Abstract:
Aberration-corrected charged-particle optical apparatus improving the resolution of charged-particle optical systems by eliminating or minimizing optical aberrations. The apparatus comprises a source of charged particles and a plurality of charged-particle lenses including non-round lenses, energized in such manner so as to correct axial aberrations of orders up to and including fifth order. The non-round lenses comprise quadrupoles and octupoles disposed in such manner that fifth order combination aberrations are precisely controlled in addition to third order aberrations. The resultant apparatus very significantly improves on resolution attainable with non-aberration corrected charged-particle round lenses. It also improves on resolution attainable with correctors of third order aberrations only.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The invention relates to charged-particle optical systems such as electron and ion probe-forming systems, electron and ion microscopes, and electron and ion microanalyzers. It relates particularly to high resolution scanning electron microscopes, high resolution scanning transmission electron microscopes, fixed-beam transmission electron microscopes, and to high resolution scanning ion microscopes, scanning ion microanalyzers, and further to focused ion beam systems used for sample erosion. It also relates to charged-particle optical systems used for lithography and mask writing.  
           [0003]    2. Description of Prior Art  
           [0004]    Round electromagnetic and electrostatic lenses normally used in electron and ion beam optical systems, hereafter referred to as charged-particle optical systems, suffer from unavoidable aberrations including spherical aberration and chromatic aberration. The aberrations can be overcome by aberration correctors comprising non-round lenses such as quadrupole and octupole lenses, as for instance described in an article entitled “Towards sub-Å electron beams” by O. L. Krivanek, N. Dellby and A. R. Lupini published in the journal Ultramicroscopy (volume 78, page 1-11), hereby incorporated by way of reference, and in an article entitled “Progress in aberration-corrected scanning transmission electron microscopy” by N. Dellby et al. published in the Journal of Electron Microscopy (volume 50, page 177-185), hereby also incorporated by way of reference. They can also be corrected by aberration correctors comprising sextupole lenses, as for instance described by Crewe in U.S. Pat. No. 4,414,474 and Rose in U.S. Pat. No. 5,084,622, hereby incorporated by way of reference.  
           [0005]    Aberration correctors comprising quadrupole and octupole lenses have several important advantages compared to correctors comprising sextupole lenses. The primary effect of an octupole lens is to act directly on spherical aberration, which is a dominant aberration that unavoidably affects all round-lens charged-particle systems. By contrast, sextupole lenses, which are responsible for correcting spherical aberration in sextupole correctors, have the primary effect of producing strong three-fold astigmatism, a second order aberration. Correction of spherical aberration by a sextupole lens arises only as a by-product of the primary action, in a sextupole of extended length. As a result, at least two sextupoles must be used in a sextupole corrector, with the second sextupole appropriately energized so that it nulls three-fold astigmatism introduced by the first sextupole. Small misalignment between the two sextupoles, for instance introduced by a small variation of the strength of an alignment dipole, or a mechanical movement of the supporting column, results in the cancellation of the strong three-fold astigmatism not being complete. It typically leads to a large parasitic first order astigmatism, which adversely affects the attainable resolution. As a result, correctors utilizing sextupole lenses need to maintain higher stability and precision than quadrupole-octupole correctors in order to reach equivalent resolution.  
           [0006]    Another important advantage of quadrupole-octupole corrector systems is that their quadrupoles may be constructed in such a way that they have negative chromatic aberration. As a result, a quadrupole-octupole corrector may be made to correct chromatic aberration in addition to geometric aberrations such as third order spherical aberration. Chromatic and spherical aberrations are typically the two most important aberrations of an uncorrected charged-particle optical system, and simultaneous correction of both the aberrations leads to considerably improved performance compared to optical systems that only correct one or the other aberration. By comparison, a sextupole corrector cannot correct chromatic aberrations unless it also incorporates extra quadrupole lenses, which do not lend themselves naturally to incorporation in a sextupole corrector.  
           [0007]    Yet another major advantage of a quadrupole-octupole corrector system is that it does not need to use any round lenses within the corrector part of the system, since this part produces the required first order trajectories purely with quadrupole lenses. In contrast, sextupole correctors usually employ round lenses within the corrector. Magnetic quadrupole lenses typically consume less than 1% of the power required by round lenses of comparable focal length, and are therefore very efficient. As a result, large thermal loads which require water cooling, and which can easily lead to long-term drifts, are avoided by the use of quadrupole lenses rather than round lenses. This simplification leads to increased long-term stability, and simplified operation and maintenance of the charged-particle optical apparatus. A further advantage of quadrupole lenses is that unlike round lenses, they produce no image rotation, and this can lead to further simplifications in systems which use quadrupole lenses rather than round lenses disposed between strong multipole lenses such as sextupoles or octupoles.  
           [0008]    On the other hand, a well-known advantage of sextupole correctors is that sextupoles correct spherical aberration uniformly in all directions that are transverse to the direction of travel of the charged-particle beam. This property makes possible sextupole correctors in which the action of the sextupoles is projected into the coma-free plane of the principal lens of the charged-particle apparatus, typically known as the objective lens. Such systems have minimized fifth order axial aberrations and also small field aberrations. They are not, however, completely free of fifth order aberrations, since six-fold astigmatism of fifth order typically remains uncorrected. An example of such a corrector system was described in an article entitled “On the fifth order aberration in a sextupole corrected probe forming system” by Z. Shao, published in the Review of Scientific Instruments (volume 59, page 2429-2437), hereby incorporated by way of reference.  
           [0009]    Octupoles affect spherical aberration differently in different transverse directions. As a consequence, a quadrupole-octupole corrector typically comprises three or more octupole lenses, and the effective plane in which undesirable third order deviations of a ray leading through an optical system are corrected, hereafter called the correction plane, typically depends on the transverse direction of the ray. In such a system, it is typically impossible to project all the planes in which aberration correction takes place into a coma-free plane of the objective lens. Not projecting the correction planes into the coma-free plane of the objective lens leads to combination aberrations such as fifth order spherical aberration, two-fold astigmatism of fifth order and four-fold astigmatism of fifth order. These aberrations limit the improvement in the resolution performance of a typical charged-particle optical apparatus originally suffering from spherical aberration of third order, but corrected by a quadrupole-octupole aberration corrector, to two to three times better than the uncorrected performance, as described for instance in N. Dellby et al. in an article in the Journal of Electron Microscopy (reference cited above).  
           [0010]    Most users of charged-particle optical systems would find significant advantage in an apparatus and a method allowing for complete cancellation of all fifth order aberrations with a quadrupole-octupole corrector system. Such an apparatus and method would improve the resolution by more than a factor of five compared to an uncorrected optical system, and more than a factor of two compared to an optical system utilizing an aberration corrector suffering from fifth order combination aberrations. The users would find significant advantage in the resultant improved resolution charged particle images that such an apparatus and method would provide, thereby enabling them to explore the structure of matter with hitherto unattainable resolution and sensitivity. They would also find advantage in the smaller diameter and more intense charged particle probes that such an apparatus and method would allow, thereby enabling users to explore matter at a higher resolution than hitherto possible, and to nano-machine matter with hitherto unattainable precision. They would further find a significant advantage in the greater immunity of a quadrupole-octupole corrector to misalignments and other instabilities than is typical with a sextupole-type corrector, the decreased power requirements of a quadrupole-octupole corrector compared to a sextupole corrector incorporating round lenses, and the absence of image rotation in a quadrupole-octupole corrector. Moreover, they would find a great advantage in the fact that a quadrupole-octupole corrector can also be made to correct chromatic aberration, thereby leading to a significant further improvement in the resolution of charged-particle images and to smaller charged-particle probes than can be attained with correctors correcting only geometric aberrations.  
         OBJECTS AND ADVANTAGES  
         [0011]    Accordingly, several of the objects and advantages of the present invention are: to provide a method and an apparatus for a quadrupole-octupole corrector charged-particle optical system that is able to correct geometric aberrations up to fifth order, and to provide an apparatus and a method for correcting geometric aberrations up to fifth order while at the same time correcting chromatic aberration or aberrations. Another object and advantage of the present invention is to provide these aberration-correcting capabilities in an apparatus relatively insensitive to misalignments, instrumental drifts and other instabilities, and to provide them in an apparatus not using any high-power round lenses within the corrector part of the total apparatus, or not using any round lenses at all.  
           [0012]    Readers will find further objects and advantages of the invention from a consideration of the ensuing description and of the accompanying figures. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]    [0013]FIGS. 1 a  and  1   b  are schematic views of a quadrupole-octupole aberration corrector of the present invention comprising a plurality of quadrupole lenses and a plurality of octupole lenses. FIG. 1 a  shows axial trajectories of charged particles through the corrector apparatus. FIG. 1 b  shows field trajectories through the apparatus.  
         [0014]    [0014]FIG. 2 is a schematic view of a charged-particle probe-forming apparatus of the present invention comprising a source of charged particles, a beam-defining aperture, a plurality of condenser lenses, a quadrupole-octupole aberration corrector, a plurality of coupling lenses, a scan/align coil assembly, a probe-forming lens comprising a pre-field lens and a post-field lens, a sample, a plurality of detector coupling lenses and a plurality of detectors.  
         [0015]    [0015]FIG. 3 is a schematic view of a charged-particle probe-forming apparatus of the present invention comprising a source of charged particles, a beam-defining aperture, a plurality of condenser lenses, a quadrupole-octupole aberration corrector, a plurality of coupling lenses, a scan/align coil assembly, a probe-forming lens, a sample, and a plurality of detectors.  
         [0016]    [0016]FIG. 4 is a schematic view of a charged-particle imaging apparatus of the present invention comprising a source of charged particles, a beam-defining aperture, a plurality of condenser lenses, an objective lens comprising a pre-field lens and a post-field lens, a sample, a plurality of coupling lenses, a quadrupole-octupole aberration corrector, a plurality of imaging lenses and an image detecting means. 
     
    
     DRAWING REFERENCE NUMERALS  
       [0017]    [0017]                                                       10   optic axis           11   source of charged particles           12   corrector mid-plane           20   axial ray           21   axial ray in x-z plane           22   axial ray in y-z plane           23   field ray           24   field ray in x-z plane           25   field ray in y-z plane           26   double field crossover           27   double field crossover           28   double field crossover           29   double field crossover           30   beam-defining aperture           31   condenser lens           32   condenser lens           33   condenser lens           34   coupling lens           35   coupling lens           36   objective lens prefield           37   objective lens postfield           38   projector lens           39   projector lens           40   scan/align coil assembly           41   transmission sample           42   bulk sample           43   field crossover           44   field crossover           45   charged-particle detector           46   charged-particle detector           47   charged-particle detector           48   charged-particle detector           49   charged particles           50   aberration corrector           51   quadrupole lens           52   quadrupole lens           53   quadrupole lens           55   quadrupole lens           56   quadrupole lens           57   quadrupole lens           61   combined quadrupole-octupole lens           62   combined quadrupole-octupole lens           63   octupole lens           64   octupole lens           68   objective lens           70   coupling lens           71   coupling lens           72   projector lens           73   projector lens           75   two-dimensional image-detecting means                        
       DESCRIPTION  
       [0018]    Referring now to FIGS. 1 a  and  1   b , a charged-particle aberration corrector of the present invention is illustrated schematically. Such a corrector would normally be incorporated in the optical column of a probe-forming charged-particle optical apparatus, or in the column of an image-forming charged-particle optical apparatus utilizing a broad beam of charged particles.  
         [0019]    A beam of charged particles enters the aberration corrector in a direction generally along optic axis  10 , which is customarily taken to point in the positive z direction. The beam enters an assembly of quadrupole and octupole lenses comprising quadrupole lenses  51 ,  52 ,  53 ,  55 ,  56  and  57 , combined quadrupole-octupole lenses  61  and  62 , and octupole lens  63  and or octupole lens  64 . The assembly acts on the first, third and fifth order focusing properties in an ideal system, and also the second, fourth, and higher order focusing properties in a real system in which physical misalignments and material and other inhomogeneities are present.  
         [0020]    Although a detailed understanding of the functioning of such an assembly of lenses requires extensive computer modeling, a sound conceptual comprehension may be gained by tracing axial and field charged-particle trajectories through the optical system, as is normal practice in the art of charged-particle optics. FIG. 1 a  depicts schematically axial ray, also known as axial trajectory,  20 . The ray is separated into axial ray  21  in the x-z plane and axial ray  22  in the y-z plane, i.e. in two different transverse directions, by the action of the quadrupole lenses of the correcting apparatus, and is again recombined into substantially identical axial rays in the last quadrupole of the aberration corrector. FIG. 1 b  depicts schematically field ray  23 , which is separated into field ray  24  in the x-z plane and field ray  25  in the y-z plane inside the corrector. Any other charged-particle trajectory through the charged-particle optical system can be modeled to first order as a linear combination of the four trajectories  21 ,  22 ,  24  and  25 .  
         [0021]    As will be shown subsequently, axial rays  21  and  22  cross the optic axis at or near the plane of the sample, while field rays  24  and  25  cross the optic axis at or near the coma-free plane of the objective lens and traverse the sample plane away from the optic axis. Axial rays therefore depict how rays traversing the sample near the optic axis travel through the apparatus, while field rays depict how the correction planes are imaged onto each other.  
         [0022]    Rays traversing the sample at a non-zero angle to the optic axis are affected by third and higher order axial aberrations. It is one of the objects of the present invention to correct these aberrations by the application of octupole fields of adjustable strength. Accordingly, axial rays  21  and  22  are arranged so as to traverse combined quadrupole-octupoles  61  and  62  some distance away from the optic axis, and likewise to traverse octupole  63  some distance from the optic axis. While traversing quadrupole-octupole  61 , axial ray  22  is much further from the optic axis than axial ray  21 . While traversing quadrupole-octupole  62 , axial ray  21  is much further from the optic axis than axial ray  22 . While traversing octupole  63 , axial rays  21  and  22  are both approximately the same distance from the optic axis. This set of conditions allows three independent 3 rd  order aberrations to be adjusted simply by changing the strength of the octupole fields in elements  61 ,  62  and  63 . The adjustable aberrations are spherical aberration C 3,0 , two-fold astigmatism of spherical aberration C 3,2 , and four-fold astigmatism of spherical aberration C 3,4 . The apparatus is thus able to set the spherical aberration C 3,0  to any desired value, including the value which optimally opposes spherical aberration introduced by other lenses in a complete charged-particle optical apparatus. Moreover, even though third order aberrations C 3,2  and C 3,4  become relatively strong inside the corrector, they can be readily adjusted by proper selection of the excitation of the corrector&#39;s octupoles so that they become zero at the exit of the corrector.  
         [0023]    In order to avoid producing 5 th  order combination aberrations as a by-product of correcting third order spherical aberration, the x-y correction planes in which third order aberrations are introduced by principal third order focusing elements must be successively imaged onto each other. This is achieved as follows: double field crossover  26  is imaged into double field crossover  27  in the center of quadrupole-octupole element  61 , which is imaged into double field crossover  28  in the center of quadrupole-octupole element  62 , again imaged into double field crossover  29  in the center of octupole  63 , and finally, as will be shown subsequently, imaged into or near the coma-free plane of the objective lens of the complete optical apparatus.  
         [0024]    Double crossovers  27  and  28  differ from double crossovers  26  and  29  in that in the former crossovers, field rays in the x-z and y-z planes have unequal angles to optic axis  10 , whereas in the latter crossovers, field rays in the x-z and y-z planes have the same or similar angles to the optic axis. This means that the magnification with which preceding crossovers are imaged into crossovers  27  and  28  is different in different transverse directions, whereas the magnification at crossovers  26  and  29  is substantially the same for all transverse directions. As a result, axial rays traverse the third order elements  61  and  62  at distances from the optic axis that are different in different transverse directions, and third order element  63  (and or  64 ) at distances that are substantially the same for different transverse directions, as has already been noted. Fulfilling this condition allows a complete correction of third order aberrations in a charged-particle apparatus. At the same time, the correcting planes are precisely imaged onto each other. Fulfilling this condition allows higher order combination axial aberrations such as fifth order aberrations to be avoided. The two conditions have not previously been simultaneously fulfilled in a charged-particle aberration-corrected optical apparatus utilizing quadrupole and octupole lenses.  
         [0025]    Readers skilled in the art of charged-particle optics will note other advantageous features of the present invention. As depicted in FIGS. 1 a  and  1   b , the optical elements are arranged in three groups, the first group comprising quadrupoles  51 ,  52 , and  53  and combined quadrupole-octupole  61 , the second group comprising quadrupoles  55 ,  56  and  57  and combined quadrupole-octupole  62 , and the third group comprising octupole  63  and or  64 . The first group causes axial electron trajectories to be extended in one transverse direction and serves principally to correct third and fifth order aberrations in a corresponding transverse plane, the second group causes axial trajectories to be extended in a second transverse direction and serves principally to correct third and fifth order aberrations in a corresponding transverse plane. The third group acts on a round or a nearly round beam, and principally serves to correct four-fold astigmatisms of 3 rd  and 5 th  order. The readers will also note that the second transverse plane is normally perpendicular to the first transverse plane, but that this is not an essential requirement for aberration correction, and that angles other than 90 degrees between the first and second transverse planes, e.g. 60 degrees, may be employed. Further, the readers will note that the optical elements of the apparatus, with the exception of octupole  63 , are arranged symmetrically with respect to the mid-plane  12 , and further that mirror-related quadrupoles are excited antisymmetrically, that is for each quadrupole which is diverging in the x-z plane on one side of mirror plane  12 , there is a corresponding quadrupole on the other side of mirror plane  12  that is converging in the x-z plane. Such a symmetry is desirable in that it allows several aberrations to be nulled by symmetry, and also because it simplifies the set-up of the apparatus. However, readers skilled in the art will also realize that in a practical apparatus, such symmetry is typically not attained precisely, and deviations from it serve to counter imperfections in machining and imprecision in the optical alignment of the apparatus. They will also note that as depicted in FIGS. 1 a  and  1   b , the above-described first and second group of optical elements each comprises 3 quadrupole lenses and one combined quadrupole-octupole lens, and that further quadrupole and octupole lenses may be added to each group without significantly altering the nature of the invention. Moreover, they will also appreciate that octupole  63  located at field crossover  29  may be replaced by octupole  64  located at field crossover  26 , or both octupoles  63  and  64  may be utilized simultaneously.  
         [0026]    [0026]FIG. 2 illustrates schematically how the aberration corrector of the invention may be incorporated into a charged-particle optical column of a probe forming system using round lenses and transmission samples. A source of charged particles  11  emits a beam of charged particles generally along the direction of optic axis  10 . The beam is defined in angle by a beam-defining aperture  30 , and conditioned in its angular range, source magnification and apparent source height by condenser lenses  31 ,  32  and  33 . The beam then enters an aberration corrector  50  whose internal construction and ray paths were illustrated schematically in FIGS. 1 a  and  1   b . Upon exiting the corrector, the beam traverses coupling lenses  34  and  35 , and further a scan/align coil assembly  40 . It then enters an objective lens shown schematically as consisting of probe-forming objective lens prefield  36  and postfield  37 , with transmission sample  41  situated within the lens. The beam then traverses coupling lenses  38  and  39  and is incident upon detectors  45  and  46 . Suitable detectors well known in the art comprise bright field and dark field detectors, and also 2-dimensional TV or CCD cameras, which capture the angular distribution of the charged particles.  
         [0027]    Axial ray  20  leaves source  11  near optic axis  10 , traverses aberration-correcting apparatus  50  as illustrated in FIG. 1 a , and arrives at sample  41  on or near axis  10 , due to the combined action of coupling lenses  34  and  35  and objective lens prefield  36 . Field ray  23  leaves source  11  some distance from axis  10 , traverses aberration-correcting apparatus  50  as illustrated in FIG. 1 b , and subsequently crosses optic axis  10  at field crossover  43 . By adjusting the strength of coupling lenses  34  and  35  appropriately, field crossover  43  may be made to coincide with the so-called coma-free plane of the objective lens prefield  36 . The coma-free plane can be viewed as the effective plane in which undesirable third order aberrations of the objective lens prefield  36  are introduced. Since field ray  23  crosses axis  10  in this plane, principal third order focusing elements, namely octupoles  61 ,  62  and  63  depicted in FIG. 1 are imaged onto the coma-free plane. This is the condition that must be satisfied in order to null 5 th  order combination aberrations, which would otherwise arise due to different third order aberration-causing elements not being precisely imaged onto each other. When the octupoles are not imaged onto the coma-free plane, the coefficient of fifth order combination aberration is given by:  
           C   5comb =3 C   3   2   L/f   2   [1] 
         [0028]    where C 3  is the coefficient of third order aberration of the objective lens prefield which is being nulled by the action of the aberration corrector, f the focal length of the objective lens prefield, and L the distance between the plane into which an image of the aberration-correcting elements is imaged and the coma-free plane of the objective lens prefield.  
         [0029]    In a quadrupole-octupole aberration-correcting apparatus not optimized for 5 th  order aberrations, the distance L may vary for different transverse directions, and in this way additional aberrations such as C 5,2  and C 5,4  may be excited. However, when L is zero or the same in all transverse directions simultaneously, these additional aberrations will not be introduced. Making L small but not zero allows C 5comb  to be adjusted as needed, for instance to compensate for the small C 5  aberration that is typically contributed by individual round and quadrupole lenses for charged particles, or to set the total 5 th  order aberration of the apparatus C 5total  total to a value that optimally opposes the next uncorrected aberration coefficient, typically 7 th  order spherical aberration C 7 .  
         [0030]    The value of L that produces the strength of the 5 th  order combination aberration that properly nulls the intrinsic C 5int  of the optical apparatus is given by:  
           L=−C   5int   f   2 /(3 C   3   2 )  [2] 
         [0031]    where negative values of L mean that the aberration-correcting elements are imaged into a plane situated downstream from the coma-free point of the objective lens prefield.  
         [0032]    As an example of the size of L required to null C 5int , assume that the aberration coefficient arising from the uncorrected intrinsic 5 th  order aberrations due to the combined action of all the individual lenses of the apparatus is equal to the focal length of the objective lens f, and that the 3 rd  order aberration coefficient due to the combined action of all the lenses of the apparatus C 3  is also equal to f. Inserting these values into expressions [1] and [2] above shows that setting L to −f/3 results in a value of 5 th  order combination aberration C5comb that precisely cancels the intrinsic 5 th  order aberration C 5int  of the optical apparatus of the invention. Since focal lengths of objective lenses used in charged-particle optics are typically equal to a few mm, whereas the distance between lenses in a charged-particle optical systems tends to be of the order of 100 mm, the example makes it clear that a relatively small adjustment away from the precise imaging of the correcting planes of the corrector onto the coma-free plane of the objective lens readily achieves the desired 5 th  order correction. A further small adjustment of the imaging of the octupoles in the same direction may additionally be used to produce a small negative C 5total , of such magnitude as to optimally oppose uncorrected 7 th  order axial aberration C 7  of the total apparatus.  
         [0033]    It is worth noting that because quadrupole-octupole correctors do not introduce any six-fold astigmatism of 5 th  order (C 5,6 ), the optical system of the present invention may be made free of all axial aberrations up to and including all 5 th  order axial aberrations, or adjusted so that its first, third and fifth order aberrations optimally oppose uncorrected seventh order aberrations. This is not possible with present-day sextupole correctors, which introduce non-negligible six-fold astigmatism of 5 th  order (C 5,6 )  
         [0034]    The first uncorrected geometric aberration of the above-described system is spherical aberration of 7 th  order C 7 . Detailed computer simulations show that in a practical aberration-correcting apparatus, this aberration will typically amount to about 1 cm. The simulations further show that in the case of a charged-particle aberration-correcting optical apparatus designed to focus an electron beam into a small probe, the aberration-limited size of a C 7 -limited probe will be about 0.2 Å for 200 kV electrons. This is about a factor of 4 smaller than has hitherto been achieved with electron-optical systems of any kind. In the highly refined art of electron optics, 3 Å probe size was reached in about 1970, and the present smallest probe size record of 0.8 Å was only reached in 2001. This shows that the present invention promises to advance this field by a factor equal to that produced by the combined developments of the previous 30 years.  
         [0035]    Attainment of the 0.2 Å probe size will only be possible provided that either the energy spread of the electron beam is smaller than about 0.2 eV, or that chromatic aberration is also corrected in addition to the geometric aberrations discussed herein. Readers skilled in the art will appreciate that in a quadrupole-octupole aberration-correcting apparatus, axial chromatic aberration of the first order may be corrected by the use of a combination of electrostatic and electromagnetic quadrupoles, or by combined electrostatic-electromagnetic quadrupoles, whose excitations are adjusted to produce negative chromatic aberration, so as to compensate for the positive chromatic aberration intrinsic to uncorrected lenses of the apparatus. Only two combined quadrupoles are needed, and they may be inserted at any location in a charged-particle optical apparatus where the rays are at substantially different distances in different transverse directions from optic axis  10 . In the apparatus of the present invention, this occurs at or near optical elements  61  and  62 . Using combined electrostatic-electromagnetic quadrupoles plus octupoles in these locations therefore allows first order chromatic aberration to be corrected at the same time as all geometric aberrations up to and including 5 th  order. The chromatic aberration-correcting elements may also be introduced elsewhere in the apparatus, either within or outside the aberration corrector  50 .  
         [0036]    [0036]FIG. 3 illustrates schematically how the aberration-correcting apparatus of the invention may be incorporated into a charged-particle optical column of a probe forming system using round lenses and bulk samples. A charged particle source  11  emits a beam of charged particles generally along the direction of optic axis  10 . The beam is defined in angle by a beam-defining aperture  30 , and conditioned in its angular range, source magnification and apparent source height by condensers  31 ,  32  and  33 . The beam then enters an aberration-correcting apparatus  50  whose internal construction was illustrated schematically in FIGS. 1 a  and  1   b . Upon exiting the correcting apparatus the beam traverses coupling lenses  34  and  35 , and further a scan/align coil assembly  40 . It then enters an objective lens  68 , and is incident on bulk sample  42 . Secondary or back-scattered charged particles  49  emanating from the area of sample  42  illuminated by the incident beam are detected by detectors  47  and  48 . Suitable detectors comprise secondary charged-particle detectors and backscattered charged-particle detectors.  
         [0037]    The entire apparatus is schematically identical, up to the plane of the sample, to a probe-forming apparatus using transmission samples as illustrated in FIG. 2. Field trajectory  23  is made to cross the optic axis  10  at a double crossover  43  located at or near the coma-free plane of the objective lens  68 , and in this way aberrations of 5 th  order are either minimized or altogether eliminated. Similar to a probe-forming apparatus utilizing transmission samples, a combination of electrostatic and electromagnetic quadrupoles or combined electrostatic-electromagnetic quadrupoles may be introduced within the aberration corrector  50  or elsewhere in the apparatus, and in this way first order chromatic aberration may be corrected in addition to purely geometric aberrations.  
         [0038]    [0038]FIG. 4 illustrates schematically how the aberration-correcting apparatus of the invention may be incorporated into a charged-particle optical column of a fixed-beam imaging system using round lenses and transmission samples. Such a system images a transmission sample  41  onto a two-dimensional detector  75 . Consequently, it is the performance of the post-sample imaging optics that is important, and an aberration corrector  50  is situated within this part of the optical column. A charged-particle source  11  emits a beam of charged particles generally along the direction of optic axis  10 . The beam is defined in angle by a beam-defining aperture  30 , conditioned by condensers  31 ,  32  and  33 , and it is then projected by objective lens prefield  36  onto transmission sample  41 . The beam transmitted though the sample is imaged by a broad-beam objective lens postfield  37  and coupling lenses  70  and  71  into aberration corrector  50 , and then imaged by projector lenses  72  and  73  onto two-dimensional image-detecting means  75 .  
         [0039]    In order to minimize or eliminate fifth order geometric aberrations, the field trajectories are so managed that a field crossover  44  occurring at or near the coma-free plane of postfield  37  is imaged into field crossovers disposed within the aberration corrector  50  as illustrated in FIG. 1 b . The actual x-y plane that is imaged into the octupoles of the corrector  50  is typically chosen to lie near a distance L=C 5 f 2 /(3 C 3   2 ) in front of the coma-free point of objective lens post-field  37 , and in this way the total fifth order aberration coefficient of the optical system is either nulled or adjusted to optimally oppose uncorrected higher order aberrations.  
         [0040]    Imaging all the principal third order focusing elements of the optical column onto each other also provides for minimized field aberrations. In a fixed-beam imaging apparatus in which many sample points are imaged at the same time, this is an important and desirable property. Further, similar to the probe-forming optical systems described above, quadrupoles within the aberration corrector or disposed elsewhere in the apparatus may be made from combined electrostatic and electromagnetic elements, or quadrupoles of both electrostatic and electromagnetic construction may be used within the total apparatus, and in this way the first order chromatic aberration of the system corrected in addition to the geometric aberrations.  
         [0041]    Readers skilled in the art will appreciate that performance-enhancing modifications to the aberration-correcting apparatus and method described herein are readily possible, without deviating from the principles and methods outlined here. For example, additional quadrupoles may be utilized in the apparatus giving advantages such as easier set-up and variable first order focusing, and greater flexibility in the available set of trajectories satisfying conditions necessary for aberration correction. Moreover, combined quadrupole-octupole elements  61  and  62  may each be replaced by a separate quadrupole or a group of quadrupoles plus octupole or octupoles, and octupoles  63  or  64  may be replaced by combined quadrupole-octupole elements, without substantially deviating from the principles and methods described above. Additional octupoles may be introduced in the apparatus, and if the centers of the combined action of local octupole groups affecting different third order aberrations are projected near or onto a double field crossover, the functioning of the apparatus will not be significantly altered.  
         [0042]    Moreover, in a practical aberration-correcting apparatus, additional multipoles including dipoles, rotated quadrupoles, sextupoles and other higher order multipoles will typically be disposed within the apparatus, either as stand-alone elements or in combination with other multipoles, thereby facilitating alignment, without significantly affecting the aberration-correction functioning of the apparatus. Furthermore, the mirror symmetry of the aberration corrector  50  may be broken without compromising its ability to correct aberrations, provided again that the arrangement of field crossovers described above is not substantially compromised. Readers skilled in the art will also appreciate that further flexibility may be gained by situating additional round lenses or apertures within the optical systems described here, for instance by increasing the number of coupling lenses disposed between the aberration corrector and the objective lens, without significantly affecting the principles and methods of the apparatus of the invention. They will also appreciate that the optical systems depicted in FIGS. 2 and 4 may be combined into one system comprising aberration correctors of the present invention correcting the aberrations of both a probe-forming and an image-forming part of an optical apparatus.  
         [0043]    Furthermore, readers skilled in the art will also appreciate that the aberration corrector depicted in FIGS. 1 a  and  1   b  may be used by itself as a final probe-forming lens in an apparatus not relying on a round lens or lenses to focus a probe, and that in this case octupole  64  will be employed in preference to octupole  63 , and quadrupole  57  may be altogether omitted without appreciably affecting the aberration-correcting properties of the apparatus of the invention. They will also appreciate that the aberration corrector depicted in FIGS. 1 a  and  1   b  may be used in place of a first imaging lens in an imaging apparatus not relying on a round lens or lenses to produce a first intermediate image. The readers will also appreciate that the aberration corrector depicted schematically in FIGS. 1 a  and  1   b  may be used with a much wider variety of charged-particle lens systems than those shown schematically in FIGS.  2  to  4 . Such systems may comprise lens-optical combinations not including any round lenses, but achieving first order focusing by the use of quadrupole lenses, bending prisms, Wien filters, or charged particle mirrors. In such systems, the locations of the coma-free planes of the principal probe-forming or image-forming optical elements may be different in different transverse planes, and the principal third order focusing elements of the aberration corrector  50  will be projected into these planes.