Applied Charged Particle Optics

136 Pages·2008·3.266 MB·English

by  Helmut Liebl

AppliedChargedParticleOptics
Helmut Liebl
Applied Charged Particle Optics
With 124 Figures
123
Dr.HelmutLiebl
Hartstr.17
85386Eching
Germany
LibraryofCongressControlNumber:2007932728
ISBN978-3-540-71924-3SpringerBerlinHeidelbergNewYork
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To my dear wife Elfie,
and our children
Bernhard, Wolfgang, Regina, Christina, Martin,
and our grandchildren.
Preface
This booklet is essentially an extended English version of a course I
taught at the Max Planck Institute for Plasma Physics in Garching/
Munich for physicists and graduate students working at the Institute
and for the nearby Physics Department of the Technical University.
ItcoversmostlyapplicationsofparticleopticswhichIhavedesigned,
builtandworked withmyselfduringmy career,suchasmassspectrom-
etry,focusingofionbeams,emissionmicroscopy,ionandelectron beam
systems, in an energy range of less than 20keV.
It is intended to help physicists who have to design their own appa-
ratus or to help them to better understand instruments they have to
work with.
Someofthesubjectsdescribeddatebackquitesometime,theoldest
references as far back as the thirties in the last century. And I am
old enough to have met some of those authors personally. But the
booklet also contains some material from my own file which has not
been published previously.
I should like to thank Dr. Dietmar Wagner for his invaluable help
with the manuscript.
Eching, August 2007 Helmut Liebl
Contents
1 Lenses: Basic Optics ................................. 1
1.1 Simple Transfer Matrices............................ 4
1.2 Passage of Charged Particles Through
a Uniform Electrostatic Field ........................ 7
1.3 Transfer Matrix of the Uniform Field ................. 13
1.4 Acceleration of Charged Particles Emitted
from a Planar Surface .............................. 14
1.5 Transfer Matrix of Electrostatic Field
Between Spherical Concentric Equipotential Surfaces ... 16
1.6 Acceleration of Charged Particles Emitted
from a Spherical Surface ............................ 16
1.7 Passage of Charged Particles Through an Electrode
with Round Aperture............................... 18
1.8 General Aperture .................................. 21
1.9 Passage of Charged Particles Through an Electrode
with Slotted Aperture .............................. 24
1.10 Emission Lenses.................................... 26
1.11 Immersion Lenses .................................. 34
1.12 Einzel Lenses ...................................... 39
2 Electrostatic Deflection .............................. 45
2.1 Parallel Plate Condenser ............................ 45
2.2 Cylindrical Condenser .............................. 47
2.3 Spherical Condenser ................................ 55
2.4 Toroidal Condenser................................. 59
3 Magnetic Deflection.................................. 67
3.1 Small Deflection Angles ............................. 67
X Contents
3.2 Magnetic Sector Fields.............................. 69
3.3 Axial Focusing with Uniform Magnetic Sector Field .... 74
3.4 Non-Uniform Magnetic Sector Fields.................. 78
4 Image Aberrations ................................... 89
4.1 Lenses ............................................ 89
4.2 General Toroidal Condenser ......................... 91
4.3 Spherical Condenser ................................ 95
4.4 Cylindrical Condenser .............................. 96
4.5 Uniform Magnetic Sector Fields...................... 98
4.6 Non-Uniform Magnetic Sector Fields.................. 101
5 Fringe Field Confinement ............................ 105
A Applications ......................................... 109
A.1 Emission Lens Combined
with Optical Mirror Objective Lens................... 109
A.2 Combined Objective and Emission Lens............... 110
A.3 Dynamic Emittance Matching ....................... 117
A.4 Energy Analyzer for Parallel Beam
with Coinciding Entrance and Exit Axes .............. 117
A.5 Elimination of Transverse Image Aberrations
of Sector Fields .................................... 123
A.6 Energy-Focusing Mass Spectrometers ................. 124
References............................................... 127
Index....................................................129
1
Lenses: Basic Optics
Summary. Basic optical formulae are derived, the transfer matrix method is ex-
plained, the lens action of apertures is shown, and emission, immersion and einzel
lenses are treated.
Alensischaracterized bythepropertythatitimpartstoaray(particle
trajectory) passing through it a deflection (∆r(cid:1)) which is proportional
to the distance r1 from the axis, at which the ray passes, but which
is independent of the original slope r(cid:1). For thin lenses this deflection
1
may be assumed to be a sharp kink, occurring at the single principal
plane P. If the entrance side – left of P – is designated by the index 1,
and the exit side – right of P – by the index 2, one can write that the
exit distance r2 equals the entrance distance r1 (Fig.1.1):
r1 = r2 , (1.1)
and the exit slope r(cid:1) equals the entrance slope r(cid:1) plus the (negative)
2 1
change of slope ∆r(cid:1):
(cid:1) (cid:1) (cid:1)
r = r +∆r . (1.2)
2 1
As stated above, −∆r(cid:1) = cr1, where c is the proportionality constant.
It can be derived from the special case that the exit ray is parallel to
the axis:
r2(cid:1) = 0, r1(cid:1) = −∆r(cid:1) = cr1, (1.3)
−∆r(cid:1) 1
c= = . (1.4)
r1 f1
In this case (Fig.1.2) the entrance ray crosses the axis at the distance
f1 from P; f1 is the entrance focal length of the lens, F1 the entrance
focal plane. Equation (1.2) can now be written as
r(cid:1) = r(cid:1) − r1. (1.5)
2 1
f1
2 1 Lenses: Basic Optics
Fig. 1.1. Principle of a lens: A trajectory crossing the lensat distance r1 from the
z-axis is deflected byan angle ∆r(cid:1) which is proportional to r1
Fig. 1.2. Trajectories starting from the axis point F – the focal point – leave the
lens parallel to the z-axis. Thedistance of thefocal plane F1 to thelens plane P is
thefocal length f1
Equations (1.1) and (1.5) can be written in matrix form
(cid:1) (cid:2) (cid:1) (cid:2) (cid:1) (cid:2) (cid:1) (cid:2)
r 1 0 r r
r(cid:1) = − 1 1 r(cid:1) = ML r(cid:1) , (1.6)
2 f1 1 1
ML is called the transfer matrix of the lens.