Nano-characterizations of low-dimensional nanostructural materials

Abstract

Nondestructive nano-characterization methods were reviewed with respect to technical aspect and practicability. Micro-photoluminescence, cathodoluminscence and Raman spectroscopy with mapping modes were investigated as optical characterization tools, while electron backscatter diffraction and piezoresponse force microscopy were introduced as monitoring techniques for the crystallographic and electromechanical properties. Especially, the spatial resolution of the data acquisition and analysis was carefully inspected in the representative semiconducting nanomaterial systems. Some of efforts to overcome the limit of these characterizations were also taken into consideration.

Introduction

The configurations of low-dimensional nanostructures have opened a new horizon in the field of electric and optoelectronic applications due to the distinct structural and physical properties. Especially when new functionalization is required in the device applications, the nanostructures can provide innovative solutions without the cumbersome additions of materials or fabrication process. The large surface to volume ratio and unique epitaxial properties along with quantum confinement effects are responsible for their excellent characteristics, such as enhanced light absorption or transmittance, either spectral or nonspectral, as well as superior electromagnetic or mechanical properties. The intensive study, regarding designs or fabrications of nanomaterials and their device potentials, has been conducted for the past decades. However, the nano-characterizations have been less focused and thus, there are few reports published [1,2,3]. In line with this idea, we investigate the technical and practical aspects of characterization tools for low-dimensional nanostructural materials and here provide an overview of them; in particular, micro-photoluminescence, Raman spectroscopy, cathodoluminescence, electron backscatter diffraction, and piezoresponse force microscopy, which are nondestructive techniques with sub-micrometer or nano-scale spatial resolutions not achievable by other conventional characterization methods.

Micro-photoluminescence and Raman imaging

Both in micro-photoluminescence (μ-PL) and Raman spectroscopy, the incident light shone onto the specimens by the lens, and the emitted signal after interacting with the solids can be collected and analyzed as a function of the wavelength. PL has been used to probe the electronic band structure, especially, for semiconducting materials. The Raman spectroscopy was utilized to investigate the structural properties such as vibration modes of the materials. If the high numerical aperture lenses are used, the spatial resolution of these techniques can be down to the order of micrometers determined by the diffraction limit [4].

PL spectroscopy is based on the process that the incident photons stimulate the consecutive emission of the photons from the target materials. The energy of the incident photons can be transferred to the electrons, which causes the transition to the higher energy electronic states. In a semiconductor, the electrons in the valence band would be excited to the conduction band that creates the hole in the valence band when the enough energy is provided. Such photo-excited carriers are relaxed toward the lowest energy state after a certain time. When these electrons and holes are recombined radiatively, the photons are emitted with an energy of the optical bandgap, which is called as ‘interband luminescence’ or ‘band-to-band luminescence’. The direct bandgap semiconductor will present relatively strong luminescence compared to the indirect bandgap semiconductor since there is no additional momentum transfer processes necessary. The Coulomb interaction can also form the bound electron–hole pairs near the bandgap which is called Wannier excitons [5]. Typically, in bulk semiconductors, the Wannier exciton binding energy is the order of a few tens of meV [6], while in two-dimensional semiconductors such as WS₂, the binding energy of a few hundreds of meV has been reported [7]. This is attributed to the reduced dielectric screening in the low-dimensional system, in which such an excitonic effect can dominate the observed PL spectra [7].

Raman spectroscopy uses the inelastic scattering of light by the quantized state of the materials. Even though the Raman process can be observed from various quantized states when the symmetries are allowed, the most common observation originates from the lattice vibration. The macroscopic description of the Raman process has root on the modulation of the polarizability by the lattice vibration [8]. Such a model successfully describes the presence of the Stokes and the anti-Stokes component of the Raman process. The monochromatic light shone onto the materials is inelastically scattered, with an energy difference corresponding to phonon modes. The Stokes component is attributed to the incident photon losing the energy to create phonons, while on the anti-Stokes side the photon will gain the energy by absorbing the phonons. For a more quantitative understanding of the microscopic Raman process, third-order time-dependent perturbation theory based on Fermi golden rule can be applied, which includes the Hamiltonian of electron–photon and electron–phonon interactions [8]. The symmetry of the crystal directly determines the Raman scattering cross section and further the Raman tensor through the electron–phonon interaction Hamiltonian. Note that the crystal can be categorized as one of the 32 crystal classes by group theory by considering spatial symmetry [8, 9]. The form of the Raman tensors can be found in the literature, which can be used to simulate the polarization-dependent Raman intensity [10,11,12,13]. Polarization dependence of the Raman intensity can be used to determine the symmetry of the Raman modes and the direction of the crystallographic axis. The resonance effect in the Raman spectra should be also considered for the materials characterizations. When the excitation energy matches with the electronic state of the crystals, the Raman intensity can be enhanced dramatically [8, 14]. The resonance effect may also modulate the electron–phonon interaction, allowing the forbidden Raman modes visible. Therefore, the polarization and the excitation energy should be carefully chosen to properly analyze the Raman spectra.

The μ-PL and Raman spectra are often used as a local probe of the optical properties of the materials. To investigate the spatial distribution of the spectrum, μ-PL and Raman mapping (or imaging) can be performed. The most used method is either by scanning the specimens or incident laser. The light is focused on one spot and the specimen is then moved. Spectra are obtained sequentially across the area of interest and the spectral image is reconstructed. This approach has the advantage to achieve high spectral resolution. However, a long measurement time will be required to get sufficient spatial information. One can use wide-field type spectroscopic measurement to get a large area image comparably in a short time. The incident light is shone in the field-of-view of the objective lens, and a two-dimensional array detector is used with proper optical filters. In this way, the intensity distribution of the spectral features can be measured directly; however, the spectral resolution will be limited since the conventional grating or prism-based spectrometer cannot be used. To get the benefit of both approaches, the one-dimensional type hyperspectral imaging can be applied. In a conventional measurement scheme, most grating or prism-based spectrometer uses a two-dimensional array detector; the horizontal axis of the detector corresponds to a different wavelength, while only a few vertical pixels will be selected for the measurement. By introducing the line illumination or slit, one can utilize the vertical axis to have spatial information while keeping the wavelength information horizontally. In this way, the high resolution can be achieved with a reasonably reduced measurement time.

Figure 1 shows an example of the μ-PL image of mechanically exfoliated MoS₂ taken by scanning specimens. The PL spectra of MoS₂ show layer number dependence due to the change of the electronic band structure. The spatial distribution of the different thicknesses can be imaged by the PL intensity of A exciton. Figure 2 presents the polarized Raman image of mechanically exfoliated black phosphorus taken by wide-field Raman imaging. Due to in-plane anisotropy, the black phosphorus shows strong polarization dependence of the Raman intensity as shown in Fig. 2b.

Fig. 1

a Photoluminescence (PL) spectra of few-layer MoS₂. b PL intensity image of A exciton. Reprinted with permission from [15]. Copyright (2015) Royal Society of Chemistry

Fig. 2

a Optical image of mechanically exfoliated BP flakes The scale bar is 20 μm. b Polarized Raman intensity ratio image taken by wide-field Raman imaging. Reprinted with permission from [16]. Copyright (2015) Royal Society of Chemistry

Cathodoluminescence and electron backscatter diffractions

Cathodoluminescence (CL) uses the phenomenon of the photon emission from materials under electrons impact, which is typically implemented in a scanning electron microscope (SEM). The CL has been adapted in many applications, such as ceramics, minerals, organics, and semiconductors or insulators. The CL emission is attributed to the band-to-band transition, exciton luminescence, extrinsic luminescence; unlocalized and localized defects associated [17]. Therefore, CL can easily identify the energy bandgap as well as the existence of structural defects, impurity, stress variations, boundary and interfaces. Furthermore, the energy of electron beams used in CL is adjustable, around a few tens eV that is much higher than the bandgap of insulators and semiconductors. As compared to photoluminescence (PL) spectroscopy using light source having a selective energy, CL has no its own limitation in the excitation of transition.

There are several dominant factors influencing the spatial resolution of CL; electron beam size, carrier interaction in solids, carrier diffusions. The electron beam size of SEM can be varied by the acceleration voltage, beam current and so on, but its minimum size can reach around 1 nm [18]. The carrier interaction volume is more crucial factor for the resolutions. When an electron beam is incident on the specimen, its interaction with host charge and lattice leads to the scattering and, during the process, the energy loss of electron by inelastic scattering determines the interaction volume [19]. Since the lateral and longitudinal resolution is approximately equal, the reduction of the interaction volume can be achieved by limiting the probed volume to the near-surface. For instance, the quantum dots and nanointerface with a few nanometers were characterized successfully by CL methods [20, 21]. The physical confinement of photon in the nanostructures may assist the enhanced lateral resolution of this technique [22]. When altering the acceleration voltage of the electron beam, the depth resolution can be also achieved [23]. Furthermore, the charge diffusion needs to be taken into consideration although its contribution is minor [24]

Imaging of panchromatic CL with a single detector has been widely used, in which contrast provides information at a certain wavelength (See Fig. 3). In turns, the spectral identification can be obtained by equipment with a spectrometer or band-pass filter, where the spectrum imaging is capable of recording the luminescence spectrum at each point and builds up the two-dimensional image by mapping with an appropriate computer processing [21].

Fig. 3

a SEM image of the GaN films, b CL image, Bar: 100 nm length. a and a´, b and b´, c and c´, and, d and d´ are the equivalent position

Electron backscatter diffraction (EBSD) is another image mode of the SEM system (Fig. 4a). Theories on formation of the diffraction patterns, Kikuchi patterns, have been well established in transmission electron microscopy [25]. An electron beam incident on the specimen loses some of its energy initially and is inelastically scattered in all random directions. A fraction of these electron beam is subsequently scattered, which results in beams of Bragg diffraction by interacting with the spaced lattice planes. The diffraction from these families of planes gives rise to the Kikuchi patterns, which consist of crossing parallel line pairs; each pair represents a set of crystallographic planes in the specimen. It adopts computer-assisted pattern recognition of each Kikuchi lines, formed by the diffracted beam of backscattered electrons, to determine crystal orientations as shown in Fig. 4b [25, 26]. The EBSD provides the direct information of crystalline structures and orientations. The lateral resolution of EBSD is quite similar to that of CL but the longitudinal (depth) resolution is estimated less than 100 nm, which is attributed from the limit of the inelastic scattering mean free path. The two- dimensional map can be also produced through pixel-by-pixel identification of crystal phase as well as crystallographic orientation of an area of concern.

Fig. 4

EBSD patterns from orthorhombic YBa₂Cu₃O₇ single crystals and illustration of Kikuchi patterns as recognized by computer

Piezoresponse force microscopy

Piezoresponse force microscopy (PFM), one of the functional atomic force microscopy modes, is a widely used scanning probe technique for nondestructive ferroelectric and piezoelectric materials imaging on a nanometer scale [27,28,29,30]. Characterization of electromechanical properties in a spatially resolved manner is useful to explore dielectric materials with inversion symmetry breaking. Recent advances of the technique contribute to disclosing intriguing phenomena in ferroelectric/multiferroic domains and walls [31,32,33,34,35]. Bulk photovoltaic effect and unusual photocurrent are important related subjects to rise recently in the aspect of optoelectronics as well as energy conversion from light to electricity [36,37,38,39]. The manifestation of the effect requires inversion symmetry breaking which is often found in ferroelectrics and interpreted in the context of shift currents [39] and flexoelectricity [37]. In addition, topological polar textures in oxide superlattices and nanoplates as well as in a ferroelectric flatland are extensively studied for potential applications in information technology [40,41,42,43]. All of these studies demand sophisticated nano-scale characterization, and PFM is at the heart of it.

PFM relies on the converse piezoelectricity that is a phenomenon whereby the strain state of a material changes corresponding to the applied electric field. The converse piezoelectric coefficients are described by a third-rank tensor, which can be non-zero only in the case that inversion symmetry is broken. Note that the direct piezoelectric coefficients that relate to the induced electric polarization and applied mechanical stress are identical to the converse piezoelectric coefficients because the stress is symmetrical tensor. A phenomenon of the direct piezoelectricity was first demonstrated by Jacques Curie & Pierre Curie in 1880 and a closely related phenomenon of ferroelectricity was also discovered in Rochelle salt by Valasek in 1920 [44]. During the past century, the dielectric research spawns a variety of fundamental phenomena and applications.

Figure 5 shows an operation principle for the PFM. A metallic tip on the cantilever is directly contacted on the top surface of a dielectric specimen and AC electric bias induces a mechanical oscillation of the specimens due to the converse piezoelectricity. The mechanical vibration is delivered to the cantilever and the focused laser is employed to sense the minute oscillation as much as picometer or less. The reflected laser beam is detected by four-sector photodetector, which is initially aligned at the center of the detector. Later on, the deviation of the beam caused by the cantilever deflection would provide the information of the direction and magnitude of polarization of the specimen. If the polarization is parallel to the applied electric field, the piezoresponse will be in-phase, where the tip deflection is described by the fundamental bending mode of cantilever and the deflection is characterized with the aid of the lock-in technique. The specimen expands the volume as the applied electric field is parallel to the polarization, while it, in the antiparallel case, shrinks. Accordingly, the phase information as well as the magnitude in lock-in amplifier determine the direction and magnitude of piezoresponse, thereby specifying the piezoresponse signal. In the conventional PFM, a frequency of ten kHz is used to avoid the mechanical resonance of cantilever. During tip scanning at a rate of a few μm/s, the phase-sensitive detection is made in real time. A moving tip is considered to stay per pixel for a period of time on the order of 10 ms, long enough to filter out the noise and average out the AC oscillations.

Fig. 5

Schematic of PFM operation scheme for the out-of-plane surface vibration

In reality, the electromechanical vibration of a crystal would be more complex. All the elements of converse piezoresponse tensor, in principle, should be taken into the consideration because the electric fields underneath the tip is not simply along an out-of-plane direction but have stray fields over the surrounding region. Also, the transverse or shear strains can play a substantial role in the electromechanical vibration. As a result, a surficial motion along an in-plane direction may occur, which induces the torsional vibration of cantilever around its principal axis (see Fig. 6). The laser spot on the four-sector photodetector oscillates along the horizontal axis as well. By employing one more separate lock-in amplifier, one can simultaneously measure the in-plane PFM signals as well as the out-of-plane ones.

Fig. 6

Schematic of torsional deformations of cantilever due to surficial electromechanical strains according to electric polarization

As shown in the following, we elucidate the effective piezoelectric tensor for a tetragonal crystal parameterized by polar angle (θ) and azimuthal angle (ψ). The direct or converse piezoelectric tensor links mechanical stress to the polarization or electric field to strain:

$$P_{i} = d_{ijk} \sigma_{jk} \;{\text{or}}\;\varepsilon_{jk} = d_{ijk} E_{i} .$$

The converse piezoelectric tensor of a tetragonal crystal can be written as a matrix form in the Voigt notation for strain (i.e., j = 1 ~ 6 for xx, yy, zz, yz, xz, xy) and the spatial coordinate for electric field (i stands for x, y, z):

$$d_{iJ} = \left( {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & {d_{15} } & 0 \\ 0 & 0 & 0 & {d_{15} } & 0 & 0 \\ {d_{31} } & {d_{31} } & {d_{33} } & 0 & 0 & 0 \\ \end{array} } \right).$$

Considering the crystal rotation (θ and ψ), the effective piezoelectric coefficients are expressed with respect to the laboratory frame (defined so that the z*-axis is the surface normal of specimens) as below [45],

$$\begin{gathered} d_{33}^{*} = (d_{15} + d_{31} )\sin^{2} \theta \cos \theta + d_{33} \cos^{3} \theta , \hfill \\ d_{34}^{*} = - \{ d_{31} - d_{33} + (d_{15} + d_{31} - d_{33} )\cos 2\theta \} \cos \psi \sin \theta , \hfill \\ d_{35}^{*} = - \{ d_{31} - d_{33} + (d_{15} + d_{31} - d_{33})\cos 2\theta \} \sin \psi \sin \theta , \hfill \\ \end{gathered}$$

where the first equation represents the out-of-plane PFM signal due to the longitudinal strain when electric field is applied to the normal of specimens (as denoted by “3” in the first subscript of $d_{3J}^{*}$), and the other two correspond to the in-plane PFM components arising from the shear deformations. By specifying all the three components, we can construct a three-dimensional vector called the piezoresponse vector. The electromechanically determined piezoresponse vectors are usually strongly correlated with electrical polarizations. So, mapping of the piezoresponse vectors can visualize ferroelectric domain textures. However, it should be also noted that the experimentally determined piezoresponse vector is the aggregate result of the piezoelectric tensor components and non-uniform electric fields around the tip, and that the piezoresponse vector is vulnerable to various PFM artifacts such as the cross-talks between in-plane and out-of-plane components.

When measuring an in-plane PFM signal, only the component of the piezoresponse vector perpendicular to the cantilever axis is sensitively detected, as shown in Fig. 6. To fully determine the in-plane vector, it is necessary to measure multiple (at least two) PFM images in the same area using different orientations of the cantilever. K. Chu and C.-H. Yang recently developed high-resolution angle-resolved PFM that enables mapping of in-plane piezoreponse vectors at a spatial resolution of less than 10 nm [30]. It is known that the misalignment issue among different images is a critical factor to limit the resolution, which is inevitably arising from many reasons such as tip drift issue, tip-sample contact variation, and piezo-scanner hysteresis. A computer-aided approach was devised for optimizing conversion matrices between multiple images through pattern recognition, automatic feature definition, and image registration algorithm. An example demonstrated by the high-resolved PFM technique is shown in Fig. 7, revealing the detailed head-to-tail ferroelectric domains and the complicated structure of a mixed phase area attributed to the phase competition that emerges in the super-tetragonal BiFeO₃ [31].

Fig. 7

adapted from Ref. [30]

High-resolution lateral PFM image for a BiFeO₃ thin film on LaAlO₃. The background color represents the curl operation. The image is reconstructed based on the same data

Lately, the versatile PFM is introduced to characterize the superstructure of the Moiré patterns in twisted 2D materials. The PFM signal is not only due to the piezoelectric effect, but can also be induced by other effects such as electrochemical effects. Extended PFM techniques are expected to be utilized more actively in the future as it provides multifarious information on defect migration and chemical reactions at a high spatial resolution.