A non-invasive sub-surface electrical probe to encapsulated layers in van der Waals heterostructures

TL;DR

This paper introduces a non-invasive electrostatic force microscopy technique capable of imaging and characterizing buried two-dimensional layers in van der Waals heterostructures, aiding in device optimization.

Contribution

The study demonstrates a versatile, fast, and non-invasive method to visualize and analyze encapsulated layers over 30 nm below the surface in heterostructures.

Findings

Effective imaging of buried layers over 30 nm deep

Distinct work function fingerprints for different materials

Insights into charge environment and structural imperfections

Abstract

Van der Waals heterostructures formed by stacking different atomically thin layered materials have emerged as the sought-after device platform for electronic and optoelectronic applications. Determining the spatial extent of all the encapsulated components in such vertical stacks is key to optimal fabrication methods and improved device performance. Here we employ electrostatic force microscopy as a fast and non-invasive microscopic probe that provides compelling images of two dimensional layers buried over 30 nm below the sample surface. We demonstrate the versatility of the technique by studying heterojunctions comprising graphene, hexagonal boron nitride and transition metal dichalcogenides. Work function of each constituent layer acts as a unique fingerprint during imaging, thereby providing important insights into the charge environment, disorder, structural imperfections and doping profile. The technique holds great potential for gaining a comprehensive understanding of the quality, flatness as well as local electrical properties of buried layers in a large class of nanoscale materials and vertical heterostructures.

Tables

Table 1. Table 1: Surface potential ( V s subscript 𝑉 𝑠 V_{s} ) and work function ( Φ s subscript Φ 𝑠 \Phi_{s} ) for different encapsulated 2D layers measured in this work. V s subscript 𝑉 𝑠 V_{s} was estimated using fit to equation (2) and Φ s subscript Φ 𝑠 \Phi_{s} was estimated using a calibrated AFM tip.

Type	Sample	$V_s\left(V\right)$	${\Phi }_s\left(eV\right)$
hBN/SLG/hBN	S14	-0.46	4.84
	S15	-0.66	4.64
hBN/FLG/hBN	S8	-0.39	4.91
	S11	-0.45	4.85
hBN/FL-MoS2/hBN	S21	-0.80	4.5
hBN/FL-WSe2/hBN	S20	-0.26	5.04

Table 2. Table 2: Table summarizing the results obtained for various graphene and TMDC-based vdW heterostructures, indicating top and bottom hBN thicknesses, lift height and fit parameters C o subscript 𝐶 𝑜 C_{o} and V s subscript 𝑉 𝑠 V_{s} obtained from equation (2). Within a stack the variations in capacitive coupling is expected to be minimal. The major factor responsible for phase variance is the change in the surface potential of the constituent layers.

Type	Sample	Bottom hBN (nm)	Top hBN (nm )	Lift Height (nm)	$C_o$ (V-2)	$V_s$ (V)
hBN/SLG/hBN	S14	28	13	30	0.031	-0.46
hBN/SLG/SiO2	S15	33	18	30	0.026	-1.06
hBN/SLG/hBN	S15	33	18	30	0.031	-0.66
hBN/FLG/hBN	S8	27	25	20	0.067	-0.39
Air/FLG/hBN	S8	27	25	20	0.072	-0.23
hBN/FLG/hBN	S11	27	27	30	0.040	-0.45
hBN/FLG/hBN	S11	27	27	30	0.050	-0.36
hBN/FL-WSe2/hBN	S20	24	18	30	0.022	-0.26
hBN/FL-MoS2/hBN	S21	34	12	30	0.028	-0.80

Equations

$$\tan (\Delta \varphi )=\frac{Q}{k}\frac{dF}{dz}=\frac{-Q}{2k}\frac{d^{2}C}{d{z}^2}(V_{dc}-V_s{)}^2$$

$$\Delta \varphi =-{\tan }^{-1}[C_0(V_{dc}-V_s{)}^2]+C_1$$

Full text

van der Waals heterostructures, electrostatic force microscopy, graphene, hBN, 2D layered materials

I I. Introduction

Two dimensional (2D) layered materials such as graphene, hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDCs) offer a new platform to create vertical heterostructures, where different atomically thin layers can be picked and assembled deterministically to suit various niche applications. These vertical stacks, popularly known as van der Waals (vdW) heterostructures vdW2 exhibit new chemical and physical phenomena that are drastically different from the constituent layers Jariwala ; Chandni ; Dean ; Wang ; Kallol . The first tested device geometry involved single layer graphene encapsulated within atomically flat, dangling bond-free hBN layers with reduced charge traps, giving rise to improved transport properties and near-theoretical electron mobilities Dean ; Wang . The device fabrication protocols have improved substantially over the years with heterostructures routinely containing five or more atomically thin layers of different materials, with precise twist angles Kim_NL . Such advances have led to the demonstration of exotic physical phenomena such as the Hofstader butterfly Hunt and magic-angle superconductivity Cao . The collective behaviour of the various heterostructure elements become relevant in these geometries, leading to superlattices, charge redistribution, modified structural properties and twist angle-dependent physical parameters Cao ; Hunt ; Mishchenko . Furthermore, encapsulating 2D layered materials between hBN layers also proves useful in studying many reactive layered materials such as phosphorene, magnetic materials such as chromium tri-iodide and various 2D topological insulators Favron ; Huang . While encapsulation offers unparalleled performance advantage, it obscures the sample characterization and device fabrication methods as these samples are often exfoliated and assembled in gloveboxes.

Characterizing the spatial extent and charge distribution profile of the buried layers in a heterostructure is currently challenging. A combination of techniques such as optical microscopy, Raman mapping, scanning electron microscopy and atomic force microscopy (AFM) are commonly employed to identify the layered materials. Raman mapping is a particularly useful technique which in addition to identifying the constituent layers non-invasively, also provides crucial information on doping, edge profiles, lattice temperature, defects and strain Anindya ; Neumann . However, the technique is hugely limited by the spatial resolution of the laser spot size which is usually of the order of 500 nm - 1 $\mu$m. Also, for large samples with lateral dimensions of the order of tens of microns, the image acquisition is a rather slow process, often running into few hours. Optical microscopy techniques such as dark field imaging and differential interference contrast imaging, and AFM topography scans provide sporadic benefits, limited by the thickness of the top-most layer (usually a thick, insulating hBN layer with thickness varying from 10 to 40 nm). Notably, these techniques do not provide any further sample specific information such as doping profile, which usually needs further invasive electrical transport measurements. A simple, fast and non-invasive method that can identify individual layers in a heterostructure, and at the same time provide useful information on the spatial distribution of charge carriers is desirable for enhanced device throughput.

In this article, we present electrostatic force microscopy (EFM) as an effective tool to spatially map and study the local surface potential variations in encapsulated vdW heterostructures. In the past, surface potential profiles in isolated 2D layered materials have been investigated using EFM Datta ; Burnett ; Panchal ; Shi ; Li_NL ; Gomez and Kelvin probe force microscopy (KPFM) Yu ; Yan ; Druga ; Ziegler ; Willke ; Robinson . These studies were found to be particularly useful in studying doping Shi , substrate Ziegler and thickness dependences Datta ; Burnett and contact resistances Panchal ; Yu ; Yan ; Druga ; Willke of graphene flakes supported on SiO2/Si Datta ; Shi ; Yu ; Yan ; Willke , copper Robinson or SiC Burnett ; Panchal ; Druga substrates. Extension of this technique to vdW heterostructures involving multiple 2D layered materials has been limited Li ; Altvater . Charge transfer mechanisms between the layers and screening of extrinsic charges from the substrate and external environment can signficantly alter the surface potentials when multiple 2D layers are stacked vertically. Hence, our current understanding of the surface potentials in isolated flakes do not work well in the context of complex, multi-layered heterostructures. Remarkably, EFM technique is capable of probing the individual layers in vdW heterostructures, which are otherwise inaccessible via conventional surface probes. In our measurements, the surface potential (or work function) acts as a fingerprint for each 2D layer, leading to a phase contrast with respect to other constituent layers. This enables us to obtain visually compelling images of various 2D layers, buried over 30 nm below the sample surface.

We fabricate a variety of encapsulated heterostructures involving graphene, hBN and TMDCs, and demonstrate the ease of visually distinguishing the encapsulated 2D layers using EFM. We observe that the EFM phase as a function of tip-sample bias (or spectroscopy) provides a quantitative estimate of the work functions of the encapsulated layers. Further, we demonstrate the effect of substrate doping and ambient atmosphere on the work functions of graphene layers by fabricating and characterizing different heterostructure architectures and comparing them with fully encapsulated regions. Finally, we show that the technique has a broad appeal and works equally well for complex heterostructures involving multiple 2D layers.

II II. Results and Discussions

II.1 A. Sample Fabrication and Characterization

Encapsulated vdW heterostructures comprising graphene, hBN and TMDCs were fabricated on SiO2/Si substrates using the dry transfer method Wang . Individual graphene, hBN, MoS2 and WSe2 flakes were mechanically exfoliated on oxygen plasma treated Si substrates with a 285 nm SiO2 top layer. The desired flakes were identified using an optical microscope. A Polypropylene carbonate (PPC)/Polydimethylsiloxane (PDMS) hemispherical stamp on a glass slide was used to pick up the top hBN at 450C, followed by graphene or MoS2 or WSe2. The stack was transferred on the exfoliated bottom hBN on SiO2/Si wafer at 1000C. To demonstrate the capability of the technique we first employed simple hBN/Graphene/hBN heterostructures. Fig. 1(a)-(c) show the constituent layers in such a stack (S14) where a single layer graphene (SLG) is encapsulated between hBN layers of thicknesses 13 nm (top) and 28 nm (bottom). Evidently, the optical image of the vertical stack shown in Fig. 1(d) does not reveal the encapsulated graphene flake. Even with a differential interference contrast optical microscopy (Fig. 1(e)), dark field imaging (Fig. 1(f)) and scanning electron microscopy (Fig. 1(g)), the encapsulated flake is not discernible. Further characterization of the encapsulated flake using Raman mapping (Fig. 1(h)) provided a reasonable estimate of the spatial extent. Raman mapping was done using a confocal microscope system ( LabRAM HR) with a 100x objective and a numerical aperture of 0.90. A 532 nm laser with a spot diameter of $\sim$ 1 $\mu$m was used to excite samples placed on a piezocrystal-controlled scanning stage. The Raman spectra were collected using a low laser power of 1.1 mW to avoid any laser induced heating effects. For the graphene samples, the 2D peak position and full width at half maximum (FWHM) were estimated using single-peak Lorentzian fits. Total acquisition time for the image shown in Fig. 1(h) was $\sim$ 4 hours.

II.2 B. EFM as a non-invasive imaging tool

In Fig. 2, we present EFM measurements on stack S14. EFM measurements were conducted under ambient conditions using a Bruker Dimension Icon AFM setup employing Pt/Ir coated silicon probes (SCM-PIT V2) with a nominal tip radius of $\sim 25$ nm. EFM is a two-pass technique, where both topography and EFM phase are recorded sequentially. In the first pass, the AFM tip traces the topographic line profile in tapping mode. During the second pass, the AFM tip is lifted by a specified lift height $z$ and a $dc$ voltage $V_{dc}$ is applied to the sample via the doped Si wafer, with the AFM tip grounded (Fig. 2(a)). The tip is mechanically oscillated and retraces the topographic profile, providing a measure of the tip-sample electrostatic forces, given by $F=-\frac{1}{2}\frac{dC}{dz}(V_{dc}-V_{s})^{2}$, where $V_{s}$ is the local electrostatic potential over the sample surface and $C$ is the tip-sample capacitance. $V_{s}=\Phi_{s}-\Phi_{t}$, also called the contact potential difference, can be used to estimate the work function (or electron affinity) of the sample ($\Phi_{s}$), provided the work function of the tip ($\Phi_{t}$) is known. The electrostatic force leads to a change in resonant frequency of the cantilever, which is measured as a phase shift, given by Staii ; Lei :

[TABLE]

where $Q$ and $k$ are the quality factor and force constant of the AFM probe respectively, which can be measured by the thermal tune calibration procedure. This gives a characteristic parabolic dependence of the EFM phase on the tip voltage. Since the EFM technique operates on the force gradient, it has a much better sensitivity compared to amplitude modulated KPFM technique Panchal . In addition, the effect of the parasitic capacitances from the cantilever part of the AFM probe is minimised as the force gradient decays faster with distance. As can be seen from equation (1), a phase contrast can appear between constituent layers in a heterostructure due to two factors: (a) capacitive coupling, which leads to a change in the curvature of the EFM phase parabola and (b) surface potential $V_{s}$, which results in an offset in the EFM phase parabola. These two scenarios are depicted in Fig. 2(b) and Fig. 2(c) respectively. In a heterostructure geometry, we expect to have a combination of these two effects, leading to a phase contrast between various constituent layers. For the device S14, the AFM topography shown in Fig. 2(e) shows wrinkles, trapped bubbles and other topographical defects. However, the encapsulated SLG is not discernible.The EFM phase image for the same region, acquired at a bias of 1 V and a lift height of 30 nm is shown in Fig. 2(f). Remarkably, the encapsulated region and all the features therein, are visible with enhanced clarity in the EFM phase image. We attribute this contrast to the difference in the surface potential and the capacitive coupling in the constituent layers. Here, the top hBN layer, being an insulator with a large band gap of $\sim$ 5.9 eV, acts as an additional dielectric layer with a dielectric constant of $\epsilon_{r}\sim 4$  Li_NL . The encapsulated semi-metallic graphene is hence visible with a good contrast in the EFM phase image. These results establish EFM as a non-invasive, sub-surface imaging technique to detect encapsulated 2D layers in vdW heterostructures.

In order to quantitatively analyse the surface potential of the encapsulated graphene layer, EFM phase images were taken at various sample bias voltages. In Fig. 3(a)-(d), we show the phase images at bias voltages $V_{dc}=-2.5$ V, -0.3 V, 0.1 V and 2.5 V respectively. We note that the phase shift of the graphene region was most often negative with respect to the background SiO2 and hBN regions. While graphene is clearly visible at $\pm$ 2.5 V and 0.1 V, the contrast is poor for -0.3 V, where it merges with the SiO2/hBN background phase. EFM phase vs. bias voltage on the graphene region (Fig. 3(e)) shows the characteristic parabolic dependence of equation (1). Fluctuations in phase within the graphene region were found to be minimal, evident from the negligible error bars. The maximum value in the parabola occurs when $V_{dc}=V_{s}$, which can be obtained by fitting the data with:

[TABLE]

where the coefficient $C_{0}=(Q/2k)(d^{2}C/dz^{2})$ and $C_{1}$ is the phase offset in the experiments. This offset has been corrected for clarity and ease of comparison in the EFM phase plots shown here.

The maximum point extracted from the parabolic fit gives a good estimate of the surface potential, which is obtained as $V_{s}=-0.46\pm 0.03$ V for the encapsulated SLG. While $Q$ and $k$ can be obtained experimentally, the capacitive coupling is rather complex with contributions from the tip apex, cone and the cantilever Lei . For the encapsulated flake, the capacitive coupling is more involved, as the metal tip-semimetal capacitance is no longer passive and cannot be analytically determined from the tip-sample geometry alone. Due to these constraints on the quantitative estimate of the capacitive coupling of the tip and heterostructure elements, we restrict our analysis to the surface potential estimation alone. In order to quantify the work function of the constituent layers, it is important to define the work function of the AFM probe tip. This calibration was done using a gold sample ($\Phi_{\text{Au}}=5.1$ eV), giving $\Phi_{t}=5.3$ eV, which is a good estimate for the Pt/Ir AFM probe. For sample S14, we obtain the work function to be $\sim$ 4.84 eV.

In order to demonstrate the versatility of the technique and its applicability to a larger class of 2D materials, we have also performed EFM measurements on encapsulated TMDCs, such as MoS2 and WSe2, the details of which can be found in the supplemental material section. Table 1 summarises the results over various encapsulated samples.

II.3 C. Probing doping in encapsulated layers using EFM

In order to further demonstrate the capability of the technique in probing electrical properties of the buried layers, we utilize diverse heterostructure geometries. In Fig. 4(a)-(c), we show the EFM phase images for two SLG regions in stack S15, with slightly different vertical architectures, as shown by regions A and B in Fig. 4(c). While region A comprises a fully encapsulated graphene flake, in region B, the graphene flake is on SiO2/Si wafer with a top hBN layer. The top and bottom hBN thicknesses measured by AFM topography were 18 nm and 33 nm respectively, and EFM phase mapping was performed at a lift height of 30 nm. Interestingly, we observe clear phase contrast in the two regions, the relative sign of which changes as the sample bias is varied. We also note that within the two regions, the fluctuation in phase is minimal. The regions are thus nearly equipotentials, with the surface potential varying only on changing the charge environment via the heterostructure geometry.

To further understand the phase contrast, we have plotted EFM phase vs. voltage plots (Fig. 4(d)) for the two regions. The parabolic curves are found to be offset with respect to each other and cross over near $V_{dc}=-1$ V. This explains the changes in the phase contrast seen in Fig. 4(a)-(c). On fitting the two parabolas with equation (2), we obtain the surface potentials for the two configurations as $V_{s}=-0.66\pm 0.01$ V and $-1.06\pm 0.05$ V for regions A and B respectively. We attribute this difference to doping from charge traps in the substrate. The encapsulated graphene regions (A) gave a work function $\approx 4.64$ eV, while region B gave lower ($\approx 4.24$ eV) value of work function, indicating electron doping. In region B, SiO2 beneath the graphene has positive trap charges which modulate the chemical potential of graphene resulting in $n$-doping, similar to previous studies Gomez ; Romero . In region A, the bottom hBN layer screens the effect of dangling bonds and trap charges of SiO2, while the effect of the ambient environment on the chemical potential of graphene is reduced by the top hBN. The substrate induced doping is also verified by Raman spectroscopy measurements, where we obtain a broader 2D Raman peak in region B (Fig. 4(e)). Encapsulated region A has the 2D peak at $\sim$ 2684 cm*-1* with a FWHM of 15.7 cm*-1*, while in region B, the peak is observed at $\sim$ 2685 cm -1 with FWHM $\sim$ 30 cm*-1*. Dielectric screening results in suppression of the electron-electron scattering in hBN supported graphene, giving a sharper peak in region A. In SiO2 supported SLG, because of poor screening the scattering process is enhanced with lower life time of photoexcited electron-hole pairs, resulting in a broader 2D peak consistent with previous reports Anindya . 2D peak depends on the phonon life time as well as the number of scattering paths to satisfy the double resonance condition and is thus sensitive to inhomogeneity at small doping levels ($\sim 10^{12}$ cm*-2*). The other factor that contributes to the electrostatic phase is the capacitive coupling between tip and sample, which should roughly be the same for both the regions. We note that the fitting indeed gives a comparable value for the coefficient $C_{0}$ to be 0.031 V*-2* and 0.026 V*-2* respectively, for the two regions A and B.

In Fig. 4(f)-(h), we show the EFM phase images for a few layer graphene (FLG) flake on hBN (stack S8), which is fully encapsulated in region C and exposed to air in region D. Top and bottom hBN flakes were 25 nm and 27 nm thick respectively, and the lift height for EFM measurements was 20 nm. Fig. 4(i) shows the EFM phase plots for the two regions. Again, we observe clear phase contrast in the two regions, with $V_{s}=-0.39\pm 0.02$ V and $-0.23\pm 0.02$ V for regions C and D respectively. The encapsulated graphene regions (C) gave a work function $\approx 4.9$ eV, while region D gave higher ($\approx 5.1$ eV) value of work function, indicating hole doping consistent with previous reports of surface potential mapping on few layer graphene films exposed to air Datta . The capacitive coupling is expected to be slightly higher in this measurement due to the reduced lift height, as validated by the coefficient $C_{0}=$ 0.067 and 0.072 V*-2* for regions C and D respectively. We note that variations in relative humidity, substrate charge environment and ambient atmosphere can modify the doping and lead to minor discrepancies across samples. However the overall trend remains as described above, in all samples measured (See supplemental material). Our observations are summarised in the energy band diagram shown in Fig. 4(j), assuming minimal doping in the fully encapsulated graphene region.

II.4 D. TMDCs-based heterostructures

We further demonstrate that the EFM phase elucidates the individual elements in complex heterostructures involving graphene, hBN and TMDCs. Such heterostructures are routinely used in many 2D-materials based optoelectronic devices Kallol , and the EFM technique can prove to be extremely useful in such studies as well. Fig. 5(a)-(d) show the optical micrographs of the constituents of stack S18 (Fig. 5(e)) consisting of hBN/MoS2/WSe2/hBN. The EFM phase images taken at bias voltages in the range $\pm 0.9$ V are shown in Fig. 5(f)-(k). We observe clear phase contrast across the device, as the bias voltage is varied. Two distinct regions consisting of encapsulated MoS2 (region A) and encapsulated WSe2 (region B) indicated in Fig. 5(k) are further explored in the phase plot shown in Fig. 5(l). As expected, the EFM phase parabolas are offset due to the difference in the surface potentials in the two layers. We obtain a value of $V_{s}=-0.26\pm 0.01$ V ($\Phi_{s}\approx 5.04$ eV) and $-0.16\pm 0.01$ V ($\Phi_{s}\approx$ 5.14 eV) for regions A and B respectively. The work functions of the MoS2 and WSe2 layers in regions A and B are found to be slightly different from the encapsulated flakes reported in Table 1. We speculate this to be due to charge redistribution in the heterostructure. Earlier studies have reported similar charge redistribution and enhanced screening effect in single layer graphene films connected to few layer graphene films Shi . Studies have also found huge variations in the work function of TMDCs, strongly influenced by thickness, substrates, charge environment and adsorbed layers Yang ; Feng ; Jong . We believe similar out-of-plane charge transfer mechanisms are possible in samples involving multiple 2D layers with overlapping regions, which will be explored in future studies. Nevertheless, the technique provides a reliable method to map elements in a complex heterostructure.

III III. Conclusions

In summary, our results unambiguously demonstrate EFM phase measurements to be a useful tool not only in determining the spatial extent of encapsulated 2D flakes, but also in better understanding the charge distributions and surface potentials in various vertical heterostructures. We show that the 2D layers are affected by the ambient atmosphere and the charge traps in the substrate, which are easily identified non-invasively using EFM measurements. Furthermore, the technique provides very clear phase contrast between different 2D materials even in complex heterostructure architectures, which in conjunction with topography scans provide an easy fabrication route to high quality devices. We believe that these results will be valuable for diverse studies involving 2D materials and also greatly advance the creation of reliable and high throughput device architectures for electronic and optoelectronic applications.

IV Supplemental Material

Fig.6 shows additional data obtained for encapsulated WSe2 and MoS2 layers. Table II summarizes the results obtained for various graphene-based vdW heterostructures reported in this work.

V Acknowledgements

We thank T. Ahmed, S. Bhattacharyya, A. Ghosh, E. A. Henriksen and A. N. Pal for useful discussions. We gratefully acknowledge the usage of the Micro and Nano Characterization Facility (MNCF) at CeNSE, IISc and oxygen plasma system from OMI Laboratory, IISc. U.C. acknowledges support from the Infosys Foundation, IISc start-up grant and ISRO-STC cell.