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A UNIFIED DESCRIPTION OF LIQUID METAL ION SOURCE ENERGY DISTRIBUTIONS
R. Hornsey
To cite this version:
R. Hornsey. A UNIFIED DESCRIPTION OF LIQUID METAL ION SOURCE ENERGY DISTRIBU- TIONS. Journal de Physique Colloques, 1989, 50 (C8), pp.C8-197-C8-202. �10.1051/jphyscol:1989834�.
�jpa-00229932�
COLLOQUE DE PHYSIQUE
Colloque C8, suppl6ment au n o 11, Tome 50, novembre 1989
A UNIFIED DESCRIPTION OF LIQUID METAL ION SOURCE ENERGY DISTRIBUTIONS R.I. HORNSEY
Department of Engineering Science, University of Oxford, Parks Road, GB-Oxford OX1 3PJ, Great-Britain
Abstract.
Energy distributions for liquid metal ion sources (LMIS) operated close to the melting point of the feedstock are well known. Despite this, reasons for the shift in voltage deficit with current have remained unclear. The change in characteristics when LMIS are operated at elevated temperatures has hitherto been treated as a separate effect and has lacked adequate explanation. Angular-resolved results presented here for a gallium LMIS confirm that a secondarx peak is formed in the energy distribution diagram at temperatures above 250 C. It is argued that a distribution based on a spectrum of energies can correlate both high and low temperature data. From comparisons between angular resolved results in these two regimes, it is concluded that LMIS behaviour with current and with temperature derives from fundamentally the same effect. It is proposed that emission is by a single ionisation mechanism but that the final distribution is distorted by additional processes. A model based on a peak splitting effect due to longitudinal movements of the LMIS apical jet is discussed. This model is shown to predict observed LMIS distribution shapes in the high and low temperature regimes and to account for the off-axis variation.
1. Introduction.
Liquid metal ion sources ILMIS) have found avvlications as the source of
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ions for focussed ion beam 'machines which can be used for materials inspection, modification and characterisation. In addition to such practical uses, LMIS represent a self-contained physical system of great interest and display many complex and puzzling characteristics. The energy distributions (EDs) of ions emitted from LMIS are important both for the designers of focussed ion beam machines and for the investigation of the fundamental processes of LMIS emission.
The study of EDs can be broken down into three main areas; the variation with source current, angular variations and the effects of source temperature. Although work has been carried out with many different liquid metal feedstocks, the material about which most is known is gallium and the following discussion is confined to LMIS of that metal, in particular the singly charged ionic species.
At low temperatures ( < - 1 0 0 ~ ~ ) and low currents, the ED shape is almost Gaussian with a mean energy that represents a deficit. As the current is increased, so the full width at half maximum (FWHM) of the distribution rises in accordance with an energy broadening process based on particle interactions in the beam \l\. At the same time, the mean energy of the ED moves towards higher energies (smaller deficit) before moving to an "energy gaint1 (negative deficit) position. Marriott \2\ has shown convincingly that this peak shift is the result of increasing asymmetry of the ED, (a finding supported for an In LMIS \ 3 \ ) . Reasons for this asymmetry were unknown.
Angular resolved measurements of the ED for Ga \4\ show that the angular intensity, the FWHM and the deficit all display a "hornedtt structure where the parameter is approximately constant for low angles before rising sharply to a maximum and then falling steeply at higher angles. The shape of the angular intensity variation with angle has been described theoretically by Kingham and Swanson \5\ but no explanation has yet been forwarded for the form of the FWHM and voltage deficit curves.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989834
Major changes in the form of the ED are seen when the source is heated to abnormally high temperatures \6\. When the LMIS is operated at a low current (eg. 2uA) and above -25ooc, what appears to be a secondary peak forms on the low energy side of the distribution. An associated occurrence is the shift of the primary peak towards higher energies. These variations are confirmed in Fig.1.
Fig.1. Normalised energy scans Fig.2. Normalised energy scans for for gallium at 2uA and various gallium at 2pA and 450 Celsius and
temperatures. various angles.
It has been proposed that gas phase field ionisation is responsible for the formation of the secondary peak \5,7\ but recent experiments in this laboratory have cast doubt upon this mechanism \8,9\. Angular resolved energy scans at elevated temperatures (Fig.2, see also ref. \g\) demonstrate that the secondary peak oformation is not limited to axial ions. As the angle is increased beyond -8
,
it is seen that the ED curves change in a way similar to that which would be expected by cooling the LMIS; the curves become almost Gaussian again at very large angles.2. Suectral Hv~othesis.
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Building on the conclusion that field ionisation is not responsible for the elevated behaviour of the ED curves, the present paper examines the hypothesis that ions are emitted by a single process but that the final ED shape results from a distortion of the normal Gaussian shape. The particular proposal is that the final ED shape is a convolution of an energy spectrum with a Gaussian from the broadening process.Because the processes that cause energy spectrum are not necessarily solely activated thermally, there is no a priori reason why both low and high temperature EDs could not result from fundamentally the same effect. Ishitani et a1 \10\ demonstrated that the elevated temperature distortion was only visible at low sources currents. As the current was increased, the increasing broadening masked out the secondary peak. The shape so created displayed a remarkable similarity to those asymmetric Gaussians seen at low temperature and high currents.
This provides the link between the two operating regimes. It is proposed here that the process giving rise to the underlying spectrum is driven either by temperature or by current. As the temperature is increased, the spectrum of energies would. also increase, giving rise to the ED distortion (this is visible because the broadening remains constant). If the current is increased, the specrum of energies would again increase but so too would the broadening, at all times masking the fine structure of the distribution thus creating an asymmetric Gaussian. In both cases, the same shift of the main peak to higher energies is seen.
A consequence of this is that the angular behaviour of the LMIS at high temperature should reveal the underlying effects that cause the low temperature angular variations. Plotting the FWHM versus angle for the LMIS
at 4 5 0 Celsius (Fig.3) and a similar curve for the voltage deficit (Fig.4),
we can see that the characteristics at elevated temperature are strikingly similar to those found under normal operating conditions \ 4 \ . From Fig. 2 it is apparent that, when the secondary peak has formed sufficiently to be below the half-height, the FWHM of the distribution will be small. Moreover, it will remain constant for as long as the distortion is below the half-height.
As the angle is increased, so the secondary peak slides up the primary until it begins to become included in the FWHM value, causing the FWHM to rise. At very large angles, the ED reverts almost to a Gaussian again and the FWHM is small. Thus the high temperature data reveal the underlying causes of the high current angular dependence of ED shape.
Angle. degrees A n g l e , degrees
Fig.3. Variation of FWHM with angle Fig.4. Variation of voltage deficit for gallium at 2fiA and 4 5 0 Celsius. with angle for gallium at 2uA and
4 5 0 Celsius.
3. Inertial Peak Swlittinq.
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From the previous section, it appears that the process causing the formation of the underlying energy spectrum is dependent on current and temperature. One physical factor that might give rise to such an effect is oscillations at the LMIS apex.If emitted from a stationary apex, the ion would achieve a final kinetic energy equal to that gained from the applied potential. If, however, the tip were moving at the time of ion emission then the ion, owing to its inertia, could arrive with an energy that would be apparently different from that which would otherwise be expected.
~nitially, the emitted ion would be moving slowly although its acceleration would be very high. In the first moments after emission, therefore, the tip velocity could be large compared to that of the ion. The extremely high field near the apex would ensure that the ion would not recombine with the metal. So, if the tip were moving forwards, the potential at the ion's position would be increasing to a value above that which would normally be present at that position. Eventually the ion would be accelerated to a velocity high enough to escape the influence of the tip. From this point onwards it would effectively fall through the full applied potential in addition to possessing its initial energy owing to the higher-than-normal initial potential.
Conversely, an ion leaving a retracting tip would "have the ground pulled from beneath its feetN. As the tip fell away below the slowly moving ion, the potential at the ion's position would be dropping and the reduced
final energy of the ion would reflect this lower apparent starting potential.
Assuming that the rate of ion emission was uniform, then a spectrum of energies would result from ions emitted at different phases of the tip oscillation.
The degree to which the final energies of the emitted ions are affected depends on the inertia of the ion and on the velocity of the tip (ie. the frequency and amplitude of oscillation). The shape of the resultant energy distribution is thus determined by the waveform (length versus time) of the longitudinal tip oscillation.
In order to investigate the peak splitting phenomenon further, a computer model has been developed to track ions, emitted throughout the tip cycle, between the source and the extractor. The motion of the ion is split up into a number of time intervals. New ion positions and velocities are calculated by assuming that the electric field is constant in that intelrval and by applying Newtonfs laws of motion. Running totals of the ionfs velocity and position enable its kinetic energy at the extractor to be determined.
An analytical expression for the electric field at any point in space is only possible for certain source/extractor geometries. The one used here is that of a hyperboloidal emitter and a plane extractor with a common focus.
The equation for the field is found to be
where E is the electric field, V is the applied potential, a is the focus extractor separation, R is the distance from the hyperboloid focus to the tip surface and r is the ionfs position (the derivation of this expression and a detailed description of the computer program are given elsewhere (submitted to J.Phys D: Appl. Phys.)).
In fact, the model was found to be insensitive to the form of the potential. The oscillating LNIS tip causes fluctuations in the potential at any given location. The steeper the drop in potential with distance from the tip, so the more effect the oscillation will have at that point. However, steeper functions will reduce the distance from the tip at which such effects are significant. These two variations tend to cancel, reducing the impact of varying the potential profile.
A number of test ions are emitted from the tip at equal intervals through the tip oscillation cycle. A base energy, corresponding to the energy of an ion run through the program with a stationary tip, is subtracted from the ion energies to give a difference. Such differences are rounded to the nearest 0.5eV and the number of ions with each energy is used to scale the intensity of a Gaussian (representing the broadening, not calculated here) at that energy. All such Gaussians are summed to give the final ED shape.
4. Peak Splittina Results.
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Several parameters have to be specified in order to apply the computer simulation. In this discussion V and R in equation 1 are fixed at 5000V and 50A respectively (giving a surface field of 8.2V/A). As noted above, the waveform of the tip oscillation determines the symmetry or otherwise of the final ED. For the present purpose a rectified sinusoidal waveform is used, of the form L = A(l
-
sin nt/T), where L is the magnitude of the oscillation, Ais the amplitude, t is the time and T is the oscillation period. Peak splitting will occur with any function but this form was chosen for its resemblence to the unstable behaviour of a conducting fluid in an electric field while retaining analytical simplicity.
There remain three parameters to investigate; oscillation frequency and
amplitude and the broadening FWHM. The effect of each separate variable has been considered in detail elsewhere (submitted to J-Phys. D: Appl. Phys.) so two families of curves are presented here to reproduce temperature and current dependent ED shapes.
Amplitude. L0 A
FWHM. 5eV
Voltage deficit, V
Fig.5. ED curves generated by the peak splitting model for the indicated frequencies (in G H z ) for constant amplitude and broadening.
Fig.6. ED curves generated by the peak splitting model for constant amplitude but for the frequencies and broadenings indicated.
Fig.5 shows curves generated for different frequencies at constant broadening and amplitude whereas Fig.6 attempts to simulate the asymmetric Gaussians seen at higher currents by varying both frequency and broadening. No attempt has been made here to relate frequency (or amplitude) to actual currents and
temperatures owing to the extreme complexity involved in the characterisation of a feature so small as the LMIS apical jet.
5. Discussion.
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It can be seen from Fig.s 5 & 6 that- the inertial peak splitting model is capable of generating ED curves that compare well with those found experimentally. Indeed, this effect is an almost inevitable occurrence if oscillations of high enough frequencies are present on the apical jet.Some experimental evidence does exist to support the notion of high frequency fluctuations at the LMIS apex, albeit indirectly. Wholescale disintegration of the jet has been cited as the cause of interruptions in the emitted current at frequencies of up to 400MHz \10,11\, measured using a sophisticated streak camera and using fourier transform technique. It has already been noted that, for the bulk Taylor cone, redistribution of the metal can occur ten times faster than the cone's formation time \12\. If the frequencies found for the jet breakup are scaled similarly, GHz oscillations may be inferred. Such oscillations may be small (-10% of the jet length) and would not impose significant modulation on the emitted current.
All the above computer simulations are for axial ions only, angular variations being hard to assess with the current algorithm. However, some qualitative arguments may be forwarded to explain the angular dependence of the ED plots.
The energy of an ion that is emitted non-axially will comprise both transverse and axial components and because the motion of the jet is essentially axial, only the latter component of the energy will undergo peak splitting. Thus, for ions emitted at larger angles, the proportion of the total energy represented by the axial component would fall and with it the effective peak splitting, leading to the apparent "cooling** of the ED curves that is seen experimentally. As has already been noted, it is this
"cooling1* that results in the observed variations of voltage deficit and FWHM with angle in both the high and low temperature regimes.
6. Conclusion.
From the preceeding paragraphs it is seen that the concept of LMIS energy distributions based, not on a single Gaussian but on a spectrum of energies, fits the available evidence very well. It has also been demonstrated that this spectrum can be caused by longitudinal oscillations of the apical jet, provided that they are at a high enough frequency. The inertial peak splitting model therefore forms a common link between high and low temperature LMIS energy distributions.
Acknowledsements.
The author wishes to thank Dr. J.C. Riviere, Dr R.G. Lord, Dr. S.G.
Ingram, Dr. P.D. Prewett and Dr. P. Marriott for many useful discussions during the preparation of this paper. This work was carried out as part of a collaboration between the University of Oxford and Harwell Laboratory and was funded by the underlying research budget of the UKAEA.
References.
\l\ Knauer W. 1981 Optik 5 9 335
\2\ Marriott P. 19879 Appl. Phys. A. 44 329
\3\ Hornsey R.I. 1989 to be published in Appl. Phys A
\4\ Marriott P. 1987 J. de Physique 48 C6-189
\5\ Kingham D.R and Swanson L.W. 1984 Appl. Phys. A 34 123
\6\ Swanson L.W., Schwind G.A. and Bell A.E. 1980 J. Appl. Phys. 5 1 3453
\7\ Komuro M. and Kato T. 1987 Proc 6th Symp. ISIAT ed. T. Takagi p63
\8\ Hornsey R.I.and Marriott P., 1989 J.Phys. D: Appl. Phys. 22 699
\9\ Hornsey R.I. 1989 to be published in Appl. Phys A
\10\ Barr D.L., Thomson D.J. and Brown W.L. 1988 J. Vac. Sci. Technol. B6 482
\11\ Barr D.L., Brown W.L. and Thomson D.J. 1988 J. de Physique 49-C6 177
\12\ Thompson S.P and Prewett P.D. 1984 J. Phys. D: Appl. Phys. 17 2305
