On the evaluation of field emission parameters of V2O5 and TiO2 nanostructure cathodes

The self-assembled V2O5 and TiO2 nanowires are prepared hydrothermally from vanadium (V) hydroxylamido complex and titanium oxide powder, respectively, and studied for their crystalline phase, morphology, and electron emission characteristics. V2O5 is shown to exhibit an orthorhombic phase with preferential growth of the (010) face along the [010] direction; wire size being diameter 100–400 nm, and length several micrometers. TiO2 nanowires depict a monoclinic β-phase with a typical diameter of ∼ 30 nm. Their bundles serve as potential cathodes giving electron emission following the Fowler–Nordheim (F-N) mechanism but from infinitely small areas with large field enhancement factors. In comparison, β-TiO2 provides better emission characteristics at similar operating parameters (e.g., low threshold voltage 250–400 V and current density 109−1013 A m−2). The unique properties (viz., tip geometry, roughness, and local field enhancement) of one-dimension (1D) nanowires make them prospective candidates for high-brightness electron sources and development of the display devices [1–7]. A simple procedure developed by the authors is applied successfully in actual evaluation of the field emission parameters from the current–voltage data. This involves F-N formulation with physical considerations like variation of work function, effective emission area, and field enhancement factor [31].

A precise and reliable analysis of the field emission characteristics of cathodes at the nano-scale is challenging. The existing formulations suffer from uncertainties in estimating the parameters accurately.
Experimental results are always used to check the theory, but the complexities involved (and realized lately) make the evaluation process difficult [27].
The evaluation of the emission characteristics is generally undertaken within F-N formulation, even though this has turned out to be inadequate for a nano-scale emitter (mainly due to a distinctive tip roughness and the presence of tiny protrusions) vis-à-vis a planar smooth cathode with a fixed work function. This exercise leads to unreliable emission parameters.Murphy andGood Jr [28] considered variation of the work function and modified the F-N equation to yield somewhat real characteristics. Also, Popov et al [29] observed morphological changes in the tungsten tip (radius of curvature ∼ 50 nm) with applied voltage in real time. Accordingly, the operational parameters like work function, field enhancement factor, and the effective emission area vary with the bias. Toijala et al [30] emphasized the importance of atomic-level defects at the emitter tip and observed reduction of the work function (e.g., from the bulk value of 4.76 eV by 0.32 or 0.51 eV in copper). Interpretation of I-V data poses significant challenges in case of 1D nanowires, as many emission parameters extracted and reported in the literature are physically unrealistic. This situation arises due to widespread use of improper field emission (FE) equations for local emission current density and discussed in detail by Forbes [27]. It is vital, therefore, to establish standard equations to describe the FE current density accurately before developing a systematic procedure for reliable analysis of measured emission data. It is worth mentioning that the existing formulations present uncertainties in the quantitative prediction of emission current density and reasonable comparison with experimental results.
With complexities in FE, a precise comparison between theory and experiment has proven to be quite difficult. To address this issue, the present authors have devised a simple method for evaluation of emission parameters, viz., effective emission area, apparent work-function, and field enhancement factor. The approach is extended here to the 1D V 2 O 5 and TiO 2 nanowire emitters and found to provide reliable emission parameters, consistent with theoretical predictions.
The analysis of the current-voltage characteristics of nanowires requires two essential elements, viz., (i) an accurate expression describing the field emission (FE) current and (ii) a simple method allowing extraction of the operational parameters from the experimental data reliably. Though the field emission arena is technological, yet scientific too because of its continuing nature (referred to as the FE-science problem). So the present authors focused on a limited and crucial aspect of the issue and proposed a scientific basis of field emission by examining all the methodologies available for the evaluation and interpretation of the measured FE current-voltage data and provided a logical and meaningful description of the phenomenon. It involves use of analytical expressions with realistic parameters based on physical considerations, leading to development of a general treatment of the emission process within the framework of Fowler-Nordheim (F-N) theory [31].
A simple procedure thus evolved for the estimation of the emission parameters is extended here to V 2 O 5 and TiO 2 nanowire bundles to check its applicability. So, the study can be treated as an extension of the previous work to oxide emitters for completeness and as a real test of the method developed. The F-N description is inadequate and cannot be used as such for understanding the electron emission characteristics of nano-scale emitters.

Synthesis of V 2 O 5 and TiO 2 powder
For synthesis of V 2 O 5 nanobelts nanowires, a procedure described by Cranes et al [32] was adopted. Accordingly, a freshly prepared [VO(NH 2 O) 2 (Gly)]·H 2 O (0.5 g, 2.3 mmol) complex was dissolved in 35 ml of double distilled with addition of a few drops of concentrated HNO 3 and stirred. The resulting blue colour solution was transferred into a polytetrafluoroethylene (PTFE, Teflon) lined autoclave having a stainless-steel shell. The autoclave volume (60 ml) was filled up to 60% and placed in a preheated furnace at 220°C for 7h and thereafter allowed to cool naturally to room temperature. The final product of yellow colour was washed several times with double distilled water and absolute ethanol to remove residue and dried at 60°C for 5 h. The procedure was repeated by varying the reaction time and temperature for ascertaining the optimum conditions. The formation of V 2 O 5 is discussed in detail by Bard and Stratmann [33]. Thus, the purpose of HNO 3 is to aid both oxidation and acidification. In the process, hydroxylamine (NH 2 O¯ligand) reduces vanadium (V) to (IV), which enables decomposition of the complex, giving [VO] 2+ species in a blue-coloured solution.
[VO] 2+ clusters are oxidized to [VO 2 ] 1+ and facilitate formation of V 2 O 5 nuclei. These grow preferentially into nanofibers and/or bundles by development of energetically favoured surfaces.
TiO 2 nanowires were synthesized using the hydrothermal process described by Armstrong et al [34]. Accordingly, 1 g of Baker's TiO 2 powder with a purity of 99.4% was added to a 12 M solution of NaOH (purity 99%) in distilled water. The resulting mixture was then enclosed in a Teflon container with a stainless-steel lining and heated at 170°C for 72 h. The product after the hydrothermal treatment was washed three times with 0.1 M HCl, rinsed with deionized water, air-dried, and finally subjected to heat treatment at 400°C for 4 h. The acid wash step facilitates the formation of layered hydrogen titanate, which on heating undertakes topotactic structural condensation leading to nucleation and growth of TiO 2 nanowires [35].

Results and discussion
3.1. Crystalline phase and morphology Figure 1 shows a typical SEM image of the V 2 O 5 powder. Interestingly, it contained fibers of average diameter ∼ 200 nm. The corresponding x-ray diffraction (XRD) pattern recorded with Cu-K α radiation is depicted in figure 2. It matches with an orthorhombic phase having a = 11.54 Å, b = 3.571 Å, c = 4.383 Å, Z = 2, and space group Pmmn of V 2 O 5 (JCPDS file # 89-0612). A notable feature in the XRD pattern, however, is the absence of the strong [110] peak. This happens because of the preferential growth of wires along [010] with the (010) face as the cross-section [20,36,37]. The crystal structure of V 2 O 5 is described by layers of edge-and-corner-shared VO 5 square pyramids, having 5-fold coordination of vanadium with oxygen ions [11] or else by the linking of highly distorted [VO 6 ] octahedral building blocks.  A scanning electron micrograph of the TiO 2 powder shown in figure 3(a) clearly indicates the formation of nanowires. Their x-ray diffraction pattern (figure 4) corresponds to a monoclinic structure with a = 12.2077 Å, b = 3.7488 Å, c = 6.5350 Å, β = 107.36°, Z = 8, and space group c2/m of β-TiO 2 (JCPDS file # 46-1238). The broadening of the diffraction peaks arises due to the tiny diameter of the nanowires [33]. Figure 3(b) depicts a typical transmission electron micrograph of a β-TiO 2 nanowire with a diameter of ∼ 30 nm. Beta TiO 2 consists of a 3D framework of sheets produced by edge-and-corner sharing of TiO 6 octahedra and has a lower density than its other polymorphs [38].
The evaluation of the average crystallite size (D) is undertaken by using Scherrer's formula, where β is the full width at half maximum (FWHM) of the (hkl) diffraction peak, θ is the corresponding Bragg angle, and λ is the x-ray wavelength. Accordingly, the estimated values of the average crystallite size are 24.   3.2. Emission characteristics V 2 O 5 and β-TiO 2 nanowires were dispersed in ethanol by sonication, laid on a 1 cm × 1 cm tungsten strip by the drop-cast method and dried. The back side of the tungsten strip was then attached to a copper disc (pre-mounted on a screw gauge head) with silver paste to act as a cathode. Another copper disc which served as an anode was held parallel to the cathode at 50 μm away (adjusted by linear motion of a screw gauge having a least count of l0 μm). Both the cathode and the anode were electrically insulated from the metal body of the screw gauge with an epoxy resin (Araldite). The electron emission behavior of each (V 2 O 5 and β-TiO 2 ) was then observed in a planar diode configuration (figure 5) under a vacuum of ∼ 10 −6 mbar using a pico-ammeter/voltage source (Keithley model 6487).
Although the field emission (FE) from a solid is vital in modern electronics,yet faces challenges from breakdown at 10 7 -10 8 Vm −1 caused essentially by local field enhancement due to the microscopic protrusions present at the surface. Consequently, the evaluation of the emission parameters in the realm of the classical Fowler-Nordheim (FN) mechanism poses difficulties with the underlying assumptions, viz., a flat/smooth planar surface and a fixed work function.
Murphy and Good Jr [28] obtained a current integral through a rigorous mathematical treatment, solved that analytically under the JWKB approximation, and arrived at the modified FN equation for field emission at low temperatures. This essentially accounts for the variation of the work function during the emission process and suggests an alternative ln{I/(V 2 − η/6 )} versus 1/V plot (where η is a function of the local work function) or the Murphy-Gold (MG) plot for determining the emission parameters from the measured I-V data [39]. Popov et al [29] compared the emission parameters of a single-tip tungsten cathode (radius of curvature ∼ 50 nm) in real time, deduced using both the FN plot and MG formulation, and observed significant morphological changes in the emitter, leading to a variation in the values of the field enhancement factor and emission area with the voltage ranges. A simple way of extracting the emission parameters from the curved (instead of linear) FN plots is suggested by the present authors [31]. Accordingly, the Fowler-Nordheim (F-N) field emission current (I) at a voltage (V ) is given by  involves the determination of (i) β for each f (and A eff ) from the A and/or B relation(s) given above, (ii) the local electric field E, (iii) Δf, and (iv) the work function (f + Δf). The acceptable values of the emission parameters are then chosen fromthe deduced figures [31]. Notice the variation found in the local work function, field emission factor, and the emission area with the voltage range. These deductions are consistent with the finding of Toijala et al [30], who used density functional theory (DFT) and quantum transport calculations to demonstrate the effect of an atomic-level surface imperfection on the bulk work function of copper (4.76 eV). Accordingly, the lowering of the work function occurs locally by 0.32 eV with an adatom and 0.51 eV with a pyramid defect present at the (111) surface, leading thereby to a significant increase in the field emission current. Figure 6(a) shows the I-V characteristics of the V 2 O 5 nanowires. These reveal an increase in the current first steadily, but then sharply above ∼ 320 V, possibly due to initiation of the Fowler-Nordheim (FN) field emission process. The corresponding ln (I/V 2 ) versus 1/V plot ( figure 6(b)) gives the signature of F-N emission, i.e., a straight line with a negative slope in the voltage range of 320-370 V. The magnitude of the slope and intercept of the straight line in figure 6(b) are B = 1,338 and ln A = -5.4, respectively. The resulting emission parameters are summarized in table 1. Accordingly, the apparent work function is 3.05 eV, with the effective emission area as 1.48 × 10 −11 m 2 (equivalent to a circular diameter ∼ 4.34 μm) and the enhancement factor β = 1291, if the work function of the nanowires is taken as 6.5 eV for bulk V 2 O 5 [40][41][42]. The enhancement factor (β) depends on the emitter aspect ratio (i.e., length to diameter), and the spatial distribution of the emission centers [43,44]. The V 2 O 5 nanowires have length several microns and diameter 100-400 nm. Their aspect ratio is quite high ( 40), and so accounts for the large enhancement factor (1291) observed above. It may be noted that the field emission properties of ZnO nanowires are found to improve significantly by increasing their aspect ratio and decreasing their density [45].

Titanium oxide
The I-V characteristics of the β-TiO 2 nanowires are shown in figure 7(a). The increase in current above ∼ 168 V can be attributed to the Fowler-Nordheim (FN) tunneling process, even though the corresponding ln (I/V 2 ) versus 1/V plot ( figure 7(b)) contains a curve (rather than a straight line with negative slope). The non-linear portion can be split into two straight lines covering distinct bias ranges. The magnitudes of the slope and intercept on the ordinate axis are B = 777 and ln A = −24.1, respectively, for the voltage range of 245-336 V, and

Operating parameters
Saito and Uemura [46] studied the field emission characteristics of carbon nanostructures (single wall / multi-wall tubes, fibers) for application as electron sources in various electronic devices, including flat panel displays, bulbs, etc. Their operating parameters were a threshold voltage of 500-1,000 V, a saturation current of 0.5 nA to 0.9 μA, a maximum current density of 10 9 −10 12 A m −2 . In addition, Miyauchi et al [47] reported promising electron emission properties of hydrothermally grown TiO 2 (oxygen-deficient anatase phase) nanotube arrays on a titanium substrate with a low turn-on field of ∼ 280 V for an inter-electrode separation of 100 μm but a maximum current density of just 1.5 A m −2 . They attributed the characteristics to the small radii of the nanotubes, added carrier generation with the formation of oxygen vacancies (after annealing in vacuum), and the emergence of energy levels of 0.75-1.18 eV below the bottom of the conduction band. In addition, high thermal conductivity, good chemical stability, non-toxicity, resource abundance, and low cost were cited as favorable aspects of titanium oxide for its application as an emitter. In the present work, β-TiO 2 nanowires exhibit attractive emission characteristics with the given operating parameters (threshold voltage 250-400 V, current density 10 9 −10 12 A m −2 ). The corresponding values for the case of V 2 O 5 are a higher turn-on voltage of 320-370 V and a low current density of ∼ 10 2 −10 3 A m −2 . In comparison, β-TiO 2 shows better emission behavior and can possibly be an alternate material to carbon nanostructures for a high current electron source. It may be mentioned that the field emission (FE) parameters of V 2 O 5 nanofiber bundles, vanadium nitride nanofibers, and laterally aligned carbon nanotube flower arrays determined using the original Fowler-Nordheim (F-N) formulation appear to be erroneous [29]. The reports mention the turn-on field and current density data directly without accounting for the actual emission area, effective work function, and local electric field. These features are explicitly considered above, and the real parameters identified with a thorough procedure using the slope and the intercept of the ln (I/V 2 ) versus 1/V plot.

Conclusions
This study focuses on the field emission characteristics of V 2 O 5 and TiO 2 nanowire bundles, synthesized via a simple hydrothermal process. Their average diameters are about 100-400 nm and 30 nm, respectively. While the V 2 O 5 exhibits an orthorhombic phase with preferential growth of the (010) face along [010], TiO 2 displays a monoclinic structure (β-phase). In a planar cathode design with inter-electrode separation of approximately 50 μm, V 2 O 5 nanowires show Fowler-Nordheim field emission above 320 V with an effective emission area of 1.48 × 10 −11 m 2 and a field enhancement factor (β) of 1291. For the case of β-TiO 2 , the corresponding values are 168 V, 1.38 × 10 −15 m 2 , and 385, respectively. These results provide insights and better understanding of the field emission phenomenon. The controlled topology of V 2 O 5 and TiO 2 nanostructures demonstrates their potential as efficient field emitters and possible practical applications in devices. Table 2. The effective emission area (A eff ), apparent work function (f), field enhancement factor (β), local field strength (E), Schottky barrier lowering (Δf), and work function (f + Δf) as deduced from the straight line portion of figure 7(b) (β-TiO 2 nanowires).