- Email: [email protected]
Prospects for aberration-free electron microscopy
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Ultramicroscopy 103 (2005) 1–6 www.elsevier.com/locate/ultramic
Prospects for aberration-free electron microscopy H. Rose Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 6, Darmstadt D-64289, Germany
Abstract Future aberration-corrected electron microscopes that will enable sub-A˚ngstroem spatial and sub-eV energy resolution are outlined . The sub-A˚ngstroem transmission electron microscope (SATEM) only compensates for the spherical aberration and reduces the chromatic aberration disc by means of a monochromator. In order to correct for both aberrations, two novel correctors, the ultracorrector and the superaplanator are proposed which will yield a resolution limit of about 0.5 A˚ and a large field of view of more than 4 106 image points. The superaplanator is best suited for obtaining an achromatic aplanat required for the realization of the high-performance in situ electron microscope of the TEAM project. r 2004 Elsevier B.V. All rights reserved. PACS: 41.85p, 41.85.Gy, 41.85.Lc, 11.80.Fv Keywords: Aberration correction; Ultracorrector; Superaplanator
1. Introduction The need to compensate for the unavoidable chromatic and spherical aberration of static rotationally symmetric electron lenses originated in the context to improve the resolution of electron microscopes. In the past, most emphasis has been put on the correction of spherical aberration because it mainly limits the resolution at voltages larger than about 100 kV. Up to about 1990 the correction of chromatic aberration had been Fax: +49 6151 166053.
E-mail address: [email protected] (H. Rose).
studied experimentally only by Hardy [1], Koops et al. [2] and Hely [3]. All aberration correctors consist of numerous elements which must be precisely adjusted and kept stable with an extreme accuracy that could be achieved only recently. Therefore, all attempts during a period of about 45 years to improve the actual resolution of electron microscopes by correcting the aberrations have failed . Correction works only if the information limit of the microscope is appreciably smaller than the resolution limit defined by aberrations. Hence, it is of prime importance to eliminate or sufficiently suppress all incoherent disturbances affecting the information limit [4]. So far the correction efforts have been proven successful for the low-voltage
0304-3991/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2004.11.017
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SEM [5], the 200 kV TEM [4,6] and the 100 kV scanning transmission (STEM) [7]. In the meantime, several other aberration-corrected electron microscopes have been installed at different laboratories and many more are in the construction phase. Quadrupole–octopole correctors are necessary to compensate for both the chromatic and the spherical aberrations, while a hexapole corrector suffices to eliminate the spherical aberration which is the dominant resolution-limiting aberration at accelerating voltages larger than about 100 kV. At present a resolution limit of about 1.2 A˚ is routinely achieved with the hexapole corrector and best contrast is obtained for crystalline objects by tuning the third-order coefficient of the spherical aberration to negative values [8]. In order to elucidate the three-dimensional structure of solid objects, a subA˚ngstroem transmission electron microscope (SATEM) enabling tomography is required. Future high-performance transmission electron microscopes aim for an instrumental resolution limit of about 0.5 A˚ and at least 2000 equally wellresolved object elements per diameter of the image field. This requirement implies that all points of a 104 nm2 object area must be transferred with the same resolution. For this purpose it is mandatory to employ an aplanatic objective lens which is free of spherical aberration and off-axial coma. However, the correction of these aberrations does not suffice for achieving a resolution limit of 0.5 A˚ at voltages below 200 kV due to chromatic aberration. Fortunately, this aberration can be sufficiently reduced by a monochromator or corrected by means of crossed electric and magnetic quadrupole elements which partly act as first-order Wien filters. Their electric and magnetic forces compensate each other for electrons with nominal energy. At present the use of a monochromator and a hexapole aplanator is most promising because the hexapole fields need not be stabilized with the high accuracy of about 0.15 ppm required for the quadrupole fields. Nevertheless, the correction of the chromatic aberration offers several additional advantages for TEM apart from the improved spatial resolution. These are: (a) use of large energy windows yielding improved signal/noise in EFTEM,
(b) high contrast transfer, (c) high currents necessary for efficient analytical TEM, (d) adequate space for the sample, required for in situ TEM, (e) use of low voltages for imaging unstained biological objects with sufficient contrast, and (f) Lorentz microscopy, where the magnetic field vanishes at the specimen plane. Future aberration corrected objective lenses will be achromatic aplanats for the TEM.
2. High-performance achromatic aplanats Achromatic aplanats are compound lenses consisting of a coma-free objective lens and a multielement quadrupole–octopole corrector with special symmetry properties. These compound lenses are free of chromatic aberration, spherical aberration and off-axial coma. Moreover, image curvature and field astigmatism stay sufficiently small allowing at least 2000 equally well-resolved object elements per image diameter. Arrangement of corrector elements and course of fundamental paraxial rays exhibit distinct symmetries. As a result eikonal terms with two-fold symmetry do not show up. Hence the number of additional aberrations introduced by quadrupole fields of the corrector is minimized. So far two appropriate correctors have been found and designed, the superaplanator and the ultracorrector. The ultracorrector is especially suited for electron projection lithography since it compensates for the chromatic aberration and all third-order geometrical aberrations. Owing to the large magnification in high-resolution TEM, the transferred object field is so small that image curvature and field astigmatism do not appreciably affect the image quality. In this case superaplanator suffices for achieving the same resolution for all image points. This corrector consists of fewer elements than the ultracorrector and can be realized with a smaller amount of expenditure. Conventional magnetic round lenses suffer from both spherical aberration and off-axial coma. In order to eliminate azimuthal or anisotropic coma,
ARTICLE IN PRESS H. Rose / Ultramicroscopy 103 (2005) 1–6
the axial magnetic field must change sign, which implies that the lens must be a dual lens consisting of two spatially separated windings with opposite directions of their currents [9]. It should be noted that the coefficient Cc of the axial chromatic aberration of the coma-free lens is appreciably (X50%) larger than that of standard objective lenses. Therefore, coma-free lenses necessitate strong reduction or correction of chromatic aberration in order to achieve sub-A˚ngstroem resolution.
2.1. Properties of the superaplanator The superaplanator consists of two symmetrical quadrupole quintuplets and at least three octopoles for correcting the third-order axial aberrations. Quadrupole fields are excited symmetrically with respect to the central plane of each quintuplet and anti-symmetrically with respect to the plane midway between the two multiplets, as shown in Fig. 1. An octopole field is centered at each of the three symmetry planes. The chromatic aberration is eliminated by placing a crossed electric and magnetic quadrupole at the center of each quintuplet and by adjusting their electric and magnetic strengths appropriately. Owing to hysteresis effects the magnetic quadrupole and octopole fields cannot be excited independently within a single multipole element. To avoid this difficulty, the largely extended central
a.u.
3 2
xα
1
Ψ2s
yδ -1 -2 y
xγ -3
0
β
2
quadrupole can be split up in two spatially separated quadrupoles placed symmetrically about the central plane where the octopole element is centered. In this case the quadrupole fields do not overlap octopole fields. The course of the fundamental rays xa ; yb ; xg ; and yd is either symmetric or anti-symmetric within each quadrupole quintuplet. In particular fundamental rays which are symmetric in one subunit are anti-symmetric in the other. As a result the corrector does neither introduce off-axial coma, distortion, and chromatic aberration of magnification nor non-rotationally symmetric aberrations with two-fold symmetry. Axial fundamental rays xa ; and yb originate from the object plane while the field rays xg and yd intersect the center of the coma-free plane of the objective lens [10]. Since the lateral distance of these rays is either very small or zero at the central planes, the octopoles do not introduce appreciable third-order off-axial aberrations. Hence the correction of the third-order aperture aberrations by means of these octopoles hardly affects the number of equally well-resolved object elements or image points, respectively. The third-order spherical aberration is corrected by means of two octopoles, each of which is centered at the midplane of one subunit. Subsequently the remaining four-fold axial astigmatism is eliminated by the third octopole placed at the plane midway between the two multiplets without affecting any other third-order aberration. To achieve a resolution limit of 0.5 A˚ for a system consisting of an objective lens with CcEf ¼ 2 mm and a superaplanator with a length of 50 cm, the following stability requirements must be fulfilled: DBr DU Q DBQ 2 107 ; 1:5 107 ; Br UQ BQ DBn 4 107 for n ¼ 1; 2; 4; 5: Bn
l
0
3
4
6 z/l
8
10
12
Fig. 1. Arrangement and strengths C2s of the quadrupoles, and course of the fundamental rays xa ; xg ; yb ; yd within the superaplanator.
Here Br denotes the magnetic field strength at the round objective lens, BQ that of the central quadrupole ðv ¼ 3Þ and Bv that of other quadrupoles of each quintuplet. UQ is the potential applied to the electrodes of the central quadrupoles which compensate for the axial chromatic aberration. Although the required stabilities are
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very high for the fields of the central quadrupoles and the objective lens, they can be achieved with present technology.
3. Ultracorrector So far, we have shown that electron optical systems exist which can be considered as equivalents of light-optical aplanats. The question remains if there exist charged-particle systems which are free of all primary chromatic and all geometrical aberrations. For example, such a system would be extremely useful in electron projection lithography for imaging an extended mask on a wafer. The novel ultracorrector can compensate for all these aberrations. This universal corrector is composed of two identical multipole multiplets each consisting of seven quadrupoles and seven octopoles which are symmetrically arranged about the center planes zm1, and zm2, respectively, as shown in Fig. 2. Twelve pole elements are used for superposing quadrupole and octopole fields. An additional octopole is centered at the plane zM midway between two multiplets. The octopole fields of the ultracorrector are symmetric, whereas the quadrupole fields are anti-symmetric with respect to the
midplane zM. Strengths and locations of quadrupoles are chosen in such a way that the two fundamental field rays xa and yb are antisymmetric and the axial rays xg and yd are symmetric with respect to the center plane of each telescopic quadrupole septuplet. In the telescopic case the axial rays run parallel to the optic axis in the region outside the septuplets. The field rays intersect the optic axis at the principal planes located at equal distances in front of and on the far side of each septuplet. The back principal plane of the first septuplet coincides with the front principal plane of the second septuplet and forms the midplane zM of the ultracorrector. The fundamental rays exhibit the same symmetry properties with respect to the plane zM and the center plane of each septuplet where a strongly first-order distorted stigmatic image of the front principal plane is formed. Owing to special symmetries of fundamental rays and multipole fields, the aberrations of the ultracorrector with two-fold symmetry cancel out and the number of aberrations with four-fold symmetry reduces significantly. If an image of the source is placed at the front principal plane of the ultracorrector, neither comas nor distortions are introduced. Therefore, it is advantageous to appropriately incorporate the ultracorrector in a system which is free of these
Fig. 2. Arrangement and strengths of the quadrupoles, and course of the fundamental rays xa ; xg ; yb ; yd within the ultracorrector.
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5
aberrations. In this case the corrector enables a feasible successive elimination of the remaining aberrations. By performing the correction in a distinct sequence, the compensation of each aberration does not introduce aberrations eliminated in the preceding correction steps. The chromatic aberrations are corrected first by employing crossed electric and magnetic quadrupoles located at the center of each multiplet and at astigmatic line images. Remaining geometrical aberrations—spherical aberration, four-fold axial astigmatism, image curvature, round-lens field astigmatism and octopole field astigmatism—are compensated by properly adjusting the five free strengths of the 15 octopoles. Each of the three field aberrations is compensated by four octopoles with the same strength starting with the image curvature. The corresponding octopole fields are superposed onto the 2nd, 6th, 9th , and 13th quadrupoles, respectively. Subsequently, the round-lens field astigmatism is eliminated by four octopoles each located in the region between the first and the second and between the 6th and the 7th quadrupole of each septuplet. In the third step the octopole field astigmatism is corrected by means of four octopoles superposed on the outer quadrupoles. Then the spherical aberration is corrected by the two octopoles placed at the centers of multiplets and in the last stage the fourfold axial astigmatism is compensated by the octopole located at the midplane zM. The elimination of the field aberrations also allows for extended electron sources in electron projection lithography resulting in low current densities and small Coulomb interactions between the electrons.
ment. If both projects have been successfully completed, their different novel components will be combined yielding the most versatile ultraresolution analytical electron microscope. The SATEM is primarily aimed for elucidating the three-dimensional structure of solid objects at a resolution of about 1 A˚ . This instrument is equipped with a Schottky emitter and a monochromator yielding a quasi-monochromatic source with an energy spread smaller than 0.2 eV. In addition a hexapole corrector and a corrected 901 omega filter are incorporated. First experiments have demonstrated that the monochromator does not affect the geometrical properties of the source. The monochromator reduces the current by about 65% for an energy window of 0.2 eV. The selection slit is centered at the maximum of the energy distribution. To largely avoid mechanical instabilities a new 300 mm column and a highly stable support frame have been developed [11]. They will also be employed for the SESAM . This instrument is equipped with the same source as the SATEM and can operate in both the STEM and the TEM mode at 200 kV. Instead of the omega filter the SESAM is equipped with the MANDOLINE filter enabling highly resolved ELNES investigations [12]. This filter has an extremely high transmissivity and provides a dispersion of 6.2 mm/eV at 200 kV [13]. Hence the MANDOLINE allows for energy-filtered imaging of large fields of view and large scattering angles (e.g. CBED) with excellent isochromaticity. The experimentally achieved dispersion is in very good agreement with the theoretical values [14].
4. SATEM and SESAM projects
5. Outline of future aberration-free electron microscopes
The ultimate goal in the development of highperformance analytical transmission electron microscopes is an instrument with a spatial resolution limit of about 0.5 A˚ and an energy resolution below 0.2 eV at voltages between 100 kV and 300 kV. Moreover, the microscope should operate in the fixed beam TEM and the STEM mode. The SATEM and the SESAM projects are the first steps on the route toward this universal instru-
The SATEM is designed for achieving a resolution limit of about 1 A˚. In order to further reduce this limit to 0.5 A˚, it is a ‘‘conditio sine qua non’’ that the parasitic incoherent aberrations resulting from mechanical and electromagnetic instabilities can be sufficiently reduced. The realization of this ambitious task poses by far the most difficult problem. By combining components of the
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SATEM and the SESAM, an extremely versatile instrument can be built. It consists of (a) a field emission gun with a monochromator, (b) a condenser system with an incorporated hexapole corrector enabling genuine Koehler illumination for the TEM mode and a subA˚ngstroem spot size for the STEM mode, (c) a hexapole corrector behind the objective lens yielding aplanatic imaging for the TEM mode, (d) the MANDOLINE filter and (e) a corrected quadrupole projector system which images with variable magnification either the energy loss spectrum or the filtered intermediate image onto the CCD array. The high-resolution TEM mode is especially useful for rapidly finding specific object details and obtaining energy-filtered images, while the STEM mode is best suited for recording highly resolved energy loss spectra of small object details such as single atom columns. The need for chromatically corrected aplanats has recently been revived in the context of high-resolution in situ electron microscopy [15]. The realization of this system is the most demanding task of the Transmission Electron Aberration-corrected Microscope (TEAM) project.
successful realization of aberration-corrected electron microscopes is the suppression of mechanical and electromagnetic instabilities and a precise computer-assisted alignment procedure within a short period of time. With the advancement in technology, the performance of the new instruments will increase to such an extent that the ultimate resolution limit of 0.5 A˚ will be realized. We can expect that future electron-optical systems will reach a degree of perfection comparable to that obtained in light optics.
Acknowledgements I want to thank Dr. Heiko Mu¨ller for placing Fig. 1 at my disposal and Dr. Rainer Spehr for valuable comments.
References [1] [2] [3] [4] [5] [6]
6. Conclusion In the last decade considerable progress has been made in electron optics. Thanks to the development of efficient procedures for calculating and designing sophisticated electron-optical systems, it has become possible to realize novel components such as monochromators, aberration correctors, and imaging energy filters. The incorporation of these elements will make quantitative analytical electron microscopy with sub-A˚ngstroem spatial and sub-eV energy resolution possible in the very near future. The basis for a
[7] [8] [9] [10] [11]
[12] [13] [14] [15]
D.F. Hardy, Dissertation, University of Cambridge 1967. H. Koops, G. Kuck, O. Scherzer, Optik 48 (1977) 225. H. Hely, Optik 60 (1982) 353. M. Haider, H. Rose, S. Uhlemann, B. Kabius, K. Urban, J. Electron Microsc. 47 (1998) 395. J. Zach, M. Haider, Nucl. Instrum. Methods A 363 (1995) 316. M. Haider, H. Rose, S. Uhlemann, E. Schwan, B. Kabius, K. Urban, Ultramicroscopy 75 (1998) 52. O.L. Krivanek, N. Dellby, A.R. Lupini, Ultramicroscopy 78 (1999) 1. C.L. Jia, M. Lentzen, K. Urban, Science 299 (2003) 870. H. Rose, Optik 34 (1971) 285. H. Rose, Optik 85 (1990) 19. G. Benner, M. Matijevic, A. Orchowski, B. Schindler, M. Haider, P. Hartel, Microsc. Microanal. 9 (Suppl.3) (2003) 38. G. Benner, E. Essers, B. Huber, A. Orchowski, Microsc. Microanal. 9 (Suppl. 3) (2003) 66. S. Uhlemann, H. Rose, Optik 96 (1994) 163. E. Essers, B. Huber, Microsc. Microanal. 9 (Suppl. 3) (2003) 20. B. Kabius, M. Haider, S. Uhlemann, E. Schwan, K. Urban, H. Rose, 59th Anual Proceedings of Microscopy and Microanalysis, 2001, p. 90.
Ultramicroscopy 103 (2005) 1–6 www.elsevier.com/locate/ultramic
Prospects for aberration-free electron microscopy H. Rose Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 6, Darmstadt D-64289, Germany
Abstract Future aberration-corrected electron microscopes that will enable sub-A˚ngstroem spatial and sub-eV energy resolution are outlined . The sub-A˚ngstroem transmission electron microscope (SATEM) only compensates for the spherical aberration and reduces the chromatic aberration disc by means of a monochromator. In order to correct for both aberrations, two novel correctors, the ultracorrector and the superaplanator are proposed which will yield a resolution limit of about 0.5 A˚ and a large field of view of more than 4 106 image points. The superaplanator is best suited for obtaining an achromatic aplanat required for the realization of the high-performance in situ electron microscope of the TEAM project. r 2004 Elsevier B.V. All rights reserved. PACS: 41.85p, 41.85.Gy, 41.85.Lc, 11.80.Fv Keywords: Aberration correction; Ultracorrector; Superaplanator
1. Introduction The need to compensate for the unavoidable chromatic and spherical aberration of static rotationally symmetric electron lenses originated in the context to improve the resolution of electron microscopes. In the past, most emphasis has been put on the correction of spherical aberration because it mainly limits the resolution at voltages larger than about 100 kV. Up to about 1990 the correction of chromatic aberration had been Fax: +49 6151 166053.
E-mail address: [email protected] (H. Rose).
studied experimentally only by Hardy [1], Koops et al. [2] and Hely [3]. All aberration correctors consist of numerous elements which must be precisely adjusted and kept stable with an extreme accuracy that could be achieved only recently. Therefore, all attempts during a period of about 45 years to improve the actual resolution of electron microscopes by correcting the aberrations have failed . Correction works only if the information limit of the microscope is appreciably smaller than the resolution limit defined by aberrations. Hence, it is of prime importance to eliminate or sufficiently suppress all incoherent disturbances affecting the information limit [4]. So far the correction efforts have been proven successful for the low-voltage
0304-3991/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2004.11.017
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H. Rose / Ultramicroscopy 103 (2005) 1–6
SEM [5], the 200 kV TEM [4,6] and the 100 kV scanning transmission (STEM) [7]. In the meantime, several other aberration-corrected electron microscopes have been installed at different laboratories and many more are in the construction phase. Quadrupole–octopole correctors are necessary to compensate for both the chromatic and the spherical aberrations, while a hexapole corrector suffices to eliminate the spherical aberration which is the dominant resolution-limiting aberration at accelerating voltages larger than about 100 kV. At present a resolution limit of about 1.2 A˚ is routinely achieved with the hexapole corrector and best contrast is obtained for crystalline objects by tuning the third-order coefficient of the spherical aberration to negative values [8]. In order to elucidate the three-dimensional structure of solid objects, a subA˚ngstroem transmission electron microscope (SATEM) enabling tomography is required. Future high-performance transmission electron microscopes aim for an instrumental resolution limit of about 0.5 A˚ and at least 2000 equally wellresolved object elements per diameter of the image field. This requirement implies that all points of a 104 nm2 object area must be transferred with the same resolution. For this purpose it is mandatory to employ an aplanatic objective lens which is free of spherical aberration and off-axial coma. However, the correction of these aberrations does not suffice for achieving a resolution limit of 0.5 A˚ at voltages below 200 kV due to chromatic aberration. Fortunately, this aberration can be sufficiently reduced by a monochromator or corrected by means of crossed electric and magnetic quadrupole elements which partly act as first-order Wien filters. Their electric and magnetic forces compensate each other for electrons with nominal energy. At present the use of a monochromator and a hexapole aplanator is most promising because the hexapole fields need not be stabilized with the high accuracy of about 0.15 ppm required for the quadrupole fields. Nevertheless, the correction of the chromatic aberration offers several additional advantages for TEM apart from the improved spatial resolution. These are: (a) use of large energy windows yielding improved signal/noise in EFTEM,
(b) high contrast transfer, (c) high currents necessary for efficient analytical TEM, (d) adequate space for the sample, required for in situ TEM, (e) use of low voltages for imaging unstained biological objects with sufficient contrast, and (f) Lorentz microscopy, where the magnetic field vanishes at the specimen plane. Future aberration corrected objective lenses will be achromatic aplanats for the TEM.
2. High-performance achromatic aplanats Achromatic aplanats are compound lenses consisting of a coma-free objective lens and a multielement quadrupole–octopole corrector with special symmetry properties. These compound lenses are free of chromatic aberration, spherical aberration and off-axial coma. Moreover, image curvature and field astigmatism stay sufficiently small allowing at least 2000 equally well-resolved object elements per image diameter. Arrangement of corrector elements and course of fundamental paraxial rays exhibit distinct symmetries. As a result eikonal terms with two-fold symmetry do not show up. Hence the number of additional aberrations introduced by quadrupole fields of the corrector is minimized. So far two appropriate correctors have been found and designed, the superaplanator and the ultracorrector. The ultracorrector is especially suited for electron projection lithography since it compensates for the chromatic aberration and all third-order geometrical aberrations. Owing to the large magnification in high-resolution TEM, the transferred object field is so small that image curvature and field astigmatism do not appreciably affect the image quality. In this case superaplanator suffices for achieving the same resolution for all image points. This corrector consists of fewer elements than the ultracorrector and can be realized with a smaller amount of expenditure. Conventional magnetic round lenses suffer from both spherical aberration and off-axial coma. In order to eliminate azimuthal or anisotropic coma,
ARTICLE IN PRESS H. Rose / Ultramicroscopy 103 (2005) 1–6
the axial magnetic field must change sign, which implies that the lens must be a dual lens consisting of two spatially separated windings with opposite directions of their currents [9]. It should be noted that the coefficient Cc of the axial chromatic aberration of the coma-free lens is appreciably (X50%) larger than that of standard objective lenses. Therefore, coma-free lenses necessitate strong reduction or correction of chromatic aberration in order to achieve sub-A˚ngstroem resolution.
2.1. Properties of the superaplanator The superaplanator consists of two symmetrical quadrupole quintuplets and at least three octopoles for correcting the third-order axial aberrations. Quadrupole fields are excited symmetrically with respect to the central plane of each quintuplet and anti-symmetrically with respect to the plane midway between the two multiplets, as shown in Fig. 1. An octopole field is centered at each of the three symmetry planes. The chromatic aberration is eliminated by placing a crossed electric and magnetic quadrupole at the center of each quintuplet and by adjusting their electric and magnetic strengths appropriately. Owing to hysteresis effects the magnetic quadrupole and octopole fields cannot be excited independently within a single multipole element. To avoid this difficulty, the largely extended central
a.u.
3 2
xα
1
Ψ2s
yδ -1 -2 y
xγ -3
0
β
2
quadrupole can be split up in two spatially separated quadrupoles placed symmetrically about the central plane where the octopole element is centered. In this case the quadrupole fields do not overlap octopole fields. The course of the fundamental rays xa ; yb ; xg ; and yd is either symmetric or anti-symmetric within each quadrupole quintuplet. In particular fundamental rays which are symmetric in one subunit are anti-symmetric in the other. As a result the corrector does neither introduce off-axial coma, distortion, and chromatic aberration of magnification nor non-rotationally symmetric aberrations with two-fold symmetry. Axial fundamental rays xa ; and yb originate from the object plane while the field rays xg and yd intersect the center of the coma-free plane of the objective lens [10]. Since the lateral distance of these rays is either very small or zero at the central planes, the octopoles do not introduce appreciable third-order off-axial aberrations. Hence the correction of the third-order aperture aberrations by means of these octopoles hardly affects the number of equally well-resolved object elements or image points, respectively. The third-order spherical aberration is corrected by means of two octopoles, each of which is centered at the midplane of one subunit. Subsequently the remaining four-fold axial astigmatism is eliminated by the third octopole placed at the plane midway between the two multiplets without affecting any other third-order aberration. To achieve a resolution limit of 0.5 A˚ for a system consisting of an objective lens with CcEf ¼ 2 mm and a superaplanator with a length of 50 cm, the following stability requirements must be fulfilled: DBr DU Q DBQ 2 107 ; 1:5 107 ; Br UQ BQ DBn 4 107 for n ¼ 1; 2; 4; 5: Bn
l
0
3
4
6 z/l
8
10
12
Fig. 1. Arrangement and strengths C2s of the quadrupoles, and course of the fundamental rays xa ; xg ; yb ; yd within the superaplanator.
Here Br denotes the magnetic field strength at the round objective lens, BQ that of the central quadrupole ðv ¼ 3Þ and Bv that of other quadrupoles of each quintuplet. UQ is the potential applied to the electrodes of the central quadrupoles which compensate for the axial chromatic aberration. Although the required stabilities are
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very high for the fields of the central quadrupoles and the objective lens, they can be achieved with present technology.
3. Ultracorrector So far, we have shown that electron optical systems exist which can be considered as equivalents of light-optical aplanats. The question remains if there exist charged-particle systems which are free of all primary chromatic and all geometrical aberrations. For example, such a system would be extremely useful in electron projection lithography for imaging an extended mask on a wafer. The novel ultracorrector can compensate for all these aberrations. This universal corrector is composed of two identical multipole multiplets each consisting of seven quadrupoles and seven octopoles which are symmetrically arranged about the center planes zm1, and zm2, respectively, as shown in Fig. 2. Twelve pole elements are used for superposing quadrupole and octopole fields. An additional octopole is centered at the plane zM midway between two multiplets. The octopole fields of the ultracorrector are symmetric, whereas the quadrupole fields are anti-symmetric with respect to the
midplane zM. Strengths and locations of quadrupoles are chosen in such a way that the two fundamental field rays xa and yb are antisymmetric and the axial rays xg and yd are symmetric with respect to the center plane of each telescopic quadrupole septuplet. In the telescopic case the axial rays run parallel to the optic axis in the region outside the septuplets. The field rays intersect the optic axis at the principal planes located at equal distances in front of and on the far side of each septuplet. The back principal plane of the first septuplet coincides with the front principal plane of the second septuplet and forms the midplane zM of the ultracorrector. The fundamental rays exhibit the same symmetry properties with respect to the plane zM and the center plane of each septuplet where a strongly first-order distorted stigmatic image of the front principal plane is formed. Owing to special symmetries of fundamental rays and multipole fields, the aberrations of the ultracorrector with two-fold symmetry cancel out and the number of aberrations with four-fold symmetry reduces significantly. If an image of the source is placed at the front principal plane of the ultracorrector, neither comas nor distortions are introduced. Therefore, it is advantageous to appropriately incorporate the ultracorrector in a system which is free of these
Fig. 2. Arrangement and strengths of the quadrupoles, and course of the fundamental rays xa ; xg ; yb ; yd within the ultracorrector.
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aberrations. In this case the corrector enables a feasible successive elimination of the remaining aberrations. By performing the correction in a distinct sequence, the compensation of each aberration does not introduce aberrations eliminated in the preceding correction steps. The chromatic aberrations are corrected first by employing crossed electric and magnetic quadrupoles located at the center of each multiplet and at astigmatic line images. Remaining geometrical aberrations—spherical aberration, four-fold axial astigmatism, image curvature, round-lens field astigmatism and octopole field astigmatism—are compensated by properly adjusting the five free strengths of the 15 octopoles. Each of the three field aberrations is compensated by four octopoles with the same strength starting with the image curvature. The corresponding octopole fields are superposed onto the 2nd, 6th, 9th , and 13th quadrupoles, respectively. Subsequently, the round-lens field astigmatism is eliminated by four octopoles each located in the region between the first and the second and between the 6th and the 7th quadrupole of each septuplet. In the third step the octopole field astigmatism is corrected by means of four octopoles superposed on the outer quadrupoles. Then the spherical aberration is corrected by the two octopoles placed at the centers of multiplets and in the last stage the fourfold axial astigmatism is compensated by the octopole located at the midplane zM. The elimination of the field aberrations also allows for extended electron sources in electron projection lithography resulting in low current densities and small Coulomb interactions between the electrons.
ment. If both projects have been successfully completed, their different novel components will be combined yielding the most versatile ultraresolution analytical electron microscope. The SATEM is primarily aimed for elucidating the three-dimensional structure of solid objects at a resolution of about 1 A˚ . This instrument is equipped with a Schottky emitter and a monochromator yielding a quasi-monochromatic source with an energy spread smaller than 0.2 eV. In addition a hexapole corrector and a corrected 901 omega filter are incorporated. First experiments have demonstrated that the monochromator does not affect the geometrical properties of the source. The monochromator reduces the current by about 65% for an energy window of 0.2 eV. The selection slit is centered at the maximum of the energy distribution. To largely avoid mechanical instabilities a new 300 mm column and a highly stable support frame have been developed [11]. They will also be employed for the SESAM . This instrument is equipped with the same source as the SATEM and can operate in both the STEM and the TEM mode at 200 kV. Instead of the omega filter the SESAM is equipped with the MANDOLINE filter enabling highly resolved ELNES investigations [12]. This filter has an extremely high transmissivity and provides a dispersion of 6.2 mm/eV at 200 kV [13]. Hence the MANDOLINE allows for energy-filtered imaging of large fields of view and large scattering angles (e.g. CBED) with excellent isochromaticity. The experimentally achieved dispersion is in very good agreement with the theoretical values [14].
4. SATEM and SESAM projects
5. Outline of future aberration-free electron microscopes
The ultimate goal in the development of highperformance analytical transmission electron microscopes is an instrument with a spatial resolution limit of about 0.5 A˚ and an energy resolution below 0.2 eV at voltages between 100 kV and 300 kV. Moreover, the microscope should operate in the fixed beam TEM and the STEM mode. The SATEM and the SESAM projects are the first steps on the route toward this universal instru-
The SATEM is designed for achieving a resolution limit of about 1 A˚. In order to further reduce this limit to 0.5 A˚, it is a ‘‘conditio sine qua non’’ that the parasitic incoherent aberrations resulting from mechanical and electromagnetic instabilities can be sufficiently reduced. The realization of this ambitious task poses by far the most difficult problem. By combining components of the
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SATEM and the SESAM, an extremely versatile instrument can be built. It consists of (a) a field emission gun with a monochromator, (b) a condenser system with an incorporated hexapole corrector enabling genuine Koehler illumination for the TEM mode and a subA˚ngstroem spot size for the STEM mode, (c) a hexapole corrector behind the objective lens yielding aplanatic imaging for the TEM mode, (d) the MANDOLINE filter and (e) a corrected quadrupole projector system which images with variable magnification either the energy loss spectrum or the filtered intermediate image onto the CCD array. The high-resolution TEM mode is especially useful for rapidly finding specific object details and obtaining energy-filtered images, while the STEM mode is best suited for recording highly resolved energy loss spectra of small object details such as single atom columns. The need for chromatically corrected aplanats has recently been revived in the context of high-resolution in situ electron microscopy [15]. The realization of this system is the most demanding task of the Transmission Electron Aberration-corrected Microscope (TEAM) project.
successful realization of aberration-corrected electron microscopes is the suppression of mechanical and electromagnetic instabilities and a precise computer-assisted alignment procedure within a short period of time. With the advancement in technology, the performance of the new instruments will increase to such an extent that the ultimate resolution limit of 0.5 A˚ will be realized. We can expect that future electron-optical systems will reach a degree of perfection comparable to that obtained in light optics.
Acknowledgements I want to thank Dr. Heiko Mu¨ller for placing Fig. 1 at my disposal and Dr. Rainer Spehr for valuable comments.
References [1] [2] [3] [4] [5] [6]
6. Conclusion In the last decade considerable progress has been made in electron optics. Thanks to the development of efficient procedures for calculating and designing sophisticated electron-optical systems, it has become possible to realize novel components such as monochromators, aberration correctors, and imaging energy filters. The incorporation of these elements will make quantitative analytical electron microscopy with sub-A˚ngstroem spatial and sub-eV energy resolution possible in the very near future. The basis for a
[7] [8] [9] [10] [11]
[12] [13] [14] [15]
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