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Measurement of the aberrations of an electrostatic quadrupole probe forming lens system
33
Nuclear Instruments and Methods in Physics Research B54 (1991) 33-37 North-Holland
Measurement of the aberrations of an electrostatic quadrupole probe forming lens system D.N. Jamieson a, C.G. Ryan b and S.H. Sie b a Microanalytical Research Centre, School of Physics, University b Heavy Ion Analytical
Facility, CSIRO,
Division of Exploration
of Melbourne, ParkviNe, 3052, Australia Geoscience, P.O. Box 136, North Ryde, 2113, Australia
A Russian antisymmetric quadruplet of precision electrostatic quadrupole lenses is used to focus a MeV proton probe for ion beam analysis of geological specimens. The aberrations of the individual lenses have been measured with the grid shadow method and
the lenses have been found to be remarkably free from parasitic sextupole contamination, commonly seen in magnetic quadrupole lenses. The most significant parasitic multipole component in the individual quadrupole lenses is octupole, possibly contributed by an imbalance in the voltages of the pair of high voltage power supplies connected to the positive and negative poles. The experimental shadow patterns of the quadruplet reveal aberration similar in nature to spherical aberration, but of the opposite sign to theory. This is consistent with the aberration being dominated by parasitic octupole components in the individual quadrupole lenses. The grid shadow method also revealed that the present quadruplet, as constructed, was free from parasitic aberration due to rotational misalignments of the individual quadrupoles.
1. Introduction Electrostatic quadrupole lenses offer some advantages over magnetic quadrupole lenses as a probe forming lens system. Electrostatic lenses do not suffer from hysteresis effects, negligible current is drawn from the power supply and the field strengths required for focusing the beam onto the target is independent of ion mass [l]. However, electrostatic lenses suffer from the disadvantage that they must be mounted inside the vacuum system, with consequent problems of alignment. Previous measurements [2-41 on magnetic and electrostatic quadrupole probe forming lens systems have revealed the presence of parasitic sextupole and octupole lens components in the quadrupole lenses. These parasitic components can significantly degrade the resolution of the focused probe. The present work aims to measure the parasitic components of an electrostatic system. The Sydney electrostatic Russian antisymmetric quadruplet [1,5] commenced operation in 1984 and is used principally to perform PIXE analyses on geological materials [6]. The best resolution of the probe achieved to date has been 50 pA of 3 MeV H+ into a 3 urn diameter probe. This used a 35 X 40 km* rectangular object diaphragm and a 0.5 mm diameter aperture diaphragm. However, typical applications use 0.5-10 nA of 3 MeV H+ into lo-20 ttrn diameter probes. The grid shadow method was applied to these lenses to determine the nature of the parasitic aberration. This 0168-583X/91/$03.50
method is described fully in refs. [2,7]; however, briefly, the method involves placing a fine grid in the real image plane of the lens under test, then observation of the shadow cast on a screen downstream. The grid is mounted normal to the beam direction with the grid bars making an angle of between 0.5 o and 2 o to the vertical. The curvature of the grid bar shadows may be quantitatively analyzed to deduce the aberration coefficients, and hence the nature of the aberration, of the lens under test. Ion optical calculations for this work were performed with the program PRAM [2,7] which uses the thin lens model [8] for the electrostatic quadrupole field and the rectangular model [9] for the parasitic octupole components.
2. Experiment 2.1 The quadrupoie singlets The layout of the present system is shown in fig. 1 and the physical parameters used in the analysis are in table 1. The first part of the experiment involved testing each lens individually. To prevent stray accumulations of beam-induced charge from introducing spurious aberration, remaining lenses were grounded and the lens under test was fitted with bleed resistors. The grid shadow patterns from the individual lenses, used to produce both a vertical (positive) and horizontal (negative) line focus on the grid are shown in fig. 2. It can be
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
I. MICROPROBE
TECHNOLOGY
34
D.N. Jamieson et al. / Electrostatic CSIRO-HIAF
electrostatic
quadruplet
-1.5; 0
1 .o
2.0
3.0
z-axis
4.0
5.0
(ml
Fig. 1. The layout of the electrostatic quadrupole quadruplet, showing a calculated raytrace through the system. The upper ray is for the XOZ plane and the lower from the yOr plane. The grid shadow method of aberration measurement used a grid located in the image plane (here at z = 4.7 m) and a scintillating screen at the shadow plane (at z = 5.3 m).
seen at once that the dominant aberration of the lenses is from a parasitic octupole component. The parasitic octupole component produces a cubic curve shaped grid shadow pattern, as does the intrinsic spherical aberration of the lenses. However, the observed curvature is too great to be accounted for by the intrinsic spherical aberration alone, as can be seen by comparing the calculated grid shadow patterns expected for lenses that do not contain any parasitic aberration (the top row of patterns in fig. 2) with the experimental patterns (the lower two rows of fig. 2). Theoretical patterns characteristic of parasitic sextupole components are also shown in fig. 2 (right-hand column) but these are quite different from the experimental patterns showing that any parasitic sextupole component is weak. The magnitude of the parasitic octupole field components in each lens was obtained by fitting cubic curves to the curved grid bar shadows and the results are shown in table 2. Generally the lenses appear to have around 1% parasitic octupole field component, which is exactly the type of parasitic aberration expected if there was an imbalance in the two power supplies used to feed the pair of positive and pair of negative poles [lo]. However, the supplies were balanced to within about 0.1% using a precision digital voltmeter and a voltage divider at a particular reference voltage, but not at the exact voltage actually used to form the grid shadow patterns. It is therefore possible that the balance is a function of the power supply voltage. Further work is required to determine whether this is the case. It is extremely unlikely that the observed parasitic aberration could result from mechanical misalignments, since any random misalignment would certainly also
quadrupole probe forming lens system
introduce parasitic sextupole field components, which would most likely dominate over the effect of the parasitic octupole components. Calculated grid shadow patterns, making use of the aberration coefficients obtained from the experimental patterns for the positive lenses are also shown in fig. 2 (second row). In the cases of lenses 3 and 4 a small displacement of the aperture diaphragm (0.5 mm along the x-axis) was necessary to produce the observed asymmetrical patterns. Remaining differences between these calculated patterns and the experimental patterns are due to small parasitic sextupole and skew sextupole field components. These components were identified by qualitative comparison of the experimental patterns with theoretical patterns for parasitic sextupole components (see fig. 2) and a more complete set of patterns simulated for most possible parasitic components [2]. 2.2. The quadrupole quadruplet The grid shadow patterns of the quadruplet are considerably more complex than those of the singlet systems, since it is difficult to isolate regions of the pattern that are dominated by a single aberration coefficient. A set of experimental patterns obtained for a range of lens excitations that put the Gaussian image plane upstream, on and downstream of the grid are shown in fig. 3. Once again, the patterns show that the dominant aberration is due to parasitic octupole field components, as expected from the analysis of the singlet systems. The curvature of the grid bar shadows is opposite to what would be expected if it were due to the intrinsic spherical aberration alone. Accurate analysis of the patterns depends on being able to see the shadow of a large number of grid bars, hence the largest possible beam divergence is required. However, in the present system this is limited to 0.25 mrad by the permanent 2 mm diameter aperture located just upstream of lens 1. This compares with divergences of up to 0.5 mrad available in the Melbourne system. Hence in order to see a large number of grid bar
Table 1 Physical
parameters
of the Sydney
quadruplet
Quantity
Value
Object to aperture diaphragm Individual lens length Bore diameter Drift length between lenses Image drift length Image to shadow plane Demagnification (0/e) = (G/G) Grid period Beam
4.2 m 0.075 m 0.00635 m 0.005 m 0.152 m 0.57 m - 0.0741 12.7 urn 3MeVH+
D.N. Jamieson et al. / Electrostatic
35
quadrupole probe forming lens system
QUAD. 3
QUAD 3 WITH
QUAD. 4
1% PARASITIC SEXTUPOLE INTRINSIC SPHERICAL ABERRATION
PARASITIC OCTUPOLE
EXPERIMENT (POSITIVE)
a3
=
15’
(NEGATIVE)
10 mm Fig. 2. Calculated and experimental grid shadow patterns for the four singlet systems. Top row: Calculated shadow patterns for lenses free from parasitic aberration which suffer only from intrinsic spherical aberration. Second row: Calculated patterns using the third-order aberration coefficients obtained by analysis of the experimental patterns for positive lenses shown in row three. Bottom row: Experimental patterns for the lenses with a negative excitation. Differences between rows two and three are most likely due to parasitic skew sextupole field components. The grid was mounted in the Gaussian image plane rotated about the beam direction (z-axis) by nominally lo and the true grid angle for each lens was calculated from the period of the grid bar shadows along the y- or x-axes [2]. The right-hand column shows some theoretical shadow patterns for parasitic sextupole components in lens 3. a3 is the phase angle of the parasitic sextupole component.
Table 2 Measured parasitic octupole components of the singlets. Units: image beam displacement, x, in urn; object beam half divergence, 6, in mrad; parasitic octupole component, Q, in I% of the quadrupole field at the quadrupole bore radius. For each lens, the measured total third-order aberration coefficient, (_~/e’)~, deduced from an experimental grid shadow pattern in fig. 2, is related to the strength of the parasitic octupole component by the expression: (x/e3)== (x/e3)+(x/e3fZ)a Lens
1 2 3 4
Theoretical spherical aberration coefficient [8]
Theoretical reduced aberration coefficient [9]
Measured total third-order coefficient, (x/83)T, and parasitic octupole component, B
(x/es)
(x/esn)
(x/e3)=
D
(x/es)=
P
- 3.34 -4.18 - 5.51 - 7.95
161 164 166 162
360 290 100 250
2.2 1.8 0.6 1.5
360 230 190 220
2.2 1.4 1.1 1.4
Positive lens
Negative lens
I. MICROPROBE
TECHNOLOGY
36
D.N. Jamieson et al. / Electrostatic
Z (mm1 EXPERIMENT
quadrupole probe forming lens system
THEORY WITH PARASITIC
THEORY WITH ROTATION
12
10
Fig. 3. Experimental and calculated shadow patterns for the quadrupole quadruplet. Calculations were made as a function of the relative position of the grid and the Gaussian image plane, using the average third-order aberration coefficients obtained by analysis of the patterns for Z = - 15 mm and Z = 12 mm (here Z < 0 means upstream of the Gaussian image plane). The experimental patterns differ from the calculated patterns mainly because the calculated patterns assume a grid aperture was precisely aligned with the optical axis, but this was not achieved in the experiment. Also, the value of Z shown is nominal for the experimental patterns, and the appearence of the shadow pattern is very sensitive to Z between the circle of least confusion (here located at Z = - 7 mm) and the Gaussian image plane (Z = 0 mm), which readily accounts for the difference between theory and experiment for - 7 < Z c 0 mm. The right-hand column shows the effect of quadrupole lens 2 rotational misalignment of 2 mrad (including the effect of the parasitic octupole components).
D. N. Jnmieson et al. / Electrostatic Table 3 Measured
aberration
coefficients
Calculated intrinsic spherical [8]
Measured from shadow patterns in fig. 3
Calculated with parasitic octupole components a
(x/O? (x/@cp2) (u/e%) (Y/$)
-180 35.2 35.2 - 19.2
800 - 2500 - 3050 -25
962 - 2840 - 2840 -31
3. Conclusion
a Calculated [9] with parasitic octupole components of -4.6%, -0.12%, 0.89 and 1.45% in quadrupole lenses 1,2, 3, and 4 respectively. It is not possible to uniquely determine the octupole components from a quadruplet shadow pattern so these are representative of the actual components.
shadows, image
it is necessary plane.
since
This
the shape
To shadow
the
were patterns
then
astigmatism
improve
corresponding
grid
from
the
of the method,
becomes
dominated
coefficients.
accuracy,
deduced
the
the accuracy
of the pattern
by the first-order coefficients
to displace
reduces
from
third-order the
displaced
grid 1.5
12 mm downstream of the Gaussian image plane. The resulting coefficients agreed within a factor of 2, and the averaged coefficients are listed in table 3. Theoretical patterns calculated from these coefficients are in good qualitative agreement with the experimental patterns (see fig. 3) hence the measured coefficients are representative of the aberrations in the system. Rotational misalignment of individual quadrupoles in the quadruplet can cause a serious degradation of the focused probe since the aberration introduced depends on the first power of the divergence. Unlike parasitic sextupole (second-order) and parasitic octupole (thirdorder) it cannot readily be reduced by stopping down the aperture diaphragm. Rotational misalignments in the electrostatic system could be a serious problem because it is generally very difficult to rotate the lenses into alignment from outside the vacuum system, indeed the construction of the present lenses does not allow for relative rotational adjustment of the individual lenses. mm
upstream
Further work is required to identify the precise origin of the parasitic octupole components observed in the lenses. If indeed the parasitic components are due to residual imbalances in the lens power supplies, which could be eliminated, then the system should be able to perform very well, since it does not appear to suffer from the large parasitic sextupole components seen in most magnetic lens systems, or from rotational misalignment aberration, which have a much greater significance for degrading resolution.
aberration
experimental
to the grid
37
However, comparison of the theoretical grid shadow patterns for a 2 mrad misalignment of lens 2 of the present system (the lens most sensitive to rotational misalignment), shown in fig. 3, suggests that the net effect of any rotational misalignment is negligible in the quadruplet.
of the quadruplet
Coefficient
quadnrpole probe forming lens system
References
and
[I] S.H. Sie, C.G. Ryan, D.R. Cousens
and G.F. Suter, Proc. 9th IBA Conf., Kingston, Canada, 1989, Nucl. Instr. and Meth. B45 (1990) 543. [2] D.N. Jamieson and G.J.F. Legge, Nucl. Instr. and Meth. B29 (1987) 544. [3] D.N. Jamieson, G.W. Grime and F. Watt, Nucl. Instr. and Meth. B40/41 (1989) 669. [4] D.N. Jamieson and U.A.S. Tapper, Nucl. Instr. and Meth. B44 (1989) 221. [5] S.H. Sie and C.G. Ryan, Nucl. Instr. and Meth. B15 (1986) 664. [6] S.H. Sie, C.G. Ryan, D.R. Cousens and W.L. Griffin, Nucl. Instr. and Meth. B40/41 (1989) 690. [7] D.N. Jamieson and G.J.F. Legge, Nucl. Instr. and Meth. B30 (1988) 235. ]8] A.D. Dymnikov, T.Ya. Fishkova and S.Ya. Yavor, Nucl. Instr. and Meth. 37 (1965) 268. [9] S.Ya. Yavor, T.Ya. Fishkova, E.V. Shpak and L.A. Baranova, Nucl. Instr. and Meth. 76 (1969) 181. [IO] M.B.H. Breese, D.N. Jamieson and J.A. Cookson, Nucl. Instr. and Meth. B47 (1990) 443.
I. MICROPROBE
TECHNOLOGY
Nuclear Instruments and Methods in Physics Research B54 (1991) 33-37 North-Holland
Measurement of the aberrations of an electrostatic quadrupole probe forming lens system D.N. Jamieson a, C.G. Ryan b and S.H. Sie b a Microanalytical Research Centre, School of Physics, University b Heavy Ion Analytical
Facility, CSIRO,
Division of Exploration
of Melbourne, ParkviNe, 3052, Australia Geoscience, P.O. Box 136, North Ryde, 2113, Australia
A Russian antisymmetric quadruplet of precision electrostatic quadrupole lenses is used to focus a MeV proton probe for ion beam analysis of geological specimens. The aberrations of the individual lenses have been measured with the grid shadow method and
the lenses have been found to be remarkably free from parasitic sextupole contamination, commonly seen in magnetic quadrupole lenses. The most significant parasitic multipole component in the individual quadrupole lenses is octupole, possibly contributed by an imbalance in the voltages of the pair of high voltage power supplies connected to the positive and negative poles. The experimental shadow patterns of the quadruplet reveal aberration similar in nature to spherical aberration, but of the opposite sign to theory. This is consistent with the aberration being dominated by parasitic octupole components in the individual quadrupole lenses. The grid shadow method also revealed that the present quadruplet, as constructed, was free from parasitic aberration due to rotational misalignments of the individual quadrupoles.
1. Introduction Electrostatic quadrupole lenses offer some advantages over magnetic quadrupole lenses as a probe forming lens system. Electrostatic lenses do not suffer from hysteresis effects, negligible current is drawn from the power supply and the field strengths required for focusing the beam onto the target is independent of ion mass [l]. However, electrostatic lenses suffer from the disadvantage that they must be mounted inside the vacuum system, with consequent problems of alignment. Previous measurements [2-41 on magnetic and electrostatic quadrupole probe forming lens systems have revealed the presence of parasitic sextupole and octupole lens components in the quadrupole lenses. These parasitic components can significantly degrade the resolution of the focused probe. The present work aims to measure the parasitic components of an electrostatic system. The Sydney electrostatic Russian antisymmetric quadruplet [1,5] commenced operation in 1984 and is used principally to perform PIXE analyses on geological materials [6]. The best resolution of the probe achieved to date has been 50 pA of 3 MeV H+ into a 3 urn diameter probe. This used a 35 X 40 km* rectangular object diaphragm and a 0.5 mm diameter aperture diaphragm. However, typical applications use 0.5-10 nA of 3 MeV H+ into lo-20 ttrn diameter probes. The grid shadow method was applied to these lenses to determine the nature of the parasitic aberration. This 0168-583X/91/$03.50
method is described fully in refs. [2,7]; however, briefly, the method involves placing a fine grid in the real image plane of the lens under test, then observation of the shadow cast on a screen downstream. The grid is mounted normal to the beam direction with the grid bars making an angle of between 0.5 o and 2 o to the vertical. The curvature of the grid bar shadows may be quantitatively analyzed to deduce the aberration coefficients, and hence the nature of the aberration, of the lens under test. Ion optical calculations for this work were performed with the program PRAM [2,7] which uses the thin lens model [8] for the electrostatic quadrupole field and the rectangular model [9] for the parasitic octupole components.
2. Experiment 2.1 The quadrupoie singlets The layout of the present system is shown in fig. 1 and the physical parameters used in the analysis are in table 1. The first part of the experiment involved testing each lens individually. To prevent stray accumulations of beam-induced charge from introducing spurious aberration, remaining lenses were grounded and the lens under test was fitted with bleed resistors. The grid shadow patterns from the individual lenses, used to produce both a vertical (positive) and horizontal (negative) line focus on the grid are shown in fig. 2. It can be
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
I. MICROPROBE
TECHNOLOGY
34
D.N. Jamieson et al. / Electrostatic CSIRO-HIAF
electrostatic
quadruplet
-1.5; 0
1 .o
2.0
3.0
z-axis
4.0
5.0
(ml
Fig. 1. The layout of the electrostatic quadrupole quadruplet, showing a calculated raytrace through the system. The upper ray is for the XOZ plane and the lower from the yOr plane. The grid shadow method of aberration measurement used a grid located in the image plane (here at z = 4.7 m) and a scintillating screen at the shadow plane (at z = 5.3 m).
seen at once that the dominant aberration of the lenses is from a parasitic octupole component. The parasitic octupole component produces a cubic curve shaped grid shadow pattern, as does the intrinsic spherical aberration of the lenses. However, the observed curvature is too great to be accounted for by the intrinsic spherical aberration alone, as can be seen by comparing the calculated grid shadow patterns expected for lenses that do not contain any parasitic aberration (the top row of patterns in fig. 2) with the experimental patterns (the lower two rows of fig. 2). Theoretical patterns characteristic of parasitic sextupole components are also shown in fig. 2 (right-hand column) but these are quite different from the experimental patterns showing that any parasitic sextupole component is weak. The magnitude of the parasitic octupole field components in each lens was obtained by fitting cubic curves to the curved grid bar shadows and the results are shown in table 2. Generally the lenses appear to have around 1% parasitic octupole field component, which is exactly the type of parasitic aberration expected if there was an imbalance in the two power supplies used to feed the pair of positive and pair of negative poles [lo]. However, the supplies were balanced to within about 0.1% using a precision digital voltmeter and a voltage divider at a particular reference voltage, but not at the exact voltage actually used to form the grid shadow patterns. It is therefore possible that the balance is a function of the power supply voltage. Further work is required to determine whether this is the case. It is extremely unlikely that the observed parasitic aberration could result from mechanical misalignments, since any random misalignment would certainly also
quadrupole probe forming lens system
introduce parasitic sextupole field components, which would most likely dominate over the effect of the parasitic octupole components. Calculated grid shadow patterns, making use of the aberration coefficients obtained from the experimental patterns for the positive lenses are also shown in fig. 2 (second row). In the cases of lenses 3 and 4 a small displacement of the aperture diaphragm (0.5 mm along the x-axis) was necessary to produce the observed asymmetrical patterns. Remaining differences between these calculated patterns and the experimental patterns are due to small parasitic sextupole and skew sextupole field components. These components were identified by qualitative comparison of the experimental patterns with theoretical patterns for parasitic sextupole components (see fig. 2) and a more complete set of patterns simulated for most possible parasitic components [2]. 2.2. The quadrupole quadruplet The grid shadow patterns of the quadruplet are considerably more complex than those of the singlet systems, since it is difficult to isolate regions of the pattern that are dominated by a single aberration coefficient. A set of experimental patterns obtained for a range of lens excitations that put the Gaussian image plane upstream, on and downstream of the grid are shown in fig. 3. Once again, the patterns show that the dominant aberration is due to parasitic octupole field components, as expected from the analysis of the singlet systems. The curvature of the grid bar shadows is opposite to what would be expected if it were due to the intrinsic spherical aberration alone. Accurate analysis of the patterns depends on being able to see the shadow of a large number of grid bars, hence the largest possible beam divergence is required. However, in the present system this is limited to 0.25 mrad by the permanent 2 mm diameter aperture located just upstream of lens 1. This compares with divergences of up to 0.5 mrad available in the Melbourne system. Hence in order to see a large number of grid bar
Table 1 Physical
parameters
of the Sydney
quadruplet
Quantity
Value
Object to aperture diaphragm Individual lens length Bore diameter Drift length between lenses Image drift length Image to shadow plane Demagnification (0/e) = (G/G) Grid period Beam
4.2 m 0.075 m 0.00635 m 0.005 m 0.152 m 0.57 m - 0.0741 12.7 urn 3MeVH+
D.N. Jamieson et al. / Electrostatic
35
quadrupole probe forming lens system
QUAD. 3
QUAD 3 WITH
QUAD. 4
1% PARASITIC SEXTUPOLE INTRINSIC SPHERICAL ABERRATION
PARASITIC OCTUPOLE
EXPERIMENT (POSITIVE)
a3
=
15’
(NEGATIVE)
10 mm Fig. 2. Calculated and experimental grid shadow patterns for the four singlet systems. Top row: Calculated shadow patterns for lenses free from parasitic aberration which suffer only from intrinsic spherical aberration. Second row: Calculated patterns using the third-order aberration coefficients obtained by analysis of the experimental patterns for positive lenses shown in row three. Bottom row: Experimental patterns for the lenses with a negative excitation. Differences between rows two and three are most likely due to parasitic skew sextupole field components. The grid was mounted in the Gaussian image plane rotated about the beam direction (z-axis) by nominally lo and the true grid angle for each lens was calculated from the period of the grid bar shadows along the y- or x-axes [2]. The right-hand column shows some theoretical shadow patterns for parasitic sextupole components in lens 3. a3 is the phase angle of the parasitic sextupole component.
Table 2 Measured parasitic octupole components of the singlets. Units: image beam displacement, x, in urn; object beam half divergence, 6, in mrad; parasitic octupole component, Q, in I% of the quadrupole field at the quadrupole bore radius. For each lens, the measured total third-order aberration coefficient, (_~/e’)~, deduced from an experimental grid shadow pattern in fig. 2, is related to the strength of the parasitic octupole component by the expression: (x/e3)== (x/e3)+(x/e3fZ)a Lens
1 2 3 4
Theoretical spherical aberration coefficient [8]
Theoretical reduced aberration coefficient [9]
Measured total third-order coefficient, (x/83)T, and parasitic octupole component, B
(x/es)
(x/esn)
(x/e3)=
D
(x/es)=
P
- 3.34 -4.18 - 5.51 - 7.95
161 164 166 162
360 290 100 250
2.2 1.8 0.6 1.5
360 230 190 220
2.2 1.4 1.1 1.4
Positive lens
Negative lens
I. MICROPROBE
TECHNOLOGY
36
D.N. Jamieson et al. / Electrostatic
Z (mm1 EXPERIMENT
quadrupole probe forming lens system
THEORY WITH PARASITIC
THEORY WITH ROTATION
12
10
Fig. 3. Experimental and calculated shadow patterns for the quadrupole quadruplet. Calculations were made as a function of the relative position of the grid and the Gaussian image plane, using the average third-order aberration coefficients obtained by analysis of the patterns for Z = - 15 mm and Z = 12 mm (here Z < 0 means upstream of the Gaussian image plane). The experimental patterns differ from the calculated patterns mainly because the calculated patterns assume a grid aperture was precisely aligned with the optical axis, but this was not achieved in the experiment. Also, the value of Z shown is nominal for the experimental patterns, and the appearence of the shadow pattern is very sensitive to Z between the circle of least confusion (here located at Z = - 7 mm) and the Gaussian image plane (Z = 0 mm), which readily accounts for the difference between theory and experiment for - 7 < Z c 0 mm. The right-hand column shows the effect of quadrupole lens 2 rotational misalignment of 2 mrad (including the effect of the parasitic octupole components).
D. N. Jnmieson et al. / Electrostatic Table 3 Measured
aberration
coefficients
Calculated intrinsic spherical [8]
Measured from shadow patterns in fig. 3
Calculated with parasitic octupole components a
(x/O? (x/@cp2) (u/e%) (Y/$)
-180 35.2 35.2 - 19.2
800 - 2500 - 3050 -25
962 - 2840 - 2840 -31
3. Conclusion
a Calculated [9] with parasitic octupole components of -4.6%, -0.12%, 0.89 and 1.45% in quadrupole lenses 1,2, 3, and 4 respectively. It is not possible to uniquely determine the octupole components from a quadruplet shadow pattern so these are representative of the actual components.
shadows, image
it is necessary plane.
since
This
the shape
To shadow
the
were patterns
then
astigmatism
improve
corresponding
grid
from
the
of the method,
becomes
dominated
coefficients.
accuracy,
deduced
the
the accuracy
of the pattern
by the first-order coefficients
to displace
reduces
from
third-order the
displaced
grid 1.5
12 mm downstream of the Gaussian image plane. The resulting coefficients agreed within a factor of 2, and the averaged coefficients are listed in table 3. Theoretical patterns calculated from these coefficients are in good qualitative agreement with the experimental patterns (see fig. 3) hence the measured coefficients are representative of the aberrations in the system. Rotational misalignment of individual quadrupoles in the quadruplet can cause a serious degradation of the focused probe since the aberration introduced depends on the first power of the divergence. Unlike parasitic sextupole (second-order) and parasitic octupole (thirdorder) it cannot readily be reduced by stopping down the aperture diaphragm. Rotational misalignments in the electrostatic system could be a serious problem because it is generally very difficult to rotate the lenses into alignment from outside the vacuum system, indeed the construction of the present lenses does not allow for relative rotational adjustment of the individual lenses. mm
upstream
Further work is required to identify the precise origin of the parasitic octupole components observed in the lenses. If indeed the parasitic components are due to residual imbalances in the lens power supplies, which could be eliminated, then the system should be able to perform very well, since it does not appear to suffer from the large parasitic sextupole components seen in most magnetic lens systems, or from rotational misalignment aberration, which have a much greater significance for degrading resolution.
aberration
experimental
to the grid
37
However, comparison of the theoretical grid shadow patterns for a 2 mrad misalignment of lens 2 of the present system (the lens most sensitive to rotational misalignment), shown in fig. 3, suggests that the net effect of any rotational misalignment is negligible in the quadruplet.
of the quadruplet
Coefficient
quadnrpole probe forming lens system
References
and
[I] S.H. Sie, C.G. Ryan, D.R. Cousens
and G.F. Suter, Proc. 9th IBA Conf., Kingston, Canada, 1989, Nucl. Instr. and Meth. B45 (1990) 543. [2] D.N. Jamieson and G.J.F. Legge, Nucl. Instr. and Meth. B29 (1987) 544. [3] D.N. Jamieson, G.W. Grime and F. Watt, Nucl. Instr. and Meth. B40/41 (1989) 669. [4] D.N. Jamieson and U.A.S. Tapper, Nucl. Instr. and Meth. B44 (1989) 221. [5] S.H. Sie and C.G. Ryan, Nucl. Instr. and Meth. B15 (1986) 664. [6] S.H. Sie, C.G. Ryan, D.R. Cousens and W.L. Griffin, Nucl. Instr. and Meth. B40/41 (1989) 690. [7] D.N. Jamieson and G.J.F. Legge, Nucl. Instr. and Meth. B30 (1988) 235. ]8] A.D. Dymnikov, T.Ya. Fishkova and S.Ya. Yavor, Nucl. Instr. and Meth. 37 (1965) 268. [9] S.Ya. Yavor, T.Ya. Fishkova, E.V. Shpak and L.A. Baranova, Nucl. Instr. and Meth. 76 (1969) 181. [IO] M.B.H. Breese, D.N. Jamieson and J.A. Cookson, Nucl. Instr. and Meth. B47 (1990) 443.
I. MICROPROBE
TECHNOLOGY