Optic column having particular major/minor axis magnification ratio

An optic column is provided to obtain a micro beam in simple structure. The optic column has a line cathode and multi-pole lenses arranged in three steps. A beam orbit in the major axis direction (X direction) and a beam orbit in the minor axis direction (Y direction) cross each other on the image plane. A ratio of magnification Mx of X-directional orbit to magnification My of Y-directional orbit is coincident with a ratio of width W to length H of the line cathode.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an optic column which can produce a micro 
beam (generally in 0.5 or less .mu.m) at large current in the low energy 
region for example of not more than 1 keV, and particularly to an optic 
column which can produce a micro beam at large current in a simple 
structure. 
2. Related Background Art 
An electron optic system for obtaining a micro beam at large current 
conventionally employs such a popular technique that a beam from a 
circular hot cathode (point source of light) is focused by a demagnifying 
lens system into a circular beam. The electron optic system is constituted 
by a lens of rotation symmetry system. In this method, the upper limit of 
obtained current is restricted by the current density of electrons emitted 
from the point source and the space-charge effect, because the electrons 
are drawn from a small area at the tip of cathode which is the point 
source. 
In order to eliminate this restriction, an attempt is made to increase an 
area contributing to the electron emission as much as possible by 
increasing the diameter of the cathode tip in electron gun or by 
face-processing the tip portion of cathode. However, even if the diameter 
of the tip end of cathode is increased, the maximum current is basically 
limited by the current density of electrons emitted from cathode and the 
space-charge effect near the tip end of cathode in case of the electron 
optic column using the lens constitution of rotation symmetry system. 
To solve the problem, there is a method considered to increase the probe 
current by using a line cathode, which increases the area of electron 
emission and relieves the restriction of emission current forced by the 
space-charge effect. The current is expected to increase in this 
arrangement as the emission area increases, because the space charge 
basically affects the current density. 
The line cathode was proposed by Brodie and Nixon (J. Vac. Sci. Technol. B7 
(6), November/December, p1878, 1989). They conducted theoretical analysis 
while observing the spread of emission energy caused by the Boersch effect 
in the space-charge effect of line cathode. They found that 27% of energy 
spread was alleviated as compared with the conventional point (circular) 
cathode. They explained it as the alleviation of space-charge effect by 
means of the line cathode. There is, however, nothing described in the 
document about the increase effect of maximum emission current amount 
itself with increase of emission area. 
The alleviation due to the Boersch effect decreases the energy spread, 
whereby the beam diameter is prevented from being widened by the chromatic 
aberration of lens system. This results in improving the performance of 
focusing lens. The chromatic aberration increases its influence in the low 
energy region, and therefore this method is very effective to obtain a 
micro beam at large current and in low energy. 
Nixon (U.S. Pat. No. 4,804,851) proposed an idea to form a line image of a 
line cathode. A beam is shaped by an aperture or slit (called as blocking 
part) to change the length (aspect ratio) of the line image. 
The proposal of Nixon concerns only the formation of line image from the 
line cathode, which is not such a method that a micro beam is formed by 
beam-shaping with adjustment of excitation condition of asymmetric optic 
system such as a multi-pole lens. 
Brodie (J. Vac. Sci. Technol. B8, p1691, 1990) proposed the method to form 
a line beam with variable aspect ratio (a ratio between length and width 
for rectangular beam) for electron beam lithography by using a doublet 
(device for shaping a beam by two steps of multi-pole lenses) or a triplet 
(device for shaping a beam by three steps of multi-pole lenses) of 
electric field type quadrupole lenses and the line cathode. The stigmatic 
focus condition is a lens condition that two-directional orbits, i.e., X 
orbit (major-axis orbit) and Y orbit (minor-axis orbit), are coincident 
with each other on image plane on the center axis (Z-axis) in multi-pole 
lens and that an X-directional magnification Mx is equal to a 
Y-directional magnification My. On the other hand, the pseudo stigmatic 
focus condition is a lens condition that the X-directional orbit and 
Y-directional orbit are coincident with each other on the image plane on 
the Z-axis and that Mx and My are different from each other. 
Brodie describes the construction of electron optic system to obtain a line 
beam in aspect ratio of approximately 1:1 to 1:100 by combinations of line 
cathode light source with quadrupole lenses, and particularly the 
operation conditions of quadrupole lenses. The electron optic system of 
Brodie comprises, as shown in FIG. 6, a line cathode light source 11, two 
steps of quadrupole lenses 12 for shaping emitted electrons into a beam of 
arbitrary aspect ratio, two steps of magnetic field type condenser lenses 
13 for demagnifying the beam shaped in rectangle to obtain a micro beam, 
and a magnetic field type objective lens 14. 
According to the operation conditions of quadrupole lenses 12 proposed by 
Brodie, the excitation condition is low, so that the demagnification ratio 
(inverse of magnification) is low, and the magnification ratio Mx/My is 
also as low as about 1/10. Thus, the quadrupole lenses 12 cannot produce a 
micro beam, and therefore the quadrupole lenses 12 are used as lenses for 
probe shaping as a result. Then, the condenser lens 13 and the objective 
lens 14 are added as demagnifying lens system to enhance the 
demagnification ratio of the entire system. This results in making the 
electron optic system complex. In particular, the example of FIG. 6 is so 
arranged that the condenser lens 13 and the objective lens 14 are formed 
as magnetic field type lenses, which makes the entire system larger and 
heavier. 
As for the technique for shaping and focusing a beam by means of multi-pole 
lens system, Okayama and Tsurushima (Japanese Laid-open Patent Application 
No. 60-233814 and Japanese Patent Publication No. 2-49533) proposed an 
idea and the optimum conditions, in which a line image is formed by 
quadrupole lens system from a point cathode and in which its length 
(aspect ratio) and current density distribution are controlled by changing 
the excitation condition of quadrupole lens system. Two steps of 
quadrupole lenses are shown as the quadrupole lens system in an 
embodiment, though they describe that the same effect can be achieved by a 
combination of more than two multi-pole lenses. However, a beam is not 
focused only by the multi-pole lens system either, as in Brodie. The 
multi-pole lens system functions only to shape the beam, and the final 
focusing is carried out by a magnetic field type objective lens in the 
conventional manner. These are applications of multi-pole lens system to 
obtain a line beam from a point cathode, but are different from the method 
for shaping and focusing a beam from line cathode into a point beam. 
As described above, the method for focusing a beam from circular point 
source of light into a circular beam has a limit for current of obtainable 
electron beam due to the emission current density of electrons from 
cathode and the space-charge effect. On the other hand, the arrangement in 
combination of line cathode with quadrupole lenses, as shown in FIG. 6, 
can greatly relax the restriction due to the emission current density from 
cathode and the space-charge effect, but has a low demagnification ratio 
of quadrupole lens system, which makes it difficult forming a micro beam 
by quadrupole lens system alone and which requires an additional 
demagnifying lens system. This results in making the electron optic system 
complex and increasing the size of apparatus. 
SUMMARY OF THE INVENTION 
The present invention has been accomplished taking the points as described 
above into consideration. It is an object of the present invention to 
provide an optic column which can form a micro beam only by a multi-pole 
lens system in a simple structure. 
An optic column comprises a line beam source emitting a beam and multi-pole 
lenses arranged in multiple steps, wherein a beam orbit in a direction of 
major axis of the line beam source and a beam orbit in a direction of 
minor axis of the line beam source cross each other on an image plane and 
a ratio of magnification of the beam orbit in the direction of major axis 
to magnification of the beam orbit in the direction of minor axis is 
coincident with a ratio of a length of the line beam source in the 
direction of minor axis to a length of the line beam source in the 
direction of major axis. 
A beam emitted from a line beam source passes through three steps of 
multi-pole lenses. In the three steps of multi-pole lenses, the major axis 
orbit and the minor axis orbit of beam cross each other on the image 
plane. The ratio of magnification of major axis orbit to magnification of 
minor axis orbit is made coincident with the ratio of width to length of 
line beam source, whereby a micro beam of substantial circle is obtained 
on the image plane.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
An embodiment of the present invention will be described in detail with 
reference to the accompanying drawings. FIG. 1 through FIG. 5 are drawings 
to show the embodiment of electron optic column according to the present 
invention. 
In FIG. 1, an electron optic column comprises an electron emission source 
consisting of a rectangular line cathode 21 for emitting an electron beam 
and quadrupole lenses 22, 23, 24 arranged in three steps (in triplet). A 
major-axis-directional orbit (X-directional orbit) of electron beam from 
line cathode 21 and a minor-axis-directional orbit (Y-directional orbit) 
of electron beam therefrom cross each other on an image plane 27. A ratio 
of magnification in the major axis direction (X direction) to 
magnification in the minor axis direction (Y direction), after demagnified 
by the three steps of quadrupole lenses 22, 23, 24, is coincident with a 
ratio of width W to length H of line cathode 21. 
The line cathode 21 has length H and width W, as shown in FIG. 1. An 
electron beam from the line cathode 21 can be focused to have the 
length-to-width of 1:1, which means that the beam is converted into a 
circular beam, on the image plane 27 by making the ratio of magnification 
in the major axis direction to magnification in the minor axis direction 
coincident with the ratio of width W to length H of line cathode 21, as 
described above. 
The magnification herein represents how much the line cathode 21 (object 
plane) can be demagnified on the imaging plane 27 (image plane). A lower 
magnification is preferable to obtain a micro beam. A magnification ratio 
is a ratio of magnification Mx of X-directional orbit in the direction of 
major axis of line cathode (in the X direction) to magnification My of 
Y-directional orbit in the direction of major axis (in the Y direction). 
The aspect ratio of line cathode (corresponding to the length of line 
cathode) can be made higher as the magnification ratio becomes lower. A 
higher aspect ratio permits a finer and longer line cathode to be used. 
The line cathode with higher aspect ratio increases an area of electron 
emission, so that a larger emission current may be obtained. Therefore, a 
lower magnification and a lower magnification ratio can provide an 
electron optic system with higher performance with respect to the object 
of the present invention. The quadrupole lenses 22, 23, 24 are not of 
rotation symmetry nor are the other multi-pole lenses. 
The line cathode 21 is a hot cathode made of lanthanum hexaboride 
(LaB.sub.6). LaB.sub.6 is featured by excellent workability and large 
emission current density. Thus, LaB.sub.6 is one of the most suitable 
cathode materials to obtain a large current. It should be noted that the 
material for cathode is not necessarily limited to LaB.sub.6. For example, 
other cathode materials used as field emission type electron gun, such as 
tungsten (W) and zirconium oxide/tungsten (ZrO/W), may be used to form an 
electron gun after processed in a line shape. 
Next described is the operation of the present embodiment constructed as 
above. The operation to form a micro beam by the electron optic column 
shown in FIG. 1 will be described with analysis of electron optic system. 
First described briefly is the general electron-optic property of 
quadrupole lens, which is the basis of analysis. 
Employing the normal treatment to approximate the field distribution k (z) 
by a rectangular model if the length l of quadrupole lens is sufficiently 
greater than the aperture a, the paraxial orbit equation of electron beam 
in field type quadrupole lens can be expressed as follows. 
EQU X"-.beta..sup.2 k(z)X=0 
EQU Y"+.beta..sup.2 k(z)Y=0 (1) 
where .beta..sup.2 =V.sub.2 /V.sub.a a.sup.2, V.sub.2 is an applied voltage 
to electrode, and V.sub.a an acceleration voltage. Also, X is an 
X-directional distance, X" a second derivative of X, Y a Y-directional 
distance, and Y" a second derivative of Y. 
The paraxial characteristics of quadrupole lens are as follows. The orbit 
of electron beam in field of quadrupole rectangular distribution can be 
expressed as follows if a X-directional distance, a X-directional slope, 
Y-directional distance, and a Y-directional slope of electron beam are 
represented by (X.sub.0, X.sub.0 ', Y.sub.0, Y.sub.0 '), respectively, on 
the entrance end plane of rectangular field. 
EQU X=X.sub.0 cosh.beta.z+(X.sub.0 'sinh.beta.z)/.beta. 
EQU Y=Y.sub.0 cos.beta.z+(Y.sub.0 'sin.beta.z)/.beta. (2) 
Accordingly, an orbit on the exit end plane of rectangular field, (X.sub.L, 
X.sub.L ', Y.sub.L, Y.sub.L '), can be expressed by the following 
matrices. 
##EQU1## 
In Equation (3), .theta. is a parameter representing the excitation 
condition of each quadrupole lens. 
The following equations provide the orbit in matrix representation on the 
end plane of final step lens in the optical system with three steps 
(triplet) of quadrupole lenses 22, 23, 24 combined as in the present 
invention. 
##EQU2## 
In Equation (4), a is a distance between the cathode 21 and the entrance 
end plane of quadrupole lens 22 of first step, s.sub.1 a distance between 
the first step quadrupole lens 22 and the second step quadrupole lens 23, 
and s.sub.2 a distance between the second step quadrupole lens 23 and the 
third step quadrupole lens 24. 
The focus condition is such that the X-directional orbit and the 
Y-directional orbit coincide with each other on the image plane 27 on 
Z-axis and that the magnification of X-directional orbit is different from 
that of Y-directional orbit (which is pseudo stigmatic). The focus 
condition can be represented by the following equation. 
EQU X/X'=Y/Y'(Mx.noteq.My) (5) 
Since the magnifications of X-directional orbit and Y-directional orbit are 
different from each other in order to focus a beam from line cathode into 
a circular (point) beam, the imaging is not carried out under stigmatic 
condition, but under pseudo stigmatic condition. 
The operation of electron optic column according to the present invention 
is next described based on the above analytic procedure. 
FIG. 2 shows a model for analysis of the present invention. In FIG. 2, each 
of first step quadrupole lens 22, second step quadrupole lens 23 and third 
step quadrupole lens 24 has a lens effective length L. The effective 
length L corresponds to a region of electric field if the lens is 
approximated as rectangular. Also, a distance between the object plane 
(the plane on which the cathode 21 is placed) and the first step 
quadrupole lens 22 is a and a distance between the third step quadrupole 
lens 24 and the image plane 27 is b. Further, a distance between the first 
step quadrupole lens 22 and the second step quadrupole lens 23 is s.sub.1 
and a distance between the second quadrupole lens 23 and the third 
quadrupole lens 24 is s.sub.2. The quadrupole lenses 22, 23, 24 have the 
excitation conditions .theta..sub.1, .theta..sub.2, .theta..sub.3, 
respectively. The excitation conditions correspond to lens powers of 
respective quadrupole lenses. 
Since the object of the present invention is to make as many electrons 
emitted from the line cathode as possible and to form a circular micro 
beam therefrom, a higher aspect ratio of line cathode (corresponding to 
the length of line cathode) is preferable for that purpose. Namely, 
electron-optic requirements for quadrupole lenses 22, 23, 24 are as 
follows. 
(1) The lens system should preferably have the structure and the operation 
conditions to decrease the magnifications both in the X direction and in 
the Y direction. However, it is meaningless to decrease only either one of 
magnifications in the X direction or in the Y direction. 
(2) The aspect ratio of line cathode should preferably be increased if the 
magnification ratio Mx/My between magnifications in X direction and in Y 
direction is made lower at the same time. 
The operation analysis was done with the model shown in FIG. 2. The results 
are shown in FIG. 3. FIG. 3 shows calculation results of respective 
magnifications Mx, My of the X-directional orbit and the Y-directional 
orbit in multi-pole lenses arranged in three steps. The calculation was 
based on the excitation condition (lens power) of first step quadrupole 
lens as .theta..sub.1 =1 and the relations between lenses as a/L=5, 
s.sub.1 /L=s.sub.2 /L=1. FIG. 3 shows the relations of magnification Mx of 
the X-directional orbit and magnification My of the Y-directional orbit 
with b/L. Here, b/L represents the operation distance (the distance 
between the third step quadrupole lens and the image plane) to the lens 
effective length. 
If the excitation condition .theta..sub.1 of the first step quadrupole lens 
is fixed, there always exist two or more excitation conditions 
.theta..sub.2 for the second quadrupole lens to provide the same b/L. One 
of them is a case that .theta..sub.2 is about 1 (.theta..sub.2 =0.9 in 
this analysis result), which is called as a low .theta..sub.2 mode. 
Another is a case that .theta..sub.2 is not less than 3 (.theta..sub.2 
=3.5 in this analysis), which is called as a high .theta..sub.2 mode. As 
shown in FIG. 3, both Mx and My decrease as b/L decreases. In FIG. 3, 
values of Mx in the high .theta..sub.2 mode are always smaller by about a 
figure than those in the low .theta..sub.2 mode. 
In contrast, My is almost identical between the high .theta..sub.2 mode and 
the low .theta..sub.2 mode. Since the Y-directional orbit is positive in 
the high .theta..sub.2 mode but negative in the low .theta..sub.2 mode, as 
will be detailed hereinafter, FIG. 3 shows absolute values of My for the 
low .theta..sub.2 mode. 
FIG. 4 shows the magnification ratio Mx/My. Since the magnification Mx in 
the high .theta..sub.2 mode is lower by about a figure than Mx in the low 
.theta..sub.2 mode according to the analysis result shown in FIG. 3, the 
magnification ratio in the high .theta..sub.2 mode can take values smaller 
by about a figure than those in the low .theta..sub.2 mode. 
Next, FIG. 1 shows the X-directional orbit and Y-directional orbit of 
electron beam obtained by the analysis as described above. As shown in 
FIG. 1, the X-directional orbit greatly diverges in the second step 
quadrupole lens 23 in the high 74 .sub.2 mode (as shown by a solid line) 
and converges in the third step quadrupole lens 24. Because of this, the 
X-directional orbit can present a low magnification in the high 
.theta..sub.2 mode. On the other hand, the X-directional orbit in the low 
.theta..sub.2 mode (as shown by a broken line) diverges little in the 
second step quadrupole lens 23. Thus, the X-directional orbit in the low 
.theta..sub.2 mode cannot present a lower magnification than the 
X-directional orbit in the high .theta..sub.2 mode can. 
The Y-directional orbit in high .theta..sub.2 mode (as shown by a solid 
line) converges in the second step quadrupole lens 23 and diverges a 
little in the third step quadrupole lens 24. After the second step 
quadrupole lens 23, the Y-directional orbit in the low .theta..sub.2 mode 
(as shown by a broken line) draws a symmetric orbit as the Y-directional 
orbit (solid line) in the high .theta..sub.2 mode is inverted in a sign. 
As seen from FIG. 1, the high .theta..sub.2 mode, in which the 
X-directional orbit greatly diverges in the second step quadrupole lens 23 
and converges in the third step quadrupole lens 24, is preferable to 
decrease the magnifications Mx, My and the magnification ratio Mx/My. 
Next considered is the excitation condition .theta..sub.1 of first step 
quadrupole lens 22 in high .theta..sub.2 mode. FIG. 5 shows relations 
between .theta..sub.1 and Mx, My, Mx/My in the high .theta..sub.2 mode. 
The magnification My monotonously decreases with increase of 
.theta..sub.1, while Mx diverges at .theta..sub.1 =0.932 (P.sub.1) or at 
.theta..sub.1 =3.4 (P.sub.2) in FIG. 5. It is seen from FIG. 5 that the 
optimum condition for stable operation, which can provide a small value of 
Mx/My and avoid the diverging points (P.sub.1, P.sub.2), is .theta..sub.1 
falling within the region A between the two diverging points (P1, P2). Mx 
can take a negative value depending upon the value of .theta..sub.1. 
Therefore, FIG. 5 shows absolute values .vertline.Mx.vertline., taking it 
into consideration. 
Let us consider a specific example of the present invention in the 
following. 
As detailed above, the following operation conditions of electron optic 
system with line cathode and the three steps of quadrupole lenses are 
necessary for obtaining a micro beam. 
(1) The operation condition of the second step quadrupole lens must be in 
the high .theta..sub.2 mode to obtain a higher magnification ratio, in 
which the X-directional orbit diverges in the second step quadrupole lens. 
(2) Mx and Mx/My can be made lower and stabilized by setting the excitation 
condition .theta..sub.1 of the first step quadrupole lens within the range 
between the diverging points of magnification Mx. 
FIG. 1 shows a conceivable electron optic column having the line cathode 
and the three steps of quadrupole lenses satisfying the above conditions. 
A specific construction of the electron optic column according to the 
present invention may be for example based on .theta..sub.1 =3, 
.theta..sub.2 =high mode (.theta..sub.2 =3.39), .theta..sub.3 =1.23, 
a/L=5, s.sub.1 /L=3 and s.sub.2 /L=1. 
In this example Mx=1.1.times.10.sup.-3, My=1.3.times.10.sup.-2 and 
Mx/My=8.4.times.10.sup.-2. Then, a beam in diameter of 0.1 .mu.m was 
obtained on a sample, with a line cathode of 100 .mu.m in a length and 10 
.mu.m in a width (aspect ratio of 10) and under b/L=1. A micro beam was 
obtained with the lens system composed only of quadrupole lenses. 
Although the above embodiment was described as an example of electron optic 
column emitting an electron beam, the present invention is not limited to 
this example but can be applied for example to an optic column emitting an 
ion beam instead of the electron beam. 
As described above, the present invention is effective to obtain a micro 
beam of substantial circle on the image plane only by the multi-pole 
lenses arranged in three steps, whereby the entire system can be made 
smaller and lighter.