Graphene can be used for high-mobility semiconductor technology because of its one of a kind band gap structure and this has caught the attention of many researchers. However, scientists have found it difficult to find an appropriate substrate and so unlocking the full potential of graphene-based high-performance technology has been slow.
Lately, progress has been made in overcoming this issue as research of the epitaxial growth of graphene on hexagonal boron nitride (hBN) looks promising [1, 2]. Hexagonal boron can be used as a substrate for graphene because it possesses nearly identical hexagonal shapes.
Graphene and hBN have only an approximate 2% difference, which produces a moiré pattern superlattice, with periodicity figures greater than each of the two materials’ lattice constants by two orders of magnitude .
Moiré patterns can be characterized by Scanning Probe Microscopy (SPM). SPM is a popular method because it can offer the best Z resolution in contrast to any other microscopy method . This means that it is crucial in the verification of a successful fabrication of graphene or hBN technologies by epitaxial growth protocols. This method, however, has three major drawbacks:
Firstly, the confusing parameter optimization requires high effort and considerable amounts of time by researchers of all abilities to master; secondly, the method is expensive due to the highly specialized tips needed to produce the high-resolution imaging; and thirdly, frictional mode SPM is destructive when characterizing graphene or hBN technologies because it uses a mechanical tip-sample, but this is common with nearly all methods that characterize moiré patterns [1, 2, 3].
In contrast, Non-contact mode Atomic Force Microscopy (AFM), which has been around since the late 1980’s, is a method that uses SPM methods but is not destructive . A requirement of non-contact mode imaging, is the accurate control of tip-sample separation, which is not an easy task and creates a huge barrier to its use. However, with advancements in the last ten years of this method, it is now carried out as the routine procedure in AFM imaging mode by Park Systems.
SmartScan™ Auto Mode is an automated non-contact mode AFM imaging technique designed by Park Systems and provides a simple, non-destructive SPM characterization of moiré pattern. This product addresses the need for moiré pattern SPM characterization technologies that are inexpensive, quick, non-destructive, and effortless, and that will reliably execute quality control of the fabricated graphene-based technologies.
Non-Contact Mode AFM Imaging
Regulation of the cantilever’s oscillation amplitude at an increased frequency to resonance frequency of the cantilever in air is required in order to achieve non-contact mode imaging. As the probe end reaches the sample surface, the interaction between the probe end and the sample becomes a positive phase. In this positive state, non-contact mode imaging is carried out.
In the attractive state, the cantilever oscillation state is negative , but in the repulsive phase, it is positive. In dynamic or tapping mode, reducing the pulling apart of the probe-end from the sample, the interaction changes from an attractive phase to a repulsive one.
Figure 1 shows the changes in amplitude as a function of probe-end to sample separation and is referenced to as the ‘A-d curve’. The oscillation amplitude is reduced as a result of the probe-end to sample interaction forces, as the oscillating cantilever reaches the surface. A tiny abrupt raise in cantilever amplitude occurs when the probe end is lowered.
This small jump of amplitude is related to the flip of the state from positive to negative, therefore suggesting a change from the attractive to the repulsive state in the probe-end to sample interaction. Meaning that the cantilever changes from non-contact mode to tapping mode.
The amplitude figure reaches zero as the probe end moves towards the sample. Following this, if the cantilever is removed and probe-end to sample separation rises, the leap from the negative to the positive phase happens again, but this time at a distance further from the surface of the sample.
If imaging is carried out with cantilever oscillation amplitudes bigger (lesser) than the second (first) leap point, imaging is carried out in non-contact (tapping) mode, and probe-end to sample interaction is kept in the positive (negative) phase.
The probe-end to sample interaction will not be stable and flips back and forth from the positive to negative states, when imaging is carried out with amplitude values lower than the first and greater than the second jump values, which is detrimental to the imaging process and is labeled in Figure 1 in the b-stable state . Whether the value is negative or positive is reliant on the AFM manufacturer.
Figure 1. AFM cantilever oscillation amplitude (upper) and phase (lower) versus tip-sample separation (d) known as the A-d curve for constant Z actuator driving power. The red curves denote the tip approaching the sample and the blue curves show the response when the tip is retracted from the sample surface. (Image used with permission from NanoScientific) 
SmartScan™ Auto Mode
Park Systems has created a new operating software, SmartScan™, to be used for AFM systems in research. This software includes Auto Mode, which is one of the exciting new features it has to offer and can be used for carrying out measurements. Flowing the placement of the probe end and the sample, Auto Mode involved a two-step process: positioning and imaging.
In the first step, positioning, the probe-end to sample Van der Waal (VdW) force interactions are identified in order to locate the sample surface, which occurs at a speed of 0.5 mm per second. Even though this process is quite time efficient, the probe end never touches the sample surface. Alternatively, the probe-end and sample positive phase and its influence on cantilever oscillation size are used to identify the sample surface.
This means that the probe-end remains sharp and the surface of the sample remains untouched. After locating the surface, the probe-end is positioned so that it is approximately 200 μm away which allows for the navigation of the sample surface and the pinpointing of the region of interest using optical microscopy. Once the location of the sample surface is determined, the optical microscope is immediately put into focus and it does not need to be done manually by the user.
Following the selection of the region to be investigated, the imaging step is initiated. Throughout the imaging process the following parameters are optimized automatically in relation to the wanted image quality: free air amplitudes, setpoint amplitudes, oscillation frequency, and feedback control parameters.
The only things that need to be chosen by the researcher are the number of scan lines, the desired image quality, and the scan size. Precise probe-end to sample separation is calculated by SmartScan™ Auto Mode based on the A-d curves illustrated in Figure 1.
Figure 2. The newly developed SmartScan™ Auto Mode which allows automated sample surface detection and imaging with minimal user interaction. On the left the major buttons including ‘positioning’ and ‘image’ are shown. Screenshot was taken while the software was collecting a 150 nm image of graphene/hBN sample in Non-Contact mode. The user only needs to select scan size, image resolution, and quality/speed.
Graphene Epitaxy on hBN
For this study, hBN samples were prepared by mechanical cleavage of BN crystals on a silicon substrate with a 300 nm SiO2 epilayer. Graphene was grown by CVD epitaxial growth. Additional information can be found in the work by Yang et al.
The graphene/hBN samples were imaged using a standard non-contact mode silicon AFM probe with a nominal tip radius of 7 nm and force constant of 42 N/m. The tip resonance frequency was chosen at 316 KHz by the software. The sample surface was detected by automated software and followed by navigating the sample through optical microscopy and automated imaging.
The images were collected in 125 nm, 250 nm and 500 nm square sizes. Firstly, lower magnification images were collected, and then image size was decreased for higher magnifications.
Non-contact mode AFM images of the graphene/hBN samples are shown in Figure 3. a) Non-contact mode images of graphene-hBN samples with 125 nm, 250 nm and 500 nm scan sizes. No filter was applied to the images. The insets indicate Fourier transformation of the image. The moiré superlattice of epitaxial graphene is easily distinguishable in all images in a hexagonal pattern.
The hexagonal pattern was evaluated and confirmed by fast Fourier transform (FFT) of AFM images, illustrated in the insets of Figure 3.a. Additional grains of the secondary layer can be seen in the 500nm image. To characterize the height of the secondary grains, a line profile of the 500 nm image was selected as illustrated in Figure 3.b. The height of the secondary grain is ~3.8Å. The moiré pattern is observable on the secondary grains, as well.
Figure 3. a) Non-contact mode images of graphene-hBN samples with 500 nm, 250 nm, and 125 nm scan sizes. No filter has been applied to the images. The insets indicate Fourier transformation of the image. b) The profile of the dashed line in the 500 nm image.
The moiré superlattice is characterized in Figure 4 by using one of the 250 nm images. A FFT filter is applied to eliminate additional signal and allow easier characterization of the pattern. The lattice constant of the moiré pattern is measured to be ~15 nm. This is consistent with the simulation results of ~14 nm, which is two orders of magnitude bigger than lattice constants of graphene and hBN.
The green and red lines indicate the axes of the superlattice and are used for measuring periodicity in either direction. The peak-to-valley value for each line is below 0.7Å. The continuity of moiré pattern over all the spaces indicates successful growth of epitaxial graphene over hBN.
It also indicates growth of graphene on hBN irrespective of the number of layers, as seen in the 500 nm image in Figure 3. The formation of the moiré pattern is the result of a ~2% mismatch between the lattice constants of graphene and hBN.
Figure 4. A FFT filter is applied to one of the 250nm images in Fig. 2.a. to characterize the moiré superlattice. Line profiles for the red and green lines are shown on the right side.
To the knowledge of the authors, imaging the moiré pattern of epitaxial graphene in non-contact mode has not until now been performed. This is highly important, as the samples are fragile (low friction between graphene and hBN). Therefore, minimized interaction between the sample and tip is desired to maintain the conditions of the sample during the characterization.
There is no mechanical interaction, and the imaging is performed in the ambient atmosphere without the need for a vacuum. Therefore, non-contact mode imaging, as a benign characterization technique, plays a key role for characterization of devices fabricated by epitaxial growth of graphene on hBN or other two-dimensional materials.
Maintaining tip sharpness is another advantage of using non-contact mode imaging. In addition to reducing the tip cost, a dependably sharp tip preserves the image quality and improves measurement repeatability.
Although finding the correct tip-sample distance for true non-contact mode imaging is difficult and could depend heavily on user experience, using automated software enables performing the measurements with minimal user interaction. It also improves repeatability, productivity and measurement throughput.
A standard non-contact mode probe (PPP-NCHR) was used for this measurement, not the special or super-sharp tip usually required for this sort of high resolution imaging. In non-contact mode, VdW interaction between tip and sample is utilized to image the moiré superlattice with high resolution and repeatability.
Note the moiré pattern lattice constant (15 nm) is almost twice the nominal tip radius (7 nm). This enables decreasing the characterization cost for potential devices fabricated based on epitaxial graphene.
The moiré superlattice of epitaxial graphene grown on hBN has been imaged in non-contact mode using a recently developed automated AFM. Images were collected using a standard silicon probe with nominal tip radius of 7 nm. The moiré superlattice was characterized, and the lattice constant of ~15 nm was verified against simulation values.
The recently developed automated AFM allows minimal user experience needed for performing this type of high-resolution measurement. It also improves productivity, repeatability and throughput. Automated non-contact mode imaging is therefore an efficient characterization technique for quality control of devices fabricated by epitaxial growth, such as graphene/hBN-based devices.
The authors are immensely grateful to David Goldhaber-Gordon and Patrick Gallagher from Stanford University and Guangyu Zhang from Chinese Academy of Sciences for providing the graphene/hBN sample and fruitful discussions.
Original authors: Ardavan Zandiatashbar, Byong Kim, Young-kook Yoo, Keibock Lee, Park Systems Inc., 3040 Olcott St., Santa Clara, CA 95054.
References and Further Reading
 W. Yang, G. Chen, Z. Shi, C.-C. Liu, L. Zhang, G. Xie, M. Cheng, D. Wang, R. Yang, D. Shi, K. Watanabe, T. Taniguchi, Y. Yao, Y. Zhang and G. Zhang, “Epitaxial growth of single-domain graphene on hexagonal boron nitride,” Nature Materials, vol. 12, pp. 792-797, 2013.
 S. Tang, H. Wang, Y. Zhang, A. Li, H. Xie, X. Liu, L. Liu, T. Li, F. Huang, X. Xie and M. Jiang, “Precisely aligned graphene grown on hexagonal boron nitride by catalyst free chemical vapor deposition,” Scientific Reports, vol. 3, no. 2666, 2013.
 C. R. Woods, L. Britnell, A. Eckmann, R. S. Ma, J. C. Lu, H. M. Guo, X. Lin, G. L. Yu, Y. Cao, R. V. Gorbachev, A. V. Kretinin, J. Park, L. A. Ponomarenko, M. I. Katsnelson, Y. N. Gornostyrev, K. Watanabe, T. Taniguchi, C. Casiraghi, H.-J. Gao, A. K. Geim and K. S. Novoselov, “Commensurate–incommensurate transition in graphene on hexagonal boron nitride,” Nature Physics, vol. 10, pp. 451-456, 2014.
 G. T. Smith, Industrial Metrology: Surfaces and Roundess, Springer, 2002.
 G. Binnig, C. F. Quate and C. Gerber, “Atomic Force Microscope,” Physical Review Letters, pp. 930-933, 1986.
 R. Garcia and R. Perez, “Dynamic atomic force microscopy methods,” Surface Science Reports, pp. 197-301, 2002.
 A. Zandiatashbar, “Sub-angstrom roughness repeatability with tip-to-tip correlation,” NanoScientific, no. Winter, pp. 14-16, 2014.
This information has been sourced, reviewed and adapted from materials provided by Park Systems Inc.
For more information on this source, please visit Park Systems Inc.