EP1547119A1

EP1547119A1 - Device with foil corrector for electron optical aberrations at low energy

Info

Publication number: EP1547119A1
Application number: EP03791500A
Authority: EP
Inventors: Pieter Kruit; Rogier Herman Van Aken
Original assignee: Stichting Fundementeel Onderzoek der Materie (FOM); Technische Universiteit Delft
Current assignee: STICHTING FUNDAMENTEEL ONDERZOEK DER MATERIE (FOM); Technische Universiteit Delft
Priority date: 2002-08-30
Filing date: 2003-09-01
Publication date: 2005-06-29
Also published as: WO2004021391A1; AU2003261023A8; AU2003261023A1

Abstract

An electron optical device for, in use, creating negative spherical and chromatic aberration and reducing the energy spread in an electron beam travelling on an optical axis, including: at least one conducting plate substantially perpendicular to the optical axis with a first aperture having a first radius around said optical axis, a thin foil of conducting material located parallel to and at a first distance from the at least one conducting plate, In use, the thin foil has an electric potential that generates an electrical field for reducing the kinetic energy of electrons in the electron beam to a value substantially close to zero at the surface of the foil, while leaving the kinetic energy of the electrons in the first aperture at a relatively higher value.

Description

DEVICE WITH FOIL CORRECTOR FOR ELECTRON OPTICAL ABERRATIONS AT LOW ENERGY

Field of the invention

The present invention relates to an electron optical device. Also, the present invention relates to an electron lens system comprising such an electron optical device. Further, 5 the present invention relates an electron microscope comprising such electron optical device. Finally, the present invention relates an electron lithography system comprising such electron optical device.

Prior art

10 In "Uber einige Fehler von Elektronenlinsen,Z. Phys.101 (1936)593", Scherzer has shown that the spherical and chromatic aberration are always positive for electron lenses that are static, rotationally symmetric and space charge free. These conditions are satisfied by virtually all common lenses. To correct for aberrations Scherzer's theorem has to be circumvented, for instance by using non rotationally symmetric

15 optical elements. Several authors have recently reported on spherical and chromatic aberration correctors based on a series of multipoles. See, for example, N.Dellby, O.Krivanek, P.Nellist, P.Batson, A.Lupini, "Progress in aberration-corrected scanning transmission electron microscopy", J. Electron Microsc. 50 (2001)177, S.A.M. Mentink, T. Steffen, P.C. Tiemeijer, M.P.C. Krijn, "Simplified aberration

20 corrector for low -voltage SEM", in: C. Kiely (Ed.), Electron Microscopy and Analysis 1999; Institute of Physics Electron Microscopy and Analysis Group Conference, Sheffield,1999,p.83., and , K. Urban, B. Kabius, M. Haider, H. Rose, in "A way to higher resolution: spherical-aberration correction in a 200 kV transmission electron microscope", J. Electron Microsc. 48 (1999)821.

25 However, the design of these correctors is complicated, they are difficult to operate, as many parameters have to be adjusted correctly, and many power supplies of sufficient stability are needed. Compared to that a thin transparent foil, with which space charge can be put on the optical axis which can also act as a corrector with negative spherical aberration, seems very simple in design and operation. The first suggestion for a foil

30 corrector was also from Scherzer in "Spharische und chromatische Korrektur von Elektronen Linsen", Optik 2 (1947)114, but at that time he still regarded the construction of a foil transparent to electrons as impossible. To avoid the problem of scattering in the foil, a gauze can be used instead. Some early examples of studies on a corrector with a gauze or foil are those by Barth in "Electrostatic correction of the spherical aberration of electron lenses", Ph.D.Thesis, The University of Arizona, 1967, and Maruse in T. Hanai, H. Yoshida, S. Maruse, "Korrektur vom Offnungsfehler der Elektronenlinse", Jpn. J. Appl. Phys. (1970)1549. Since then, Hanai, Hibino and Maruse have done a lot of theoretical and experimental work on foil correctors. For a recent example, see T. Hanai, H. Yoshida, M. Hibino, "Characteristics and effectiveness of a foil lens for correction of spherical aberration in scanning transmission electron microscopy", J. Electron Microsc. 47 (1998)185.

In order to avoid too much scattering in the foil, usually these correctors are operated at a beam energy at the foil of 100 keV and larger. The pressure in an electron microscope is usually 10^" mbar at best and mobile adsorbants will be present on the foils surface. Electrons impinging on the surface with an energy larger than ~5 eV will crack these adsorbants and create a carbon species that locally sticks to the surface. As the adsorbants move over the surface, new adsorbants move into the beam and are cracked continuously. So the electron beam will cause a carbon build up on the foils surface. This contamination and its associated scattering and charging is a major problem for the use of phase plates in electron microscopes (see for example: R. Danev, K. Nagayama, "Transmission electron microscopy with Zernike phase plate", Ultramicroscopy 88 (2001) 243, and, K. Danov, R. Danev, K. Nagayama, "Reconstruction of the electric charge density in thin films from the contrast transfer function measurements", Ultramicroscopy 90 (2002)85. This problem has prevented the wide spread use of foil correctors in electron microscopes. Seah and Dench in: M.P. Seah, W.A. Dench, "Quantitative electron spectroscopy of surfaces: a standard data base for electron inelastic mean free paths in solids", Surf. Interface Anal. 1 (1979)2, have made an extensive compilation of measurements of the dependence of the scattering length on the beam energy. In general, the scattering length decreases for lower energy. However at very low energy, the electron mean free path increases again. For most metals the mean free path is about 5 nm for electrons entering the foil with almost zero kinetic energy. Nowadays the fabrication of 5 nm thick free-standing foils is a practical possibility, see for example, LS. Stepanov, R.H. van Aken, M.R. Zuiddam, C.W. Hagen, "Fabrication of ultra-thin free-standing chromium foils supported by a Si₃N₄ membrane-structure with search pattern", Microelectron. Eng. 46 (1999)435. Thus, the development of a foil corrector operating at low kinetic energy has become interesting.

Summary of the invention It is an object of the present invention to provide an electron optical device as mentioned above, which overcomes the disadvantages of the electron optical device from the prior art.

The object of the present invention is achieved by an electron optical device for, in use, creating negative spherical and chromatic aberration and reducing the energy spread in an electron beam travelling on an optical axis, comprising:

• at least one conducting plate substantially perpendicular to the optical axis with a first aperture having a first radius around the optical axis,

• a thin foil of conducting material located parallel to and at a first distance from the at least one conducting plate, the thin foil having, in use, an electric potential generating an electrical field for reducing the kinetic energy of electrons in the electron beam to a value substantially close to zero at the surface of the foil, while leaving the kinetic energy of the electrons in the first aperture at a relatively higher value. Compared to high voltage foil correctors, the very low voltage operation advantageously makes the electron optical device according to the present invention, or foil corrector, more attractive for low voltage SEM and it greatly reduces the contamination problem.

An additional advantage is that by retarding the electrons to substantially zero eV, the foil of the device may act as a high-pass energy filter: electrons with insufficient forward energy are reflected at the foil.

Also, the present invention relates to an electron lens system, using an electron optical device as described above for a compensation, in use, of a positive spherical aberration of other lenses in the electron lens system.

Moreover, the present invention relates to an electron lens system, using an electron optical device as described above for a compensation, in use, of a positive chromatic aberration of other lenses in the electron lens system.

Furthermore, the present invention relates to an electron microscope, using an electron optical device as described above. Also, the present invention relates to an electron microscope, using an electron lens system as described above.

Further, the present invention relates to an electron lithography system, using an electron optical device as described above. Moreover, the present invention relates to an electron lithography system, using an electron lens system as described above.

Brief description of diagrams

For the purpose of teaching of the invention, preferred embodiments of the method and devices of the invention are described below. It will be appreciated by the person skilled in the art that other alternative and equivalent embodiments of the invention can be conceived and reduced to practice without departing form the true spirit of the invention, the scope of the invention being limited only by the appended claims. Figure 1 shows schematically a basic design of a foil corrector according to the present invention (not to scale) wherein D denotes a diameter of an aperture and s denotes a gap between a foil and the aperture;

Figure 2 shows schematically positive spherical aberration for a positive and a negative lens, by means of two rays entering the lens at different radii, r_/ and r₂. In both cases, the intercept with the z-axis shifts in the negative z direction for increasing radius of incidence; Figure 3 shows a schematic sketch of electric field lines in the foil corrector according to the present invention;

Figure 4a, 4b, 4c, 4d and 4e show a plot of the axial potential Φ and its first ( '), second (Φ "), third (Φ '") and fourth (Φ*) derivative, respectively, with respect to z as calculated by the finite element program Elens for an aperture diameter D = 0.2 mm and different corrector gaps, indicated by the numbers in the plots (1 : s = 0.01 mm; 2: s = 0.03 mm; 3: s = 0.05 mm; 4: s = 0.07 mm; 5: 5 = 0.1 mm), the foil being at 0 V and the aperture at unit potential;

Figure 5 shows schematically a foil corrector according to the present invention with equi-potentials as calculated by Elens; Figure 6 shows a plot of focal distance coefficients C_S3 and C_ss of respectively 3^r and 5^th order spherical aberration and coefficient of 1^st order chromatic aberration C_cι versus the voltage on the aperture, all normalized to the aperture diameter D, for a gap- diameter ratio slD = 0.1; Figure 7 shows a plot of focal distance coefficients C_S3 and C_ss of respectively 3^rd and 5' order spherical aberration and coefficient of 1^st order chromatic aberration C_cι versus the corrector gap, all normalized to the aperture diameter D, for a voltage on aperture: V= 100 V; Figure 8 shows a plot of coefficient of 2ⁿ order chromatic aberration C_c2, normalized to the aperture diameter!⁾, versus the corrector gap, for a voltage on aperture: V= 100 V;

Figure 9 shows a plot of coefficient of 2" order chromatic aberration C_c2, normalized to the aperture diameter D, versus voltage V on the aperture for gap-diamter ratio slD = 0.1, and ,

Figure 10 shows schematically an electron microscope column with the foil corrector according to the present invention.

Detailed description of embodiments

A) Geometry A foil corrector in its most basic form is sketched in figure 1. Figure 1 shows schematically a basic design of a foil corrector according to the present invention (not to scale) wherein D denotes a diameter of an aperture and 5 denotes a gap between a foil and the aperture. It consists of a flat free-standing foil of nanometer size thickness with apertures on both sides. In the low energy foil corrector according to the present invention, the foil is put on a retarding potential, such that the electrons (e-) have almost 0 eV kinetic energy when they enter the foil (and also when they have just left the foil at the other side).

B) Origin of aberration correction

Figure 2 shows schematically positive spherical aberration for a positive (left) and a negative (right) lens, by means of two rays entering the lens at different radii, r; and r₂.

In both cases, the intercept with the z-axis shifts in the negative z direction for increasing radius of incidence.

In a positive lens, positive spherical aberration is the effect that the focussing power of the lens increases for increasing radius of incidence. In a negative lens with positive spherical aberration, the defocusing power of the lens decreases for increasing radius of incidence. This is illustrated in figure 2. In a spherical aberration corrector the opposite effect is desired. In order to explain the behaviour of the corrector in terms of easy to understand physics, an approximative description of its properties will be obtained by a simple analysis of the radial momentum the electron obtains in the electric field. Because of the symmetry around the foil, the calculation can be limited to one half part of the corrector: a flat surface (representing the foil) with an aperture in front of it. First, the calculation will be done for a conventional foil corrector operating at high beam energy. Thereafter the calculation for the low voltage foil corrector will be done according to the same reasoning and the difference between both correctors will be pointed out.

In a rotationally symmetric system, the radial momentum change obtained by an electron travelling in an electric field is:

r∞ PO 0O0 ^■ -eehE_rr ((zz,, ^• r)

Ap_r — / -eE_r(z r)dt = / dz Jo Jo v_z{z, r)

0)

where E_r(z,r) is the radial component of the electric field, and v_z(z,r) is the electron's axial velocity component. A cylindrical coordinate system is adopted here in which the positive z-direction is perpendicular to the foil and directed towards the aperture, and the radial coordinate r is perpendicular to the z-axis. Close to the axis the potential Φ (z,r) can be expanded as

(z, r) = Φ(z) - - ^rτ®"{z) + τ ^rr- ⁾ {z) + 0{r⁶)

^{4 64} (2) where Φ "(z) and Φ (z) are the second and fourth derivative with respect to z, respectively. See: P.W. Hawkes, E. Kasper, "Principles of Electron Optics", Vol. 1,

Academic Press, London, UK, 1989. Then, the radial component of the field can be written as

Inserting this in equation 1 and neglecting the 0(r⁵) term, one obtains

Δp, « /^∞ - ^ ( "{Z) - ll W (*)) dz

Jo vΛz 'r) \ 2 16 / (4) Far from the corrector the field is almost zero, such that all derivatives of Φ become zero for z → oo. For a high beam energy, the electron velocity may be assumed constant and its height change can be neglected. In that case, the radial momentum change becomes:

Δ_ft « J 'Z (l*(0)r- l*-(0)

(5)

The deflection angle due to this radial momentum is:

Δ = ^APr

Vz (6) p_z is the axial momentum of the electron leaving the corrector. If the velocity of the electron is assumed to be constant and the radial velocity component is negligible, the following substitution is allowed:

p_zυ_z ∞ 2eU

(7) with [/the beam potential. Inserting equations 5 and 7 into equation 6, a relation between the radius of incidence and the deflection angle is obtained:

The first term l nd term proportional to r is the 3^r order focal strength and is a measure for the 3^r order spherical aberration.

It is expected that the radial momentum change is somehow related to the electric field in the z direction at the foil because the right end of the corrector is field free. Indeed, for this situation Gauss law states that for a cylindrical box of radius R along the z-axis, the axial electric field flux entering this box at the foil is equal to the radial electric field flux leaving it through its side. In formula: Jo E_z2πrdr = J₀ E_r2ττRdz An explicit relation between the deflection angle and the field is easily obtained when noting the similarity between equation 8 and the series expansion of the electric field in the z-direction at the foil: £,(0, r) = 0) = -Φ'(0) + i '"(0)r² + 0(r⁴)

(9) Thus, the deflection angle can be expressed in terms of the z-field at the foil (neglecting the 0(r") term):

Δα « - ^_F7 (£₂(0, r) + £_z(0, 0)) U (10)

Figure 3 shows a schematic sketch of electric field lines in the foil corrector according to the present invention.

In figure 3, the electric field lines in the corrector are sketched. It is evident that the absolute field strength on the foil is lowest at r = 0. This means that in the expression for E_z(0,r), the constant term and the term proportional to r² must have the same sign and thus that Φ '(0) and Φ '"(0) always have opposite sign. This is also illustrated in figures 4a-4e which are obtained by calculating the electric field by means of a finite element method (see section on calculation method). Figure 4a, 4b, 4c, 4d and 4e show a plot of the axial potential Φ and its first (Φ '), second (Φ ' '), third (Φ ' ' ')and fourth (Φ ) derivative, respectively, with respect to z as calculated by the finite element program Elens for an aperture diameter D = 0.2 mm and different corrector gaps, indicated by the numbers in the plots (1 : s = 0.01 mm; 2: s = 0.03 mm; 3: s = 0.05 mm; 4: s = 0.07 mm; 5: s = 0.1 mm), the foil being at 0 V and the aperture at unit potential.

When the foil is put on a retarding potential with respect to the aperture, Φ '(0) is positive and the corrector is a negative lens with negative spherical aberration. When the distance between the foil and the aperture is decreased, Φ '"(0) increases and thus the spherical aberration correction increases as well. This calculation also applies to a set-up of two apertures without a foil, because somewhere in between the apertures there will be a flat equi-potential plane as well. Therefore one may wonder whether the calculation is consistent with the well known fact that such a two aperture lens has a positive spherical aberration. In case of a foil corrector, both apertures can be put on a higher potential than the foil and both sides have a negative spherical aberration. Without the foil, this is not possible. The side at the aperture with the lower potential has a positive spherical aberration. Because the electron velocity is lower at this side, its contribution is larger than the side with the negative spherical aberration and the net result is always positive.

The derivation above is not adequate for the low energy foil corrector. We must return to equation 4 and substitute a suitable expression for v_z. v_z is lower for the electrons closer to the axis. Thus they will spend more time in the corrector and obtain a larger deflection away from the axis than when v_z was assumed constant. This effect contributes to a positive spherical aberration. In the low energy foil corrector, the velocity is reduced to almost zero at the foil. Consequently, the kinetic energy depends mainly on the difference between the local potential at the position of the electron and the foil potential. In approximation, v_z can be taken equal to the total velocity:

E_t is the kinetic energy and m is the electron mass. After substitution into the integral in equation 4, a new expression for the radial momentum change is obtained. The l/v_z term in the integral can be expanded into a series of r using equation 2. The deflection angle is Δp0p_z (equation 6). As »_z is the axial momentum of the electron when leaving the corrector, it is (under the same approximation for v_z as above)

with Φ (oo) the axial potential at z → o which is equal to the potential on the aperture. The deflection angle is then evaluated as:

Only terms up to third order in r have been kept in this expression. The integral over the 4^X derivative of Φ (z) is always positive, contributing to a negative spherical aberration. The integral over the square of the 2^nd derivative contributes to a positive spherical aberration. Which term dominates, depends on the size of the gap between foil and aperture, relative to the aperture diameter. In figure 4 the axial potential and its derivatives, as obtained by the finite element method to be described in section 4, are plotted for a fixed diameter and different gap sizes. For increasing gap size, the 4^th derivative decreases rapidly and hence the spherical aberration correction will become smaller and eventually turn into a positive spherical aberration. The presence of the term with Φ "(z), originating from the fact that the electron velocity decreases for lower radius of incidence, is the difference with its high voltage counterpart. For a foil corrector operating at high voltage, the spherical aberration correction decreases as well for increasing gap size, but does not change sign. Furthermore, equation 13 shows that the deflection angle is independent of the magnitude of the voltage applied to the aperture, provided this voltage remains positive. When the voltage on the aperture is increased with a factor n, all terms with , including its derivatives, increase with a factor n. The net result is that Δα remains the same.

A positive electrostatic lens will, in general, have a positive chromatic aberration: electrons with a larger velocity will spend less time in the lens field and are less deflected. So the focussing power is weaker for higher energies. In a negative lens, the higher energy electrons are less deflected as well and the defocusing power is weaker. This results in a negative chromatic aberration for negative electrostatic lenses. Therefore a foil corrector with the foil on a retarding potential is expected to have a negative chromatic aberration.

C) Methods to determine C_s and C_c

The analytic evaluation above is not intended to obtain exact results. Existing aberration integrals, such as given by Typke, "Der Ofhungsfehler von rotationssymmetrischen Elektionenlinsen mit Raumladung", Optik 28 (1968)488 and by P.W. Hawkes, E. Kasper, "Principles of Election Optics", Vol. 2, Academic Press, London, UK, 1996, are not suitable for this problem. They can not be applied in a situation where the electron energy goes to substantially zero. A derivation of the aberration integrals that is suitable for this problem has been pointed out to us by prof. Lenc (private communication, 2002). Meanwhile, the properties of any optical element can also be determined, when the electron trajectories in the exit plane are known as function of their radius and angle of incidence. Therefore, the spherical and chromatic aberration can be determined from ray tracing results. This will be discussed below. Again, the symmetry around the foil is used. The electrons start just in front of the foil, perpendicular to its surface with almost zero kinetic energy.

C.1) Spherical aberration

Coefficient C_s is obtained from ray tracing results in two steps (see figure 2 for visual illustration): 1. Evaluate the deflection angle as function of the radius of incidence:

Λa = aj r + a₃ r³ + a^ r⁵ + . . . (i4) in which the focal distance is:/= -Mai.

2. Plot the z-intercept versus the radius of incidence:

9 A z = z₀ - C_s3 ι - C_s5 aj + . . . (i5) z₀ is the intercept with the axis in absence of any aberration, GJ_/ is the angle under which the ray would intercept the optical axis, when only the 1 ^t order lens effect is taken into account.

For rays that have entered parallel to the optical axis, this angle is equal to the deflection angle due to the 1^st order lens effect:

So C_S3 and C_s5 are obtained by fitting to: z = z₀ + C_s3 (a rf + C_s5 (aj rf + . . . ₍ι₇) ai is obtained from equation 14, by fitting the deflection angle to the polynomial in r.

C.2) Chromatic aberration

The chromatic aberration coefficients are obtained from

in which E_start is the starting energy of the electron, U_end the potential in the exit plane and C_ci and C_c2 the coefficients of 1^st and 2^nd order chromatic aberration.

D) Calculation method

The electric field was calculated with Elens (B. Lencova, G.Wisselink, "Electron Optical Design Program Package Elens 3.7", 2002), a finite element program. The geometry for the calculation is shown in figure 5.

Figure 5 shows schematically a foil corrector according to the present invention with equi-potentials as calculated by Elens.

Elens divides this geometry into a fine mesh of maximum 100,000 points. The potential on every mesh point is determined such that the total energy is minimized. The electron trajectories are calculated with Trasys (B. Lencova, G.Wisselink, "Electron Optical Design Program Package Trasys 3.7", 2002). Trasys uses a high accuracy interpolation in z and r to determine the potential in between the mesh points, as described by J. Chmelik and J.E. Barth, "An interpolation method for ray tracing in electrostatic fields calculated by the finite element method", SPIE Charged-Part. Opt. 2014 (1993) 133. With this information, it can calculate the electric force on the electron at any point and thus trace its trajectory.

Trajectories starting at different radii of incidence and different energies must be calculated in order to determine the geometrical and the chromatic aberrations respectively. For every setting, a total of 16 trajectories are calculated: starting at r = 0.05; 0.075; 0.1 and 0.125 * D, with forward kinetic energy E_start = 0; 0.1; 0.3 and 0.6 eV.

E) Results

The corrector has 3 independent parameters: the gap s between foil and aperture, the diameter D of the aperture (both as shown in Figure 1) and the voltage V applied to the aperture.

Figure 6 shows a plot of focal distance coefficients C_S3 and C_ss of respectively 3^rd and 5^th order spherical aberration and coefficient of 1^st order chromatic aberration C_cι versus the voltage on the aperture, all normalized to the aperture diameter D, for a gap- diameter ratio slD = 0.1.

Figure 7 shows a plot of focal distance/ coefficients C_S3 and C_s$ of respectively 3^r and 5^th order spherical aberration and coefficient of 1^st order chromatic aberration versus the corrector gap, all normalized to the aperture diameter D, for a voltage on aperture: V= 100 V. An important result of the calculations is that the magnitude of the voltage on the aperture has little influence on the trajectories. The/ C_S3, C_ss and C_cj are hardly affected by the voltage, as is illustrated in figure 6, only the C_c2 is. For a fixed ratio between corrector gap and diameter, the results scale linearly with the size of the corrector. Therefore the corrector properties as function of the gap are normalized to the diameter of the aperture, see figure 7. For s«D the/ C_S3 and C_c/ converge to a constant value: f=-D

C_c, = -2D (i9)

Figure 8 shows a plot of coefficient of 2^nd order chromatic aberration C_c2, normalized to the aperture diameter D, versus the corrector gap, for a voltage on aperture: V = 100 V.

Figure 9 shows a plot of coefficient of 2^nd order chromatic aberration C_c2, normalized to the aperture diameter D, versus voltage Fon the aperture for gap-diameter ratio slD = 0.1. Figures 8 and 9 show that the coefficient of second order chromatic aberration is independent of the gap and increases for increasing voltage respectively.

F) Discussion

The results show that it is possible to obtain a correction for both the spherical and the chromatic aberration. To obtain a negative spherical aberration, the gap between foil and aperture should be sufficiently small, with respect to the aperture diameter. This is in agreement with the analytical evaluation presented above. Also the observation that the magnitude of the voltage on the aperture is of little influence on the trajectories is in good agreement with the analytical evaluation. For use in a microscope system, additional optics will be necessary to tune the corrections to a desired value and to focus the beam.

Figure 10 shows schematically an electron microscope column with an electron optical device or foil corrector according to the present invention.

A typical microscope system with this corrector is sketched in figure 10. The focussing lenses have to be put close to the corrector because the corrector is a very strong negative lens. Therefore, focussing the beam with magnetic lenses is not favourable, as the foil would have to be placed in the magnetic field. The consequence of this field would be that the electrons obtain a tangential velocity. Then, depending on the radius of incidence at the foil, the path length in the foil is increased, causing more scattering, and the forward energy is reduced, causing more electrons to be reflected at the foil. These problems are avoided with electrostatic lenses. We have performed calculations on a realistic set-up with some additional electrodes, showing that it is possible to focus the beam and still maintain a negative spherical and chromatic aberration. In a similar manner as outlined above for a microscope system, the corrector can be used in an electron lithography system for the reduction of the spherical or chromatic aberration. As mentioned above, the foil will act as a high pass energy filter because the electrons in the lower part of the energy distribution do not have sufficient energy to pass the foil. Furthermore, a quantum mechanical effect due to the wave character of the electrons has to be taken into account. When the electrons enter the foil, their kinetic energy is increased with around 10 eV, being the difference between the vacuum level and the bottom of the conduction band. As a consequence the wavelength is decreased. Opposed to its high voltage counterpart, this effect is not negligible for the low energy foil corrector. The electrons form a standing wave in the foil and a quantum mechanical reflection at the foils surfaces can occur. Calculations of the transmission as function of the electron kinetic energy show an oscillating behaviour, causing a high cut-off as well.

As the electron energy is decreased to 0 eV in the foil corrector, Coulomb interactions may become significant. This will set a limit to the current that can be allowed. The angular deflection caused by Coulomb interactions has been calculated with the slice method using Jiangs formulas (see: X. Jiang, J.E. Barth, P. Kruit, "Combined calculation of lens aberrations, space charge aberrations, and statistical Coulomb effects in charged particle optical columns", J. Vac. Sci. Technol. B 14 (1996) 3747) and is compared to the illumination angle.

A corrector geometry is assumed of identical apertures on both sides of the foil, gap sizes 30 μm, aperture diameters 200 μm and a voltage between foil and apertures of 300 V, which is based on the practical limit of 10 kV/mm. It has been taken into account that in this case the field on the optical axis is considerably lower, see fig. 4. Then for an electron beam with a reduced brightness of 10 Am^" sr^" V^" , a diameter of 40 μm at the foil (20% of the aperture diameter) and current 1 nA (assuming no current loss in the foil), the illumination angle is 5.8x10^" rad and the Coulomb interactions angular deflection is 2.2x10^" rad. This causes an increase of the spot size of about 7%. When the third order C_s and the first order C_c are corrected, the fifth order C_s and the second order C_c can limit the spot size. The calculations show that the C_ss of the corrector can be zero, giving no extra contribution to the spot size due to aberrations. Preliminary calculations indicate that the spot size due to the second order chromatic aberration can be kept sufficiently small.

The main uncertainty is whether the transmission of electrons through the foil will be sufficient, as this has not yet been experimentally verified. There is some experimental work on the transmission of free electrons through foils at very low energies. Ee, for example, H. Kanter, "Slow-electron mean free paths in aluminum, silver, and gold", Phys. Rev. B 1 (1970) 522.

However, to obtain conclusive results for the low energy foil corrector, the transmission should be measured for sub 10 nm foils and with a sub 0.1 eV energy resolution because of the quantum mechanical reflection. The principal scattering mechanism at the energy of interest is electron-electron scattering. See: P. Wolff, "Theory of secondary electron cascade in Metals", Physical Review 95 (1954) 56. Therefore, a semiconductor foil may be favourable over a metal foil. Because of its lower density of conduction electrons, scattering is expected to be much less and the transmission will be better or such a foil needs to be less thin. Another option to improve the transmission is the use of a gauze or perforated foil. The gauze mazes or perforations should be sufficiently small, that they do not significantly disturb the electric field. In summary, a low voltage spherical and chromatic aberration corrector is proposed based on a thin transparent foil sandwiched between two apertures. The electrons are retarded to almost zero energy at the foil, at which energies the electrons may travel ballistically through the foil. From an approximate analytical model the feasibility to correct spherical and chromatic aberrations was shown. The third and fifth order spherical aberration coefficients as well as the first and second order chromatic aberration coefficients were obtained from electric field simulations and ray tracing. A schematic design of a corrector for potential use in a low- voltage scanning electron microscope or in the gun-section of a scanning transmission electron microscope has been described.

Claims

1. An electron optical device for, in use, creating negative spherical and chromatic aberration and reducing the energy spread in an electron beam travelling on an optical axis, comprising: • at least one conducting plate substantially perpendicular to the optical axis with a first aperture having a first radius around said optical axis, • a thin foil of conducting material located parallel to and at a first distance from said at least one conducting plate, said thin foil having, in use, an electric potential generating an electrical field for reducing the kinetic energy of electrons in the electron beam to a value substantially close to zero at the surface of said foil, while leaving said kinetic energy of said electrons in the first aperture at a relatively higher value.

2. An electron optical device according to claim 1, wherein the kinetic energy at the surface of said foil is lower than 10 electron Volt.

3. An electron optical device according to claim 1, wherein said foil is thinner than 50 nanometer, e.g. thinner than 5 nanometer.

4. An electron optical device according to claim 1, wherein said first distance between said foil and said plate is smaller than said first radius of said first aperture in said at least one conducting plate.

5. An electron optical device according to claim 1, further comprising a second conducting plate substantially perpendicular to the optical axis with a second aperture having a second radius around said optical axis, said second conducting plate located at a side of said foil opposite to said side of said at least one conducting plate relative to said foil.

6. An electron optical device according to claim 1, wherein the dimensions of said second aperture are substantially identical to the dimensions of said first aperture.

7. An electron optical device according to claim 1, wherein additional conducting electrodes are being arranged in such a manner that in use, a beam of electrons which enters the device as a substantially parallel beam exits the device as a substantially parallel beam.

8. An electron optical device according to claim 1, wherein said electric potential at said surface of said foil is such, that, in use, a part of the electrons in said electron beam having a kinetic energy below a predetermined threshold value are reflected by said electric potential of said foil and a further part of the electrons in said electron beam having a kinetic energy higher than the predetermined threshold value are passed through said foil.

9. An electron optical device according to claim 1, in which said foil has perforations for increasing, in use, transmission of electrons in said electron beam.

10. An electron optical device according to claim 1, wherein said foil comprises a conducting or semi-conducting material.

11. An electron optical device according to claim 1 , wherein said foil comprises an insulating material comprising a conducting surface layer.

12. An electron lens system, using an electron optical device according to any one of the claims 1 to 11 for a compensation, in use, of a positive spherical aberration of other lenses in said electron lens system.

13. An electron lens system, using an electron optical device according to any one of the claims 1 to 12 for a compensation of a positive chromatic aberration of said other lenses in said electron lens system.

14. An electron microscope, using an electron optical device according to any one of the claims 1 to 11.

15. An electron microscope, using an electron lens system according to any one of the claims 12 or 13.

16. An electron lithography system, using an electron optical device according to any one of the claims 1 to 11.

17. An electron lithography system, using an electron lens system according to any one of the claims 12 or 13. Abstract

An electron optical device for, in use, creating negative spherical and chromatic aberration and reducing the energy spread in an electron beam travelling on an optical axis, including: • at least one conducting plate substantially perpendicular to the optical axis with a first aperture having a first radius around said optical axis, • a thin foil of conducting material located parallel to and at a first distance from the at least one conducting plate, In use, the thin foil has an electric potential that generates an electrical field for reducing the kinetic energy of electrons in the electron beam to a value substantially close to zero at the surface of the foil, while leaving the kinetic energy of the electrons in the first aperture at a relatively higher value.

[Figure 3]