Thickness determination of few-layer hexagonal boron nitride films by scanning electron microscopy and Auger electron spectroscopy

We assess scanning electron microscopy (SEM) and Auger electron spectroscopy (AES) for thickness measurements on few-layer hexagonal boron nitride (h-BN), the layered dielectric of choice for integration with graphene and other two-dimensional materials. Observations on h-BN islands with large, atomically ﬂat terraces show that the secondary electron intensity in SEM reﬂects monolayer height changes in ﬁlms up to least 10 atomic layers thickness. From a quantitative analysis of AES data, the energy-dependent electron escape depth in h-BN ﬁlms is deduced. The results show that AES is suitable for absolute thickness measurements of few-layer h-BN of 1 to 6 layers. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

We assess scanning electron microscopy (SEM) and Auger electron spectroscopy (AES) for thickness measurements on few-layer hexagonal boron nitride (h-BN), the layered dielectric of choice for integration with graphene and other two-dimensional materials. Observations on h-BN islands with large, atomically flat terraces show that the secondary electron intensity in SEM reflects monolayer height changes in films up to least 10 atomic layers thickness. From a quantitative analysis of AES data, the energy-dependent electron escape depth in h-BN films is deduced. The results show that AES is suitable for absolute thickness measurements of few-layer h-BN of 1 to 6 layers. © 2014 Author(s). All  Two-dimensional materials, 1 such as graphene, hexagonal boron nitride (h-BN), and a family of transition metal dichalcogenides (MX 2 ) have attracted significant interest for their electronic, optical, chemical, and mechanical properties. Positioned between 2D materials and the bulk crystals from which they are derived, layered materials with several atomic layers are increasingly recognized for their unique properties, which are typically different from those of the monolayers 2 and the bulk and often vary substantially with thickness. 3, 4 Hexagonal boron nitride (h-BN), a layered insulator with a bandgap of nearly 6 eV, 5 whose surface is both topographically flat and contains a low density of scattering centers for charge carriers, 6 is expected to play a key role in a range of emerging applications. For example, graphene supported on few-layer h-BN has shown record carrier mobilities, 7 and h-BN is the substrate of choice for exploring new physical phenomena associated with low-dimensional charge carriers in graphene 8 and other 2D materials. 9 Heterostructures comprising few-layer h-BN sandwiched between graphene layers are being explored for novel tunneling devices. 10 To harness the desired dielectric properties, h-BN films with a uniform thickness of several atomic layers are often required. A precise thickness measurement is therefore among the most important elements of h-BN metrology, irrespective of the approach used to fabricate the few-layer films. For h-BN exfoliated from bulk crystals, optical reflectivity provides quantitative thickness information, 11,12 but it requires a special substrate-typically SiO 2 /Si with a well-defined oxide thickness-to enhance the optical contrast. Recently, different approaches have been developed for the scalable synthesis of monolayer [13][14][15][16] or few-layer 17,18 h-BN on metal substrates. In this context, methods are needed for determining the thickness of h-BN layers while still supported on the metal substrate, or alternatively after transfer to a different support, which may not necessarily be SiO 2 /Si.
Here, we establish the basis for using scanning electron microscopy (SEM) and Auger electron spectroscopy (AES) to measure the thickness of few-layer h-BN. SEM is available in many research laboratories and enables facile mapping of surfaces. AES is a well-established surface science a Author to whom correspondence should be addressed. Electronic mail: psutter@bnl.gov method for elemental and chemical analysis that can be used for both spatially averaging and local measurements. If a focused electron beam is used to excite Auger electrons, AES measurements can be performed within nanometer areas. In the context of thickness measurements, the inelastic mean free path (IMFP) of Auger electrons, which determines the electron escape depth and hence governs the film thicknesses that can be measured reliably, is a key parameter in the quantitative analysis of AES data. While the so-called "universal curve" provides approximate values of the energy-dependent IMFP (λ(E)), measured values for particular materials and crystal structures are required for metrology applications.
To explore the potential of SEM and AES for h-BN thickness characterization, we have synthesized few-layer h-BN samples on Ru(0001)/Al 2 O 3 (0001) thin films using a recently demonstrated growth method based on reactive magnetron sputtering of boron in N 2 /Ar, which has allowed us to achieve the controlled growth of high-quality few-layer h-BN dielectric films on metal substrates. 18 In previous work, the goal has been to achieve BN films with uniform thickness across the entire sample. Here, we use growth conditions that cause a partial wetting of the BN film on the Ru substrate to generate staircases of few-layer h-BN with extended (several μm) atomically flat terraces and thickness increasing in monolayer increments up to ∼10 atomic layers. Characterized by AES excited by the focused electron beam of an ultrahigh-vacuum (UHV) SEM, these samples provide direct measurements of the thickness dependent intensity of Auger electrons from few-layer h-BN or the underlying substrate, which can be analyzed to extract the IMFP, λ(E).
Hexagonal BN was grown on epitaxial Ru(0001) substrates by reactive magnetron sputtering of a solid B target in Ar/N 2 (ratio 4:1; total pressure: 10 −2 Torr). 18 The epitaxial Ru(0001) thin film substrates were prepared in situ, following procedures described previously. 19 The h-BN films were investigated using an UHV-SEM (Zeiss Gemini UHV) and nano-Auger electron spectroscopy (Omicron Nanoprobe) 20 at 3 keV incident electron beam energy and a beam current between 300 pA and 3 nA. The surface microscopy and spectroscopy was complemented by high-resolution transmission electron microscopy (TEM) in an aberration-corrected microscope (FEI Titan 80-300) of cross-sections prepared by focused ion-beam milling combined with lift-off techniques. 21 The negligible chemical reactivity and low sticking coefficient of h-BN poses substantial challenges in realizing the controlled synthesis of h-BN films beyond monolayer thickness. Uniform fewlayer h-BN films have been formed by reactive magnetron sputtering via alternating low-temperature deposition and crystallization at high temperatures. 18 Deposition of several atomic layers by magnetron sputtering followed by annealing at high temperature (>900 • C) produces partially dewetted crystalline h-BN. Figure 1(a) shows an overview of the typical morphology of these films. The substrate is covered by large (up to ∼100 μm base size) aggregates of few-layer h-BN. A zoomed-in view demonstrates that these islands consist of a well-defined stack of individual sheets ( Fig. 1(b)). Additional characterization shows that the thickness of these layer stacks varies from 1 atomic layer near the periphery to ∼10 atomic layers in monolayer increments. Sections with uniform thickness often comprise large, atomically flat terraces. Auger electron spectroscopy, discussed below, shows that the areas between the h-BN islands consist of bare Ru metal, not covered by h-BN.
Cross-sectional TEM results are consistent with the conclusions drawn from surface imaging by SEM. Overview TEM images show the overall sample structure consisting of the sapphire substrate, epitaxial Ru(0001) film and few-layer h-BN near the surface (Fig. 2(a)). Highresolution cross-sectional TEM demonstrates a high degree of crystallinity of the layered BN film (Fig. 2(b)), whose thickness reaches up to ∼20 atomic layers in some areas. Comparing experimental high-resolution images with multislice TEM image simulations, we find that the BN film is predominantly A-A -A stacked, i.e., shows the stacking sequence of hexagonal BN. After several atomic layers with perfect h-BN stacking, the sequence is interrupted by stacking faults (Fig. 2(c)), but the layered structure persists throughout the film. In most cases, the in-plane orientation of the layers is preserved across stacking faults, but occasionally we find that the characteristic high-resolution contrast becomes blurred, suggesting an in-plane rotation in these layers.
UHV SEM of stepped few-layer h-BN stacks (Fig. 3(a)) shows that secondary electron intensity maps provide a convenient tool to track local changes in h-BN thickness. Analyzing the image contrast, we find that the secondary electron intensity is proportional to the number of BN layers (Fig. 2(b)) over a wide thickness range, extending to at least 10 atomic layers (the thickest film sections probed here). Only very thin films (i.e., monolayer h-BN) deviate from this behavior. We find that the transition from bare Ru(0001) to single-layer h-BN is accompanied by a small increase in the secondary electron intensity, whereas each subsequent h-BN layer causes a much larger (and constant) increment. This reflects the fact that the interaction with the substrate and the moiré structure give monolayer h-BN/Ru(0001) distinct electronic and chemical properties, 15 whereas with the completion of the second layer bulk-like h-BN properties are reached. 18 The observed linear intensity increase implies that the SEM contrast is sensitive to monolayer changes in film thickness. From the fact that thicker areas give rise to higher secondary electron intensity, we conclude that the detected secondary electrons originate primarily in the h-BN layer, and the linear increase suggests that the total intensity is the sum of contributions from the individual atomic layers of the film, consistent with a large escape depth of the energetic secondary electrons. This behavior is different from that observed for few-layer graphene on Ru, where the secondary electron intensity decreases for thicker graphene films, implying that the detected secondary electrons originate in the Ru substrate and are attenuated by the graphene sheets. 22 A possible origin of the difference between graphene and h-BN is the partially ionic character of h-BN, in contrast to the purely covalent bonding of C atoms in graphene.
In addition to monitoring monolayer thickness variations, which are conveniently mapped by SEM, the characterization of few-layer h-BN requires absolute thickness measurements. Previous reports for graphene have shown that Auger electron spectroscopy (AES) can be used to routinely determine film thickness. 23 However, precise values of the inelastic mean free path Auger electrons are required for a quantitative thickness analysis. We have used our stepped BN stacks in conjunction with spatially resolved AES measurements on terraces with known film thickness to quantify the IMFP of Auger electrons in h-BN, and to identify a reliable method for measuring the thickness of h-BN films on metals. Figure 3 shows the results of such an AES measurement. As expected, the Auger lines of all three elements in our system, B KLL , N KLL , and Ru MNN , show a systematic intensity change with increasing BN thickness: with the addition of each BN layer, the B KLL and N KLL signals increase in intensity, whereas thicker h-BN progressively attenuates the Ru MNN intensity.
The spectra in Fig. 4 provide several independent measurements of the IMFP at different electron energy, which together yield λ(E) of h-BN. For Auger electrons originating in the h-BN film itself (B KLL and N KLL transitions), we assume that the electrons from the outermost h-BN layer reach the detector unattenuated (intensity I 0 ), whereas those from deeper layers undergo an exponentially depth dependent attenuation with IMFP λ. The intensity of the B KLL and N KLL Auger electrons from n-layer h-BN is then given by where d is the layer spacing in h-BN (3.3 Å) and θ = 45 • is the takeoff angle in our AES system.
For Auger electrons originating in the Ru substrate (Ru MNN transition), the analogous attenuation by n-layer h-BN from an initial intensity, I Ru,0 , to a final intensity at the surface, I Ru,n (after traversing n h-BN layers) is given by  A comparison with the "universal curve" of energy-dependent electron escape depths (Fig. 5(b)) shows good general agreement, with the measured values of the IMFP in h-BN lying somewhat above the "universal curve" but well within the scatter of individual IMFP values. 24 Finally, our measurements allow us to estimate the range of h-BN thicknesses that can be measured by AES. Tracking the intensity of the N KLL transition, and assuming that intensity changes of 5% can be detected in the derivative spectra, AES measurements can provide reliable thickness measurements for h-BN films of 1 to 6 atomic layers.
In conclusion, we have used large, partially wetting islands of stacked h-BN layers on Ru(0001) to explore electron-based approaches for determining the thickness of few-layer h-BN films. We find that the intensity of secondary electrons in scanning electron microscopy depends linearly on the number of h-BN layers up to thicknesses of at least 10 layers. SEM thus provides a simple and sensitive means of tracking thickness variations in h-BN films, giving robust contrast for monolayer changes in thickness. Within a limited thickness range from 1 to ∼6 BN atomic layers, Auger electron spectroscopy provides an absolute film thickness measurement if referenced against a proper standard, for example, monolayer or bulk h-BN. Evidently, the reference standard should be as close as possible to the structure and composition of the sample whose thickness is to be determined. In practice, a h-BN monolayer grown by CVD on a metal substrate should represent a convenient reference, since attributes such as perfect stoichiometry, full substrate coverage, and uniform thickness and density are relatively easy to achieve. With such a standard, possible sources of uncertainty, for instance in routine thickness measurements while developing synthesis approaches for few-layer h-BN, would be variations in the composition, crystal quality, or adsorbates on the surface of the few-layer samples. The primary utility of AES thickness metrology lies in the fact that the measurement is quite generally applicable, independent of the material of the substrate supporting the h-BN film. AES thus provides a versatile complement to other methods, e.g., optical reflectivity, which require a special substrate.
Research carried out at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.