Cold and Laser Stimulated Electron Emission from

Copyright © 2009 American Scientific Publishers All rights reserved Printed in the United States of America

Journal of Nanoelectronics and Optoelectronics Vol. 4, 1–13, 2009

Cold and Laser Stimulated Electron Emission from Nanocarbons Alexander N. Obraztsov1 2 ∗ and Victor I. Kleshch1 3 2

1 Department of Physics, Moscow State University, Moscow 119991, Russia Department of Physics and Mathematics, University of Joensuu, Joensuu 80101, Finland 3 General Physics Institute, Russian Academy of Science, Moscow 119991, Russia

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Various types of electron emission are being nowadays applied for the creation of electron beam sources in the vacuum electronic devices such as X-ray, and cathode-ray tubes, microwave devices etc. Study of the electron emission is also an important tool for determination of basic characteristics and specific features of different materials. Carbon based materials have been the focus of many studies of their electron emission properties from fundamental and applied points of view. This is particularly owing to strong atomic bonding in graphite and diamond which provides chemical inertness and sustainability of carbon cathodes under the action of residual gas ion bombardment. Recently great emphasis has been attracted to nanostructured forms of carbons. The field (or cold) emission characteristics of carbon nanotubes are commonly attributed to geometric effects, and other more complex effects associated with field penetration, electronic structure and stationary states. Nanocrystalline diamond films have displayed similar field emission characteristics at relatively low applied fields, and this effect has been assigned to the graphitic carbon inclusions. The efficient field enhancement from these nanodiamond films has been attributed to both morphological effects and grain boundary electrical conductivity. In this paper we review basic theoretical approaches, our computer simulations and recent experimental studies of the electron emission from nanocarbon materials.

Keywords: Field Electron Emission, Graphite, Diamond, Nanocarbon, Laser, Light Source. CONTENTS 1. 2. 3. 4. 5.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Characteristics of Multi-Emitter Cold Cathode . . . . . . . . Graphitic Materials for Field Emission . . . . . . . . . . . . . . . . . . . Laser Assisted Electron Emission . . . . . . . . . . . . . . . . . . . . . . . Nanographite Cold Cathodes Application for Light Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 5 7 10 12 12 12

1. INTRODUCTION Field electron emission (FE) phenomenon has been a matter of considerable interest for purely academic and applied science since it was discovered in 1897.1 In contrast to other electron emission mechanisms (thermionic or photo emission) the field emission doesn’t need any power supply. Owing to this reason the field emission is frequently referred to as “cold” and corresponding electron ∗

Author to whom correspondence should be addressed.

J. Nanoelectron. Optoelectron. 2009, Vol. 4, No. 2

emitters as “cold cathodes.” The FE is registered only at large electric field strength requiring an extremely high voltage to be applied between the flat cathode and anode. To reduce the voltage down to the values, which are practically suitable for vacuum electronic devices and for research purposes, the creation of emitters in form of needles with high aspect ratio is required. One of the most attractive features of the FE is its potential ability to provide the electron emission with very high current density. However, emitting surface area of a single emitter with high aspect ratio is usually quite small. Thus, to obtain electron beams with reasonable value of total current, the FE cathodes must contain arrays of numerous emitters. The abilities to produce such kind of micron-sized FE cathodes were demonstrated previously using Si and some other semiconductors and hard metals (see e.g., Ref. [2]). However conventional lithographic technique of fabrication of such FE cathodes is complicated and expensive hampering wide application of the cold cathodes made of these materials. Since 1990s the interest to the FE has been triggered by the discovery of carbon nanotubes (CNT)3 and other 1555-130X/2009/4/001/013

doi:10.1166/jno.2009.1023

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Cold and Laser Stimulated Electron Emission from Nanocarbons

Obraztsov and Kleshch

types of nanocarbons. Having graphitic type atomic structure these nanostructured materials possess advantageous properties for efficient field emission: strong interatomic bonds and corresponding chemical inertness and robustness to ion bombardment; high conductivity and electron mobility, providing low resistive heating and voltage drop across emitter body; and high aspect ratios of the individual nanostructures, allowing usage of moderate voltages. Besides, the nanocarbon multi-emitter FE cathodes with large surface area can be produced by reasonably simple methods compatible with vacuum electronic technology.4 This attracts great attention to various potential applications of the FE cathodes. However, there are still a lot of questions concerning basic principles of field emission from nanocarbons. In particularly, despite unambiguous demonstration that the FE from diamond and nanodiamond is controlled by non-diamond graphite-like carbon impurities,5 there is no penetrative understanding of the influence of diamond-like components on the emission from CNT and other nanographite carbons.6 7 In this paper we analyze basic principles and peculiarities of the FE from nanocarbons and review our recent results in this scope. In particularly, we present here the experimental results for the field and laser assisted electron emission from nanocarbon cathodes and propose corresponding empirical models of observed phenomena.

such a field strength the potential barrier between metal and vacuum is reduced down to several nanometers and electrons can tunnel through it into vacuum. For the flat metal surface at 0 K the current density is given by the Fowler-Nordheim (FN) equation: A 2 3/2 −1/2 (1)

exp −B jF N E = E exp C E

2. BASIC CHARACTERISTICS OF MULTI-EMITTER COLD CATHODE Field electron emission occurs when an electric field applied to the conducting surface exceeds 1 V/Å.1 8 With

where E—the electric field applied to the surface; —the work function of the metal; A = 15414×10−6 A ·eV·V−2 ; B = 64894 × 107 eV3/2 · V · cm−1 ; C = 101 eV1/2 . Due quantum nature, the field emission process is a spontaneous process requiring essentially no energy supply and can provide extremely high current densities at narrow enough potential barriers. The highest value of the FE current, achievable for an ideal metal, can be estimated as a current for the potential barrier with transparency equal to 1:8 jmax = meh−3 EF2 ≈ 1011 A/cm2 (2) where m, e—the electron mass and charge; EF —the Fermi energy of metal. For the estimation we used the most common value for metals of EF = 5 eV. The least current density from flat surface may be associated with the emission of a single electron e in a time unit t. The single electron emission occurs in some point on the emitter surface (or in some area if quantum nature of electron is taken into account). The emission current I = e/t is produced by voltage drop near the emitting point. This voltage drop lowers the external local field E. The reduction of the field strength down to threshold value will diminish the probability of emission in some area

Alexander N. Obraztsov obtained his degrees (M.Sc. – 1981, Ph.D. – 1986, D.Sc. – 2002) from the Moscow State University (Moscow, Russia). Since 2002, he is a full professor at Physics Department of MSU. Since 2006 he is also working at the University of Joensuu (Joensuu, Finland) as a Professor and a Director of Research. His main current interests are research and developments in the fields related to carbon and, especially, to nano-carbon materials. These include elaboration of chemical vapor deposition methods for production of carbon materials, characterization of structural and physical properties of different carbons and development of principles of their application in electronics and optics.

Victor Kleshch was born in Tambov, Russia in 1984. Since 2004 he worked at Physics Department of Moscow State University on field emission properties of nanographite films. He has received his diploma in physics in 2007 under supervision of Professor A. N. Obraztsov. Currently, he is doing his Ph.D. in A. M. Prokhorov General Physics Institute of Russian Academy of Science. He works on experimental and theoretical investigation of field emission from various nanostructured materials.

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around the point where the first electron escaped into vacuum. The size of this “dead” area can be estimated by the square of the Debye screening length, which is about d = 1 Å for metals. So the minimum current density for homogeneous surface is given by:

variation the real metal surface always has topology irregularities, structural defects or impurities. The natural surface defects are usually unstable and thus the field emission from flat surfaces exhibits unstable behavior. The FE stabilization may be achieved by special surface treatment or by creating special topology on the cathode surface to localize emission sites in predefined areas. Immediately to this the topology features allows reduction of the applied voltage due to geometrical enhancement of electric field on tip- or edge-like structures. The geometrical effect is characterized usually by a field enhancement factor which for a single emitter is approximately equal to ≈ h/r for cylindrically shaped tip-like (needle) emitter, were h and r—height and radius of the cylinder. As it was mentioned above, usually the cold cathodes contain numerous emitters to increase total emission current. However, the decrease in the distance between the emitters reduces the field enhancement factor due to the electrostatic screening effect. Therefore the FE current from each emitter decreases also. To estimate an optimal emitter density (corresponding to the maximum value of the total current) it is useful to consider an idealized case of a regular array of the emitters on a flat substrate separated by a distance L. To exemplify how the shape of the emitter influences the current density two types of emitters may be considered. The first is tip-like (needle shaped) emitter which may be represented by a cylinder with radius r and height h. The second is edge-like emitter shaped as a parallelepiped with height h, width 2r and infinite length. The electrostatic calculations for these emitter arrays have been performed by finite element method.10 The values of the parameters have been chosen similar to those for real nanostructures r = 1 nm, h = 1 m. The calculations have shown that starts to decrease as the distance between emitters L reaches several values of h Maximum values of (L are about 500 and 50 for the needles and the edges correspondingly. The whole current density can be expressed as:

jmin =

e ≈ 10−3 A/cm2 td 2

(3)

For the estimation we used a time unit t = 1 s. From the FN Eq. (1) field intensity E corresponding to jmin and jmax can be eliminated by solving the FN equation for E. The solution can be expressed as: Ej = C1 j 1/2 expW C3 j −1/2 expC2 −1/2 − C2 −1/2 (4)

where W x—is the Lambert function which is defined as the inverse function to f x = xex ; C1 = A−05 ; C2 = 05C; C3 = 05 BA05 . For practical estimations it is useful to derive an asymptotic analytical formula for E. For this purpose the FN Eq. (1) can be rewritten as j = exp −B 3/2 E −1 + lnE 2 + lnA + C −1/2 − ln )]. The estimations of each term under the exponent disclose the first term to be by an order of magnitude greater than other terms at fields up to 2 V/nm and for the work function ranging from 1 to 10. Neglecting other terms an asymptotic formula for j can be rewritten as: ja = j0 exp−B 3/2 E −1

(5)

where j0 is a constant which value can be derived from the comparison to the FN formula (1). Upon solving this equation an analytical asymptotic formula for E may be expressed as: −B 3/2 (6) Ea = lnj/j0 For a value of j0 = 35 × 1010 A/cm2 the accuracy of this formula is better than 10% for the given range of parameters. Using this formula the field strength values corresponding to jmax and jmin are Emax = 25 × 104 V/m and Emin = 024 × 104 V/m. Accordingly to these estimations the range of electric field strength suitable for observation of the FE from ideal metal surface spans rather short range (about one order) of magnitudes. Observations made for real surfaces show that the FE does never occur homogeneously but always from discrete emission sites. The emission sites location is determined by variations of surface topology and electronic properties. The main characteristic of the surface electronic properties is work function which is a parameter in the FN Eq. (1). The experiments with metallic emitters reveal that the work function value can vary depending on the crystal face by approximately 10%.9 Thus usual polycrystalline metal surface must contain emission sites corresponding to certain crystal faces. Additionally to the work function J. Nanoelectron. Optoelectron. 4, 1–13, 2009

J E L = jF N L × E sn

(7)

where E—the external field, L × E—the local field on the emitter apex, s—the area of emitting surface. The optimal distance L, corresponding to maximum current density, can be determined from the equation $J E L/$L = 0. The dependence of J L at fixed value of E is shown on Figure 1 for the emitters with tip and edge configurations. The dependencies of the optimal distances Lmax and corresponding maximal current density values Jmax versus E are presented on Figure 2. The optimal distance between emitters is about 2h for the cylindrical (needle) emitters and 5h for the rectangular (edge) emitters. The FE cathodes are generally characterized by a value of threshold electric field Ethr , corresponding to a minimal (threshold) emission current density Jthr . Definition of the threshold current level depends on the experimental conditions and/or application of the cathode and 3

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Fig. 1. Dependence of the current density J for the emitters array versus interemitter distance L at fixed values of E for needle and edge like emitters.

can be varied widely in a range of 10−6 10−9 A/cm2 . For example, Figure 2 shows that for the conditions used in our models and for a current value of 10−9 A/cm2 the threshold field Ethr is about 5 V/m and 50 V/m for the tip- and edge-like emitters, correspondingly. The threshold fields of about Ethr ∼ 1 V/m for current densities in a range of 10−6 10−9 A/cm2 are achievable with the field


enhancement factors of about 1000. This value is practically available for many real nanostructures with different shapes. It is important to note that the minimal value of current density (Jthr depends on intrinsic experimental conditions and usually is limited by noise or leakage in the current measuring facility. Thus obtained the total current magnitude is the sum of the noise current and the FN cathode current: IV = IF N V + Inoise V . The current–voltage (I–V ) characteristics were computed assuming normal statistical distribution of the noise current for the cathode parameters stated above (see Fig. 3). The FN plot of the I–V dependence (Fig. 3) contains a linear part, representing an area with the FE current values exceeding noise level, and a tail, corresponding to the noise current. The dashed line in Figure 3 shows the maximum magnitude of the noise current. This analysis provides a practical criteria for choosing the minimal current (Jthr and the threshold field (Ethr in the experimental studies—these values may be chosen from the I–V FN curves to correspond (or exceed) the intersection of the noise level (dashed line in Fig. 3) and the linear part (solid line in Fig. 3). Taking into account potentially high current density for each individual emitter it may be instructive also to estimate possible values of total current for the multiemitter cold cathode. With the optimal distance between the emitters L = 2h (for the emitters with the needle shapes) the whole current density is given by (7) with n = L−2 = 2h−2 . The emitting surface can be estimated to be of the order of s ≈ r 2 . Substituting these expressions to (7) the maximum current density can be expressed as: Jmax = jmax s

1 1 j ≈ jmax r 2 ≈ max 2 2 L 2h 2

(8)

where jmax is the maximum local current density of the individual emitter. Following (2) the theoretical maximum for the FE current density jmax is about 1011 A/cm2 . Assuming that field enhancement is in the range of

Fig. 2. Dependence of the optimal distance Lmax and corresponding maximal current density Jmax versus electric field E for needle and edge like emitters.

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Fig. 3. Current–voltage characteristic of cold cathode model with an addition of current noise.




100 < < 1000, the maximum current density for the array of the needle emitters should be in the range of 105 A/cm2 < Jmax < 107 A/cm2 . However, the experiments with the isolated emitters reveal the highest local current densities of about jmax = 107 –108 A/cm2 .8 9 Moreover in the case of the multiemitter arrays the usual stable values of the order of magnitude of the local current jmax do not exceed 105 A/cm2 . Therefore the maximum stable total current density for the array of emitters may be found in a range of 0.1 A/cm2 < Jmax < 10 A/cm2 .

3. GRAPHITIC MATERIALS FOR FIELD EMISSION


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The estimations of the previous section were made without any reference to the emitter material properties. However very strong values of electric field used for observation of the FE and very high local current densities suppose that the suitable materials for the cold cathodes must be electrically well-conductive, highly refractory and mechanically strong. The typical examples of the materials used for FE cathode production are the refractory metals (e.g., W, Mo, Ta, Re), their compounds and semiconductors (Si, GaAs).9 11 From this point of view, one of the most ideal materials for this purpose is graphite in its different forms. The graphitic materials consist of hexagonal carbon lattice with very strong '–' atomic bonding energy (('−' ≈ 7 eV per one atom).12 The field strength, corresponding to this energy, can be estimated as ('−' /ed, where e is the electron charge and d =0.14 nm is the interatomic distance in the hexagonal graphite lattice. The obtained field value E'−' = 5 × 104 V/m is higher than the field strength Emax = 25 × 104 V/m estimated above for the maximum current density jmax , and thus materials with essentially graphitic lattice would easily stand mechanical stress induced during field emission. Despite this strong interatomic bonding usual graphite is not applicable for the FE due to its layered structure with very weak interlayer bonding energy about ( = 004 eV 12 per atom. With the interlayer distance d = 0.34 nm the field strength, corresponding to these weak bonds, is about 0012 × 104 V/m, which is less than Emin = 024 × 104 V/m estimated above as the field strength producing the minimum current density jmin . It means that the stack of atomic layers of graphite can be destroyed easily by the electric field before the field emission starts. This weakness of the graphitic materials displayed in the FE experiments may be eliminated by providing additional interlinking between adjacent graphitic atomic layers. For example, such linking is realized in carbon nanotubes (CNT) due to their cylindrical configuration demonstrating stable field emission.13 Other advantages of the CNT emitters are their high aspect ratios providing large value of the field enhancement factor and relatively simple and inexpensive production technology providing the multiemitter

Fig. 4. (a) Scanning electron microscopy (SEM) image of a nanographite film surface. (b) SEM image of nanographite film cross-sectional chip. (c) Transmission electron microscopy image of an individual graphite nanocrystallite.

arrays.14 Similar FE properties may be expected from other forms of nanocarbon materials consisting of curved atomic layers of graphite.15–17 An example of such nanographite materials is presented in Figure 4 by electron microscopy images. The material of this type is obtained by chemical vapor deposition (CVD) from a mixture of hydrogen and methane activated by direct current discharge18 and consists of graphite crystallites of nanometer thickness having predominant orientation of the atomic layers perpendicular to substrate surface. The typical thickness of the crystallites is about 5 nm, while their length and height is of the order of 1 m. The distinctive feature of the crystallites is bending of the graphite atomic layers on crystallite edges. This bending is inambiguously seen in high resolution transmission electron microscopy images (see Fig. 4(C)) and provides additional linking in between the atomic layers. A typical current voltage 5


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Fig. 5.

Typical current voltage characteristic of a nanographite cathode.

characteristic obtained for the CVD nanographite film is shown on Figure 5. The threshold field corresponding to the current density 1 nA/cm2 equals to 1.5 V/m. Current density value of 10 A/cm2 is reached at 2.4 V/m. These parameters are close to the FE characteristics obtained for other carbon cold cathodes. The shape of the graphite crystallites is intermediate between the discussed above types of needle- and edgelike emitters. To calculate field enhancement for this type of structure electrostatic calculations was performed.10 The emitter was represented as a rectangular parallelepiped with a thickness of d = 2r, length l and height h. The corners of the emitter were rounded in order to obtain finite values of . The calculations show that for such confined plates the enhancement factor equals to ≈ 025 h/r at the corners. This value is much higher than that for infinite edge like emitters ≈ 005 h/r and close to the value ≈ 05 h/r, corresponding to needle-like emitters. The emitting area is also similar for the cylindrical and edge configurations providing practically the same emission current densities if the other conditions during the FE observation are the same. At the same time, the density of current inside the emitting structures is determined by its cross section and specific conductivities. The specific conductivity may be assumed to be the same for different nanographite structures. But difference of their geometrical shapes leads to difference in the cross section values Sc . For the discussed case of cylindrical needles and rectangular edges this difference is of the order of L/r ≈ 1000. It means that at the same emission current density the current density inside the edge-like emitting structures should be smaller in comparison with the needles by a factor of 1000. Similar conclusion may be made for the contact resistance in between the graphite material and substrate. The significant reduction of the electrical resistance should increase stability of the edge-like emitters due to reduction of the Joule heating in their body and in their back contacts. This simple modeling of the nanographite emitters shows that 6


Fig. 6. Typical current voltage characteristic of a nanographite cathode in FN coordinates (circles). I–V curve is divided into three field strength regions: (1) low field region with bend of I–V curve (2) moderate field region with linear behavior (3) high field region with current saturation. Solid line is an approximation using Eq. (11).

the presence of sharp corners on the periphery of platelike crystallites can provide better conditions for the FE in comparison with needle carbon nanotubes. This conclusion is perfectly confirmed by our experimental observations.6 7 Figure 6 shows other important features of the current– voltage characteristic of a nanographite film: (i) at a moderate field values the I–V curve follows the linear dependence predicted by the FN theory; (ii) at low fields there is a bend in the I–V dependence; this bend is absent in the above ideal model of the cathode (see Fig. 3); (iii) at high fields the saturation of the FE current is usually observed. The nonlinear behavior of the FE current at low voltages may be explained by difference of geometrical parameters.19 The emission current at the lowest field originates from the emitters with the highest enhancement factor . Gradual field increase results in rising the emission current from the individual emitters and accompanied by increase in the number of the emitters contributing to the total current. For the simplicity variations of may be assigned to variations of curvature radius r (this simplification does not affect on the general conclusions). The distribution of r may be considered as normal: nr = √

N 2' 2

exp −r − r0 2 /2' 2

(9)

where r0 —the average of distribution, '—the mean-square deviation and n—the whole number of emitters per square unit. Assuming that the square area of each emission site J. Nanoelectron. Optoelectron. 4, 1–13, 2009



is s = 2r 2 and that there is no screening between the emitters the total current from the multi-emitter cathode can be written as:

the emitters into vacuum. The outer barrier is similar to that presented in classical FN theory and can be considered by as a triangular one. The inner barrier, in a simplest approximation, can be described by a rectangular shape. The height of the rectangular inner barrier - should be smaller than the work function of the graphite and can be assumed to be equal to - ≈ 4 eV. The thickness w of the interface region between the sp2 and sp3 parts should be of the order of magnite of the interatomic distance in graphite i.e., w ≈ 4 Å. Taking into account this double barrier model we calculated the probability of electron tunneling from the emitter to vacuum. An essential increase of the tunneling probability is possible only when the specific electron states are in the potential well between the barriers with the energy close to Fermi level. For this resonant tunneling the transmission coefficient and the corresponding FE current density can be obtained by analytical calculations (see Ref. [20] for details):

I=

J dS =

rmax

2J rr 2 nr dr

(10)

r min

Substituting of J r with the FN formula (1) the final formula can be written as: 2 2 D ' D (11) I = CnF 2 exp − r0 + F 2 F


jE =

−2 e3 1/2 w −√ 8h eE √ 4 2m 2 3/2 √ × exp − − -w (12) h 3eE

This formula differs from the usual FN expression (1) by the presence of an additional term under the exponent −- 1/2 w. This term leads to the increase of the emission current in comparison with the FN formula by four orders of magnitude. But this increase is possible only if there are the electron states in the quantum well with energies equal to Fermi level in the graphitic part of the emitter. The density of states corresponding to the resonant energy levels should be much less than that inside the emitter. Upon increase of the electric field these resonant levels are populated and the current density will saturate. In high electric field range the resonant energy levels may be shifted down due to field penetration resulting in detuning of the resonance and leading to the current saturation and decrease. This behavior is expected for the emitters independently of their geometrical characteristics and thus FE current deviation from the linear dependence for the multiemitter nanographite cathode (region 3 in Fig. 6) can be explained by this saturation mechanism. The linear part of the I–V curve (region 2 in Fig. 6) corresponds to the experimental conditions when emission from the main part of the emitters follows the formula (12).

4. LASER ASSISTED ELECTRON EMISSION The experimental study of laser assisted electron emission from the nanographite cathodes21–23 were performed to obtain electron beams with current densities overcoming the limitations mentioned above for the multiemitter FE cathodes. The other goal of these experiments was independent evaluation of local values of work function 7

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where F = r/LE is a macroscopically averaged √ electric field, C = 2AL2 −1 exp 101/ and D = 095B 3/2 L−1 . The formula (11) for I–V dependence differs from classical expression deduced from the FN theory8 9 by the second term in the exponent. This term is responsible for nonlinear behavior of the experimental I–V curves at low fields whereas it can be neglected at high fields. An approximation of the experimental curve with expression (11) (see Fig. 6) gives the following relationship for the mean-square deviation: ' ≈ 01r0 . The values of r0 = 5–10 nm obtained from electron microscopy correspond to ' ≈ 5–10 Å, i.e., the difference in the size of the nanocrystallites is about several graphene layers. The approximation expressed by the expression (11) gives the following relation of work function and enhancement factor: 3/2 −1 = 74 × 10−3 eV. Using the formula for the field enhancement = 025 h/r obtained above and the values of the characteristic geometrical parameters h = 1–5 m and r = 5–10 nm, is estimated to be in a range of 25 to 250. The corresponding value of work function is < 15 eV which is much smaller than that typical for graphite materials—4–5 eV. Other contradiction follows from the formula (11) for evaluation of density of the emitter’s n. The best fitting of the experimental I–V dependence by formula (11) is reached at n of an order of 1013 cm−2 . This value corresponds to inter-emitter distance of about 3 nm, which is less than the emitter thickness and, thus, practically impossible. Summarizing the previous analysis one may conclude that the obtained values of and n are in contradiction to the initial cathode model and to the experimental observations. These contradictions can be settled by an assumption of a specific mechanism of the low field emission which can provide essential rise of the current density comparing to the FN equation.20 The proposed mechanism supposes that diamond-like clusters situated on the top edge of graphite-like nanocrystallites. Such clusters with sp3 type of structure can be formed due to bending of the graphene sheets.20 Existence of the bended atomic layers is evident from the HRTEM images (Fig. 4(c)). The combination of conductive sp2 graphitic material and dielectric sp3 diamond-like atomic chains on the bended part creates double potential barriers for electrons escaping from


and field enhancement factor for the nanographite emitters. Since graphitic materials exhibit zero-gap semimetal behavior, the main effect caused by laser irradiation was expected to be of a thermionic nature, i.e., material heating due to absorption of laser radiation. In this case electron emission should follow the Richardson-Dushman (RD) theory of thermionic emission.24 The most important difference between FN and RD mechanisms of the electron emission is that field emission is a spontaneous process that can take place even at T = 0 K, while thermionic emission can takes place at high temperature when a considerable number of electrons that are able to overcome the potential barrier at the metal–vacuum interface and leave the metal surface exists. The current density of the thermionic emission process is expressed in the relation:

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J T = AT 2 e /kB T

(13)

where the emission current density J [A/cm2 is described in terms of the work function [eV], the Richardson constant A [A/cm2 K 2 , the temperature T [K] and the Boltzmann constant kB . The emission current is then determined by two parameters, the work function, , as the barrier for emission and Richardson’s constant, A as a parameter of the emission current density for a given material. A theoretical derivation of A has shown its value to be fundamentally described by A=

emkB2 2 2 3

(14)

Moreover, a surface morphological contribution to the value of A results in a variation from its theoretical value of 123 A/cm2 K2 . To account for the standard barrier lowering field dependent effects in thermionic emission, the RD equation can√also be modified by adding the field dependent term, e3 E, in the exponent which effectively results in a reduction of the work function, i.e., the effective work function of the emitter. For a nanostructured surface the applied field is again modified to E = F . This relation is also referred to as the Schottky formula: J F T = AT 2 e−

−

√

e3 F kB T

(15)

where F represents the macroscopically averaged field. The pulsed laser radiation was used in the experiments with the duration of the pulses in nanosecond and femtosecond ranges. Figure 7 presents an experimental result on visualization of the emission site distribution for the electron emission stimulated by nanosecond laser irradiation. This experiment was carried out using a cylindrical diode configuration with the cathode made as Ni 1 mm wire covered by the nanographite film material and with anode containing a layer of phosphor material glowing under the action of electrons (see description of similar configuration below). This experimental set-up allows characterization of emission sites distribution over 8


Fig. 7. Images of the emission site distribution taken for the cylindrical diode vacuum lamp in case of field emission (A) and thermionic laser assisted (B) regimes.

the cathode surface and, as it follows from images in Figure 7, this distribution is dramatically different for field and thermionic emissions. While the images obtained for the FE at near threshold field strength (Fig. 7(A)) demonstrates separate spots corresponding to the emission sites with the highest field enhancement, the thermionic laser assisted emission produces single homogeneously glowing spot (Fig. 7(B)) corresponding to the size of laser beam irradiated cathode surface. In particularly this observation allows us to conclude that the field and thermionic emissions arise from different emission sites and the emitter parameters (work function, field enhancement) evaluated from the thermionic laser assisted experiments are not valid for the FE description. The temporal profile of the electron emission pulse was found to vary depending on the applied voltage and the laser intensity. However, in our experimental conditions, its duration is comparable with that of the incident laser pulse (for the case of 10 ns laser pulses) when the applied electric field is above 0.06 V/m. At a low electric field, the magnitude of the emission current is proportional to the applied electric field. However, this dependence shows signs of saturation at electric fields above 0.5 V/m (see Fig. 8(A)). When the irradiated area of the cathode is 0.07 cm2 , the magnitude of the emission pulse measured at a laser intensity of 36 MW/cm2 and F = 1 V/m is as high as 0.35 A. By further focusing the laser beam we achieve a current density of 10 A/cm2 at an intensity of laser radiation of 50 MW/cm2 . The electron emission is essentially a nonlinear function of the light intensity. It grows exponentially as soon as the intensity of the incident pulse exceeds the threshold value, which depends on the applied electric field (see Fig. 8(B)). The experiments with femtosecond laser pulses showed very different behavior of the electron emission.22 23 The dependence of the emitted electric charge on the laser power is presented in Figure 9. One can observe that in J. Nanoelectron. Optoelectron. 4, 1–13, 2009


the femtosecond regime there is a threshold energy of the laser pulse of W = 04 mJ, which corresponds to an intensity of 3 × 104 MW/cm2 . The number of the electrons emitted per photon in the nano- and femtosecond

Fig. 9. Dependencies of electron emission, measured as total emitted charge versus laser pulse energy using a 60 fs laser radiation at wavelength of 800 nm.


regimes is of the same order (2 × 10−8 and 15 × 10−7 , respectively). However, the obtained results indicate that in the femtosecond regime, the emission is not described by the RD equation. This is probably because hot electrons can not be described in terms of the Sommerfeld theory of metals. Since the specific heat of the electron sub-system is much smaller than that of phonons, the characteristic relaxation time for the electron temperature (1e is much shorter than the corresponding time for phonons (1ph . In an order of magnitude, they are usually ∼1 ps and ∼100 ps, respectively.25 Therefore, when electrons are excited by femtosecond laser pulses, they behave as if they are thermally isolated from the lattice. The electron temperature grows very steeply until the energy flux from electrons to phonons equals the absorbed power. During a time of ∼1ph , the phonon temperature increases with the electron temperature. If we assume that the duration of the electron emission pulse is comparable with that of the excitation laser pulse, the obtained amplitude of the emission current in the femtosecond regime is as high as 5×103 A/cm2 . This makes the laser-assisted electron emission to be a prospective method for the generation of dense electron bunches. The obtained results are summarized in the diagram shown in Figure 10 where electron emission current densities obtained in different regimes are indicated. The maximum emission current density obtained for the nanographite material in the field emission regime with the use of 10 s voltage pulses is about 1 A/cm2 . For the laser assisted emission the current density values are about 10 A/cm2 for nanosecond laser pulses and 1000 A/cm2 for femtosecond laser pulses.

Fig. 10. The densities of the electron emission current achievable for the FE regime with pulsed voltage (the lowest point) and for the laser assisted emission with the nanosecond laser heating (the middle point), and with the femtosecond laser excitation of hot electrons (the uppers point).

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Fig. 8. The electron emission dependencies measured for the nanographite cathode under 10 ns pulsed laser irradiation with wavelength of 1600 nm.



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5. NANOGRAPHITE COLD CATHODES APPLICATION FOR LIGHT GENERATION One of the most attractive applications of the cold cathodes is generation of light. Artificial lighting is critically important for every day life because only sunshine and moonshine provide us more or less appropriate natural lighting. This is why artificial light sources are exploited even when their power efficiency is extremely low. For example only small part of total consumed energy is transferred into light by the sources based on thermoluminescence process. In such sources as open fire, candelas and usual incandesced lamps light is produced by a body heated up to a high temperature. Glow of discharges in different gases allows transformation of electricity into light with higher power efficiency but the obtained light spectrum contains discrete narrow lines upon low gas pressure. This type of lighting is appropriate only for some special purposes. It is possible to improve spectral characteristics of gas-discharge light source by increasing gas pressure but in this case ignition and support of discharge requires extreme power concentration and corresponding high current and voltage. This circumstance limits applicability of such light sources. Improvement of the spectral characteristics of the low pressure gas discharge lamps is possible via exploitation of photoluminescence (PL) effect occurring in the suitable materials under excitation by high energy (ultraviolet) photons. The highest efficiency of such kind of PL lamps is achievable using mercury vapor as the gas-discharge media. In comparison with other gases (xenon, vaporized zinc etc.) application of mercury provides the highest efficiency of energy transformation from electricity into light. This is why such kind of mercury based lamps is referred to as “energy saving” or “economic.” But total energy efficiency of the PL lamps is still about 10%. That is about 90% of consumed energy is transformed into heat. Moreover mercury is recognized as extremely toxic material creating enormous ecological problem due to huge number of lamps to be utilized after exploitation. It is believed nowadays that essential improving of light production efficiency may be obtained with the use of solid sate or organic light emission diodes (LED, OLED). However, efficiency and life time of OLEDs is reduced with the increase of energy of the irradiating photons that significantly limits their applicability. In fact only LEDs which are based on materials providing ultraviolet (UV) or blue light emission (GaN, SiC) may be considered now for production of light sources for general purposes. The UV emission produced in the LEDs is transformed then into white light by using PL materials similar to those in mercury gas-discharge lamps. The power efficiency of such kind of white LED lamps is currently close to that for mercury based luminescent lamps but LEDs manufacturing is much more costly. The manufacturing costs may be reduced with mass production but in such a case new ecological problems are very probable because of toxicity 10


of used materials (Ga, In, As, Te, Cd) and environment pollution by waste products of the LED fabrication technological process. An alternative way for light generation is cathodeluminescence (CL) where kinetic energy of electrons is transformed into light via excitation and consequent glowing of the CL phosphor materials. In the CL process light generation results from electron–hole recombination in the light-emitting centers which are excited by “secondary” electrons. These electrons are created by multiplication of energetic electrons generated in collision of primary electron beam with the phosphor material. The energy efficiency of the CL process (i.e., efficiency of energy transformation from primary electron beam to light) is estimated theoretically to be up to 35%.26 Taking into account that electrons may be produced by the FE cold cathodes without any power consumption (see above) it creates possibility for the development of the highly efficient CL light sources, including flat panel displays4 13 and lamps for general lighting.27 28 However real characteristics of the most common phosphors are very different from the theoretical estimations made for an ideal case. The power efficiency of these phosphors is much lower and furthermore to reach the maximum efficiency of the CL the primary electrons must be accelerated up to energy of about 10 keV. These phosphors were developed for application in the cathode ray tubes (CRT). To provide the best results for lighting the properties of the phosphors must be optimized (or new phosphors must be developed) taking into account the ability of the FE cathodes to produce electron beams of high current density by applying rather low voltages. Nevertheless these CRT’s phosphors are suitable to demonstrate potential ability of the lighting devices based on the nanographite cold cathodes. Figure 11 shows the photographs of the sealed vacuum lamps containing the FE cathode. The lamps are made of a glass tube with the outer diameter of about 25 mm and with the electrodes welded into the glass of tube flat end. The opposite side of the tube is ended by another flat glass plate with a conductive indium-teen-oxide (ITO) layer covered by a phosphor on its inner side. The cold cathode made of CVD nanographite film is fixed on the electrodes at the bottom part of the lamp. A gate electrode is made as a flat metallic mesh fixed using other electrodes

Fig. 11. The photographs of the CL triode lamps made using red, green and blue CRT phosphors.



in between the cathode and anode. The anode is connected with one of the electrodes in the bottom part by a metallic wire electrically connected with the ITO layer. The lamp is pumped out through the exhaust tube in the bottom part. A gas absorber (getter) is used to provide appropriate vacuum inside the lamp after sealing. With a distance between the cathode surface and the mesh of about 200 m electrons may be obtained by applying cathode-to-gate voltage (Vg of about 200–250 V. To provide the optimal conditions for the phosphor luminescence the voltage applied in between the gate and the anode (Va is about 10 kV. The photographs shown in Figure 11 are taken for the CL lamps operating on a pulsed gate voltage with a magnitude of 500 V and a direct current (DC) voltage Va = 10 kV. This allows selection of appropriate average total current on the level excluding excessive heating and evaporation of the phosphor with typical values of the pulse duration of about 10 to 20 s and the pulse repetition rate of about 1 kHz. There are few drawbacks of this triode lamp design. One of the most important is waste of significant amount of light which is generated in the phosphor layer but its direction is opposite to the output window of the vacuum the lamp housing. Additionally to that the highest intensity of light is generated on the inner size of the phosphor layer. The part of light directed out of the lamp is scattered and partially absorbed into the phosphor layer. All together this leads to a reduction of the power efficiency. Some improvement may be obtained with the use of a thin alumina layer deposited on the inner side of the phosphor. The alumina will reflect light in the proper direction. The lamps of this type are shown in Figure 12. The electrons accelerated up to 10 keV are able to penetrate trough the alumina with a thickness of a few micrometer. However some part of energy of electrons is wasted in the alumina producing heat and reducing power efficiency.

Other disadvantage of the triode CL lamps is small divergence of the electron trajectories for flat cathode and gate mesh. As a result the size of the glowing area on the anode surface is practically the same as the size of the cathode emitting area. Thus to produce more light using the triode CL lamps the increase of the size of the cathode and the lamp housing is necessary. This is not acceptable in many cases. The problem may be solved by the application of a diode lamp design that provides larger divergence of the electron beam. An example of such lamp is shown in Figure 13. In this lamp the cathode is made as 1 mm nickel wire with the CVD nanographite film deposited on its end located in the center of the anode having semi-spherical shape of about 8 mm diameter. This configuration of the electrodes provides appropriate value of the electric field on the cathode surface for high voltage between the cathode and anode. Also the increase of the glowing spot size on the anode surface occurs due to scattering of the emitted electrons.29 Significant improvement of the total power efficiency and increase of the light amount is achievable with a cylindrical diode configuration of the CL lamp described in details elsewhere.30 Figure 14 shows the photographs of the CL lamps of cylindrical diode type. In these lamps the cold cathodes are made as a cylindrical Ni wire of about 1 mm in diameter with the CVD nanographite film on its side surface. The wire is situated along an axis of a cylindrical tube (the photo on top of Fig. 14) or semi-cylindrical segments (the on bottom of Fig. 14). Similar to that for the semi-spherical anode lamp (Fig. 13) the nonplanar electrode configuration in the cylindrical diode lamps provides appropriate electric field strength with application of the voltage of about 10 kV which is optimal for the CL phosphor glowing. Additional improvement of these cylindrical lamps consists in the usage of an alumina layer deposited onto inner surface of the glass tube as the anode.

Fig. 12. The triode CL lamps made with alumina layer covering inner surface of the phosphor layer.

Fig. 13. The photograph of the diode CL lamp with the tip shaped cathode and semi-spherical anode.


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Fig. 14. The photographs of the cylindrical diode lamps with single emitting element (top) and with three emitting elements joined in one vacuum housing: side view without light emission (bottom left) and front view in working regime (bottom right).

The phosphor layer is deposited onto the alumina anode. The alumina anode layer covers one half of the tube and another half is transparent. This configuration provides the most optimal conditions for phosphor excitation, elimination of any lose of the electron beam energy and light outcome. An additional effect is provided by mirror light reflection from the alumina anode layer. As a result such type of the CL lamps demonstrates record parameters with the standard CRT phosphors. For example light brightness up to 2 × 105 cd/m2 and total power efficiency more than 10% has been achieved with the green CRT phosphor.


interface. The developed theoretical models allow adequate description of obtained experimental data. Significant increase of the current density for the electron beam produced by the nanographite cathode has been obtained with the use of laser assisted emission. The nanosecond pulsed laser radiation provide electron beams with the current density magnitude up to 10 A/cm2 and the femtosecond laser radiation is able to stimulate electron emission with the current density up to 1000 A/cm2 . While mechanism of the laser assisted electron emission with the nanosecond pulse duration may be assigned to usual thermionic emission, in the case of femtosecond laser pulses the most appropriate model supposes hot (thermionic) electron emission from cold cathode. Applicability of the nanographite FE cathodes has been demonstrated in prototypes of the cathodoluminescent light sources (lamps) of various designs. Optimization of the lamp design in accordance with the parameters of nanographite FE cathodes and existing CRT phosphor has been realized in the cylindrical diode lamps. These lamps have shown record characteristics in brightness (up to 2 × 105 cd/m2 and power efficiency (more than 10%). Further improving of the lamps characteristics is expected with developing of new phosphor materials. Acknowledgments: It is a pleasure to thank Drs. A. P. Volkov and A. A. Zakhidov for their collaboration in synthesis and field emission characterization of the nanographite cathodes, Professor Yu. P. Svirko and Dr. D. A. Lyashenko for their contributions into laser-assisted emission investigations, and Drs. Yu. V. Petrushenko and N. P. Abanshin for manufacturing of the CL lamps. This work was partially supported by grants of Academy of Finland (projects 123252, 124133).

6. CONCLUSIONS The analysis performed on the base of the FowlerNordheim tradition approach has shown that the expected values of the macroscopically averaged FE current density for the multiemitter nanocarbon cold cathodes are expected in a range of 0.1 to 10 A/cm2 . These values of the FE current are achievable for the cathodes containing the needle-like emitting structures of carbon nanotubes as well as the plate-like graphite crystallites of nanometer thickness. While the threshold fields and values of the FE current density are comparable for the both types of the nanocarbon emitting structures, it is expected that the nanographite crystallites will have much more robustness to the action of strong electric field and Joule heating by the current. The experimental observations confirm these conclusions and display some anomalous behavior which may be explained taking into account statistical distribution of the geometrical parameters of the emitting structures and their structural peculiarities providing formation of the double-barrier potential on the emitter-to-vacuum 12

References and Notes 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

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Received: xx Xxxx xxxx. Accepted: xx Xxxx xxxx.