New electrostatic energy analysers with a bounded cylindrical field

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2005 Meas. Sci. Technol. 16 1798

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INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 16 (2005) 1798–1801 doi:10.1088/0957-0233/16/9/012

New electrostatic energy analysers with abounded cylindrical fieldA M Ilyin1 and I A Ilyina2

1 Physical Department, Kazakh National University, 96a, Tolebi Str., Almaty, 480012,Kazakhstan2 TRIO, Moscow, Russia

E-mail: ilyin@mail.kz

Received 10 March 2005, in final form 4 July 2005Published 29 July 2005Online at stacks.iop.org/MST/16/1798

AbstractA new class of electrostatic energy analysers with a bounded cylindricalfocusing field is presented. The focusing field used is a solution of a Laplaceequation ∇2U(R, Z) = 0 with boundary conditions U(R1, Z) = U(R, 0) =U(R, L) = 0 and U(R2, Z) = V, and restricted by concentric cylindricalsurfaces and two flat surfaces perpendicular to the axis of symmetry. Acharged particle beam enters the field through a face window in a flatboundary electrode. Regimes of second-order focusing have been found forconfigurations with a point source, located on the axis of symmetry and foran extended source of large angular size. In particular, the new analysers canbe used for electron spectroscopy of distant surfaces or surfaces with largeroughness or even with deep dimples. These instruments in principle haveno perceptible end-fields, which usually distort focusing in most of theanalysers known. The design of a compact analyser for remote Augerelectron spectroscopy and some experimental results, showing the capabilityof using these instruments for scientific and technological applications, aregiven.

Keywords: analyser, cylindrical, electrostatic, bounded field,electron spectroscopy

1. Introduction

In many problems related to surface analysis in materialsscience and surface physics, the object of investigation withelectron spectroscopy techniques is located at a relativelylarge distance from the analyser. Moreover, in manyapplications the flow of secondary electrons originates froman extended surface area, for instance when using soft x-raysor ultraviolet light as primary irradiation. In our recent papers[1, 2], focusing properties of a cylindrical mirror field fora configuration with a charged particle beam entering fromone side, directly between cylindrical electrodes, for fullrelativistic energy region were theoretically investigated. Itwas shown that a cylindrical mirror field provides only first-order focusing for such configurations. Previously [3], wesuggested the use of a well-known cylindrical mirror analyser(CMA) [4] bounded with two electrodes at z = 0 and z = L,where the first one held a set of annular ring electrodes and the

second one (arranged behind the exit window) was grounded.It should be noted that very interesting possibilities for CMAmodified in order to perform parallel acquisition of the energyspectrum of charged particles over a wide range of energieshave been proposed recently in papers [5, 6].

In the present paper, a new class of electrostatic energyanalysers based on the bounded cylindrical field is described.The analyser, also based on this field and providing the second-order focusing in the case of a parallel flow of charged particles,was previously considered in our paper [7].

2. A focusing field of the instruments

The field that has been used for all configurations is asolution of the Laplace equation ∇2U(R, Z) = 0 with boundaryconditions: U(R1, Z) = U(R, 0) = U(R, L) = 0, U(R2, Z) = Vand restricted by concentric cylindrical surfaces with radii R1

0957-0233/05/091798+04$30.00 © 2005 IOP Publishing Ltd Printed in the UK 1798

New electrostatic energy analysers with a bounded cylindrical field

(b)

(a)

Figure 1. The schematic cross-section views (the upper parts) oftwo main configurations of the focusing systems. (a) 1, the innercylinder; 2, the outer cylinder; 3, a first face electrode with theentrance window (4); 5, the exit window; 6, a second face electrode.S is the point source of charged particles and Fc is a circle focus nearthe axis of symmetry. (b) 1–3, 5, 6, the same as for the (a)configuration; 4, the narrow ring gap with a radius equal to R0. S isthe extended source and F is a point focus at the axis of symmetry.

and R2 (R1 < R2) and two flat surfaces perpendicular to theZ-axis (see figure 1).

The potential distribution for this electrostatic system canbe written as follows:

U(r, z) = 4V

π

∞∑n=0

sin((2n + 1)

πz

l

) Fn(r)

Fn(β)(2n + 1). (1)

The lengths in (1) and below were scaled with a radius ofthe inner cylinder R1, in order to introduce the dimensionlessparameters: r = R/R1, z = Z/R1, rc = Rc /R1, l = L/R1, β =R2/R1 (see figure 1). We will also use h as the dimensionlessdistance (h = H/R1) between a source and analyser. Here,Fn(r) = (I0 (knr)K0 (kn) − I0 (kn)K0(knr))/K0 (kn), kn = (2n +1)π/l. I0 and K0 are modified Bessel and Hankel functions,respectively.

Figure 1 represents two main configurations of theanalysers that use the bounded cylindrical field (1) andparticularly its face boundary region, which can be called theface field. The potential distribution (1) becomes very differentfrom a simple cylindrical mirror field near flat face boundaries.If the dimensionless distance l between the flat boundaries ismuch greater than β − 1, the potential distribution (1) in thecentral part is similar to the field used in the well-known CMA.

3. Calculations and design

The non-relativistic equations of motion in the field (1) aregiven by

Figure 2. The point-source analyser typical configuration:aberration figures, selected to show the second-order focusing, for aset of distances between a source and the analyser: (a) h = 10, G =2.80; (b) h = 8, G = 2.55; (c) h = 6, G = 2.30; (d) h = 4, G = 1.977;(e) h = 3, G = 1.835; for all graphs: l = 5, β = 2. Here, re is theentrance radial coordinate of a trajectory.

r̈ = − e

m∂U(r, z)/∂r (2)

z̈ = − e

m∂U(r, z)/∂z. (3)

Here, e and m are the charge and mass at rest of a particle,respectively. Unfortunately, it is impossible to solve theseequations analytically because of the complexity of the generalpotential (1). The system of equations (2), (3) has beenintegrated numerically to determine the trajectories of chargedparticles of a single kinetic energy E0 entering the field.The beam central trajectory entrance radial coordinate isr0 = R0/R1 and the central entrance angle is marked withθ0, corresponding to configurations shown in figure 1.

An investigation of focusing properties was performed bynumerically determining the crossing points for trajectories.Calculations were performed using the Runge–Kutta methodwith an absolute accuracy of the final coordinate of about0.002r1 for the configuration with a point source. In the caseof an extended source, the precision demanded was higher—near 0.001r1. In particular, the effect of addend numbersinvolved in calculations of the sum in (1) was investigated.Direct calculations of the sum in the right-hand terms of (2)and (3) were made from n = 0 to n = 90, considered to be theoptimal value. In order to obtain better processing conditionswith a sufficient accuracy, the cylindrical mirror analyser fieldwas simulated as a particular case of a central part of the field(1) by large l value. Results of calculations were comparedwith the results of the analytical solution in our paper [2] for anideal cylindrical mirror field with a distant source. All detailsand features of numerical calculations of focusing propertiesof the field (1) in our papers [7, 8] were given.

Figure 2 presents typical aberration figures (thedependence of the focusing length zf on re, the entranceradial coordinate) for a point-source configuration relatedto different values of a distance h between the source andanalyser. Regimes with a point focus, located on the axis ofsymmetry and with a circle focus of small diameter rc, coaxialto the symmetry axis were investigated. All curves have theshape of a cubic curve with a central twisting point, indicating

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A M Ilyin and I A Ilyina

Figure 3. Calculated dependence of relative values RrE of energy

resolution ability on a source size for an FFA analyser with a pointsource (filled symbols) and with CMA (open symbols). Sizes arescaled with R1 units, Rr

E are scaled with values of resolution abilityfor a point source. Values were obtained for the following set ofparameters: l = 5, β = 2, h = 8, G = 2.55.

the second-order focusing that is kept for each value of h bythe corresponding choice of G = E0/eV (where E0 is an initialkinetic energy of a focused particle and V is the potential ofthe outer cylinder).

It should be noted that one of the features of the newinstrument with a point-source configuration is that the anglebetween the central trajectory and the axis of symmetry can bekept small, especially by remote measurements. This providesthe possibility of analysis for objects located even inside deepholes and channels. In the case of CMA, it is not possiblebecause of the essential shielding effect [9].

Figure 3 presents the results of theoretical calculations ofenergy resolution ability for the analyser with a point sourcedepending on source size (or, in other words, on the size of thearea scanned). All resolution ability values are scaled with thatfor a point source, the size is scaled with R1. For comparison,data calculated for the CMA are presented. A jointconsideration of the results given shows that the resolutionability decreases with increasing source size. But, evidently,the range of permissible sizes is much larger for the FFA thanfor the CMA. In particular, this property is especially usefulin the applications of scanning Auger electron spectroscopy.

We have also considered the configuration which providesthe ability to analyse an extended area of surface. It seems avery promising instrument, by using the electron spectroscopytechniques, when the flow of charged particles originatesfrom an extended area under the influence of soft x-rays orultraviolet light as primary irradiation.

Graphs in figure 4, for the extended-source configuration,show that for some selected parameters regimes with sharpfocusing can be found. The angular interval is large enough.Obviously, if the radius of the ring source in the flat boundaryincreases, the angular interval with sharp focusing decreases.For this configuration with small circular diaphragm arrangedin the narrowest part of the beam, the energy resolution can behigher than that for the point focus.

The dispersions of these systems for each configurationwere calculated by using the expression

DE = (�z/�E)E, (4)

where �z were the finite segments obtained by trajectorycalculations for the small energy shift �E.

Figure 4. Typical behaviour of the aberration figures for theextended-source configuration. Graphs were calculated for thefollowing set of parameters: l = 4, β = 2; (a) y0 = 1.12; G = 1.34;(b) y0 = 1.15; G = 1.30 and (c) y0 = 1.18; G = 1.275.

Figure 5. The view of the face-field analyser for applications inscanning Auger electron spectroscopy. 1, the flange; 2, the outercylindrical electrode; 3, the face electrode (corresponds to 3 infigure 1); 4, the entrance window (corresponds to 4 in figure 1).

According to (4), DE was estimated to be on average aslarge as 5.1 for the point-source configurations and nearly 3.7for the extended-source configuration. The energy resolutionability was defined, as shown in [7, 8] for processing the setsof aberration figures:

RE = DE/�zf . (5)

Here �zf , as is well known, is a projection of the part of theaberration figure around a central point on the zf -axis. Theenergy resolution ability was found to be on average near 310for a point-source configuration with a point focus located onthe axis of symmetry. For comparison, the calculations fortypical CMA performed in the same way of estimation gavean energy resolution about 290. For the configuration withan extended source and a point focus the energy resolutionability was nearly 200, with an accepted angle interval 10–25◦. For the configuration with an extended source and thecircle focus (rc is equal nearly 0.09), the resolution ability wasnear 350 with the acceptance interval 5–30◦. A high enoughtransmission is provided for all cases because of cylindrical

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New electrostatic energy analysers with a bounded cylindrical field

Figure 6. Typical Auger spectrum obtained by the face-fieldanalyser from the 11Cr10Ni2Ti steel fracture surface. Analysis wasperformed directly in the UHV chamber of a home-made Augerspectrometer after high-temperature tensile testing. The specimenwas 22 cm distant from the analyser.

symmetry and a large acceptance angle—on average 6◦ for adistant point source and 20◦ for an extended source.

A typical view of the instrument for scanning Augerspectroscopy is given in figure 5. This compact shortenedanalyser with second-order focusing was designed for the‘point-to-circle’ scheme with object–analyser distance h = 9.8.The inner cylinder radius is equal to 2.2 × 10−2 m.

Figure 6 represents an Auger spectrum obtained from afracture surface of the steel 11Cr10Ni2Ti, fractured directlyin the UHV chamber of a home-made Auger spectrometer.The distance between the entrance window of the analyserand the target point was approximately equal to 0.22 m. Theprimary electron beam energy and the current intensity were3000 eV and 10 µA, respectively. The electron probe wascentred on the specimen fracture surface and analyser axis of

symmetry by maximizing the intensity of the elastic scatteredelectron peak. The measurements were performed using aspecial magnetic shield around the analyser, with the distancebetween the analyser and magnet block of a Penning-typepump of about 0.7 m.

4. Conclusion

Brief theory and designs of new types of electrostatic energyanalysers developed on the basis of a cylindrical boundedfield are presented. These instruments do not require anyfringe-field correction systems; they provide high-energyresolution ability and transmission, and the useful propertyof performing study of surfaces with large roughness and evenobjects situated inside deep holes and channels. Two mainfocusing configurations were studied numerically, which canbe used for building new electrostatic energy analysers withboth high-energy resolution ability (second-order focusing)and high transmission. Two different configurations of sourceanalyser, described in the paper, allow the investigation ofobjects having different sizes and geometries, and moreover,they make possible the remote electron spectroscopy of distantobjects. Some experimental results obtained by remote Augerelectron spectroscopy of a steel fracture surface are given forillustration.

References

[1] Ilyin A M 2000 About some focusing properties of a cylindricalfield J. Electron Spectrosc. Relat. Phenom. 113 1

[2] Ilyin A M 2002 Relativistic consideration of a cylindrical mirrorfield focusing for a distant charged particle source Nucl.Instrum. Methods Phys. Res. A 485 234

[3] Ilyin A M 1995 Some focusing properties of a cylindricalmirror field Pis. Zh. Tekh. Fiz. 21 42

[4] Risley J S 1972 Design parameters for the cylindrical mirrorenergy analyzer Rev. Sci. Instrum. 43 95

[5] Read F H 2002 The parallel cylindrical mirror electron energyanalyzer Rev. Sci. Instrum. 73 1129

[6] Read F H, Cubric D, Kumashiro S and Walker A 2004 Theparallel cylindrical mirror analyzer: axis-to-axisconfiguration Nucl. Instrum. Methods Phys. Res. A 519 338

[7] Ilyin A M 2001 Focusing properties of a bounded cylindricalfield J. Electron Spectrosc. Relat. Phenom. 120 89

[8] Ilyin A M and Borisov B A 2001 Second-order focusing of abounded cylindrical field for a distant source Meas. Sci.Technol. 12 2015

[9] Ilyin A M 1994 Surface roughness correction of data in Augerspectroscopy Zh. Tekh. Fiz. 64 188

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