Stacking Order Dependent Second Harmonic Generation and

Oct 14, 2013 - the τ = 0 configuration (AA, Figure 1b) is energetically unstable; instead ... DF-TEM image of single layer h-BN crystals (outlined by...
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Stacking Order Dependent Second Harmonic Generation and Topological Defects in h‑BN Bilayers Cheol-Joo Kim,† Lola Brown,† Matt W. Graham,‡,§ Robert Hovden,∥ Robin W. Havener,∥ Paul L. McEuen,‡,§ David A. Muller,§,∥ and Jiwoong Park*,†,§ †

Department of Chemistry and Chemical Biology, ‡Laboratory for Atomic and Solid State Physics, §Kavli Institute at Cornell for Nanoscale Science, and ∥School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, United States S Supporting Information *

ABSTRACT: The ability to control the stacking structure in layered materials could provide an exciting approach to tuning their optical and electronic properties. Because of the lower symmetry of each constituent monolayer, hexagonal boron nitride (h-BN) allows more structural variations in multiple layers than graphene; however, the structure−property relationships in this system remain largely unexplored. Here, we report a strong correlation between the interlayer stacking structures and optical and topological properties in chemically grown hBN bilayers, measured mainly by using dark-field transmission electron microscopy (DF-TEM) and optical second harmonic generation (SHG) mapping. Our data show that there exist two distinct h-BN bilayer structures with different interlayer symmetries that give rise to a distinct difference in their SHG intensities. In particular, the SHG signal in h-BN bilayers is observed only for structures with broken inversion symmetry, with an intensity much larger than that of single layer h-BN. In addition, our DF-TEM data identify the formation of interlayer topological defects in h-BN bilayers, likely induced by local strain, whose properties are determined by the interlayer symmetry and the different interlayer potential landscapes. KEYWORDS: Hexagonal boron nitride, second harmonic generation, topological defect, stacking order, inversion symmetry, energy landscape

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In this paper, we study the correlation between the stacking configuration and the physical (optical and topological) properties of h-BN bilayers by applying multiple imaging techniques: DF-TEM with electron diffraction measurements,19,20 DUV−vis-NIR hyperspectral imaging,21 and scanning SHG mapping.22−24 Our h-BN bilayers were grown on copper surfaces using a CVD method that produces areas of single-, bi-, and multilayer samples.25,26 These samples were transferred onto TEM compatible SiN substrates (5 nm thick) thus enabling both TEM and optical characterizations of the same sample regions17,18 (see Supporting Information for experimental details). We first discuss the various stacking configurations and the associated symmetry of bilayer h-BN (Figure 1). The h-BN and graphene bilayer structures are characterized by the two order parameters: the relative interlayer rotation angle (θ) and the interlayer translation vector (τ) (see Figure 1a). While it is known that there is only one energetically stable configuration (Bernal stacking) in bilayer graphene, there are two interlayer orientations (θ = 0° and θ = 60°) that each produce stable configurations in bilayer h-BN. Figure 1b,c shows the

nderstanding the correlation between various stacking structures and associated crystal symmetry is central to determining the overall physical properties of two-dimensional layered materials. For instance, the inversion symmetry of Bernal stacked bilayer graphene, which gives rise to unique electrical and optoelectronic properties,1−5 can be broken by rotating one layer relative to the other, giving twisted bilayer graphene,6,7 or by stacking additional graphene layers in noncentrosymmetric configurations (such as a trilayer graphene in ABA stacking).8−10 Single layer hexagonal boron nitride (hBN), a structural analogue of graphene in which alternating boron and nitrogen atoms substitute for carbon atoms, lacks the inversion symmetry of graphene with 3-fold (instead of 6fold) rotational symmetry. As a result, it allows an additional stacking configuration in h-BN bilayers by spatially inverting one of the layers. This additional structural diversity in h-BN bilayers, which has been imaged using high-resolution TEM before,11−13 is predicted to result in different electronic and phonon properties.14−16 However, experimental reports on the structure−property relationship in this system are rare due to the difficulty of performing structural and property measurements on the same samples, even though such measurements were reported for graphene samples investigating the optical and electrical properties of bilayer and polycrystalline graphene after TEM measurements.17,18 © XXXX American Chemical Society

Received: September 5, 2013 Revised: October 13, 2013

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Figure 1. (a) Schematics of bilayer h-BN structures, determined by two interlayer structure order parameters; θ and τ. (b,c) bilayer h-BN’s interlayer potential energy plots for (b) θ = 0° and (c) θ = 60° cases. Darker color indicates lower interlayer potential energy. For BN/BN, AB or AC structures are the most stable, while for BN/NB, AA′ is the most stable structure and AB′ is predicted to have the energy close to that of AA′. Interlayer energies are adapted from a previous report.27

previously reported interlayer energy landscape as a function of τ for these two rotation angles, where both NB (instead of BN) and (′) denote the rotated h-BN layer.14,27 Here, the strength of the attractive (repulsive) interlayer interaction between heterogeneous (homogeneous) atomic pairs change depending on the interatomic distance, causing the total interlayer potential energy to be strongly dependent on τ. At θ = 0°, the τ = 0 configuration (AA, Figure 1b) is energetically unstable; instead, the energy finds the minima for graphite-like stacking structures (AB and AC, Figure 1b) with only heterogeneous pairs vertically overlapping. For θ = 60°, the τ = 0 configuration (AA′ in Figure 1c) minimizes the energy with vertical heterogeneous atomic pair overlaps. In addition, another stacking structure for θ = 60° (AB′, Figure 1c) has been predicted to have the energy close to that of AA′.14,27 Significantly, h-BN bilayers in AA′ and AB′ configurations possess inversion symmetry, whereas the AB and AC configurations do not. Often, these structural variations are overlooked in the study of multilayer h-BN. However, as we will show later, the differences in the crystal symmetry are crucial to explaining properties such as SHG and topological defects. The stacking structure and crystal symmetry of h-BN bilayers are directly imaged using DF-TEM and selected area electron diffraction (SAED).20,28 Figure 2a first shows a representative DF-TEM image of single layer h-BN crystals (outlined by triangles), which is obtained by selecting an inner diffraction spot (Φi, inset) with a selective aperture in the diffraction plane. All three h-BN crystals show the same hexagonal SAED pattern (inset, Figure 2a) and similar brightness in the DF-TEM image. However, we observe two different orientations for the h-BN triangles, pointing in opposite directions. This is consistent with the previous studies for h-BN grown on crystalline Cu surfaces and suggests an epitaxial relationship between h-BN and Cu, producing h-BN along two energetically equivalent orientations.29,30 (see Supporting Information) It is also known that the h-BN triangles are terminated by zigzag edges with nitrogen atoms outside when they are grown under the conditions similar to the one we used.31,32 This suggests that the two sets of triangular shapes observed in Figure 2a are h-BN crystals that are rotated by 60° relative to each other (denoted by BN and NB in Figure 2). Figure 2b shows the schematics of atomic

Figure 2. (a) DF-TEM image of single layer h-BN crystals (outlined by triangles), which is obtained by selecting an inner diffraction spot, Φi (inset). They show two different orientations for the h-BN triangles, pointing in opposite directions. Scale bar is 1 μm. (b) Schematics for two h-BN monolayers, BN and NB, on a copper surface. (c) DF-TEM image of multilayer h-BN obtained by selecting an outer diffraction spot, Φo. Local number of layers is designated based on the observed intensity. The nesting triangles in the multilayer region on the left are all in the same orientation with parallel edges, but the region on the right show rotated edges for nesting triangles. (d) DF-TEM image over the (c) region, obtained by selecting Φi. Intensities change for different stacking features as highlighted by dotted lines. The diffraction lattice vectors, go and gi, corresponding to the Φo and Φi are presented by arrows. Scale bar is 300 nm.

arrangements in BN and NB crystals. However, they show no measurable difference in their SAED patterns. In contrast, DF-TEM and SAED data of bilayer and multilayer h-BN regions show strong dependence on the stacking configuration. Figure 2c,d shows DF-TEM images obtained from two adjacent multilayer h-BN regions by selecting different diffraction spots (Φo in Figure 2c and Φi in Figure 2d, corresponding to a (12̅10) and a (01̅10) crystal diffraction lattice). We observe that the nesting triangles in the multilayer region on the left are all in the same orientation with parallel edges, but the region on the right show rotated edges for nesting triangles. This suggests that the left h-BN multilayer has the aligned stacking (BN/BN/BN/...) while the right one has an alternating orientation for each layer (BN/NB/BN/...). The exact stacking structure for each multilayer region can be further determined based on the measured intensity of the SAED and DF-TEM images, as the electrons diffracted from one layer of h-BN interferes constructively or destructively with those diffracted from adjacent layers depending on τ.19 Figure 2c shows that the electron diffraction intensity increases approximately as n2 for either multilayer regions, where n is the number of h-BN layers. This is consistent with all four stacking configurations (AB, AC for θ = 0° and AA′, AB′ for θ = 60°) discussed earlier, where electron waves diffracted from each pair of adjacent h-BN layers constructively interfere. However, the DF-TEM image measured with Φi (Figure 2d) B

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Figure 3. (a) DF-TEM image over a region of AB and AA′ bilayers and a combined diffraction pattern from the two areas (inset) (b) SHG image from the same area. Dotted lines indicate the region of two different stacking structures, revealed by DF-TEM. Inset shows a polar plot of the parallel component of the SHG signal measured as a function of γ (see the main text for definition). The gray line shows a theoretical fitting. Scale bar is 1 μm. (c) The left plot shows averaged SHG intensities measured from mono layer, AB and AA′ bilayers in panel b. The error bars indicate spatial nonuniformity mainly caused by adsorbates on the sample surfaces. Right schematics depict the second harmonic polarization in each layer of AB and AA′ stacking structures by red arrows. (d) Optical absorption spectrum data from monolayer, AB and AA′ bilayers with 0.1 intervals for clarity. The peaks appear at a same energy, as indicated by a dotted line. Right plot shows the position of the peak energies and amplitudes, showing no substantial difference between AB and AA′ regions.

λSH was detected from the h-BN bilayer with AB stacking (upper left), the signal is relatively very small for the AA′ stacking region (lower right). The strong signal observed only from the AB stacking region clearly arises from a nonlinear twophoton SHG process, as the signal increases quadratically with the incident laser intensity (see Supporting Information). Furthermore, a polar plot of the parallel component of the SHG signal (inset, Figure 3b) measured as a function of the relative angle (γ) between the in-plane polarization of the incident laser and the sample shows a clear 6-fold symmetry. It also shows its minimum (maximum) values when the incident laser polarization is parallel to the zigzag (armchair) orientations of h-BN, deduced from the SAED image (inset, Figure 3a). This can be explained by the symmetry; if the incident laser polarization is along the zigzag direction, the parallel components of the second order susceptibility and polarization (χ(2) and P(2)) must vanish because the electric field of the laser is perpendicular to a crystal mirror plane. Indeed, a theoretical model predicts a sin2(3γ) dependence, which provides a good fit to our data (gray lines, inset to Figure 3b).22−24 Furthermore, we find that AB-stacked h-BN gives the strongest SHG among monolayer, AB and AA′ bilayer h-BN (left, Figure 3c). This is significant because the previous work showed that AA′-stacked exfoliated h-BN samples with an odd number (1, 3, 5, ...) of layers all show similar SHG intensities. In contrast, our AB bilayer sample shows approximately four times higher SHG value than that of monolayer. A model of two electrically decoupled h-BN mono layers provides a general explanation for our observations. Because of the much smaller thickness of h-BN bilayers compared to the laser wavelength, the phase difference of incident laser beams between the top and bottom layers is negligible. As a result, the phase difference between SHG signals originating from each layer is determined by their relative orientation of the constituting h-BN layers. The coherent signals thus constructively interfere when both layers of h-BN are in the same orientation (AB stacking, upper schematic, Figure 3c) increasing the SHG signal by four times,

shows different behaviors for the two regions. The intensity in the multilayer region on the right again increases strongly with n, which suggests that the stacking configuration for this area is AA′ (τ = 0) causing constructive interference for diffracted electron beams. However, the left multilayer region remains much darker throughout. This is consistent with a graphitic stacking structure (AB or AC) that causes destructive interference.19,33 Indeed, comparing the measured electron diffraction intensities with our theoretical calculations confirms the assignment of the two main stacking structures we observe: AB (or AC) stacking for BN/BN (θ = 0°) and AA′ stacking for BN/NB (θ = 60°). We do not observe AB′ stacking from our bilayer samples. (see Supporting Information) Now, we study the optical properties of the two different stacking structures identified above for θ = 0° and θ = 60°, showing a clear structure−property relationship in h-BN bilayers. For this, we measure the SHG for noncentrosymmetric samples with AB (or AC) stacking (θ = 0°) and for centrosymmetric samples with AA′ stacking (θ = 60°). It is well-known that a SHG signal vanishes in materials with inversion symmetry, which is consistent with a recent study on exfoliated h-BN samples, where the crystal symmetry is determined only by the number of layers for the single type of AA′ stacking configuration. As a result, a SHG signal in this previous work was observed only from samples with an odd number of layers and thus with broken inversion symmetry.22−24 In contrast, our CVD grown h-BN samples provide different bilayer regions with or without inversion symmetry that should result in different SHG intensities depending on the local stacking structures. Figure 3a shows a DF-TEM image of a region containing both AB and AA′ stacking configurations with similar electron diffraction patterns (see inset). Figure 3b shows an image of SHG intensity measured for the same region. It is based on pixel-by-pixel measurements of frequency-doubled reflectance signal (λSH = 405 nm), obtained by scanning a high power pulse laser (λ = 810 nm) over the area (see Supporting Information for measurements details.) While a strong signal at C

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Figure 4. (a,b) DF-TEM images of (a) BN/BN (θ = 0°) and (b) BN/NB (θ = 60°) h-BN bilayer regions, taken by selecting different diffraction spots (Φo1 and Φo2 in panel a and Φi1 and Φi2 in panel b). Strain-induced topological defect lines are observed as dark lines as seen in the middle images of (a) and (b). The displacement vectors of topological defects are deduced from their different imaging conditions; defects are invisible at Φo2 for BN/BN, while they disappear at Φi2 for BN/NB. The lower images are schematics of defect structures under a shear strain, as the displacement vectors T are in the arm-chair and ziz-zag directions for BN/BN and BN/NB, respectively. go2 and gi2 indicate diffraction lattice vectors perpendicular to the diffracting planes for Φo2 and Φi2, respectively. For clarity, transitions are exaggerated with respect to the lattice constants. (c) Widths of topological defect lines measured as a function of the relative angle, α between T and a vector normal to the defect line. The inset shows a schematic of topological defect lines with α. Solid lines are fits, calculated using our model (see manuscript and Supporting Information). (d) DFTEM images of topological defects at α ∼ 0° in both stacking structures, showing larger width for a BN/BN sample. All scale bars are 30 nm.

properties are determined by a unique displacement vector T as well as the overall energy landscape, as shown below. Significantly, this T also varies for each stacking configuration; it is along one of the arm-chair directions for θ = 0° (arrows in Figure 1b; Ta‑c) similar to the case of bilayer graphene,34,35 but it is along one of the zigzag directions for θ = 60° (arrows in Figure 1c; Tz‑z). As previously shown, the location and displacement vector of a topological defect can be directly imaged by DF-TEM.19,34,35 Figure 4a,b shows representative DF-images of two BN/BN (θ = 0°) and BN/NB (θ = 60°) h-BN bilayer regions, respectively, taken by selecting different diffraction spots (Φo1 and Φo2 in Figure 4a and Φi1 and Φi2 in Figure 4b). It shows a dark line (Figure 4a, middle) or a set of dark lines (Figure 4b, middle) with their widths ranging between 5 and 25 nm, surrounded by brighter regions. Interestingly, these dark lines uniformly disappear when imaged using Φo2 instead of Φo1 (Figure 4a, right) or using Φi2 instead of Φi1 (Figure 4b, right). As discussed in Figure 2, a bright DF-TEM signal measured with a certain diffraction spot implies that it satisfies the constructive interference condition for the corresponding crystal diffraction lines. The dark lines seen in Figure 4a,b thus suggest that the relative position of atoms in one layer relative to the other is now shifted from the ground state configuration, by a gradually varying distance inducing destructive interference along the width of the line. However, if this relative shift is along a translation vector T, the destructive interference does not occur when the electron diffraction is measured off of crystal lines that are parallel to T (see the schematics in Figure 4a and 4b). Therefore, the disappearance of dark lines seen only for a certain diffraction spot provides a direct way to measure T of each topological defect line. Indeed, we find all T measured in our experiments are assigned to arm-chair directions in BN/BN (θ = 0°) bilayers, but they are all along zigzag directions in BN/ NB (θ = 60°) bilayers, consistent with our discussion above. Figure 4c plots the widths (defined by fwhm of intensity variation) of 13 topological defect lines, from both stacking regions, as a function of α, the relative angle between T and a

while they destructively interfere when the two layers are in the opposite orientations (AA′, lower schematic, Figure 3c) with inversion symmetry. In principle, the SHG intensity can be further enhanced by adding additional layers in AB stacking order, as long as the phase difference remains negligible, as was also reported in CVD grown few layer MoS2 samples.24 We note that the explanations above are only valid if the hBN intralayer optical properties are not modified by the number of layers, or by different stacking configurations. Indeed, we find that the linear absorption spectra of single layer and bilayer h-BN in different stacking configurations show similar characteristics with little dependence on the stacking structures. Figure 3d shows the broadband absorption spectra measured from mono- and bilayer h-BN in two different stacking regions, using a DUV−vis-NIR hyperspectral imaging microscope.21 Here, absorption is deduced from the equation, 1-TR/TR0, where TR and TR0 are transmission values obtained from the sample on the SiN and the bare SiN substrate, respectively. We observe dominant absorption peaks appear at ∼6.1 eV for all three regions (monolayer, AB and AA′ bilayers) with no observable difference between AB and AA′ stacking regions in the peak amplitude (∼23% absorption) and energy within our experimental resolution (see the right plot, Figure 4d). Our data thus confirms that the strong SHG intensity variation in h-BN bilayers is caused by the difference in the local lattice symmetry. In addition to the ground-state lattice symmetries, h-BN bilayers in θ = 0° and θ = 60° orientations display clear differences in their interlayer energy landscapes (Figure 1b,c). As a result, they show strikingly different topological defects, which we now explore. One key difference in their energy landscapes is related to how the ground-state structures are organized. For θ = 0° (Figure 1b), there are two equivalent (twin) ground-state structures (AB and AC), whereas there is only one ground state (AA′) for θ = 60° (Figure 1c). When two adjacent states (AB/AC, or AA′/AA′) are connected over space within the same stacking region, a topologically protected defect line, or topological defect, forms at the boundary, whose D

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ACKNOWLEDGMENTS The authors thank M. P. Levendorf for help with preparing the manuscript. This work was mainly supported by the NSF through the Cornell Center for Materials Research (NSF DMR-1120296). Additional funding was provided by the AFOSR (Grants FA9550-09-1-0691, FA9550-10-1-0410), the Samsung Advanced Institute for Technology GRO Program, the Nano Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (2012M3A7B4049887) as well as the Kavli Institute at Cornell for Nanoscale Science (KIC). C.-J.K. was partially supported by the Basic Science Research Program through the NRF funded by the Ministry of Education, Science, and Technology (2012R1A6A3A03040952). Sample preparation was performed at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765).

vector normal to the defect line (inset, Figure 4c). The gray circles and black squares indicate data from BN/BN (θ = 0°) and BN/NB (θ = 60°), respectively. We observe that the width ranges between 5 and 25 nm and that it generally decreases as α increases to 90°. Significantly, while having broad variations in their shapes, dislocations from BN/BN (θ = 0°) are wider than those from BN/NB (θ = 60°) at similar α, as clearly seen in DF-TEM images in Figure 4d (α ∼ 0°). The width of a topological defect line in bilayer materials is determined by two fundamental quantities: the mechanical stiffness (Young’s and sheer moduli) of a monolayer and the stabilization energy of the ground state (relative to that of a saddle point). Quantitatively, it is determined by energy minimization, involving competition between the interlayer potential energy (AU0w) and strain energy (BM/w), where A and B are constants, U0 is the average potential energy per atom in the dislocation region, and M is the strain modulus, which is a function of α depending on the type of the applied stress (shear or tensile stress).36 It has a minimum energy when w = (BM/(AU0))1/2. It suggests that a higher U0 results in a narrower dislocation width and the h-BN bilayers in AA′ stacking has larger stabilization energy. In fact, this model provides a good quantitative fit to our data by using the previously reported theoretical U0 values for BN/BN (θ = 0°) and BN/NB (θ = 60°) (solid lines, Figure 4c)27 (see Supporting Information). Altogether, our data show that the associated displacement vector and the energetics of strain dislocations in h-BN bilayers are determined by the different interlayer energy landscape unique to each stacking configuration. In summary, we examined the structure−property relationships in h-BN bilayers in two different stacking configurations for θ = 0° and θ = 60°. We found the stable structure of AB (or AC) for θ = 0° and AA′ for θ = 60°. Our measurements of optical SHG show strong enhancement only in noncentrosymmetric AB stacking, while linear optical absorption properties are similar for all bilayer h-BN. Furthermore, we observe the distinct properties for topological defects, which is consistent with different energy landscapes for the two stacking structures. Recently, various dichalcogenides (ex. MoS2 and WS2) have been introduced and studied bringing new physical properties in the atomically thin material pool.37 In principle, these materials similarly allow various rotational and translational degrees of freedom in stacked structures.38,39 Understanding the structure property relationships as discussed in our work, will provide a powerful means for designing and optimizing the properties of new layered materials and the performance of devices based on them.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed descriptions of the epitaxial growth of h-BN, TEM characterization of h-BN stacking structures, and measurement of the second harmonic generation. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. E

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