Radiant energy – With charged particle beam deflection or focussing – Magnetic lens
Reexamination Certificate
2000-04-24
2003-11-11
Lee, John R. (Department: 2881)
Radiant energy
With charged particle beam deflection or focussing
Magnetic lens
C250S311000, C250S3960ML, C250S398000
Reexamination Certificate
active
06646267
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Technical Field of the Invention
The invention relates to a method for eliminating first, second and third-order axial image deformations during correction of the third-order spherical aberration in electron optical systems with hexapoles.
2. Description of the Prior Art
It is generally known that the resolution of circular lenses in electron optical systems is limited by the third-order aberration (spherical aberration). In numerous fields of application, such as electron microscopy, the capacity of an electron optical system is defined by the resolution so that to improve such devices considerable efforts are made to eliminate the third order spherical aberration. One of the most promising solutions is the use of corrective means comprising noncircular lens systems, as for example described in EP 0451370, where a corrective means constituted by circular lenses and hexapoles, in the direction of the optical path, is disposed behind the lens system to be corrected, which is usually the objective lens of the electron microscope. In the case of the above mentioned corrective means, as with all other electron optical systems with correction of the third-order spherical aberration, in practice, adjustment errors occur that among other things impair the resolution, such errors relating primarily to first, second and third-order axial image deformations, the elimination of which is necessary in order to achieve the optimal resolution. The axial image deformations that occur as adjustment errors during correction of the third-order spherical aberration are as follows:
C
1
defocusing
A
1
first-order axial astigmatism with twofold symmetry
B
2
second-order axial coma
A
2
second-order astigmatism with threefold symmetry
A
3
third-order astigmatism with fourfold symmetry
S
3
third-order star aberration with twofold symmetry
It holds for adjustment errors, which are also termed parasitic errors, that their value is of a small magnitude, and in case of ideal adjustment vanishes. The previous methods are characterised therein that the adjustment errors are eliminated successively for every mapping element of the electron optical system and sequentially in the direction of the beam propagation.
SUMMARY OF THE INVENTION
On the basis of this state-of-the-art, the invention has the object of creating an adjustment method with the aid of which the elimination of first, second and third-order axial image deformations can be effected.
As a solution, the following correction methods are explained, which put forward a theory by means of which individual second and third-order axial image deformations can be corrected; on the other hand, an adjustment method is specified for eliminating all first as well as second and third-order axial image deformations during correction to eliminate the third-order spherical aberration. The values {overscore (&agr;)} and {overscore (&ggr;)} denote the respective complex conjugates. Subsequently, the correction of the individual image deformations are explained in greater detail in conjunction with the description of the adjustment method.
The first step as a prerequisite for eliminating the adjustment error is to determine the values of the respective aberration coefficients. A decisive difference in comparison to methods known in the state-of-the-art consists therein that the image deformations are measured behind the total system, as a rule comprising several lenses, exactly in the image plane so that the deformation is captured only in its entirety and mutual superposition. In order to determine the value of the respective image deformation coefficients, images are recorded with beam paths tilted against the optical axis, where the individual images have differences in the angle of inclination and azimuth of the illumination axis in relation to one another. Here the number of images is so great that the system of equations is at least determined. The evaluation is effected in the manner that a diffractogramm is produced, either in an analogue manner through diffraction or through a Fourier transform in mathematical treatments. From the diffraction patterns, the image deformations C
1
, A
1
can be determined according to a known method. We refer to the contribution from F. Zemlin et al., Ultramicroscopy 3 (1978) 49. The further four complex adjustment aberrations and the real spherical aberration can be determined through a system of equations which is derived from the eikomal (see Zemlin aaO). With the five aforementioned image deformations, especially a system of equations, which comprises nine real equations, is to be derived and solved. In this way, the determination of the aberration coefficients to be eliminated is performed.
In order to eliminate the adjustment errors, steps are to be performed in the order described below.
Influencing and eliminating the defocusing and the first-order axial astigmatism with twofold symmetry are trivial; they are performed by changing the focussing (in case C
1
) and through superposition of a quadrupolar field (in case A
1
). After the first-order deformation is eliminated, the second-order deformations are to be corrected next, that is, the axial coma B
2
and the axial astigmatism A
2
with threefold symmetry, because only then a sufficiently exact determination of the third-order image deformation can be performed and thus its correction.
After the value has been determined in the prescribed way, the correction is performed as described below:
Second-order axial coma B
2
:
The elimination can be effected by means of a so-called coma stigmator. To that end, in the corrective system, a pair of hexapoles are superpositioned respectively by a quadrupolar field of the same intensity, whereupon the product from the sign of the hexapole field and that of the associated quadrupolar field are antisymmetrical, that is, are opposed to each other. This condition ensures that no first-order astigmatism is generated. The intensity and orientation of these quadrupolar fields is determined by the measured coma.
In order to implement the quadrupolar fields various options are available. This may be achieved in practice by generating an additional quadrupolar field in the hexapoles of the corrective system.
A different possibility of creating the quadrupolar fields can consist therein of effecting a shifting of the optical axis parallel to the axis of the hexapole.
Second-order axial astigmatism with threefold symmetry A
2
:
Here the correction is achieved through an additional hexapole field whose intensity and direction is likewise defined through the determined aberration coefficient. Implementation is attained through generation of such a hexapole field. A further possibility for generating a field consists in the virtual twisting of the hexapoles of the correction system against one another, whereupon a field with threefold symmetry is also generated. Implementation is achieved through the arrangement of a magnetic circular lens between the two hexapoles or the use of already existing ones. The advantage of this method consists therein that one saves the otherwise necessary path of use of a twelve-pole lens to generate a hexapole field of option size and alignment.
After first and second-order image deformations are now corrected, the values of the third-order image deformations can be determined in the way described above, namely the axial astigmatism A
3
with fourfold symmetry and the star aberration S
3
with twofold symmetry. The correction of these axial image deformations follows a common and general principle proposed for the first time by the invention. In order to correct the axial image deformation, the same extra-axial image deformation of higher order is used and by shifting or tilting the optical axis made effective until a compensation is achieved. Equality of the image deformation within the meaning of the invention means the same behaviour, that is, the same dependence on complex aperture angle &agr; and its complex conjugate {overscore (&agr;)}. Thereby the power of the image
Haider Maximilian
Uhlemann Stephan
Hashmi Zia R.
Lee John R.
Schindler Edwin D.
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