Review of Field Emission from Carbon Nanotubes: Highlighting Measuring Energy Spread

  • M. H. M. O. Hamanaka
  • V. P. Mammana
  • P. J. Tatsch
Part of the Carbon Nanostructures book series (CARBON, volume 3)


This paper is a review of the research on field emission properties of carbon nanotubes (CNTs), the basic properties of CNTs, the main emission properties with highlighting in energy spread and the work done in applying CNTs for field emission microscopy (FEM). In this work there are explanations about the density of states (DOS) of the conduction electrons responsible for the emission; comparison of the characteristics of CNTs emission from single nanotube or films; comparison of the different types of electron sources and the introduction of CNTs electron sources applying in retarding field analyzer (RFA).


High Occupied Molecular Orbital Lower Unoccupied Molecular Orbital Electron Source Energy Spread Field Emission Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Introduction

In the Division of Information Displays of CTI several topics on displays are investigated, for instance: Liquid Crystal Displays (LCDs), Organic Light Emission Displays (OLEDs), Polymer Stabilized Cholesteric Texture Displays (PSCT), Polymer Dispersed Liquid Crystals Displays (PDLCs) and Field Emission Displays (FEDs). Although FEDs are not playing an important role in the display world anymore, the range of applications of carbon nanotubes CNTs) is still growing, as will be described hereafter. We are mainly interested in the field emission properties of CNTs in applications such as electron microscopes and other electron optic devices.

A good understanding of the field emission properties of CNTs is paramount to improve these devices and reduce the failure mechanisms. Therefore, the purpose of my work is a fundamental investigation of the field emission of CNTs.

The understanding of the emission mechanism of CNTs also allows us to use them in other applications that will be listed below. I shall pay special attention of using CNTs as a source of electrons in a Retarding Field Analyzer (RFA). The first scientific papers on CNTs properties reported extremely low turn-on fields, high current densities, good field emission stability compared to metallic emitters in various devices since 1995 [8]; however, the energy distribution of the emitted electrons was not particularly well understood, CNT sources continues offer several attractive characteristics such as instantaneous response to electric field variation, resistance to temperature fluctuation, and high degree of focusability in electron optics due to their sharp (0.2–0.3 eV) energy spread [57, 60]. An RFA is pre-eminently suited to study the energy distribution and the low-energy of an electron source [88, 16]. The first idea is characterize the CNT source and then use the RFA system in the work function measurements of materials.

The main applications of CNT’s are:
  1. a)
    Lighting elements [50, 71], i.e., produce light by bombarding a phosphor-coated surface with electrons. The first device with a CNT cathode to be demonstrated was the field-emission lamp, Fig. 1 [11, 71];
    Fig. 1

    Longitudinal cross-section of a CRT fluorescent display with a FE cathode made of carbon [71]

  2. b)

    Over-voltage protection with nanotubes, in this case the over voltage between a nanotube cathode and a counter-electrode reaches a threshold value for field emission, the emitted current induces a discharge in the noble gas [67];

  3. c)

    Flat-panel field-emission display [14, 71], the CNT electron source provides a high-brightness display. Field-emission panel displays were demonstrated 10 years ago [98] using Spindt-type emitters [75]. An inherent problem with FEDs is the need for vacuum between the anode and the cathode. Degradation of the vacuum results in ionization of the residual gas by the emitted electrons and poisoning of emitting material resulting in degraded performance. The difficulty in obtaining a robust well packaged display with a long lifetime maybe one reason why the FED has not succeeded commercially. However the main issue is almost certainly the success of the AMLCD. The improvements in LCD quality have reduced the potential market for FEDs to such an extent as to make them commercially unattractive [68];

  4. d)

    A FED-based backlight unit for LCDs [34, 35] could have lower power consumption than the cold cathode fluorescent lamp and there is severe competition since the development of emitting diode (LED) backlights [68];

  5. e)

    X-ray sources such as, hand-held X-ray spectrometers and mini-X-ray tubes for medical and other applications [76, 87];

  6. f)

    High-resolution electron-beam instruments such as electron microscopes, electron-beam-assisted-deposition instruments and electron-beam-lithography instruments [62, 9, 91];

  7. g)

    Various types of sensors can be applied in different segments of the industries, such as biomedical, automotive, food, agriculture, fishing, manufacturing, security, environmental monitoring and others [69, 93];

  8. h)

    Transparent conductive thin films for certain niche applications such as organic light emitting diodes (OLED) or Organic photovoltaic (OPV) devices [85, 92];

  9. i)

    Carbon nanotube electron sources for electron microscopes and other electron beam equipment [60]

  10. j)

    Power transmission lines with CNTs cables to transport the electricity [2]. The cables exhibit high current-carrying capacity of 104 ~ 105 A/cm2 and can be joined together into arbitrary length and diameter, without degradation of their electrical properties [95];

  11. k)

    Supercapacitor electrodes prepared from thin films of carbon nanotubes [51, 53];

  12. l)

    Carbon nanotube transistors are considered the replacement for silicon technology due of their characteristics of low operation voltage. [38].


Carbon nanotubes are one of the most important materials under investigation for nanotechnology, suggesting potential applications in different fields of scientific and engineering, as were described above. The first section of paper is the introduction; the second presents a brief description on basic properties of CNTs. The third section give a review of the electron emission properties by field emission, the fourth section discuss the applications in Field Emission Microscopy (FEM) and fifth section discuss electron Source with a comparison of energy spread between different sources. In sixth section present the measurements of energy-spread, the next sections are conclusions and acknowledgments.

2 Carbon Nanotube

Carbon nanotubes are formed by one or more graphene sheets rolled to form a cylinder with hollow inside and closed ends. There are two main types of CNTs: Single Wall Nanotube (SWNT), Fig. 2a, consists of one graphene sheet rolled with cylindrical form and the MultiWall Nanotube (MWNT) consists in several concentric graphene tubes with an interlayer spacing of 0.334–0.340 nm, Fig. 2b, [45].
Fig. 2

High resolution transmission electron microscopy (HRTEM) images of CNTs: a SWNT micrograph of individual rope, b and c MWNT Micrograph (by Iijima) with the cap drawing [45]

The layer structure of MWNT shows arrangements like “Swiss-roll” and “Russian doll”. These two possible arrangements are illustrated in Fig. 3 and also the variation of these two arrangements are a “papier mâché” suggest by [96] and the model by Amelinckx et al. [3] and [45]. The knowledge of these arrangements is important to understand the results obtained by several authors throughout this review.
Fig. 3

Schematic drawings (top and side view) of arrangements s for MWNT a “Russian doll”, b “Swiss roll” c “Papier mâché” suggested by [96] and d modeled by Amelinckx et al. (1995)

CNTs have three basic structures or families. The direction in which the graphene sheet is wrapped is represented by the chiral vector with indices (n,m). The name of these families are Armchair (Fig. 4a) if the chiral angle θ is equal to 30° and the indices n = m ≠ 0, Zigzag (Fig. 4b) if θ = 0° and m = 0 and n ≠ 0 and Chiral when the angle 00 ≤ θ ≤ 300 and n ≠ m ≠ 0. The lengths of SWNTs and MWNTs are usually well over 1 μm and their diameter range from 1 nm (SWNTs) to 50 nm (MWNTs). Virtually all of the tubes are closed at both ends with caps by fullerene like half spheres, but the tubes can be open at one end or both ends and can be semiconducting or metallic conductors. Observe the example in Fig. 4.
Fig. 4

Schematic drawings of CNTs, example of: a armchair, b Zig-Zag [45]. and c Chiral fiber with hemispherical caps at both ends [69]

The most common techniques used for CNT synthesis are vaporization methods like arc discharge or laser ablation and the catalytic decomposition of hydrocarbons over metal catalysts or chemical vapor deposition (CVD) [45, 91].

3 Field Emission

The emission of electrons from a metal or semiconductor into vacuum under the influence of a strong electric field is explained in terms quantum-mechanical tunneling. In theory there is a finite probability of the electron being found on the other side of a barrier. Although the electron total energy is lower than the barrier potential. The electrons will be tunneling through the potential barrier [48], rather than escaping over it as in thermionic emission or photoemission.

The process is shown in Fig. 5. The metal has an intrinsic potential and the Fermi level is filled with electrons. The distance between the Fermi level to vacuum level is called the work function (ϕ). The vacuum level represents the potential energy of an electron at rest outside the metal, in the absence of an external field. In the presence of a strong field, the potential barrier will be deformed along the line AB, so that a triangular barrier is formed, through which electrons can tunnel. Most of the emission occurs it the vicinity of the Fermi level where the barrier is thinnest.
Fig. 5

Diagram of the energy level for electron emission from a metal at absolute zero temperature. a comparison between different types of electron emission and b diagram of electron field emission

In other words the field emission involves the extraction of electrons from a solid by tunneling through the surface potential barrier. The Fowler–Nordheim theory describes the field-emission process. The current density (J) of tunneling is given by Eq. (1):
$$ J = \frac{{e^{3} F^{2} }}{{8\pi h\phi t^{2} \left( y \right)}}\exp \left\{ { - \frac{{8\pi \sqrt {2m} \phi^{3/2} }}{3heF}v\left( y \right)} \right\} $$
where, m is the electron mass, F is the electric field, h is the Planck’s constant, e is the electron charge and ϕ is a work function. A plot of log (J/F2) versus 1/F (Fig. 6), the so-called Fowler–Nordheim plot, is approximately a linear curve.
Fig. 6

Fowler-Nordheim plot example of the field emission current density

The t(y) and v(y) were calculated by Good and Mueller [24] and can be approximated by t(y) = 1 + 0.1107y1.33 and v(y) = 1 − y1.69. The y is expressed by Eq. (2)
$$ y = \frac{1}{\phi }\sqrt {\frac{{e^{3} F}}{{4\pi \varepsilon_{0} }}} $$

ε0 is the permittivity of free space.

In the case of a triangular surface potential barrier, such that t(y) and v(y) are unity, the current density function by can be approximated as shown Eq. (3)
$$ J = 1.54 \times 10^{ - 6} \frac{{F^{2} }}{\phi /e}\exp \left\{ { - 6.83 \times 10^{9} \frac{{\left( {\phi /e} \right)^{3/2} }}{F}} \right\} $$

Here ϕ/e is the work function in electron volts [23, 24]. The model is valid for emission from flat surfaces at 0 K, but it was adapted to describe field emission from sharp tips up to temperatures of several hundred degrees Celsius. Corrections of this model are required for tips with extremely curved surfaces. An additional correction may be necessary in the case of nanotubes since the density of states is not energy independent around the Fermi level as in ‘real’ metals [70].

The Fowler–Nordheim model shows the dependence of the emitted current on the electric field and the work function. The intensity of electric field shows dependence with some variables as shape of tip, voltage applied and distance between cathode and anode. As a consequence, a small variation of the shape or surrounding of the emitter (geometric field enhancement) and/or the chemical state of the surface has a strong impact on the emitted current.

The local field enhancement factor β is often introduced in the Fowler–Nordheim equation to represent the geometrical effects at the surface of the cathode, where β = F n /F 0 for macroscopic applied field F 0 . Local variation of β determines the local normal surface electric field, F n , resulting in local dependence of injection current by the Fowler–Nordheim law. A constant macroscopic electric field F0 = 1 U/m is applied setting the top boundary at a constant surface charge density given by σ = ε 0 F 0 , where ε 0 is the permittivity of vacuum. In most field enhancement simulation studies the top boundary is at constant voltage Uanode in which case the evaluation of β depends on the anode-cathode distance. The maximum field, F max, normalized by the F 0 is the field enhancement factor (β = F max/F 0). For capped CNTs with radius R, hight h and separation L the aspect ratio f = h/R and normalized separation s = L/h are sufficient to determine β.

These models are applied to a hemisphere on a cylinder, which corresponds to a nanotube with a smooth and clean hemispherical cap. In real situations, however, this condition is not often met. The tip of nanotube emitters (especially for MWNTs) is seldom hemispherical but tapered, and may furthermore be flat, opened and/or present nanometer sized protrusions. Numerical simulations reveal that a deviation from the hemispherical shape produces an increase in the field-enhancement factor up to a factor of two, which can easily lead to a factor of ten in the emitted current.

Irregularities on an atomic level of the tube end are not expected to influence the emission properties for a metallic cap, as the electron cloud smoothes out these irregularities as in metals [41].

3.1 Field Emission Energy Distribution

The Density Of States (DOS) of a system describes the number of states per interval of energy at each energy level that are available to be occupied. In metals, the DOS of the conduction electrons, which are responsible for the emission, is described by the Fermi–Dirac statistics. Above the Fermi level the tunneling probability increases, but the DOS decreases very sharply. Below the Fermi level the DOS increases slightly but the tunneling probability decreases strongly.

These considerations are directly reflected in the specific shape for the Field Emission Energy Distribution (FEED) of the electrons predicted by the Fowler–Nordheim theory. The FEED peaks around the Fermi level with exponential tails that depend on the Fermi temperature of the electrons and on the slope of the tunneling barrier for the high and low energy tail, respectively [36, 40]. Any deviation from this metallic shape is due either to adsorbates or to a nonmetallic DOS. FEED can therefore be used to gain information on the DOS of the emitting electrons as well as to determine ϕ. The Full Width at Half Maximum (FWHM) of the FEED is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value, for example, in the metal is typically 0.45 eV [40]. Figure 7 shows a typical energy distribution obtained from a film of MWNTs just at the onset of emission. The FWHM is in this case 0.18 eV only, and it was reported an average FWHM over 10 samples of 0.2 eV, without taking into account the broadening due to the finite resolution of the energy analyzer [6]. The experimental setup to Fig. 7 was 3 mm diameter cylindrical counter electrode was placed at a distance of 125 μm for the film emitters and the measurements were carried out at pressures of 10−7 mbar.
Fig. 7

Field electron energy spectra obtained on a MWNT film showing a single peak, along fits obtained with the F–N distribution (dotted line) and with the modified F–N distribution including a Gaussian band of states (dashed line) [6]

The shape of the FEED of MWNTs therefore strongly suggests that the electrons are not emitted from a metallic continuum, but from energy bands of 0.2–0.4 eV width. Observe in Fig. 8 the models for the emission.
Fig. 8

Models for the field emission showing the energy bands, and the corresponding FEED: a emission through energy bands corresponding to DOS at the nanotube cap, b adsorbate resonant tunneling, c emission from a typical metallic SWNT DOS [8]

Fransen et al. [39] observed two kinds of behavior with the applied field for single MWNT emitters. Some spectra showed one peak of ~0.3 eV FWHM that shifted with the field and others with peak of ~0.15 eV FWHM did not shift. The small FWHM was attributed to the presence of resonant states in the DOS at the tube cap.

Dean et al. [29] detected one peak located at the Fermi level on a single SWNT at room temperature consistent with a metallic, localized or adsorbate state at the Fermi level, Fig. 8b). No peak shift was observed on changing the applied field. A decrease in the emitted current was attributed to adsorbate removal. Since the FEED is a convolution of the tunneling barrier and the electronic DOS of the nanotube, they concluded that tunneling states are present above the Fermi level in clean SWNTs, Fig. 8a).

The low energy showed in FEED spectra from individual SWNT has unusual features at room temperature [58] and were attributed to singularities in the DOS of the SWNT [69, 83], that is, some features of the DOS of the tubes or caps, such as resonant localized states and/or singularities, are reflected in the FEED spectra [58]

Experimental results from [39, 55, 58] on the work function are not conclusive. Fransen et al. determined a workfunction of 7.3 + 0.7 eV on one MWNT. Kuttel et al. found a workfunction in the range of 5 eV for a CVD MWNT film which was refined to 5.3 eV in a subsequent study. Lovall et al. deduced a value of 5.1 eV for a SWNT. It is not clear if the work functions of closed MWNTs, open MWNTs or SWNTs are different.

It seems far safer to make an assumption on the work function and to deduce the field amplification and emitter shape than work the other way around.

FEED is a reliable method to determine simultaneously the work function of a field emitter and the field amplification. Another observation by ultraviolet photoelectron spectroscopy measurements performed on MWNT films gave a clear indication that the work function can vary significantly with the surface state of the tubes [1]; in other words, the properties may be significantly influenced by the synthesis and purification methods [8].

3.2 Charged States

Several groups reported that the local DOS at the tip showed sharp localized states that were correlated with the presence of defects and also with various tip geometries. The DOS, in the Fig. 9, shows the effective work function, ϕeff, which is defined as the difference of the energy between the Fermi level and the lowest unoccupied molecular orbital level (LUMO), i.e., half the band gap in case of a semiconductor. The difference between the LUMO and the vacuum level Δϕ would vary when the strength of the applied electric field is changed. The effective work function of the capped armchair nanotubes decreases linearly with increasing electric fields, whereas that of the metal tip decreases quadratically. The Mulliken charge population shows that the charge accumulation is not dependent on the local atomic geometry but on the sharpness of the tip [54].
Fig. 9

Schematic drawing showing the effective work function (Φeff) with the applied electric field [54]

Figure 10 shows change of highest occupied molecular orbital (HOMO) and LUMO for various charged states under the applied electric field for neutral states, Q = −2e and Q = 2e. Drawings showed in the left are local charge densities under no applied electric field and the right column shows those under an electric field of 1 V/Å. It is possible to observe where the charge transfers occur. For negatively charged states, the HOMO and LUMO are localized at the cap under an electric field. Because the local field can be enhanced easily at the cap by the local field enhancement factor, these electrons can be easily emitted by the external electric field. For positively charged states, on the other hand, the HOMO and LUMO are not always localized at the cap under an electric field. These states are not affected much by the external electric field.
Fig. 10

Charged states drawings of armchair nanotube cap (5,5). The left column shows local charge densities under no applied electric field and the right column shows those under an electric field of 1 V/Å. a Neutral state (Q = 0); b Q = -2e and c Q = 2e [54]

3.3 Field Emission Mechanism

Rinzler et al. [66] proposed a model that higher emission efficiency is from open MWNTs but this could not be confirmed experimentally yet, and probably will be valid only for open tubes [64, 63]. Obraztsov et al. [63] proposed that model would be valid only for open MWNT.

The observations of the experiments is possible to consider that the electrons are emitted from sharp energy levels due to localized states at the tube cap [26] like in the theoretical calculations and was confirmed experimentally by scanning tunneling microscope (STM) measurements on MWNTs [10], as well as, on SWNTs. The FWHM of these states and their separation is in good agreement with the values measured for the light emission and with FEED observations carried out at 20 °C and at 600 °C [30]. In this hypothesis is necessary to consider two points. First, if several energy levels participate in the emission, the occupied level nearest to the Fermi energy will supply nearly all the emitted electrons and this level is strongly depend of atomic configuration. Therefore, exist significant differences of the emitted currents from one tube to another and second it is necessary observing the carrier densities in the states because the field emission current depends directly on this carrier density [8].

Dean et al. [29, 31] suggest that nanotubes emission is more complex than the metallic tip emission. Different emission regimes on single SWNTs were identified and depend on applied field and temperature. One regime is a resonant tunneling through an adsorbate, in this case, the water molecule. These molecules desorb either at high fields and emitted currents or at temperatures higher than 400 °C. The other regime correspond to the intrinsic emission from the cleaned tube and show a far lower emitted current for comparable voltages with strongly reduced current fluctuations. The origin of these intrinsic regimes is not clear yet, but the emission mechanism involves probably non-metallic electronic states, such as enhanced field emission states above the Fermi level or a non-metallic DOS [8].

Thus, the results observed by different groups shows that emissions involve a non-metallic DOS and/or adsorbate-resonant tunneling. Supplementary information on electronic and structural properties of individual nanotubes, on the nanotube cap and on the influence of absorbates or bonded groups are required for a better comprehension of the emission.

3.4 Setup for Arrangements of CNTs Emissions Experiments

In the electron emission of the CNTs normally it is necessary to use a support that in some cases is a substrate to CNTs films, a wire or a filament to individual nanotube. Following is a description of some types of setup.
  1. a)

    The nanotubes are mounted on a support tip by a simple method. Under an optical microscope equipped with two three-axes micromanipulators used to move independently two supports, normally one to the tungsten filament and other to move nanotubes with conductive characteristics [66, 39]. Individual carbon nanotubes stick to the tip either by Van der Waals forces alone or by first applying a bit of adhesive to the tip. The resolution of an optical microscope is not sufficient to observe one nanotube and it is therefore necessary to characterize the emitters by scanning or transmission electron microscopy [4].

  2. b)
    To improve the previous method it is necessary to use a piezo-driven nanomanipulator in a Scanning Electron Microscope (SEM). A tungsten wire is fixed by laser-welding on a filament. The tip is transferred into the SEM and carefully pierced into carbon tape. In this case also it is used a glue on the tip for firm attachment of the nanotube [22]. These nanotubes were broken by running a current through it the break-off occurring at a weak spots along the length of the nanotube (Fig. 11c), possibly a defect in its structure. Figure 11 shows the schematic drawing of the procedure. [25].
    Fig. 11

    a A CNT protruding from a thin substrate containing many nanotubes is selected and b attached to a tungsten support tip. c The CNT is broken by Joule heating. d The open tube end is finally closed [25]

  3. c)

    Fix the individual nanotubes on the support, for instance, using low-energy electron microscope equipped with micromanipulators, or using a mat of SWNT material in this case after the contact with the support under the optical microscope, a small voltage (10 V) is applied to break the attached rope from the mat, another method operates inside a scanning electron microscope [58]. Individual nanotubes can be picked up and attached to AFM cantilevers by electron beam irradiation [21]. These deposits are mechanically strong and the electrical contact between the tube and the support should be strongly enhanced by the electron-beam irradiation and finally the direct growth of one nanotube on a support by CVD [15, 84].

  4. d)

    In the case of carbon nanotubes films can be made from ‘bulk’ samples (by pressing nanotube powder or spraying a nanotube-containing suspension on a support) or can be grown directly on desired positions on a support structure using CVD techniques. However, the relation between the morphology and the emission properties cannot be properly investigated, since the emission of a single nanotube is different from the emission of a nanotubes film [9].


It was observed in some experiments with impure material it is more difficult to isolate an individual nanotube, in these cases a macroscopic fragment is picked up and is fixed on top of a filament tip. Purified material is better; the tubes are segmented and well separated in the solution following an oxidation treatment. But the effect of the purification of the tubes is not well known and the cap removal is not controlled and may affect the emission properties.

3.5 Field Emission from CNT Films

After Iijima identified the carbon nanotubes in 1991, [12, 49] reported field emission from “tubulene’’ films (MWCNT). Due to its high density, the tube protruded only a few nanometers above the surface and consequently the voltages needed to extract the current were very high (<25 V/μm). De Heer et al. [19] observed electron emission from a continuous film of randomly oriented (MWNT), with macroscopic current densities as high as 100 mA/cm2.

The field emission is excellent for nearly all types of nanotubes. The threshold fields are as low as 1 V/μm (minimum field to emission) and turn-on fields are around 5 V/μm (ideal field to emission). Nanotube films are capable of emitting current densities up to a few A/cm2 at fields below 10 V/μm. One interesting parameter is the emitter density on the films [8]. Typically, a film has a nanotube density of 108 ± 109 cm−2. The effective number of emitting sites, however, is quite low. Typical densities of 103 ± 104 emitters/cm2 were reported at the onset of emission [19, 5, 97]. By using an optical microscope combined with a phosphor screen, [63] was able to enhance the resolution of the measurement and reported densities of 107 ± 108 cm−2 [8].

3.5.1 Emission Characteristics

Electrostatic Screening

Several studies reveal that the electric field at the apex of the emitters decreases with decreasing spacing between the emitters, more exactly for a spacing less than twice the height [7, 61].

In other words, the field enhancement is largest for a single nanotube and decreases as the as nanotubes are positioned close, as shown in Fig. 12. [43, 61]. So, the optimum configuration is the largest distance with the highest density.
Fig. 12

a Equipotential lines of the electrostatic field for an single CNT and b with five CNTs showing the electrostatic screening. The others are images of three experimental situations by SEM; c Emission was observed at 90 V, d and e Emissions were observed up to 200 V in both cases, the results were the same [23]

Height and Diameter of CNT

Theoretical considerations on the field emission of CNTs indicate their outstanding feature, because of their high aspect ratio. That is the length of a vertically oriented CNT divided by the diameter. From this point of view long vertically aligned CNTs should be super cold emitters.

But experimental results showed that less densely populated ‘‘short and stubby’’ nanotubes showed the best emission characteristics with a threshold voltage of 2 V/μm and saturation emission current density of 10 mA/cm2 [13].

Alignment in an Electric Field
The influence of an applied electric field on CNT was observed, CNTs flexed to orient themselves parallel to the electric field lines. For moderate field strengths below the electron field emission threshold, the flexed nanotubes relaxed back to their original shapes after the electric field was removed, Fig. 13 [82].
Fig. 13

SEM images showing the CNT bending under different electric fields a 0 V, b 20 V, and c 0 V. Observe the alignment of CNT with the electric field lines [82]

Emitted Current

The emitted current varies in an exponential way with the electric field. A small variation in the field produces a huge difference in the emitted current (this is demonstrated by the Fowler–Nordheim model). The consequence is difficult to predict the emission with precision, for instance, in the experiments measurements of some individual nanotubes to compared with the values predicted from the measured parameters; length and diameter of the nanotube and the distance between the cathode and anode resulted in two very different values. These results are very interesting because is possible to conclude that the emission process is highly sensitive to the exact structure of the cap. Other possible conclusion is that for a film just a single or a few nanotubes are necessary to provide the emitted current for a pixel area because a nanotube needs to be only slightly thinner, longer or sharper than the surrounding nanotubes to dominate the emission. This effect can even be increased when nanotubes have an adsorbed species on the cap.

This effect in the emitted current has been investigated by comparing the measurements on a nanotube film and on individual emitters from the same film and this experiment showed that the field enhancements are far higher in the former case (nanotube film) than in the latter (individual nanotube) [9]. This effect is critical for most devices, where an homogeneous emission and high emission site density is needed. In fact, the dispersion on γ (and hence on the combination of nanotube height, length and spacing) should be less than 4 %, which is difficult to achieve even when the growth is well controlled [73]. One possibility to avoid this problem is to include a suitably scaled ballast resistor in series with the emitter to produce a voltage drop.

3.6 Emission from Individual CNTs

The first electron field emission from a single nanotube was reported by [66]. He studied MWNT mounted on a carbon fiber with emission currents of 100 nA at 0.12 V/μm. [8] studied closed and open MWNT nanotubes mounted on gold fibers. It was found that open tubes emitted at about twice the voltage needed for the closed ones, as is shown in Fig. 14. In contradiction Saito et al. found that open MWNTs began to emit electrons at the lowest fields. The results are inconclusive so more research is needed in this area [8].
Fig. 14

Field emission I × V Curves acquired on a cap of the SWNT and MWNT on etched gold fiber [8]

3.6.1 Emission Stability

The Fowler–Nordheim model is used to explain the tunneling current in field emission although the I x V characteristics of nanotubes do not follow the predicted behavior over the whole current range model [26, 4]. Two different current regimes were observed: fluctuations at low emitted currents with a switching frequency that increased with the current and became maximal at the onset saturation, followed at higher currents by stable emission with flicker noise [71]. Observed current fluctuations at low currents and attributed the observed saturation to the presence of non-metallic resonant states at the cap.

Stable emissions were observed by several groups [19, 37, 90, 59], the highlight is [71]. They observed the emission during 8000 h with emission current of 10 mA/cm2. The problem of the instable emission can be due the degradation and can be reversible or permanent, but the origin is not clear. The other possibilities observed for the instability are the residual gases and the intrinsic proprieties of nanotubes. Comparing films of SWNTs and MWNTs in the same chamber pressure conditions and emitted current density observed a faster degradation of SWNT probably because the single wall is more sensitive to ion bombardment and irradiation [26, 5].


Several aspects that provide failure were observed. The electrostatic deflection or mechanical stresses can cause alterations in the shape and/or surroundings of the emitter, which may lead to a decrease in the local field amplification. High currents can rapidly damage a nanotube. A gradual decrease in field enhancement due to field evaporation was found on SWNTs when the emitted current was increased beyond a given limit between 300 nA–1 μA [32].

On MWNTs, a shortening of the emitter over time, (Fig. 15) [82] or damage to the outer walls of the nanotube due to high currents [81] were also reported. The CNTs can be operated at currents of up to 10 μA, but the current should be kept below 1 μA for stable operation and long life-time [20].
Fig. 15

Images by SEM showing the permanent deformation of the CNT after field emission: a image before field emission; b Image obtained after field emission and after the strong electric field was removed. The nanotube stayed in the straight shape [82]

Bonard et al. [8] observed reversible degradation in the emissions of CNTs films and permanent for the individual nanotube is in nearly all cases abrupt, the emission happened on most emitters as a irreversible failure that occurred in less than 10 ms.

De Heer et al. [19] presented recently some experiments of field emission on single MWNTs in a transmission electron microscope. It appears that tube failure occurs on a very short time scale (<1 ms) at currents above 0.1 mA and that it involves an irreversible damage to the tube. Tube layers or caps are removed, peeled back, or the end of the tube is amorphized [81]. In all cases a strong decrease in the emission current occurs and the voltage has to be substantially increased to obtain comparable currents. Cumings et al. [18, 17] observed single MWNTs with a similar setup. They were able to “peel’’ the tube layer by layer by applying a strong current through the tube. [26] proved that the location of the electrical failure on a single MWNT could be correlated with the presence of a defect in the nanotube.

Another problem is arcing, i.e. an arc between cathode and anode that is initiated by field emission. Such arcing events are commonly observed on diamond and diamond-like carbon films [45]. They are usually caused by a high field-emission current, anode out-gassing, or local evaporation of cathode material that creates a conducting channel between the electrodes.


The fluctuations of the emitted current over time are caused by the exponential behaviour of field emission: small changes in the electric field and the workfunction have already large effects. Small molecules absorbed on the cap may lead to slight changes in the workfunction or of the cap geometry, resulting in large differences in the emitted current, in other words, the nanotube emitter is sensitive to surface diffusion of emitter material in the presence of the large electric field required for field emission [44]. Dean et al. [31] observed this phenomenon on single SWNTs. These fluctuations disappeared nearly completely at higher currents. This behavior was ascribed to the presence of adsorbates (most probably water) at the cap that enhance the field emission as compared to clean caps [23].

There are several ways to reduce the emission current fluctuations.
  1. 1.

    Cleaning of the CNTs, but the main problem is that the clean nanotube is sensitive to molecules in the vacuum, and especially to oxygen, which can cause irreversible damage to the tube [27].

  2. 2.

    Heating the emitter to 1000 K in ultra-high vacuum to remove adsorbed molecules or impurities [27, 22, 70, 86]

  3. 3.

    Self-heating of the nanotube to remove adsorbed molecules [65]

  4. 4.

    Using a series resistor of several MΩ to regulation of the current (ballast resistor)

  5. 5.

    The stability can be largely increased when keeping the temperature at 600–900 K, so that absorbed molecules are continuously driven off the nanotube [20]


Noble gases and H2 usually cause an increase in the current fluctuations, but the emission stability is restored after evacuation of the gas. No degradation was measured on a single nanotube after exposure to Ar and H2. Conversely, irreversible continuous decreases in the current were provoked by exposure to oxygen and water and were attributed to reactive sputter etching [28].

The vacuum level should be of the order of 10−9–10−10 mbar for emission stability of a few percent, but lower vacuum levels are also allowed at the cost of stability. At lower vacuum levels it would be advantageous to reduce the partial pressure of oxygen and water.

An important question is how stable the average electric field around the cap is in time. It was found by electron holography experiments that the electric field remained remarkably constant, although large fluctuations of the emitted current did take place [18].

4 Field Emission Microscopy

The electron beam that is emitted from a nanotube is not uniform, but shows certain patterns when projected on a phosphor screen. The images projected depend on the type of cap. Emission patterns with a clearly visible symmetry were observed for MWNTs [72], and after heated at 1300 K some bright spots showed in the image disappeared in time, this behavior was typical for absorbed species on the cap.

The emitted current decreased as each molecule (bright spot) was removed. The current emitted by the clean tube was lower by a factor of three than the “dirty” tube (e.g. gas molecules on the cap): this shows that, on CNTs, adsorbed species enhance the field emission, observe some images in Fig. 16 [31, 46].
Fig. 16

Images of capped MWNT by FEM; a After heat cleaning and b–e showing a sequence of adsorption of gas molecules [46]

SWNT films showed ring patterns that were interpreted as coming from nanotube caps because of the circular symmetry [97]. Others patterns like circular arcs and rings on films were attributed to emission from the open edges [59].

Movements in the patterns were observed. These patterns started to rotate when the applied electric field was above a certain threshold value [33]. They observed similar patterns for samples made of individual multi-walled CNTs mounted on tungsten tips [20].

Bonard et al. [8] also detected bright spots from MWNT and SWNT emitters along with well-defined patterns of two or fourfold symmetry. These patterns persisted after applying high positive fields in desorbing possible adsorbates and reflect probably the electronic density of the emitting states at the nanotube cap. The non-homogenous density would identify them as localized states at the cap and not as delocalized conduction-band states as in metals.

Dean et al. [29] showed patterns of SWNTs at room temperature with one to four lobes that are typical and behaved like molecules adsorbed on the tube cap. These patterns disappeared above 600 °C, and fine structured patterns with sometimes five or six fold symmetry were detected. Dean et al. [29] argue that these patterns represent the electronic distribution of the emitting states at the nanotube cap and not the atomic structure of the cap.

In some results of field emission microscopy it is possible observe some characteristics such as:
  1. a)

    a pattern emission with a clearly visible symmetry, but when the symmetry of the pattern is disturbed some authors attribute the problems in the cap shape, because emission process is highly sensitive to the exact structure of the cap, as described in the emitted current section.

  2. b)

    bright spots, usually explained by the existence of adsorbed species [29] in the emission, but it should also be noted that the cap may contain small protrusions [56].

  3. c)

    no pattern emission, it may mean problems in the cap. The open caps should produce irregular and changing patterns, due to their sharp edges and dangling bonds. Irregular patterns were also observed for damaged caps, consisting of amorphous carbon.

The images in Fig. 17 exemplify the FEM emissions, the images between a) and f) show the FEM patterns of nanotubes. These patterns are interpreted as the typical emission of SWNT or thin MWNT with caps. These emissions were highly stable with time for emitted currents up to 1 μA. The images g) and h) with red dotted lines showing images changing their positions and intensities every few seconds and even rotated and are interpreted as images of nanotubes without cap. The electron emission from a capped CNT exhibits a high current stability in contrast to emission from CNTs with open cap [25].
Fig. 17

FEM images of electron sources. The images: a–f showing patterns of closed caps; g and h The emission patterns of CNTs with open caps [25]

In summary, some tubes produce homogenous spot or ring patterns that are quite similar to those observed on metal tips. On the other hand, the observation of fine-structured stable patterns strongly suggests that the electronic distribution of the emitting states is not homogenous. The origin of this discrepancy is explained by different cap geometries because the topology of the cap affects the strength and position of the peaks observed in density of states spectra near the Fermi energy. In other words the cap has different electronic structures [52]. Some experiments using TEM, shown that the work function is sensitive to atomic structure and the surface specification of the emitting tips [52].

5 Electron Source

The traditional types of electron sources are the thermionic, Schottky and cold field emission source. The diagram of the electron sources was presented in the first section in Fig. 5, the energy level scheme to each type of source. In the thermionic electron source, a material is heated to a high temperature and its electrons gain sufficient energy to overcome the material’s work function to be emitted. The Schottky emitter, sometimes also referred to as the field enhanced thermionic emitter or thermal field emitter, combines heat, low work function, and a moderate applied electric field to create a stable electron source. The Cold field emission is obtained under an applied electric field, in this case the CNT embodies a unique combination of properties which make a potentially and extraordinary electron source [79, 60], the advantages over other field-emitting materials including high aspect ratio (hence a high field enhancement and brightness), strong covalent bonding preventing electromigration of surface atoms and a high conductance, high stability, energy spread as little as 0.2 eV and reduced brightnesses of the order of 109 A/srm2V [60].

CNTs have some advantages when applied in electron sources of microscopes: a cold electron source, providing a high current density and high brightness; however, a more important consideration is the effect of the field emission mechanism on the energy spread of the electron beam.

The expected energy spread of field emission can be calculated by expressing the current density as function of the energy using the Fowler–Nordheim theory, Eq. (4) [47]:
$$ J\left( E \right) = \frac{4\pi med}{{h^{3} }}\exp \left\{ { - \left( {E - \frac{2v\left( y \right)}{3t\left( y \right)}\phi } \right)\frac{1}{d}} \right\}\left( {1 + \exp \left( {\frac{E}{{k_{B} T}}} \right)} \right)^{ - 1} $$
kB is the Boltzmann constant, T is the temperature, the other symbols are defined in Eqs (1) and (2), and the tunneling parameter d is given by Eq. (5).
$$ d = \frac{ehF}{{4\pi \sqrt {2m\phi } t\left( y \right)}} $$
The parameter d can be expressed for t = 1 as Eq. (6).
$$ d = 9.76 \times 10^{ - 11} \frac{eF}{{\left( {\phi /e} \right)^{1/2} }} $$

The energy spread ΔE of the source is defined by the full width at half maximum (FWHM) of the energy spectrum and is determined by d and T [23].

Several experiments revealed a small energy spread of 0.2–0.3 eV as expected for a cold field emitter and only small deviations from the Fowler–Nordheim theory [6, 22, 43], but in some cases turned out to be somewhat larger of up to 0.5 eV. Data of [46] obtained values between 0.3 and 0.4 eV, and their energy spectra contained a relatively large shoulder at the high-energy side [78]. Probably by self-heating of the nanotube, because the experiments of Purcell et al. [65], in which the effect of self-heating was investigated, demonstrated a significant broadening of the high-energy side of the energy spectra as function of the emitted current.

In some applications such as electron probes for microscopy or lithography or electron beam equipment the stability, energy spread, noise, emission pattern, brightness and current per emitter are important parameters of electron source, as an example the narrow energy spread is desirable as it improves the focus ability of the beam using electrostatic lenses [79, 60]. The carbon nanotubes have some properties that make them attractive material for field emission source as described in the beginning of section.

To perform the energy measurements we should take account the brightness parameter of electron source. Generally there is a direct proportionality between useful beam current and brightness, observe the explanation below.

5.1 Brightness of CNT Electron Sources

The reduced brightness (Br) is another important parameter of electron sources, because it indicates the amount of current that can be focused into a spot of a certain size and from a certain solid angle. Note the Eq. (7), it is a function of the radius of the virtual source rv, the angular current density I’ corresponding to the brightest fraction of the emitted electron beam and the beam potential U [44, 47]:
$$ B_{r} = \frac{I'}{{\pi r_{{^{v} }}^{2} U}} $$
The virtual source of an electron emitter is the area from which the electrons appear to originate inside the CNTs [44]. Figure 18 shows some electron trajectories, from which the magnitude of rv is obtained. The virtual source sizes of individual multi-walled CNTs were determined by operating the nanotubes as electron sources in a point-projection microscope [89]. It was found that the radius of the virtual source size varied between 2.1 and 3.0 nm [20]. This result was larger than expected for the emitter with a hemispherical cap and was explained by a flat, or open cap [23].
Fig. 18

Electron trajectories a Nanotube with Spherical cap and radius R; b Nanotube with a flat cap and c Nanotube with an open cap [23]

The results from reduced angular current density were observed between 19 and 50 nA sr−1 V−1. The angular current density was measured for a cleaned nanotube and the maximal current in the stable emission was 1 μA [44, 77, 850].

Table 1 compares the nanotube electron source with the thermionic, Schottky, and metal (tungsten) field emission sources. The tungsten cold field emission source is used in applications where heat is a problem or where a very small energy spread is required. However, it is applied at the expense of poor stability. The Schottky source offers excellent stability at the expense of energy spread and heat.
Table 1

Properties of different electron sources, observe the energy spread to each case [79]


Thermionic (Tungsten/LaB)6

Schottky (Tungsten + ZrO)

Metal cold FE (Tungsten)

Carbon nanotube FEa

Virtual source size (nm)





Energy spread (eV)





Brightness (A/m2srV)





Stability (%)





Operating temp

1,500–2,100 °C

1,500 °C

25 °C

25 °C–400 °C


100–1,000 h

>1 year

>1 year

>1 year

aFor the carbon nanotube field emission source, it can either be operated at room temperature (25 °C) or slightly warm (400 °C) to prevent re-adsorbtion of residual molecules in the vaccum and enhance its ability. Even when hot, carbon nanotube,which are covalently bonded, remain stable and do not suffer from diffusion/electromigration like metal emitters [5]

From Table 1 it can be concluded that a CNT field emitter, which has the same stability and noise as the Schottky source, delivers a high-brightness electron beam with narrow energy spread and therefore, it is a formidable contender as a source for electron optical applications [79].

6 Measurement of Energy Spread

The knowledge of the beam energy spread (or width) with accuracy is important because is possible characterize the electron source. A retarding field analyzer (RFA) is our choice to measure the energy spread of electron beams because of its simplicity, compactness and high signal-to noise ratio output.

There are different types of RFAs and the simplest is with parallel plate [16]. It consists of the CNT electron source and two parallel plates. The first plate is grounded and the second one is biased to a negative high voltage to retard the electron beans, only those particles whose longitudinal kinetic energy is higher than the retarding potential can thus pass second electrode and reach the Copper collector plate forming a current signal. Other electrons will be reflected. To improve the system we insulate the mesh electrically from the retarding and apply a controllable small voltage between the second plate and the collector. By varying the voltage the associate electric field provides changes in the slopes of the trajectories so that the beam can be made to pass the lowest potential before the mesh with no transverse velocity [16].

7 Conclusion

The studies of nanotube films with different densities and measured under identical conditions shows that a film of low density and short tubes are inefficient cathode. The medium density films show a very homogeneous and strong emission with a large number of emitting sites. A very dense film, however, shows a decreased quality of the emission. These results from a combination of two effects: the intertube distance and the number of emitters. When the intertube distance is large, the field amplification factor is determined only by the diameter and the height of the nanotube. As the distance between the tubes is decreased, screening effects become significant.

Different properties of carbon nanotubes proved that they are excellent electron sources, providing a stable current at very low fields and capable of operating in moderate vacuum. Different methods are available to deposit of nanotubes on surfaces with different density and orientation and therefore to control their emission properties. The degradation remains also a big unknown in spite of its utmost importance for applications.

Carbon nanotube electron sources clearly have interesting properties, such as low voltage operation, good emission stability, long lifetime, high brightness and low energy spread. Several applications could possibly benefit from the use of CNTs, and considerable research efforts in both academy and industry have been allocated to evaluate these possibilities. The most promising applications are the field-emission display and high-resolution electron-beam instruments. Yet many hurdles remain.

The results of several researchers cannot get a more incisive conclusion because the comparison and interpretation of the results is difficult because most groups use different designs of cathodes, materials and experimental procedures. Also, it is difficult to compare data reported by the various authors since they frequently use different definitions of the emission parameters and their measurements depend upon a variety of experimental conditions, many of which are unreported [94].

These facts make a thorough comparison of results delicate, particularly because the methods used for synthesis, purification, presence of contaminating material, and film deposition are quite varied. The interpretation is further complicated by the different experimental setups, e.g., the uses of planar, spherical or sharp tip anodes, and different distances to emissions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • M. H. M. O. Hamanaka
    • 1
    • 2
  • V. P. Mammana
    • 1
  • P. J. Tatsch
    • 2
  1. 1.Centro de Tecnologia da Informação Renato Archer – CTICampinas-SPBrazil
  2. 2.Universidade Estadual de Campinas – UNICAMPCampinas-SPBrazil

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