ELECTRON TRANSPORT PROPERTIES OF MONOLAYER GRAPHENE MEASURED FROM SECONDARY ELECTRON MICROSCOPY ACCORDING TO THE SUBSTRATE VARIATIONAL METHOD

摘要

Surface analysis techniques, such as X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES), are powerful tools to quantitatively investigate the chemical-state information of materials. With advances in materials science technology, the analysis of atomically thin materials has become practical, although still extremely challenging. The main difficulty lies in the notorious "reflection configuration" of ultrathin materials, which are normally supported by substrates. The material signals are thus inevitably diluted by the signals from the underlying substrates, even in a low-speed electron operation mode. Here, we develop a substrate variational method that enables isolating the pure electron-electron (e-e) signals of ultra-thin materials with four interrelated measurements in secondary electron (SE) microscopy using a white beam technique as shown in Fig. 1. The elastic electron transmission of mono- and bilayer graphene over a wide energy range from 0 to 600 eV can be accurately extracted from a single substrate variational measurement. Furthermore, the electron transport properties of the effective attenuation length (EAL) and the inelastic mean free path (IMFP) can be determined with extremely high efficiency from these measured elastic transmission spectra by using a so-called reverse Monte Carlo (RMC) programme. The RMC programme used herein was inspired by a method of the same name [2] widely applied in the condensed matter sciences to produce atom-based structural models that are consistent with experimental data and subject to a set of constraints. In this work, however, the target has been changed to the unknown IMFP at different energies instead of atom-based structural models, and the corresponding constraints are the elastic transmission measured by the substrate variational method. The RMC programme herein can be summarised as an iterative process for improving IMFP in a conventional Monte Carlo (MC) simulation of electron interaction with graphene. This improvement is accomplished by minimising the differences between the simulated and measured elastic electron transmission of the nanomaterial, as shown in Fig. 2. The substrate variational method represents a benchmark for surface analysis of supported ultra-thin materials, which can provide "free-standing" information that is particularly suitable for two-dimensional (2D) group IV materials, such as silicene, germanene and stanine, which are stable only on particular substrates. This technique expands the energy scale of analysis down to several electron volts and hence allows one to quantitatively probe the e-e interactions of ultra-thin materials on very-low-energy scales. Furthermore, with the use of ordinary SE signals, the new method rivals conventional methods based on core-level signals in signal-to-noise ratio by orders of magnitude, holding great potential for manufacture monitoring and quality control. The substrate variational method: There are multiple names for the present substrate variational method, such as nano-chop-nod method, backscatterer perturbation method and virtual substrate method named in the aspects of the origins, the principle and functions, respectively. When we want to investigate the microscopic and electronic responses of nanomaterials such as electron-electron (e-e) interactions and electron transport, the first approach is to design an experimental setup in transmission mode with an electron probe, as shown in Fig. 3a. A high-energy monochromatic electron beam is used as an electron probe to obtain a well-focussed beam that minimises chromatic aberration of the electron lens. Focussing on measuring the electron transport properties of nanomaterials, only those properties at the energy of the incident beam can generally be obtained from a single measurement according to the signal attenuation of the elastic peak (zero-loss peak). Although these properties can theoretically be obtained by repeating this measurement with different incident electron energy, this is generally difficult because of time-consuming realignment of the electron beam at each electron energy. Particularly for the low energy range (below 1 keV), it is extremely difficult to align the electron beam so that the electron beam size remains constant at any low energy. In addition, we cannot study substrate-supported nanomaterials in this transmission-mode experimental setup, especially 2D group-IV materials such as silicene, germanene and stanine, which are only stable on metal surfaces. This point is particularly important because almost all existing practical applications of nanomaterials in nanometre devices need "semi-infinite" substrates. To investigate the properties of a substrate-supported nanomaterial, we attempted to improve the transmission experimental setup, as shown in Fig. 3b. In this experimental setup, a polychromatic beam composed of a mixture of energies is used to investigate the properties of a target nanomaterial in a more efficient way than the basic transmission configuration. A monochromatic electron beam is injected into the back side of the substrate and corresponding secondary electrons (SEs) are produced as the incident electrons travel through the substrate. Therefore, the substrate acts as a scatterer, scattering a monochromatic electron beam to obtain dispersed electrons. The transmitted spectra emitted from the other side of substrate can be considered as a white electron beam to probe the properties of the attached nanomaterial. The initial energy distribution of these white electrons can be obtained from the control setup measuring only the substrate under the same experimental conditions. Therefore, comparing spectra obtained from these two different experimental setups allows the properties of the target nanomaterial over the whole energy range to be extracted from one pair of measurements. Unfortunately, the transmitted spectrum is not a good choice as a white electron beam to microscopically probe the target nanomaterial because the spatial distribution of the transmitted electrons composed of the primary beam and SEs is broadened by the cascade of elastic/inelastic collisions in the substrate. This broadening is more visible in the lower energy region of the transmitted spectrum of the white electron beam than at higher energy. In other words, the information carried by the white electrons in the SE energy range is completely obscured by the undesired electron signals produced by energy loss or formation of new SEs in inelastic collisions, while white electrons with higher energy travel into the target nanomaterial. Therefore, this primary designed experimental setup is difficult to implement in practical microscopic applications because it is difficult to find a suitable thin substrate. In addition, the energy distribution of transmitted electrons depends on the thickness of the substrate. This dependence complicates the definition of the white beam. If the substrate is too thin, an intense high-energy primary beam is dominant in the white electron beam, which makes the evolution of the low-energy transmission properties of the nanomaterial complicated. Eventually, a suitable thin film substrate was used in this experimental setup as an approximation of a semi-infinite substrate. This possibly makes the final result inaccurate despite the use of a specially designed machine for the transmission experiment. Fortunately, the reflected spectra produced from a semi-infinite substrate are suitable as a white electron beam to investigate the properties of a covering nanomaterial without such shortcomings, as illustrated in Fig. 3c. Reflected SEs from a semi-infinite substrate that can be treated as a backscatterer generally have very high signal intensities that increase dramatically as the electron energy decreases. This reflection-mode experimental setup is often used in commercial electron spectroscopy such as AES and reflection electron energy-loss spectroscopy. It seems that these reflected SE spectra are perfect for use as a white electron beam; however, there is one inherent problem when using reflection mode instead of transmission mode: the incident electron beam will be blocked by the covering nanomaterial before injection into the substrate. Although the attenuation effect can be neglected by using high incident electron energy (generally above 5 keV), the accompanying excited and emitted SEs (denoted as SEs(in) in Fig. 3c) make this experimental setup fail. To overcome this limitation in reflection mode, the substrate variational method is developed and introduced here. The same measurement as that shown in Fig. 3c is performed again using a discriminating substrate in Fig. 3d. It is obvious that the white electron beams produced by the two different substrates are different; however, the accompanying excited and emitted SEs (SEs(in)) should be exactly the same because the attenuation of the incident electron beam by the covering nanomaterial should be totally independent of underlying substrate. As mentioned above, in reflection mode, the energy distribution of the white electron beam depends not on the substrate thickness but on the substrate material, and the white electron beam is mainly composed of SEs. If high-energy electrons are dominant in the white electron beam, low-energy electrons from the nanomaterial originate from two different sources: SEs transmitting the nanomaterial information and SEs newly excited by high-energy electrons. By using the reflected SE spectra as a white electron beam, the former process of transmission of SEs is dominant, and the evaluation of white electrons inside a target nanomaterial can be considered as a linear system in which the response of the target nanomaterial to inject white electrons is a linear operator. Evolution of moving electrons inside any sample can be considered as a linear system. Every linear system satisfies the property of superposition; therefore, different results obtained from different inputs (i.e., white electron beams) or different linear response systems (i.e., target nanomaterials) can be superposed to reveal the linear response systems. It is noted that there are SEs (SEs(in) in Figs. 3c and 3d) excited by the high-energy monochromatic electron beam in the reflection mode. These SEs are offset and not involved in the linear response system. Therefore, it is natural to remove the disturbance of accompanying SEs(in) by simply subtracting two measured spectra through the same target nanomaterial on different substrates under the same experimental conditions. In this case, the white electron beam (that is, the input) for the linear response system of the subtracted SE spectrum (that is, the output) is a newly introduced effective white electron beam that is the subtraction of two spectra measured on two different bare substrates. This new effective white electron beam can be obtained from the subtraction of two spectra measured for a covering nanomaterial layer to evaluate the transmission properties of the target nanomaterial. It is obvious that in this technique, the reflection-mode experimental setups shown in Figs. 3c and 3d together can play the same roles as those in transmission mode, as expected in Fig. 3b, including the coupling of the underlying substrate. The essence difference between substrate variational method and standard data treatment: Generally, the essence of standard data treatment of measured spectra in surface analysis is identifying weak features in core-level signals against a background with the naked eye. To identify these weak features more clearly, spectral subtraction and ratioing techniques are used to supplement standard data treatment. By using these spectral subtraction and ratioing techniques, weak features of signal peaks in measured AES or XPS spectra become relatively obvious, making it easier to judge the origin of these detected signals according to the features in measured spectra. Regardless of whether or not spectral subtraction and ratioing are used, the only way in standard data treatment to judge the origin of a detected signal in a measured spectrum is by analysis of features in the measured spectrum with some prior knowledge such as Auger excitation and X-ray photoemission processes. Therefore, in the standard data treatment, only the measured spectra that have expected signal features contribute to the study of a target sample, as shown in Fig. 4a. The technological process followed in a material study by surface analysis techniques when using the standard data treatment is outlined in Fig. 4b. Generally, three separate steps to study a given material: measuring spectra, identifying signal features and obtaining information, are involved in standard data treatment. First, spectra are measured on the surface of a target sample, generally based on gut instinct without any specific requirements. Spectral subtraction and ratioing techniques are used to help the analyst identify the signal peaks according to the spectral features identified with the naked eye. Finally, information about the target sample can be obtained by analysis of these identified signal peaks with the help of prior knowledge like the electron transport behaviour in the target material. In this standard data treatment, only the signal data points in the measured spectra contribute to the final results or conclusions, while other detected data points, the overwhelming majority of measured spectra, are completely disregarded as unwelcome background. This means a huge amount of information is lost in the standard data treatment, and the concomitant possibility is that only qualitative information about a target sample can be extracted from measured spectra. All of the data points in measured spectra are generally focussed into one piece of information by standard data treatment; i.e., signal intensity. Of course, it is impossible to obtain any valuable quantitative information about a target sample based on this sole piece of information without any support from theoretical approaches. With the help of theoretical support or a control group, limited quantitative information about a target sample can be obtained from the single piece of data (core-level peak intensity) obtained using traditional data treatment. For instance, the transmission properties of a nano-overlayer can be evaluated by a so-called overlayer method (thin film method) from the changes of core-level intensities of substrates in two spectra measured on a bare substrate and covering nano-overlayer in which the core-level intensities are determined using traditional data treatment. Although the interrelationship between spectra measured under different experiment configurations is determined in these techniques, they can be considered as an extension of traditional data treatment because the essence of these techniques is still identifying features in measured spectra with the naked eye. In this work, a new idea is proposed and further implemented to obtain useful information from a combination of interrelated spectra instead of identifying the signal features in these measured spectra. A well-chosen combination of interrelated spectra gives us both an input probe of a "white electron beam" and quantitative output information. In contrast, the traditional spectral subtraction and ratioing of AES and XPS spectra do not give us an input probe. It is obvious that that the type of properties that can be obtained using this combination of interrelated spectra is only determined by how the combination of experimental setups is designed. In the present work, the substrate variational method is one example of many possible combinations of experimental setups to extract information about covering nano-overlayers from measurements of substrate-supported nanomaterial samples with explicit physical meanings. Typical spectra used in the substrate variational method are presented in Fig. 4c. Instead of requiring a signal feature like when using standard data treatment, "white electrons" over the whole energy range, which are equivalent in function to traditional core-level signals, can be created by combining two interrelated measured spectra according to the substrate variational method. Creating trackable "white electrons" from the interrelation between absolute intensities of two interrelated measured spectra instead of expecting a realistic signal in a measured spectrum (relative intensities in one spectrum) is a completely new approach in surface analysis that helps data treatment to move away from depending on identifying signal features with the naked eye. These created "white electrons" can be used to probe the physical properties of target nanomaterials because they can be easily identified before and after interacting with the target nanomaterial. Their changes can be accurately estimated by elementary arithmetic, and are even better than realistic core-level signals because they overcome the weaknesses of core-level signals like weak signals, poor signal-to-noise ratios, limited energies and inapplicability at low energy range. A typical measurement based on the substrate variational method can be generalised into two parts because the experimental setups and corresponding data analysis are designed together following the same guiding principle and cannot be considered as separate processes, as shown in Fig. 4d. Prior knowledge like the physical picture of the experiment should be carefully considered throughout the whole process of implementing the substrate variational method. Because of this, the final results obtained by this method generally have explicit physical meaning, such as electron transmission and reflection of a target sample. Furthermore, all detected data points in measured spectra are useful and contribute equally to the final results when using the substrate variational method. In other words, there is no information about the target sample is lost when the substrate variational method is used, and every two data points in paired spectra measured with and without covering nano-overlayer play an equal role to the sole data point (signal intensity) in standard data treatment. The high efficiency of information obtained by this substrate variational method is the reason why quantitative information about a target sample can be obtained. In fact, the train of thought in the substrate variational method is completely different from almost all existing methods to obtain information from measured electron spectra. The essence of almost every existing method is to screen out useful data points from measured spectra, and draw a conclusion according to the information obtained from these selected data points. Only relative intensities of these useful data points may have the potential to reveal physical properties of a target sample, even absolute intensities are meaningless. Every existing method can be considered as a filtering process in which the "useless" information is removed to leave useful information, which means the absolute amount of information in measured spectra, regardless of its usefulness, is decreased by this process. The presented substrate variational method uses a completely different train of thought, allowing "useless" information to become useful. With the help of substrate variational method, two data points that are useless alone can be converted into one useful data point, which breaks out from the old pattern of thinking in which the useless and useful data points are completely isolated from each other. In this case, the absolute intensity of a measured spectrum has some physical meaning, or more precisely, two absolute intensities of data points including information about both the nanomaterial and substrate can be combined to provide one data point that provides information about just the nanomaterial. Therefore, the efficiency of information transfer in the substrate variational method is very high and none of the information provided by the energy of detected electrons is lost.