Potential of a cerium hexaboride electron gun as a monochromatic and high current beam via a virtual source mode

Abstract

Advancements in surface science hinge critically on the evolution of high-performance electron sources, which are essential for achieving the precision level and resolutions required for nanoscale characterization, modification, and fabrication. Cerium hexaboride (CeB₆) electron guns, despite being underutilized, stand out for their advantages such as high brightness and operability under high-vacuum environment. This study explores the intrinsic properties and emission conditions of CeB₆ electron guns, demonstrating their remarkable performance potential. By carefully controlling the heating temperature and local electric field in a novel virtual source mode, we significantly enhance the electron emission characteristics of CeB₆ as a thermal electron source. Operating in the proposed virtual source mode, CeB₆ electron guns can reduce chromatic aberrations, offering significant opportunities for high-resolution patterning, spectroscopy, and applications requiring high emission currents. The micrometer-sized electron source exhibits a high angular current density of 48 mA/sr and an energy distribution of 0.32 eV. Additionally, the stability of the virtual source mode was determined to be ± 0.071% at a beam current of 370 nA, a substantial improvement over the ± 0.36% stability value in the crossover mode. With the development of the proposed electron source, new avenues for advanced material characterization, nanoscale fabrication, and precise modifications of material properties will be explored.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-37502-1.

Introduction

From basic science to advanced industry, the performance of electron sources has played a key role in technology fields such as electron microscopy^1,2, lithography^3,4, particle accelerators^5,6, electron beam machining^7–11, and irradiation^12–16. As electron source technology advances, key properties such as the electron beam brightness, angular current density, energy distribution, and source size strongly affect the performance capabilities of the electron guns used in advanced equipment¹⁷. It should be noted that the properties of the electron beam may vary not only depending on the type, configuration and operation mode of the electron source but also based on the structure design of the electron gun¹⁸. Therefore, the configuration and operating conditions of the electron source should be chosen and set appropriately to optimize them for the application at hand. Electron sources are broadly classified into three types, each distinguished by its unique properties. These main types are the field emission (FE)¹⁹, extended Schottky emission (ESE)²⁰, Schottky emission (SE)²¹, and thermal electron emission (TE)²¹. FE occurs when an electric field (> 10⁹ V/m) is formed at the tip of a sharp point, causing electrons to be emitted mainly through quantum mechanical tunneling¹⁹. Electron sources, using the FE principle have been employed in high-resolution microscopy due to their excellent brightness, coherence, and narrow energy distribution (< 0.4 eV)²². Despite their excellent electron-optical properties, FE electron sources have disadvantages, such as requiring an ultra-high vacuum (UHV) (< 10^{− 8} Pa) environment for operation and current instability due to tip surface contamination¹⁹.

To overcome the limitations of FE electron sources, significant efforts have been made. Various high-performance FE electron sources have been developed, such as individual carbon nanotubes (CNT)^22,23, tungsten (W) nanowires²⁴, and LaB₆ nanowires^25,26, including automated mild flashing types²⁷. More recently, conical nanoneedle- or nanotip-based electron sources fabricated by focused ion beam techniques have been reported to further enhance emission stability, brightness, and energy spread^28–30. These devices exhibit improved performance outcomes, such as high brightness, a narrower energy distribution and better stability. Among them, CNT and W nanowire types still require UHV conditions to operate as well as periodic heating. Additionally, some of these sources require complex tip manufacturing processes. As a result, the zirconium oxide/tungsten (ZrO/W) Schottky electron source based on the ESE principle is the mostly widely used type in imaging and metrology instruments due to the excellent stability of the beam-current, despite its relatively low brightness, wider energy distribution and larger source size compared to the FE case. However, the ZrO/W Schottky electron source still requires a UHV component²⁹. State-of-the-art electron sources are predominantly based on field emission, providing nanometer-scale effective source sizes, high brightness, and narrow energy spreads under ultra-high vacuum conditions. Most commercial field emitters are based on the (310) surface of W single crystals. In addition, conical nanoneedle- or nanotip-based electron sources fabricated by focused ion beam techniques have been reported to further enhance emission stability, brightness, and energy spread^31–34. In contrast, the CeB₆ virtual source mode, while not reaching the ultimate performance of field emission–based emitters, offers significantly improved characteristics compared to conventional thermionic crossover modes, together with highly stable operation under relatively relaxed vacuum conditions. This combination makes the CeB₆ virtual source a practical and complementary solution for modern electron-beam instrumentation.

A typical TE type of electron gun has a structure that uses a Wehnelt electrode which creates a crossover point forward relative to the electrode, with the electrons emitted from a heated emitter, after which the electrons are accelerated, passing through the anode³⁰. This method is referred to as the crossover mode and features an electron-optical system that reduces the source size. This mode is characterized by a high emission current, but it has the disadvantages of low brightness, a large source size, and a wide energy distribution³⁵. These parameters limit the spatial resolution and image contrast in high-resolution microscopy and lithography applications. Cerium hexaboride (CeB₆) is a type of electron source that utilizes the TE phenomenon^36,37. It operates on a principle similar to that of the tungsten (W) hairpin and has been traditionally used in the crossover mode with Wehnelt electrodes. In terms of cost, CeB₆ is more expensive than W hairpins, but it is preferred in certain applications due to its stability, higher brightness, and smaller source size. However, compared to FE or ESE sources, it remains challenging to apply CeB₆ to high-performance equipment.

In this research, a new electron gun structure was constructed to explore the unveiled potential of the CeB₆ (CeBix^®: Applied Physic Technology) electron source, termed the ‘virtual source mode of CeB₆’. The virtual source mode proposed in this study refers to an operating mode of the electron gun in which, when the electron beam trajectories are traced backward, the electrons appear to originate from a single point located in front of the actual tip surface, as shown in Fig. 1b and Fig. S11(d). In this mode, electrons diverge without forming a crossover, which eliminates electron crowding near the Wehnelt electrode. When the electron trajectories are extrapolated backward, a very small virtual source point is defined within the tip region. Owing to this geometric characteristic, a reduced energy spread, high angular current density, and stable emission behavior can be achieved. The virtual source mode uses the ESE principle³⁸. This principle combines FE and TE through a pointed tip to generate an electron beam with a high angular current density and narrow energy distribution. This approach not only achieves superior high-resolution patterning in applications requiring high currents but also improves precision and selectivity in spectroscopy and diffraction experiments. Using a CeB₆ electron source with an elliptical flat shape, a high angular current density and monochromatic energy distribution were achieved by emitting the electron beam without crossover. This configuration allows for the application of electric fields greater than 10⁸ V/m to the tip, enabling more precise control of the electron gun properties. Compared to conventional crossover modes, the improved emission current (> 3 mA) and reduced virtual source size may be capable of achieving higher beam brightness. We confirmed the excellent performance of the CeB₆ electron source in this modified electron gun structure using a pre-lens retarding field energy analyzer (RFEA)^39,40. Capable of observing changes in electron emissions due to variations in tip temperatures and electric fields, the pre-lens RFEA used here serves as an important tool for optimizing the performance capabilities of electron guns and analyzing the parameters that affect the electron emission. The virtual source mode of CeB₆ enables smaller effective source sizes, and its improved electron emission characteristics lay the foundation for achieving higher resolutions and enhanced beam focusing compared to the crossover mode. We expect that this approach will pioneer new levels of precision and clarity in applications requiring delicate electron beam manipulation.

Fig. 1.

Schematic of the CeB₆ electron gun and its operating modes.

Results

Composition of the CeB₆ electron gun

In our experiments, the CeB₆ electron gun operates in a chamber maintained under a high vacuum of under 10^{− 5} Pa using an O-ring. Its properties are evaluated using a custom-made pre-lens RFEA. For additional information, readers can refer to the literature⁴⁰. The tip temperature, which varied as the current of the floating heating power supply was adjusted from 1.3 to 1.7 A, was measured using a pyrometer (TR-630D; Minolta), as shown in insets of Figs. 1a and b. The measurement results showed that the tip temperature range was 1300 to 1700 K, as shown in Supplementary Fig. S2. Figures 1c and d show SEM images of the CeB₆ electron source, which has an oval-shaped facet. The minor axis was measured and found to be 3.4 μm, and the measurement of the major axis showed a value of 5.8 μm. This becomes an important parameter when estimating the local electric field applied to the tip in a commercial OPERA-3D simulator (Opera; Dassault Systèmes UK Ltd.: Kidlington, UK). The band diagram presented in Fig. 1e is a conceptual illustration intended to express the differences in potential barrier under the operating conditions of each emission mode employed in this study. In the crossover mode, the electron beam is controlled by the Wehnelt electrode to form a crossover, while the anode electrode is operated at ground potential. Under this voltage configuration, the local electric field applied to the CeB₆ tip remains relatively weak. In contrast, in the virtual source mode, a strong local electric field is generated at the cathode tip by the voltage applied to the extraction electrode, which in turn induces the experimentally observed reduction in the potential barrier. Therefore, the differences between the two operating modes arise from the local electric field distributions determined by the electrode configuration and voltage application conditions adopted in this study. The energy distribution represents the probability distribution of electrons emitted by heat or an electric field from the Fermi sea of a metal into a vacuum, as shown in Fig. 1e. In the crossover mode, the energy distribution broadens as electrons emitted by heat form a crossover through the electron-optical system. This distribution follows a Gaussian shape rather than the familiar Maxwell-Boltzmann (MB) distribution. In the virtual source mode, a local electric field strength () is applied by the extraction voltage (V_E), effectively reducing the work function by ⁴¹. This clearly distinguishes between electron emission from a thermal electron source and electron emission by an electric field.

1

(a) Illustration of the crossover mode and (b) the virtual source mode. The distance between the tip and the Wehnelt electrode is D_W, and the voltage applied to the Wehnelt electrode is V_W. The distance between the tip and the suppressor electrode is D_S, and the voltage applied to the suppressor electrode is V_S. The inset images show pictures captured by a pyrometer through a viewport. The two electrodes are insulated from each other and are fixed to a piezo stage. The distance between CeB₆ and the electrodes can be adjusted by the piezo stage. (c), (d) SEM image of the CeB₆ tip in two different views. (e) Qualitative illustration showing the electron emission mechanism of CeB₆ in each operating mode. The work function of the CeB₆ electron gun in the virtual source mode is reduced by depending on the electric field strength, and electron emission by heat and electron emission by the electric field can be distinguished.

The principle of electron emission from a metal heated in a vacuum can be explained by the Richardson-Dushman equation and the effective work function () is expressed as follows:^41,42

2

3

In the Richardson-Dushman equation, each element represents a specific parameter, where is the Richardson constant, is the tip temperature, is the Boltzmann constant, e is the electron charge, is the work function of the metal, and is the permittivity of the vacuum. The effective work function of the electron source can be estimated from the Richardson-Dushman equation, and the total emission current and Richardson plot as a function of tip temperature are given in Fig. 2b. The slope of the plot is , from which the work function of the material can be obtained. The intercept, ln (), provides the Richardson constant. For each electron gun condition, ten measurements of the tip temperature (T)-total emission current (I) characteristics were taken, and the mean value and standard deviation of the effective work function were obtained from ten Richardson plots. Figure 2 shows the average data of the ten T-I characteristic and Richardson plots for each condition. A detailed description of the effective work function is given in Supplementary Note 1. The T-I characteristics appear similar when D_W = 200 and 100 μm with the Wehnelt voltage (V_W) at − 490 V in the crossover mode, and the effective work function is also the same at 2.651 eV, as shown in Figs. 2a and b. The total emission current characteristic depends on V_E of the electron gun, and as V_E increases, the T - I characteristic improves at a suppressor voltage (V_S) of − 510 V. The effective work function of the electron source was observed to decrease from (2.642 ± 0.019) eV to (2.611 ± 0.015) eV. The effective work function tended to decrease with V_E in the virtual source mode. Additionally, from the Richardson plot, applied to the micrometer-sized tip of the CeB₆ electron source is estimated to be 10⁷–10⁸ V/m as V_E increases from 200 V to 800 V. We can also confirm that the Richardson constant increases from 114 to 180 A/(cm²žK²). In classical theory, is defined only through fundamental physical constants and material properties. However, in the CeB₆ electron gun operating in the virtual source mode, the material properties of the electron source, particularly the work function, are influenced by V_E. This leads to a discrepancy between the theoretical and experimental values of . Therefore, the electron emission model of the virtual source mode cannot be fully described by the TE model. To provide a comprehensive understanding of the CeB₆ electron gun in the virtual source mode, the SE model should be applied. The current density of the SE model is expressed as follows:^43,44

4

5

Fig. 2.

Electron emission characteristics.

In the SE model, is the effective mass of the electron and h is Planck’s constant. The dimensionless parameter , which is one of the indices of electron emission due to the tunneling effect, is included to express the ESE model. The current density depends on the dimensionless parameter , which determines the boundary of the SE or ESE regions, with the boundary condition of equal to 0.3³⁸. In the virtual source mode of the CeB₆ electron gun, when V_E = 800 V, applied to the tip was 1.31 × 10⁸ V/m, resulting in = 0.113. Although this value is too low to apply the ESE model, it is clear that V_E affects the electron emission, even with a small contribution from the FE. These aspects are discussed in more detail in the section describing the energy distribution analysis.

Electron emission characteristic with the gun structure

The distance between the electron gun and the pre-lens RFEA is 180 mm, and the aperture size is 0.5 mm. In our measurement setup, the semi-angle of the electron beam is defined as 1.3 mrad, as shown in Supplementary Fig. S6. Therefore, the solid angle of the electron beam measured in the RFEA is 6.06 × 10^− 6 sr. A detailed description of the solid angle is given in Supplementary Note 2. Figure 2c shows the changes in the beam current and angular current density related to the potential difference between the CeB₆ tip and the electrode, with the tip temperature maintained at 1600 K and the acceleration voltage at -500 V. In the crossover mode, it is observed that the angular current density increases as the electrode approaches the tip when D_W = 0, 100, and 200 μm. V_W shows the highest beam current around − 490 V. As V_W approaches the acceleration voltage, the beam current tends to decrease rapidly, and when it exceeds the acceleration voltage, the beam current approaches zero current. This occurs because when V_W is higher than the acceleration voltage, electrons are repelled near the Wehnelt electrode and cannot be emitted outside of the electron gun. Therefore, the voltage of the Wehnelt electrode is important to create a crossover point while efficiently extracting the generated electrons. On the other hand, in the virtual source mode with = − 100 and − 200 μm, the Wehnelt electrode is located behind the tip and acts as a suppressor from that position, similar as in standard Schottky electron gun. Its function applies when voltage exceeding a certain threshold (relatively high compared to the acceleration voltage) is applied. When this occurs, a zero field is formed by the potential difference between V_S and V_E. Based on the zero field, electrons can be emitted from the front of the tip, and electrons can be prevented from being emitted from the side of the tip. Therefore, unlike in the crossover mode, the beam current does not converge to zero current, even when V_S reaches − 600 V, and the maximum beam current also appears higher than in the crossover mode.

The virtual source mode of the CeB₆ electron gun shows a tendency for the angular current density to increase linearly as increases, as shown in Fig. 2d. When = − 100 μm, the angular current density shows a linear increase up to about = 400 V, after which the slope decreases and the increase becomes more gradual. However, when D_S = − 200 μm, it increases linearly to 800 V, resulting in a higher observed angular current density. This increase occurs because decreasing (e.g., from − 100 to − 200 μm) physically reduces the spacing between the tip and the extraction electrode, placing the electrode closer to the emitter and thereby strengthening the local extraction field . The maximum angular current density was measured and found to be 89 mA/sr. When = − 300 μm, the tip and extractor electrode spacing becomes too small, and the large number of electrons emitted from the heated tip leads to a rapid build-up of space charge in the narrow gap. This leads to an unstable extraction condition where the beam current suddenly drops to zero, which is detected as a short-circuit behavior. Thus, under our experimental conditions, the optimal configuration for the virtual source mode of the CeB₆ electron gun is D_S = − 200 μm. A commercial ESE electron gun with a ZrO/W Schottky electron source was used to verify the measurement precision of the custom-made pre-lens RFEA fabricated for this study. For the Schottky electron gun, the full width at half maximum (FWHM) of the energy distribution was measured and found to be 0.92 eV at a tip temperature of 1800 K, an acceleration voltage of − 500 V, a V_E value of + 2500 V, and an angular current density of 91 µA/sr. After this calibration step, we measured the energy distribution of the CeB₆ electron gun and determined its accuracy and reliability by comparing it with known reference points provided by the Schottky electron gun^40,44.

(a) Electron emission characteristics from the CeB₆ cathode as a function of the tip temperature. In the virtual source mode, V_S is maintained at -510 V.( b) Richardson plot. (c) Comparison of the current and angular current density according to the operating mode. (d) Angular current density variation with V_E in the virtual source mode.

To analyze the energy distribution, we performed simulations using the commercial program OPERA-3D, which employs the 3D finite element method, as shown in Supplementary Fig. S8. This program is suitable for calculating the detailed local electric field distribution induced by an applied field for given 3D structures. As shown in Fig. 3a, the model structure of the CeB₆ electron source consists of a suppressor electrode and an extraction electrode with a 1 mm hole and a 0.4 mm gap between the electrodes, identical to the experimental setup. We obtained the contour map of around the tip end with an oval-shaped geometry, as presented in Fig. 3a. The cross-sectional graph along the black dashed line in Fig. 3b and the corresponding V_E dependence are presented in Fig. 3c. These results showed that the maximum that formed at the edge of the tip under an applied field V_E of 800 V is 1.31 × 10⁸ V/m. Under a range of V_E values of 200, 400, 600, and 800 V, the corresponding range of was found to be 10⁷~10⁸ V/m, in good agreement with the experimental range derived from the Richardson plot in Figs. 2a and b. Differences in the energy distribution due to are explained in Supplementary Note 4.

Fig. 3.

Computational simulations of local electric field () at the CeB₆ tip surface.

(a) Model structure of the virtual source mode CeB₆ electron gun used for the simulation. (b) Calculated field distribution contour map at the tip apex. (c) Simulation results for the electric field distribution across the cross-section of the CeB₆ tip surface (black dashed line in (b)) depending on V_E.

Experimentally measured energy distribution of the CeB₆ electron gun using the pre-lens RFEA

The energy distribution was measured with a custom-made pre-lens RFEA, as shown in Supplementary Fig. S7(a). The pre-lens RFEA consists of a lens, GND, retarding, and collector electrodes, and a shield surrounding them. The shield-lens-GND electrode acts as a focusing unit and the GND-retarding-collector electrode measures the energy distribution of the focused electron beam as a retarding unit. We record the pre-lens RFEA collector current (I_C) - retarding voltage (V_R) curve, and differentiate it to measure the energy distribution, as shown in Supplementary Fig. S7(b). For detailed measurement methods, readers can refer to Supplementary Note 3. The energy distributions of the CeB₆ electron gun according to D_W in the crossover mode are shown in Figs. 4a and b. At V_W = − 490 V, as D_W increases to 0, 100, and 200 μm, the angular current density decreases and the FWHM of the energy distribution narrows. The FWHM was confirmed to decrease from 1.1 eV to 0.85 eV. This indicates that as D_W becomes relatively distant, the emission current decreases and the degree of the electron-electron interaction becomes smaller, resulting in a narrower energy distribution. In the crossover mode, when the electron beam passes through an electrostatic lens, such as a Wehnelt electrode, electron-electron interactions inevitably occur at the crossover point. These interactions can lead to an increase in the energy distribution and a decrease in the beam coherence, which is unsuitable for electron beam-based equipment requiring a narrow FWHM and high brightness⁴⁵. The Boersch effect was experimentally investigated in the past using Schottky electron emission sources⁴⁶. Barth and Nykerk proposed a bell-shaped function, to describe the Boersch effect, which accounts for the broadening of the electron beam energy distribution due to electron-electron interactions⁴⁷.

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Fig. 4.

Analysis of energy distributions in different two modes.

Here, is the energy of the electron beam, and the function is characterized by two shape parameters: the FWHM of energy distribution and the shape factor . Jansen’s research on electron-electron interactions identified four distinct regions, which can be distinguished based on the particle density and beam geometry. When the values are 0.63, 1, and 2.17, they correspond to pencil beam, Lorentzian, and Holtsmark (bell-shaped) distributions, respectively. If exceeds 5, it represents a Gaussian distribution⁴⁸. In the crossover mode at V_W = − 490 V, the highest angular current density was 43 mA/sr at a tip temperature of 1600 K, and the measured energy distribution width was 0.88 eV, as shown in Fig. 4b. At a tip temperature of 1600 K, the MB distribution (black dash line) width is calculated and found to be 2.45, which is 0.338 eV^49,50. This indicates that the expansion of the FWHM of the energy distribution is due to the Boersch effect (red dash line) in the crossover region. In the crossover mode, the FWHM () of the energy distribution measured in Eq. (6) was substituted, and fitting was performed while varying the shape factor . In this case, D_W changed to 0, 100 and 200 μm and, the optimized shape factor value decreased to 6, 5.5 and 5, respectively, as shown in Fig. 4a. Under the D_W = 100 μm condition, the result shows an expansion of the energy distribution of 0.54 eV towards the low energy region and 0.34 eV towards the high energy region based on the acceleration voltage at the crossover point. Figure 4b shows that in the crossover mode at the D_W = 100 μm, as V_W approaches the acceleration voltage, the energy distribution narrows and becomes similar to the MB distribution. At this point, the value of the Boersch effect decreased to 5.5, 2, and 1 as the energy distribution decreased to 0.88, 0.55, and 0.4 eV, respectively. In accordance with above energy distribution values, the shapes of the energy distribution are matched in the order of Gaussian, Bell-shape, and Lorentzian respectively. The energy distribution narrows due to the decreased electron-electron interactions. Ultimately, the electron beam is detected only by TE, and the energy distribution is formed in an energy region higher than the acceleration voltage. The crossover mode allows for control of the electron beam with a simple electrode configuration, but it has the disadvantage of a rapidly broadened energy distribution as the angular current density increases.

On the other hand, the virtual source mode of the CeB₆ electron gun shows an asymmetric energy distribution rather than the Gaussian shape. The energy distribution expression of the ESE should consider the effects of the tip temperature and local electric field. Therefore, the intrinsic total energy distribution (TED) of the ESE is expressed as follows:^20,35

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In this equation, is the electron energy and (Eq. (1)) is the Schottky reduction of the work function barrier. Even in the virtual source mode, electron-electron interactions still exist due to the high angular current density. Fitting of the energy distribution using the intrinsic TED does not match the experimental results, as shown by the black dashed line in Figs. 4c and d. In particular, the energy distribution becomes broad in the low energy region, which is the field-induced electron emission region. Therefore, the energy distribution considering electron-electron interactions can be fitted as . Based on obtained from OPERA simulation results, the FWHM value of the intrinsic TED is calculated. The obtained FWHM() is then substituted into Eq. (6) and convolution fitting is conducted while varying the value to match the experimental results.

(a) Energy distribution dependence on D_W in the crossover mode. Energy distribution measured when V_W = − 490 V and at a tip temperature of 1600 K. The energy distribution shows a Gaussian shape due to electron-electron interactions at the crossover point. (b) Energy distribution dependence on V_W in the crossover mode. Comparison of experimental measurements with Maxwell-Boltzmann (black dash line) and Boersch effects (red dash line). When the acceleration voltage and V_W become equal, only electron emission due to a TE characteristic appears. (c) Experimentally measured energy distributions of the virtual source mode of CeB₆ electron gun with different tip temperatures. Measured under the conditions of V_E = 600 V, D_S = − 200 μm the FWHM of the energy distribution increases by 0.02 eV as the temperature increases by 100 K. (d) Energy distribution of the virtual source mode of CeB₆ electron gun under varying V_E conditions. This was measured at a tip temperature of 1600 K and with = − 200 μm and the monochromatic energy distribution shows a FWHM of 0.32 eV with an angular current density of 48 mA/sr at = 200 V. Fit results obtained by fitting the convolution (blue solid line) of the intrinsic TED (black dash line) and the Boersch effects (red dash line) to the experimental energy distribution using two fitting parameters ( and 1/).

The energy distribution of the virtual source mode was measured at an acceleration voltage of -500 V and when D_S = − 200 μm and V_S = − 510 V. Figure 4c shows that as the tip temperature increases at V_E = 600 V, the energy distribution shifts to a higher energy region relative to the acceleration voltage. The FWHM values of the energy distribution at tip temperatures of 1500 K, 1600 K, and 1700 K are 0.55 eV, 0.57 eV, and 0.59 eV, respectively. It can be seen that the energy distribution broadens in the high energy region, indicating that the probability of TE increases as the tip temperature increases. This phenomenon is consistent with the trend of broadening at 0.02 eV considering the energy at 2.45 when the tip temperature increases by 100 K.

When the tip temperature is 1600 K and V_E = 600 V, is 0.112. For the Boersch effect, is 2.5, and a bell-shaped function is applied, resulting in the fit represented by the blue solid line. The fitting results are in good agreement with the experimental data, which allows us to determine the contribution of the Boersch effect in the virtual source mode of the CeB₆ electron gun. When the tip temperature changes to 1500, 1600, and 1700 K, the Boersch effect tends to increase to 0.36, 0.37, and 0.38 eV, respectively. The energy distribution measured by increasing V_E in Fig. 4(d) tends to increase from 0.32 eV to 0.63 eV. Unlike the change in the tip temperature, it does not broaden by a consistent amount but rather widens sharply from V_E = 600 V. Additionally, there is a small shift in the peak position from − 500.05 V to − 499.75 V towards the low energy region. At V_E = 200 V and at 400 V, the energy distribution is similar to the intrinsic TED, and the Boersch effect appears to be almost non-existent. However, under the conditions of V_E = 600 and 800 V, the FWHMs resulting from the intrinsic TED are 0.347 and 0.348 eV, respectively, and the corresponding Boersch effect values are 0.367( = 2.5) and 0.383( = 1.8) eV. The root power sum of the FWHMs of the intrinsic TED and the Boersch effect is a suitable fitting method when the distribution has a Gaussian shape²¹. For a bell-shaped distribution, only the FWHM result obtained through convolution fitting matches the experimental value.

The energy distribution due to the Boersch effect in relation to the tip radius has been reported in studies of ZrO/W Schottky electron sources⁵¹. In nanoscale electron sources, the Boersch effect increases rapidly with an increase in the current, while the effect decreases as the tip radius increases from 300 nm to 4.2 μm. The virtual source mode of the CeB₆ electron gun shows a pronounced Boersch effect starting at 75 mA/sr. The virtual source mode of the CeB₆ electron gun exhibits narrow energy broadening, even at high angular current densities, compared to the ZrO/W Schottky electron source, due to the relatively large tip diameter. This larger diameter reduces the electron density at the emission surface⁴². Additionally, unlike in the crossover mode, the peak position of the energy distribution shifts and responds sensitively to changes in the tip temperature and V_E. Although TE dominates in the virtual source mode, the electric field applied to the tip also induces electron emission. This results in a narrower energy distribution compared to that in the conventional crossover mode.

Figure 5a presents an experimental comparison of the energy distributions of a CeB₆ electron gun with different operating modes (crossover mode and virtual source mode) and a ZrO/W Schottky electron gun. The comparative analysis was conducted at an acceleration voltage of 500 V, with measurements taken under typical scanning electron microscope (SEM) operating conditions (1800 K, V_E = + 2500 V, V_S = -300 V) as mentioned above. The energy distribution for the virtual source mode of CeB₆ is 65.2% shorter at half maximum than that for a ZrO/W electron gun. The trend, which includes reference data of 19, 20, 28, and 49, can be seen in Fig. 5b, where the energy spread for the CeB₆ electron gun increases as the angular current density increases. The virtual source mode of CeB₆ provides a much narrower energy distribution compared to other electron emission sources, demonstrating excellent performance. This mode is suitable for a high-resolution structural analysis and is also expected to have significant potential for applications in material synthesis using high-current electron beam irradiation^12–16. (a) Electron energy distribution from CeB₆, (Crossover and virtual source modes) and the Schottky emitter at angular current densities of 43 mA/sr, 48 mA/sr and 91 µA/sr., (b) Dependence of the energy spread ΔE on the angular current density and its comparison with a W, (310) and Schottky emitter.

Fig. 5.

Comparison of energy distributions.

Stability and SEM imaging

Stability is a critical factor determining the reliability of all advanced analytical instruments. Figures 6a and (b), present the results of the stability evaluation conducted. In the crossover mode(V_W = − 490 V), the average angular current density for one hour was 43.4 mA/sr, with a sample standard deviation of ± 0.16 mA/sr, resulting in a relative standard deviation of ± 0.36%. The virtual source mode (V_S = -510 V, V_E = 400 V) showed a higher average angular current density of 61.0 mA/sr for one hour, with a sample standard deviation of ± 0.043 mA/sr. At this point, the relative standard deviation was ± 0.071%, demonstrating that the virtual source mode provides more stable operation compared to the crossover mode. Figure 6b shows a comparison of the stability for both modes for ten minute period. Each data point represents the average stability for ten minutes, with the sample standard deviation for that period shown as an error bar. Despite the beam current exceeding 100 nA in the virtual source mode, it demonstrated stability of (369.64 ± 0.26) nA, corresponding to a relative standard deviation of ± 0.068%. In this study, the crossover mode and the virtual source mode were implemented by adjusting only the inter-electrode distances and voltage application schemes while maintaining the same cathode and electrode configuration. The CeB₆ electron source used in this work operates at an elevated temperature of approximately 1700 K; therefore, surface condition changes due to impurity adsorption during emission are considered to be suppressed. In the crossover mode, electron trajectories converge in front of the Wehnelt electrode to form a crossover region with high electron density. Under these conditions, the potential difference between the cathode and the Wehnelt becomes relatively small, and the electrons pass through a space-charge-dominated region at low energy. In contrast, in the virtual source mode, electron emission is controlled by a stronger local electric field than in the crossover mode. The electron is emitted divergently and distributed spatially, and the space charge is not concentrated at a specific location. Additionally, the electron is accelerated to higher energy in the vicinity of the cathode. These differences of two modes in electron density distribution and sensitivity to electric field variations suggest that the emission characteristics and stability of the electron gun may vary depending on the operating mode.

Fig. 6.

Stability and SEM imaging.

The key is to find an optimal balance between the energy distribution and the angular current density

In order to verify the excellent characteristics of the CeB₆ electron gun in the virtual source mode, we compared SEM images of different operating modes. The SEM images were acquired using a custom-made SEM column consisting only of a scanning coil, an objective lens, and a secondary electron detector operating at a low acceleration voltage of 2.0 keV. This SEM is described in detail in Supplementary Note 5. The electron gun and specimen chamber were maintained at around 10^− 5 Pa, and the electron beam generated from the emitter is focused on the specimen surface by a single objective lens. Depending on the operating mode of the electron gun, the secondary electron images exhibit distinct differences, as shown in Figs. 6c and d. Tin-on-carbon particles (AGS1967; Agar Scientific) were used as the specimen for comparison. For the crossover mode, V_W was maintained at − 1.98 kV. The image of in the crossover mode was blurred due to the relatively large source size. In contrast, the virtual source mode produced a sharper image using the same SEM column, with the resolvable distance between two tin particles was measured and found to be 52 nm at a V_S value of − 2.05 kV with a V_E equal to + 400 V, as shown in the inset image of Fig. 6d. From this experiment, we were able to confirm that the source size in the virtual source mode is much smaller than in the crossover mode. In this study, SEM images were acquired using the same electron optical column while only the operating mode of the electron gun was changed. Accordingly, the achieved resolution of 52 nm reflects the difference in electron gun characteristics under identical column conditions. It should be noted that the electron optical system employed here was intentionally simplified as a minimal column designed to compare electron gun performance, rather than to achieve the ultimate resolution of a fully optimized commercial SEM.

(a) Stability comparison between crossover and virtual source modes for one hour. The stability outcomes are ± 0.071% and ± 0.36% in the crossover mode and the virtual source mode, respectively. (b) A short-term stability comparison was carried out across these configurations for 10 min at each point. The stability of the virtual source mode is ± 0.068%, and that of the crossover mode is ± 0.24%. (c) A low-voltage SEM image of a tin particle-on-carbon specimen taken in the crossover mode via the custom-made SEM. Scale bar: 3 μm, magnification: ×10,000, acceleration energy: 2.0 keV, working distance: 4.1 mm. (d) SEM image of the same sample taken using the virtual source mode in the custum-made SEM. Scale bar: 3 μm, magnification: ×10,000, acceleration energy: 2.0 keV, working distance: 4.2 mm. The inset shows an enlarged view of the region indicated by the black rectangle.

Discussion

We have realized a virtual source mode for a CeB₆ electron gun with an unprecedentedly high angular current density of 48 mA/sr and a monochromatic energy distribution of 0.32 eV as an example of a new utilization of a thermal electron source. Given that stable operation is possible even under a high vacuum (10⁻⁵ Pa), it has the advantages of operability in a chamber composed of O-rings and easier maintenance compared to UHV conditions. Furthermore, through a Richardson plot and a simulation, it was verified that an electric field of 10⁸ V/m can be applied even with a large tip size in the micrometer range. Therefore, it is possible to analyze the degree of energy distribution broadening via the Boersch effect, which requires accurate electric field information. By establishing the virtual source mode operation as realized here, we have enhanced the functional range of thermal electron guns and demonstrated a method for achieving higher efficiency and stability in practical applications. The significantly reduced energy spread and high angular current density characteristics of the virtual source mode open up significant opportunities for advanced electron beam irradiation and precision patterning.

Methods

Structure of the CeB₆ electron gun

We fabricated the CeB₆ electron gun, designed to operate with the selection of the crossover or the virtual source mode. Figures 1a and b show schematic diagrams of the electron emission in these two operating modes. Two electrodes are fixed and move together along the optical axis with a piezo stage (GO-LLS4545HVH; PRECIBEO). The two electrodes have a hole with a diameter of 1 mm and a thickness of 0.3 mm, with a fixed distance of 0.4 mm between them. The piezo stage can be used to move these electrodes simultaneously, allowing them to be positioned closer to or further away from the electron source. The insets in Figs. 1a and b show the CeB₆ emitter heated during the emission of the electron beam. The two electrodes can move in real time, enabling switching between the operating modes. In this research, as shown in Fig. 1a, the distance between the tip and the Wehnelt electrode in the crossover mode is denoted by D_W. Conversely, in Fig. 1b, which shows the virtual source mode, the Wehnelt electrode is positioned behind the tip to act as a suppressor, and the distance is denoted by D_S. In the virtual source mode, the electrode behind the tip acts as a suppressor, while the second electrode serves as an extractor electrode. The virtual source mode effectively utilizes the voltage tuning function of the suppressor to control the electron emission from the facet surface of the emitter.

Electron emission and energy distribution measurements using the pre-lens RFEA

The electron emission properties of the CeB₆ electron gun were measured in a vacuum chamber at a pressure level of 10^− 5 Pa. Supplementary note 2 provides a schematic of the experimental electron gun setup, utilized to analyze the performance of the CeB₆ electron source. This aperture size and distance between the aperture and CeB₆ cathode determine the divergence angle of the electron beam. When measuring using the pre-lens RFEA as a Faraday cup, positive voltage was applied to the lens electrode to measure the current.

To measure the energy distribution, the pre-lens RFEA must be aligned parallel to the optical axis of the electron gun, and for this purpose, an analyzer was mounted on a stage that can be adjusted along three axes, X, Y, and Z. The energy distribution can be calculated by measuring the graph of I_C versus the retarding voltage V_R. The differentiation of the I_C-V_R curve obtained in this way provides the measured energy distribution as described in Supplementary note 3. Before the measurement, the pre-lens RFEA was calibrated using a ZrO/W Schottky electron gun.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

H.R.L. and Y.H. performed the experiments and simulation. T.O., J.W.L. and J.H. contributed to the preliminary characterization of the electron gun properties. H.R.L., T.O., and I.Y.P performed the experimental data analysis with the help of D.J.Y. and H.J., and S.L. assisted the experiment set up and vacuum system control. S.P supported the simulation analysis. H.R.L., T.O., I.S. and I.Y.P. wrote the manuscript based on the discussions with the other authors. I.Y.P and S.L supervised the study. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Ministry of Science and ICT, (Project No.: RS-2022-CP000123) and Commercialization Promotion Agency for R&D Outcomes(COMPA) and the Technology Innovation Program (IRIS number: RS-2024-00419426, Development of light-electron beam based measurement and analysis instrument technologies for advanced packaging) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea).

Data availability

The datasets used and/or analyzed of this study can be obtained from the corresponding authors on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.