Abstract
There are more or less dopants or defects existing in nanomaterials, so they usually have different conducttypes even for the same substrate. Therefore, fast identification of the conductiontype of nanomaterials is very essential for their practical application in functional nanodevices. Here we use the field emission (FE) technique to research nanomaterials and establish a generalized SchottkyNordheim (SN) model, in which an important parameter λ (the image potential factor) is first introduced to describe the effective image potential. By regarding λ as the criterion, their energyband structure can be identified: (a) λ = 1: metal; (b) 0.5 < λ < 1: ntype semiconductor; (c) 0 < λ < 0.5: ptype semiconductor. Moreover, this method can be utilized to qualitatively evaluate the dopingdegree for a given semiconductor. We test numerically and experimentally a group of nanomaterial emitters and all results agree with our theoretical results very well, which suggests that our method based on FE measurements should be an ideal and powerful tool to fast ascertain the conductiontype of nanomaterials.
Introduction
With the rapid development of IT industry, more and more device integration is intensively demanded, which inversely drives the scientists and researchers all over the world to explore new approaches to break through the size limit of traditional semiconductor devices. Under this circumstance, nanodevices have been believed as the necessary choices for meeting their increase requirements. Quasi onedimensional nanomaterials (nanowires, nanorods, etc.) are the ideal building blocks for fabrication of nanodevices because of their distinctive and excellent properties, such as Si nanowires^{1,2,3,4} and ZnO nanowires^{5,6,7}. Up to date, various preparation methods^{8,9,10,11,12,13} have been developed to synthesize different nanomaterials, but there inevitably exist some impurity dopants or defects in their formation process. As a result, nanomaterials by different preparation ways usually exhibit diverse conductiontype in comparison with their perfect single crystal counterparts. Therefore, accurately differentiating the conductiontype of nanomaterials is of great significance for nanodevices because their conductiontype directly determines their application area (photovoltaic, memory, switching or electronsource devices).
As known to all, there are two commonlyused methods for identification of the conduction type of bulk or thin film materials, which are respectively the hot and cold probe method and Hall effect method^{14}. The former utilizes the thermoelectric effect of bulk materials while the working mechanism of the latter is based on the calculation of the steady electric potential difference between the top and down surface of the sample resulting from the carrier charges under electromagnetic field. But for nanomaterials, integrating them into field effect transistor (FET) and measuring their working behaviors is the only known method to identify their conductiontype to our knowledge ^{15,16}. Although this method has a nice measurement accuracy, the fabrication process of FET nanodevices is quite complicated and the yield of nanodevices with nice working performances is usually rather low. So finding an easy and accurate method to differentiate the conductiontype of nanomaterials becomes a challenging issue for all the researchers.
In this paper, we will apply the simple FE techniques to identify the conductiontype of quasi onedimensional nanomaterials. Based on the FE experiments, we further establish a generalized SchottkyNordheim (SN) field emission model, in which an important factor will be first introduced to describe the effective image potential in Sec. II. Also, we will present a programmed scheme to fit the JE curves and the slope of FN plots by introducing several parameters, by which the connection between the important factor and the energyband structure of nanomaterials can be obtained in Sec. III. The numerical and experimental testing will be presented in Sec. IV. Finally, we give some detailed discussions and conclusions.
Generalized SchottkyNordheim model
The currentvoltage (IV) curve plays a crucial role in understanding the basic physics of field electron emission. The first theoretical field emission (FE) model was proposed by FowlerNordheim (FN) based on Sommerfeld model with some approximations, which was widely used in analyzing the FE behaviors of metallic emitters. Subsequently, it was further modified by SchottkyNordheim (SN), in which the image potential is taken into account according to electrodynamics^{17}. It is known that both of FN and SN models are assumed that the emitters are metallic. However, recently many newtype nanomaterials are applied in FE process. The schematic diagram of quasi onedimensional nanomaterials during FE measurements is provided in Fig. 1(a). In FE process, the electrons emit from the cathode sample surface at negatively biased. The emergence of image potential at boundary will lower the surface barrier height, which results that the electron emission is easy to occur at applied field, as seen in Fig. 1(b). Commonly, the energyband structures of nanomaterials are quite different from those of metals. As a result, the image potential effects will differ with the energyband structures of nanomaterials because their electric conductivity is various in the band diagram.
In order to analyze the FE behaviors from nanomaterials, we first introduce a parameter λ (0 < λ < 1) to generalize the SN model, in which λ is defined as the image potential factor. So the current density J _{ GSN } can be rewritten as
where “a” is the parameter related to the emission area, b = 6.83(eV)^{−3/2}(V)(nm) is the field emission constant, Φ is the surface work function of emitters, T is the nanostructured emitter’s temperature and F is the effective electric field fallen between the cathode and the anode. F can be obtained by the expression of F = βE, in which E is the applied electric field and β is the field enhancement factor. Also, ν _{ F } and τ _{ F } are two correction factors that come from the image potential effects:
where \(c=\frac{{e}^{3}}{4\pi {\varepsilon }_{0}}\). In addition, Θ_{ GSN }(T) describes the finite temperature effect, which can be expressed as:
where k_{B} is the Boltzmann constant, \({d}_{F}={({g}_{e}\frac{{\Phi }^{1/2}}{eF})}^{1}\) and \({g}_{e}=2\sqrt{\frac{2{m}_{e}}{{h}^{2}}}\) are also the constants.
It should be remarked in the generalized SN model that λ is introduced to describe different effective image potential effect from various nanomaterials. When λ=0, the model is simplified as the classical FN model. And the model becomes the idealized SN model when λ=1. Figure 1(a) shows the schematic diagram of quasi onedimensional nanomaterials during FE measurements. The interface barrier between cathode nanomaterials and vacuum at negatively biased is given in Fig. 1(b) according to the generalized SN model. As found in Fig. 1(b), the image potential factor λ is 1 for metallic nanomaterials, which is easy to understand because the ideal SN model just aims at metal. So the mirror charges should be equal to the surface charges for metallic nanomaterials, which corresponds to the case of λ=1. If nanomaterials belong to semiconductors, the mirror charges will vary with their dielectric constant or electric conductivity, unequal to the surface charges. In this situation, λ ranges from 0 to 1, which should qualitatively reflect the change of the effective mirror charges for different quasi onedimensional nanomaterials.
In general, it can be believed that the metallic emitters contribute a perfect image potential effect in FE process, namely λ=1, corresponding that the mirror charges should be equal to the surface charges. For semiconductor emitters, the major carriers of the ntype semiconductors are electrons in the bottom of the conductionband while the major carriers of the ptype semiconductors are holes in the top of the valenceband by doping. In this situation, the mirror charges will vary with their dielectric constant or electric conductivity, unequal to the surface charges. So λ ranges from 0 to 1, which should qualitatively reflect the change of the effective mirror charges for different quasi onedimensional nanomaterials. In addition, the electrons in the ntype semiconductors emit from the bottom of the conduction band, which should induce the image potential effect a little less than that of metals. In contrast with ntype semiconductors, the contribution of the holes to the image potential in the ptype semiconductors is far less than that of the ntype of semiconductors because the valenceband electrons have to go across the energyband before they become the free electrons involving in the transportation. Thus, the values of λ also reveal the characteristic of the energyband structures of nanostructured emitters and reflect the magnitude of the image potential at interface between vacuum and nanomaterials’ surface. Therefore, if we can find out the relationship between the values of λ and the IV curves of field emission, the conductiontypes of nanostructured emitters from field emission can be indeed identified.
On the other hand, the slope of the FN plots has been used to analyze the behaviors of the IV curves for FN and SN models in our earlier work^{18}. Based on Eqs (1)–(3), the slope (S_{GSN}) of the FN plots in the generalized SN model can be worked out:
where \({\rm{G}}=\frac{{\tau }_{F}{k}_{B}T\pi }{{d}_{F}}\) and \(\eta =\frac{1In(\frac{c\lambda F}{{\Phi }^{2}})}{{\tau }_{F}}\). It is found in Eq. (4) that the slopes of FN plots are quite different and depend on the effective electric field and temperature in our generalized SN model. These different behaviors of the slopes of FN plots also provide us another guideline to identify the conductiontype of nanostructured emitters according to the hints of the slope behaviors of the FN plots. Compared with the classical FN or SN models, the slope of the FN plots for the generalized SN model is dependent on the image potential factor λ, which promises us a way to understand the material properties of the nanostructured emitters.
We established the connection between λ and the JE curves of field emission by combination of the generalized SN model and the slope of FN plots techniques. The basic idea of this scheme is that we use the experimental JE curves from different nanomaterial emitters to fit the formula in Eq. (1) to obtain the λ values and subsequently calculate the slopes of the FN plots to ascertain the connection between λ and the conductiontypes of emitter materials.
For given nanostructured emitters, their work function can be easily measured by UPS or KPFM techniques. So in the fitting process of the JE curves, only four parameters need to be considered according to Eq. (1), which are respectively a, β, T and λ. In fact, we constrain the a and β within a practical and reasonable region to turn out λ, and then we investigate the slope of FN plots by these parameters and the JE curves. Different λ values and slopes of FN plots can reveal different nanomaterials’ properties.
The nonlinear fitting method with the Levenberg Marquardt iteration algorithm is utilized in the datafitting of the JE curves^{19}, which is a standard approach used to solve the nonlinear least squares problems implemented by OriginPro 2016 software (version: Sr2 b9.3.2.303).
Connection between λ and IV curves
Based on our generalized SN model, we fit the experimental JE curve data from three typical kinds of emitter materials, which are respectively metal (LaB_{6}), ntype (ZnO) and ptype (CuO) semiconductors. They are all nanowire materials, whose conduction properties actually have been confirmed by the traditional FET technique. The experimental curves of FE current density of these three types of nanomaterials versus the applied electric field are shown in Fig. 2(a), in which the matching degree of these three fitting curves to the generalized SN equation (Eq. (1)) is over 0.99. Table 1 lists the curvefitting parameters to further compare their image potential in FE process.
Figure 2(b) shows the corresponding FN plots. As observed in Fig. 2(b), the FN plots of these three typical nanowires all exhibit a little deviation from linearity, which suggest that they may obey the generalized SN model. And the curves of the partial derivative of the FN plots to 1/F are shown in Fig. 2(c), in which one can see that these three nanomaterials have different variation tendency. It should attribute to their different effective image potential. It is found in Fig. 2(d) that the curves of the FN plots’ slope (S_{GSN}) versus the effective electric field (F) have a different variance tendency for various nanomaterials with different conductiontype. In addition, the slope (S_{GSN}) of the FN plots is found to increase linearly with the effective electric field (F) for these three typical nanowires. As seen in Table 1, the image potential factor (λ) is 1 for metallic LaB_{6} nanowires and 0.65 for ntype ZnO nanowires, which is far larger than ptype CuO nanowires (λ = 0.2). It suggests that the image potential factor (λ) may be regarded as the key criterion for identifying the conductiontype of nanomaterials.
To better comprehend the physical nature of the image potential factor (λ), the energyband diagram of the nanostructured emitters is shown in Fig. 3. The doping concentration or the relative Fermi level position (E_{F}E_{i}) of nanomaterials may be mainly responsible for the magnitude of the image potential factor (λ), in which E_{F} and E_{i} respectively refer to the actual Fermi level and intrinsic Fermi level. As depicted in the above illustrations, λ depends on the surface charges having an intense relationship with the electric conductivity, and thus it should be determined by the major carrier density (n or p) or (E_{F}E_{i}).
Based on the semiconductor physics, the electric conductivity (σ) of nanomaterials can be worked out by the equation of σ = nqμ or σ = pqμ ^{20}. In these expressions, μ is the mobility of major carriers in semiconductors and q stands for elementary charge. According to the classical band theory, E_{F} is just above E_{i} for ntype semiconductors whereas E_{F} is lower than E_{i} for ptype semiconductors, as seen in Fig. 3. The major carrier density (n or p) can be deduced by the Fermi distribution law:
where k_{B} is the Boltzmann’s constant, T is the temperature and n_{i} is the intrinsic carrier density. Based on the semiconductor physics, n_{i} can be expressed as:
where E_{g} is the bandgap of nanomaterials, m_{0} is the electron mass, m_{n} ^{*} and m_{p} ^{*} are respectively the effective masses of electron and hole. Substituting Eqs (5) and (6) into the above equation on the electric conductivity σ, we can obtain:
In general, the energyband structure, the carrier density, the electric conductivity and temperature may modify the image potential, and thus take effect on the JE curves of field emission. Although the effective image potential factor λ is introduced to describe these nanomaterials in our generalized SN model, the connection between λ and the conductiontype of emitters can be preferred that (1) λ = 1 for metals; (2) 0.5 <λ < 1 for ntype semiconductors; (3) 0 < λ < 0.5 for ptype semiconductors. Therefore, the relationship between the JE curves and the conductiontype of emitter in FE process can be easily revealed by this simple way instead of fabricating complicated FET nanodevices. Moreover, this connection should have another application, which is to comprehend the FE mechanism and analyze the doping degree of the nanomaterials when we know what material the emitters belong to.
Based on the abovementioned analysis, our identification method of the conductiontype of nanomaterials can be summarized into three standard steps:

(1)
Fitting the JE data based on the generalized SN model presented in the above section;

(2)
Calculating the slope of FN plots based on the parameters obtained by the fitting data in the first step;

(3)
Obtaining the λ values and drawing the curve of the slope (S_{GSN}) of FN plots to λ for different quasi onedimensional nanomaterials.
Furthermore, we investigate a group of samples to testify the asobtained λ criterion based on this method. The samples include Mo nanocones, SmB_{6} nanowires, individual Si nanoapex, C nanotubes, W_{18}O_{49} nanowires, WO_{3} nanowires, WO_{2} nanowires, AlN nanowires and B nanowires. All of them are prepared by our group, and their fabrication techniques can be found in the Supporting information. The nonlinear curvefitting and calculation process of these experimental JE data is just the same as the aforementioned three quasi onedimensional nanomaterials (LaB_{6} nanowires, ZnO nanowires and CuO nanowires), as found in Figs S1 and S2 in Supporting Information. Before the measurements, the conductiontype of these nine kinds of nanomaterials remain unknown to us. The S_{GSN}F curves of these nine quasi onedimensional nanomaterials are shown in Fig. S2(c). As observed in Fig. 4(a), the slopes (S_{GSN}) of FN plots versus the electric field (F) are found to be different for these nanomaterials. Based on the generalized SN model, the parameters can be solved, as summarized in Table 1. According to the criterion of the aforementioned image potential factor (λ), it can be concluded that Mo nanocones and SmB_{6} nanowires are metallic because the λ values are equal to 1; Individual Si nanoapex, C nanotubes, W_{18}O_{49} nanowires, WO_{3} nanowires and WO_{2} nanowires can be ascertained to be ntype semiconductors in that their λ value ranges from 0.5 to 1; Likewise, AlN nanowires and B nanowires should belong to ptype semiconductors since their λ values locate at the range from 0 to 0.5. The conductiontype of these nine quasi onedimensional nanomaterials differentiated by the image potential method is in good consistent with those by traditional FET method, which proves that our method is accurate and suitable for determination of the conductiontype of quasi onedimensional nanomaterials.
It is also found that there are three kinds of behaviors of the slopes (S_{GSN}) of FN plots with F. One is seen to remain almost unchanged for AlN, B and CuO nanowires; The second is observed to increase linearly with F for Mo nanocones, SmB_{6} nanowires, C nanotubes, W_{18}O_{49} nanowires, WO_{3} nanowires and WO_{2} nanowires. The third exhibits a very sharp negative slope with F for individual Si nanoapex. It should be noted that all the temperatures of nanomaterials during FE process are 300 K except individual Si nanoapex (T = 1059 K), which can be illustrated as follows. The FE properties of nanowire films can be believed to be roomtemperature measurements by transparent anode way because the nanowires contact well with the substrate and can rapidly conduct the heat to the external circumstance, in which the Joule heat at nanowire films can be neglected. But for the individual Si nanoapex prepared by EBL technique, a native oxide layer usually formed on the surface of Si substrate, which inevitably leads to a large interface resistance between individual Si nanoapex and Si substrate. This high interface resistance produces Joule heat in FE process without a nice channel to timely dissipate the heat to external circumstance during insitu microprobe measurements. Under this circumstance, it results that the temperature of an individual Si nanoapex reaches over 1000 K, which coincides with our experimental observations very well^{21}. Therefore, it is reasonable that the fitting temperature T is adopted to 1059 K for individual Si nanoapex. Moreover, it can be identified that Si nanoapex belongs to the ntype semiconductor because S_{GSN} decreases with the increase of temperature based on Eq. (4). The variance tendency of S_{GSN} to F is totally different at 300 K and 800 K for the original SN model as shown in ref.^{18}. Moreover, it provides another powerful proof for differentiating the conductiontype of quasi onedimensional materials. It is noted that the variable behaviors of S_{GSN} with the temperature also give us a signal to estimate the working temperature of different conductiontype nanostructured emitters.
The image potential may affect the FE properties of quasi onedimensional nanomaterials, so here the JE curves of SmB_{6} nanomaterials are provided in Fig. 4(b) as an example. If λ is decreased by 20% in the curvefitting process, J will accordingly decrease by 61.4% in comparison with that before change at the same turnon field of 6.5 V/μm. Therefore, it suggests that the image potential should have a strong impact on the FE behaviors of quasi onedimensional nanomaterials, which is also beneficial to identify the conduction types by the image potential method because λ significantly differs with their conductiontype.
We endeavor to explore what is the determinant factor for the image potential factor (λ), and the curve of λ to the relative Fermi level position (E_{F}E_{i}) is first given in Fig. 4(c). The electric conductivity of nanomaterials measured by the insitu microprobe technique were listed in Table 2 ^{21,22,23,24,25,26}, and their mobility and bandgap adopt the averaged value of their corresponding bulk counterparts in recent studies^{15,24,27,28,29,30,31,32,33}. Combined Eq. (7) with the measurement results, the difference (E_{F}E_{i}) between E_{F} and E_{i} can be solved for all nanomaterials, as summarized in Table 2. One can see that (E_{F}E_{i}) is positive when λ ranges from 0.5 to 1, which reveals these nanomaterials (ZnO nanowires, individual Si nanoapex, C nanotubes, W_{18}O_{49} nanowires, WO_{3} nanowires and WO_{2} nanowires) should be ntype semiconductors. These results concide with our abovedmentioned conclusions very well. Simultaneously, (E_{F}E_{i}) appears to be negative if λ is located in the range from 0 to 0.5 for all ptype semiconductors, which is also in good agreement with the given criterion. Therefore, it proves that our way by regarding the λ value as the criterion should be reasonable and accurate for idenficiation of the conductiontype of nanomaterials.
It is clearly seen in Fig. 4(c) that the image potential factor (λ) shows two quite different changing tendency for different conductiontype of nanomaterials. For ntype semiconductors, λ will increase with (E_{F}E_{i}) and gradually moves close to 1 (ideal metal plane), in which (E_{F}E_{i}) actually reflects the doping degree of nanomaterials. But for ptype semiconductors, λ will decrease with the increase of (E_{F}E_{i}) and even be close to 0 for heavilydoped ptype semiconductors or widebandgap semiconductors with quite a few conductionband electrons. The possible explanations are given as follows. Theoretically speaking, the image potential (V_{image}) can be written as \({V}_{image}=\frac{{e}^{2}}{16\pi {\varepsilon }_{0}x}\), in which “e” represents the mirror charges at vacuum side and x stands for the distance between surface charges and cathode surface. As a result, the magnitude of the image potential (V_{image}) depends on the mirror charges at vacuum side. As explained in aforementioned descriptions, the intrinsic nature of λ directly reflects the image potential (V_{image}) at interface as well as reveals the contribution of the effective image charges to V_{image}, which has an intense relationship with the conductiontype of nanomaterials. So it can be understood that V_{image} should be determined by (E_{F}E_{i}) or (E_{C}E_{F}) as found in Fig. 4, which also conforms to Eqs (5)–(7). In this situation, the λ values increase with the increase of (E_{F}E_{i}) for the same ntype semiconductors and close to 1 for ideal metal, which implies the behaviors of ntype semiconductors become more and more closer to those of metal with the increase of λ. Unlike ntype semiconductors, the hole density of valenceband turns larger with the increase of (E_{F}E_{i}) for ptype semiconductors. Accordingly, the conductionband electron density decreases with the increase of (E_{F}E_{i}), which suggests that ptype semiconductors gradually deviate far way from ideal metal. Consequently, λ turns smaller and smaller with the increase of (E_{F}E_{i}) and is even close to zero (tiny conductionband electrons) for ptype semiconductors, which suggests that the doping degree of ptype semiconductors increases with the decrease of λ. So it is reasonable that there exists different variance tendency of λ for ntype and ptype semiconductors with (E_{F}E_{i}). Most of all, qualitatively identification of the doping degree becomes possible by comparing their λ values for the same semiconductor nanomaterials.
The relationship between λ and the difference (E_{C}E_{F}) between E_{C} and E_{F} is also discussed in Fig. 4(d). One can see in Fig. 4(d) that λ will increase with the decrease of (E_{C}E_{F}) for all semiconductor nanomaterials. The possible explanations are given as follows. Theoretically speaking, the conductionband electron concentration (n) of semiconductor can be written as \(n={N}_{C}ex{p}^{(\frac{{E}_{C}{E}_{F}}{KT})}\), in which N_{C} represents the effective density of states (DOS) of the conductionband. Therefore, the conductionband electron density (n) will turn larger with the decrease of (E_{C}E_{F}) based on the aforementioned equation for conductionband electron density. Under this circumstance, the image potential V_{image} will accordingly increase with (E_{C}E_{F}), which leads to the increase of λ value. So it is well understood that λ should exhibit the identical variance tendency whether for n or ptype quasi onedimensional nanomaterials. It comes to a conclusion that the conductionband electron density (n) of quasi onedimensional nanomaterials should be the determinant factor for λ in comparison with other parameters because it overall considers the contribution of the bandgap (E_{g}) and the doping degree of the semiconductor. This method may be expanded to the identification of the conductiontype or the doping degree of other twodimensional nanostructures or bulk materials, and the relevant researches are still undergoing.
Conclusions
In summary, we have developed a simple FE technique to fast identify the conduction types of nanomaterials. Furthermore, we established the generalized SchottkyNordheim (SN) model and introduce the image potential factor (λ) to describe the effective image potential in FE process. By our method, the relationship between λ and the energyband structure of the nanomaterial emitters can be obtained: (a) λ = 1: metal; (b) 0.5 < λ < 1: ntype semiconductor; (c) 0 < λ < 0.5: ptype semiconductor. This criterion provides us a simple and effective way to identify the conduction types of the nanomaterial emitters and understand the physical mechanism of field emission. We test a group of nanomaterial emitters, and all results agree with both our theoretical predictions and other measurement results by FET technique. In contrast with the conventional hot and cold probe or Hall effect methods, our method is not only more convenient and effective but also can qualitatively determine the doping degree for the same semiconductor nanomaterials. Therefore, our method based on the FE technique should be a powerful tool to identify the conductiontype of nanomaterials and may shed new light on other two or threedimensional materials.
Experimental
Synthesis methods of twelve kinds of quasi onedimensional nanomaterials
In our work, twelve kinds of quasi onedimensional nanomaterials (Mo, LaB_{6}, SmB_{6}, ZnO, Si, C, W_{18}O_{49}, WO_{3}, WO_{2}, CuO, AlN and B) prepared by our laboratory were randomly chosen as the research goals. Nearly all of these nanomaterials were grown by chemical vapor deposition method^{22,34,35,36} except Mo nanocones^{25} (physical vapor deposition) and Si nanoapex^{21} (electron beam lithography). Moreover, these onedimensional nanomaterials were found to have identical morphology and uniformly distributed all over the substrate, which can eliminate the effect of nonuniformity on the physical property measurements and further assures the accuracy of the experimental results.
Physical property measurements of quasi onedimensional nanomaterials
FE measurements on quasi onedimensional nanomaterial thin film were carried out in our field emission analysis system, and the measurements on individual nanomaterials were performed in our modified SEM system, as described in our recent works^{23}. The schematic diagram of nanomaterials during FE measurements is provided in Fig. 1(a). The base pressure of the measurement chamber is lower than 5 × 10^{−5} Pa, and the distance between cathode and anode ranges from 100 to 500 μm except individual Si nanoapex (100 nm). UPS (Thermo Fisher Scientific, ESCALAB 250) and Kelvin probe force microscopy (KPFM, Omicron VTAFM) techniques were respectively used to measure the work function of ZnO^{37}, CuO^{38} and B^{39} nanowires while other onedimensional nanomaterials adopted the work function of their corresponding bulk counterparts^{24,35,39,40,41}. Their electric conductivity was also obtained by our modified insitu microprobe measurement technique.
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Acknowledgements
The authors are very thankful for the support of the National Key Basic Research Program of China (grant No. 2013CB933601), National Project for the Development of Key Scientific Apparatus of China (2013YQ12034506), the Fundamental Research Funds for the Central Universities of China, the Science and Technology Department of Guangdong Province and the Education Department of Guangdong Province as well as the financial support of the Natural Science Foundation of Guangdong Province (No. 2016A030313313).
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X.Y. wrote the main manuscript. H.G., L.P. and Y.T. carried out the properties measurement of the sample. F.L. and S.L. established the generalized SN model, N.X., S.D., J.C. and H.C. gave the helpful discussion and polished this paper.
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Correspondence to Shaozhi Deng or ShiDong Liang or Fei Liu.
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Further reading

Electron Emission Devices for Energy‐Efficient Systems
Advanced Intelligent Systems (2019)

Theory of field emission
The European Physical Journal B (2018)
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