DE1905937B1 - Stigmator for the electrical compensation of imaging errors in electron-optical systems with hollow beams and annular diaphragms - Google Patents

Description

1 2

The invention relates to a stigmator for elec- In a stigmator of the type mentioned Irish compensation for aberrations is according to the invention to solve the above electron optical systems with hollow beams and task provided that the center electrode tightly Ring diaphragms, one at their end faces from behind an aperture diaphragm in that of the lens field two metal ring 5 lying at ground potential free space is arranged that the in the beam direction dazzle limited, cylindrical and seen front part of the center electrode a larger Ground potential, with a diameter greater than that of the electrode than the rear part of the ring system at a radial distance surrounded center indicates that the center electrode of at least two electrode in the beam path of the electron op- axially spaced apart, Kotischen System is arranged, the two front io axial, sector-shaped electrode ring systems surfaces the central parts of the two ring diaphragms of different diameters is surrounded that form. each of the two electrode ring systems into several,

Stigmators of this type are known (see. The one provided with contacts and on various German interpretation document 1 236 097). In addition, it is subdivided into sectors and that lie potentials known to use sector-shaped electrode systems, the electrode ring system with the larger turnaround (see the German Auslegeschrift 1 179 313). knife the front part of the center electrode and the

Electron-optical focusing and imaging electrode ring system with the smaller through-system with a circular ring diaphragm, systems can surround the rear part of the center electrode with a simple circular perforated diaphragm at a radial distance. Disturbances of the rota can be superior to the stigmator according to the focussing or imaging properties 20 according to the invention. It is only essential that a symmetry is used very simply by a suitable choice of hollow beam; on the other hand, it plays to compensate for the potentials of the sectors. Twelve no decisive role, whether there is a metallic sectors in each electron ring are sufficient, \ ring diaphragm is in the beam path or not. if a compensation for the particularly harmful Experimental has achieved H. Nο ve n (Z. angew. Physik, 18.4, 25 two-, three- and four-fold astigmatisms p. 329 [1965]) the cone-edge focusing should be realized.

siert, which has a greater current density in the focal point. The invention is illustrated with reference to FIGS. 1 and 2

allows, than with the usual focusing by and the description of a in the F i g. 3 and 4

rotationally symmetrical lenses can be achieved. illustrated embodiment explained in more detail.

F. L e η ζ and A. P. W i 1 s k a (Optik, 24, p. 383 [1966]) 3 ° F i g. 1 shows a schematic representation of the geometrical

have a system with a diaphragm for correcting Irish relationships in image space;

the spherical aberration of magnetic electrons- F i g. 2 shows the roughly schematically in axial section

Lenses proposed that thus also a magnification construction principle of a stigmator;

tion of the resolving power of the electron micro- Fig. 3 shows an axial section of a stigmator;

should enable scops (K. J. Hanszen, K. J. 35 Fi g. 4 shows a section along the line IV-IV

Rosenbruch and F. A. Sunde r - P 1 a s - des in FIG. 3 stigmators shown,

Mann, Z. angew. Physik, 18, 4, p. 345 [1965]). Because the deviations from rotational symmetry

Systems with a larger number of ring diaphragms in the lens systems used for focusing

are zone lenses (A. Boivin, Theory et calcul in general are not known, can general

des figures de diffraction de revolution, [1964], 4 ° Statements initially only from the existence of regular ones

Gauthier-Villars, Paris, p. 405), as well as Hopp e - wave surfaces in the image considered to be field-free

Plates for correcting the spherical aberration are obtained behind the lens system,

ration (W. Hoppe, Optik, 20, p. 599 [1963]; It is assumed that the aperture plane of the

W. D. Ri ecke, Z. Naturforschung, 19 a, 10, p. 1228 system in the field-free image space. The aperture

[1964]). 45 have the mean radius R and the ring width 2b,

The prerequisite for the optimal functioning of the distance to the image plane is D; This is in Fig. 1 of all of these systems that are deviations from that shown. The object or the cathode and the rotational symmetry of the electromagnetic focus lens system have been omitted in the figure, the sierungsfeldes remain so small that the resulting At each object point P ₀ there is a wave aberration δ W due to the aperture at the output of the 50 plane regular eikonal function

System is smaller according to Rayleigh's - ^ - rule

is than a quarter of the electron wavelength. This η ^Λ
Under certain circumstances, the requirement can refer to significant W [P ₀ , P _A ) = / nds. Q-)
technical difficulties lead, especially since the 55 _p
Disturbance of the rotational symmetry of the system caused errors increase sharply with the distance of the electron orbits from the system axis and thus the integral is _{far more pronounced over the path leading from P 0} to P _A than it does in devices orbits. The electron-optical Brem with a paraxial beam path. ^6o chung index n which is constant in the image space, would the present invention addresses the problem there arbitrarily to one normalized, so the normalization of providing a stigmator which it is clearly defined overall in the rest room.
From the fact that the geometrical-optical stems with hollow beams and ring diaphragms, especially electron trajectories in the image space, caused the orthogonal radius through the ovality of the electron lenses, ⁶ 5 projections of the wave surfaces are straight and run through simple, rotational symmetry , one can avoid the following relation between the astigmatism-eliminating means and coordinates (x _A , y _A , z _A ) of an arbitrary point P _A. in the aperture plane and the coordinates (x _B , y _B ,

² B = zA + D) of the intersection point P _{8 of} the path going through P ₀ and P _A with the image plane: The eikonal function is divided into two parts in the following way:

dW

y _B =

It is

(2)

D = PaPa = Zb-

- * a? + iy _B

as in Fig. 1 is shown. It is not necessary

»That the triangle P _A P _A P _B lies in one plane with the system axis, as in FIG. 1 has been adopted in a simplified manner.

W (P ₀ , P _A ) = W ™ (P ₀ , P _A ) H- δ W (P ₀ , P _A ); (3)

(P ₀ , P _A ) =

(P ₀ ,

- Ρ _Α ΡΓ . (4)

The term W ⁱ⁰⁾ (P ₀ , P _A ) describes the eikonal of an electron beam that is focused exactly on an ideal image point P ^ ^o) _{conjugated to P 0} . For the sake of clarity, this is shown in FIG. 1 has not been shown. The function W ^w (P ₀ , P ₄ ) exactly fulfills the equations (2), if the coordinates (x ^ ° \ y ^) of Pj ^{o) are} inserted into them for! 5 (xbi yß) and z ^ = z _B sets. The quantity W ^m (P ₀ , P ^) is a constant. _{The quantities S 0} , ε ₀ used in the following have the same meaning as s, ε , but refer to the point Pjf>.

The term δ W (P ₀ , P _A ) represents the wave aberration in the aperture plane caused by imaging errors in the system. This should be viewed as a small disturbance. It has the effect that P _B deviates slightly from P _B ^i0).

Developments are made in the following ways:

Xb = xP + öx _B , y _B = yi ⁰⁾ + δ y _B , S = S ₀ + ös, δζ _Β = O,

where δ x _B , δ y _B , δ s are viewed as small quantities. When restricting to linear terms one obtains:

Xr =

y _B =

δ s ■ sin F ₀

dW ^{0) D d dx _A cos ε ₀ dx _Ä

_s . d

δ s ■ sin ε ₀ ■ -

cos _eo dy _A Now, however, δ s is of the same order of magnitude as «5 x _B and δ y _B , furthermore

LV d Xa J

+ ("5) = SUIf ₀ ,

\ 8y _A J J

thus the terms in (6) containing the factor <5 s are of the order of magnitude δ x _B sin ² ε ₀ or δ y _B sin ² ε ₀ . Although the aperture angle ε ₀ in the image space will certainly be much larger than in paraxial systems, sin ² ε ₀ «c 1 can still be assumed. Then the higher-order terms with <5 s are small and negligible. It is then allowed to use cos ε ₀ äs 1 in the remaining terms. This gives:

δ x _B = D

ÖW,

ÖW.

(7)

It is expedient. To use polar coordinates q, φ in the aperture plane, which is through

x _A = (R + ρ) cos φ, y _A = (R + _e ) sm <p, (-b < _e ^

are defined, and to introduce a complex geometric aberration, for which applies:

In the following, the investigations will be specialized in the case that P ₀ lies on the axis of the system. Then the ideal image point P $ ^] must also lie on the axis, ie

X ^ = _y p = 0

be. It is always possible to develop the wave aberration δ W (ρ, φ) into a Fourier series.

+ CO

δ W ( _e , φ) = y ^ F _v (ο) e ' ^v ".

r = -oo

The reality of δ W requires:

F_ _v (e) = F * ( _e ).
The geometric aberration in the image plane is obtained from (9)

du _B (e, _Ψ ) =

(10)

(11)

This expression is examined in more detail below for the geometric aberration.

What is essential in the expression (12) for the geometric aberration is the explicit dependence on φ. The consequence of this is that even if the ring width 2b (at the point ρ - 0) disappears, a finite aberration still occurs, which under certain circumstances can render the focusing system unusable. This is a disadvantage of systems with an annular diaphragm compared to systems with a circular pinhole, in which the purely geometric aberrations can be made as small as desired by narrowing the diaphragm.

The terms that result from rotationally symmetrical wave aberrations, ie the terms with ν = 0, are of no interest here. The lowest order terms dependent on azimuth φ are those with ν = ± 1:

Au ₁ = D

_{+ D}

(13)

For every fixed value ρ between - b and + b , the aberration figure is a circle with radius

(Ρ) = I) IF ₁ '(ρ)

its center is now the line

u \ - η \ π'ί \ _Li7 (\ ΚΏ j. \\
ί (ρ) - VIr ₁ (O) + ΐΊ (ρ) / (Κ + ρ) \

shifted sideways from the axis. If the point P _A in the aperture plane traverses a circle of radius R + ρ once, the associated aberration circle in the image plane is traversed twice in the same sense. The entire aberration figure is a coma, which differs from the usual coma in that even for ρ = 0 there can be an aberration circle of finite radius and finite lateral displacement, _i.e. no g ^ need be present. Can also

Line on which all circle centers lie must be curved.

The terms in δ W (ρ, φ) with an n-fold symmetry (ν - ± m) give rise to a geometric aberration

öu _m = a _n j ~ ⁾ (o) e ^{i (1 + m) (} '+ α _ι <, ⁺⁾ * (ρ) ε ^Η1 ~' ^{η) φ} (14)

Reason. The following has been used as an abbreviation:

■ n TT f "\\

m> \. (15)

If ρ is kept constant, the aberration curves resulting from the ^ -dependence have a number of simple properties. For aJ ₁ ⁺⁾ (ρ) = 0 or Om ^- He) = 0 one obtains a circle which is traversed (m + l) times in the same direction or (m - l) times in opposite directions if the point P _A runs through the associated circle once in the aperture plane. Apart from these special cases, it is clear that the aberration curves in odd meters are run double in the aperture per revolution as occur in the exponent of the expression for <5 u _m only even multiples of the angle <p; with an even m , on the other hand, the aberration curve is simply traversed. From this fact and from the relationship valid for all integer η

_öu ( _{φ +} ΞΞ \ ₌ i_n » _e xD (- \ Ow (ο ω)
° "» [?> * + _M ) < ¹ ^ ^ex P ^ _m ) * «miß> 9)

7 8

further follows that for odd m aberration curve has a m-fold symmetry, in contrast, a straight m (2 m) -zählige.
From (14) it also follows:

k'-f + 2 \ α ^ \\ α ^ \ οο ₅ (2ηι _φ + _Υη ), (17)

where y _{m is} the phase of a £ ⁺⁾ ■ a ^ ' . The absolute value of bu _m thus fluctuates between the extreme values Il a £ ⁺⁾ ± a ^ -% If | aJ, ⁺⁾ \ = \ α ^ \ , i.e. the aberration curve passes through the origin in the image plane, it is a rosette curve. If, on the other hand, I öm ⁺⁾ l: I α, ΓΊ = (m + 1): (m - 1), then there are points

in which - =. - (6u _m ) disappears. These points are

then peaks of the curve. In the general case, an aberration curve will neither go through the origin still go own tips.

In practice, aberration curves with the simple properties discussed above will usually not be observed. As a result of the ρ-dependence of the curve parameters at a finite width of the diaphragm, one has to expect a continuous superimposition of such curves, which vary in size, shape and orientation in the image plane, with the fact that aberrations of different symmetries are linearly superimposed. The intensity distribution of the radiation emanating from a single object point P ₀ in the image plane can therefore assume very complicated forms.

An electrostatic stigmator should be built into the beam path in the space free from the lens field right behind the aperture diaphragm. This is shown in FIG. 2. Obviously, only systems with only one ring opening in the diaphragm come into question here. The following will examine in more detail which construction conditions must be complied with. It is assumed that the stigmator field has a short extension \ z _E - z _A \ <: D in the z-direction, it should only be different from zero for z _A : g ζ - z _E. This can be implemented in practice by using metallic diaphragms to limit the field, which have a sufficiently narrow opening and are at external potential. The toad cover is also shown in FIG. 1 shown circular diaphragm.

On the very short path through the stigmator, the electron orbits can be viewed as practically parallel to the z-axis, ie ignoring the changes in the coordinates ρ and φ along each orbit.

Since the wave aberration δ W is supposed to be a small perturbation, it will be possible to correct it with small changes in potential F (ρ, φ, ζ) in the stigmator; so it applies

\ ν (ρ, φ, ζ) \ <^ Φ * = Φ (ί + ηΦ).

Here Φ is the acceleration voltage of the electrons and η = e / (2mc ² ). The normalization π (Φ *) = 1 results in the change in the electron-optical refractive index

δη {ρ, ψ, ζ) = π-

= - ν (ρ, ψ, ζ)

with the voltage constant
2 Φ (1 + η Φ)

U =

ί + 2η Φ

(18)

(19)

From this, the additional wave aberration is calculated at the output ζ = ζ _{Ε of the stigmator}

z _E z _E

= J öndz = U- ¹ JV (q, φ, z) dz.

(20)

Now adjust the field in the stigmator so that δ W + δ W _{s is} minimized. To find the conditions for this, V (ρ, φ, ζ) is first expanded into a Fourier series with respect to the angle φ and a power series with respect to ρ around the point ρ = 0:

V (ρ, φ, Z) = ">

(21)

This is inserted into the Laplace equation AV = O , then a coefficient comparison according to powers of ρ is carried out individually for each term e ^{iv <p.} If you specify Ff (z) and F _v ⁽¹⁾ (z) as you like, you always get recursion formulas for all higher _{expansion coefficients F v} ^(fc) (z) with k> 1. By specifying the functions Ff ^} (z) and F / ¹ '(z) for all values of ν the potential field is uniquely determined. In particular, receives

(22)

(23)
009 583/247

9 10

At the field boundaries ζ = z _A , ζ = z _E , all V ^ ^k) and all their derivatives should vanish. Introducing the abbreviation:

= J VfHz) dz, B _v = J z '

dz,

(24)

so you get

⁽²⁵⁾

For each index pair ν = ± m one has two arbitrarily variable field parameters A _n and B _m available if the reality of V is taken into account. This means that for every value of ν in the wave aberration δ W, precisely the two lowest development terms are compensated for with respect to ο. For this purpose, the expansion (10) is completed first:

V = - X fc = 0

where the F ™ (0) are the derivatives of the function F _v ( ₂ ) at the point ο = 0. Comparison of (20), (25), (26) provides the compensation conditions for F _v (0) and F ^ (O); these are:

A _y = - t / F _v (0), B _v = -UF ' _V (0).
This results in the remaining, uncorrectable aberration

(27)

(J.Ö)

This expression no longer depends on the special form of the stigmator field, ie if the terms o ° and o ¹ have been compensated for, further correction by attempting a suitable modification of the electric field is no longer possible. One must choose the width 2b of the diaphragm so that according to Rayleighs

- rule I.

6 W + δ W _s | 5Ξ -

what applies when restricting to the essential, in quadratic terms

λ / T Ζ, F ' (0) ν ² , ν ¹ ' ²

Z> <Mm Ι / --Πρ; '(0) + - ^ F, (0) | J (29)

leads when one type of aberration is dominant.

From the fact that one needs two available field parameters for every symmetry number [ν j = m , it follows that the stigmator must contain at least two electrode ring systems in which fields with any azimuth dependency can be approximated sufficiently well. For this purpose, each of the two electrode ring systems must be divided into a sufficient number of sectors which can be at different potentials. This is shown in Fig.2. If one wants to correct an aberration with the symmetry number m = I »» j, one must place the individual sectors on such potentials that the distributions

50 ⁾ (ψ) = Φ ™ e ^{im <p} + Φ / ¹ * Q

/ ¹ * Q- ^imt >

j = 1.2 (30)

arise on the two electrode rings. Here for j = 1.2. Because of the linearity of the i

j g

Relationship between the potential distribution in space and the boundary values Φ}, there must also be linear

Drawings of the form

^ al, Φ [

ΦΙ

_B _V = oJi Φ [+ a ^ Φ \

(31)

give. One must demand that the coefficient determinant Det (a \) must not vanish. Then the system of equations can always be found in terms of <P [ and Φ | dissolve. This means that in the area in which the approximation of weak correction fields can be expected, there are always exactly two boundary values Φι, Φ] for each ν, which enable the correction. In order to ensure the conditions Det (a ^v _ik ) = j = 0, it is necessary to choose different radii of the two electrode rings and also to vary the diameter of the inner electrode at external potential, as in FIG. 2 is shown. If the radii of the two outer electrode rings were the same and the radius of the inner electrode were constant, with a sufficiently narrow gap along the electron paths the electrical potential would be approximately proportional.

nal to the radial component of the field strength, which would mean linear dependence of equations (31). This need not be the case for systems with a larger gap, but a too small, non-vanishing determinant would also be unfavorable. If the determinant is sufficiently large, details in the geometrical shape of the electrode system are not important; these determine the numerical values of the matrix elements af _ik . For the adjustability of the stigmator it is only essential that there are always values Φ [, ΦΙ which satisfy (31) and which are in reasonable ranges. As stated above, the remaining uncorrected aberration no longer depends on the geometric shape of the stigmator.

So far, only the aberrations of the path or path emanating from the object point on the axis have been Investigated wave system. However, this is not an essential limitation of the general public. The electrode potentials Φ} can always be adjusted in such a way that one also applies to object points outside

»Compensate the additional silk astigmatism and the coma in the image can. So you can always image sufficiently small object areas sharply. However, the diameter will of the sharply imageable object area be smaller than in systems with paraxial focusing, because the coma is more pronounced due to the larger aperture angle. With the greatly enlarged Imaging of very small object areas or when producing foci with a very small diameter but systems with a ring diaphragm can be superior to the conventional ones if the aberrations are minimized by disturbances of the rotational symmetry.

In Fig. 3 shows a stigmator in axial section, and FIG. 4 shows a section along line IV-IV of this stigmator. In these two figures, the same parts are provided with the same reference numerals.

The stigmator consists of a cylindrical design, located on outer potential center electrode 1, which is preferably made from V2A steel manufacturing m. The center electrode 1 is delimited at its end faces by two annular diaphragms 2, 3. The two central parts of the annular diaphragms 2, 3 form the two end faces of the cylindrical center electrode 1. The front part 4 of the center electrode 1 has a larger diameter than its rear part 5, as shown in FIG. 3 can be seen. The center electrode 1 is surrounded by two sector-shaped electrode ring systems 6, 7 which are arranged at a distance from one another and have different diameters. The electrode ring system 6 with the larger diameter surrounds the front part 4 of the center electrode 1, while the electrode ring system 7 with the smaller diameter surrounds the rear part 5 of the center electrode. For the voltages to be applied, the individual sectors of the electrode ring system 6 are provided with the lead contacts 8 and the individual sectors of the electrode ring system 7 are provided with the electrical contacts 9. '

For hanging and adjusting the center electrode 1 in the beam path of the electron-optical system suspension devices 10, 11 are attached to the two end faces 2, 3 of the center electrode 1. The suspension is expediently carried out in the manner shown by three externally adjustable, Metallic rods 11 offset by 120 ° in the field-free space in front of each end face 2, 3 of the center electrode 1, so that the center electrode 1 is easily adjustable. Since those with the end faces 2, 3 of the center electrode 1 through the metal part 10 in contact metallic rods 11 at the same time an electrical Represent connection, it is guaranteed that the "center electrode 1 of the stigmator at external potential lies.

Each electrode ring system 6, 7 preferably consists of twelve sectors (as shown), so that one Compensation of the particularly harmful two-, three- and four-fold astigmatisms is made possible.

The diameter of the in the F i g. 3 and 4 with the dashed lines 12 indicated electron hollow beam is 20 mm. Of course, other absolute dimensions can also be used if necessary, z. B. 5 mm diameter for the electron beam.

For electrical insulation of the electrode ring systems 6.7, a plastic, preferred material designed in the manner shown in FIG. wise polytetrafluoroethylene layer 13.

As a material for the suspension devices 10, 11, the two ring diaphragms 2, 3 and the electrodes of the Stainless steel is preferably suitable for both electrode ring systems 6, 7.

Claims (8)

Patent claims: 1. Stigmator for electrical compensation of imaging errors in electron-optical systems Systems with hollow beams and annular diaphragms. the one at their end faces of two Metal ring diaphragms lying at ground potential are limited, cylindrically designed and . Center electrode at ground potential, surrounded by an electrode ring system at a radial distance is arranged in the beam path of the electron optical system, the two end faces of which are the central parts of the two ring diaphragms form, thereby geke η η draws, that the center electrode is close behind an aperture diaphragm in the one free from the lens field Space is arranged so that the front part (4) of the center electrode (1) seen in the beam direction has a larger diameter than the rear part (5) that the central electrode (1) of at least two axially spaced, coaxial, sector-shaped Electrode ring systems (6, 7) of different diameters is surrounded that each of the two Electrode ring systems (6, 7) in several, provided with contacts (8, 9) and on different Potential lying sectors is divided and that the electrode ring system (6) with the larger Diameter of the front part (4) of the center electrode (1) and the electrode ring system (7) with the smaller diameter the rear part (5) of the center electrode (1) with a radial distance surround. 2. stigmator according to claim 1, characterized in that for hanging and adjusting the Center electrode in the beam path of the electron-optical system on the two end faces suspension devices (10, 11) are attached to the center electrode (1). 3. stigmator according to claim 2, characterized in that the suspension device (10, 11) consists of a central metallic part (10), on the three offset by 120 °, adjustable from the outside attack metallic rods (11) radially. 4. Stigmator according to one of claims 1 to 3, characterized in that each of the electrode ring systems (6, 7) comprises twelve sectors. 5. stigmator according to one of claims 1 to 4, characterized in that for mutual Isolation of the Elektrodennngsysteme (6, 7) a plastic is used. 6. stigmator according to claim 5, characterized draws that as plastic for mutual insulation of the electrode ring systems (6, 7) polytetrafluoroethylene Is used. 7. Stigmator according to one of claims 1 to 6, characterized in that the central electrode (1) and the two ring diaphragms (2, 3) are made of stainless steel. 8. stigmator according to one of claims 1 to 7, characterized in that the electrodes of the both electrode ring systems (6,7) are made of stainless steel. 1 sheet of drawings