The Development of Ion Nano-beams-A Review

With the advent of the super-tip ion source very favourable conditions for generating ion nano-beams have been provided. The basic physical principles for a super-tip-gas field ion source are described As a consequence of a very small source emittance of ε ~ 10 msr ultra-bright rare gas ion beams of about 10 A/m.sr can be produced. As a further consequence, very narrow probe sizes are obtainable, of dp< 1 nm, with spatial resolutions far below the classical limits of light-optics and even below the novel stimulated-emission-depletion microscopy [*STED (microscopy) = stimulated emission depletion (microscopy) Th. A. Klar, S. W. Hell, Opt.Lett. 24 (1999) 954-956]. Various ion-nanobeam applications in both materials modification, and analysis are envisaged.


Introduction
The fundamental question of how to generate ion nano-beams is intimately connected with the ionisation mechanism of the source operated with gaseous media.
The decisive figure of merit is beam emittance, which controls the properties of the image spot, e.g. the diameter of the beam probe.If nanometre dimensions are intended, almost all presently known ion source types can be excluded because of very unfavourable emittance figures.So far, only by using very narrow apertures, with concomitant high losses of intensity, fine ion beams have been obtained, as often practised in PIXE applications.Thus, the only remaining option is the development of the Müller field-ion microscope, with proven atomic resolution, to an efficient gas field ion source.It is the aim of this paper to follow this development over a period of more than 10 years.

Base Tip Preparation
The central element of a gas field ion source, GFIS, usually is a 111-monocrystalline tungsten wire of a few tenths mm in diameter with an acute tip.The starting base tip can be produced by anodic dissolution of W in a solution of NaOH within a few minutes of exposure to dc or pulsed-current treatments.Tip radii of 100-1000 nm are readily obtaind by electrolytic etching.(S.Pinter, 1985)

Formation of the Super-tip
The experimental set-up is shown in fig1.(K.Jousten, K. Böhringer, & S. Kalbitzer, 1988).It provides both cooling to low cryogenic temperatures and heating to about 2500 K. Also high voltages of U ~ 50 kV can be applied.While Müller's ion-field microscope is useful for exploration of atomic surfaces with atomic resolution, the emitted ion beam, however, comes from a large number of emission sites distributed over the apex zone.With a regular W-tip He + emission occurs over a broad angular range of α/2 ~ 50°.
For use as an ion source, however, both emission angle and number of emitting sites have to be strongly reduced in order to provide a high-brightness beam and also an intense ion probe.The experimental task, therefore, has been to produce a single emitter point with a small virtual source size as illustrated by fig. 2. This goal can be achieved by a relatively complex procedure to form the so-called super-tip.(K.Jousten, K. Böhringer, & S. Kalbitzer, 1988).First experimental attempts along these lines, however, did not result in long-term stable protrusions.(P.R. Schwoebel, & G.R. Hanson, 1985) In a short description, the etched tip has first to be cleaned from any adhering impurity layer by heating to about 2500 K for a few minutes.Thereafter, the tip is operated in the electron emission mode in a He atmosphere of about 0.1 Pa.He ions generated by electron impact are accelerated back to the tip, where W surface atoms, created by impact of He + , diffuse at temperatures of T ~ 1000 K to preferred crystallographic surface sites.Within one minute's time they self-organise into a nano-crystalline structure, constituting the super-tip.While single W adatoms, lacking bulk binding forces, constitute less stable configurations against thermal and electrical attack, the crystalline structure of our super-tip offers enhanced stability against all desorption processes.Because of the rapid increase of the electron emission during super-tip formation, as fig. 5 demonstrates, a fast switch-off of the bias volt has to be performed in order to prevent thermal self-destruction of the growing super-tip.(R. Börret, 1989) A single emission centre of a super-tip was displayed on the phosphorescent screen of fig. 1. (K.Jousten, 1987) The spot diameter was 1.1mm at a distance of 0.07m, so that the emission half-angle amounts to α/2 ~ 0.55.10 -3 /0.07~ 0.08.mrad.Thus, the goals of fig.4 appear feasible.An ion-field micrograph of this super-tip with He as imaging gas is shown in fig.4, displaying a W. nano-crystallite of about 100 W-surface-atoms on top of the initial apex of the base tip.(Th. Miller, 1996).This is established by all experimental observations with our multi-atom super-tip for all rare gas elements.Fig 5 is a statistical survey over about 40 super-tip formation sites placed within an average angular range of about 10° off the center direction of 111-tips.(Th. Miller, A. Knoblauch, & S. Kalbitzer, 1997)

Current-field Characteristics of GFIS Sources
The thermal gas supply to the emitter shank is given by the relation where the atomic velocity v is given by v= (2kT/m). 1/2 (2) The flux enhancement factor σ(Φ) contains the variable Φ = ½αF 2 /kT, the ratio of the gas polarisation energy ½.αF 2 and the thermal energy kT.Φ is the most important parameter for a gas field ion source controlling both gas supply to and an efficient transport along the tip surface to the emitting apex.As suggested by fig. 9 the exposed emitter area of a hemispherical tip-surface, with a diameter of d~300 nm, is estimated as A~¼πd 2 ~8.10 -14 m 2 , respectively.Using the approximation for a paraboloidal emitter tip (H. A. M, van Eekelen, 1970): we note that σ(Φ) substantially enhances the gas flow to the emitter area.For σ(0) and a gas pressure of 0:1 Pa J 0 amounts to roughly 3.10 19 at/s.m 2 , and with v~10 3 m/s and Φ ~20 we have j(Φ) ~ 6.10 23 at/m 2 .s.Thus, the total gas flow to a tip area of about 10 -13 m 2 amounts to about 6.10 10 at/s.orroughly to an electrically equivalent ion current of 10 nA for a fictitious 100% ionisation yield.Figs.6 and 7 confirm the linear dependence on gas pressure in (1) with very strong emission currents of up to j(H 2 + ) ~ 100 nA at 0.1 Pa.Table 1 provides a survey over some basic rare gas properties.In agreement with experimental data, we see that the supply gas flow (1) approximately depends on the quantity ρ ~ α 2/3 /m 1/2 ~ 0.2 Å 2 /amu 1/2 for all heavier rare gases at same source operation conditions.Thus, we very roughly expect similar current-field characteristics for all of them.In general, the very steep rise of j(F) observed at the lower electrical fields levels off at higher fields.Explanations invoking temperature independent tunnelling processes, however, have to be replaced by loss of adsorbed gas atoms from the surface with an activated exponential temperature dependence, as will be shown below.In the flat region of supply limited current a linear dependence on gas pressure exists as shown in fig 11.Fig. 8 shows two typical I(V) characteristics of H 2 + at different gas temperatures of 90K and 270K.We note that σ(Φ) can explain the observed current differences.(H. A. M, van Eekelen, 1970) It is interesting to see from fig. 9 that tip geometry has a strong influence on the emitted current intensity: I ∞ r t 2 , indicating spherical supply areas.(R. Börret, 1989)

Beam emittance and brightness of super-tips
With the above value of α/2 ~ 8 mrad and a calculated virtual source size of d ~ 1Å, the emittance amounts to 10 -24 m 2 srd (S.Kalbitzer & A. Knoblauch, 2004) which is the most important parameter for the design of a low aberration ion optical column.Assuming probe currents of up to 10 nA the correlated brightness amounts to B = I/ε < 10 16 A/m 2 sr, hitherto unparalleled by any other particle source, as shown in fig.12.

Optical consequences
A tip surface of a hemi-sphere of A ~ 1.10 -13 m 2 captures about 3.10 11 atoms/s.with a minimum of r min = 0.773 , where r 0 and α 0 are the key constituents of the correlated source emittance ε.Fig. 13 is a plot of probe size d p and correlated probe current I p vs. convergence angle α p .(S. Kalbitzer, 2004) Employing the emittance variable ε for the limiting cases of purely chromatic and spherical aberrations d Legge, 1996) we clearly see that a major reduction of source emittance is absolutely necessary to a sizeable improvement of former probe spots of d p ~ 30 nm to presently d p ~1nm.
We note that the tip geometry enters eq(3).as the target area of the incoming gas flux.In particular, experimental findings show a dependence on the tip radius by r t 2 as shown above by fig.9.(R. Börret, 1989) For conservative values of the aberration coefficients C c = 0.1 m and C s = 1 m we find with η:~ 10 -5 limiting values of d c ~ 2 nm and d s ~ 2 nm, i.e. resolutions in the atomic regime.Thus, a GFIS* promises intense Xenon beam-probes of nano-metre dimensions.
There is some uncertainty about the diffusion behaviour of Xe on W surfaces.(R.Gomer, 1961) While Kr and Ar exhibit relatively low diffusion activation energies of Q D ~ 40 -30 meV, Q(Xe) ~ 130 meV is distinctly higher.(R.Gomer,1961).Nevertheless, as fig.14 shows, even for Q D values of 80, 100 and 130 meV probe currents of j(Xe) ~ 5nA are possible with appropriately chosen super-tip temperatures and fields.

Thermodynamic theory of a GFIS*-source
The emitter current is given by the integral over several physical processes: where z is the distance from the emitter apex, A(z) the tip surface elemental area, F the electrical field strength, T the tip temperature, j 0 the gas kinetic supply from the gas phase, σ the field enhancement factor of gas supply, θ the Langmuir equilibrium state of occupied surface states, η the transport efficiency of adsorbed atoms and ζ the ionisation probability at the super-tip.Ion source properties: Current: I < 10 − 8 A, source emittance:10 − 24 m 2 sr, source brightness: B = I/ε < 10 16 A/m 2 sr.
Fig. 12 presents a comparison of different types of ion sources and emphasizes the unique properties of our GFIS*.
A(z) is the tip surface elemental area.A detailed description of the functions in the above integral was published elsewhwere.(S.Kalbitzer, 2004).Here we just emphasize that the predicted steep slopes of dI/dF = m range up to m= 60 in the low field emission regime compatible with experimental observations.Also, emitter currents of the system Ar-W with a paraboloidal emitter shape are correctly predicted as of the order of I ~ 10 nA in the supply limited regime.In conclusion, we maintain that eq.( 3) is a valid description of the GFIS* emitter current.strength.(S.Kalbitzer, 2004;Th. Maisch, et al., 1991;S. Kalbitzer & A. Knoblauch, 2004;S. Kalbitzer & V A. Zhukov, 2011)
In final conclusion, rare gas ion nano-beams constitute a unique tool for materials nano-research and technology.
Fig.13 displays probe diameters and correlated current intensities as a function of the probe convergence angle.(S.Kalbitzer & V A. Zhukov, 2011).The above figures are very consequential for ion probe dimensions.A general estimate of limiting probe spot radii r p = d p /2 reads (G.F. J.Legge,

Figure 1 .
Figure 1.Experimental set-up for super-tip production

Table 1 .
Rare gas properties