Local electrical characterization of two-dimensional materials with functional atomic force microscopy

Abstract

Research about two-dimensional (2D) materials is growing exponentially across various scientific and engineering disciplines due to the wealth of unusual physical phenomena that occur when charge transport is confined to a plane. The applications of 2D materials are highly affected by the electrical properties of these materials, including current distribution, surface potential, dielectric response, conductivity, permittivity, and piezoelectric response. Hence, it is very crucial to characterize these properties at the nanoscale. The Atomic Force Microscopy (AFM)-based techniques are powerful tools that can simultaneously characterize morphology and electrical properties of 2D materials with high spatial resolution, thus being more and more extensively used in this research field. Here, the principles of these AFM techniques are reviewed in detail. After that, their representative applications are further demonstrated in the local characterization of various 2D materials’ electrical properties.

Graphical abstract

Keywords

advanced AFM techniques / nanoscale characterization / electrical properties / 2D materials

1 Introduction

The atomically thin two-dimensional (2D) materials are one of the most extensively studied materials, driven by continues discoveries of new physics in them [1, 2]. The single-layer graphene, known as the first stable 2D material [3, 4], exhibit unique and fascinating physical properties, such as zero-band gap [5-7], high thermal conductivity [8, 9], high carrier mobility [10, 11] and quantum hall effect [12, 13], which are highly different from its bulk. Because of these unusual properties, graphene shows promising potentials in a wide range, including nanoelectronics [14, 15], optoelectronics devices [16, 17], chemical sensor [18, 19], transparent electrodes for displays [20, 21] and solar cells [22, 23]. But its deficiency of an electronic band gap has enthused the search for others 2D materials with semiconducting characteristics. So far, a variety of 2D materials have been studied and new materials are still being discovered around the world [5, 24].

2D materials beyond graphene [25, 26] span the entire range of electronic structures, e.g., insulator h-BN [27, 28], semiconductor MoS₂, metal NbSe₂, and display interesting properties. h-BN is acknowledged as one of the ideal inert substrates to investigate intrinsic properties of atomic layers [29, 30]. MoS₂ monolayers [31, 32] can be used to prepare field effect transistor [33] and they have strong photoluminescence [34]. NbSe₂ layers exhibit unique properties such as superconductivity, quantum metallic state, and strong enhancement of the charge density wave (CDW) [36-38]. The great diversity of structure and remarkable properties of 2D atomic crystals make them suitable for applications in next generation of ultrathin flexible electronics [39, 40], catalyst [41, 42], chemical sensor [43, 44], lithium-ion batteries [45, 46], photo sensor device [47, 48] and field effect transistor [49, 50].

Atomic Force Microscopy (AFM) has provided a vast and valuable contribution to the understanding of the fundamental electrical properties of graphene and other 2D materials. It was invented by Nobel Prized Binnig along with his colleagues in 1986 [51]. Initially, AFM was developed to investigate the surfaces of insulators at nanoscale [52]. It obtains sample surface information by detecting the interaction forces between probe and sample other than depending on electrons or photons to detect a sample, so AFM can be applied to a wide range of systems and has predominant applications in many fields including physics, chemistry, material science and engineering.

In early period of AFM, the tip was always in mechanical contact mode with the sample surface. For instance, the first AFM image was taken by contact mode and showed nanoscale spatial resolution [52]. After a few years, Martin, Perez, and many other researchers applied dynamic operation in AFM [53-55]. The cantilever is deliberately excited at a single frequency while scanning on the sample surface [56, 57]. And a feedback loop holds one parameter of the oscillation, either the frequency or the amplitude, at a fixed value. Therefore, in the field of dynamic AFM, there are two basic methods. One is frequency modulation AFM (FM-AFM) that uses frequency as a feedback parameter and is usually operated in vacuum [58]. The other mode is amplitude modulation AFM (AM-AFM) that uses amplitude as feedback parameter and is usually operated in the atmosphere. During the last two decades, AFM and its applications have obtained broad attention from the topographic imaging to electrical mapping [59-63].

Several AFM reviews have been published to introduce the various properties of semiconductors [64, 65], material science [66], food technology [67] and biomaterials [68-70]. Considering the importance of 2D materials electrical properties, this review highlights the principles of AFM based electrical characterization methods and their further applications in 2D materials. Firstly, the principles of conductive atomic force microscopy (C-AFM), scanning Kelvin probe microscopy (SKPM), conventional electrostatics force microscopy (EFM), multi-harmonic electrostatic force microscopy (MH-EFM), scanning microwave impedance microscopy (sMIM), agilent technology-scanning microwave microscopy (AT-SMM) and piezo force microscopy (PFM) are introduced in detail. Then, the applications of these techniques in characterization of the electrical properties of 2D materials are demonstrated. Finally, we summarize this review and present the prospects for new functional AFM technologies.

2 AFM-based electrical characterization techniques

Various AFM-based techniques have been developed to characterize the electrical properties of sample, such as C-AFM for current distribution or spreading resistance, SKPM for surface potential, EFM for electrostatic potential, dielectric constant or surface potential, SMM for permittivity and conductivity, and PFM for an electromechanical response. Here, the above mentioned AFM-based techniques and their applications are summarized in Table 1.

Apart from the above AFM technologies, there are many other methods to explore the electrical properties samples, such as scanning capacitance microscopy (SCM) [65] and scanning tunneling microscopy [104, 105]. Limited by the length of this review, we will focus on the methods summarized in Table 1.

2.1 Conductive-Atomic Force Microscopy (C-AFM)

C-AFM is a significant mode of AFM, which was firstly developed by Murrell and his co-workers in 1993 [106]. And now it has been referred in the literature with several names, including conductive probe AFM (CP-AFM), conductive scanning probe microscopy (C-SPM), conductive scanning force microscopy (C-SFM), and local-conductivity AFM (LC-AFM). C-AFM mode cannot only obtain current mapping of sample, but also provide I-V curve at a certain position [107]. It is sensitive in exploring the current signal of sample. Usually, the currents sensitivity can reach to nanoampere (nA).

Before describing the working principle of C-AFM, we will introduce the concept of spreading resistance. Ideally, the sample is treated as a semi-infinite uniform slab of resistivity (\rho ), and tip-sample makes Ohmic contact with radius a. Then the measured resistance R will be dominated by the spreading resistance [109]:

\begin{array}{}\text{(1)}& R=\frac{\rho }{4a}\mathrm{.}\end{array}

During C-AFM operation, a conductive tip is placed in contact with sample surface, where the tip acts as a counter electrode [106, 108]. Then a bias voltage is applied between the conductive probe and the other counter electrode. This mode has two standard measurement geometries, as depicted in Fig. 1. Fig. 1(a) shows a vertical geometry that records the out-of-plane current distribution. Figure 1(b) shows a horizontal geometry that records the current distribution in-plane [110]. In the vertical geometry, the sample is deposited on top of a conductive substrate and the conductive tip scans over such a surface by measuring the current flowing vertically point by point. On the other hand, in a horizontal configuration, the sample is deposited on an insulating substrate and the electrical connection is obtained by laterally patterning a metal electrode. In this way, current can flow from the biased lateral contact to the moveable metal-coated scanning probe tip, and in-plane current through the material can be obtained.

C-AFM enables us to study the correlation between topography and current distribution mapping. Moreover, force feedback, rather than current feedback, is used to control the tip height in C-AFM, making it possible to study surfaces with electrically insulating regions.

2.2 Scanning Kelvin Probe Microscopy (SKPM)

SKPM is a well-established AFM technique that has the capability to measure the surface potential with high lateral resolution [111]. It was invented by Nonnenmacher in 1991 [54]. This technique also has different names, such as scanning Kelvin force microscopy (SKFM) [112], Kelvin probe force microscopy (KPFM) [111] and scanning Kelvin microscopy (SKM) [113]. Recently, it has provided deep insights into the local surface potential of 2D materials [114-121].

The work function \phi and contact potential difference V_{\text{CPD}} are important parameters for understanding the working principle of SKPM. The \phi is defined as the energy difference between the vacuum level and the Fermi energy, as shown in Fig. 2. The V_{\text{CPD}} is defined as the difference in the \phi of two materials:

\begin{array}{}\text{(2)}& {\phi }_{\text{sample}}-{\phi }_{\text{tip}}=\text{Δ}\phi =V_{\text{CPD}}\cdot e\mathrm{.}\end{array}

Here {\phi }_{\text{sample}} and {\phi }_{\text{tip}} are the work function of sample and tip respectively, and e is the electric charge.

Figure 2(a) depicts the energy level of the tip and sample surface, when the tip and the sample are not electrically connected. The vacuum levels are associated but Fermi levels are different. Equilibrium required Fermi levels to line-up at steady state, if the tip and sample close enough for electrical contact. The Fermi energy level will align through electron current flow, and the system will achieve an equilibrium state, as shown in Fig. 2(b). If the applied V_{\text{DC}} has the same magnitude as the V_{\text{CPD}} and opposite sign of it, the applied voltage eliminates the F_{\text{el}}, as shown in Fig. 2(c). Hence, the V_{\text{CPD}} can be measured by SKPM, thereby the work function of sample can be obtained when the tip work function is known.

Figures 3(a) and (b) demonstrate that SKPM is performed in two passes (nap mode) to explore the surface potential of sample. In the first pass, the topography can be obtained same as standard AC mode (tapping mode) [114, 115]. In the second pass, the tip is raised above the sample surface by lift mode. The mechanical excitation is switched off, and then V_{\text{DC}} and V_{\text{AC}} [116] are applied between the tip and sample [117]. The electrostatic force between tip and sample is given by

\begin{array}{}\text{(3)}& F_{\text{el}}=\frac{1}{2}\frac{\partial C}{\partial z}\text{Δ}{V}^2\mathrm{.}\end{array}

Here, \frac{\partial C}{\partial z} and \text{Δ}V are the capacitance coupling and voltage difference between AFM tip and sample respectively. The total voltage difference between the tip and the sample is

\begin{array}{}\text{(4)}& \text{Δ}V=(V_{\text{DC}}-V_{\text{CPD}})+V_{\text{AC}}\sin ({\omega }_{\text{e}}t)\mathrm{,}\end{array}

where {\omega }_{\text{e}} is the angular frequency of the applied AC voltage. Then the electrostatic force applied to the AFM tip:

\begin{array}{}\text{(5)}& \begin{array}{l}\text{}\\ \text{}\text{}\begin{array}{ll}{F}_{\text{el}}\text{}=\hfill & \frac{1}{2}\frac{\partial C}{\partial z}(\left[{(V_{\text{DC}}-V_{\text{SP}})}^2+\frac{1}{2}{V}_{\text{AC}}^2\right]\hfill \\ \hfill & \text{}+\text{}2[(V_{\text{DC}}\text{}-\text{}{V}_{\text{CPD}})V_{\text{AC}}\sin ({\omega }_{\text{e}}t)]\text{}-\text{}\text{}\left[\frac{1}{2}{V}_{\text{AC}}^2\cos (2{\omega }_{\text{e}}t)\right])\mathrm{,}\hfill \end{array}\end{array}\end{array}

where

\begin{array}{}\text{(6)}& F_{{\omega }_{\text{e}}}=\frac{\partial C}{\partial z}[V_{\text{DC}}-V_{\text{CPD}}]V_{\text{AC}}\sin ({\omega }_{\text{e}}t)\mathrm{.}\end{array}

In order to get higher signal-to-noise ratio, researchers generally set {\omega }_{\text{e}} equals to {\omega }_{\text{r}} (which means F_{{\omega }_{\text{r}}}=F_{{\omega }_{\text{e}}}) in SKPM mode. If F_{{\omega }_{\text{r}}} reaches minimum, the V_{\text{CPD}} can be acquired which shows the local surface potential of sample [118, 119].

2.3 Electrostatic Force Microscopy (EFM)

Up to now EFM technology has many branches [120], such as conventional EFM [124-128], MH-EFM [121, 122] and dynamic contact EFM (DC-EFM) [123]. Through recording long-range electrostatic forces between tip-sample, EFM can measure the electric field gradient distribution, and allow the extraction of capacitance changes, distribution of electrical potential and embedded conductor of sample. In this review, we are going to introduce the principles of conventional EFM [124-128] and MH-EFM in detail [121, 122].

2.3.1 Conventional Electrostatic Force Microscopy (EFM)

A general illustration of the principle of conventional EFM is shown in Figure 4. Conventional EFM operates in two-pass processes, also known as lift-mode. In the first scan, the topography image can be obtained same as standard tapping mode [130]. In the second scan, the tip is raised up (by lift mode) to a controllable height z above the sample surface at a specific distance (usually z is about 20–50 nm). Meanwhile, V_{\text{DC}} is applied between the tip and sample in lift mode, phase shift of the cantilever oscillation is monitored to explore the electrostatic gradient of sample [131, 132].

2.3.2 Multi Harmonic-Electrostatic Force Microscopy (MH-EFM)

MH-EFM is a newly-developing powerful EFM mode that uses multi-frequency for the characterization of electrical properties [90, 133-135]. Different from the conventional EFM, it has the ability to quantitative/semi-quantitative measure the various physical quantities, such as carrier type and carrier concentration.

To describe the working principle of MH-EFM, it is important to understand the effect of frequency on the capacitance–voltage (C–V) curve, as shown in Fig. 5. Figure 5(a) shows schematic of ideal metal-insulator-semiconductor (MIS) structure. Here we use p-type silicon as an example. Figure 5(b) shows the C–V curves of p-type silicon under different frequency. From the C–V curves, the carrier concentration and carrier type can be obtained [10].

In MH-EFM, dual pass mode was used to detect topography and electrical properties of sample. In the first pass, the AFM works the same way as the typical AC mode (tapping mode) [122]. In second pass (lift mode), a V_{\text{AC}} with a frequency of f_{\omega e} is applied between the tip and sample, resulting in multi-harmonic electrostatic force [58, 137]. The electrical force is as follows [121]:

\begin{array}{}\text{(7)}& \begin{array}{ll}{F}_{\text{el}}=\hfill & -\frac{1}{4}\{\frac{\partial C}{\partial z}{V}_{\text{AC}}^2+\frac{{\partial }^{2}C}{\partial V\partial z}{V}_{\text{AC}}^3\cos ({\omega }_{\text{e}}t)\hfill \\ \hfill & +\frac{\partial C}{\partial z}{V}_{\text{AC}}^2\cos (2{\omega }_{\text{e}}t)\hfill \\ \hfill & +\frac{1}{2}\frac{{\partial }^{2}C}{\partial V\partial z}{V}_{\text{AC}}^3[\cos (3{\omega }_{\text{e}}t)+\cos ({\omega }_{\text{e}}t)]\}\mathrm{.}\hfill \end{array}\end{array}

Accordingly, the second and third harmonic components are given by

\begin{array}{}\text{(8)}& F_{2{\omega }_{\text{e}}}=-\frac{1}{4}\frac{\partial C}{\partial z}{V}_{\text{AC}}^2\cos (2{\omega }_{\text{e}}t)\mathrm{,}\end{array}

\begin{array}{}\text{(9)}& F_{3{\omega }_{\text{e}}}=-\frac{1}{8}\frac{{\partial }^{2}C}{\partial V\partial z}{V}_{\text{AC}}^3\cos (3{\omega }_{\text{e}}t)\mathrm{.}\end{array}

The \frac{\partial C}{\partial z} and \frac{\partial C}{\partial V} can be obtained by detecting the 2{\omega }_{\text{e}} and 3{\omega }_{\text{e}} components. In another word, the A_{2\omega } and A_{3\omega } can reflect the dielectric constant (or capacitance) and carrier concentration of the sample surface, respectively [90, 134, 138]. Furthermore, this method is not affected by stray capacitance.

2.4 Scanning Microwave Microscopy (SMM)

Scanning microwave microscopy (SMM) is a technique which combines of microwave technology and AFM. It is a tool for the investigation of various properties of 2D material, which including conductivity, permittivity, impedance etc. at nanoscale. SMM has received extensive attention and has many branches recently, such as scanning microwave impedance microscopy (sMIM), agilent-technology scanning microwave microscopy (AT-SMM) and interferometric scanning microwave microscopy (iSMM). In this review, we are going to introduce the principles of sMIM and AT-SMM in detail because they are more widespread popularity than iSMM.

2.4.1 Scanning Microwave Impedance Microscopy (sMIM)

sMIM is a quantitative near-field tool [139, 140] that operates at high frequency ~GHz range [140] and can detect the electrical properties of various samples, including conductors, semiconductors, insulators, and other functional materials at macro/nano scale. Currently, it has been widely used to explore the electrical properties of 2D materials such as conductivity, permittivity [96, 97], charge carrier variations, doping density and dielectric constant [94, 96, 97, 141-143].

During sMIM operation, a microwave signal at high frequency (few gigahertzes) is applied into tip apex, as shown in Fig. 7, and then this signal is transmitted to sample [139, 140, 145]. As the microwave signal strikes on the sample surface, some of the microwave signals are reflected from the sample surface and some pass through. The reflection coefficient \Gamma of microwave signals from the contact point to measure the tip-sample impedance mismatch can be written as

\begin{array}{}\text{(10)}& \Gamma =\frac{Z_{\text{tip}-\text{sample}}-Z_0}{Z_{\text{tip}-\text{sample}}+Z_0}\mathrm{.}\end{array}

Here, Z_{\text{tip}-\text{sample}} and Z₀ are tip-sample impedance and characteristic impedance of the transmission line system, respectively [139]. Thus, the reflected signal is suppressed by the common-mode cancellation through directional couplers so that small changes can be amplified by the amplifier (A) without saturating the output. Finally, reflected signals resolve by radio frequency mixer (RF mixer) into MIM-Im and MIM-Re, as shown in Fig. 7 [146]. For semiconductors or insulators, the MIM-Im and MIM-Re are corresponding to the capacitance (C) and resistance (R) between tip-sample respectively, as shown in the insert image lumped element model. Furthermore, the dC/dV and dR/dV can be obtained when another modulation voltage is applied to sample [144].

2.4.2 Agilent Technology-Scanning Microwave Microscopy (AT-SMM)

Except sMIM, agilent technology put forward the AT-SMM mode, which consists of AFM and a vector network analyzer (VNA), as depicted in Fig. 8. It has been designed to exploit the flexibility and outstanding accuracy of a vector network analyzer (VNA) to measure impedance [147]. It is also possible to engineer the SMM to determine differential capacitance (dC/dV) [148].

During AT-SMM, an RF cable is connected between VNA and conductive AFM-tip. A microwave signal is injected from VNA to AFM-tip, and then this signal is transmitted to the sample. As the microwave signals strike on the sample surface, some of the microwave signals are reflected and some pass through the sample surface. Then the reflected signal from the tip is detected by VNA again. To reduce impedance mismatch, there is a transmission line resonator between the probe and the 50\text{Ω} resistor splitter, allowing only specific frequency microwave passes through [149-151].

2.5 Piezo Force Microscopy (PFM)

Piezoelectric materials, which respond mechanically to applied electric field and vice versa, are essential for electromechanical transducers. The fundamental electromechanical response of these material has been investigated by PFM [152-154], which was invented by P. Guthner and K. Dransfeld in 1992 [155]. Up to now, PFM has given valuable contribution to explore the ferro/piezoelectricity response of 2D piezoelectric materials. [81, 156, 163].

In PFM, the conductive tip is brought in contact with the sample surface [159-161], as shown in Fig. 9. Meanwhile, V_{\text{AC}} with driving frequency ω is applied between tip and back electrode of the sample [157, 162],

\begin{array}{}\text{(11)}& V_{\text{tip}}=V_{\text{DC}}+V_{\text{AC}}\cos (\omega t)\mathrm{.}\end{array}

Then the deflection induced by V_{\text{AC}} at the ω is obtained by a lock-in amplifier. Hence, the electromechanical response of sample is detected as the first-harmonic component (A_{1\omega }) of biased induced tip deflection:

\begin{array}{}\text{(12)}& d=d_0+A_{1\omega }\cos (\omega t+{\phi }_0)\mathrm{,}\end{array}

Where d is the tip deflection response that describes the local electromechanical response and d₀ represents the deflection of the set point [35]. Meanwhile, the phase {\phi }_0 provides yield information about the polarization underneath the tip. For c^- domains (polarization vector oriented normal to the surface and pointing downward), the application of a positive tip bias results in the expansion of the sample, which means {\phi }_0=0. For c⁺ domains, the response is opposite and {\phi }_0={180}^{\circ }.

But there is difficulty in the acquisition of PFM signals from non-negligible electrostatic interactions between the tip and the surface [164-166]. In the general case, the measured amplitude of the piezoresponse can be written as

\begin{array}{}\text{(13)}& A=A_{\text{el}}+A_{\text{piezo}}+A_{\text{nl}}\mathrm{,}\end{array}

where A_{\text{el}}, A_{\text{piezo}} and A_{\text{nl}} are the amplitudes of electrostatic contribution, electromechanical contribution and nonlocal contribution due to capacitive cantilever-surface interaction respectively [167]. Quantitative PFM mapping requiresA_{\text{piezo}} to be maximized to accomplish electromechanical contrast. Except the real space imaging of piezoelectric coefficient (d_{33}), the displacement-voltage and d_{33}–V curves can also be obtained in PFM mode.

The usage of above techniques requires the users not only have clear physical concepts, but also are familiar with electronic circuit design. We believe one can choose and use appropriate methods to start their study after reading above section. The application of AFM-based electrical characterization of 2D materials is an emerging field. In the following part, we will introduce recent studies of local electrical characterization of 2D materials with these AFM methods.

3 Electrical characterization of 2D materials

3.1 Current distribution investigated by Conductive-Atomic Force Microscopy (C-AFM)

C-AFM is a powerful technique for studying the spatial variability of electronic properties of materials at nanoscale through the current measurement. Many researchers have described that this tool can be used to detect the topography and current distribution between respective layers of few-layers 2D materials.

Figures 10(a) and (b) show the topography and current mapping of rGO on SiO₂ by C-AFM. The defective regions (marked by 1) are far more easily visualized in the current channel than in the topography. In Fig. 10(c), the local I–V curves reveal currents over monolayer regions are 3.9±0.5 times smaller than the currents over multilayer regions. By considering the stacked rGO layers as an approximation of parallel conductors, they claim that the current per layer in the multilayer is 1.3 times larger than the current in the monolayer. It shows that the current density of rGO depends on their thickness and defects concentration [168].

Furthermore, the current distribution in other 2D materials has also been investigated by C-AFM, such as defective monolayers WS₂ [75], MoS₂ and WSe₂ after immersion in solvents [175, 176]. Here, the topography and current mapping of h-BN flakes on gold-coated mica substrate are shown in Figs. 10(d–f) [169] in detail. The profile lines in Figs. 10(d–f) depict the changes of thickness and current of h-BN. They conclude that current is a function of thickness, as predictable, and that the insulation quality is uniform within the areas of the same thickness. These results confirm that h-BN is the most perfect candidate for ultrathin insulator.

Through detecting the current signal, numerous properties of 2D materials can also be obtained. For instance, dielectric breakdown in h-BN layers [170, 171], local conductivity in heterostructure of MoS₂/WS₂ and graphene oxide [172, 173], contact resistivity between the heterostructure of MoS₂/GaN [174] and so on.

3.2 Surface potential investigated by Kelvin Probe Force Microscopy (KPFM)

KPFM has advantages in quantitative measurement of surface potential of sample, and it provides countless studies about 2D materials recently [80, 177-184]. Figures 11(a) and (b) show topography and surface potential (and/or work function) images of multilayers MoS₂ investigated by KPFM. [177] Surface potential of MoS₂ flakes with different layers thickness is demonstrated. It is known that the larger (smaller) surface potential means lower (higher) work function and the higher (lower) Fermi surface. Thus surface potential of SiO₂ is lager (work function is lower) than MoS₂. The surface potentials of MoS₂ depend on the thickness of the layer. The thicker the MoS₂ is, the smaller the surface potential is. For instance, the surface potential of monolayer and three-layers MoS₂ are -95 mV and -240 mV respectively. Additionally, surface potential [81, 181-198] of other 2D materials have also been studied, which we would not introduce in detail here.

Except 2D materials, the van der Waals heterostructures are investigated by several groups [82]. Here, the surface potential of MoS₂ (monolayer)/WS₂ (multilayer) (abbreviated as WS₂/MoS₂) heterostructure on SiO₂/Si substrate is introduced as an example [178]. Electrical transport studies demonstrate that the special MoS₂/WS₂ serves as intrinsic lateral p-n diodes, and depletion-layer width and built-in potential are obtained by KPFM. Figures 11(d) and (e) show AFM topography and surface potential images of low-pressure CVD grown MoS₂/WS₂ heterostructure. The Fermi levels of WS₂ or MoS₂ in the heterostructure can be estimated from value of their surface potential. Figure 11(f) shows profile of surface potential along the blue dash line in Figure 11(e). According to this section line, the built-in potential ~95 mV and the depletion-layer width W ~3.84 μm are obtained.

Furthermore, through monitoring the surface potentials, micro mechanisms of some phenomenon have been studied by different groups [179, 199-201]. Verdaguer et al. have characterized the discharging of graphene induced by water in controlled ambient conditions [199]. Zhou et al. have explored the contact electrification process both in polarity and magnitude of the charge transfer through an applied electric field between two materials [200]. We confirm the SKPM method will provide more help in understanding the electrical properties in the future.

3.3 Application of Electrostatic Force Microscopy (EFM)

EFM is also a crucial mode to study the electrical properties of sample. It can be used not only in detecting the electronic perturbations, domains and/or atomic defects of materials, but also in understanding the underlying work mechanisms of nanodevices [89, 202-205].

Datta et al. employed EFM to explore the electrostatic potential and charge distribution in few-layer graphene (FLG) on SiO₂/Si substrate grown by mechanical exfoliation method [88]. Figures 12(a) and (b) demonstrate the topography of FLG with different thickness and their corresponding EFM mapping. FLG regions with different numbers of graphene layers exhibit different values of phase shift \text{Δ}\text{Φ}, as shown in Fig. 12(c). Furthermore, local surface potential V_{\text{SP}} of sample can be quantified by measuring phase shift \text{Δ}\text{Φ} as a function of V_{\text{tip}}, as shown in Fig. 12(d). They reported that the FLG surface potential increases with film thickness, approaching a bulk value for samples with five or more graphene layers.

The EFM can also be used to elucidate the work mechanism in device. Sangwan et al. have studied the switching mechanism in memristor device of MoS₂ on SiO₂/Si substrate [203]. Figure 12(e) shows the AFM phase image of an electroformed bisecting-Grain Boundary (GB) device. It shows the GB (highlighted by a black arrow) divides the channel into two regions connected to drain and source electrodes. Figures 12(f–h) show corresponding EFM images of MoS₂ device with different tip biases. The abrupt change of the phase across a bisecting-grain boundary indicates that electrostatic potential drop occurs primarily at the grain boundary. This confirms the overall higher resistance of the bisecting-GB memristor compared to the bridge-GB memristor. Furthermore, the switching mechanism of devices with GBs is obtained with the help of EFM.

The MH-EFM is also a promising tool for quantitative characterization of 2D materials with nanometer resolution [90]. Collins et al. employed MH-EFM (DH-KPFM) to explore the surface potential of CVD grown monolayer graphene on Cu foil substrate. First harmonic response demonstrates a clear contrast in charge density between graphene and substrate. Meanwhile, second harmonic response depicts the contrast consistent with changes in the capacitance gradient associated with changes in the probe-sample capacitor geometry. The surface potential was determined to be 157\pm 9 mV and -47\pm 5 mV, for the tip-graphene and tip-Cu interactions respectively, shown in Fig. 13(c). Then the relative surface potential difference between the graphene and Cu can be obtained, which is 204\pm 10 mV [134].

Recently, Lei et al. employed MH-EFM to explore the mobile charge carrier of MoS₂ on SiO₂ with circle holes arrays [135]. They describe the A_{3\omega } images of MoS₂ with different gate voltages V_G [206]. The A_{3\omega } contrast of whole MoS₂ is uneven, which confirms the difference of carrier concentration in MoS₂ flakes. The buried holes can also be observed, which indicate that the MH-EFM has sub-surface scanning ability (penetration depth in MoS₂~75 nm).

Up to now, several groups have employed EFM to investigate other 2D materials, such as charge injection in reduced graphene oxide [207], dielectric response of h-BN layers [89], surface potential of few-layer graphene [208, 209], capacitance behavior of graphene [210, 211], electrostatic properties of MoS₂ [212, 213] and so on.

3.4 Application of Scanning Microwave Microscopy (SMM)

SMM is a quantitative near-field tool that operates at high frequencies in the GHz range and can detect the local changes of various properties of 2D materials [94, 96, 97, 141, 142]. Kundhikanjana et al. employed sMIM to explore the conductivity of graphene flakes and its derivatives on SiO₂/p++Si substrate. The MIM-Im signal of PG sample is brighter than substrate due to higher conductivity, while its MIM-Re images show homogeneous contrast, as shown in Figs. 14(a) and (b). Using the finite-element analysis (FEA), they claim that conductivity of PG is \sigma >{10}^6 S/m. Whereas AGO pieces appear darker in MIM-Im images [Fig. 14(c)], which indicates the conductivity of AGO is 10–100 S/m. Moreover, the experiment data and simulation conductivity of other derivatives are shown in Fig. 14(e). The results show GO, RGO and AGO are low conductivity, while PG, AGS and GS are high conductivity [97].

In addition to above material classification, sMIM can also provide help in study of 2D materials thermal oxidation mechanism. It is known that the fully oxidized products is WO₃, however the oxidation process is not well understood. Liu et al. used sMIM to characterize thermal oxidation process of mechanically exfoliated WSe₂ layers on SiO₂/Si substrate. Figures 14(f–h) shows that AFM topography and sMIM mapping was obtained simultaneously from the same region. sMIM mapping exposes that the electrical conductivity is higher in certain region of the sample. The theoretical analysis in Fig. 14(i) indicates that these bright areas correlate with the intermediate product WO_3-x in the oxidation process [96].

What’s more, local conductivity of several 2D materials has been further investigated by SMM, such as MoS₂, black phosphorous, WS₂ and graphene [141, 142, 147, 214-216]. Besides that, dielectric constant of In₂Se₃ and MoS₂ [94, 95], local permittivity of multi layers phosphorene [217] and local impedance of graphene [218] have also been studied recently.

3.5 Piezo/ferroelectric response investigated by Piezo Force Microscopy (PFM)

PFM is a powerful tool for investigating ferroelectric and piezoelectric materials at nanoscale. Recently, it has been used to detect the electromechanical response of 2D materials [101, 163]. Lu et al. employed PFM to investigate the piezoelectric response which occurs through out-of-plane deformation in CVD grown MoSSe monolayer on highly oriented pyrolytic graphite (HOPG) substrate [81]. In randomized alloy MoSSe monolayer, as shown in Figs. 15(a–c), there is no mechanical/electrochemical contrast. However, Janus MoSSe experimentally shows an intrinsic vertical piezoelectric response, as shown in Figs. 15(d–f). The reason is that, in Janus MoSSe monolayer, the distortion of Mo–S and Mo–Se bonds under an electric field does not cancel, and a net thickness change is induced by applying a vertical voltage. Figure 15(g) illustrates line profiles of both topographic and piezoelectric response along red dashed lines. The different piezoelectric amplitude levels of the Janus MoSSe monolayer and the substrate are also indicated, from which we estimate an out-of-plane d₃₃ of Janus MoSSe. The value of d₃₃ is calculated as 0.1 pm/V. This is the first demonstration of the vertical piezoelectric response in single-molecular-layer crystal.

Subsequently, Zhou et al. used PFM to investigate the out-of-plane piezo and ferroelectric response in α-In₂Se₃ flakes on gold substrate [220]. Figure 15(h) shows the topography of α-In₂Se₃ flakes with the thickness ranging from 3 to 60 nm. Meanwhile, clear out-of-plan domains are demonstrated in PFM images, as shown in Figs. 15(i, j). It is worth noting that some domains wall coincides with the location of the flakes edges, which suggest that PFM phase contrast most likely comes from real polarization contribution rather than other artifacts between different layers. They have also demonstrated that the PFM amplitude and phase hysteresis loops on a 20nm thick In₂Se₃ flakes which are shown in Figs. 15(k) and (l). The amplitude response shows a butterfly loop with an opening of ~1.5 V, whereas the phase switches 180° at the same turning points. Furthermore, the electromechanical response [101, 156] and switching behavior [102] of other 2D materials have also been studied by PFM.

4 Conclusion and perspectives

The electrical properties of two-dimensional materials differ from their bulk counterparts, and further research about their electrical properties at nanoscale is needed. This review highlights the principles of AFM based electrical characterization methods and their further applications in 2D materials. As we have shown, usage of these AFM based electrical characterization methods requires the researchers not only have clear physic concepts, but also are familiar with electronic circuit knowledge. In C-AFM, AFM probe acts as a counter electrode to directly measure the current distribution of sample [221], which is performed in contact mode. KPFM and EFM modes are based on AC mode, which is non-destructive for the sample surface [209]. KPFM can detect the work function of sample, while EFM has the potential to explore the carrier concentration, electrostatic gradient, mobile charge carrier and so on. In SMM, the dielectric constant, doping density, conductivity and permittivity can be obtained (semi-) quantitatively by combining the FEA analysis. In PFM, the piezoelectric coefficient can be measured through detecting the first-harmonic component A_{1\omega }.

During the applied research on electrical properties of 2D materials, we found that these AFM modes still need further development and improvement. For example, (i) owing to electrical properties are always coupled with other properties, a method that can explore the mechanical-thermal-electrical-optical coupling is needed. Although PFM and Near-field scanning optical microscopy (SNOM) [219, 222] provide possibility to study the mechanical-electrical and optical-electrical characteristic, we still need to develop advanced technology to achieve multi-field coupling investigation. (ii) It is expected that one can monitor the carrier distribution and electric field distribution of device in work condition. Improving the application of 2D materials and optimizing performance of their devices require the understanding of properties under work condition. A method can detect devices under work condition is crucially required for the future research.

All the above-mentioned AFM techniques provide a key insight in the fields of 2D materials to explore the electrical properties with high-resolution images. With the development of the AFM technology and 2D material preparation, we expect more and more exciting achievements obtained in this field.

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