a thin film of dispersed MoS₂ nanosheets on the substrate surface. The morphological characterization was performed by scanning electron microscopy (SEM, Quanta 200 FEG microscope, FEI, Eindhoven, The Netherlands). SEM observations were performed both at normal incidence (0° stage tilt) and under grazing-incidence conditions. The reported tilt angle refers to the angle between the sample normal and the incident electron beam direction, as defined by the SEM stage tilt axis. In the grazing configuration, the sample was tilted to 90° relative to the horizontal stage position, corresponding to an electron beam incidence condition approaching parallelism with the sample surface plane.

For the 0°-tilting observations, a standard aluminum pin stub was used, while for the ~90°-tilting observations, a stable vertical sample positioning was achieved by using a special aluminum slotted specimen stub (slot diameter: 12.5 mm, with a 4 mm wide cavity, and height: 10 mm; an allen key is present in this stub, see Figure 2b).

Sobel edge detection was applied to quantify morphological feature detectability through edge density and mean gradient magnitude [17]. SEM micrographs were analyzed as exported from the instrument and converted to grayscale without additional filtering or contrast enhancement. The gradient magnitude was computed using standard 3 × 3 Sobel kernels. A fixed-size region of interest (ROI) with identical pixel dimensions was selected for each image, excluding borders and scale bars, to ensure quantitative comparability. The gradient magnitude map was scaled in the range 0–1, and edge maps were obtained by binarization using a fixed threshold applied identically to both 0° and 90° images. Edge density was defined as the fraction of edge pixels within the ROI, while mean gradient magnitude was calculated as the spatial average of gradient magnitude.

3. Results

3.1. Optical Characterization of MoS₂ Colloids

Optical characterization was carried out to assess the presence of ultrathin MoS₂ nanosheets, including monolayer and few-layer flakes, in the prepared colloidal samples. The grazing-incidence SEM methodology proposed in this work is particularly suitable for the morphological investigation of multiscale nanostructures such as MoS₂ nanosheet coatings, where micrometric lateral dimensions coexist with a nanometric thickness. In such systems, morphological information along the Z direction is often difficult to access under conventional SEM imaging conditions and therefore benefits from complementary techniques capable of probing thickness-dependent properties. Optical absorption spectroscopy provides an effective and widely adopted approach to indirectly evaluate the thickness distribution of two-dimensional transition metal dichalcogenides. In MoS₂, both the presence and the spectral position of characteristic absorption features, together with the estimation of the optical bandgap, are strongly correlated with the number of layers. Consequently, optical spectroscopy represents a suitable tool to verify that the exfoliation and settling stages adopted in the present preparation route led to the formation of predominantly ultrathin nanosheets. Figure 3a reports the optical absorption spectrum of the MoS₂ colloidal suspension dispersed in acetonitrile. The spectrum exhibits three characteristic absorption features centered at approximately 680 nm, 622 nm, and 458 nm, corresponding to photon energies of 1.82 eV, 1.99 eV, and 2.71 eV, respectively. These features are well-established optical signatures of mono- and few-layer MoS₂ and arise from interband electronic transitions, as is widely reported in the literature [15,18].

Specifically, the absorption bands at 680 nm (band A) and 622 nm (band B) are assigned to the so-called A and B bands, which originate from the direct transitions at the K-point of the Brillouin zone (see scheme shown in Figure 3b) [19]. These absorptions arise from the spin–orbit splitting of the valence band, which is particularly significant in transition metal dichalcogenides (TMDs) due to the heavy transition metal atoms. The A absorption (at 1.82 eV) involves transitions from the upper valence band (with lower spin) to the conduction band minimum, while the B absorption (at 1.99 eV) originates from the lower valence band (with higher spin) to the same conduction band minimum. The energy separation between the A and B absorptions in this spectrum is approximately 0.17 eV, which is in agreement with theoretical predictions and previous experimental reports for MoS₂ monolayers [20]. The presence of well-resolved A and B absorption bands suggests that the MoS₂ flakes in the colloid are monolayers and few-layers. The third absorption band, located at 458 nm (2.71 eV), indicated as band C in Figure 3a, is associated with transitions involving higher-energy states in the Brillouin zone. This band is attributed to a phenomenon known as ‘band nesting’, which indicates that parallel bands in the electronic structure led to a high joint density of states and enhanced optical absorption. The observation of this peak further supports the presence of well-dispersed, crystalline MoS₂ nanosheets in the prepared colloid.

A simple linear model can be used to estimate the average number of layers (N) in the nanoparticle from the A absorption energy value (E_A) [15,21]:

E_A(N) = E_bulk + K/N

(1)

where E_bulk = 1.29 eV (bulk MoS₂), K = 0.8 eV (empirical constant). Replacing the measured E_A value of 1.82 eV (absorption energy of the A band in our sample), it yields N ≈ 1.5, thus confirming the presence of MoS₂ monolayers in the obtained colloidal suspension with a minor amount of MoS₂ bilayers [15].

The bandgap energy of the MoS₂ colloid, E_g = 1.37 eV, has been optically estimated by using the modified Tauc plot method [22] based on the data in the optical absorbance spectrum (see Figure 4). The Tauc plot was constructed using the absorbance (A) values directly, without conversion to the absorption coefficient, α, since the effective optical path length is unknown for colloidal systems. This approach is particularly suitable for colloidal systems where the exact concentration and path length may not be precisely known or controlled.

According to the literature, the direct allowed electronic transitions model better describes this colloidal MoS₂ semiconductor, and the Tauc equation written by using the absorbance for this model is typically expressed as

(Ahν)² ∝ (hν − E_g)

(2)

In more detail, this method assumes that absorbance is proportional to the absorption coefficient (i.e., A ∝ α), and is valid for a qualitative estimation of the optical bandgap. The vertical axis of the plot was expressed in units of (eV)², as recommended in the recent literature [15], avoiding the incorrect use of arbitrary units or units involving cm⁻¹, which would imply a path-length-dependent α value. The linear portion of the (Ahν)² vs. hν plot was extrapolated to the energy axis to determine the optical bandgap.

This optical bandgap value estimated from the modified Tauc plot is approximately 1.37 eV (Figure 4). This value is lower than the A absorption energy (1.82 eV), which is reasonable for colloidal MoS₂ dispersions. In such systems, the Tauc analysis probes the absorption onset of the ensemble rather than the excitonic transition of a single monolayer. Therefore, the extracted bandgap reflects the combined contribution of nanosheets with different thicknesses.

In particular, few-layer and multilayer MoS₂ flakes possess indirect fundamental bandgaps in the range 1.3–1.5 eV, significantly lower than the direct gap of monolayers. Their presence in a polydisperse colloidal suspension naturally shifts the absorption onset, and hence the Tauc intercept, toward lower energies. Consequently, the Tauc-derived bandgap indicates a non-negligible fraction of multilayer flakes coexisting with monolayers in the suspension.

In addition, the A absorption band at 680 nm (1.82 eV) corresponds to an excitonic transition and does not directly represent the fundamental bandgap, since it includes the electron–hole binding energy, typically on the order of 0.3–0.5 eV in monolayer MoS₂. Moreover, defect-related tail states introduced during liquid-phase exfoliation may produce sub-gap absorption that further lowers the apparent optical onset [19].

Taking into account the coexistence of mono-, few-layer and multilayer flakes, together with excitonic effects and defect-related band tails, the Tauc intercept at 1.37 eV is fully consistent with a polydisperse MoS₂ colloid predominantly composed of ultrathin nanosheets.

3.2. Application of Grazing-Incidence SEM to MoS₂ Nanosheet Coatings

A comparison between SEM standard configuration (non-tilted) and under grazing-incidence conditions (~90° tilting) is reported in Figure 5a,b. Representative SEM micrographs acquired at an accelerating voltage of 30 kV under non-tilted and grazing-incidence conditions are shown in Figure 5c and Figure 5d, respectively. Under standard imaging conditions, ultrathin nanosheets deposited on a flat substrate often exhibit weak topographical gradients, making subtle morphological cues difficult to distinguish. In contrast, grazing-incidence imaging enhances surface sensitivity and improves the detectability of morphological features such as sheet edges, folds, wrinkles, overlapping regions, fracture sites, and thickness-related variations. While visual inspection already suggests an improved visibility of surface features in the tilted configuration (Figure 5d), a more objective assessment of feature detectability requires image-based analysis.

The accelerating voltage of 30 kV was chosen considering that, in the grazing-incidence geometry, the electron–sample interaction volume becomes geometrically elongated parallel to the sample plane. As a consequence, the primary electron trajectory remains closer to the surface over a longer path, favoring the emission and escape probability of secondary electrons generated in the near-surface region. This angular dependence of the interaction volume and penetration depth is well-established in SEM physics and has been described in detail in Monte Carlo simulations and theoretical treatments of oblique-incidence electron–matter interaction [6,23]. A more detailed discussion of the geometrical implications of tilted incidence on secondary electron emission is provided in Section 4. The same accelerating voltage was used for both normal- and grazing-incidence images to ensure direct comparability.

To further assess this effect beyond visual inspection, SEM images were post-processed by edge detection using a Sobel operator (Figure 5e,f) [24,25,26]. Sobel filtering highlights local intensity gradients, which in SEM images are directly associated with morphological discontinuities (e.g., edges and folds). The edge map obtained from the non-tilted micrograph shows only sparse and discontinuous edge responses, indicating that only the most pronounced features are detectable under standard geometry. Conversely, the grazing-incidence micrograph produces a markedly richer and more continuous edge response across the entire field of view, revealing a higher density of detectable morphological features.

The Sobel-processed images were analyzed quantitatively by extracting two independent descriptors directly related to morphological feature detectability. The first parameter is the edge density, defined as the ratio between the number of pixels identified as edges after thresholding and the total number of pixels in the analyzed region. This quantity provides a measure of the fraction of the image area associated with sharp intensity gradients, which in SEM images are directly linked to morphological discontinuities such as sheet edges, folds, overlaps, and fracture lines. The second parameter is the mean gradient magnitude, calculated as the spatial average of the Sobel gradient magnitude over the entire image. This metric reflects the overall strength of local intensity variations and is therefore sensitive to the presence and sharpness of surface-related features. Unlike edge density, which depends on binarization, the mean gradient magnitude captures more subtle variations in surface contrast.

Quantitative results extracted from representative regions of interest with identical pixel dimensions are reported in Figure 5. For the non-tilted configuration, the edge density was found to be approximately 5.9%, with a corresponding mean gradient magnitude of 0.151 (arbitrary units). In contrast, grazing-incidence imaging yielded a substantially higher edge density of approximately 7.6%, together with an increased mean gradient magnitude of 0.172. These values correspond to an increase of about 30% in edge density and about 14% increase in mean gradient magnitude under grazing-incidence conditions. This quantitative enhancement demonstrates that tilting the sample does not simply amplify image brightness but significantly increases the amount of retrievable morphological information. The higher edge density indicates that a larger fraction of the surface morphology becomes detectable, while the increase in mean gradient magnitude reflects stronger and more spatially extended surface-related contrast. Taken together, these metrics provide objective evidence that grazing-incidence SEM enhances sensitivity to nanoscale morphological features in ultrathin MoS₂ coatings.

To further strengthen the statistical robustness of the Sobel-based analysis, the quantitative evaluation was extended beyond the full-image comparison by subdividing each SEM micrograph into multiple non-overlapping regions of interest (ROIs) of identical pixel size. Each ROI was treated as an independent sampling area of the same morphological ensemble, allowing a local statistical assessment of edge density and mean gradient magnitude. The Sobel analysis was then applied identically to each ROI using the same preprocessing and threshold parameters adopted for the full-image evaluation. The resulting values are A = 1.3% ± 0.9% and B = 0.320 ± 0.007 for the normal-incidence (0°) configuration and A = 6.9% ± 2.4% and B = 0.372 ± 0.013 for the grazing-incidence (90°) configuration, confirming that both edge density and mean gradient magnitude increase systematically under grazing-incidence conditions, and thus supporting the interpretation that the observed enhancement in morphological detectability is not a localized artifact but a statistically reproducible effect.

Importantly, this analysis supports the interpretation that grazing-incidence SEM does not merely increase global image brightness but rather enhances the accessibility of surface-related morphological information in ultrathin 2D coatings by amplifying near-surface signal variations associated with nanoscale topography and local thickness changes.

4. Discussion

The results presented in this study demonstrate that SEM imaging performed under grazing-incidence conditions (~90°-tilting) significantly improves the quantitative detectability of surface-related morphological features, as confirmed by Sobel-based descriptors, in ultrathin MoS₂ nanosheets compared to conventional 0°-tilt imaging. In addition to direct visual inspection (Figure 5c,d), this improvement is supported by Sobel edge maps (Figure 5e,f), which highlight a denser and more continuous network of edges and gradients associated with sheet boundaries, folds, wrinkles, overlapping regions, and fracture sites.

Grazing optical observation is a visualization strategy widely adopted in nature by living organisms [27,28,29] to enhance the perception of surface textures and morphological details, particularly when subtle variations must be detected. In biological visual systems operating with visible photons, oblique illumination increases the visibility of edges and contours mainly through shadowing effects, which emphasize height variations and discontinuities.

In scanning electron microscopy, however, grazing-incidence observation operates according to a fundamentally different physical principle. The enhanced visibility of surface features observed under tilted conditions does not arise from shadow formation, but from a modification of the electron–sample interaction geometry, which increases the sensitivity of the detected signal to near-surface morphological variations. Specifically, tilting the sample with respect to the electron beam–detector axis enhances the emission and collection of secondary electrons generated in the immediate subsurface region, thereby amplifying local intensity gradients associated with edges, folds, wrinkles, and thickness-related discontinuities.

Nevertheless, in both cases, the grazing orientation of the probing radiation plays a central role in enhancing image contrast, albeit through fundamentally different physical mechanisms: reflection and shadowing in optical imaging, and increased secondary electron emission in SEM.

This distinction is particularly relevant for ultrathin two-dimensional coatings, such as MoS₂ nanosheets, where conventional SEM imaging often fails to provide sufficient information on surface morphology due to the limited topographical contrast generated under normal incidence. Under grazing-incidence conditions, instead, even weak morphological gradients become detectable, as confirmed by the denser and more continuous edge responses observed in the Sobel-processed images. In this sense, the proposed approach can be regarded as bio-inspired in its conceptual motivation, while remaining fundamentally electron-based in its physical mechanism, enabling a more effective visualization of nanoscale surface features without relying on shadowing or interference phenomena.

The quantitative Sobel-based analysis provides a complementary and objective interpretation of this effect. The observed increase in both edge density and mean gradient magnitude under grazing-incidence conditions reflects a genuine enhancement of surface-related contrast rather than a simple amplification of image brightness. From a physical standpoint, this behavior is consistent with the reduced penetration depth of primary electrons at shallow incidence angles, which confines secondary electron generation to the near-surface region. As a consequence, morphological discontinuities such as sheet edges, folds, wrinkles, and overlapping regions contribute more efficiently to local intensity gradients. Importantly, the increase in edge density indicates that a larger fraction of the surface morphology becomes detectable, while the higher mean gradient magnitude reveals that these features are resolved with greater contrast. This confirms that grazing-incidence SEM improves not only the visibility but also the effective information content of SEM images of ultrathin 2D coatings.

Such behavior can be easily understood on the basis of geometrical considerations. The SE path (x) in the sample subsurface region depends on the PE penetration depth (d) and on its incidence angle value (α), as x = d·sin(α).

The relative variation in the SE path (Δx/x) as a function of the incidence angle relative variation (Δα/α) is Δx/x = [cos(α)/sin(α)]·Δα/α. In the case of a very shallow angle of incidence (α ≈ 0), the cos(α) value can be taken as approximately equal to 1 and the sin(α) value can be approximated by α. Therefore, Δx/x ≈ (1/α)·Δα/α. Since α is quite close to zero, the 1/α value is extremely large and therefore a significant relative variation in the SE path is obtained as a result of a small variation in the grazing angle. Under extreme grazing conditions (i.e., a sample surface almost vertically positioned), a little increase in the tilting angle (α decreases) determines an important decrease in the SE path. Since secondary electrons have very low energy (typically below 30 eV), they possess a short inelastic mean free path and rapidly lose energy while traveling through the subsurface region. Consequently, a reduction in the effective path length, achieved by tilting the sample toward grazing-incidence conditions, facilitates the escape of SE from near-surface regions. This increase in escaping SE enhances the detected signal and ultimately improves the image contrast of the micrograph. Indeed, in the hypothesis that the number of emitted secondary electrons, N_SE, is inversely proportional to the distance from the surface, x, it results in ΔN_SE/N_SE ≈ −(1/α)·Δα/α. The only limitation in this tilting operation is represented by the sharpness of the observation field that must be retained during the observation in tilting conditions. In particular, the tilting degree must be as high as possible; however, it does not have to compromise the SEM image sharpness.

It is also important to note that, unlike grazing-incidence X-ray scattering, where coherent photon–matter interaction leads to interference or diffraction features, secondary electron emission in SEM is incoherent. SEs result from localized inelastic collisions and have low energies (<30 eV), short mean free paths and randomized phases. Consequently, no diffraction-like effects can form at the detector. Nevertheless, under grazing-incidence, the SE signal may exhibit small intensity fluctuations due to geometric factors, such as variations in local surface slope, roughness, or changes in escape probability, rather than true interference phenomena.

Compared to previous approaches that attempt to enhance SEM contrast through variations in accelerating voltage, detector positioning or surface metallization, the method proposed here is simpler, non-destructive and does not require instrument modification, and relies solely on standard stage tilting. Furthermore, it is conceptually related to natural optical strategies based on grazing illumination, adopted in biological systems to improve edge recognition and surface defect detection. In contrast to optical systems, however, the mechanism active in SEM is not shadow formation but maximization of SE collection from near-surface regions.

This methodology is particularly advantageous for ultrathin two-dimensional coatings such as the MoS₂ system investigated here, whose functional properties strongly depend on nanoscale morphology. Although the technique may be less effective for thick, highly corrugated or insulating samples, where shadowing effects or charging may occur, it is expected to be applicable to other layered systems such as graphene, WS₂, and h-BN, and to nanostructured films and biomimetic surfaces, since the underlying contrast mechanism is not material-specific.

Overall, the proposed approach provides a practical route to improve surface-sensitive feature detectability in representative ultrathin 2D coatings such as MoS₂ within the operational constraints of SEM focusing and depth of field.

5. Conclusions

In this work, a simple and effective grazing-incidence SEM methodology has been proposed to improve the morphological characterization of ultrathin two-dimensional coatings, using MoS₂ nanosheets as a representative case study.

By tilting the sample close to 90°, the electron–sample interaction geometry is modified in a way that enhances surface sensitivity and facilitates the detection of morphological features that are often suppressed under standard SEM imaging conditions.

The proposed method is simple, non-destructive and does not require instrumental modifications, making it suitable for routine SEM analysis of ultrathin 2D materials (e.g., graphene, h-BN, WS₂) and nanostructured coatings.

The application of grazing-incidence observation enabled the visualization of nanoscale features such as sheet edges, folds, wrinkles, overlapping regions, and fracture sites. Beyond qualitative inspection, the introduction of Sobel-based edge detection provided an objective, feature-oriented analysis, demonstrating that the observed improvement arises from enhanced detectability of surface-related morphological discontinuities rather than from a mere global increase in image brightness.

Optical characterization of the MoS₂ colloids supported the presence of monolayer and few-layer nanosheets, validating the structural information obtained from SEM analysis. The combined use of optical spectroscopy and grazing-incidence SEM thus offers a reliable approach for the characterization of ultrathin 2D coatings and layered nanomaterials.