New multichannel electron energy analyzer with cylindrically symmetrical electrostaticfieldP. Cizmar, I. Müllerová, M. Jacka, and A. Pratt Citation: Review of Scientific Instruments 78, 053714 (2007); doi: 10.1063/1.2737759 View online: http://dx.doi.org/10.1063/1.2737759 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/78/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in High Voltage-Cylinder Sector Analyzer 300/15: A cylindrical sector analyzer for electron kinetic energies up to 15keV Rev. Sci. Instrum. 81, 043304 (2010); 10.1063/1.3398441 Design Considerations of Distorted Field Cylindrical Mirror Electron Energy Analyzers AIP Conf. Proc. 899, 569 (2007); 10.1063/1.2733310 The parallel cylindrical mirror electron energy analyzer Rev. Sci. Instrum. 73, 1129 (2002); 10.1063/1.1435841 A fast, parallel acquisition, electron energy analyzer: The hyperbolic field analyzer Rev. Sci. Instrum. 70, 2282 (1999); 10.1063/1.1149753 Ion energy loss spectroscopic apparatus using cylindrical electrostatic energy analyzer equipped with theMatsuda plate Rev. Sci. Instrum. 68, 3042 (1997); 10.1063/1.1148238

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New multichannel electron energy analyzer with cylindrically symmetricalelectrostatic field

P. Cizmar,a� I. Müllerová, M. Jacka,b� and A. Prattc�

Institute of Scientific Instruments, ASCR, Královopolská 147, Brno CZ-61264, Czech Republic

�Received 14 November 2006; accepted 16 April 2007; published online 23 May 2007�

This article discusses an electron energy analyzer with a cylindrically symmetrical electrostaticfield, designed for rapid Auger analysis. The device was designed and built. The best parameters ofthe analyzer were estimated and then experimentally verified. © 2007 American Institute of Physics.�DOI: 10.1063/1.2737759�

I. INTRODUCTION

One of the nearly nondestructive methods to examinesurfaces of materials is the analysis of Auger electrons.These have energies from the range roughly from 50 to 2000eV and are emitted from the top few nanometers givingunique valuable surface sensitivity.

Most common sequential analyzers, such as cylindricalmirror analyzer �CMA� and concentric hemispherical ana-lyzer �CHA� that are often used for Auger analysis are dis-cussed in Ref. 1. There are other electron energy analyzers,e.g., toroidal mirror analyzer.2 This analyzer allows simulta-neous acquisition of electron energy and angular distributionof electrons and electron pairs.3

Although many tens of percents of emitted electrons canbe collected by some analyzers, this still may not be suffi-ciently fast because energies are analyzed sequentially. Eachtime the particular detection energy is changed, there is adead time needed by the system to get into the desired state.Such analyzers then need much more time to obtain a spec-trum. This can be a serious issue for time dependent experi-ments, if the sample can be easily damaged by the electronbeam or if a spectrum is acquired for each pixel in an entireimage.

In general, in order to reduce the time needed to acquirea spectrum, either the solid angle intercepted by the analyzercan be increased or parallel detection can be employed. Itwas shown4 that it is possible to acquire the entire energyspectrum of interest simultaneously. The basis of the ana-lyzer used was the two-dimensional hyperbolic field.5,10

The approach in this work is the development of an ana-lyzer that keeps all the advantages of parallel acquisition andthat also has a possibility to increase the solid angle by add-ing cylindrical symmetry with a new focusing property �Fig.1�. The advantage of this solution is a further decrease of thetime needed to acquire the spectrum.

II. CYLINDRICALLY SYMMETRICAL ELECTROSTATICFIELD

There are several conditions for the electrostatic field tobe usable for electron energy analysis. First, Laplace’s equa-tion has to be satisfied. The trajectories of the electrons ana-lyzed by the field have to be focused in the detector plane. Inthis case, the field has cylindrical symmetry, therefore thefocusing mode must be axis to axis.6 This means that theelectrons starting from one point on the axis are focusedback to the axis of symmetry, on which the detector is situ-ated. The electrostatic field satisfying all above conditionsmay be defined by the potential,

� = V0z log�r/R0� , �1�

where V0 is a constant characterizing the strength of the field,R0 is the internal radius, below which there is no field, and rand z are cylindrical coordinates. Knowing the potential, theequations of motion in the cylindrical coordinate system canbe written,

m�r − r�2� = − qV0z/r ,

m�r� + 2r�� = 0,

mz = − qV0 log�r/R0� . �2�

When the axis to axis focusing mode is employed, it can besupposed that the particles are starting from the axis, andthus the angular component of the velocity is zero. Then theequations of motion can be simplified to

mr = − qV0z/r ,

� = 0,

mz = − qV0 log�r/R0� . �3�

In contrast to the hyperbolic field case,5 this set of differen-tial equations does not have an analytical solution; it has tobe integrated numerically. The trajectories �Fig. 2�a�� werecalculated using the Runge-Kutta integration method.9

It is also necessary to find the parameters of the field thatproduce the best focusing and thus also the best resolutionfor a specified solid angle of acceptance. One possible solu-tion for this problem is using a minimization algorithm. In

a�Electronic mail: petr@cizmar.orgb�Formerly at the University of York, Heslington, York YO10 5DD, United

Kingdom.c�Also at the University of York, Heslington, York YO10 5DD, United

Kingdom.

REVIEW OF SCIENTIFIC INSTRUMENTS 78, 053714 �2007�

0034-6748/2007/78�5�/053714/5/$23.00 © 2007 American Institute of Physics78, 053714-1

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this case for various energies several trajectories were mod-eled. The sum of squares of deviations of the end point po-sitions is a satisfactory function to minimize.

From the trajectories of electrons in the field it is pos-sible to calculate the dispersion and the best reachable reso-lution of the analyzer employing this kind of electrostaticfield.

The dispersion can be calculated just from the centraltrajectory for each energy. Instead of the traditional defini-tion of the dispersion,

Dr�E� = E�z/�E ,

where the dispersion is relative to the energy, the absolutedispersion,

Da�E� = �z/�E ,

is more suitable. For the CMA or other analyzers, where thedetected energy is tuned, the relative definition is more ap-plicable because then the dispersion is nearly independent ofenergy. For the parallel analyzer the absolute definition ismore suitable for the same reason.

A similar problem is the definition of the resolution. Incase of the CMA the relative definition is used.

Rr�E� =E

�E�E�.

The reason is again the fact that this value is almost constant.For the same reason, in the case of the cylindrically sym-metrical field analyzer or hyperbolic field analyzer �HFA� theabsolute definition is more suitable,

Ra�E� = �E�E� .

To be able to calculate the best possible resolution �theresolution affected only by the properties of the electrostaticfield� for each energy, a set of calculated end points of elec-tron trajectories is needed. Because the analytical expres-sions of the trajectories are not known, whole trajectorieshave to be calculated instead of the end points only. Thecalculation then takes more time than in case of the HFA.

Calculation of the trajectories and their end pointsshowed that for different angles of entry, different end pointsare obtained as expected. When the entry angle is increased,the end point is getting farther, until a turning point isreached. Then the detected coordinate is decreasing �see Fig.2�b��. In fact, the existence of this turning point enables fo-cusing �first order focusing in this case�. The dependence of

the end point coordinate on the angle of entry can be verywell approximated by a cubic polynomial for all energies.The coefficients of such polynomials are then dependent onenergy and can be also very well approximated by quadraticpolynomials. The detected coordinate of the end point canthen be expressed as

z�E,�� = �i=0

2

�j=0

3

kijEi� j . �4�

The coefficients kij can be calculated, and then from Eq. �4�any number of end points can be interpolated. Then it ispossible to calculate resolution from the histogram of posi-

FIG. 1. The hyperbolic field �left-hand side� and the cylindrically symmetri-cal field �right-hand side�. The trajectories in the cylindrically symmetricalfield are focused onto the detector, increasing the detected signal. Anotherfocusing property is added.

FIG. 2. The cylindrically symmetrical field. �a� Equipotentials and trajecto-ries of electrons in the field for energies in the range of 900–2100 eV. Theenergy step is 100 eV. Trajectories start at �0,0�m, �b� Dependence of the zcoordinate of the trajectory end point on the entry angle. �The presence of amaximum indicates first order focusing.� �c� The point spread function�PSF� for the energy of 2100 eV. �d� Dependence of the z coordinate of theend points on energy �integral of the dispersion�.

053714-2 Cizmar et al. Rev. Sci. Instrum. 78, 053714 �2007�

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tions �Fig. 2�c�� and dependence of the end point position onelectron energy, which is, in fact, the integral of the disper-sion �see Fig. 2�d��. For the resolution, the �z is needed. Inthis case, the density of end point positions �point spreadfunction �PSF� in this case� is divergent because of the exis-tence of turning points. �z must be defined as the distancebetween 20% and 80% of the distribution function. The �zvaries with energy. The calculation showed that the absolutedispersion Da is very close to a constant. �see Fig. 2�d��.Thus,

�E = �z/Da.

The modeling of the trajectories in the analytical fieldshowed that the best focus is obtained when the energies ofthe analyzed electrons are between 1000 and 2000 eV in-stead of the desired range of 50–1000 eV, considering thatthe position of the detector is given. It is possible to use thishigher range of energies by placing an accelerator in front ofthe analyzer entrance.

III. SIMULATIONS

To create a real analyzer with a field that has the sameanalytical properties as the field defined by Eq. �1�, elec-trodes of a particular shape must be placed. The outer shapeof the analytical area of the analyzer is determined by thespace clearance in the chamber limited by electron column,detectors, and other devices. The electrodes must be placedwhere the equipotentials cross the outer shape of the ana-lyzer. In order to calculate the functions describing theshapes of the electrodes, use of numerical methods is re-quired in some cases due to the fact that the problem leads totranscendental equations. However, the functions can mostlybe obtained analytically.

To examine the behavior of the electrons in the analyzerwhich consists of charged electrodes, simulations are appli-cable. The CPO �Ref. 8� software is a suitable tool becausethis is a pure electrostatic and three-dimensional problem.This software employs the boundary integral method to cal-culate the electrostatic potential at any particular point in theanalyzer. It is also used to calculate the trajectories of ana-lyzed electrons. The boundary integral method is based oncalculations of charge distributions on electrodes. Becausethe electrode shapes are rather general, they are divided intoa set of smaller triangular or rectangular segments, which thesoftware is able to work with, see Figs. 3�a� and 3�b�. Whenthe charge distribution is calculated, electron motion withinthe field can be simulated and for each electron, and the endpoint of the trajectory can be obtained.

In order to calculate the dispersion and resolution, nu-merous trajectories are simulated. For the end points ob-tained from the simulations, Eq. �4� is also valid which re-duces the number of end points to be simulated andsignificantly speeds up the calculation. Then the calculationof the dispersion and resolution is analogous to the one de-scribed in the previous section. The dependence of the reso-lution on energy is presented in Fig. 3�c�.

IV. THE DEVICE

The analyzer must satisfy several conditions to be usablein an ultrahigh-vacuum electron microscope system.

• The analyzer must fit into the chamber and not collidewith other parts of the microscope.

• Only ultrahigh-vacuum compatible materials must beused.

• All parts of the analyzer have to be bakeable. Theymust be stable at higher temperatures.

• Magnetic materials must be avoided.

The conditions above strongly limit the usable materials.The device had to be designed with respect to the systemused. In this case the experiment took place in the electronmicroscopy laboratory at the Department of Physics of theUniversity of York, UK. In the past a hyperbolic field ana-lyzer was used in this system and the new cylindrically sym-metrical field system was designed to work in the same po-sition in the microscope. Therefore, the new analyzer had tohave similar shape. The shapes of the electrodes were thencalculated according to this requirement.

Polyetheretherketon �PEEK� and Kapton materials wereused for the insulating parts of the device. Both materialsare very stable at high temperatures and ultrahigh-vacuumcompatible. The PEEK was used to make insulating spacers.The top cover was made of Kapton. The electrodes wereaccurately etched of stainless steel sheet. The side coversand lower cylindrical electrode were made of an aluminiumalloy.

FIG. 3. The three-dimensional �3D� simulation with the CPO-3D software. �a�Subdivided electrodes and description of the electrodes. �b� Side view atelectrodes and simulated trajectories. The sample is positioned in the centerof the hemispherical accelerator. �c� Dependence of the analyzer resolutionon kinetic energy of analyzed electrons at the sample.

053714-3 New multichannel electron energy analyzer Rev. Sci. Instrum. 78, 053714 �2007�

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A set of two concentric hemispheres was used as theaccelerator, which produces the radial electrostatic field, ac-celerates the electrons emitted from the sample, and deceler-ates primary electrons before they land on the sample. Thepoint where the primary beam hits the specimen has to be inthe center of the hemispheres. As an inlet and outlet forelectrons, two round holes need to be drilled in the hemi-spheres. These affect the electron trajectories because theyform a lens, but the negative effect on the trajectories enter-ing the analyzer is significant only at the lowest energies. Athigher energies this effect is negligible.

The analyzer was developed and built in the Institute ofScientific Instruments of the Academy of Sciences of theCzech Republic. Figure 4�b� shows a photograph of thedevice.

V. EXPERIMENT

The device was also tested in an experiment, see Fig.4�a�. The experiment showed that the device can operate inultrahigh-vacuum conditions, the pressure in the samplechamber was in the order of 10−8 Pa. In order to reach thispressure a bake out is necessary. A piece of copper foil wasused as a sample, although it was not cleaned. For a detectorthe electrons were multiplied by microchannel plate and thenconverted to light quanta with a phosphor screen. A digitalcamera �Konica-Minolta Z3� was applied to digitize thespectrum on the phosphor screen. The cylindrical focusingwas demonstrated; analyzed electrons were focused onto aline on the phosphor screen, see Fig. 4�c�. The energy of theprimary beam was varied, the position of the relaxation peakwas then changing. The dispersion was calculated from theenergies and corresponding positions of the relaxation peak.The value of the dispersion was 1.9�10−2 mm eV−1. Themaximum resolution limited by the pixel resolution of thecamera was 3 eV. The relaxation peak for the primary en-ergy of 1500 eV was 1 pixel wide, which showed that theresolution of the device was below 3 eV for this primaryenergy.

VI. DISCUSSION

From the simulation, the absolute dispersion is nearlyconstant at 1.97�10−2 mm eV−1. This well correspondswith the experimental value of dispersion of −1.9�10−2 mm eV−1. The resolution varies from 10 to 2 eV, formost energies keeps below 2 eV �Fig. 3�c�� which corre-sponds with Ref. 7. The result of the experiment is a400 pixel long spectrum �see Fig. 4�d�� The measured reso-lution is limited by the pixel resolution of the used camera.Therefore, it can be improved if other detector is applied.However, despite this limit, the resolution is still lower thanthe resolution of the CMA or retarding field analyzer1 �RFA�for high energies �see Table I�. The result of the experimentalso shows the cylindrical focusing. Different widths of the

TABLE I. Comparison of different kinds of electron energy analyzers. Thevalues for the retarding field analyzer �RFA�, cylindrical mirror analyzer�CMA�, and spherical concentric analyzer �SCA�/concentric hemisphericalanalyzer �CHA� are from Ref. 1. The values in the last row �analyzer withcylindrically symmetrical field� are calculated from simulations, the valuesfrom the experiment are in the parentheses.

Analyzer type

Relativeresolution �%���E /E�

Absolute resolution �eV�

at 800 eV at 1500 eV

RFA 0.3 2.4 4.5CMA 0.25 2.0 3.8SCA/CHA 0.05 0.40 0.75Analyzer with cylindricallysymmetrical field n/a

1.5 �3� 1.9 �3�

FIG. 4. �a� Sketch of the experimental setup. �b� Photograph of the analyzer.�c� Photograph of the phosphor screen when acquiring an uncorrected elec-tron energy spectrum emitted from the contaminated copper sample taken atprimary beam energy of 2500 eV. �d� Measured spectrum �sum of threeacquisitions�. �e� Detail of the relaxation peak displayed as a bar graph.

053714-4 Cizmar et al. Rev. Sci. Instrum. 78, 053714 �2007�

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illuminated area appear in the photograph of the screen �seeFig. 4�c��. These are probably caused by a slight misalign-ment of the bottom electrodes which occurred during bakeouts.

ACKNOWLEDGMENTS

This work was supported by the ASCR grant agencyunder Project No. IAA1065304. The authors also gratefullyacknowledge help of Professor B. Lencova and Pavel Klein.

1 F. Reniers, J. Electron Spectrosc. Relat. Phenom. 142, 1 �2005�.

2 C. Miron, M. Simon, N. Leclercq, and P. Morin, Rev. Sci. Instrum. 68,3728 �1997�.

3 R. W. van Boeyen and J. F. Williams, Rev. Sci. Instrum. 76, 063306�2005�.

4 M. Jacka, A. Kale, and N. Traitler, Rev. Sci. Instrum. 74, 4298 �2003�.5 M. Jacka, M. Kirk, M. M. El Gomati, and M. Prutton, Rev. Sci. Instrum.70, 2282 �1999�.

6 F. H. Read, Rev. Sci. Instrum. 73, 1129 �2002�.7 F. H. Read, D. Cubric, S. Kumashiro, and A. Walker, Nucl. Instrum.Methods Phys. Res. A 338, 519 �2004�.

8CPO Programs, available on the website http://www.electronoptics/.com

9 J. R. Dormand and P. J. Prince, J. Comput. Appl. Math. 6, 19 �1980�.10 Ch. G. H. Walker, A. Walker, R. Badheka, S. Kumashiro, M. Jacka, M. M.

El Gomati, M. Prutton, and F. H. Read, Proc. SPIE 3777, 252 �1999�.

053714-5 New multichannel electron energy analyzer Rev. Sci. Instrum. 78, 053714 �2007�

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