Nuclear Instruments and Methods in Physics Research A 645 (2011) 245–247

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/nima

Improvement of a second-order focusing toroidal spectrometer by use ofa pre-collimating lens

H.Q. Hoang n, A. Khursheed

Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore

a r t i c l e i n f o

Available online 10 December 2010

Keywords:

Electron energy spectrometer

Toroidal spectrometer

Scanning electron microscopy

02/$ - see front matter & 2010 Elsevier B.V. A

016/j.nima.2010.12.009

esponding author.

ail address: hunghq@nus.edu.sg (H.Q. Hoang)

a b s t r a c t

This paper presents a method for improving the performance of a second-order focusing toroidal spectrometer

using a pre-collimating lens. Simulation results predict that the degree to which the energy resolution can be

improved depends on the relative size of the lens. For a pre-collimating lens having a radius 180 times smaller

than the spectrometer radius, the relative energy resolution is predicted to improve by an order of magnitude.

The simulated relative energy resolution of the spectrometer with such a pre-collimating lens is 0.021% for an

entrance aperture angular spread of 761, and 0.088% for an entrance angular spread of 7101.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Recently, a new second-order focusing electrostatic toroidalelectron spectrometer has been reported by Khursheed and Hoang[1] for 2p rad detection in electron microscopes. The spectrometeris predicted to have a relative energy resolution of 0.146% for aninput angular spread of 761 (corresponding to 20% transmission),about 7 times better than that of previous first-order focusingtoroidal spectrometers [2]. This paper describes further designdevelopments to the second-order focusing toroidal spectrometer,based upon using a pre-collimating lens. The degree to which thepre-collimating lens improves the spectrometer’s energy resolutiondepends on its relative size; smaller lenses are predicted to performbetter. For a lens radius approximately 180 times smaller than thespectrometer radius, simulations indicate that the energy resolu-tion of the spectrometer will improve by an order of magnitude(to 0.021% for 761 entrance angular spread). Entrance lenses foranalyzers usually have a strong focusing action, and often providethe possibility of retarding electrons down to a smaller pass energy.A hemispherical analyzer normally utilizes a column of rotationalsymmetric lenses [3], whereas toroidal analyzers use cylindrical slitlenses and conical slit lenses [4,5]. The pre-collimating lensproposed here is only weakly focusing, and uses an accelerationelectric field to minimize the effect of spherical aberration.

2. Pre-collimating lens and spectrometer layout

The pre-collimating lens used in this design is a three-elementannular slit lens, in which the outer electrodes are grounded and thetwo middle electrodes are biased positively at potentials VL1 and VL2

ll rights reserved.

.

as shown in Fig. 1. The lens radius is denoted by RL. An acceleratinglens of this type has relatively low spherical aberration. Fig. 1 alsoshows the simulated electrostatic equipotential distribution of thepre-collimating lens and direct ray tracing of electrons emitted fromthe specimen as they travel through the lens; 14 equipotential linesof uniform steps and 21 electrons with emission angles between391 and 511 are used (central ray at 451). The lens bias voltages werechosen to be VL1¼VL2¼EP, where EP is the pass energy through thetoroidal spectrometer. These simulations were carried out usingthe Lorentz-2D program [6]. The collimating action of the lens on thescattered electron beam is evident from the simulated ray paths.The present design improvement involves using this lens to reducethe angular spread of scattered electrons before they enter thespectrometer. The pre-collimating lens action causes electrons totravel closer to the spectrometer’s central region, thereby improvingthe energy resolution (incurring less spherical aberration).

Fig. 2 shows simulated ray paths of electrons through both thetoroidal spectrometer and pre-collimating lens design, in which21 electrons leave the specimen with the same emission angles asthose shown in Fig. 1. The potentials on the spectrometer deflectorplates are V1¼ +1 V and V2¼�1 V, and the pass energy is 2.293 eV(derived from simulation). The toroidal spectrometer design ischaracterized by five geometrical parameters, as defined in Fig. 2,f1¼�p/2.25, f2¼3p/4, R2¼1.57R1 and RT¼2R2, and an entrycentral ray angle (y) of 451. No value of RT is deliberately given here,since the spectrometer’s optics does not depend on its absolutesize; it can in practice, be scaled up as required for differentapplications; therefore, only relative dimensions are specified.

3. Simulated energy resolution improvements

The energy resolution of the spectrometer depends on therelative size of the pre-collimating lens, compared to the toroidal

Specimen

Specimen holder

Lens holder

VL1

VL2

Primary beamRL Scattered Beam

Fig. 1. Simulated equipotential lines and electron trajectory ray paths from a

numerically solved field distribution of the pre-collimating lens. 14 equipotential

lines are taken between 0 and 2.293 V (VL1¼VL2¼2.293 V) and 21 electrons leave the

specimen with an emission angular spread between 391 and 511 in uniform steps.

0V shielding

Pre-focusinglens

PE

R1R2

O

RT

Rotationalaxis

�1

�2

V1

V2

Fig. 2. Simulated ray paths of electrons through spectrometer and pre-collimating

lens design at spectrometer pass energy for a wide variety of entrance angles.

Central ray enters in at 451 and 21 trajectories are plotted over uniform steps for

input angular spread varying from �61 to +61.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25

Ene

rgy

Res

olut

ion

(%)

Lens Radius RL (xRT)

Toroidal spectrometer resolution ΔE=0.146%

RL ≈ 0.09RT

Fig. 3. Dependence of energy resolution on relative size of pre-collimating lens

(normalized to toroidal spectrometer radius).

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Rel

ativ

e en

ergy

res

olut

ion

(%)

VL1/EP

Base resolution

Best resolution

Lens aberrationlimitToroidal

aberration limit

Fig. 4. Dependence of base and best energy resolutions on voltages of pre-

collimating lens; parameter g is chosen to be 0.94.

H.Q. Hoang, A. Khursheed / Nuclear Instruments and Methods in Physics Research A 645 (2011) 245–247246

spectrometer. This is because the focusing effect of the pre-collimating lens has a certain spherical aberration, resulting in avirtual source size for electrons entering the spectrometer (insteadof a point source at the origin). This virtual source is projected on tothe spectrometer detector (image) plane. This means that the finalspot-size of the scattered electron beam is a combination of the sizeof both the spherical aberrations of the spectrometer and the pre-collimating lens. Since the spherical aberration width produced bythe pre-collimating lens is proportional to its size, a well-knownproperty of electrostatic lenses, the final energy resolution ispredicted to improve with decrease in lens size.

Fig. 3 shows the simulated dependence of the best energyresolution on the relative size of the pre-collimating lens and the

spectrometer. The energy resolution is derived from the energywidth corresponding to half the final trace-width, at the pointwhere the trace-width is a minimum (not on the Gaussian plane).The lens radius RL is normalized to RT, the spectrometer radius. Thisgraph shows that when the pre-collimating lens radius is smallerthan 0.09 times the spectrometer radius, the energy resolution canbe improved. Beyond this size, the spherical aberration of the lens istoo large, degrading the final trace-width, causing it to be largerthan the one obtained by the spectrometer alone. This resultpredicts that the energy resolution of the spectrometer can beenhanced using a small pre-collimating lens at the entrance of thespectrometer. The predicted energy resolution obviously improvesas the relative size of the pre-collimating lens decreases.

Consider the case where RT/RL¼180. If for instance, RL¼3 mm,spectrometer radius RL needs to be 540 mm. In order to achieve thebest energy resolution results, it was found that lens centralvoltages VL1 and VL2 need to be slightly different from one another.If a parameter g defines the ratio between the two excitationvoltages VL1 and VL2 then the best energy resolution is achievedwhen g¼0.94. Fig. 4 shows the dependence of both the base and thebest energy resolutions on the excitation voltages of the pre-collimating lens. The base resolution is derived from the size ofthe trace-width at the Gaussian plane, while the best resolutioncomes from the point where the trace-width is minimum. Theenergy resolution reaches a minimum value at a certain excitationvoltage, which occurs when voltage VL1 is around 1.22EP. The energy

EP +0.05% EP

EP - 0.05%EP

EP (pass energy)

Fig. 5. Simulated electron trajectories around output focal plane for 3 emission

energies EP�0.05%EP, EP and EP+0.05%EP, where EP is pass energy, and input angles

range from �61 to +61 around central ray in uniform steps.

Fig. 6. Simulated electron trajectories around output focal plane for 11 emission

energies ranging from 95% to 105% of pass energy and 11 input angles from �61 to

+61 around central ray in uniform steps: (a) without pre-collimating lens and

(b) with pre-collimating lens.

H.Q. Hoang, A. Khursheed / Nuclear Instruments and Methods in Physics Research A 645 (2011) 245–247 247

resolution is limited by the toroidal spectrometer spherical aberra-tion when the excitation voltage of the lens is smaller than thisvalue, and limited by the pre-collimating lens spherical aberrationwhen it is higher than this value.

By choosing the parameter g¼0.94 and excitation voltageVL1¼1.22EP, the best simulated relative energy resolution wasfound to be 0.021% for an input angular spread of 761, correspond-ing to a transmittance of 20% (assuming a polar angle cosinedistribution), which is an order of magnitude better than that of thesecond-order focusing toroidal spectrometer without the pre-collimating lens [1]. For an input angular spread of 7101,corresponding to a transmittance of 34%, the best relative energyresolution was simulated to be 0.088%. These predicted resolutionsare around an order of magnitude better than the well-knowncylindrical mirror analyzer (CMA), and is comparable to thespheroidal spectrometer recently proposed by Cubric for the sametransmittance [7].

The predicted energy resolution improvement of the spectro-meter using the pre-collimating lens can be visually demonstratedby examining simulated ray paths at the detection plane, in whichthree electron beams of different energies with an input angularspread of 761 were plotted as, shown in Fig. 5. The difference inenergy between these electron beams is 0.05% of the pass energy. Itis clear that these three electron beams are well separated, visuallyconfirming that the spectrometer design has a relative energyresolution well below 0.05%.

Simulation results predict that the addition of the pre-collimatinglens will also improve the parallel energy detection mode of thetoroidal spectrometer. A comparison of ray paths around the detectionplane with different energies and angles for the toroidal spectrometerwith and without the pre-collimating lens is shown in Fig. 6. There areeleven different energies uniformly spread over an energy intervalranging from 95% to 105% of the pass energy (indicated by EP in thediagram). For each energy, there are eleven trajectories whose inputangles are uniformly spread between �61 and +61 around the central

entrance angle of 451. Fig. 6a shows trajectory ray paths for the toroidalspectrometer only, while Fig. 6b shows trajectory ray paths producedin addition to the pre-collimating lens. The improvement in energyresolution is clearly maintained across the entire energy pass bandrange (75% of the pass energy).

References

[1] A. Khursheed, H.Q. Hoang, Ultramicroscopy 109 (2008) 104.[2] C. Miron, M. Simon, N. Leciercq, P. Morin, Rev. Sci. Instrum. 68 (1997) 3728.[3] E.P. Benis, T.J.M. Zouros, J. Electron Spectrosc. Relat. Phenom. 163 (2006) 28.[4] J. Lower, R. Panajotovic, S. Bellm, E. Weigold, Rev. Sci. Instrum. 78 (2007) 111301.[5] M.R.F. Siggel-King, R. Lindsay, F.M. Quinn, J. Pearson, G. Fraser, G. Thorntom,

J. Electron Spectrosc. Relat. Phenom 137 (2004) 721.[6] Lorentz-2EM, Integrated Engineering Software Inc., Canada.[7] D. Cubric, N. Kholine, I. Konishi, Proceedings of the 8th International Conference

on Charged Particle Optics, Singapore, July 2010.