applied sciences

Article Current-Fluctuation Mechanism of Field Emitters Using Metallic Single-Walled Carbon Nanotubes with High Crystallinity

Norihiro Shimoi * ID and Kazuyuki Tohji

Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-22-795-4584

Received: 17 November 2017; Accepted: 14 December 2017; Published: 19 December 2017

Abstract: Field emitters can be used as a electrode in a cathodoluminescence device, and single-walled carbon nanotubes (SWCNTs) that are synthesized by arc discharge are expected to exhibit good field emission (FE) properties. However, a cathodoluminescence device that uses field emitters radiates rays whose intensity considerably fluctuates at a low frequency, and the radiant fluctuation is caused by FE current fluctuation. To solve this problem, is very important to obtain a stable output for field emitters in a cathodoluminescence device. The authors consider that the -emission fluctuation is caused by Fowler–Nordheim electron tunneling and that the in the Fowler–Nordheim regime pass through an inelastic potential barrier. We attempted to develop a theoretical model to analyze the power spectrum of the FE current fluctuation using metallic SWCNTs as field emitters, owing to their electrical conductivity by determining their FE properties. Field emitters that use metallic SWCNTs with high crystallinity were successfully developed to achieve a fluctuating FE current from field emitters at a low frequency by employing inelastic electron tunneling. This paper is the first report of the successful development of an inelastic-electron-tunneling model with a Wentzel–Kramers–Brillouin approximation for metallic SWCNTs based on the evaluation of FE properties.

Keywords: field emission; metallic single-walled ; high crystallinity; current fluctuation; inelastic electron tunneling; Fowler-Nordheim tunneling

1. Introduction Field emitters can be used as cathodoluminescence (CL) devices, which radiate rays with a wide range of frequencies from X-ray to far infrared rays. However, they have a serious problem in that the field emission (FE) current depends on the degree of , owing to the adhesion of contaminants such as residual gas or water on the field emitter surface [1,2]. The emitter surface needs to be clean because the FE and carbon nanotubes (CNTs) are expected to enable field emitters to realize stable emission. However, the emission current from field emitters, including CNTs, has been reported to fluctuate even in a high-vacuum atmosphere [3,4]. A CL device that uses a field emitter as a cathode electrode radiates rays that considerably fluctuate or flicker. The fluctuation or flicker from a CL device mainly has low frequencies of under 200 Hz [5–10]. On the basis of the above problems, a cathode structure that can reduce the fluctuation of emission has been studied [9,10]. However, a technique to reduce the fluctuation is not yet well established. In the case of FE, the electrons that are emitted from field emitters probabilistically and quantum-mechanically pass through a quantum barrier with a thickness of nm order before they are emitted in vacuum. This distance is estimated from the thickness of the electron-tunneling barrier when electrons cause Fowler–Nordheim tunneling [11,12]. In the case

Appl. Sci. 2017, 7, 1322; doi:10.3390/app7121322 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1322 2 of 11 of Fowler–Nordheim tunneling, electrons have been considered to inelastically pass through a barrier, and the electrons that are emitted from an FE cathode exhibit fluctuation. Therefore, we have carried out basic research to develop FE devices using single-walled CNTs (SWCNTs), and, for the first time, succeeded in employing SWCNT field emitters as the cathode of a planar lighting device with good emission stability at a high of over 10 mA/cm2 [13,14]. Since CNTs were first reported by Iijima [15], it has been shown that they exhibit one-dimensional confinement effects and can be used as coherent quantum wires [16–18]. Among the CNTs, the Young’s modulus of SWCNTs is particularly high [19]. SWCNTs have been used in a wide range of applications, including field emitters, probes in scanning microscopes [20], gas-storage materials [21], and electrode materials for secondary batteries [22], and have been studied in a wide range of applied research fields. In recent studies of applications using CNTs, the development of electrical stability as field emitters requires the fabrication of efficient CL devices, such as flat panel displays with high brightness efficiency and low power consumption [23]. We considered that an FE cathode comprising well-dispersed SWCNTs in a high-vacuum atmosphere is indispensable for decreasing the current fluctuation of field emitters and for improving the homogeneity of planar emission from a planar lighting device [13]. However, we consider that the FE fluctuation cannot be reduced to zero. In this study, to demonstrate the above consideration, the fluctuation effect on the properties of field emitters that use metallic SWCNTs with high purity and crystallinity was examined. We developed field emitters using these SWCNTs, and theoretically analyzed the fluctuation of their power spectrum in terms of their electrical conductivity by determining their electrical properties (FE properties).

2. Experimental A wet coating process was adopted to fabricate a cathode with stable FE at a low driving voltage using metallic SWCNTs (NanoIntegris Technologies Inc., Boisbriand, QC, Canada). The homogeneous dispersion of the SWCNTs in a medium is the key factor for obtaining a planer electron emission homogeneously as a field emitter. Highly crystalline metallic SWCNTs are expected to lower the threshold field and stably emit electrons at a low driving voltage. However, it is difficult to homogeneously disperse highly crystalline SWCNTs in [24]. In general, a dispersant is used to facilitate the homogeneous dispersion of nanocarbon materials in liquids. However, highly crystalline SWCNTs cannot bind to the functional groups in a dispersant because there are very few defective binding sites in their carbon network that can be used for binding to the functional groups in the dispersant. We attempted to physically separate highly crystalline SWCNT aggregates into uniform single nanotubes in a low-viscosity solvent, containing In2O3-SnO2 [tin-doped indium oxide (ITO)] precursor solution. A non-ionic dispersant was added to the solvent to facilitate the dispersion of individual SWCNTs, and the mixture was agitated using a homogenizer. To prepare the coating film, butyl acetate (99%) and ethyl cellulose (EC) (~49%, ethoxy 100 cP), which were obtained from Wako Pure Chemical Industries, Ltd., Osaka, Japan, and an ITO precursor solution (Kojundo Chemical Laboratory Co., Ltd., Sakado, Japan) were used. The initial mixture was prepared by mixing metallic SWCNTs, which were purified from solutions from NanoIntegris Technologies Inc., the ITO precursor solution, butyl acetate added as required to control the viscosity of the solution, and EC as a surfactant at a weight ratio of 1:8:600:10. Then, the mixture was agitated using the homogenizer for 30 min at room temperature. The agitated mixture was sprayed on a silicon substrate to form a film. The film was dried at approximately 420 K and sintered at 720 K in vacuum to remove any organic-solvent components. As a result, ITO films were obtained from each type SWCNT, which were used as cathode plates. In addition, to facilitate field emission, the sintered ITO film with dispersed SWCNTs was scratched to activate the film surface and obtain stable FE properties [25]. Figure1 shows (a) a schematic diagram of SWCNTs that were protruding from a scratched groove, (b) a scanning electron microscopy (SEM, SU-8000, Hitachi High-Technologies Corporation, Tokyo, Japan) overview after activating the FE for the ITO film, including metallic SWCNTs, and (c) an Appl. Sci. 2017 7 Appl. Sci. 2017, ,, 7 1322, 1322 3 of3 11 of 11

Tokyo, Japan) overview after activating the FE for the ITO film, including metallic SWCNTs, and (c) enlarged view of the protruding SWCNTs in the circled region of (b). After the film that was coated an enlarged view of the protruding SWCNTs in the circled region of (b). After the film that was withcoated the mixturewith the wasmixture sintered was sintered in vacuum, in vacuum, it was activatedit was activated by scratching by scratc usinghing using a thin a thin metal metal rod to obtainrod to the obtain FE properties the FE properties at a low turn-onat a low field.turn-on We field. observed We observed that the bundlesthat the bundles of SWCNTs of SWCNTs protruded fromprotruded both sides from of both the sides edge of of the the edge scratched of the ITOscratched film. ITO The film. exposed The SWCNTsexposed SWCNTs in the ITO in the film ITO were homogeneouslyfilm were homogeneously dispersed and dispersed were oriented and were in randomoriented directions.in randomFurthermore, directions. Furthermore, the SWCNTs the that wereSWCNTs used for that an were FE thin used film for were an FE checked thin film for highwere crystallizationchecked for high by transmissioncrystallization electron by transmission microscope (TEM)electron (HR-3000, microscope Hitachi (TEM) High-Tech. (HR-3000, Co. Hitachi Ltd., Tokyo, High-Tech. Japan) Co. measurement Ltd., Tokyo, in Japan) Figure measurement1d. Each SWCNT in inFigure a bundle 1d. ofEach Figure SWCNT1d exhibits in a bundle a clear of TEMFigure image 1d exhibits of each a tubeclear wallTEM identified image of each as straight tube wall lines. Theidentified TEM image as straight in Figure lines.1d explains The TEM that image a SWCNT in Figure has highly 1d explains crystalline that carbona SWCNT network. has highly Namely, wecrystalline can expect carbon to develop network. field emittersNamely, employingwe can expe thesect to SWCNTs, develop andfield theoretically emitters employing analyzethe these effect ofSWCNTs, the increased and crystallinitytheoretically of analyze SWCNTs the on effect their of electrical the increased conductivity crystallinity by determining of SWCNTs their on electrical their propertieselectrical (FEconductivity properties). by determining their electrical properties (FE properties).

FigureFigure 1. Tin-doped1. Tin-doped indium indium oxide oxide (ITO) (ITO) film imagesfilm images after fieldafteremission field emission (FE) activation. (FE) activation. (a) Schematic (a) diagramSchematic of the diagram scratched of the area scratched and single-walled area and sing carbonle-walled nanotubes carbon (SWCNTs)nanotubes (SWCNTs) protruding protruding from the ITO film;from (b )the Scanning ITO film; electron (b) Scanning microscope electron (SEM) microscope overview (SEM) after scratchingoverview after the ITO scratching film, including the ITO metallicfilm, including metallic SWCNTs to activate FE; and, (c) Enlarged SEM view of the metallic SWCNTs SWCNTs to activate FE; and, (c) Enlarged SEM view of the metallic SWCNTs protruding from the ITO protruding from the ITO film; (d) Transmission (TEM) overview of bundles of film; (d) Transmission electron microscope (TEM) overview of bundles of metallic highly crystalline metallic highly crystalline SWCNTs that were used in the ITO film (b,c). SWCNTs that were used in the ITO film (b,c). Appl. Sci. 2017, 7, 1322 4 of 11 Appl. Sci. 2017, 7, 1322 4 of 11

A diodeA diode structure structure with with a afixed fixed gap gap (1.2 (1.2 mm) betweenbetween thethe ITOITO film film (cathode) (cathode) and and a phosphora phosphor plate platecoated coated on ITOon ITO electrode electrode (anode) (anode) was adoptedwas adopted for the for FE measurement.the FE measurement. Figure2 showsFigure a2 schematic shows a of schematicthe system of the used system for FE us measurement.ed for FE measurement. TheThe obtained obtained sample sample was was placed placed in a in vacuum a vacuum chamber chamber system system and and maintained maintained at a at pressure a pressure of of 10−106 Pa.−6 Pa.Direct Direct current current (DC) (DC) voltage voltage was was applied applied across across the thecathode cathode and and anode anode to determine to determine the the FE FE propertiesproperties after after baking baking the the sample sample to reduce to reduce the the amount amount of gas of gas contaminating contaminating the theSWCNT SWCNT surface. surface. A powerA power supply supply unit unit and and a PC a PC were were connected connected to toautomatically automatically store store data. data.

ITO electrode

Phosphor plate

Phosphor plate anode with area of 50 mm2 Glass substrate coated on ITO electrode

Spacer gap Electrode to Gap 1.2mm connect ITO coating and earth ITO coating film Glass substrate including SWCNTs as a cathode

FigureFigure 2. Schematic 2. Schematic diagram diagram of the of theFE measurement FE measurement system system with with a diode a diode structure. structure.

3. Theory3. Theory of FE of FEFluctuation Fluctuation TheThe field field emission emission tunneling tunneling model model was was originally originally represented represented by bythethe electron electron tunneling tunneling model, model, as expressedas expressed by by the the Spindt Spindt model model based based on on the the Fowler Fowler and and Nordheim (F-N) modelmodel [[26].26]. TheThe model model has hasthe the basis basis of of the the electron electron tunneling tunneling with with ballistic ballistic electrons electrons considered considered to pass to pass through through the energythe energy barrier barrierfrom from SWCNTs, SWCNTs, however however it is valid it is onlyvalid whenonly thewhen flow the of flow electrons of electrons in the field in the emitter field isemitter prevented is preventedby an energy by an barrier.energy barrier. In the FEIn the model FE model used in us thised in study, this study, we assumed we assumed that electrons that electrons are emitted are emittedfrom SWCNTsfrom SWCNTs to the to outside, the outside, and we and constructed we constructed an FE an model FE model by combining by combining the model the model of inelastic of inelastictunneling tunneling electrons electrons passing passing through through SWCNTs SW intoCNTs the into F-N the tunneling F-N tunneling model ofmodel electrons of electrons emitted to emittedthe outside. to the outside. In Inthe the inelastic-electron-tunnelin inelastic-electron-tunnelingg model, model, the thestates states of the of the electrons electrons before before and and after after tunneling tunneling throughthrough an anenergy energy barrier barrier are estimated are estimated by considering by considering the energy the energy transfer. transfer. According According to Laks to and Laks →  ∗→ ∗ →  Millsand [27], Mills [(27,],)Jˆ inx , thet in current–current the current–current correlation correlation 〈(,hJˆ ) x(, t,)〉Jˆ xcan, t ibecan expressed be expressed in the in the followingfollowing form: form: Z →  Iˆ(t) = dx// Jˆ x , t (1) () = (,) (1) ˆ I(t) is the quantum-mechanical tunneling-current operator and represents the current flow at time () is the quantum-mechanical tunneling-current operator→  and represents the current flow at time t. Thet. normalization The normalization P of Ptheof the function (,ψ ) xis, t expressedis expressed as the as theprobability probability density density of the of the existenceexistence of electrons of electrons in a in quantum a quantum barrier, barrier, as asfollows: follows:

(→ ) | → | 2 ∗ →  →  P , = ( ,) = (∗, )(,) (2) P x , t = ψ x , t = ψ x , t ψ x , t (2) when an electron exists in sphere Ω (,)= ∗ (3) Appl. Sci. 2017, 7, 1322 5 of 11 when an electron exists in sphere Ω

δ R →  → R  ∗ δψ  → δt Ω P x , t d x = Ω ψ δt d x → = 1 R (ψ∗ Hψ − ψHψ∗)d x (3) i} Ω → i} R ∗ ∗ = 2m A(ψ ∇ψ − ψ∇ψ )dA

→  } ∗ ∗ when S x , t ≡ 2im (ψ ∇ψ − ψ∇ψ ),

∂ Z →  → Z →  → P x , t d x = − ∇S x , t d x . (4) ∂t Ω Ω

∂ →  →  when ∂t P x , t + ∇S x , t = 0,

→  →  Jˆ x , t = −eSˆ x , t (5) ie} ∗ ∗ = 2m (ψ ∇ψ − ψ∇ψ ) where e is the electric charge and Iˆ(t) is expressed as h i ˆ r+ l ∗ l+ r I(t) = ∑ TkqCq (t)Ck(t) + TkqCk (t)Cq(t) , (6) k·q where Tkq is the tunneling matrix element between state k in the source electrode and state q in the r+ l vacuum through the tunneling barrier. Cq (t) and Ck(t) are the creation and annihilation operators of the electron, respectively. Using the Wentzel–Kramers–Brillouin (WKB) method to calculate the electron wave functions, the tunneling matrix element can be expressed as [28–30]

2     } Z zr Z zr Tkq ∝ ∗ exp − dz|kz(z)| exp − dz|qz(z)| (7) 2m zl zl where m* is the effective mass of an electron in the tunneling barrier, and kz and qz are the components of the electron wave vector in the barrier that is perpendicular to the CNT surface.

√ 1 ∗  2  2 2m } 2 kz(z) = V(z) − E + k (8) } 2m∗

√ 1 ∗  2  2 2m } 2 qz(z) = V(z) − E + k + }ω . (9) } 2m∗ here, V(z) is the barrier potential and z is the coordinate of the axis perpendicular to the interfaces. The average of the current–current correlation in state i is expressed as:

∗ 1 ∗ hIˆ (t)Iˆ(0)i = ∑hi Iˆ (t)Iˆ(0) ii. (10) N i

|I(ω)|2 is the power spectrum of the fluctuation of the tunneling current for the FE mechanism.

Z ∞ |I(ω)|2 = hIˆ∗(t)Iˆ(0)ie−iωtdt (11) −∞ By substituting Equations (6)–(9) into Equation (11), we finally obtain the following expression for the power spectrum of the FE current fluctuation: Appl. Sci. 2017, 7, 1322 6 of 11

2 Z  Z   Z  2 e Am |I(ω)| = dE × exp − dz|kz(z)| exp − dz|qz(z)| . (12) 2π2}3 where A is corresponding to the total area of the FE site, which electrons emit from the SWCNTs the cathode and m is the effective mass of an electron that moves parallel to the emission site in the source electrode, from which tunneling electrons are injected into the barrier. Appl. Sci.Equation 2017, 7, 1322 (12) should be transformed into a more suitable form for an FE cathode using metallic6 of 11 SWCNTs. FE model was carried out in the Fowler–Nordheim tunneling regime with the barrier Equation (12) should be transformed into a more suitable form for an FE cathode using metallic potential V(z), and a simplified form for the power spectrum is expressed as: SWCNTs. FE model was carried out in the Fowler–Nordheim tunneling regime with the barrier √ potential (), and a simplified3 form for the power−1 spectrum( is expressed as: ) 2 e A 2 }ω 2 2m  3 3  | ( )| ·| | + × − ( ) 2 + ( ) 2 I ω ∝ 2 E 1 exp }ω eφB . (13) 4π }φB eφℏB 32}√e|2E| |()| ∝ ∙ || +1 ×exp− (ℏ) + () . (13) 4 ℏ 3ℏ|| here, φB, as shown in Figure3 is the barrier height potential, which is the difference from the vacuum levelhere, to the, as energy shown level in Figure of thebottom 3 is the of barrier the Fermi height level potential, in the case which of metallic is the SWCNTs, difference and fromE is the fieldvacuum applied level to to the the SWCNTs, energy level which of the is enhanced bottom of by the the Fermi tip shape. level Thein the enhancement case of metallic factor SWCNTs,β of E is calculatedand is the by simulationfield applied using to the the SWCNTs, surface-charge which method is enhanced with a three-dimensionalby the tip shape. modelThe enhancement of SWCNTs protrudingfactor β of from is calculated the ITO film by [simulation31–33], where: using the surface-charge method with a three-dimensional model of SWCNTs protruding from the ITO film [31–33], where: E = βE0. (14) E=. (14) there, E0 is is the the actual actualelectrical electrical fieldfield suppliedsupplied betweenbetween thethe cathode and anode electrodes. Moreover, Moreover, fieldfield emission site A on the SWCNTs of the cathode was estimatedestimated from the comparison between the simulated and measured brightbright spotsspots [[31].31].

eEz (E～102 V/mm) e- Coulomb φ potential B x

SWCNT field emitter z

Fermi level e-

barrier

SWCNT vacuum

Figure 3. Primitive model of the FE using an SWCNT emitter based on Fowler–Nordheim tunneling. Figure 3. Primitive model of the FE using an SWCNT emitter based on Fowler–Nordheim tunneling.

4. Results and Discussion 4. Results and Discussion Figure 4 shows the relationship between the current density and of the SWCNTs Figure4 shows the relationship between the current density and electric field of the SWCNTs that were obtained using the FE measurement system (Figure 2). The threshold field of the metallic that were obtained using the FE measurement system (Figure2). The threshold field of the metallic SWCNTs was 4.1 V/µm at a line-current density of 0.1 mA/cm2, as shown in Figure 4. Moreover, the SWCNTs was 4.1 V/µm at a line-current density of 0.1 mA/cm2, as shown in Figure4. Moreover, planar lighting at 2 mA/cm2 was shown in the inset of Figure 4. the planar lighting at 2 mA/cm2 was shown in the inset of Figure4. Appl. Sci. 2017, 7, 1322 7 of 11

Appl. Sci. 20172017,, 77, ,1322 1322 7 of 117 of 11

FigureFigure 4. Current4. Current density–electric-field density–electric-field characterist characteristicsics of ofmetallic metallic SWCNTs. SWCNTs. The inset The shows inset showsthe the planar lighting. planarFigure lighting. 4. Current density–electric-field characteristics of metallic SWCNTs. The inset shows the planar lighting. Figure 5 shows the FE current density of metallic SWCNTs with different supplied DC voltages overFigure Figure40 5s shows(a) 5 and shows thethe thedistribution FE FE current current of density densitythe power of of metallic metalspectrumlic SWCNTs SWCNTs of the frequency with different different based onsupplied supplied information DC DC voltages on voltages overoverthe 40 FE s 40 (a) current s and(a) and thefluctuation, the distribution distribution as obtained of of the the by power thepower Fourier spectrum spectrum transform of the method frequency frequency (b). The based based sample on on informationwas information biased on on the FEtheusing current FE a current DC fluctuation,power fluctuation, supply, as and as obtained obtained the current by by the densitythe Fourier Fourier from transformtransform the DC power method method supply (b). (b). wasThe The measuredsample sample was to was bebiased biased 1.2 mA/cm2 at 5.2 V/µm (6 kV), 2.0 mA/cm2 at 5.5 V/µm (6.6 kV), 4.6 mA/cm2 at 5.9 V/µm (7.1 kV), usingusing a DC a DC power power supply, supply, and and the the current current density density fromfrom the DC power power supply supply was was measured measured to be to be and 10 mA/cm2 at 6.3 V/µm (7.6 kV). We observed a high stability of the FE current, owing to the 1.2 mA/cm1.2 mA/cm2 at25.2 at 5.2 V/ µV/µmm (6 (6 kV), kV), 2.0 2.0 mA/cm mA/cm22 atat 5.55.5 V/V/µmµm (6.6 (6.6 kV), kV), 4.6 4.6 mA/cm mA/cm2 at2 at5.9 5.9 V/µm V/ µ(7.1m (7.1kV), kV), desorption of gases on the SWCNTs that was caused by the annealing before the FE measurement. and 10 mA/cm2 2 at 6.3 V/µm (7.6 kV). We observed a high stability of the FE current, owing to the and 10We mA/cmwould haveat observed 6.3 V/µ msome (7.6 damped kV). We current observed distributions a high stabilityin the FE ofcurrent the FE if the current, annealing owing of to the desorption of gases on the SWCNTs that was caused by the annealing before the FE measurement. desorptionthe sample of gaseshad been on insufficient. the SWCNTs However, that was Figure caused 5a shows by the no annealingdamping, and before the SWCNT the FE surfaces measurement. We would have observed some damped current distributions in the FE current if the annealing of We wouldwere considered have observed to have some been sufficiently damped current cleaned distributions before the FE measurement. in the FE current The spectrum if the annealing of each of the the sample had been insufficient. However, Figure 5a shows no damping, and the SWCNT surfaces sampleFE hadcurrent, been as insufficient.shown in Figure However, 5a, is normalized Figure5a showsby the peak no damping, at 0 Hz, and and indicates the SWCNT that periodic surfaces were were considered to have been sufficiently cleaned before the FE measurement. The spectrum of each consideredcurrent fluctuation to have been is present sufficiently in the FE. cleaned A peak before exists theat 50 FE Hz, measurement. as shown in Figure The spectrum5b, originating of each FE FE current, as shown in Figure 5a, is normalized by the peak at 0 Hz, and indicates that periodic current,from as the shown noise inof Figurethe DC5 a,power is normalized supply, which by the corresponds peak at 0 to Hz, the and frequency indicates of the that commercial periodic current currentpower supply fluctuation in the iseast present of Japan. in theWe observedFE. A peak that exis thets stable at 50 DC Hz, current as shown in the in FE Figure images 5b, obtained originating fluctuation is present in the FE. A peak exists at 50 Hz, as shown in Figure5b, originating from the from thethe power noise spectrum,of the DC as power shown supply,in Figure which 5a, ha scorresponds an alternating-current to the frequency component, of theparticularly commercial noisepowerat of low the frequenciessupply DC power in the of supply, undereast of approximately Japan. which We corresponds observed 100 Hz. that toMoreover, the the frequency stable the DC spectrum current of the distribution commercial in the FE images depends power obtained on supply in the eastfromthe magnitude of the Japan. power Weof spectrum, the observed FE current, as thatshown and the thein stable Figure alternatin DC 5a, g-current currenthas an alternating-current in component the FE images of each component, obtained spectrum fromincreases particularly the power spectrum,atwith low the asfrequencies DC shown power. in of Figure under5a, approximately has an alternating-current 100 Hz. Moreover, component, the spectrum particularly distribution at low depends frequencies on of underthe magnitude approximately of the 100 FE current, Hz. Moreover, and the thealternatin spectrumg-current distribution component depends of each on spectrum the magnitude increases of the FE current,with the and DC thepower. alternating-current component of each spectrum increases with the DC power. (a) 12 -2

cm 10 (a)・ 12 -2 8 cm 10 ・ 6 8 4 6 2 4 FE Current FE Current density / mA 0 2 0 10203040

FE Current FE Current density / mA Measurement time / sec 0 0 10203040 Measurement time / sec

Figure 5. Cont. Appl. Sci. 2017, 7, 1322 8 of 11 Appl. Sci. 2017, 7, 1322 8 of 11

(b) 600

500

400 10 mA/cm2

300 4.6 mA/cm2 2.0 mA/cm2 200 Noise on DC supply fluctuationarb. unit / 100

Normalized power spectrumcurrent of 0 0 20406080100120 1.2 mA/cm2 Frequency / Hz Figure 5. Distributions of (a) FE current fluctuation and (b) spectrum of the FE current fluctuation Figure 5. Distributions of (a) FE current fluctuation and (b) spectrum of the FE current fluctuation obtained by the Fourier transform method. obtained by the Fourier transform method. We compared the above experimental results with the theoretical predictions described in SectionWe compared2. The parameters the above that experimental determine the results tunnelin withg characteristics the theoretical of predictions the field emitters described that inused Section 2. Themetallic parameters SWCNTs that (shown determine in Figures the tunneling4 and 5) are characteristics listed in Table 1. of The the enhanced field emitters field E that in Equation used metallic SWCNTs(13) was (showndetermined in Figures by simulation4 and5) using are listed the surfac in Tablee electrical1. The enhancedmethod used field in Ref.E in [30], Equation with the (13) was determinedSWCNT model. by simulation The emission using site theA at surfacethe SWCNT electrical surface method was estimated used in and Ref. calculated [30], with from the the SWCNT model.comparison The emission between sitethe simulatedA at the SWCNT and measured surface bright was estimatedspots [31]. φ andB was calculated estimated from from the the comparisonwork function of bulk carbon. between the simulated and measured bright spots [31]. φB was estimated from the of The power spectrum |I(ω)|2 obtained from Equation (13), which is based on the WKB bulk carbon. approximation, and Table 1 show the dependence on the voltage applied between a cathode with SWCNTsTable 1.andParameters an anode usedelectrode, in the as theoretical shown in calculations. Figure 6. EachA and spectrumβ were distribution obtained by depends simulation on usingthe magnitudethe method of the in Ref.FE current, [29,30]. and the alternating-current component of each spectrum increases with the DC power. For the metallic SWCNTs, the experimentally obtained results are shown in Figure 5, and those that are obtained by simulation are shown in Figure 6, which are in good agreement. e () 1.60 × 10−19 C Distribution of the energy of electrons that pass through an energy barrier by WKB approximation −24 2 expands when an applied voltageA between(FE site) a cathode and an anode6.48 electrode× 10 increases.m Namely, this φ (work function of bulk carbon) 4.3 eV means that the high frequencyB components of FE current increase, and it is guessed that high } (= h/2π, h: ) 6.58 × 10−16 eV·s frequency components of the power spectrum relatively increase by increasing in an applied β (enhancement factor) 2.56 × 103 voltage. On the basis of thism (freeagreement, electron the mass) experimental results9.11 were× 10 −modeled31 kg by the inelastic tunneling model based on the Fowler–Nordheim tunneling of electrons emitted from the ends of the SWCNTs using the current-fluctuation power spectrum given by Equation (13). The results that are 2 shownThe in power Figures spectrum 5 and 6 | Iindicate(ω)| obtained that an fromelectr Equationon passing (13), into which a barrier is based in the on Fowler–Nordheim the WKB approximation, andregime Table constantly1 show the exhibit dependence an electrical-charge on the voltage fluctuation applied in betweenthe inelastic a cathode tunneling with model, SWCNTs and the and an anodeshape electrode, of the power as shownspectrum in Figuredepends6. on Each the spectrum quantity of distribution electrical charge depends that onis emitted the magnitude from the of the FEfield current, emitters. and the alternating-current component of each spectrum increases with the DC power. For the metallic SWCNTs, the experimentally obtained results are shown in Figure5, and those that are obtainedTable 1. byParameters simulation used arein the shown theoretical in Figure calculations.6, which A and are β were in good obtained agreement. by simulation Distribution using of the the method in Ref. [29,30]. energy of electrons that pass through an energy barrier by WKB approximation expands when an applied voltage between a cathodee (elementary and an anode charge) electrode increases. 1.60 × 10−19 Namely, C this means that the high frequency components of FE currentA increase,(FE site) and it is guessed 6.48 that× 10−24 high m2 frequency components of the power spectrum relativelyφB increase(work function by increasing of bulk carbon) in an applied 4.3voltage. eV On the basis of this agreement, −16 the experimental results wereℏ (=ℎ/2 modeled, h: byPlanck the inelastic constant) tunneling 6.58 × model10 eV·s based on the Fowler–Nordheim β (enhancement factor) 2.56 × 103 tunneling of electrons emitted from the ends of the SWCNTs using the current-fluctuation power m (free electron mass) 9.11 × 10−31 kg spectrum given by Equation (13). The results that are shown in Figures5 and6 indicate that an electron passing into a barrier in the Fowler–Nordheim regime constantly exhibit an electrical-charge fluctuation in the inelastic tunneling model, and the shape of the power spectrum depends on the quantity of electrical charge that is emitted from the field emitters. Appl. Sci. 2017, 7, 1322 9 of 11 Appl. Sci. 2017, 7, 1322 9 of 11

Figure 6. Dependence of power spectrum by simulation on the applied voltage. E indicates the Figure 6. Dependence of power spectrum by simulation on the applied voltage. E00 indicates the original fieldfield suppliedsupplied betweenbetween thethe cathodecathode andand anodeanode electrodes.electrodes.

FE using metallic SWCNTs waswas thusthus successfullysuccessfully modeledmodeled asas aa phenomenonphenomenon basedbased onon inelasticinelastic electron tunneling using metallic SWCNTs, as shown in FigureFigure6 6.. AlthoughAlthough manymany researchersresearchers havehave reportedreported thatthat fieldfield emittersemitters realizerealize Fowler–NordheimFowler–Nordheim tunneling with elastic electrical conductivity, no demonstrative experiments have been presented toto thethe bestbest ofof ourour knowledge.knowledge. The current paper presentspresents thethe firstfirst successfulsuccessful developmentdevelopment ofof anan inelastic-electron-tunnelinginelastic-electron-tunneling model with the WKBWKB approximation for metallic SWCNTs basedbased onon thethe evaluationevaluation of FEFE properties.properties. The FE current from fieldfield emitters, for for example, example, SWCNTs, SWCNTs, fluctuates, fluctuates, and and the the I–IV–V characteristicscharacteristics of ofFEs FEs were were examined examined by byconsidering considering the the power power spectrum spectrum at atω ω= =0 0in in Equation Equation (13), (13), which which represents represents the the magnitude magnitude of the current duedue toto the the electrons electrons passing passing through through a potentiala potential barrier barrier from from the SWCNTs,the SWCNTs, in accordance in accordance with Equationwith Equation (13), constructed(13), constructed by the by inelastic-electron-tunneling the inelastic-electron-tunneling model. model.

5. Conclusions We considerconsider that that field field emitters emitters can can be be used used as anas electron-emissionan electron-emission source source in CL in devices. CL devices. The fieldThe emittersfield emitters that arethat used are used in CL in devices, CL devices, including including lighting lighting devices devices employing employing visible visible rays, rays, X-rays, X-rays, and ultravioletand ultraviolet radiation, radiation, suffer suffer from thefrom problem the problem that the that radiation the radiation from the CLfrom device the CL has device a fluctuating has a outputfluctuating that output depends that on depends the electrical on the properties electrical ofprop theerties field of emitters the field in emitters time and in space. time and In this space. study, In wethisanalyzed study, we the analyzed fluctuation the fluctuation of the output of the when outp fieldut when emitters field are emitters used in are a CL used device, in a CL where device, we employedwhere we metallicemployed SWCNTs metallic as SWCNTs field emitters. as field The em homogeneousitters. The homogeneous dispersion of metallicdispersion SWCNTs of metallic with highSWCNTs crystallinity with high is onecrystallinity of the essential is one of design the essential requirements design in requirements the fabrication in the of the fabrication cathode of in CLthe devicescathode inin orderCL devices to obtain in highorder output to obtain stability. high However,output stability. it was difficultHowever, for it thewas highly difficult crystalline for the SWCNTshighly crystalline to control SWCNTs homogeneous to control dispersion homogeneous into a mixture dispersion to make into an FEa cathodemixture device.to make We an have FE realizedcathode thedevice. homogeneous We have dispersionrealized the of metallichomogeneou SWCNTss dispersion with high of crystallinity metallic SWCNTs for the first with time high by ancrystallinity agitation processfor the first with time the by ITO an precursor agitation solution,process with butyl the acetate ITO precurso added, asr solution, is required butyl to controlacetate theadded, viscosity as is required of the solution, to control and the EC viscosity as a surfactant of the solution, at a weight and ratio EC as of a 1:8:600:10. surfactant It at was a weight difficult ratio to disperseof 1:8:600:10. highly It crystalline was difficult carbon to nanotubesdisperse high homogeneously,ly crystalline because carbon no na surfactantnotubes canhomogeneously, combine to a surfacebecause of no a surfactant nanotube withcan combine high crystallization. to a surface of In a thisnanotube study, with we succeeded high tolization. disperse In the this solution study, withwe succeeded the designed to disperse composition the solution by controllable with the wet designed dispersion composition process. by The controllable metallic highly wet dispersion crystalline SWCNTsprocess. The were metallic employed highly as field crystalline emitters toSWCNTs analyze thewere fluctuation employed in as the field FE of emitters conventional to analyze materials. the fluctuationWe succeeded in the FE in of constructing conventional a physicalmaterials. mechanism to examine FE fluctuation. Fluctuation of the FEWe current succeeded was observedin constructing using thea physical metallic mechanism SWCNTs as to field examine emitters, FE whichfluctuation. was compared Fluctuation with of thethe theoreticalFE current spectrawas observed calculated using using the metallic a current-fluctuation SWCNTs as field theory emitters, that incorporates which was a compared realistic power with spectrumthe theoretical of the spectra current fluctuationcalculated inusing the Fowler–Nordheima current-fluctuation tunneling theory regime.that incorporates Good agreement a realistic was seenpower between spectrum the observedof the current and the fluctuation theoretically in calculated the Fowler–Nordheim spectra of the FEtunneling current obtainedregime. usingGood agreement was seen between the observed and the theoretically calculated spectra of the FE current obtained using the SWCNTs. We consider that inelastic electron tunneling causes the current Appl. Sci. 2017, 7, 1322 10 of 11 the SWCNTs. We consider that inelastic electron tunneling causes the current fluctuation in the FE. The mechanism behind this can be explained by the superposition of the high frequency components of FE current in time and space. We also succeeded in developing a theoretical model of the flow of electrons (current) by considering the fluctuation of the tunnel current due to electrons passing through a potential barrier in the FE regime. The tunneling matrix based on the potential barrier that was obtained using the WKB approximation method is an important parameter for developing an inelastic-electron-tunneling model, and was used to obtain the power spectrum in this study. The FE model was obtained by combining the Fowler–Nordheim tunneling model with the power spectrum obtained using the tunneling matrix. From the above results, the use of metallic SWCNTs with high crystallinity as field emitters was found to generate a fluctuating FE current, where the fluctuation originated from inelastic electron tunneling. We have provided a brief explanation of the FE current fluctuation of metallic SWCNTs in terms of their electrical conductivity, and described the development of a conduction model for electrons that passed through a potential barrier. Highly crystalline SWCNTs are expected to be used as field emitters with stable FE.

Acknowledgments: This work was supported in part by DOWA Holdings Co. Ltd., Tokyo, Japan. The authors would like to thank the co-researchers from DOWA for the discussions and suggestions, and are grateful for the technical instructions provided during the device-assembly process and the assembly work. This study was conducted as a project consigned by the New Energy and Industrial Technology Development Organization and supported by JSPS KAKENHI Grant Number 26220104, and the authors would like to express their sincere gratitude for the guidance received. Author Contributions: The two authors equally contributed to the paper. Conflicts of Interest: The authors declare no conflict of interest.

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