In this study, stable and long-term field emission properties that completely follow the Child–Langmuir law were successfully observed. A tungsten tip covered with a liquid gallium metal was used. The current characteristics showed three phases. The electron emission first began below half of the threshold voltage for the emission from a bare W chip, and the current increased by 20 μA. Then, the field emission pattern showed multiple disordered blinking spots, which originated Ga Taylor cones and the emission current value reached several mAs. Then, emission current began to follow the Child–Langmuir law, and a clear field emission pattern from {011}-oriented tungsten was observed. Electrons emitted from the submicrometer sized area that is heated by itself with joule heating of current densities greater than 107 A/cm2.

We aim to increase the brightness (β) of the field emission cathode by increasing emission current to develop next-generation lithography and electron microscopy using multiple electron beams.1, β is one of the most important factors for determining the spot size of a focusing electron beam and its spatial resolution using a focused electron beam. β is defined as β = I / ( S Ω ) [ A / c m 2 sr ], where S and Ω denote the emission area and the solid angle of the electron beam, respectively. Increased β can be achieved by reducing S. 1D materials, such as nanowires2–4 and carbon nanotubes,5 realize higher β than that of a ⟨310⟩ tungsten (W) field emission cathode. However, the emission area is limited by its shape, and the emission current eventually remains around several tens of nA. Moreover, decreasing work function is an effective means of increasing emission current. This can be realized using a zirconium oxide Schottky cathode6 or a cerium hexaboride emitter.7 However, emission current exceeding 1 mA from a single tip has not been reported.

It has long been confirmed experimentally that field emission current is affected by space charge. The field emission microscopy (FEM) experiments of Dyke et al. showed that in regions with a current density greater than 6 × 106 A/cm2, the current–voltage property begins to deviate slightly from the Fowler–Nordheim (FN) equation owing to the effect of space charge.8–11 High current density operation is realized via pulse driving; however, high current density operation causes serious damage to cathodes through changes in tip geometry, such as melting, making long-term operation impossible.9–11 Based on these experimental results, a theoretical expression for field emission current suppressed by a space charge was reported.8 On the other hand, FN field emission subject to space-charge effects has been actively studied in systems with nanogap diode structures.12–16 Quantum effects arising from a reduction in the gap width to a level comparable to the de Broglie wavelengths12,13 and the Mott–Gurney law due to collisions in a gas atmosphere14–16 have been reported. In this study, we report the successful observation using classical FEM of the transition from field emission to a space charge in a region beyond a critical current density of 106 A/cm2.

The current density defined by the Child–Langmuir (CL) law is described as follows:
J CL = 4 ε 0 9 ( 2 e m ) 1 / 2 V 3 / 2 d 2 ,
(1)
where ɛ0 is the dielectric constant, e is the elementary charge, m is the electron mass, and A/cm2 is the unit for JCL.16–18 Assuming two parallel plate electrodes with spacing d and an electron initial velocity of zero in this equation, the electric field intensity at the cathode plane is zero. The transition from FN field emission to the CL law has also attracted much attention. Dyke reported a theoretical proof of the experimental emission characteristics through solving the Poisson equation in consideration of the FN emission current.8 Recently, the transition from FN emission to CL law was calculated by Lau et al.20 The transition was also reported by Darr et al. for a system involving collisions in a gas atmosphere.14,15

In this study, we focused on a liquid metal–diffused field emission cathode. Gallium was chosen for the current study for its ease of handling and safety. The emission current is shown to be strongly limited by space charge, and the voltage–current characteristics follow the CL law completely. Moreover, continuous operation exceeding 60 h was achieved. Even after such a long-term operation for high emission current, the cathode did not show any damage. It is believed that these properties are a new way to substantially improve β.

All experiments in this study were carried out using a simple vacuum diode system. The experimental FEM apparatus is shown in Fig. 1(a). The main components of this system included a field emission cathode and an anode electrode. To measure the emission current precisely, the cathode and anode currents were monitored at the same time. In addition, a Faraday cup-shaped anode was prepared for precise current measurements. By using a plane-shaped anode, the cathode current did not coincide with the anode current. The anode current decreased to more than 25% of the cathode current because secondary electrons were not collected by the plane-shaped anode. However, when the Faraday cup-shaped anode was adapted for emission current measurements [Fig. 1(a)], the cathode current showed good agreement with the anode current. The Faraday cup-shaped anode was only used for the experiment shown in Fig. 2. For the other experiments, a copper plate coated with a phosphor screen was used as the anode electrode for emission pattern observations. The phosphor screen anode was used for all experiments, except those depicted in Fig. 2. However, the measured anode currents were approximately 75% smaller than the cathode currents.

FIG. 1.

Field emission microscopy apparatus. (a) Faraday cup-shaped and phosphor screen anodes were applied for precise current measurements and observations of the emission pattern, respectively. The inset is a photograph of the W-tip prepared with a Ga reservoir. (b) Scanning electron microscopy images of the W-tip after Ga diffusion. The white lines indicate a 100 nm scale bar.

FIG. 1.

Field emission microscopy apparatus. (a) Faraday cup-shaped and phosphor screen anodes were applied for precise current measurements and observations of the emission pattern, respectively. The inset is a photograph of the W-tip prepared with a Ga reservoir. (b) Scanning electron microscopy images of the W-tip after Ga diffusion. The white lines indicate a 100 nm scale bar.

Close modal
FIG. 2.

Experimental emission characteristics using (a) a Faraday cup-shaped anode and (b) a plane-shaped anode. The current (I) is plotted against voltage (V) at 1 / V for seven measurements of the Ga-diffused W-tip and the bare W-tip. The dashed black line represents 20 μA, and the solid black line represents the CL law as a function of V 3 / 2. Two step changes and three phases were observed, bordering on CL law and 20 μA. The three phases were named Region 1 (up to 20 μA), Region 2 (from 20 μA to the CL law line), and Region 3 (according to CL law).

FIG. 2.

Experimental emission characteristics using (a) a Faraday cup-shaped anode and (b) a plane-shaped anode. The current (I) is plotted against voltage (V) at 1 / V for seven measurements of the Ga-diffused W-tip and the bare W-tip. The dashed black line represents 20 μA, and the solid black line represents the CL law as a function of V 3 / 2. Two step changes and three phases were observed, bordering on CL law and 20 μA. The three phases were named Region 1 (up to 20 μA), Region 2 (from 20 μA to the CL law line), and Region 3 (according to CL law).

Close modal

The anode was located 30 mm from the front of the W-tip. The voltage applied to the W-tip could be increased up to −10 kV. The emission current was monitored using a current meter (Model 6485; Keithley Instruments, Inc.). A 100-k Ω resistor was inserted between the current meter and the anode for protection from electrical discharge. The voltages applied between the cathode and the anode were determined by subtracting the voltage drop across the resistor from the output voltage of the high-voltage source. Here, 0.1 mm diameter {110}-oriented polycrystalline W wires were electrically etched in a 25.0 wt. % potassium hydroxide water solution and attached to the top of a W hairpin filament using a spot welder. Liquid Ga was then dripped onto the root of the W-tip to form a reservoir, as shown in Fig. 1(a). The prepared W-tip was then set into the FEM chamber. The FEM chamber was evacuated by using a turbomolecular pump. After 12h of baking at 100 °C, the residual pressure decreased to 6.0 × 10−7 Pa. To diffuse the Ga before the experiment, the W-tip was heated electrically by a hairpin filament at 0.7 A for 30 s. Scanning electron microscopy images were used to examine the tip surfaces after Ga diffusion, as shown in Fig. 1(b). The radius of the curvature at the apex was estimated at 100 nm. Ga droplets were observed on the nearby apex. The hairpin filament was kept heated (0.7 A) during the experiments for the stable supply of Ga.

Current–voltage (I-V) characteristics were evaluated using two types of anodes: Faraday cup-shaped and plane-shaped anodes. Figure 2(a) shows the emission characteristics measured using a Faraday cup-shaped anode from the bare W-tip and seven measurements made when using Ga-diffused W-tips. The emission properties were plotted with 1 / V similar to that reported by Dyke and co-workers.8 

The radius of the roughly hemispherical emission surface was 100 nm. The solid and dashed black lines in Fig. 2(a) represent CL law and 20 μA current, respectively. For the first measurement, the emission started at around 1100 V. When the emission current reached approximately 20 μA, by applying 1800 V, the curve stepped for the first time. The emission current then rapidly increased, exceeding 1.0 mA at 2800 V, before gradually slackening. The emission curve then stepped for a second time at an emission current of 2.5 mA and an applied voltage of 3100 V. Following this, the curve converged with the black line shown in Fig. 2(a). The emission curve as a function of voltage was evaluated seven times. During the second measurement, the curve shifted to a high voltage. However, after the third measurement, all the curves overlapped, as shown in Fig. 2(a). We assumed that the large emission current seen during the first measurement changed the surface morphology of the W-tip. As a result, the electric field on the cathode surface changes. However, two step changes were observed in all the measurements. The first step appeared at around 20 μA, as indicated by the dashed black line in Fig. 2(a). After the second step at several mAs, all the curves perfectly followed the black solid line, which represents the CL law, where C V 3 / 2, and C and V are the fitting constant and the applied gap voltage, respectively. The boundary transition from FE to CL has been reported by Lau et al.20 and Darr et al.14,15 The emission properties of the bare W-tip are also displayed in Fig. 2(a) for comparison with those of the Ga-diffused W-tip. It was found that all the curves mainly consisted of three states, distinguished by two lines, as shown in Fig. 2(a), and named Regions 1, 2, and 3. The curves changed from the first state, with a moderate slope, in Region 1, to the second state, with a steep slope, in Region 2. Finally, all the curves converged to the third state in Region 3.

Similar curves were observed for the plane-shaped anode [Fig. 2(b)]. However, in Region 3, the curves deviate from the CL law. For accurate measurement, the emitted electrons must be collected.

Figure 3 indicates the typical observed FEM patterns of each state. The emissions began with a few emission sites in Region 1, as shown in Fig. 3(a). This pattern was similar to unclear {110}-oriented tungsten despite the etched W-tip being covered with Ga.21 The bright areas, surrounded by dashed triangles in Fig. 3(a), correspond to the agreed {310} orientation of tungsten. The {310} orientation has a lower work function of approximately 4.3 eV in all the orientations of tungsten.22,23 Several spots appeared on {111} facets, where they stayed for tens of seconds.

FIG. 3.

Typical field emission microscopy patterns observed in (a) Range 1, (b) Range 2, and (c) Range 3. The red dashed-line triangles and the white dashed-line circle point to the {310} facets and the whole emission area, respectively.

FIG. 3.

Typical field emission microscopy patterns observed in (a) Range 1, (b) Range 2, and (c) Range 3. The red dashed-line triangles and the white dashed-line circle point to the {310} facets and the whole emission area, respectively.

Close modal

When the emission current exceeded 20 μA, by increasing the voltage, the emission state shifted to Region 2, and countless blinking spots appeared, as shown in Fig. 3(b). It was believed that every spot originating from the Ga Taylor cone and the spot could be confirmed everywhere in the emission pattern. This indicated that Ga was diffused and adsorbed everywhere, regardless of orientation. Emission from the Taylor cone–shaped liquid metal that was reported by Hata24–28 and Gotoh29 concluded that maintaining the shape is difficult for the Ga Taylor cone in a strong electric field. When a much higher voltage was applied and the emission current closely achieved the CL law, the blinking period became increasingly shorter, and multiple spots abruptly disappeared. A clear and stable FEM pattern from {110}-oriented tungsten suddenly appeared in Region 3.30 Moreover, when a higher voltage was applied in Region 3, there were no significant changes in the FEM pattern. Comparing the sizes and positions in the FEM patterns of Regions 1, 2, and 3, the emission site {310} and the whole emission area were marked with dashed triangles and circles (Fig. 3). The size of the entire emission area and the emission angle was at the same level in each region. This denoted that the shape of the apex did not change during the emission state transitions.

An orthodoxy test was conducted to evaluate whether the emission property was FN-like.16,31,32 FN current density J FN is expressed theoretically by Eq. (2) as follows:
J FN = 1.4 × 10 6 ( β V ) 2 ϕ exp ( 6.49 × 10 9 ϕ 3 / 2 β V v ( y ) ) ,
(2)
where β is the electric field enhancement factor, ϕ is the work function of the cathode material, and v ( y ) is the correction value, and the unit of measurement for J FN is A/cm2.33–35, In ( J FN / V 2 ), as a function of V 1, named an FN plot, can be fitted with a straight line. Figure 4 shows the seven-measurement current–voltage curve of Fig. 2(a) redrawn using the FN plot. Three straight lines, which were drawn in the FN plot, were observed, including the transition zone from Regions 2 to 3. The orthodoxy parameters of each line were calculated using Eq. (3), as follows:
f e x t r = 0.95 η S f i t V 1 ,
(3)
where η = 4.73, S f i t is the slope of each line, and V is the voltage. The work function was 4.3 eV for Ga.23 The obtained values used for calculation, f u p e x t r, f l o w e x t r, and S f i t, are summarized in Table I. According to Forbes’ hypothesis, if the work function is assumed to be 4.5 eV, the emission regime is considered FN-like if the parameter is between 0.15 and 0.45.31,32 Therefore, only A is within this range. This implies that the heat generation at the emission site was limited owing to the heat dissipation resulting from gallium evaporation. However, for Lines B and C, the reason for the deviation from an FN-like quality is not clear, and some points remain unresolved, such as the threshold voltage for emission being less than half that of a bare W-tip [Fig. 2(a)].
FIG. 4.

Fowler–Nordheim (FN) plot. The seven-measurement I-V curve in Fig. 2(a) was redrawn in the FN plot using In ( I / V 2 ) and V 1. The three linear portions observed are designated as Lines A, B, and C.

FIG. 4.

Fowler–Nordheim (FN) plot. The seven-measurement I-V curve in Fig. 2(a) was redrawn in the FN plot using In ( I / V 2 ) and V 1. The three linear portions observed are designated as Lines A, B, and C.

Close modal
TABLE I.

Summary of the results of the orthodoxy test on the three straight lines in the FN plot (Fig. 4). The summary includes the values used in the calculation and the orthodoxy parameters for each line.

Line ALine BLine C
1/Vhigh 0.000 274 52 0.000 337 17 0.000 436 84 
ln(I/V2)high −22.093 −26.089 −27.175 
1/Vlow 0.000 325 26 0.000 431 21 0.000 602 42 
ln(I/V2)low −25.86 −27.073 −29.757 
Sfit −74 241.23 −10 463.63 −15 593.67 
f h i g h e x t r 0.22 1.28 0.66 
f l o w e x t r 0.19 1.00 0.48 
Line ALine BLine C
1/Vhigh 0.000 274 52 0.000 337 17 0.000 436 84 
ln(I/V2)high −22.093 −26.089 −27.175 
1/Vlow 0.000 325 26 0.000 431 21 0.000 602 42 
ln(I/V2)low −25.86 −27.073 −29.757 
Sfit −74 241.23 −10 463.63 −15 593.67 
f h i g h e x t r 0.22 1.28 0.66 
f l o w e x t r 0.19 1.00 0.48 

Transitions between thermal emission, field emission, and CL law have been discussed by Darr et al.15,16 In our experiments, a similar situation can be considered at transition from Regions 2 to 3; for example, in Region 3, the emission site is heated, and thermal electron emission should be considered. If the temperature is 3695 K, the melting point of tungsten, and the electric field is 108 V/cm, the thermal emission current density is estimated to be about 104 A/cm2 by the Richardson–Laue–Dushman equation.36 However, this current density is three orders of magnitude smaller than the experimental result. It is reasonable to consider the emission regime in Region 3 as a mixed mechanism of thermal and field emissions.

Short-term current stability was evaluated by plotting the emission currents as functions of time for the Ga-diffused W-tip at various current values for 200 s in a logarithmic scale [Fig. 5(a)].

FIG. 5.

Stability of emission. (a) Emission current as a function of time for 200 s. The current was described with a logarithm scale, and (b) statistics for current fluctuations, including maximum runout, standard deviation, and percent of them, were analyzed.

FIG. 5.

Stability of emission. (a) Emission current as a function of time for 200 s. The current was described with a logarithm scale, and (b) statistics for current fluctuations, including maximum runout, standard deviation, and percent of them, were analyzed.

Close modal

There was a noticeable fluctuation in the time charts of currents lower than 1 mA. It is believed that this fluctuation originated in the Taylor cone’s formation and breakdown, as supported by the FEM pattern [Fig. 3(b)]. However, the time chart for currents greater than 1.0 mA appeared to be more stable, whereby the FEM pattern from {011}-oriented tungsten was observed in Region 3. The current fluctuations were analyzed using standard deviation (SD), the gap between the maximum and minimum current, and the ratios obtained from the SD and gap values divided by the average current [Fig. 5(b)]. The current fluctuation, which diminished when the emission current was increased, showed a rapid reduction at an average current of 3.4 mA. The ratios of the SD and the gap to the average current decreased by 2% and 10% of the initial values of 26.7% and 277.1%, respectively, at average currents of 3.4 mA and 12 nA, respectively.

We also evaluated durability. The Ga-diffused W-tip was continuously operated in Region 3, with the emission current at the phosphor screen anode set at 2.0 mA as the initial state and the cathode current achieved about 2.6 mA. However, there was a constant periodic oscillation with an amplitude of several tens of μA, as summarized by the current fluctuation from 13 to 30 h at the inset table in Fig. 5. During continuous operation, the residual gas pressure was degraded by 1.0 × 10−5 Pa by outgassing from the heated phosphor screen by electron beam injection. It is believed that one of the reasons for the lack of stability was the degradation of the vacuum. Figures 6(b) and 6(c) show the FEM patterns at the bottom and top of the periodic oscillation with cycles of about 1 h. The bottom FEM pattern from {011}-oriented tungsten is shown in Fig. 3(c). The dark areas had {110}, {211}, and {321} orientations, and the bright areas had {310} and {111} orientations. The contrast between these orientations was distinguishable, as shown in Fig. 6(b). However, at the top of the oscillation, the dark areas became bright, and the borders between the facets became less clear. The locations of the dark areas did not change in the FEM patterns. Furthermore, an outer rim began to appear, and the emission area expanded [Fig. 6(c)]. This long-term oscillation had a cycle of about 1 h. After 34 h, the anode current increased to 2.5 mA, and the cathode current rose to 3.3 mA after the applied voltage was increased to impose more load because there had been no changes in the FEM patterns and the average emission current. These conditions were maintained for 60 h. However, in the long run, no other meaningful changes were found in the FEM patterns of the Ga-diffused W-tip and the emission performance.

FIG. 6.

(a) Continuous 60 h operation in Region 3 with emission current greater than 2 mA. The inset table summarizes the statistics for current fluctuations, including the average current, gap (maximum current–minimum current), standard deviation (SD), and the percentages of gap and SD divided by average current from 13 to 30 h. Changes in the field emission microscopy patterns during continuous operation at the (b) bottom and (c) top of the oscillation.

FIG. 6.

(a) Continuous 60 h operation in Region 3 with emission current greater than 2 mA. The inset table summarizes the statistics for current fluctuations, including the average current, gap (maximum current–minimum current), standard deviation (SD), and the percentages of gap and SD divided by average current from 13 to 30 h. Changes in the field emission microscopy patterns during continuous operation at the (b) bottom and (c) top of the oscillation.

Close modal

Based on the experimental results obtained in this study, the mechanism of the Ga-diffused W field emission cathode can be considered as follows. The emission mechanism changes in three stages: field emission in the low electric field region with emission current <20 μA (Region 1), electron emission from Ga Taylor cones (Region 2), and space-charge-limited current defined by CL law (Region 3). In Region 2, a large number of Ga Taylor cones are repeatedly destroyed and regenerated, and the gallium vapor pressure increases owing to the increase in the emission current density and joule heat. The FEM pattern changes according to the W crystal facets (Region 3). The orthodoxy test results show that the emission mechanism in Region 2 is FN-like. In the transition from Region 2 to Region 3, mixed emission regimes of thermal and field emissions should be considered. Dyke et al.9–11 used pulsed operation at field emission currents >1 mA because the chip shape changed; however, the proposed Ga-diffused field emission cathode can be operated continuously for more than 60 h without any change in shape. This is because of the heat dissipation owing to a large current emission density exceeding 107 A/cm2 and evaporation of gallium atoms, which is in equilibrium with the heat generation. The hourly current fluctuations shown in Fig. 6(a) may be caused by a change in the temperature at the tip owing to the breakdown of the equilibrium condition. However, the exact emission mechanism is still unclear.

In this study, we succeeded in observing field emission completely limited by space-charge-limited current. This emission is considered to be a heat-assisted field emission phenomenon caused by self-joule heating. There is no remarkable change in the emission area even when operating in the space-charge-limited current region, indicating that this is a submicrometer sized point electron source with a large current density exceeding 107 A/cm2. The novel results obtained in this study will contribute to further improvement in the performance of an existing cathode.

This work was supported by JSPS KAKENHI (Grant No. JP22H01955).

The authors have no conflicts to disclose.

Yoichiro Neo: Conceptualization (lead); Data curation (equal); Formal analysis (lead); Funding acquisition (lead); Investigation (equal); Methodology (lead); Writing – original draft (lead). Rikuto Oda: Investigation (equal). Jonghyun Moon: Supervision (equal).

The data that support the findings of this study are available within the article.

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