Understanding how the liquid-metal ion source works

Vacuum/volume 48/number l/pages 85 to 9711997 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0042-207x/97 $17.00+.00

Pergamon PII: SOO42-207X(96)00227-6

Understanding works* R G Forbest, University Surrey

GU2 5XH, UK

received

27 February

how the liquid-metal

of Surrey,

Department

of Electronic

and Electrical

ion source Engineering,

Guildford,

7996

There is some interesting physics in how the liquid-metal ion source (LMIS) works. This short review describes our current understanding, covering the following topics. Distinction between the real Taylor-Gilbert cone and Taylor’s mathematical cone. Thermodynamic origin of the pressure-difference formula. Shape of an operating LMIS: the cusp-on-a-cone as expected shape and as an electrically driven vena contracta. Onset behaviour and Taylor’s slender-body formula. Ion energy distributions, and interpretation in terms of surface processes and space-charge. Swanson’s proof that the emission mechanism is field evaporation. Predicting the low-current Ga LMIS apex radius as 1.5nm. The low-current Ga LMIS as a device driven by a negative pressure of order 40atm. Re-examination of Mair’s formula for LMIS current/voltage characteristics, and the role of space-charge. Cusp length as a function of emission current: theory and modelling. Emitter stability and control mechanisms: space-charge stabilisation, inertial/geometrical stabilisation, pressure-change destabilisation. Secondary emission phenomena: electrons, neutrals and photons. The high-temperature anomaly in the ion energy distribution, and a possible explanation. Instability and the formation of microdroplets and nanodroplets. Numerical modelling of basic LMIS behaviour: current/voltage characteristics for sources with and without viscous drag; modelling of cusp length and limiting half-angle; modelling of time-dependent effects. Current research tasks. Copyright 0 1996 Elsevier Science Ltd

Introduction A liquid metal ion source (LMIS) produces an optically bright, finely focused, ion beam. These sources now have many practical applications, well surveyed elsewhere,‘x2,3 that include scanning ion beam instruments and integrated circuit mask repair. Over the years, steady progress has been made in establishing how the LMIS works. Obviously, one hopes that a better understanding of LMIS behaviour may lead to improvements in the design both of sources and of the associated Focused-Ion-Beam (FIB) systems, to improvements in their methods of use, and to clearer interpretation of experimental results. In addition, the liquid-metal ion source is a fascinating device involving some very complex physics, and physical understandings gained from LMIS studies can be applied in other areas, notably to electrostatic atomisation. The paper is intended as a short review, with some tutorial content. An elementary familiarity with the technological facts

*Based on an invited paper presented at the 9th International School on Vacuum, Electron and Ion Technologies (VEIT’95), organised in Sozopol, Bulgaria. in September 1995, by the Bulgarian Academy of Sciences. tE-mail: R.Forbes(@ee.surrey.ac.uk.

of LMIS construction and operation is assumed. The paper discusses the main features of LMIS behaviour and the related physical explanations, outlining background theory as appropriate and indicating where current understanding is still incomplete. Conventions of the International System of Measurement, including use of rationalised equations, are followed.

Background Gilbert’s cones and Taylor’s cones. A liquid under the influence of strong electric forces adopts a roughly conical shape. This effect was first reported by Gilbert,4 in 1600. The first person to produce an adequate theory was Taylor.’ in 1964. He showed that an exact conical solution of Laplace’s equation was possible under very special circumstances, simulated these circumstances in experiments, and observed conical shapes. Hence experimentally-observed electrified liquid cones are often called ‘Taylor cones’. However, Taylor notes that Gilbert reported them first, so I prefer to call these observed shapes ‘Taylor-Gilbert cones’, and reserve the name ‘Taylor’s mathematical cone’ for Taylor’s theoretical shape. The special circumstances required by Taylor’s mathematics are that the hydrostatic pressures inside and outside the surface of the liquid cone be everywhere zero, that the surface tension of 85

R G Forbes: Understanding

how the liquid-metal

ion source works

the liquid be a constant (i.e. not be a function of the local electric field value or of the surface radii), that the cone be infinite in extent, and that the counter-electrode have the shape of one of the family of electrostatic equipotentials to which the cone itself belongs. It also needs stressing that Taylor’s solution applies to the static situation where there is no liquid flow and no ion emission. In these circumstances, Taylor showed that there is a cone half-angle &, approximately equal to 49.3’, at which the liquid cone is in mechanical equilibrium, with the ‘inwards’ surfacetension forces on the liquid surface exactly balanced everywhere by the ‘outwards’ electrostatic (Maxwell) forces. &is now known as the ‘Taylor angle’. It is not implied here that this equilibrium is necessarily stable, and Taylor’s analysis did not investigate this issue.

The liquid-metal ion source. A liquid-metal ion source (LMIS) produces ion emission from the apex region of a liquid-metal Taylor-Gilbert cone. The LMIS is a dynamic device, that involves liquid flow; further, most experimental geometries do not correspond to Taylor’s mathematical constraints. So observed LMIS shapes are not expected to correspond exactly to Taylor’s mathematical cone. However, under conditions of low ion emission and low liquid flow, and with electrodes that approximate Taylor’s geometry, observed shapes do closely approximate Taylor’s mathematical cone, particularly away from the cone apex. This has been elegantly demonstrated by Kingham and Be11.6 It is possible to have linear arrays of Taylor-Gilbert cones, as used in prototype space-vehicle engines7 in which the cone spacing is determined by electrohydrodynamic effects; and square arrays have also been investigated.’ But it is more usual to ‘anchor’ a single cone on an underlying mechanical structure: all normal liquid-metal ion sources are of this type. The underlying structure may be a narrow-bore capillary tube through which the liquid flows, or a pointed needle. The needle-type emitter is more usual. Grooves or roughness left in the needle surface during fabrication can, by means of capillary action, assist the liquid flow to the apex;’ the result is the so-called ‘viscous-drag-free’ source. Early needle sources used very sharp needles. But an undergraduate student on industrial placement accidentally blew the end off a sharp emitter by applying too high a voltage, and in this way it was discovered that ‘blunt’ needles (with an apex radius of a few pm) gave much higher emission currents. The improvement is associated with the formation of a Taylor-Gilbert cone on the needle apex, and all modern needle sources use blunt needles. The student was S Ventnakesh and her supervisor R Clampitt. During source operation, the end of the liquid cone pulls out into a cusp or ‘incipient jet’, as illustrated in Figure 1, and ion emission occurs from the apex of this, by means of field evaporation.9 The radius of the emitting apex is typically 1.553 nm, so there is high space-charge immediately above the emitting surface. Secondary processes can occur in space above the emitter, and secondary electrons can impinge onto the emitter. Further, it seems that from time to time the end of the liquid emitter may break off: the source ‘spits’ a microdroplet, and then ‘heals’ itself to resume ion emission. Actual LMIS emission products may therefore be: ions (in various charge stages); clusters (in various charge states); neutrals; microdroplets; and light. As the applied voltage and the

emission current increase, sources tend to emit a higher proportion of neutrals, mainly as microdroplets. Thus at higher currents there is a ‘spraying mode’, normally attributed to greater tendency to hydrodynamic instability; at lower currents there is the ‘ion emission mode’, in which the sources are normally operated. It is believed, however, that both ions and microdroplets are emitted under all circumstances. The ion emission mode has been studied in some detail, and I concentrate on it in this paper. The droplet emission mode is less well understood. The gallium LMIS is particularly simple, because gallium produces mainly singly-charged ions. Also, the gallium melting point is only slightly above room temperature, which means that a gallium source is self-sustaining once started, and does not require continuous external heating. Further, gallium has an unusually low vapour pressure, so relatively few gallium atoms thermally evaporate into the vacuum as neutrals. For all these reasons, basic LMIS work has often employed gallium, and numerical illustrations here relate to gallium. The basic behaviour of other source materials is generally similar. Aspects of source behaviour that we might wish to explain include: shape, and its dependence on applied voltage; current/voltage characteristics; onset phenomena; ion emission mechanisms; ion-energy distributions and their variation with emission current; ion-optical properties of the ion beam; instability phenomena and the emission of microdroplets; and light emission phenomena. Not all these topics can be covered in detail here, but references are provided. Note that there exists a comprehensive bibliographylO of research in LMIS theory and applications up till 1990, and that the International Field Emission Society hopes to make a full bibliography (including papers up to 1995) available in due course. The basic origin of LMIS shape The formula for local pressure difference across a charged surface. Fundamental to Taylor’s analysis is the formula for the local pressure difference (Ap) across a static charged conducting liquid surface, namely: AP = ~,nt- pent = N/r,

+ l/d

- U/~)EC@,

where P,“~and pcXtare the hydrostatic pressures inside and outside the liquid surface, r, and r2 are the principal radii of curvature of the surface, jr is the surface tension of the liquid, E is the external field acting on the liquid surface, and a,, is the electric constant. Some years ago, the validity of this equation and of Taylor’s analysis were challenged.” This led to debate,6s’2.‘3 which did not change the majority view that Taylor’s analysis was correct for the special circumstances and geometry he was considering, but did stimulate wider discussion about the derivability of eqn (1) from energy considerations. It was clear that formula (1) could be derived by force-based arguments, and that its correctness could be argued from the absence of experimental falsification; but no energy-based derivation analogous to (say) Gibbs’ derivation14 of the corresponding zero-field formula could be found in the literature. It was eventually shownI that eqn (1) can be rigorously derived from thermodynamics, by treating the static ion-source configuration as a heterogeneous thermodynamic system in equilibrium. Because the external high-voltage generator can do electrical work on the system, the condition for thermodynamic equilibrium needs to be written:

R G Forbes: Understanding

how the liquid-metal

ion source works

, A: 40 pA

Figure 1. To show how, for a gallium LMIS, the shape of the Taylor-Gilbert cone develops as a function of recorded current. Parts (a) (i = 2pA) and (b) (i = 30pA) are micrographs taken with a 3 MeV microscope at Toulouse” (the marker represents 100 nm); the progressive development of the shape is seen more clearly in the profiles drawn in part (c). At very high emission currents the LMIS cusp can be very pronounced, as shown in part (d) (i> 100 PA), taken with a Phillips EM 300 TEM in Paris” (the marker represents 1 pm). (From Figures 2 and 5 in Ref. 18, and Figure 14 in Ref. 17.)

dlY=ddU-TdS-Vdq=O,

(2)

where T is the system temperature, U and S are its total internal energy and entropy, V is the voltage applied between the ion source and a counter-electrode, and q is the electric charge stored capacitatively. Y represents a unfamiliar form of free energy, that needs to be used when the surroundings can do electrical work, but not mechanical work, on a thermodynamic system. Substitution of expressions for the various components of the terms appearing in eqn (2) leads eventually to the conclusion that

a necessary condition for thermodynamic equilibrium is that eqn (1) holds at all non-singular points of the liquid surface. For real experimental circumstances (as opposed to Taylor’s ideal situation), it may be impossible to find a surface shape such that eqn (1) holds at every point of the liquid surface. In such circumstances it would be,formall,v impossible for real liquid cones to exist in a state of static equilibrium. Steady-state emitter

shape. As already

noted,

at low emission 87

R G Forbes: Understanding

how the liquid-metal

ion source works

currents the mathematical Taylor cone is a good approximation for the shape of a steadily operating emitter (except close to the emitter apex), but at higher emission currents the shape clearly becomes a ‘cusp on a cone’. This cuspoidal LMTS shape was first seen by Clampitt and co-workers,‘6 in Scanning Electron Microscope observations on a capillary-type caesium source. It was later confirmed that blunt-needle-type gallium sources also behaved in this way, by means of High-Voltage Transmission Electron Microscope (HVTEM) observations on operating sources.‘7.‘8 The length and other dimensions of the cusp increase with emission current. This is clearly seen in Figure 1, taken from the work of Benassayag, Sudraud and Jouffrey.18 Under steadystate conditions the liquid flows through this cusp-like shape, and is field evaporated at its apex. It is easy to understand why the apex of the mathematical Taylor cone develops into a cusp-like shape when the voltage is increased slightly. From eqn (l), if the shape doesn’t change, the local change 6(Ap) in pressure inside the cone resulting from a change 6, in the applied voltage V is given by:

6(Ap) = -E&~V/V).

(3)

6 V/V is the same for all points on the original

surface, so the lowering of hydrodynamic pressure inside the liquid is greatest where the field is highest, i.e. at the cone apex. Under the influence of these induced pressure differences, the liquid begins to move towards the apex, and pushes this out into a cusp, which grows until the field is high enough for field evaporation to occur. This cusp-like shape can be understood most simply as an electrical variant of the Cenu contracta of classical hydrodynamics.” The basic effect has been known for hundreds of years. The main differences in the present case are that the pressure difference is provided by the electrical (Maxwell) stresses rather than by gravitation and a head of water, and that the hydrostatic pressure in the emerging jet is negative rather positive (i.e. the electric field ‘pulls’, whereas a head of water ‘pushes’). Modelling of LMIS shape is discussed in more detail below.

Further basic aspects of behaviour Onset behaviour. An individual LMIS turns on at a well-defined voltage (the onset voltage V,,), and turns off at a well-defined voltage (the extinction voltage V,). V, is normally slightly less than V,,. These phenomena are associated with the formation and collapse of the liquid cone, which are general features of Taylor-Gilbert cone behaviour. In an interesting series of experiments,20 using the geometry shown in Figure 2, Taylor measured the critical voltage VA at which liquid began to leave the top of a tube, and observed that in many cases (if p,,, = 0) the liquid had a conical form immediately prior to the onset of instability or jet formation. In these circumstances, he identified his critical voltage with the condition that the total electrostatic force f;_ acting on the cone as a whole be equal and opposite to the total surface-tension force ,fi, exerted on the cone as a whole by the supporting capillary tube. Defining the positive direction to be from base to apex of the cone, we may write expressions for these forces: _&( v,) = - 271Rb Y cos $T, fl( V,) = zt,,

VkZ/k ,

where R, is the radius of the base of the Taylor-Gilbert 88

(4) (5) cone,

Figure 2. To show the geometry involved in Taylor’s experiments on cone formation. B and E are parallel metal plates separated by a distance H. A long metal (hypodermic) tube A, of length L and radius R, protrudes through B. A voltage V is applied between A and B. (From Figure 3 in Ref. 20.)

and k is a constant that relates to the geometry of the situation and the system of measurement in use. Hence we obtain: nt,, V,Z/k = 2rtR, ‘rcos &.

(6)

Since the electrostatic forces on the sides of the tube are at right angles to its axis, fL as defined above also represents the total force on the tube parallel to its axis. In earlier work by himself and Van Dyke, Taylor” had derived an expression for the total force on a long thin cylinder in the geometrical situation of Figure 2: the equivalent expression (in rmks form) for k is:

k = (H2/L2){ In (2L/R) - 3/2} This leads to the following

formula

(7) for critical voltage:

V: = (2Rhy cos &/&,,)(H2/L2){ln (2L/R) - 3/2}.

(8)

Good agreement was obtained between this formula and experimental data derived using water, glycerin, and mixtures of such fluids.‘O Bell and Swanson’ have reported equally good agreements between this formula and onset voltages measured for liquidmetal ion sources: Taylor’s intuition is again confirmed as correct. Ion-energy distributions. Energy distribution measurements have been carried out for various LMIS materials,3 often as a function of emission current; results are most extensive for gallium. The observed energy of an ion reflects its mode of formation, its position of origin, and any energy gains or losses during flight. Two distribution features are of particular interest: the full width at half maximum (FWHM) and the mean energy deficit. For gallium, the variation of the FWHM with emission current is illustrated in Figure 3, which is taken from old work by the present author and colleagues.22 Over the range of emission currents from 2pA to about 20/*A, the FWHM increases linearly with i. Most other materials measured behave in a broadly similar fashion,3,2’ although the range of linearity may be different. The work of Knauerz4 and (later) of Gesley and Swanson,” makes it clear that most of this broadening is due to coulombic particleparticle interactions in the ion beam. This implies the existence of a high space-charge close above the liquid emitter surface. Especially when a retarding potential analyser is used, ion energy distributions are often plotted as a function of the socalled energy deficit D. The energy deficit is normally positive in

R G Forbes: Understanding

how the liquid-metal

ion source works

50 ( 1 ,..,,

1

Ga:-300

K

Figure 3. Logarithmic

plot of the dependence of the energy-distribution on emission current, for Ga+ ions. (From Figure 3 in

width (FWHM) Ref. 22.)

sign and is given by -reGV, where e is the elementary positive charge, re is the final charge on the ion, and 6 V (= V, - VJ is the voltage difference between retarding electrode r and the ion emitter e. Because of the energy broadening due to coulombic interactions, in LMIS work a feature of significant interest is the so-called ‘peak energy deficit’ Dpk which is the energy deficit corresponding to the peak of the energy distribution. Figure 4 is derived from the early review by Swansonz3 and shows DPk plotted as a function of emission current i, for various gallium ion species. The basic theory of energy deficits is related to the theory of field-ion appearance energies. 26.27These theories are based on the principle of conservation of energy and are well understood. In

0

“P=I

I

4

E

01

0

Go+

= I

L

I

!

I

,

I2

16

20

24

28

32

i

i (PA) Figure 4. Dependence various

gallium

of peak energy deficit on emission current, for the ion species indicated. (From Figure 5 in Ref. 23.)

applying them to the LMIS situation, the quantity DPk (or, more strictly, the mean energy deficit) plays much the same role as does the so-called onset energy deficit in the standard theory. So, if ion emission occurs via a normal high-field surface process (i.e. field-evaporation or surface-field-ionization), and no energychange mechanisms other than coulombic particle-particle interactions operate during flight, then we can predict a value for the peak energy deficit. For Ga+ ions field-emitted in an apparatus where the retarding electrode has a work function of (say) 4.3 eV, DPkshould be about 4.5 eV. There is some prediction error in this value, due to uncertainty in the numerical values of some parameters involved and uncertainty about details of broadening, so observed values may be slightly less than 4.5eV; but it is incompatible with enegy conservation that they be significantly less It is dillicult to state precisely what constitutes ‘significantly less’, but for gallium emission currents in the range I-20pA I have in mind a maximum prediction error of l-2 eV. The results in Figure 4 demonstrate that, for a gallium LMIS operating at close to room temperature, both the Ga’ ions and the Ga++ ions originate at or very near the surface of the liquid emitter, for all emission currents measured, and that the boundary between the liquid metal and its surroundings is very well defined at an atomic level. The Ga: ions, however, appear to be formed in space above the liquid surface (or, alternatively, suffer significant energy losses during flight). Emission field values and the dominant emission mechanism There are basically two mechanisms whereby ionization could take place at or very near the liquid-emitter surface, namely ‘field evaporation’ and ‘surface field ionization’. Field evaporation involves the escape of ions from the liquid surface by a singlestage process that simultaneously involves ionization and the breaking of atom-surface bonds. Surface field ionization is a two-stage process involving as its second stage the ionization, at or very near the emitter surface, of neutral atoms that have previously been removed from the surface in some other way, usually from a site remote from the point of ionization. In both cases further field ionization events, to higher ionic charge states, can take place after the first ionization, and this is called ‘postionization’. The values of the characteristic electric fields at which these various processes take place rapidly are known from the theory of field-ion emission. Surface field ionization will take place at significantly lower fields than field evaporation, With gallium emission, a small percentage of Ga+ + ions are formed. It is clear from ion-energy measurements that these ions are formed close to the surface, and it is clear on other theoretical grounds that they must be formed by post-ionization. From the relative abundances of Ga++ and Ga+ ions, it is possible to derive (via the theory of post-ionization) the value of electric field at which the post-ionization took place. A similar procedure can be applied in the case of other materials. Following Swanson,23 the surface fields E,, obtained in this way are shown in Table 1. This table also shows values Erecharacteristic of field evaporation for the materials in question. The calculated values are those derived by Tsong** for a singly-charged ion, using Mtiller’s formula. (The status of this formula, which - contrary to statements in the literature-does not rely on the image-hump model of field evaporation, has recently been discussed by Forbes.‘) The observed values, where available, are derived from lowtemperature field-evaporation experiments, and are taken from 89

R G Forbes: Understanding

Table 1. Comparison (see text).

Material

Al Ga In Au Bi

of LMIS

how the liquid-metal

between field strengths

ion source works

E,, derived from relative-abundance

measurements

and field strengths

Relative abundance M++/M+ at i 10 PA

I!$,,derived (V/nm)

E,, for M + calculated

2.2 x lo-’ 9 X 1o-5 2 X lo--’ 1.5 2.3 x IO-’

20 21 17 35 19

19 15 13 53 18

(V/nm)

Efecharacteristic

of field evaporation

EFr for M+ observed (V/nm)

27 15 35

the list compiled by Biswas and Forbes.‘9 The field values applicable to LMIS operation at elevated temperatures are expected to be somewhat less than the tabulated EFevalues. Normally the agreement between observed evaporation fields and the values predicted from Miiller’s formula is very good: agreement to within about 10% has been reported for a wide range of materials.28 So, from this point of view, the materials listed in Table 1 are unrepresentative: the evaporation fields for In and Bi have not been measured; and both Au and Al behave anomalously. The anomaly with Au is well known, and the experimental value is to be preferred. With Al, the low-temperature evaporation field observed in vacuum is significantly greater than the Miiller’s formula result; the anomaly is the greatest of its kind known to the author, and is unexplained. Given this background, Table 1 indicates that (except possibly for Al) the fields _Epiderived from the LMIS energy measurements correspond well to evaporation-field values. More to the point, in no case (except Al) is the field EpI significantly lower than the corresponding observed value of El,, where this exists, or the corresponding predicted value when no observed value exists. From a similar table, Swanson23 concluded that the dominant emission mechanism must be field evaporation. If we accept this as a general conclusion, then we can reliably predict surface fields in the emitting region of a liquid-metal ion source. For gallium, the position is particularly clear cut. The observed and calculated values of evaporation field agree, and the field E,, derived from LMIS data is a little higher. Since surface field ionization would take place at significantly lower fields than &, the ion emission mechanism must be field evaporation. Further confirmation comes from calculations by Castilho and Kingham:‘” they have shown that, for a surface field of 15 V/nm, any neutral Ga atom approaching the liquid emitter from space is ionized well before it reaches the emitter surface.

cylinder, because this assumption would imply a pressure discontinuity of around 5000 atm across the flat surface of the hemisphere, which must be unphysical. In reality, the cap cannot be exactly hemispherical, and the transition from cylinder to cap must take place more gradually. But it is geometrically reasonable to assume that the radius of the cylinder is approximately equal to the radius of curvature at the apex of the cap, and it is physically reasonable to assume that the electric field at this position is equal to the evaporation field. In this way we derive a theoretical value of 3 nm for the diameter of the liquid cusp or jet, just below its apex. This value is in agreement with the best experiments.”

Size of the cusp apex at low emission currents. As suggested long ago by Krohn,3’ we may use this surface-field information to estimate the apex size of the emitting liquid cusp, at low emission currents. We initially assume that the cusp has a hemispherical ‘cap’, of radius r,, and that the hydrostatic pressure inside this liquid cap is zero. Equation (I) thus reduces to:

Pt = -u/%d.

Ap = 2y/r,--(1/2)~~E~~ = 0;

(9)

and the only unknown is r,. For gallium, 7 = 0.72 N/m, so we obtain Y,= 1.48 nm. Note that the individual terms in eqn (9) are each equal to about lo9 Pa, i.e. about 10 000 atm. It is not, in fact, hydrodynamically consistent to assume that the shape of the end of the liquid cusp is a hemisphere on a 90

Pressure at the cusp apex. For an operating source, the assumption of zero pressure at the cap is an approximation, since in reality a small pressure drop is needed between the base of the Taylor-Gilbert cone and the cap, in order to drive the liquid flow. A better approximation is to assume that the liquid flow is streamline and non-turbulent and then use Bernouilli’s equation. The approach below is a corrected version of Kingham and Swanson’s.32 We assume that the pressure in the cylindrical section of the liquid cusp, close to the cap, is equal to the pressure pt at the apex of the cap, with p, given by: Pt = 2ylrt - (1 /%Gc. The Bernouilli the hydrostatic p +

(1 /2)pc2

(10)

equation implies that, at each point in the liquid, pressure p and the liquid speed v are related by: =

pb,

(11)

where p is the liquid density and pb is the pressure at the base of the Taylor-Gilbert cone. If, in the cylindrical part of the liquid cusp close to the cap, the liquid speed is v,, and we take pb as zero, then: (12)

A further equation can be obtained by assuming that all the liquid flowing through the liquid cusp is emitted in the form of singly-charged ions, and that the radius of the cylindrical cusp, close to the cap, can be taken as r,. In this case the emission current i relates directly to the flux of atoms crossing a plane at right angles to the axis of the cylinder, close to the cap, so: i = enr:v,(p/m),

(13)

where m is the atomic mass for the liquid material in question, and (p/m) is the number density of atoms in the liquid. A gallium liquid-metal ion source is often operated at an emission current of about 2 PA. For gallium, p = 5910 kg/m3 and

R G Forbes: Understanding

how the liquid-metal

ion source works

[a/Cc

1.16 x lo-” kg. So, taking i = 2 PA and approximating rt as 1.48 nm as derived earlier, we obtain U, as about 38 m/s. Hence, from eqn (12) we obtain pt as approximately - 43 atm. We thus get a picture of a liquid-metal ion source as a device driven by a negative pressure at its apex. Liquid flows because the negative pressure at the apex of the liquid cusp ‘sucks’ the liquid towards the apex of the cusp. Since each of the individual terms on the r.h.s of eqn (10) is about 10 000 atm in size, and the driving force is a small difference between two large terms, it is not too surprising that the LMIS tends to be hydrodynamically unstable. The amazing thing, perhaps, is that the device works stably at all. We return to this m =

v;$l / j_trn

issue below. Current/voltage characteristics

An important LMIS property is its current/voltage (i/v) characteristic. For an operating LMIS, there is a range immediately above the extinction voltage I’, where the current is nearly linear as a function of (V- I’J. In this range we may write: i = a( V/V,-

l),

(14)

where a is a constant that depends on the system geometry and on the nature of the source. The slope of the characteristic in this linear regime is of major interest. For a given cone base-radius, sources with viscous drag in the liquid supply along the supporting needle have ‘flatter’ slopes than those without viscous drag. For viscous-drag-free sources, and on the assumption that space-charge nant controlling influence, Mair33,34 has developed argument that gives a as: a = { 3rry(2e/m)“*}

I’,,- I,‘*& cos &,

is the domian ingenious

UW

where Rb is the radius of the base of the Taylor-Gilbert cone, and the other symbols have the same meanings as earlier. All the parameters in this expression are either known constants or measurable for a given source, so values for a can be predicted. Mair’,34 has shown that, for several materials and for a range of base radii, there is very good agreement between predicted values of slope u and values measured from experimental i/V characteristics, provided that the sources in question are viscousdrag-free (i.e. have a ‘rough’ supporting needle or are of capillary type). To illustrate this, we follow his approach and rearrange eqn ( 15a) as follows: a =

cv, cos &Rbr

(15b)

4(cVx) = cm (PA,,

(15c)

where c is defined as the quantity in curly brackets in eqn (lSa), and is constant for a given material. Figure 5 is a logarithmic plot of eqn (1%) and shows how the agreement holds good over a wide range in Rb. This strongly suggests that the underlying argument must be essentially correct. We therefore examine it in detail. Complexities in the original papers have recently been clarified,35,36 giving new physical insight; the treatment here derives from the later papers. We now know” that the best starting point is to apply Newton’s Second Law to the motion of the liquid emitter as a whole. With steady-state LMIS operation, the Second Law may be written: f = d(Mv)/dt

= v,dM/dt

,

Figure 5. Comparison between values of the quantity a/(cV; I’*)predicted from eqn (15), and values derived from experimental i/V characteristics. The full line is derived from eqn (15~); each plotted point is derived from a measurement of the slope of a current,’ voltage characteristic, as described by Mair.3.34(From Figure 4 in Ref. 34.)

where f is the resultant force acting along the axis of the liquid emitter, towards its apex, dM/dt is the total mass of material evaporated per unit time from the emitting liquid apex, u is velocity, and z+(as before) is the velocity to which the liquid has been accelerated when approaching the tip of the liquid cusp. Further, if it is assumed (temporarily) that all material is emitted as singly-charged ions, then dM/dt is related to the emission current i by:

dM/dt

= mile.

(17)

We next define force contributions. The total force f acting on the liquid emitter is the sum of: (a) the total electrostatic force due to the integrated effect of the Maxwell field stresses (discussed further below); (b) the surface-tension forcef,, acting around the perimeter of the base of the liquid cone; and (c) the hydrostatic ‘pressure x area’ force& acting on the base of the liquid cone. For a viscous-drag-free source, the pressure pb at the base of the liquid cone is taken as zero, which implies thatf, also is zero. Letfp denote the total electrostatic force actually acting on the whole liquid emitter, when the source is operating and spacecharges are present (fp may be called the ‘Poisson force’); and let .f, denote the total electrostatic force that would act on the whole liquid emitter if the applied voltage and the shape of the emitter were the same, but there were no space-charges present vi, may be called the ‘Laplace force’); and let L\fbe defined by:

Af= .A-h.

(18)

Af represents the amount by which the total electrostatic force on the liquid emitter is reduced from the Laplace force, as a result of the presence of the space charges. Clearly, iffb is zero, then the total forcefacting on an operating LMIS is:

f=fP+fst =f~-Af+_L.

(19)

Mair’s theory derives expressions for these terms as follows. Using Taylor’s ‘slender body approximation’,20 discussed earlier, the dependence of the Laplace force on applied voltage V is written: 91

R G Forbes: Understanding

.L( v

how the liquid-metal

ion source works

= (%lN K

(20)

where k is a constant relating to the geometry of the situation. At the extinction voltage V,, the electrostatic and surface-tension forces are equal and opposite, i.e.: fL( VT) +&I( VX) = 0.

(21)

If it is assumed that the shape of the base of the liquid cone changes little with applied voltage, then the surface-tension force may be taken as independent of applied voltage, so:

= {fL( v) -JL( VX)>. So collecting f‘=

(i/e)(mu,)

terms together = (~a&)(

(22)

we obtain:

Z” - P’x’)- A$

An expression in now needed for Af Mair’s argument can be approximated by:

(23) is that Af

Af= $&-~;)W),

(24)

where: Ep is the field at the apex of the operating liquid emitter, in the presence of space charges; EL is the field that would exist at the liquid emitter apex, at the applied voltage in question, if the emitter shape were the same but there were no space charges; A is the cross-sectional area of the liquid column just below the cap (A = nr:); and ,B, is a correction factor of value close to unity. (This correction factor allows for the fall-off in field strength along the surface of the ‘cap’, as we move away from its apex.) The physical thinking behind formula (24) is that the spacecharge is concentrated mainly around the apex of the liquid emitter, so it is only in this region of the Taylor-Gilbert cone that there is any significant spacecharge-induced reduction in the surface electric field. Mair then uses the so-called ‘small spacexharge approximation’j7 to obtain the formula: (EL’ - Er2) = (8/3.sO)(m/2e)”

Pj,

(25)

i = (3/4)(2e/m)“*(71&,V,2/k)

VxM2V”2(

V+ Vx)( V-

V,).

(28) Equation (6) above (with Vk identified as V,) is used to replace the bracket involving k; further, since the range of voltage corresponding to the linear emission-current regime is relatively small, we may approximate V as V, everywhere except in the bracket (V- VJ. This leads to the earlier result, namely: a = i/(V/Vx--

1) = 3n(2e/m)‘~2R,ycos~TV,“2.

(29)

The physical implications of this analysis are very interesting. The obvious one is that space-charge effects strongly influence LMIS behaviour. A more subtle point concerns the approximation whereby (mtl,i/e) in eqn (27) is set equal to zero. This is equivalent to requiring that the total forcefon the liquid emitter be approximately zero, independent of emission current or applied voltage. So the conclusion appears to be that the spacecharge behaves in such a fashion as to ‘cancel out’ any increase in the total force on the emitter when voltage is increased, thus ensuring that the total force on the liquid emitter remains approximately zero, independent of emission current. (A small imbalance in the forces acting on the liquid, integrated over time, provides the momentum carried by the liquid flow as it approaches the emitter apex.) Some form of ‘feedback’ process must presumably operate when the voltage is changed, in order to take the system to its new equilibrium situation; Swanson and Kingham3’ have discussed this, but in my view the full details of the mechanism(s) involved are not yet clear. Cusp length as a function of emission current The length of the liquid cusp is of interest because it may affect the hydrodynamic stability of sources. It is observed from the HVTEM experiments (see Figure 1) that the cusp length I steadily increases with emission current i. Mair and Forbes39,40 have established an analytical theory that leads to the following linear relationship between 1 and i: I = [(3ny)-

‘(2m V,/e)“‘]i.

(30)

As shown in Figure 6, this fits the experimental

results of Sudraud

wherej is the emission current density. This can be related to the total emission current i by: j = i/P2A,

(26)

where /$ is another correction factor, close to unity, that takes into account the distribution of emission current across the tip of the liquid emitter. Collecting the above equations together gives: ,f = mu&/e = (n~,/k)( V2 - V,‘) - (4/3)(B,/BZ)(m/2e)‘!?iV1’2 (27) There are terms linear in the emission current i on both sides of the equation. For a given i-value the velocity v, can be estimated as described earlier. Hence we find that the term in i on the left hand side of expression (27) is normally small in comparison with the term in i on the right hand side, and may be set equal to zero in a first approximation. (This result also justifies neglecting the fact that not all the emitted material is in the form of singlycharged ions.) If /$//$ is then approximated to unity, the mathematics reduces to that originally presented by Mair and we may write: 92

0

000’0 0.0

0

20.0

40.0

Current

60.0

I

60.0

(PA)

Figure 6. Comparison of results for dependence ofcusp length on emission current. The full circles denote points derived from measurements on Transmission Electron Micrographs provided by Sudraud;4’ these are joined by linear segments to guide the eye. The dotted line is derived from equation (30), using values of V, provided by Sudraud. The open circles denote the results of numerical modelling!’

R G Forbes: Understanding

how the liquid-metal

ion source works

and co-workers” really rather well, given the difficulties in deriving accurate assessments of I from electron micrographs.

Emitter stability: steady-state control effects From analysis and modelling of the LMIS emission region, it emerges that the space-charge reduction in surface field is very marked (Swanson and Kingham suggest that at the emitting liquid surface the Poisson field Ep may be only one fifth of the Laplace field EL.) This provides a clue as to one reason for shortterm emitter stability. Suppose that, for some statistical reason, the ion emission rate decreases at the emitter tip. The space charge rapidly diminishes as the ions forming it move away, so the field at the liquid surface rapidly rises. The field evaporation rate-constant is very sensitive to the value of electric field, so ion emission rapidly resumes. This control process is sometimes called ‘space-charge stabilisation’. The above, however, cannot be the whole of the story. For if the ion emission rate decreases, even momentarily, then the liquid jet will extend in length (because it’s moving at very high speed!). This also will lead to an increase in field, but for geometrical rather than space-charge reasons; again, field evaporation will rapidly resume, and will presumably ‘eat back’ the jet to its original length. For want of a better name I call this ‘inertial/geometrical stabilisation’. Analogous feedback mechanisms exist if, for some statistical reason, the ion emission rate suddenly increases: the enhanced space-charge, and/or the reduced length of the cusp, will reduce the surface field, and hence reduce the evaporation rate. In engineering terms, all the above are mechanisms with intrinsic negative feedback. They all tend to encourage emitter stability. In addition to the above, changes in the surface field will change the pressure difference between the body of the liquid cone and the tip of the liquid cusp, and hence the rate at which liquid flows to the cusp apex. With this mechanism, if the cusp increases in length, then (if we disregarded the stabilisation effects just discussed) the field at its apex would increase for geometrical reasons; this would increase the pressure difference between the tip of the cusp and the body of the liquid cone; this would increase the flow rate; and the cusp would tend to grow further. In engineering terms, this mechanism has positive feedback: it is a destabilising mechanism, that I refer to as ‘pressure-change destabilisation’. The author’s belief is that pressure-change destabilisation effects of this type normally act more slowly than the stabilisation effects discussed above. and that this is a major reason why liquid-metal ion sources can provide relatively stable ion emission, at least for short periods of time. A further issue is what might happen if the shape of the liquid cap changes temporarily from its steady-state shape. It is difficult to imagine that large hydrostatic pressure differences could exist stably in a volume of liquid about 3nm across. So the steadystate shape of the cap must be such that the same difference exists everywhere between the magnitudes of the electrostatic and surface-tension stresses, although the stresses themselves may change with position on the surface as the local radius of curvature changes. If, as a result of some statistical fluctuation, the shape changes locally away from its steady-state shape, resulting in too high a local field, then expectation is that the field-evaporation rate will increase locally, and will locally ‘eat back’ the cap to its local steady-state radius. This control mechanism is easy to understand, since a very similar mechanism operates in

the low-temperature field evaporation of solids, where it produces the so-called field evaporation endform. For the LMIS we may call this process ‘liquid endform stabilisation by field evaporation’. Obviously, the rather basic discussion in this section has not dealt with the possible creation of fast-moving pressure waves in the liquid, and the possible effects of these:43 it is these waves, the author suspects, that are responsible for (at least part of) the instability observed in real sources. Certainly we do not yet understand the details of the complicated interactions that may exist between the various processes mentioned above. Secondary emission phenomena Various secondary phenomena that may occur in connection with LMIS operation are now briefly considered. These phenomena are well discussed in Prewett and Mair’s book. and original references may be found therein. Secondary electrons. When fast ions or neutrals hit the extraction electrode or other surfaces in the vacuum system, secondary electrons are emitted and travel back towards the ion source. In most systems, some of these strike the Taylor-Gilbert cone and/or its supporting needle and/or other parts of the support and liquid-supply arrangements. These electrons can be suppressed with a magnetic field; hence we find that they have no significant effect on LMIS operation. Secondary electron emission does need to be taken into account when deriving ion emission currents from measured currents: if no special precautions are taken to suppress secondary electrons, then true ion emission currents may well be about half the measured currents. Currents reported in the literature are often total measured current rather than true ion emission current; so caution needs to be exercised, since sometimes the nature of a reported current is not made clear. Optical phenomena. An operating LMIS emits a small amount of light. There is light emission from the shank of the supporting needle, where high-energy secondary electrons hit the shank; this can be eliminated by deflecting the secondary electrons. There is also a small spot of light at the ion-emitting liquid apex: this spot is not affected by magnetic fields and is therefore intrinsic to the operation of the source. Spectral analysis shows that (certainly for gallium) the lines are mainly excited neutral lines. There have been various investigations into how the intensity of the light depends on emission current and other relevant factors; Hornsey and MarriottJ4 give a useful summary. The fdvoured explanation is that ion-neutral collisions are responsible for the excitation of neutrals. Neutral emission. Careful measurements (originally by Mair and von Enge145) suggest that at low emission currents some 30% of the liquid mass is emitted in non-ionic form; this percentage increases with emission current. These results, and the optical phenomena reported above, raise questions as to ‘how is this mass lost’ and/or ‘how are neutral atoms emitted into the gas phase’. There seems insufficient heat input into the system for thermal evaporation to be the cause,’ and it has also been reported44 that the incidence of optical emission is not compatible with a mechanism based on thermal evaporation of neutrals. The explanation currently favoured is that most of the non-ionic mass loss is associated with the emission of microdroplets, and that 93

R G Forbes: Understanding

how the liquid-metal

ion source works

neutral atoms are then emitted from these microdroplets as a result of bombardment by fast ions; once released, the neutral atoms will drift back towards the emitter under the influence of polarisation forces, as do helium atoms in a field-ion microscope.4h The high-temperature anomaly in the energy distributions

It has long been knowr?’ that, when a gallium LIMS is operated at high temperature, the peak in the ion energy distribution splits into two. Some more recent measurements on this effect44.4x are illustrated in Figure 7. The anomaly is that the ions in the lowerenergy-deficit peak have, on average, an energy that is too high to be explained by standard theory based on energy conservation in a thermodynamic cycle. In recent years these effects have been investigated more systematically. A useful summary of the various investigations and proposed explanations has been given satby Hornsey,48 who found none of the earlier explanations isfactory. Instead, Hornsey has suggested49.50 that the source of the additional energy is a fast ‘vibration’ of the end of the liquid emitter, possibly associated with the formation of very small microdroplets (which I prefer to call ‘nanodroplets’) as the end of the liquid cusp breaks off. The argument is that ions in the low-energy-deficit peak may be created preferentially under conditions such that the emitting electrode is ‘moving forwards’ behind them, and acquire additional energy by this means. Initial simulations are compatible with this idea, but much detailed research remains to be done.

‘liquid globules’ from the back end of the Taylor-Gilbert cone and/or from the supporting needle. For indium, some spectacular HVTEM observations relating to the release of liquid globules have recently been reported by Praprotnik et al.;” Figure 8 reproduces some of their observations. Suggested causes of microdroplet and nanodroplet emission from Taylor-Gilbert cones have included both bulk oscillationss4 and the excitation of surface waves;43 the precise mechanisms involved are a topic of current research interest. The phenomena on the needle shank are probably the result of ‘balling up’ processes due to the interaction of surface-tension forces with weak Maxwell stresses.

Numerical modelling of basic LMIS behaviour In some respects it is surprising that the analytical investigations of basic LMIS behaviour have taken us as far as they have done. In practice, the analytical approaches have for many years been paralleled by treatments based on numerical modelling. Early numerical modelling of liquid-metal ion sources was mainly carried out in various American laboratories,24~55~56~5’~58 and often had the aim of improving understanding of the ion optical behaviour of the sources. Modelling ofbasic LMIS behaviour of the kind discussed above was initiated by Kingham and Swanson.3’ who were the first to write a program in which liquid emitter geometry was in any way calculated rather than assumed. Numerical modelling, specifically of basic behaviour, was then taken up by the present author and colleagues. Our basic

Instability and the formation of microdroplets Liquid-metal ion sources emit microdroplets and possibly nanodroplets. Some of the evidence for this has just been discussed. There is also other evidence. For example, microdroplets have been observed indirectly by means of an ion-streak camera;” and high-frequency oscillations in emission current are usually attributed to microdroplet emission.’ It needs to be stressed that microdroplet emission is not at all surprising: there are clear affinities between some aspects of LMIS behaviour and the wellknown behaviour of electrostatic atomisers and electrohydrodynamic sprayers.” Expectation is that microdroplets and nanodroplets form as a result of (electro-)hydrodynamic instabilities in the liquid metal. There seem to be at least three modes of formation: detachment of a nanodroplet from the end of the liquid cusp; detachment of the whole liquid cusp and probably part of the Taylor-Gilbert cone; and detachment of

-

A

I\

6gGa+

I

I

I

I

I

I

I

I

94

H 1w

7QOC 175oc 275% 375oc

I

I

10 20 30 Voltage deficit, V Figure 7. To show how the energy distribution for on-axis “Ga’ ions varies as a function of temperature, at a total emission current of 2 /LA. (From Figure 2 in Ref. 48.) -20

-10

-----

H

1w

0

H

IOpm Figure 8. Some examples supporting

of liquid globules seen on the shank of the needle of an indium LMIS. (From Figure 7 in Ref. 53.)

R G Forbes: Understanding

how the liquid-metal

ion source works

geoapproach, described elsewhere, 59is based on a parametrised metrical model for the liquid cusp, first used by Kingham and Swanson3’ The Forbes-Ljepojevic program optimises certain of the geometrical parameters involved (those corresponding to the length and limiting half-angle of the liquid cusp) in order to produce a minimum in a certain mathematical ‘residual’. This residual represents how well, on average, the pressure-difference formula is obeyed at each point of the liquid surface, taking into account pressure drops within the liquid that arise as the result of liquid flow. The calculation of external electrical fields has to take space-charges into account, and the optimisation also requires that, for a given emission current, the program finds a value of applied voltage such that the surface field at the emitter apex is equal to the evaporation field. The optimisation is complicated, and as many as 10 000 iterated solutions of the Poisson equation may be needed in order to determine a single set of self-consistent values of current, voltage, cusp length and cusp limiting half-angle. We have recently introduced a parallel computation approach in which copies of the calculation are automatically distributed over a number of workstations.“’ This has speeded up the time taken to obtain a set of values from the best part of a day to less than half-an-hour. Modelling the viscous-drag-free source. As demonstrated in Figure 9, both the Kingham-Swanson and the Forbes-Ljepojevic programs are well able to reproduce the slope of the current/voltage characteristic for a rough needle. (The non-correspondence of the extinction-voltage values is of no scientific significance, since it means only that the overall geometries assumed in the experiments and in the two computer programs - for example, the placing of any extractor electrode - are different.) However, as seen earlier, Mair’s analytical treatment does as well or better when it comes to predicting slopes. Thus, a major interest has been to model how the length and limiting half-angle of the liquid cusp vary with emission current. As shown for gallium in Figure 6, as far as cusp length is concerned there is now good agreement between the results of

p=OAbl K+S /

i

10 t

30 :

-k--k

5 Voltage

(kV)

5.5

I 6

e-

Figure 9. Current/voltage characteristics for a gallium LMIS, supported on a needle of radius 3 pm. Shown are: experimental results for ‘rough and ‘smooth’ emitters, from Ref. 32; numerical results for ‘rough’ emitters (pb = 0) obtained by Kingham and Swansor?* (K+ S) and by Forbes and Ljepojevi? (F + L); and numerical results for ‘smooth’ emitters, obtained by Forbes and Liu,16 for three values (0.5 h. b, 2 h) of the coefficient of proportionality between base-pressure pb and emission current i. The constant b equals - IO5 Pa/PA.

numerical modelling, the results of analytical modelling, and the experimental results. As far as limiting half-angie is concerned, our numerical calculations59.42 show a progressive decrease in half-angle as the emission current increases, which is the trend observed in experiments;‘7*‘8.53 but, in the cases where a quantitative comparison has been mades3,@‘, agreement is less satisfactory, possibly due to difficulties in ensuring the comparability of the model assumptions and the conditions under which experimental data are taken and analysed. Modelling of sources exhibiting viscous drag effects. Viscous drag effects presumably influence LIMS emission via the hydrostatic pressure pb in the base of the liquid cone. In the viscous-dragfree case this base-pressure is set equal to zero, but in the presence of viscous drag the base-pressure must presumably be somewhat negative. Thus, our model has been adapted to explore the effects of making base-pressure pb negative and proportional to the emission current (and hence to the liquid flow along the needle). Initial results,36 shown in Figure 9, indicate that numerical modelling with negative base-pressure can reproduce qualitatively the well-known differences between the characteristics of ‘smooth’ and ‘rough’ emitters. However, in these initial calculations the switch from ‘rough’ to ‘smooth’ behaviour is associated with a relatively high value of the coefficient of proportionality between base-pressure and emission current. This value looks to be too high to be plausible, and further research is needed. The need for time-dependent modelling. Although useful progress has been made, the steady-state approximation has its limitations. It would be helpful to know how the shape of a liquid emitter evolves. And, obviously, a steady-state approach cannot address questions concerning cusp stability and the conditions for droplet emission. Time-dependent modelling of the electrohydrodynamics (EHD) of shape change is thus much needed. There has been useful earlier work,h’ but a better treatment is required. Forbes, Liu and Djuric have thus recently started to develop time-dependent numerical modelling. Preliminary results36 suggested the possibility of explaining liquid-surface fragmentation as an effect of the combined influence of surface-tension and electrostatic stresses, as shown in Figure 10. The observed shapes are vaguely reminiscent of the effects illustrated in Figure 8, and so to an extent may represent real effects. However, it is also possible that these numerical results are in some measure a consequence of instabilities in the preliminary computation. From the standpoint of computational fluid dynamics, the possibility of instability seems very high in this problem: high electric fields create high local surface stresses, and the local size of these after a time-step depends sensitively on the local surface curvature calculated by a fitting procedure. A poor fitting procedure could in principle lead to derivation of a spuriously high local curvature, and consequently to spuriously high local fields and stresses. And in the next time-step such effects could be amplified. The special methods needed to deal with such difficulties are a topic of current research. Other aspects of LMIS behaviour. Various other aspects of LMIS theory deserve more attention than space permits here, but two need special mention. The first is modelling of the effects of emitter shape and beam coulombic interactions on the ion-optical characteristics of the beam, especially its angular characteristics. This has obvious relevance for Focused-Ion-Beam (FIB) systems. There is also some interesting workh’.h’ by Orloff and colleagues 95

R G Forbes: Understanding

how the liquid-metal

ion source works

The liquid-metal ion source has significant technological applications, and it is important to understand how it works. I hope I have persuaded you that these sources also involve some highly interesting basic physics.

References

(4 Figure 10. To show a mode of evolution of the shape of a ‘broken dam’ under the combined influence of electrostatic, surface-tension. and gravitational forces: (a) initial shape and (b) shape after evolution.

on the ion optics of beam transfer, which suggests that the optimisation of different applications may require different focusing conditions. Second, I have concentrated in this paper on LMIS basic physics, as illustrated by the behaviour of gallium. But some other LMIS materials, notably gold. produce significant abundances of a much greater variety of ionic species. There are many questions (often unanswered in detail) as to the pathways by which these species are produced, and the consequences for LMIS behaviour and beam characteristics. Conclusions I conclude with a brief personal assessment situation. l

96

of the present research

We now understand much of the basic behaviour of liquidmetal ion sources; and in many areas there is good agreement between experiment and analytical theory and/or numerical models. A major need is to understand in more detail the hydrodynamic instabilities that lead to microdroplet and nanodroplet emission We need analytical theories for, and numerical modelling of, time-dependent electrohydrodynamic effects. Another major need, especially for some source materials, is to understand better the ‘ion chemistry’ that is occurring in free space above the emitter surface. New problems of understanding are raised by the liquid-alloy ion source (LAIS). The basic behaviour described above is applicable to alloy sources, but such sources also exhibit many special features. Much experimental data now exists, but detailed theoretical understanding of LAIS special behaviour is extremely limited. The area is wide open for research. With recent developments in the theory of electrostatic atomisation and EHD spraying,5’ there is growing convergence between this theory and the theory of LMIS behaviour; useful progress may perhaps be made by comparing the theories of the two subjects.

I. Cabovich, M.D., Soa. Phys. (isp., 1983, 26,447. 2. Melngailis. J., J. Vat. Sri. Tech., 1987, B 5, 469. 3 Prewett, P.D. and Mair, G.L.R., Focused Ion Beams from Liquid Me/al Ion Sources. Research Studies Press, Taunton, UK, 1991. 4. Gilbert, W., De Magnere, Book 2, Chapter 2. London, 1600. Translation by P.F. Mottelay. Dover, New York, 1958. 5. Taylor, G.I., Proc. Roy. Sot. Lond., 1964, A 280, 383. 6. Kingham, D.R. and Bell, A.E., Appl. Phys., 1985,36. 67. 7. Bartoli, C., von Rhoden, H., Thompson, S.P. and Blommers, J., Vacuum, 1984,34,43. 8. Bell, A.E. and Swanson, L.W., Appl. Phys., 1986, A41, 335. 9. Forbes, R.G., Appl. Surface Sri., 1995,87, I. IO. Mackenzie, R.A. and Smith, G.D.W., Nanotechnology, 1990, I, 163. Il. Sujatha. N., Cutler, P.H., Kazes, E., Miskovsky, N.M. and Rogers, J.P., Appl. Phys., 1983, A 32, 55. 12. Allen. J:E.. J..Phys. D: Appl. Phys., 1985, 18, 59. 13. Cutler. P.H.. Feuchtwane. F.E., Kazes, E.. Chung, M. and Miskovsky, N.M., J. Ph_w. D: A;pl. Phys., 1986, 19, Ll31 14. Gibbs, J.W., Trans. Connecricur Acad., Vol. III, 1875, p. 108 and 343. Reprinted in The Srientific Papers qf J. Willard Gibbs. Vol. 1. Thermodynamics Dover, New York, 1961. IS. Ljepojevic. N.N. and Forbes, R.G.. Proc. Rolj. Sot. Lond., 1995, A 450, 177. 16. Aitken, K.L., Field Emission Day - Proceedings @a Meeting held a/ ESTEC. Noordwijk, 9 April 1976 (Report No. ESA SP 119). European Space Agency, Paris, 1977, p. 23. 17. Gaubi, H., Sudraud. P., Tence, M. and van de Walle, J., Proc. 29th Intern. Field Emission Symp. Almqvist and Wiskell, Stockholm, 1982, p. 357. 18. Benassayag, G.. Sudraud. P. and Jouffrey, B., Ulrramicroscopy, 1985, 16, 1. 19. For example, Faber, T.E., Fluid Dynamics for Physicists. Cambridge University Press, Cambridge, 1995. 20. Taylor, G.I., Proc. Roy. Sot. Lond., 1969, A 313, 453. 21. Taylor, G.I.. Proc. Roy. Sot. Lond., 1966, A 291, 145. 22. Mair, G.L.R., Forbes, R.G., Latham, R.V. and Mulvey, T., Microcircuit Engineering ‘83. Academic Press, London, 1983, p, 171. 23. Swanson. L.W., Nucl. Insrr. Meth., 1983, 218, 347. 24. Knauer, W.. Optik, 1981.59, 335. 25. Gesley, M.A. and Swanson, L.W.. J. Phys. (Paris), 1984,45X9, 167. 26 Forbes. R.G.. SurJaw Sri., 1976, 61, 221. 27. Ernst, N., Appl. Swface. Sci., 1993, 67. 82. 28. Tsong, T.T., Surf&e Sci.. 1978, 70, 211. 29. Biswas. R.K. and Forbes. R.G., J. Phys. D: Appl. Phys., 1982, 15, 1323. 30. de Castilho, C.M.C. and Kingham, D.R., J. Phys. D: Appl. Phys., 1986. 19, 147. 31. Krohn, V.E., J. Appl. PhJs., 1974,45, 1144. 32. Kingham, D.R. and Swanson, L.W., Appl. Phys., 1984, A 34, 123 33. Mair. G.L.R., J. Phvs. D: Appl. Phvs., 1984, 17, 2323. 34. Mair. G.L.R., Vacu&. 1986;36,847. 35. Mair, G.L.R., Nucl. Insrr. Meth., 1994, B 88, 435. 36. Forbes, R.G., Mair, G.L.R.. Ljepojevic, N.N. and Liu, W., Appl. Surfiw sci.. 1995, 87. 99. 37. M&r. G.L.R., J. PhJs. D: Appl. Phys., 1982, 15, 2523. 38. Swanson, L.W. and Kingham, D.R., Appl. Phys., 1986, A 41,223. 39. Mair. G.L.R. and Forbes, R.G., J. Phys. D: Appl. Phys., 1991, 24, 2217. 40. Mair, G.L.R. and Forbes, R.G., Surfhce Sci., 1992, 266, 180. 41. Sudraud, P., private communication to G.L.R. Mair. 42. Liu, W. and Forbes, R-G., Appl. Surface Sci., 1995,87, 122. 43. Vladimirov, V.V., Badan, V.E., Gorshkov, V.N., Grechko, L.G. and Soloshenkco, A., J. Vat. Sci. Tech., 1991, B9, 2582. 44. Hornsey, R.I. and Marriott, P., J. Phys. D: Appl. Phys., 1989, 22, 699. 45. Mair, G.L.R. and von Engel, A., J. Phys. D: Appl. Phys., 1981, 14, 1721. ..v

R G Forbes: Understanding

how the liquid-metal

ion source works

46. Mtiller, E.W. and Tsong. T.T., Field Ion Microscopy: Principles and Applications. Elsevier, New York, 1969. 41. Swanson, L.W., Schwind, G.A. and Bell, A.E., J. Appl. Phys., 1980, 51, 3453. 48. Hornsey, R.I., Appl. Phys., 1989, A 49, 697. 49. Hornsey, RI., PhD Thesis, University of Oxford, 1989. 50. Hornsey, R.I., Jap. J. Appl. Phys., 1991, 30, 366. 51. Barr, D.L. and Brown, W.L., J. Vat. Sci. Tech., 1989, B7, 1806. 52. Electrohydrodynamic spraying was a special topic in: J. Aerosol. Sci., 45, 1994, 1005-1252. 53. Praprotnik, B., Driesel, W., Dietzsch, Ch. and Niedrig, N., Surface Sri., 1994,314, 353.

54. Mair, G.L.R., J. Phys. D: Appl. Phys., 1988, 21, 1654. 55. Kang, N., Orloff, J., Swanson, L.W. and Tuggle, D., J. Vat. Sci. Tech., 1981, 19, 1077. 56. Ward, J.W. and Seliger, R.D., J. Vat. Sci. Tech., 1981, 19, 1082. 57. Miskovsky, N.M. and Cutler, P.H., Appl. Phys., 1982, A 28, 73. 58. Kang, N.K. and Swanson, L.W., Appl. Phys., 1983, A 30,95. 59. Forbes, R.G. and Ljepojevic, N.N., Surface Sci., 1991, 246, 113. 60. Driesel, W., private communication. 61. Cui, Zheng and Tong, Linsu, J. Vat. Sci. Tech., 1988, B 6,2104. 62. Sato, M. and Orloff, J., J. Vat. Sci. Tech., 1991, B 9, 2602. 63. Orloff, J. and Li, J.-Z., Sato, M., Vat. Sci. Tech., 1991, B 9, 2609.

97