Variable gaseous ion beams from plasmas driven by electromagnetic waves for nano-micro structuring: a tutorial and an overview of recent works and future prospects

In gas field ion sources (GFIS), ions are generated by field ionization on expose of gas to a high voltage ∼10¹⁰ V m⁻¹ with the help of a needle tip of tungsten having end radius ∼20–100 nm [16, 40–43]. Ion are extracted through an aperture of 0.5 mm. However, GFIS have some limitation such as: (i) tip has to be maintained at cryogenic temperature <77 K (ii) provides small beam current (∼0.1–10 pA) and (iii) therefore, leads to slow volume milling.

Liquid metal ion sources (LMIS) use a tungsten needle and liquid metal slowly come to end (tip) of the needle by capillary action, and a high voltage is applied to the extractor in the range ∼2–10 kV [16]. Due to balance between surface tension force and electrostatic (extraction) force, a conical shape 'Taylor cone' is formed at the tip, and ions come out from the tip due to field ionization. Conventionally, Ga based focused ion beams (FIB) are employed which has a few limitations such as : (i) primarily Ga ions are employed due to its low melting point ∼30 °C (ii) Ga introduces metallic contamination to the substrate [44], which can be a disadvantage in certain applications, and (iii) the beam current is small and lies in the range ∼1 pA–10 nA, therefore it takes long milling time to process the sample [17, 18].

Since plasma is a fourth state of matter and a collection of electrons, ions and neutral particles [45], ions can be extracted from matter in the plasma state. Plasmas are attractive because they can be also created of inert gaseous elements. Therefore, in order to overcome the above mentioned limitations, plasma based focused ion beams are being developed worldwide, which has the capability to address emerging research applications and can provide both non-toxic beams by the application of inert gaseous ions, and support rapid processing of materials due to availability of higher beam currents [18–22]. Currently, plasma ion beam processing is becoming increasingly important for processing biomaterials with applications in artificial heart valves and orthopedic prostheses [46]. Moreover, employing a variety of ion beams of different masses leads to controllability of the momentum transferred to the substrate and one can create structures with widely varying aspect ratios. There are different types of plasma ion sources which are briefly mentioned below.

2.3.1. Penning ion source

2.3.2. Filament driven ion source

2.3.3. RF driven ion source

2.3.4. Microwave plasma ion source

Ion energy spread (${\rm{\Delta }}E$) is an important parameter to tell about quality of the beam. Spread in ion energy is the reason of chromatic aberrations in ion beam optics. If ${\rm{\Delta }}E$ is small then almost mono-energetic beam is obtained at the target sample. ${\rm{\Delta }}E$ is measured at the extraction region of multicusp using an ion energy analyser (IEA) probe [50] and it is found to be small ∼5 eV which is comparable to conventional LMIS based FIB [61]. Figure 2 shows the ion energy distribution (IED) obtained from IEA probe where it is compared with Maxwellian (f_M) and Druyvesteyn (f_D) energy distribution having same mean energy. It is observed that low energy and high energy tail ions are absent in IED and almost mono-energetic beam with energy spread ∼5 eV is obtained [50].

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Focused beam current is another parameter which tells about current density at the target sample. It also gives an idea about milling time i.e. sample processing time is less for larger current. Beam current in microwave plasma based MEFIB system is measured using a Faraday cup and it is found to be in the range ∼5 pA–10 μA [25] which is much larger and has significantly wide range in comparison to the conventional Ga FIB (∼1 pA–10 nA) [17, 18].

Beam emittance is another figure of merit of the beam and it represents the optical performance of the beam which is the product of beam width and transverse velocity spread [62]. Beam emittance is represented more appropriately as normalized beam emittance as,

$$\begin{eqnarray}&&{\varepsilon }_{n}=4\tilde{x}\displaystyle \frac{{\tilde{v}}_{x}}{c}\approx 2{r}_{s}\sqrt{\displaystyle \frac{{k}_{B}{T}_{i}}{{M}_{i}{c}^{2}}}\left(m \mbox{-} \mathrm{rad}\right)\end{eqnarray} \tag{ 1 }$$

where, $\tilde{x}$ is the root mean square (rms) beam width and ${\tilde{v}}_{x}$ is the transverse velocity spread respectively, T_i : ion temperature, r_s : beam radius, M_i : ion mass, and c: speed of light.

Whereas a better figure of merit of the beam is brightness of the beam which is given as the ratio of beam current (I_C ) to ${\varepsilon }^{2}$ for an axisymmetric beam. Beam brightness is given as [62],

$$\begin{eqnarray}&&B=\displaystyle \frac{{I}_{C}}{{\varepsilon }^{2}}\left({\rm{A}}\,{{\rm{m}}}^{-2}\,{{\rm{rad}}}^{-2}\right)\end{eqnarray} \tag{ 2 }$$

and since ε is found to change with beam energy, therefore the normalized beam brightness B_n is defined as [62],

$$\begin{eqnarray}&&{B}_{n}=\displaystyle \frac{2{I}_{C}}{{\pi }^{2}{\varepsilon }_{n}^{2}}=\displaystyle \frac{{J}_{s}}{2\pi }\displaystyle \frac{{M}_{i}{c}^{2}}{{k}_{B}{T}_{i}}\left({\rm{A}}\,{{\rm{m}}}^{-2}\,{{\rm{rad}}}^{-2}\right)\end{eqnarray} \tag{ 3 }$$

where, J_s is the source current density. The above equation (3) is for beam brightness at source side. The image side brightness is given by [62],

$$\begin{eqnarray}&&{B}_{i}=\displaystyle \frac{{J}_{i}}{d{\rm{\Omega }}}=\displaystyle \frac{4{I}_{{\rm{C}}}}{\pi {D}^{2}}\displaystyle \frac{1}{\pi {x}_{m}^{{\prime} 2}}\left({\rm{A}}\,{{\rm{m}}}^{-2}\,{{\rm{Sr}}}^{-1}\right)\end{eqnarray} \tag{ 4 }$$

where, J_i is the current density at the image side. dΩ is the beam solid angle given as $\pi {x}_{m}^{{\prime} 2}$ where ${x}_{m}^{{\prime} }$ is the beam divergence and D is the beam diameter at the image.

The estimated reduced source side brightness for the MEFIB (${B}_{rs}=e{J}_{ion}/{T}_{i};$ where ${J}_{ion}$ is the current density at PLE aperture, ${T}_{i}$ is the ion temperature) for 1 mm plasma electrode (PLE) aperture size and ${T}_{i}$ ∼0.2 eV, is found to be ∼1 × 10⁵ Am⁻² sr⁻¹ V⁻¹, which is close to the LMIS based FIB [22].

In beam optics aberrations are found in a similar manner as in geometrical optics and parallel beams are focused at different points, which arise from (i) spherical and (ii) chromatic aberrations. Spherical aberrations occurr due to radial variation of the focusing electric field, and ions at different radial positions are focused at different positions of beam axis. The narrowest beam size i.e. diameter of the circle of least confusion defined as spherical aberration, is given by [63–65],

$$\begin{eqnarray}&&{d}_{s}=\displaystyle \frac{{K}_{s}{r}_{a}^{3}}{{D}^{2}},\end{eqnarray} \tag{ 5 }$$

where, ${K}_{s}$ is a dimensionless constant and found to lie in the range 2–10 for Einzel lenses, $D$ is a scaling parameter which is related to the axial extent of the field, ${r}_{a}$ is the beam radius at the entrance. ${d}_{s}$ is calculated for the MEFIB lens and it is found to be ∼0.008 μm where ${K}_{s},$ $D,$ and ${r}_{a}$ are taken as 10 (for decal-accel Einzel lens), 5.17 cm and 130 μm respectively.

Whereas, chromatic aberration occurr due to spread in ion energy of the beam because ${f}_{l}$ is higher for ion beam energy $E+{\rm{\Delta }}E$ than for ions having energy $E-{\rm{\Delta }}E.$ The diameter of the circle of least confusion for chromatic aberration is given by [63–65],

$$\begin{eqnarray}&&{d}_{c}={K}_{c}{r}_{a}\displaystyle \frac{{\rm{\Delta }}E}{E},\end{eqnarray} \tag{ 6 }$$

where, ${K}_{c}$ is a dimensionless factor which lies in the range 1–5 for Einzel lenses. ${d}_{c}$ is calculated for the MEFIB and it is found to be 0.125 μm where ${K}_{c},$ $E,$ and ${\rm{\Delta }}E$ are taken as 5 (decel-accel), 26 keV and 5 eV [50] respectively.

Therefore it is observed that chromatic aberration is the main reason of aberrations in ion beam optics of MEIB. The estimated maximum deviation in the focal length ($\tfrac{{f}_{l\left(E\right)}-{f}_{l\left(E\pm {\rm{\Delta }}E\right)}}{{f}_{l\left(E\right)}}$) has been found to be ∼4.5% [26].

Figure 3 shows a comparison of different ion sources for FIB applications based on figure of merit, B_rs/${\rm{\Delta }}$E² (B_rs is the reduced source brightness and ${\rm{\Delta }}$E is the ion energy spread) and focused current density [23, 66]. The performance of microwave plasma (MWP) ion source is better than conventional LMIS in terms of focused current density which can further be improved by reducing the beam size. The figure of merit, B_rs/${\rm{\Delta }}$E² of MWP ion source is comparable to other ion sources, however it has several other advantages as mentioned above and will be further elaborated in the later sections.

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To address some of the issues faced by other ion sources and meet the requirements of emerging applications, a microwave plasma based multi-element focused ion beam (MEFIB) system has been developed [24, 25, 27, 35, 36, 67–71] . The system provides variable projectile masses by employing different gaseous plasma ions and higher beam currents can be obtained. A detailed study of MEFIB system is presented in section 4.

The experimental system has mainly four parts which are: (i) plasma column, (ii) beam column, (iii) experimental chamber, and (iv) stage manipulator as shown in figure 4(a) [24, 25, 27]. In plasma column, microwaves of frequency 2.45 GHz is launched into a vacuum chamber (∼10⁻⁷ Torr) and a high-density plasma is formed, which is confined using an octupole magnetic multicusp [25]. The plasma density in the central region of the multicusp (∼r = 2–2.5 cm) is overdense for the input wave frequency (∼10¹¹ cm⁻³). The cut-off density is 7.44 × 10¹⁰ cm⁻³ for EM waves of frequency 2.45 GHz. The working pressure of the neutral gas is maintained at ∼0.25 mTorr. Typical ion and electron temperatures are ∼0.2 eV [69] and 10 eV respectively, and the plasma frequency is ∼2.83 GHz [26]. It is noted that the plasma frequency is slightly higher than the wave frequency. Wave propagation through a bounded overdense plasma has been earlier demonstrated [72]. The beam column has many electrodes which are used to extract and focus the ion beam. The first electrode which faces the plasma is called plasma electrode (PLE), and at PLE a plasma sheath is formed which further helps to extract the ions. The sheath accelerates the surrounding ions toward the PLE wall and ions emerge out through the aperture. Thereafter, decel-accel type Einzel lens [26] EL₁ is used to further extract and accelerate the ions towards the lens axis, the beam limiter (BL) trims the beam and finally EL₂ provides the required focusing field and energy to the beam [25]. In the experimental chamber, several experiments are performed such as beam current measurement and beam writing. Microstructures are created by moving the sample in X and Y directions, and the sample is positioned along the beam direction (Z-axis) using a XYZθ stage manipulator.

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For capillary guiding experiment, the beam column of the MEFIB is replaced with the capillary experimental setup as shown in figure 4(b) [26, 39]. In beam column, a plasma electrode (PLE) having central aperture 500 μm, a puller electrode (PE) and collector (C) are employed. A straight (SC) or tapered capillary (TC) of inlet ID 860 μm and variable outlet ID 860 μm–20 μm is attached to the PLE using a Perspex holder. To extract the ions, a PE of central aperture 1.5 mm is kept 8 mm away from PLE. C is kept at a gap of 6 mm from PE to measure the transmitted beam current (figure 4(b)). Insulating (Teflon) spacers are used to maintain fixed distances between PLE, PE and C as mentioned above. PE and C are commonly connected to same negative high voltage which is varied in the range 0 to −10 kV and the PLE is grounded, therefore an accelerating beam is transmitted through the capillary with the increase in PE voltage [26].

Argon plasma is ignited at neutral gas pressure at 0.25 mTorr and the microwave power of 250 W as mentioned above. Plasma sheath is created on PLE and Ar ions hit the PLE with Bohm velocity ($=\sqrt{{k}_{B}{T}_{e}/{M}_{i}},$ where T_e is the electron temperature, ${k}_{B}$ is the Boltzmann constant, and M_i is the mass of Ar ions) ∼4.9 × 10³ m s⁻¹ for a ${k}_{B}T$ ∼10 eV [36], and come out through the PLE aperture. Further, ions are accelerated by a negative voltage (V) applied to PE and simultaneously ion beam current (I_C ) is measured at C using collector current measurement unit (Ionics Ltd, India). Figure 4(c) shows different capillaries that have been fabricated for experiments, of 860 μm inlet inner diameter (ID) and of varying outlet ID as 500 μm, 300 μm, 200 μm, 110 μm, 45 μm, and 20 μm. For measurement of beam size, the beam impression is obtained by irradiating the beam for 6 min on a sample comprising of 50 nm copper thin film, which is deposited on an aluminium foil and attached to PE.

An overview of plasma generation and sustenance of the plasma in the multicusp magnetic field of the ion source is presented. It is observed that initially launched electromagnetic (EM) waves are not permitted to freely pass through the circular plasma chamber because the dimension of the chamber (referred here as a waveguide having radius R = 3.5 cm) is smaller than the cut-off radius (R_c = 3.6 cm) for the fundamental TE₁₁ mode of frequency 2.45 GHz. However, initially at the waveguide entrance, gaseous breakdown occurs due to an evanescent wave and a plasma is formed [24]. The refractive index of the medium at the entrance varies radially with the plasma density. After the formation of the plasma at the entrance of the circular chamber, EM waves can propagate though the waveguide in the peripheral regions, where the plasma density is lower and the wavelength is reduced because of the collisionally broadened upper hybrid resonance region [24]. The propagation of the EM waves is possible when λ∕λ_c < 1, where λ is the microwave wavelength in the magnetized plasma region and λ_c is the cut-off wavelength in the waveguide without any plasma [24]. It is demonstrated that at lower pressures near the peripheral plasma, the incident microwaves can propagate through the small annular windows [24]. Moreover, it has been later shown that in the presence of a magnetic field for waves launched in the k ⊥ B mode, wave propagation through a central overdense plasma is significant when the cross-sectional size of the conducting boundary of the plasma is decreased [70]. Electron cyclotron (ECR) and upper hybrid resonances (UHR) take place near the wall of the multicusp and these are the active particle generation regions. The charge particles diffuse towards the central region of the waveguide and is radially confined by the multicusp magnetic field [73]. Larmor radius of the charged particles decreases as the particles move towards the wall of the multicusp, due to increase in the magnetic field, and particles get reflected to the central region due to magnetic mirror effect. The particle loss percentage is estimated to be about 1% through the loss cones of the multicusp [74]. End plugging of the multicusp prevents axial diffusion of the particles, which is realized by reversing the polarity of the end magnets at the two ends of the multicusp [75] and in this way, a high-density plasma is confined along the axial length of the multicusp. Typically, the plasma density is found to lie in the range 10¹⁰–10¹¹ cm⁻³, and electron temperature in the range 5–20 eV which is lower at the centre of the multicusp and higher near the peripheral region where resonances occur. An almost monoenergetic (Δ E ∼ 5 eV) ion beam is extracted from the central uniform high density plasma [50].

The mechanism of beam extraction and focusing is summarized below. Ions arrive from the bulk plasma to the sheath edge of PLE with the Bohm velocity v_b (= $\sqrt{{k}_{B}{T}_{e}/{M}_{i}}$) [76]. The ions then get accelerated toward the PLE aperture from the sheath edge because of the negative potential of the PLE wall (with respect to the bulk plasma) and attain a velocity v_i , which is given by $\tfrac{1}{2}{M}_{i}\left({v}_{i}^{2}-{v}_{b}^{2}\right)=e{\varnothing }_{W},$ where ${\varnothing }_{W}$ is the wall potential of PLE. The reference is the plasma potential which is taken as zero. Further, the incoming ions from the PLE aperture are accelerated by the EL₁ voltage to a velocity ${v}_{{f}_{1}}$ given by,

$$\begin{eqnarray}&&{v}_{{f}_{1}}={\left({v}_{i}^{2}+\displaystyle \frac{2e{V}_{1}}{{M}_{i}}\right)}^{1/2},\end{eqnarray} \tag{ 7 }$$

where, ${V}_{1}$ is the voltage applied to EL₁. Since EL₁ is an accel-decel (Einzel) lens, the ions emerge out of EL₁ with velocity ${v}_{{f}_{1}}.$ The ions then get accelerated by the voltage applied to the BL aperture and come out from it with a velocity ${v}_{{f}_{2}}$ given by,

$$\begin{eqnarray}&&{v}_{{f}_{2}}={\left({v}_{{f}_{1}}^{2}+\displaystyle \frac{2e({V}_{S}-{V}_{1})}{{M}_{i}}\right)}^{1/2},\end{eqnarray} \tag{ 8 }$$

where, ${V}_{S}$ is the voltage applied to BL. Thereafter, the ions are further accelerated by the second set of Einzel lens EL₂, and finally attain a velocity ${v}_{z}$ given by,

$$\begin{eqnarray}&&{v}_{z}={\left({v}_{i}^{2}+\displaystyle \frac{2e{V}_{2}}{{M}_{i}}\right)}^{1/2},\end{eqnarray} \tag{ 9 }$$

where, ${V}_{2}$ is the applied voltage to EL₂. This is the final velocity with which ions come out from the lens and hit the target sample. From equation (9), it is seen that the final velocity of ions depends only upon ${V}_{2}$ and is independent of the intermediate voltages applied to the other electrodes (EL₁ and BL). The off axial ions are pulled toward the centre by the focusing field, which finally focuses the beam with beam energy ∼$\tfrac{1}{2}{M}_{i}{v}_{z}^{2}.$ Equation (9) is employed to calculate the total momentum transferred from the beam to the target sample in section 3.1.

Figure 5 shows the equipotential lines in the neighbourhood of each electrode, which are curved and behave like optical lenses (which focuses the optical rays) for the incoming beam. The beam is extracted, accelerated and focused due to applied electric fields, where ion beams are guided along the perpendicular direction to the developed equipotential lines in the electrostatic lens system [26].

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Beam current is measured for different gaseous plasma ion beams (Ar, Kr, Ne and H₂) for a 31 μm PLE aperture using a Faraday cup (National Electrostatics Corporation, USA). Beam current is extracted through micro apertures whose sizes are reduced to even smaller than the Debye length of the plasma. The Debye length is a plasma length scale below which external electrical disturbances are shielded off and is given by [25],

$$\begin{eqnarray}&&{\lambda }_{D}=\sqrt{\displaystyle \frac{{\varepsilon }_{0}{k}_{B}{T}_{e}}{{n}_{e}{e}^{2}}},\end{eqnarray} \tag{ 10 }$$

where ${\varepsilon }_{0},$ ${k}_{B},$ T_e and n_e are free space permittivity, Boltzmann's constant, electron temperature and electron density respectively. The PLE apertures of size 31 μm, 40 μm and 45 μm are employed in the experiments which are well below the typical Debye length of the plasma (∼100 μm for a density of 1.15 × 10¹¹ cm⁻³ and a temperature of 10 eV). Therefore, neither the plasma meniscus nor plasma-sheath interface bends near PLE aperture nor plasma leaks through the aperture and a highly directional beam is obtained [77].

Figure 6(a) shows that beam current increases with EL₁ voltage and tends to saturate after ∼1.5 kV. The observed trend is found to be similar for ion beams of each species (H₂, Ne, Ar, Kr). From the saturation region, maximum value of I_C is plotted with ion mass (${M}_{i}$), which shows that as expected, I_C is inversely proportional to the square root of ion mass (${I}_{C}\propto \,1/\sqrt{{M}_{i}}$) as shown in figure 6(b) [25, 27]. The error in the beam current measurement is very small ∼0.026 nA, which lies within the width of the symbols (figures 6(a) and (b)), and is not discernable. The beam current is measured for different EL₂ voltages (V₂) and values of saturated beam currents are found to be more or less similar and independent of V₂. Further, stability of the extracted ion beam current with time is investigated using a high precision current measurement unit (Keithley picoammeter, model 6485) at different values of EL₂ voltage in the range 18–30 kV as shown in figure 7. It is found that the beam is stable with time with a very small deviation ∼0.026 nA.

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For future applications of the beam, the sample to be processed needs to be kept at the focal point (FP). It has been found that precise determination of FP is difficult by simply creating and measuring the circular beam spots along the beam axis (Z-axis), because of over irradiation of the beam which makes accurate measurement of beam spot radius difficult near the FP [25, 78, 79]. Therefore, a method involving minimum irradiation time is considered for FP determination, because beam current density is highest at FP and the beam can create a spot in minimum time [25]. In order to experiment this, beam writing is carried out as shown schematically in figure 4(d), by moving the sample in X and/or Y direction with different writing speeds in the range 1.5–15 μm s⁻¹ and by placing the sample at different axial (Z) positions. Computer controlled LAB-VIEW program is used to move the sample in X and Y directions with the help of XYZ $\theta$ stage manipulator where X and Y directions are perpendicular to the beam and Z is along the beam axis. The created beam impressions (lines) are analysed under the optical microscope and minimum irradiation time is calculated using ${t}_{\min }=D^{\prime} /{v}_{\max },$ where $D^{\prime}$ is the line width of the created line at maximum writing speed ${v}_{\max }$ for creating a clear line. The line width $D^{\prime}$ is measured using ImageJ software [80]. From figure 8, FP is found to be 6.7 mm away from the last electrode of EL₂ for 40 μm PLE and 26 keV beam energy. FP is determined for different PLE aperture sizes and beam energies, and while performing experiments, the samples are kept at the determined focal point.

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Then sample is kept at FP and beam writing is performed for 40 μm PLE aperture. Lines are created on Cu thin films of thickness ∼150 nm, for different writing speeds (dwell time) using 26 keV, Ne, Ar and Kr ion beams. The aspect ratio a_r (line width/depth) of the created lines is calculated and it is found that variable high aspect ratios in the range ∼100–1000 are realized in the created structures as shown in figure 9(a) [25]. For Ar ion beams, distinct lines are obtained at higher writing speed, because Ar has a combination of beam current and ion mass such that the mass is not as small as that of Ne ions nor the obtained current is as low as that for Kr ions. a_r is found to be higher for Ne ion beams because Ne has higher beam current (∼20 nA) and therefore higher line width due to self-coulomb repulsion and smaller line depth because of lower ion mass are realized. Grating like microstructures are created on 50 nm Cu thin film employing 26 keV Ne, Ar and Kr ion beams for 40 μm PLE as shown in figures 9(b)–(d) [25]. To calculate the impact of the beam on the target sample and to determine the efficacy of beam processing, a parameter called 'current normalized force (CNF)' which is the total momentum transferred per unit time, normalized with the beam current, given by [25], Reproduced from [Maurya S K, Paul S, Shah J K, Chatterjee S, and Bhattacharjee S 2017 Momentum transfer using variable gaseous plasma ion beams and creation of high aspect ratio microstructures J. Appl. Phys. 121 123302], with the permission of AIP Publishing.

$$\begin{eqnarray}&&\gamma =\displaystyle \frac{\,p}{t\,I}=\displaystyle \frac{N{M}_{i}{v}_{z}}{t\,I}\left[\displaystyle \frac{2\cos {\theta }_{\max }+{\sin }^{2}{\theta }_{\max }+4}{3\cos {\theta }_{\max }(1+\cos {\theta }_{\max })}\right],\end{eqnarray} \tag{ 11 }$$

where, p, N, ${M}_{i},$ t and I are transferred momentum, number of ions and ion mass, beam irradiation time and beam current respectively and ${\theta }_{\max }$ is the maximum beam angle at FP, is defined. ${v}_{z}$ is determined from equation (9). Detailed calculation of CNF can be found in [25].

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The beam size can be further reduced by employing capillary at the exit of the PLE, this reduces the beam source size and enhances the demagnification of the lens. Therefore, micro-glass capillary guiding is demonstrated below for different smaller capillary outlet IDs.

The ion beam guiding capability of insulator capillaries has become a subject of interest [33–39, 81–88] after the first observation of keV ion beam guiding through nano-capillaries by Stolterfoht et al [33]. In the early work [33], it is reported that the capillary inner wall gets charged while beam transmission and the initial charge state of the ions are maintained throughout the capillary. This guiding capability offers an unique opportunity to manipulate the beam by varying the capillary geometry (outlet inner diameter size). The beam guiding capability is also investigated by tilting the capillary up to tilt angle ±100 mrad and maintaining the initial charge state [34]. Capillaries of tapered geometry have been used to generate microbeam [34] and nanobeam [81, 82]. There are reports of ion beam guiding through a curved capillary [83, 84] which may be used as a beam bender like optical fibre. Charged particle guiding has applications such as beam steering [85], focused charge particle beams [38, 86], including biological applications such as irradiation of single living cells [87].

Therefore, to further reduce the final beam size of MEFIB, micro-glass capillary can be employed to reduce the source size without significant loss in beam current. Before implementation, guiding capability of plasma ion beam through micro-glass capillary is investigated. The experimental details are mentioned in section 4.1. Current density at the capillary outlet, which is a ratio of the beam current to the capillary outlet area, is measured for capillaries of different outlet inner diameters. Beam transmission is found to occur when the ion energy is greater than a certain threshold voltage as shown in figure 10(a). It is observed that the current density increases with decrease in capillary outlet ID because of loss less guiding of the ion beams, and a high current density is obtained ∼600 Am⁻² for 20 μm capillary outlet ID [39]. It is found that the ratio of the outlet to inlet current density η > 1 for each capillary outlet ID employed in the experiments, i.e. guiding is efficient. The value of η is a measure of the guiding capability of the capillary for ion beams [35, 83, 88].

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Directional guiding capability of the capillary is also demonstrated by tilting the capillary of outlet ID 200 μm [39]. Capillary is tilted from −5° to +5° in step of 2.5° relative to incident beam direction and beam spots are created on Cu thin film deposited on Al foil substrate by maintaining the extraction voltage at 10 kV. The step size is chosen as 2.5° because a small capillary of length 7.5 mm and outlet inner diameter (ID) 200 μm is employed and the sample is kept maintaining a gap of ∼0.5 mm from the capillary outlet. Therefore, for a smaller step size of tilt angle (∼1°), the vertical distance of shifted beam spot is only ∼136 μm from the center of beam axis. Hence, beam spots for tilt angles of ∼1° may overlap at these small angular step sizes for the 200 μm capillary outlet ID. Moreover, when we tilt the capillary with an angle $\theta ,$ the ion beams hit the target sample with an angle (90−$\theta$), which results in elliptical spot size and may artificially increase the beam spot size. Therefore a step size of 2.5° was chosen to avoid spot size overlapping.

Variation of beam deflection angle with capillary tilt angle is shown in figure 10(b), which demonstrates that beam is guided well along the tilt direction of the capillary [39]. Therefore, capillary guiding of the beam is found to be efficient. Beam spots for different tilt angle is shown in the inset of figure 10(b).

Hysteresis in beam current with extraction voltage (ion energy) is observed as shown in figure 11(a) and the mechanism of hysteresis is explained below [34, 35, 39]. While increasing the extraction voltage V, charges start to accumulate on the inner wall of the capillary and a retarding potential barrier develops and therefore beam transmission through the capillary is difficult and beam current is negligible until about 8 kV. When ion energy becomes greater than the retarding potential barrier, most of the deposited charges diffuse to the electrode and a sudden increase in beam current is observed; this particular extraction voltage is called 'upper threshold voltage'. While decreasing V, beam current is obtained up to 2 kV because retarding potential barrier has decreased due to diffusion of deposited charges, and therefore hysteresis is observed due to dissipation of charges [39]. The sharp decrease in current occurs at a particular voltage called 'lower threshold voltage'. Dissipated charge is calculated from the hysteresis area by dividing the area into n vertical strips of width ΔV and heights I_k↑ and I_k↓ , where I_k↑ and I_k↓ denote beam current while increasing and decreasing V for k^th strip, and is found to be [39],

$$\begin{eqnarray}&&Q=\displaystyle \frac{{\rm{\Delta }}t}{{\rm{\Delta }}V}{P}_{d},\end{eqnarray} \tag{ 12 }$$

where, Δt is the time taken to increase the extraction voltage by ΔV, P_d is the dissipated power which is the hysteresis area. The dissipated charge Q is calculated from equation (12) for different capillary outlet IDs as shown in figure 11(b) and it is observed that the dissipated charge is maximum for 300 μm capillary outlet inner diameter, because of higher hysteresis area which is a combined effect of higher beam current and large difference in lower and upper threshold voltages.

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Further, created beam spots on Cu thin film (thickness ∼50 nm) deposited on Al foil substrate for different capillary outlet ID, are analysed under optical microscope (Carl Zeiss, AXIO imager.A1m). Variation of beam size (experimental and theoretical) with capillary outlet ID is investigated and shown in figure 12(a), it is found that the spot size decreases with decrease in outlet ID. The theoretical beam spot size is calculated from the knowledge of theoretical self focusing factor F (calculated below using PIC simulation) and capillary outlet ID ${d}_{o}.$ Experimental spot size (${d}_{s}$) is fitted with a nonlinear equation as shown below [39],

$$\begin{eqnarray}&&{d}_{s}=a\left(1-{e}^{-\alpha {d}_{o}/{d}_{\max }}\right),\end{eqnarray} \tag{ 13 }$$

where, ${d}_{o}$ is the capillary outlet ID and it is a variable here, a = 140.92 μm and $\alpha$ = 8.39 are constants and ${d}_{\max }$ is the maximum value of ${d}_{o}$ i.e. inlet ID of the capillary ∼860 μm.

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A self focusing of the beam inside the capillary is observed i.e. spot size is obtained to be smaller than the outlet ID of the capillary, and maximum compression of beam obtained is ∼81% for 860 μm capillary outlet. Therefore, a parameter called self focusing factor (F) is defined to investigate the self focusing effect and given as [39],

$$\begin{eqnarray}&&F=\displaystyle \frac{{d}_{o}}{{d}_{s}}.\end{eqnarray} \tag{ 14 }$$

where, d_o and d_s are capillary outlet ID and corresponding spot size respectively. When, d_o = d_s and F = 1, unfocused parallel beam is expected. From figure 12(b), it is observed that F decreases linearly up to ∼300 μm capillary outlet ID, and then it is observed to vary nonlinearly with decrease in capillary outlet ID and finally tends to saturate for a capillary outlet ID of around 20 μm. For smaller capillary outlet, beam is compressed in a smaller region at the outlet, and therefore self-coulomb repulsion in the beam increases. The inward radial focusing force due to accumulated charges on the capillary wall is then unable to further compress the beam, therefore, F is found to decrease with decrease in capillary outlet ID and tends to unity for smaller outlet ID (20 μm) [39], which could indicate in the self-focusing limit.

Further, self focusing factor is calculated theoretically. There are three types of forces inside the capillary which guide the ion beam : (a) radially inward coulomb force due to accumulated charges on the capillary inner wall (b) radially outward self-coulomb repulsion force due to charges in the beam and (c) axial force ${F}_{a}$ due to applied potential to the electrodes [39]. It is assumed that the current density $\vec{J}$ flows in the z-direction and because of $\vec{J},$ a magnetic field ${\vec{B}}_{\theta }$ is generated in the $\theta$ direction. Therefore, a pinch force $\vec{J}\times \,{\vec{B}}_{\theta }$ (Nm⁻³) on the ion beam acts in radially inward direction which compresses the beam and is calculated by ampere's law. $\vec{J}\times \,{\vec{B}}_{\theta }$ force of a considered beam volume of length 100 μm near the capillary outlet is obtained as ∼2.6 × 10⁻²⁰ N, whereas resultant radial force ${F}_{r}$ on a single ion due to (i) accumulated charges on the wall and (ii) self-repulsion force in the beam, obtained from PIC simulation is ∼2.3 × 10⁻¹⁴ N which is in radially inward direction. Therefore, ${F}_{r}$ is significantly larger than the pinch force and in radially inward direction, therefore ions follow the trajectory inside the capillary due to resultant radial (${F}_{r}$) and axial force (${F}_{a}$) [39].

To calculate the self-focusing factor theoretically in terms of radial and axial force, spot radius and distance of the sample from the capillary outlet, it is assumed that beam gets self focused with an angle $\theta$ during beam transmission as shown in figure 13. Here, L is the distance between sample and capillary outlet, ${R}_{S}$ and ${R}_{O}$ are the measured beam spot radius and capillary outlet radius respectively. The self focusing factor is found as [39],

$$\begin{eqnarray}&&F=\displaystyle \frac{L}{{R}_{S}}\left(\displaystyle \frac{{F}_{r}}{{F}_{a}}\right)+1.\end{eqnarray} \tag{ 15 }$$

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F is calculated for different capillary outlet IDs (figure 12(b)) where values of ${F}_{r}$ and ${F}_{a}$ are taken from particle in cell (PIC) simulations, which is carried out as described below. Figure 12(b) shows that calculated F matches well with the experimental F and follows similar behaviour. F is also calculated by considering 10 times lower and higher beam current in the simulation and it is found that F is higher for higher current because of deposition of charges on the capillary inner wall and corresponding ${F}_{r}$ increases for larger beam current [39].

Particle in cell (PIC) simulation is carried out to understand the underlying physics of the capillary guiding of ion beam [34, 35, 39]. It self-consistently calculates the potential, electric field and ion trajectory for the input beam inside the capillary. The 2D simulation code developed in house, considers the azimuthal symmetry for parallel and collinear axis of the capillary and beam. The region of interest has been divided into 325 × 925 square grids of grid size 0.02 × 0.02 mm² where grid parameter h is chosen to be 0.02 mm. The potential at each grid point (I, j) is calculated by solving Poisson's equation and using successive over relaxation method [89], where the over relaxation coefficient (w) is taken as 1.95 for fast convergence. Potential ${{\rm{\Phi }}}_{i,j}$ at each grid point (I, j) for a charge density ${\rho }_{i,j},$ is given as,

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{\Phi }}}_{i,j}=\left(1-w\right){{\rm{\Phi }}}_{i,j}+\displaystyle \frac{w}{4}\left[\left(1+\displaystyle \frac{0.5}{i-1}\right){{\rm{\Phi }}}_{i+1,j}\right.\\ \,+\,\left.\left(1-\displaystyle \frac{0.5}{i-1}\right){{\rm{\Phi }}}_{i-1,j}+{{\rm{\Phi }}}_{i,j+1}+{{\rm{\Phi }}}_{i,j-1}+\displaystyle \frac{{h}^{2}{\rho }_{i,j}}{{\varepsilon }_{0}}\right],\end{array}\end{eqnarray} \tag{ 16 }$$

where, ${\varepsilon }_{0}$ is the free space permittivity and equation (16) is solved until a stable solution is obtained.

PIC simulations are performed for different capillaries to investigate the self focusing and guiding of the beam. Figures 14(a)–(d) shows the charges distribution inside the capillary and figures 14(e)–(h) shows ion beam trajectory through the capillary, which clearly demonstrate the self focusing of the beam though the capillary. From figure 14, it is observed that self focusing decreases with decrease in the outlet ID and matches with experimental results as shown in figure 12(b) [39].

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The axial and radial fields obtained from the simulation are employed to calculate ${F}_{r}$ and ${F}_{a},$ which are used in equation (15) to calculate the self focusing factor. As mentioned earlier, the parametric dependence of beam current on F is investigated by taking 10 times higher and lower beam current than the experimental beam current in the simulation as shown in figure 12(b).

Further, as discussed in section 1, the sample is kept at the focal point (for fabrication) to get a maximum current density (small milling time) and minimum beam size (highest resolution). Therefore, a detailed study of focal point is needed. To address this, effect of plasma and beam parameters on focal dimensions in MEFIB system are presented below.

Effect of plasma parameters and beam parameters on focal dimensions are investigated [26]. Variation of focal length with ion mass and beam energy is shown in figure 15, which are plasma and beam parameters respectively where applied voltages to EL₁, BL and EL₂ lenses are tabulated in table 2. Focal length (f_l ) is found to depend on ion mass and increases with decrease in ion mass, because energy of ions are higher for light mass ions as reported earlier (cf figure 4 of [90]) and f_l is proportional to the initial ion energy E_i [2]. f_l is also found to decrease with beam energy (EL₂ voltage) because at higher value of EL₂ voltage, the focusing field is strong and focuses the beam closer to the last electrode of EL₂. The focal length is investigated using experiments, simulations and theoretical calculations, and the results are shown in figure 15. AXCEL-INP and SIMION beam simulation tools are used to estimate the beam size and focal length. Theoretical calculation of focal length is carried out by employing thick lens method of optics and transfer matrix method for ion beam [63, 91, 92]. Detailed calculations may be found in reference [26].

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The negative high voltages applied to the different electrodes are tabulated in table 2.

Variation of beam size and corresponding demagnification (beam size/PLE aperture) with plasma electrode aperture size is investigated and the results are shown in figure 16. It is observed that for plasma based MEFIB, sudden decrease in beam size is observed below the Debye length (∼100 μm) and enhanced nonlinear demagnification (beam size/PLE aperture) is obtained because penetration of electric field into the plasma becomes weak for plasma electrode (PLE) apertures below the Debye length, and beam extraction decreases and therefore beam size due to reduction in space charge effects [26].

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Next the effect of the BL aperture size on the beam size is investigated. The BL aperture size is varied in the range 50 μm–260 μm for different PLE aperture size (∼40 μm–250 μm). At first the beam current is measured using the Faraday cup (FC) and thereafter beam spots are obtained on Cu thin films. Figure 17 shows the beam current measurement result for 100 μm PLE, and 50 μm, 100 μm and 260 μm BL aperture sizes. It is observed that with decrease in BL aperture size, beam current is found to decrease, as smaller BL trims the beam. In figure 17, sudden increase in current is observed at a particular value of EL₁ voltage when the beam gets focused and maximum current is registered in the FC. Thereafter, as the EL₁ voltage is increased further the beam gets defocused at the BL aperture and the current decreases due to interception of the beam by the BL. For 50 μm BL, the aperture size is very small to extract the beam and therefore results in a small current ∼5 pA. Further, SIMION beam simulation is carried out, which shows trimming of beam with increase in EL₁ voltage as shown in figure 18. Variation of beam current with PLE aperture size is also studied for 260 μm BL, and has been shown in [26].

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Further the beam spots are created on 50 nm Cu thin film for 100 μm PLE, and 260 μm and 100 μm BL aperture sizes. As observed in the figure 17, the beam current decreases with decrease in BL aperture size and therefore corresponding space charge effects also decrease, hence the beam size (beam diameter) is found to reduce (∼1.3 μm) for 100 μm BL, as compared to ∼6.24 μm for the 260 μm BL aperture size, as shown in figures 19(a)–(b).

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Beam spots are also created by reducing PLE aperture size (source size) and minimizing the space charge effects. Source size is reduced by employing 50 μm PLE and space charge effects are minimized by trimming the beam using 140 μm BL aperture size (small beam current ∼20 pA). A submicron size beam (diameter ∼600 nm) is obtained which is analysed under scanning electron microscopy (SEM) as shown in figure 19(c).