Nuclear Instruments and Methods in Physics Research A 500 (2003) 62–67

New class of electrostatic energy analyzers with acylindrical face-field

A.M. Ilyin

Kazakh State University, Research Institute of Experimental and Theoretical Physics, Tolebi str., 96a, Almaty 480012, Kazakhstan

Received 27 February 2002; received in revised form 13 August 2002; accepted 21 November 2002

Abstract

A new class of electrostatic energy analyzers based on a cylindrical face-field is presented. The focusing field used is a

solution of a Laplace equation r2UðR;ZÞ ¼ 0 with boundary conditions UðR1;ZÞ ¼ UðR; 0Þ ¼ UðR;LÞ ¼ 0 and

UðR2;ZÞ ¼ V and restricted by concentric cylindrical surfaces and two flat surfaces perpendicular to the axis of

symmetry. Regimes of a second-order focusing were found for different types of sources, including a point-source, an

extended surface source of large angular size and a flow parallel to the symmetry axis, while charged particles entered

into the analyzer through a face-window arranged in a boundary electrode. Some results are described showing the

capability of utilizing the prototype cylindrical face-field-analyzer for distant surface chemistry monitoring.

r 2002 Elsevier Science B.V. All rights reserved.

PACS: 87.64 Pj Electron and photoelectron spectroscopy

Keywords: Electrostatic cylindrical face-field energy analyzer; Face-entrance-window; Focusing properties

1. Introduction

A cylindrical mirror analyzer (CMA) [1] is oneof the most widespread instruments in modernelectron spectroscopy. Unfortunately, its essen-tially restricted electron-optical configuration,where a point object must be located very closeto the analyzer, limits the field of its application. Itis known that a CMA is characterized by a beamcentral trajectory slope angle equal to 42:3� whilethe entrance window is made in the inner cylinder.So, an object must be located at a short distancefrom the CMA.

In many problems related to nuclear physics aswell as to materials science, and even to fusionreactor technology, an object of investigation, as arule, is arranged at relatively large distances fromthe analyzer. Moreover, in space investigationsand plasma diagnostic the flow of chargedparticles originates from an extended source or isparallel to some direction. In our recent papers[2,3], focusing properties of a cylindrical mirrorfield for full relativistic energy region weretheoretically investigated for end-entrance-windowconfiguration. It was shown that for a distantpoint source and for a flow parallel to thesymmetry axis entering between cylindricalelectrodes, CMA-field provides only first-orderfocusing.E-mail address: ilyin@mail.kz (A.M. Ilyin).

0168-9002/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0168-9002(03)00334-6

A first application of a cylindrical field boundedto the axis of symmetry was investigated in ourwork [4] as an attempt at improving CMA ‘‘point-to-point’’ second-order focusing. Essentially newresults were obtained in our recent papers [5,6]where the configurations with charged particlebeam entering the analyzer through a face-windowwere investigated. In the present paper newsystems of this kind are described in general.Three interesting configurations were studied, thatcan be used for building new electrostatic energyanalyzers with both high energy resolution andtransmission. These new types of instruments canbe called cylindrical face-field-analyzers (CFFA).

2. A focusing field of the instruments

The field that has been used is a solution of theLaplace equation r2UðR;ZÞ ¼ 0 with boundaryconditions: UðR1;ZÞ ¼ UðR; 0Þ ¼ UðR;LÞ ¼ 0;UðR2;ZÞ ¼ V and restricted by concentriccylindrical surfaces with radii R1 andR2 ðR1oR2Þ and two flat surfaces perpendicularto Z-axis (see Fig. 1).

The potential distribution for this electrostaticsystem can be written as follows:

Uðr � zÞ ¼4V

p

XNm¼0

sin ð2m þ 1Þpz

l

� �

�FmðrÞ

FmðbÞð2m þ 1Þ: ð1Þ

The lengths in Eq. (1) and below were scaledwith a radius of the inner cylinder R1; in order tointroduce the dimensionless parameters: r ¼R=R1; z ¼ Z=R1; l ¼ L=R1; b ¼ R2=R1 (seeFig. 1). We also will use h as the dimensionlessdistance ðh ¼ H=R1Þ between a source and analy-zer. Here FmðrÞ ¼ ðI0ðkmrÞK0ðkmÞ I0ðkmÞK0ðkmrÞÞ=K0ðkmÞ; km ¼ ð2m þ 1Þp=l: I0 and K0 are modifiedBessel and Hankel functions, respectively.

If the dimensionless distance l between the flatboundaries is much greater than b 1; thepotential distribution (1) in the central part isequivalent to the field used in CMA:

UðrÞ ¼ VlnðrÞlnðbÞ

: ð2Þ

When the entrance window is made in the innercylinder and the central trajectory slope angle isequal to 42:3�; the CMA is ‘‘second-order focus-ing’’. In order to obtain the potential distribution(2) for a practical device of a limited length, CMAshould be equipped with special end-field correc-tion systems.

The potential distribution (1) becomes verydifferent from a simple expression (2) near flatface-boundaries.

Fig. 1 represents three main configurations ofthe analyzers that use a cylindrical field (1) andparticularly its face boundary region, which can be

Fig. 1. The schematic cross-section views (the upper parts) of

three main configurations of the focusing system investigated.

(a): 1—the inner cylinder , 2—the outer cylinder, 3—a first face-

electrode with the entrance window 4, 5—the exit window, 6—a

second face-electrode, S—the point source of charged particles

with impulse P0; EM—the electron multiplier; (b) and (c): 1, 2,

3, 5, 6—the same as that for the above configuration; (b only):

4—the narrow ring-gap with a radius equal to R0; S—the source

of charged particles with large angular size.

A.M. Ilyin / Nuclear Instruments and Methods in Physics Research A 500 (2003) 62–67 63

called the face-field. The (a) configuration relatesto a ‘‘point-to -point’’ focusing with a point sourcethat is distant from the analyzer (further—P-configuration). The (b) one represents the‘‘ring-point’’ focusing configuration with an ex-tended source, (hereafter—E-configuration). Inthis case the entrance window is made as a verynarrow ring gap. The (c) configuration (that isfurther marked as PF) can be used for measuring aparallel flow (with a momentum parallel to the axisof symmetry).

3. Calculations and design

The non-relativistic equations of motion in thefield (1) are given by

.r ¼ e

m

@Uðr; zÞ@r

ð3Þ

.z ¼ e

m

@Uðr; zÞ@z

: ð4Þ

Unfortunately, it is impossible to solve theseequations analytically because of the complexity ofthe general potential (1). The system of equations(3), (4) has been integrated numerically to deter-mine the trajectories of charged particles of asingle kinetic energy E0; entering into the field. Thebeam central trajectory entrance radial coordinateis r0 ¼ R0=R1 and the entrance angle is marked y0;corresponding to configurations shown in Fig. 1.

An investigation of focusing properties for thethree configurations, shown in Fig. 1 was per-formed by determining the axial crossing pointsfor trajectories of charged particles. Some impor-tant points relating to the accuracy of calculationscan be noticed here.

Calculations were performed using Runge–Kutta method with an absolute accuracy of thefinal coordinate of about 0:002r1: In particular, theeffect of added numbers involved in calculations ofthe sum in Eq. (1) was investigated. Directcalculations of the sum in the right-hand termsof Eqs. (3) and (4) were made for m from m ¼ 0 to90, considered to be the optimal value. In order toobtain optimal processing conditions with suffi-cient accuracy, the CMA field was simulated as aparticular case of Eq. (1) by large l value, and

results of calculations for end-entrance-windowwere compared with the results of the analyticalsolution in our paper [2] for an ideal cylindricalmirror field. The detailed description of the fieldand some features of the numerical calculations ingeneral case with l ranged in wide interval weregiven in our papers [5,6]. In this paper calculationswere made for the low values of l (ranging fromabout 4–6) in order to provide a theoreticalground for practical compact devices withoutany end-field correction systems.

Fig. 2 presents selected aberration figures (thedependence of the focusing length zf on rent; theentrance radial coordinate) for P-configurationrelated to three different values of a distance h

between a source and analyzer. All curves have theshape of a cubic curve with a central twistingpoint, indicating the second-order focusing that iskept for each value of h by corresponding choice ofG ¼ E0=eV ðE0—an initial kinetic energy of aparticle focused, V—a potential of the outercylinder).

It should be noticed, that the P-configurationprovides a very useful property—within someinterval of values a distance h to the source canbe changed by negligible variations of focusingquality for the constant value of zf ; which iscommonly a definite parameter of the device. Forexample, regression (5) gives values of focusing

Fig. 2. P-configuration of the analyzer: a typical aberration

figures, shown the second order focusing, for a set of distances

between a source and the analyzer: 1: h ¼ 10; G ¼ 2:80; 2 :h ¼ 8; G ¼ 2:55; 3 : h ¼ 6; G ¼ 2:30; all graphs: l ¼ 5; b ¼ 2:Here rent—the entrance radial coordinate of a trajectory.

A.M. Ilyin / Nuclear Instruments and Methods in Physics Research A 500 (2003) 62–6764

parameter G; needed for keeping the second-orderfocusing, by changing distance h from the analyzerto an object in relatively large interval, whenfocusing length zf is equal to 6.09:

GðhÞ ¼ 3:991 þ 0:022h 1:197104h2: ð5Þ

This regression was obtained by considerationof appropriate aberration figures obtained fromnumerical calculations of the trajectory. Values ofh in Eq. (5) are varying from 20 to 100 in R1 units.

It should be noticed, that the new instrumentwith a P-configuration has one more advantage incomparison with a CMA: the angle between thecentral trajectory and the axis of symmetry can bemade relatively small. This provides a possibilityof analysis for objects located even inside deepholes. In the case of CMA, the roughness ofobjects is a problem, because of essential shieldingeffect. It was studied theoretically in our work [7].

Fig. 3 presents the results of theoretical calcula-tions of energy resolution ability for P-configura-tion (for a definite set of parameters) independence on a source size, which is scaled withR1: All resolution ability values are scaled with aresolution ability for a point source. For compar-ison, data calculated for a CMA are presented. Itshould be noted that the latter are in goodagreement with the resolution values behavior,given in Ref. [8]. A joint consideration of the

results presented shows that the resolution abilitydecreases with increasing a source size. But,evidently, the range of permissible sizes is muchlarger for the face-field analyzer. In particular, thisproperty is very useful for the application ofscanning Auger Electron Spectroscopy.

For PF-configuration with entering flow parallelto the axis of symmetry, it was also shown that aradial size of the entrance window—and accord-ingly transmission—can increase with increasing bvalue. The results of the large number of calcula-tions are collected in regressions (6) and (7), givingthe possibility to use device with large b: Sub-stituting the certain value of b between 1.8 and 3.0one can obtain the corresponding values of themain focusing parameters—zf and G:

zf ðbÞ ¼ 0:473 þ 3:819b 0:452b2 ð6Þ

GðbÞ ¼ 87:031 þ 96:402b 25:031b2: ð7Þ

Expression (6) corresponds to the centraltrajectory of a beam, entering the field at a radialcoordinate r0:

Some regimes were also found that are suitablefor measuring high-energy charged particles,characterized by large value of the relation G:For instance, b ¼ 2; G ¼ 5:65; r0 ¼ 1:56; withfocal length equal to 6.3.

Graphs in Fig. 4 concerning E-configuration,allow the selection of a sharp focusing regimewhich is characterized by the following set ofparameters: l ¼ 4; G ¼ 1:42; b ¼ 1:8; and r0 ¼1:2 (graph 3) for entering beam with angle varyingwithin ymin ¼ 0 and ymax ¼ 25�:

The dispersion of the system was calculated foreach configuration using the expression

DE ¼ ðDz=DEÞE ð8Þ

where Dz were the finite segments obtained bytrajectory calculations for the small energy shiftDE:

According to Eq. (8) DE was estimated to be onaverage as large as 4.0 for the P- and PF-configurations and 2.5 for the E-configuration.The energy resolution ability was defined, as it wasshown in Ref. [6] for processing the sets ofaberration figures:

RE ¼ DE=Dzf : ð9Þ

Fig. 3. Calculated dependence of relative values RrE of energy

resolution ability on a source size for P-configuration analyzer

(black marks) and for CMA (light marks). Sizes are scaled with

R1 units. Values were obtained for a following set of

parameters: l ¼ 5; b ¼ 2; h ¼ 8; G ¼ 2:55:

A.M. Ilyin / Nuclear Instruments and Methods in Physics Research A 500 (2003) 62–67 65

Here Dzf ; as it is well known, is a projection ofthe part of the aberration figure around a centralpoint on the zf -axis. The energy resolution ability

was found to be on average near 230 for a P- andPF-configurations and about 180 for E-configura-tion. A high enough transmission is provided forall cases because of a cylindrical symmetry and alarge acceptance angle.

A typical view of the instrument with a wideentrance window, related to P-configuration, isgiven in Fig. 5. This compact shorten analyzerwith the second-order focusing without any fringefield correction system was designed for ‘‘point-to-point’’ scheme by l ¼ 5:6; b ¼ 2:2; h ¼ 8: Theinner cylinder radius is equal to 2 � 102 m:

Fig. 4. Typical behavior of the aberration figures for E-

configuration—analyzer. Graphs were calculated for a follow-

ing set of parameters: l ¼ 4; y0 ¼ 1:2; b ¼ 1:8; G ¼: 1–1.38; 2–

1.40; 3–1.42; 4–1.44.

Fig. 5. The view of the face-field analyzer designed in config-

uration with a point object (‘‘axis–axis’’ focusing) for applica-

tions in Auger Electron Spectroscopy. The analyzer was

performed with a short length ðl ¼ 5:5Þ; without any fringe-

field correction systems. 1—the flange, 2—the holder, 3—the

outer cylindrical electrode, 4—the face boundary electrode

(corresponds to 3 in Fig. 1), 5—the entrance window (corre-

sponds to 4 in Fig. 1), 6—the ceramic insulators.

Fig. 6. The Auger spectra from a surface area of an Auger-

spectrometer chamber-wall. Distance of the analyzed point

from the face-window of the analyzer was about 16 cm: The

upper spectrum was obtained after technological baking the

chamber ð250�C; 15 hÞ; by P ¼ 107 Pa; at room temperature.

The lower spectrum was registered after short-time—heating of

a titanium sublimation pump accompanied by a pressure

increase to 105 Pa:

A.M. Ilyin / Nuclear Instruments and Methods in Physics Research A 500 (2003) 62–6766

Fig. 6 represents Auger-spectra obtained by thefirst testing above of the P-configuration proto-type-analyzer. The analyzer and an electron gunwere placed on the flange of an Auger electronspectrometer. The inner surface of the chamberwall was used as a target. The distance between theentrance window-plate of the analyzer and thetarget point located on the opposite area of thechamber wall was approximately equal to 16 cm:The primary electron beam energy and the currentintensity were 2500 eV; and 20 mA; respectively.The electron probe was centered on the analyzeraxis of symmetry by maximizing the intensity ofelastic scattered electron peak. All measurementswere performed without a special magnetic shieldaround the analyzer, for a distance between theanalyzer and magnet block of a penning-typepump of about 0:7 m:

The above spectrum was obtained at roomtemperature, in vacuum P ¼ 107 Pa; after thetechnological baking the chamber of spectrometerat 250�C for 15 h: It demonstrates the usual highlevel of carbon on the surface (likely related tohydrocarbon layer), nitrogen, oxygen and chlor-ine. The lower spectrum was registered after short-time—heating of a titanium sublimation pumpingdevice accompanied by unexpected pressure riseup to 105 Pa: Evidently, this simulated ‘‘acci-dent’’ lead to some pollution of the wall surfacewith Ti, N, C.

4. Conclusion

Brief theory and design of a new type ofelectrostatic energy analyzers developed on thebase of a cylindrical bounded field are presented.These instruments can be called cylindrical face-field analyzers (CFFA). Three different configura-tions of the object-analyzer allow the study ofpractically all kinds of objects. These analyzers arevery useful for experimental and technologicalapplications in the field of electron spectroscopyand nuclear physics. The prototype-analyzer thathad been designed for the application in Augerelectron spectroscopy was successfully used fordistant surface chemistry monitoring.

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A.M. Ilyin / Nuclear Instruments and Methods in Physics Research A 500 (2003) 62–67 67