US2452919A - Electron optical system - Google Patents

Description

NOV. 2, 1948. K- D, GABOR 2,452,919 ELEcTRoN OPTICAL SYSTEM Filed may 9, 1946 l @2 sneek-sneek 1 Fifl.

m Pag?? NOV..2, 1948. I D, GABOR I 2,452,919

ELECTRON OPTICAL SYSTEM Fileduay 9, 194e 2 sheets-sheet 2 Piggy 3 ,4

Inventor:

l Dennis Gabor, bym zvhn* Patented Nov. 2, 1948 ELEc'rRoN OPTICAL SYSTEM Dennis Gabor, Rugby, England, assignor to General Electric Company, a corporation ofrNew York Application May 9, 194e, serial No. 668,613v In Great Britain August 28, 1945 8 Claims.

My invention relates to electron optical systems and it has for its primary object to provide new and improved means and methods for correcting the spherical aberration encountered in electron lenses.

It is Well known that the spherical aberration of electron lenses of the conventional type, whether electric or magnetic, is always of the same sign and, hence, cannot be corrected by any combination of such lenses. Accordingly, it is an object of my invention to provide a new type of lens which, alone or in combination with lenses of the conventional type, permits the correcting of the spherical aberration within a certain annular zone defined by the lens elements.

A lens constructed in accordance with my invention includes, along the axis thereof, a rotationally symmetrical conductor or core which is preferably a straight cylindrical wire, and coaxial with the core one or several rotationally symmetrical electrodes which are so arranged as to produce in the neighborhood of the core several fields which are of prevailingly radial direction. The core is supported by members which are not themselves rotationally symmetrical and which are arranged in such position as to be shielded from intense electric fields.

One of the features of my improved electron lens system is that electrons are permitted passage in an annular zone which extends to less than a full circle. Moreover, the fields in the system are so dimensionedthat at least a part of the electron trajectories issuing from an axial orslightly eXtra-axial point-are brought to a sharp focus.

The features of my invention which I believe to be novel are set forth with particularity in the appended claims. My invention itself, however` both as to its organization and method of loperation, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawings in which Fig. 1 illustrates a phenomenon of spherical aberration as produced by electron lenses of the conventional type; Fig. 2 is a lens according to the invention with a single extra-axial electrode; Figs. 3 and 4 illustrate electron trajectories in the lens of Fig. 2 showing, respectively, the case of attractive and repulsive core potentials; Fig. 5 shows the combination of the lens of Fig. 2 with a magnetic lens of the conventional type and illustrates the zonal correction of. spherical aberration; Fig. 6 is a modification illustrating the combination of two vlenses embodying the inven- (Cl. Z50-49.5)

tion; Fig. 7 is a graph showing the calculated focussing characteristic of the lens illustrated in Fig. 6 and its characteristic in combination with a magnetic lens of the conventional type; and Fig. 8 is a cross-section of a lens according to the invention with two extra-axial electrodes in combination with a magnetic lens and illustrates certain constructional details ofthe system.

Theory and experiment have demonstrated, that in all electron lenses of the conventional type the spherical aberration has the sign as illustrated in Fig. l. An lobject point O is imaged by paraxial rays in an image `point I0. However, for rays which forni initiallylarge'r angles a'with the axis the image point Ic shifts progressively nearer to the objectpoint. In other words,v the lens strengthY increases monotonously with increasing initial angle a.. For small angles the law is approximatelyl where fu is the paraxial focal length, and f.. the focal length corresponding to the angle a. C is the coefficient of .1'lrst order" spherical aberration, which is always positive, and according to best theoretical evidence cannot be made smaller than about 0.2 with'any lens combination of the conventional type.

Fig. 2l shows the simplest type of lens according to the invention. Conducting wire I is the core and is supported at both ends by thin radial ture.

wires 2 and 3 of sufficientv stiffness to .keep it stretched. At one-or both ends the core may be fitted with spherical ends 4 and 5 which, apart from facilitating a neat connection with the supporting wires serve as parts of the limiting aper- The supporting wires are clamped in rods 6 and 1, of which oneis"shown elastically supported by a spring 8. These in turnv are fixed to the shields or outer electrodes 9 and I0 'with apertures Vsufficiently small toA define the limits of the electric field and insure that no appreciable electric elds will penetrate to the neighborhoods of the supports! and 3, sov that the fields in the lens can be considered as rotationally symmetrical. In operation shields '9 and EQ are connected, whereas' before operation they may be connected temporarily to some low voltage source, in order to heat the wire and clean its surface from contaminations and absorbed gases. In operation the annular electrode ll is maintained at apotential positive or negative relative to the core, as will beexplained in connection with the .following figures.

portional to 1, not to 1/1'.

Fig. 3 illustrates electron trajectories if the annular electrode is negative with relation to the core, that is to say, if the core has a positive charge which attracts the electrons. It can be seen that by itself this system has no focussing eiect. -Tlie deflection -of the electrons decreases very rapidly with increasing initial angle, that is, an effect of opposite sign to that illustrated in Fig. l. Similarly, if the core has a repellent, negative charge, as illustrated in Fig. 4, the trajectories will not come to a real or virtual focus, but will suffer deflections rapidly descreasing with increasing initial angle.

In order to understand these effects quantitatively, it is sufficient to assume, as a first approximation, that the charge Q on :the 'core wire is concentrated in a point of the axis. The d'ynamical problem is thus reducedl to Newtons problem of'two bodies, vattracting or repelling one another with an inverse square law. If Ian electron with charge -e and'lenergy eV (V ybeing the volt energy) s shot towards the charge Q in 'such a way that in the absence of attraction or repulsion it would pass it at a distance p, and if y;

`Vis large enough, the trajectory will be .a hyperbola. The angle between the asymptotes gives the total deflection which the electron has suffered .in the field of Q. This is given bythe equaonly small `deflections will be considered, `tan pressed 'Qa-LCE, where c is the mutual capacity of the core and the extra-axial electrode, ahd'E :is the voltage applied between them. As the deflections are small, p can be replaced by the distance r of the trajectory from the axis where it passes nearest to O. Thus we obtain the useful approximative formula In this formula both c' and r are to be measured in centimeters, E and V in volts. The formula sh'o'ws clearly that a system according to the invention as illustrated in Figs. v2-4 is not by itself a lens in the usual sense of the word, as a lens proper must have a deflecting effect pro- V Hen-ce these systems are to be used not by themselves, but as components of combinations, to be described later.

In order to estimate the deecting power, vthe capacity c may be substituted from the approximative formula c=2L/log (vb/a) (4) where L is the axial length of the annular lelectrode H, b its inner diameter, and a is the diameter, of the core. This Aequation is exact only in the case of long, cylindrical systems, but `permits to estimate the order of the elicot. As 'an example let L=0.`2 centimeter, b=0.2` centimeter. and c='0.01 centimeter. This gives c=0.068c'en timeter. Let the applied voltage be E=500 volts and assume electrons vof 50 kilovolts energy, i. e.,

50,000 volts. If these electrons pass through the electrode system at a distance of 0.05 vcentimeter from the axis the deflection is 0 :0.0272 radians=134' 4 tional type. It corresponds to a focal length of 0.05/0.0272=l.34 centimeters for electrons traversing the lens at an axial distance of 0.05`centimeter. The limiting feature for the strength of these new systems is the electric gradient at the surface of the core, which is approximately 2E log (b/a) /a, and in the above case 30,000 volts per centimeter. In the case of a negative core this is not far from the limit at which autoelectronic discharge s'ets in. With a positive core considerably higher gradients are permissible. The danger .of autoelectrcnic discharge can be reduced byusing wires of clean, smooth metallic surface, which .are cleaned and freed from absorbed gases by hashing before operation.

l5 :is 'a combination of a simple system as described i-n connection with Figs. 2 and 3 with a magnetic lens I2 of the conventional type. The core I is assumed to carry a positive, attractive charge. Electron trajectories which are permit- Ated t'o vpass the system are shown in continuous lines, trajectories which are cut out by the aperture in interrupted lines. The spherical aberration 'of the magnetic vlens is overcorrected for those trajectories which pass too near to the core, and under-corrected for those which pass at a too large distance 'from it. It is compensated in a certain narrow annular Zone which alone is admitted for imaging, and these trajectories image the point lO in the point vI.

A focussing 'effect according to the invention is "produced also by a vcombination of two systems,V one With attracting, the other with repellent core charge, as shown in Fig. 6. The first annular electrode H has a negative, the second, I3, a positive potential relative 'to the core. Trajectories which passnearer to the core suffer stronger positive deflections in the iirst, and stronger negative dence-tions in the second part `of the vsystem than trajectories at a larger distance from the axis, and as a result they are united in the same axial image point.

Fig. '7 is a quantitative illustration of this effect. In this graph lthe abscssae are the sines of the angles a, only little different from the angles themselves, measured 'in radians. The 'ordinates correspond `to the power or strength 5 oi the lens, which is deiined by l 1 s=xn+x1 (5) where .to is vthe* distance of the object lpoint O, to the left ofthe lens, measured from the center of the secondpart of the system l'3, :c1 is the -distance of the image point, considered as positive when it is 'at the right. `It 'can vbe seen that this denition is formally the same vas for the power of an oldinary lens, but ywith the ldifference that s 'depends en 'the angle u. In the graph of Fig, 7, not s is plotted, but the dimens'ionless product www@ (o which is 'a convenient relative measure. It assumes the value unity when 351:09, that is to say, if vO is the focal point for a ray with a, certain angle a, and it is Zero if :ci=:ro, i. e. if the total de'ilection is zero. In all systems according to the invention the Value zero is approached for large values of a, so long vas the conventional lens eiiect is neglected for the 'sake of simplicity.

,The curve labelled II-'l-IS shows the calculated values of smo for a combina-tion as illustrated n Fig. 6. For simplicity the distance `of the center of, Il from O `may 'be lvassumed as 1 centimeter,

though it is evident `that the curve remains unchanged if all dimensions are increased or reduced in lthe same proportion. The distance between the centers of II and I3 is 0.5 centimeter. The constant cE/V, which occurs in Equation 3 is assumed as -I-.0015 -centimeter for the rst part ci the system, and *.00125 centimeter for 4the second. That is to say, that the repulsive part of the lens has 5/6 of the .power of the attractive part. It can be seen from Fig. l that for a 0.075 the lens is dispersive, but for larger angles a it has a slight positive power, which reaches a maximum of 0.0165 at a=0.105. This in itself is not sufficient to produce a real image of O, in fact the image is virtual and only 0.0165 centimeter behind Othe object point. yBut the lens with the data as described is suitable for correcting the spherical aberration of `a strong magnetic lens. This is illustrated by the curves I2 yand II-I-IS-HZ. The

iirst of these shows the :spherical aberration of a magnetic lens, according to Equation 1, with fo=1 centimeter and 020.4. As a first approximation, the errors of the combination can be `obtained by addi-tion. This is carried out in the curve II-l-I3-l-I2. of the combination is almost constant between about a=0.l2 and c=0.17. In practice the best compensation `can be found experimentally, by adjusting the vol-tages S of the annular electrodes.

Even ybetter combinations than the one here described can be obtained by three annular electrodes, of which the two outer ones have negative potentials, while the I niddle electrode is positive.

A particularly important application of the invention is 'the correction of the objectives of electron microscopes. Fig. 8 is a section of the magnetic objective of a microscope, embodying .a two-electrode system according 'to lthe invention. The Whole system is shaped as `a cone, which ts accurately into a conical bore machined into the pole pieces I4 and I5, separated by the nonmagnetic distance piece I6, 4so that it can be easily removed and replaced. The object carrier I 'I fits into a cartridge I8. The cartridge I8 carries at its lower end the supporting Wire 2, which assures elastic tension of the core I. The lower end of core I is iixed in a rod I9 which is made of aductile metal, such as soft copper, so that it can be used for centering core i The electrodes II and I3 are machined in top-hat shape, and are accurately distanced by means of ins-ulators 20. The whole system, including `the pole-piece inserts 2l and 22 is screwed together by means of screws 23. The screw holes are Ion as large a diameter as Ipossible, and polygonally distributed, in order` `to clisturb the rotational symmetry of the magnetic field as little as possible. The potentials of the annular electrodes are applied through leads 24 of which I have shown only the lead connected to electrode II.

In operating this objective it is not necessary, nor practical, to flood the Whole annular aperture with electrons. The `theory of the diffraction of a microscope with an annular aperture shows that little is gained by opening up the annular aperture beyond a `sector about as wide in tangential direction as the diierence of the radii. This limitation need not be effected by material apertures,

but can be obtained by directing an illuminating beam of suitable restricted divergence on a part oi' the aperture. It may be noted that the magnetic lens twists `the electron trajectories around the axis, hence it can happen that the supporting wires at both ends of the core must be arranged in It can be seen that the power .6 different meridian planes, not in the same plane. as shown in this, `and all the previous figures.

Only the principle anda few embodiments 'of the invention have been described in this application. Other modifi-cations and applications will be obvious to ythose skilled in the art. I, therefore, desire in the appended claims to cover all such modifications as fall within the true spirit and scope of the foregoing disclosure.

What I claim as new and desire to secure by Letters Patent of the United States is:

l. An electron lens comprising a disk-like electrode having a central` aperturetherein along which an electron beam is adapted to be projected, and a conductive member transverse to said electrode and extending substantially axially of said aperture, said conductive member being maintained at a potential difference with respect to said electrode to correct the spherical aberration of said beam caused by said electrode.

2. An electron lens comprising a rotationally symmetrical conductor, a rotationally symmetrical electrode coaxially aligned therewith, said electrode having a central aperture through which said conductor projects, said electrode being arranged to produce a radially directed electric field, and said conductor being maintained at a potential diierence with respect to said electrode.

3. An electron lens comprising a rotationally symmetrical conductor, a rotationally symmetrical electrode coaxially aligned therewith, said electrode having a central aperture through which said conductor projects, said electrode being arranged to produce a radially directed electric eld, and means for dening said field and supporting said conductor, said conductor being maintained at a potential diierence with respect to said electrode,

4. An electron lens comprising a disk-like electrode having a central aperture therein along which an electron beam is adapted to be projected, a conductive member arranged substantially transverse to said electrode and extending substantially axially of said aperture, said conductive member being maintained at a potential difference with respect to said electrode, and means surrounding said member and said electrode for exerting a deecting force on said beam, the magnitude of said force and the potentials of said member and said electrode being adjusted to permit passage of said beam through said aperture substantially without any spherical aberration thereof.

5. An electron lens comprising a pair of disklike electrodes having axially aligned central apertures therein through which an electron beam is adapted to be projected, and a conductive member arranged transverse to said electrodes and extending substantially axially of said apertures, said electrodes being maintained at diierent potentials with respect to each other and with respect to said member to compensate the spherical aberration of said beam during passage through said apertures.

6. An electron lens system comprising a pair of rotationally symmetrical electrodes having axially aligned apertures, a rotationally symmetrical conductor supported along' the axis of said electrodes, said electrodes being maintained at potential differences with respect to each other and with respect to said conductor, and magnetic means surrounding said electrodes and said conductor to deflect an electron beam projected axially of said apertures.

7. In an electron optical system of the type which employsa narrow beam of electrons, means for delecting said beam, said means being subject to spherical aberration of a predetermined characteristic, and means to compensate said aberration comprising means for causing spherical aberration of said beam of opposite characteristics and of substantially equal magnitude as -saidpredetermined characteristics.

8. In an electron lens system, means for compensating spherical aberrations of said system comprising three rotationally symmetrical and substantially parallel elcetrodes having coaxially aligned apertures, a rotationally symmetrical conductor arrangedalong the .axis of said electrodes, the `outer-of saidelectrodes being maintained at a negative potential with respect to said conductor and the central of Ysaid electrodes being maintained at a positive potential with respect to said conductor.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,090,001 Hamacher Aug. 17,1937 2,243,362 Sukumlun May 27, 1941 2,305,617 Hansell Dec. 22, 1942 l5 2,354,287 Zworykin et al July 25, 1944

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