Particle-beam imaging system

In an ion optical imaging system, especially for lithographic imaging on a wafer, two collecting lenses are provided between the mask and the wafer. At least one of the collecting lenses is a three-electrode grid lens, i.e. a lens in which a grid is disposed perpendicular to the optical axis between a pair of tubular electrodes.

FIELD OF THE INVENTION 
Our present invention relates to a particle-beam imaging system and, more 
particularly, to an ion-beam imaging system for use in projection ion-beam 
lithography, especially for producing semiconductor components and the 
like. 
BACKGROUND OF THE INVENTION 
Of the various steps which are required for the production of semiconductor 
elements, the lithographic step is especially important. Stated most 
simply, each lithographic step begins by coating a wafer, especially a 
silicon wafer, with a thin layer of photosensitive material referred to as 
a photoresist or, simply, a resist, the material of this coating being 
sensitive to a beam of radiation, for example an ion beam or other 
particle beam. 
A lithographic apparatus projects the beam through a mask provided with a 
structure to be imaged on the resist, usually in the form of openings in 
the mask. 
Between the mask and wafer, optical elements, i.e. elements capable of 
modifying the configuration of the beam, can be provided. 
The image on the wafer has an extent which is usually far smaller than that 
of the wafer surface upon which the image is produced. Subsequent to the 
projection, therefore, the wafer may be shifted and the process repeated 
so that the same structure of the mask is projected on other locations of 
the wafer. 
The stepping of the wafer through a series of exposures by which the same 
pattern is imaged on the resist can be repeated until the entire wafer 
surface coated by the resist is utilized. 
A subsequent development of the resist provides the desired pattern on the 
wafer in the form of resist-free locations. The wafer can then be 
subjected to any of numerous processes, including etching, ion 
implantation or coating and diffusion to apply doping elements. After 
these further steps, the wafer is inspected, recoated with resist and the 
entire sequence described above is repeated some 8 to 15 times until the 
result is a checkerboard arrangement of identical microcircuits on the 
wafer. 
Most of the projection lithographic processes used heretofore employ light 
to irradiate the resist. However, the continuous need for imaging ever 
smaller structures and the ever higher densities of the components of the 
microcircuit has mandated the investigation of other radiation methods 
which are not as limited in resolution as is light with its relatively 
long wavelength. 
Considerable efforts have been made, for example, to attempt to use X-rays 
in lithographic systems while other processes such as particle-beam 
lithography and, especially, ion-beam lithography, have been considered as 
well but with significantly less attention. 
In U.S. Pat. No. 4,985,634, an imaging system for lithography purposes is 
described which comprises a particle source, especially an ion source, a 
mask provided with a structure to be imaged in the form of one or more 
components in the mask along the particle or ion beam, means for 
supporting a wafer in the path of that beam downstream of the mask and, 
between the mask and the wafer, at least two collecting lenses which are 
capable of affecting the beam. These collecting lenses are in the form of 
rotationally symmetrical electrostatic lenses with electrodes of 
conventional shapes (tubular, diaphragms or combinations thereof) each 
lens suffering from considerable third-order image distortion which can be 
only limitedly influenced by the special configuration of the lens 
geometry. However, by the selection and arrangement of the two lenses this 
system allowed third-order image distortion to be largely eliminated while 
a significant fifth-order image distortion, resulting from the product of 
the aberration coefficient matrix, remained. 
OBJECTS OF THE INVENTION 
It is the principal object of the present invention to provide a 
particle-beam imaging system, especially an ion-beam imaging system, 
particularly for lithographic purposes, and capable of imaging a mask 
structure formed of one or more openings on a wafer, especially a wafer 
coated with resist, which substantially eliminates the effect of image 
distortion of the third order and largely reduces fifth-order distortion. 
Another object of this invention is to improve upon earlier two-lens 
systems so that higher-order image distortion may be eliminated or 
reduced. 
Still another object of this invention is to provide an imaging system of 
the particle beam and especially the ion-beam type, especially for 
projection lithography in the production of microcircuits, whereby 
drawbacks of earlier systems are avoided. 
SUMMARY OF THE INVENTION 
These objects and others which will become apparent hereinafter are 
attained, in accordance with the invention, in an imaging system which 
improves upon the system of this latter patent and reduces the drawbacks 
thereof or overcomes drawbacks of such systems by providing at least one 
of the collecting lenses as a three-electrode lens of particular 
configuration. 
More particularly, a particle-beam imaging system, especially for 
lithographic purposes and generating microcircuits on a wafer, can 
comprise: 
a particle source generating a beam of particles trained on an image plane 
and traveling along an optical axis of the imaging system; 
a mask disposed in a path of the beam upstream of the imaging plane and 
provided with at least one opening forming a structure to be imaged on the 
imaging plane; 
means for supporting a wafer upon which the structure is to be imaged by 
the beam at the imaging plane; 
two collecting lenses for the beam of particles disposed along the beam 
between the mask and the wafer, 
at least one of the lenses being a three-electrode lens including two tube 
electrodes and a third electrode in the form of a grid between the tube 
electrodes, the third electrode having a multiplicity of openings and 
being disposed normal to the optical axis, the grid subdividing the 
three-electrode lens into a first refractive region including one of the 
tube electrodes and a second refractive region including the other of the 
tube electrodes, the regions having different refractivities; and 
means for applying different potentials to the electrodes of the 
three-electrode lens. 
According to another aspect of the invention, the ion-optical imaging 
system comprises: 
a particle source generating a beam of particles trained on an image plane 
and traveling along an optical axis of the imaging system; 
a mask disposed in a path of the beam upstream of the imaging plane and 
provided with at least one opening forming a structure to be imaged on the 
imaging plane; 
means for supporting a wafer upon which the structure is to be imaged by 
the beam at the imaging plane; and 
two collecting lenses for the beam of particles disposed along the beam 
between the mask and the wafer, 
at least one of the lenses being a three-electrode lens including two tube 
electrodes and a third electrode between the tube electrodes, the third 
electrode (or grid electrode) being formed as a plate having a plurality 
of openings and disposed normal to the optical axis, the plate subdividing 
the three-electrode lens into a positively refractive region including one 
of the tube electrodes and a negatively refractive region including the 
other of the tube electrodes. 
The perforated plate or grid, therefore, can be located perpendicular to 
the optical axis and subdivides the lens into two regions, the three 
electrodes having different voltages applied thereto. 
The use of three-electrode lenses with grids as described, especially when 
both collecting lenses are of this configuration, enables a respective 
third-order image-distortion coefficient of the imaging equations to 
vanish for each lens and the remaining image distortion coefficients to be 
significantly less problematical by comparison with those of conventional 
electrostatic lenses. 
In the imaging system of the invention, for each collecting lens, the 
third-order distortion can be so greatly reduced that it is practically 
eliminated. As a result, there is a reduction of the residual distortion 
at the distortion minimum. 
The use of three-electrode lenses with grids, as described, enables the 
reduction of the mask-wafer distance by comparison with earlier systems 
for the same distortion values and same image field size. 
Furthermore, the depth of field of the imaging system can be substantially 
increased because the three-electrode lenses with grids as described have 
only very small image distortions and hence the compensation of image 
distortions by the lenses between the wafer and mask is significantly less 
critical. 
With the use of three-electrode lenses with grids, moreover, it is possible 
to provide a particle beam and especially an ion-beam imaging system in 
which the particle energies at the locations of the mask and wafer are 
substantially identical. The resist-coated wafer can thus be irradiated 
with low energy ions or particles (e.g. 10 KeV) so that the particles can 
be stopped within the resist layer. As a consequence, there is a reduced 
tendency to generate defect structures and radiation defects generally in 
the device because of the particle irradiation thereof and the function of 
the microcircuitry is not affected by high energy particle defects. There 
is a defect-free transfer of the mask structure to a wafer substrate by 
the particle beam. 
It is also possible to achieve lithographic systems with the 
three-electrode grid lenses of the invention in which the ion energy at 
the wafer is very much higher than that at the mask, for example, by a 
factor of 25, so that higher ion energies (e.g. 100 KeV) can be achieved 
at the wafer which enables a sufficient penetration depth of ions for a 
variety of purposes. 
To the extent that masks may be used which have only a single aperture, 
imaging systems can be constructed which employ a singular beam of 
relatively low energy with high resolution. 
According to a feature of the invention, one of the lens regions of the 
three-electrode lens has positive refractivity while the second lens 
region has negative refractivity. According to another feature of the 
invention, the absolute value of the refractive power of the negative lens 
region (dispersive region) is less than the refractive power of the 
positively refractive lens region (collecting region). 
Such an imaging system allows compensation of the image-error coefficients 
in spite of the different absolute values of the refractive power when the 
dispersive region has greater third-order image distortion than the 
collecting regions. 
This construction can be achieved in a simple way, according to a further 
feature of the invention by providing the tubular electrode of the 
negatively refractive lens region so that its diameter is smaller, 
particularly one-half that of the tubular electrode of the positively 
refractive lens region and when the voltage ratio between the electrodes 
of the negatively refractive region is significantly less, especially 
one-half the voltage ratio between the electrodes of the positively 
refractive region. 
The disturbance by, the openings in the plate or grid can be reduced when, 
according to the invention, substantially identical field strengths are 
provided for the ion beam on both sides of the perforated plate electrode 
or grid electrode. 
According to a further feature of the invention, the grid electrode is 
displaceable in the grid plane in two directions including an angle of 
90.degree. between them, reciprocatingly. This reciprocating movement 
reduces the effect of the webs between the openings in the plate or grid 
electrode on the imaging (transfer of the mask structure to the wafer). 
This reciprocation by a stroke which is greater than the width of the web 
between openings of the perforated plate or grid, ensures that particles 
from each point of the mask will reach the wafer. Furthermore, within the 
exposure time, each point in the perforated plate or grid plane is 
transmissive to the same fraction of the total ion flux. Preferably the 
frequency of reciprocation differs in the two directions of movement of 
the perforated plate or grid electrode. 
Most advantageously, the amplitude of reciprocation is a multiple, 
generally 5 to 15 times, the width, of the grid openings The reciprocation 
frequency can be in the range of 100 to 1000 Hz. 
The mask-wafer transmission can be improved and fluctuations resulting from 
the periodicity of the grid reciprocation can be reduced when, according 
to a further feature of the invention, the diameter of the virtual source 
of particles or ions is a multiple of the diameter of the grid openings 
and, especially in the case of grid openings with a width of 5 .mu.m, 
amounts to about 60 .mu.m. For reference to the effect of a virtual 
source, see European patent application publication A2 0 344 646 published 
Dec. 6, 1989. 
The enlargement of the size of the virtual source does result indeed in an 
enlargement of the radiation cone deriving from the mask points, but 
without significant reduction in the resolving capacity since the 
three-electrode lenses with the grids generate only very small aberrations 
by comparison to previously used lenses. This allows a much larger virtual 
particle source to be used, a greater particle flux per unit time to be 
extracted from the plasma chamber of the source and a more extensive 
irradiation of the mask. 
Improvement in the mask-wafer transmission with the imaging system of the 
invention can be obtained as well by providing downstream of the particle 
source, especially an ion source, a multipole to which a variable voltage 
can be applied and which can be disposed between the source and the mask. 
The configuration and construction of a multipole is described in European 
publication 0 344 646 mentioned previously. 
The multipole can effect a wobbling of the virtual source 
electrostatistically and corresponds to comparative shifting of the 
position of the virtual source with essentially the same effect as an 
enlarged particle or ion source.

SPECIFIC DESCRIPTION 
Referring first to FIG. 6, it can be seen that an ion beam lithographic 
column or system, according to the invention, can comprise an ion source Q 
for directing a beam of ions onto a mask M so that the structure thereof, 
in the form of one or more openings in the mask, can be imaged upon a 
wafer W which can be assumed to have a resist coating on a surface thereof 
turned toward the mask and source. 
Between mask M and the wafer W are two collecting lenses L1 and L2. Between 
the ion source and the mask M, an illumination lens B, L is provided to 
generate a parallel bundle or beam. At least one and preferably both of 
the collecting lenses L1 and L2 can be a three-electrode lens as will be 
described in greater detail. 
As can be seen from FIG. 6, as well, a multipole 10 can be provided along 
the optical axis between the source Q and the mask M and can be energized 
by a variable voltage source 11 so as to increase the spread of the 
virtual source. An appropriate multipole for this purpose is described in 
the above-mentioned European patent which also describes the illumination 
lens and an appropriate ion source. The ion beam 12 is collimated by the 
illumination lens BL, passes through the mask M and the collecting lens L1 
before reaching a crossover C between the lenses L1 and L2 and then is 
projected by the lens L2 on the wafer W. 
The means for supporting the wafer has been represented diagrammatically at 
13 and is provided by a drive 14 for stepping the wafer in two mutually 
perpendicular directions so as to provide the checkerboard pattern of 
imaging on the wafer as has been described. 
The lenses have, as noted, dispersive parts formed by two of the electrodes 
as illustrated, for example, in FIGS. 1 and 2 and a typical lens L1 or L2 
is shown in FIG. 3. The latter comprises tubular electrodes R1 and R2 
between which a third electrode in the form of a perforated plate or grid 
G is provided with a multiplicity of openings. 
The grid G can be connected with a further drive 15 (e.g. a piezodrive) 
capable of displacing the grid in the plane thereof in two mutually 
perpendicular directions with a reciprocating action. A voltage source 16 
is connected to the electrode to apply different potentials to them as 
will be described in greater detail below. 
The perforated plate electrode can be a thin plate provided with a 
multiplicity of openings, but preferably is a grid in which the openings 
are separated by mutually perpendicular webs. The grid G is perpendicular 
to the optical axis D of the imaging system and subdividing the respective 
lens, e.g. lens L1, into two regions P and N. 
The different voltages U1, U2, U3 are applied to the tube electrode R1, the 
grid G and the tube electrode R2. 
To avoid damage to the grid G, the optics of the system are such that no 
crossover is provided in the region of the or either grid. 
For the first lens L1, the optics are such that, for a parallel radiation 
bundle entering this lens, the crossover (at C of the system) is at the 
image side focal plane thereof. 
In the example given, the lens region P has positive refractivity and the 
lens region N has negative refractivity. The absolute value of the 
refractive power of the lens region N of negative refractivity is less 
than the refractive power of the lens region P of positive refractivity so 
that the overall refractive power of the three-electrode lens L1 is 
positive. 
As will be apparent also from FIG. 3, the diameter (2r.sub.2) of the 
tubular electrode R2 of the lens region N of negative refractivity is less 
(approximately half) the diameter (2r.sub.1) of the tubular electrode R1 
of the lens region P of positive refractivity. The voltage ratio 
(U3-UO)/U2-UO) between the electrodes of the lens region N of negative 
refractivity is also smaller than the voltage ratio (U3-UO)/U1-UO) 
(substantially half) between the electrodes of the region P of positive 
refractivity UO representing that potential at which the kinetic energy of 
the charged particles used is 0. 
To both sides of the grid electrode G or the perforated plate electrode, 
the field strength for the two regions P and N are as close to equal as 
possible. 
The perforated plate or grid electrode can be oscillated in two mutually 
perpendicular directions in the grid plane by the drive 15 as mentioned 
previously. 
The multipole 10 between the source Q and the mask N can be energized with 
a voltage which continuously varies during operation and has the effect of 
providing an apparent oscillating movement of the virtual source, thereby 
preventing imaging of the ribs or webs between the openings of the plate 
or grid upon the wafer W. 
In a concrete embodiment of the three-electrode lens with a grid, the 
spacing between the ends of the tubular electrodes R1, R2 turned toward 
one another is 90 mm. The electrode forming the grid G is spaced axially 
by 60 mm from the discharge mouth of the tubular electrode R1 which has a 
diameter of 200 min. The inlet mouth of the tubular electrode R2 has a 
diameter of 100 mm. 
The discharge mouth of the tubular electrode R2 is removed from the grid G 
by 450 mm and the inlet mouth of the tubular electrode R1 lies 900 mm 
ahead of the grid G. 
At a distance of 520 mm from the outlet mouth of the tubular electrode R1, 
the inner diameter is stepped down from 200 mm to 100 min. 
To provide dispersive lens systems, as contrasted with the collecting 
lenses described, combinations of tubular and plate electrodes can be 
provided as have been illustrated in FIGS. 1 and 2. The plate must be 
formed with a multiplicity of openings so that it can effectively 
constitute a grid, or by a grid having its opening between cross bars, the 
openings enabling the passage of the particles. 
Up to now, grid lenses have not been considered for this use in 
applications which require high imaging quality, since the bars of the 
grid do absorb a minor portion of the beam flux, and the individual grid 
openings effectively act as minilenses or fly-eye lenses. 
The grid lenses of the invention, have been developed and improved in such 
a way that avoid the negative effect of any grid is avoided and only its 
advantage come into effect. 
FIG. 3 shows the principal structural elements of a three-electrode grid 
lens. As indicated, the lens can comprise two tubular electrodes R1, R2 
with radii r1, r2 and a thin grid electrode between them, subdividing the 
lenses into two regions P and N. 
The potentials U1, U2, U3 applied to the three electrodes R1, G and R2 are 
so selected that the field strengths on both sides of the grid electrode G 
are as much as possible identical to one another. Distortion through the 
grid is largely eliminated by this combination. The voltages can be chosen 
U1&lt;U2&lt;U3&lt;U0 or U0&gt;U1&gt;U2&gt;U3. 
For positively charged particles, and the voltages chosen according to the 
first case (U1&lt;U2&lt;U3&lt;U0), the first region of the lens is dispersive 
(negative refractivity) and the second region of the lens is collecting 
(positive refractivity). In the second case (U0&gt;U1&gt;U2&gt;U3), the first lens 
region P functions as a collecting lens and the second region N as a 
dispersive lens (FIG. 3). 
For negatively charged particles, a corresponding relationship applies. In 
the first case (U0&gt;U1&gt;U2&gt;U3), the first lens region P has positive 
refractivity and the second lens region N has negative refractivity. In 
the second case (U1&lt;U2 &lt;U3&lt;U0), the opposite applies. 
The resulting refractive power (refractive power of the total lens) is thus 
given approximately as the sum of the refractive powers of the two partial 
lenses (regions P and N). 
Similarly, the aberration coefficients of third order are given as the sum 
of the aberration coefficients of the lens regions. Since the aberration 
coefficients of third order are of opposite sign for collecting lenses and 
dispersive lenses, it is possible to hold the third order aberration image 
distortion coefficient sums so that they will be very low and, in many 
cases, so that one or more of these coefficients can vanish precise- 
The dispersive part of the lens can have a lesser refractive power than the 
collecting part of the lens and since the third order aberration is 
relatively worse for the dispersive part, it is possible to compensate the 
aberration coefficients by ensuring the above-mentioned relation-ship of 
the absolute value of the refractive power of the dispersive part. 
In a practical way this is achieved by making the diameter of the tubular 
electrode and the voltage ratio for the dispersive part smaller than (in 
the case of FIG. 3, half) the diameter of the tubular electrode and the 
voltage ratio for the collecting part of the lens. 
As evidence of the aforedescribed effect of a three-electrode grid lens, 
the characteristics of a series of lenses of the construction of FIG. 3 
were numerically calculated. For this purpose, the lens parameters of 
first, third, and fifth-order for different values of the radius ratio 
r.sub.1 /r.sub.2 as well as the spacing of the two tubular electrodes R1 
and R2 from the grid G were calculated as a function of the voltage ratio 
(U3-UO)/U1-UO). 
The potential of the grid electrode G is determined by the condition that 
equal field strengths will be present on both sides of the grid G. 
These calculations are effected as follows: 
(1) Calculation of the potential distribution for a given lens geometry by 
numerical solution of the potential equation by the method of finite 
differences. 
(2) Calculation of the first and third order lens parameters as a function 
of the voltage ratio (U3-UO)/(U1-UO) as follows: 
Initially the electric field is calculated from the potential values as 
determined by solution of the potential equation whereby in order to 
obtain a necessary sufficient precision it is necessary to perform a two 
dimensional cubic interpolation. 
Then a number of particle trajectories through the lenses distributed over 
the interesting calculation range of the lenses are generated by means of 
numerical integration. From the positions of the particles at the lens 
end, the transfer matrix for the first, third and fifth-orders are 
determined and the errors of the matrix elements are also established. 
Calculations of this type at different injection energies of the ions [q . 
(UO-U1), where q =charge of the ions] give the transfer matrix for 
different voltage ratios. 
As results of the sequence of calculations, one obtains from the 
asymptotically projected trajectories paths the image side and object side 
focal lengths f, f', the positions of the principle planes and the 
aberration coefficients of the third and fifth order for the transfer 
matrix from the object side to the image side focal planes. 
From these matrix elements one obtains finally the aberration coefficients 
m.sub.ik defined by the equations (1) and (2) (c.f.E. Harting and F. H. 
Read, Electrostatic Lenses, Elsevier Scientific Publ. comp., Amsterdam, 
1976, P. 15): 
EQU r.sub.2 =f.THETA..sub.1 +m.sub.23 f.THETA..sub.1.sup.3 +m.sub.24 
(f/f')r.sub.1 -.THETA..sub.1.sup.2 +m.sub.25 (f/f'.sup.2)r.sub.1.sup.2 
.THETA..sub.1 +m.sub.26 (f/f'.sup.3)r.sub.1.sup.3 (1) 
EQU .THETA..sub.2 =-r.sub.1 /f'+m.sub.13 .THETA..sub.1.sup.3 +m.sub.14 
(1/f').THETA..sub.1.sup.2 r.sub.1 +m.sub.15 (1/f'.sup.2)r.sub.1.sup.2 
.THETA.+m.sub.16 (1/f'.sup.3)r.sub.1.sup.3 (2). 
In this relationship we present r.sub.1, .THETA..sub.1 location (r distance 
from the Z axis coinciding with the optical axis and direction (angle 
included with the positive Z axis) respectively of an ion in the object 
side focal plane and r.sub.2, .THETA..sub.2 are the location and angle of 
the same ion in the image side focal plane of the lens. 
The so defined coefficients m.sub.ik are normalized in the sense that they 
are independent from an optional similar enlargement or reduction of the 
dimensions of the respective lens. They can be used, therefore, directly 
to compare the quality of different lenses. 
FIG. 4 shows several of these normalized image distortion coefficients for 
the three-electrode grid lens shown in FIG. 3 in dependence upon the 
voltage ratio (U3-UO/U1-UO). FIG. 6 shows, for the purpose of comparison 
of these coefficients, those of field lenses of the type hitherto used in 
ion projection lithography and which are formed as tubular lenses with two 
electrodes. 
A comparison of the graph of FIG. 4 with that of FIG. 5 demonstrates 
immediately the improvement of the three-electrode grid lenses of FIG. 3. 
It is possible, with the three-electrode grid lens of the invention to 
exactly nullify each of the image distortion coefficients m.sub.13, 
m.sub.16, m.sub.23, m.sub.26, with a given voltage ratio (U3-UO)/U1-UO) 
whereby at these locations the remaining three coefficients which have not 
yet exactly vanished will have nevertheless very low values by comparison 
with those of the field lens (tubular lens). 
In order to estimate the image distortions which arise from the grid itself 
and thereby to determine a suitable degree of fineness of the grid it is 
sufficient to consider the focusing effect of a structure opening of a 
radius R which separates a region with a homogeneous field E.sub.1 from a 
region with a different field E.sub.2. 
This problem has already been dealt with in M. Szilagyi, Electron an Ion 
Optics, Plenum Press, New York (1988). An arrangement of this kind assumes 
a collecting lens with the focal length equation 
f.sub.g =4(U-UO)/E.sub.2 -E.sub.1) (3) 
where U is the potential at the location of the opening and E.sub.2 and 
E.sub.1 are field strengths ahead of and behind the grid G. 
An ion which traverses the opening is deflected by a maximum angle 
EQU .vertline..DELTA..THETA..vertline.=R/.vertline.f.sub.G 
.vertline.=R.vertline.(E.sub.2 
-E.sub.1).vertline./.vertline.4(U-UO).vertline. (4). 
This deflection effects a reduction in the image quality y To hold this 
effect as small as possible, the diameter (2R) of the grid openings and 
the field strength difference (E2-E1) between the front and back sides of 
the grid G must be held as small as possible. With modern grid fabrication 
techniques it is possible to provide diameters 2R in the range of 5 .mu.m 
and grid webs with widths of 1 .mu.m to 2 .mu.m between the openings. 
With respect to the field strength difference E.sub.2 -E.sub.1 it should be 
observed that it is indeed possible at a given location on the grid, by 
appropriate selection of the gird potential U2 to ensure exactly equal 
field strengths E.sub.1 and E.sub.2 to both sides of the grid G. However, 
because of the necessary different radii r.sub.1 and r.sub.2 of the two 
tubular electrodes R1 and R2 and the radial dependency of the field 
strengths, the field strengths E.sub.1 and E.sub.2 are generally different 
and over the grid range corresponding to the opening of the lens, relative 
field strength differences of (E.sub.2 -E.sub.1 /E.sub.1) of about 1% are 
inevitable. 
If this value is introduced into equation 
EQU .vertline..DELTA..THETA..vertline.=R/.vertline.f.sub.g 
.vertline.=R.vertline.(E.sub.2 
-E.sub.1).vertline./.vertline.4(U-UO).vertline. (4), 
the equality becomes .vertline..DELTA..THETA..apprxeq.10.sup.-8 /L(m), 
where L is a measure of the linear extent of the field of the grid lens 
and corresponds or is approximately equal to the distance between the 
tubular electrodes R1, R2 (FIG. 3 ). 
Since the dimension L lies in a range of multiples of 10 cm, it is possible 
to reduce the angular deflection according to equation (4) to a value of 
1.times.10.sup.-8 to 10.times.10.sup.-8, which in most cases is negligible 
by comparison to other aberrations (for example, chromatic blurring). Of 
course this only applies when the field strengths E.sub.1 and E.sub.2 are 
optimally matched as has been described. 
For simple grid lenses as in FIGS. 1 and 2, in which a field is provided 
only to one side of the grid, the deflection is higher by a factor of 
about 100, i.e. (.vertline..DELTA..THETA..vertline..apprxeq.10.sup.-6 to 
10.sup.-5). Lenses of this type without the second field, therefore, 
cannot be utilized for the purposes of the present invention. 
FIG. 6 details the effect of two collecting lenses L1 and L2, each of which 
is a three electrode grid lens, in an ion optical imaging system. 
The mask M which can form the structure to be imaged in the form of 
openings in a foil, for example silicon foil, is illuminated from an ion 
source with a very small virtual source size (approximately 10 .mu.m) 
through an illuminating lens BL transforming the ion beam divergent from 
the virtual source over into a parallel beam on irradiation of the mask. 
The mask is located approximately at the focal plane of the first 
collecting lens L1 following the mask M. 
The collecting lens L1 generates a crossover C (real image of the ion 
source Q) shortly behind the image side focal point. 
The object side focal point of the second collecting lens L2 disposed 
directly ahead of the wafer W is found at the location of the crossover C. 
As a consequence, the beam leaves the collecting lens L2 as a parallel 
bundle and is directed onto the wafer. The result is an approximately 
telecentric imaging system. 
This has the advantage that the imaging reduction ratio does not change 
with small changes in the position of the wafer W along the ion optical 
axis. 
This system has the following characteristics which are independent of the 
particular construction of the two collecting lens L2 and L2. 
(a) The image field resolving the structure of the mask is reproduced in 
the vicinity of the image side focal point of the lens L2 disposed ahead 
of the wafer W when the mask, as described, is located in the region of 
the object side focal point of the collecting lens L1 immediately 
following the mask M. 
(b) The ion beam bundle traversing a conventional collecting lens L1 
following the mask M generally has a barrel shaped distortion (region A) 
that after the crossover C is transformed into a pin cushion distortion 
(region B). With the use of the three-electrode grid lens as collecting 
lenses L1 and L2 it is possible to provide in the region A a pin cushion 
distortion and in region B a barrel shaped distortion. 
FIG. 7 shows the case where a barrel shaped distortion in region A and a 
pin cushion distortion in region B can result, utilizing the invention, in 
an additional deflection ahead of the wafer side collecting lens L2 which 
reduces the pin cushion distortion in region B and generates a region A' 
with a barrel shaped distortion. 
As a result, behind the wafer side collecting lens L2 there is a plane in 
which the distortions through the lens L1 and L2 are compensated. This 
applies only for the image distortion of third order and there remain, 
although highly reduced, image distortions of fifth order, i.e. 
distortions which are not completely nullified although they are reduced 
to a minimum. 
For a given image field size, these residual distortions are inversely 
proportional to the fifth power of the spacing between the mask M and the 
wafer W, all other parameters being the same and a corresponding change 
being made in the other dimensions of the optical system with the mask M 
and the wafer W. 
(c) In the arrangement of FIG. 6, as will be apparent from FIG. 8, there is 
also a compensation for the chromatic aberration or blurring as a result 
of the effects of the two collecting lenses L1 and L2 for a given image 
plane E behind the second collecting lens L2 ahead of the wafer W. A beam 
(represented in FIG. 8 by a broken line for the case in which the index of 
refraction change of the collecting lens L1 is less than that of 
collecting lens L2) with a somewhat smaller energy E.sub.0 -.DELTA.E.sub.0 
than the set point energy E.sub.0 is more strongly deflected in the first 
collecting lens L1 following the mask M and, as a result, enters the 
second lens L2 arranged ahead of the wafer W at a greater distance from 
the axis than the setpoint beam (shown as a continuous line trace) and for 
this reason and because of its lesser energy is deflected back toward the 
optical axis to a degree that it will meet the setpoint beam at a given 
distance behind the collecting lens L2 arranged ahead of the wafer W. In 
this plane E there is a disappearance of the chromatic aberration of first 
order. There remains even here, however, a residual distortion in the form 
of a second order chromatic aberration i.e. an aberration proportional to 
the square of the energy deviation from that of the setpoint beam. (The 
combination of two three-electrode grid lenses can also be so operated 
that the refractive power change of the lens L1 is greater than that of 
the lens L2. An analogous result is then obtained). 
(d) The three relevant planes, i.e. the Gaussian image plane of the mask M 
(FIG. 6), the plane of minimal distortion (FIG. 7) and the plane of 
minimal chromatic distortion (FIG. 8) in general do not coincide. By 
suitable choice of the collecting lenses L1 and L2 and the position of the 
ion source Q in the ion-optical axis, it can be observed that, while 
maintaining the approximate parallel beam path the three mentioned planes 
will coincide. In that case, the wafer W is located at the plane in which 
the three planes coincide so that in the thus selected image plane of the 
mask M, i.e. the location at which the wafer W is disposed, there is 
simultaneously a minimum image distortion as well as a minimum in the 
chromatic blurring. 
(e) The imaging ratio, i.e. the reduction factor, with which the structure 
of the mask M is imaged on the wafer W is given approximately by the ratio 
of the image-side focal length of the first collecting lens L1 following 
the mask M to the object side focal length of the second collecting lens 
L2 arranged ahead of the wafer W, by scaling (e.g. increasing or 
decreasing the size of the lens L2) it is, however, possible to vary the 
reduction factor of the imaging system while maintaining all other 
characteristics (simultaneous correction of image distortion and chromatic 
blurring at the Gaussian image point of the mask). 
The three-electrode grid lenses of the present invention in the context of 
the ion optical imaging system described have a number of advantages: 
(a) Third order image distortions can be sharply reduced for each of the 
two collecting lenses L1 and L2. Since the beam in the object side focal 
plane of lens L1 is approximately a parallel beam and the crossover C lies 
in the object side focal plane of lens L2,the distortion generated by 
these lenses is given by coefficients m.sub.26 for lens L1 and m.sub.13 
for lens L2 respectively as previously described which can vanish exactly 
by appropriate selection of the voltage ratios at the electrodes of the 
lenses. The freedom from third order distortion, therefore, no longer 
occurs in a single plane but rather over an entire range which reduces the 
boundary conditions which must be complied with and hence reduces 
limitations on the construction of the system. 
(b) A still greater advantage is the reduction of the residual image 
distortion at the location of the distortion minimum. This is a 
consequence of the fact that at the location of the distortion minimum, 
the significant coefficient for the fifth-order distortion is largely a 
product of the third order distortion coefficients of the two lenses L1 
and L2. With the three electrode grid lenses of the invention, the 
contributions to this product are practically vanishing and thus the 
residual distortion is any caused by the very small fifth order terms of 
the lenses. 
As examples two separate arrangements were numerically simulated with high 
precision: 
One arrangement A utilized approximately identical ion energies at the mask 
and wafer and the second arrangement B accelerated the ions between mask 
and wafer by a factor greater than unity. 
Corresponding to requirements of the semiconductor industry, the imaging of 
a mask M formed with a structure of openings within an area of 60.times.6 
mm.sup.2, was effected on a chip area of 20.times.20 mm.sup.2 on a wafer W 
utilizing a lens system as shown in FIG. 6. The illuminating lens BL was 
an Einzel lens which generated an approximately parallel ion beam at the 
location of the mask M. 
The first collecting lens L was a three electrode grid lens according to 
FIG. 3 on the electrodes of which voltage ratios were applied which caused 
vanishing of the coefficient m.sub.26 (equation 1 and FIG. 4). 
The second collecting lens L2 was also a three electrode grid lens as shown 
in FIG. 3. In case A this lens was traversed from right to left and 
utilized as a retarding lens so that, the ion energies at the location of 
the mask M and at the location of the wafer W were approximately the same. 
In case B, the second collecting lens L2, like the first collecting lens 
L1 was operated as accelerating lens, i.e. traversed from left to right. 
The voltage ratio at collecting lens L2 in both cases was chosen so that 
the coefficient m.sub.13 vanished. 
The simulation of the imaging of the mask structure was effected by the 
standard method of matrix manipulation. For the collecting lenses L1 and 
L2 the fifth-order transfer matrices were calculated by the above 
mentioned methods. 
These calculations were repeated utilizing an optimization program with 
slight variation in the starting parameters until a minimum of the image 
distortion and a chromatic aberration at the location of the Gaussian 
image point of the mask structure on the wafer was achieved. 
The following considerations also apply: 
(a) Parallel beam at the output of the imaging system (i.e. ahead of the 
wafer and behind the collecting lens L2 position ahead of the wafer. 
(b) Gaussian imaging of the mask M on the wafer W. 
(c) Imaging ratio mask: wafer 3:1. 
The following parameters were varied for the determination of the image 
distortion minimum while the boundary conditions were maintained. 
(a) Distance between the mask M and the collecting lens L1 following same. 
(b) Distance between the two collecting lenses L1 and L2. 
(c) Distance between the wafer W and the collecting lens L2 ahead of the 
wafer. 
(d) Scaling factor, i.e. enlargement or reduction of the collecting lens L2 
ahead of the wafer W. 
For further optimization, the voltage ratios between the electrodes of the 
two collecting lenses L1 and L2 are varied. It turned out that the ratios 
selected to start with corresponding to m.sub.26 =O for L1 and m.sub.13 =O 
for L2, were almost optimal. 
An effort was also made to determine whether resolution limitations 
developed as a function of the final size of the grid openings. A diameter 
2R of 5 .mu.m was selected for the grid openings. This investigation was 
based upon the following: 
1. The maximum value of the field strength difference E.sub.2 -E.sub.1 for 
the illuminated part of the grid was calculated from the potential 
distribution of the lenses. 
2. With the aid of equation (3), the focal length of the "grid opening mini 
lens" and the resulting maximum deflection of the boundary beam of a grid 
opening were calculated. 
3. By the described matrix methods, the deflection angle was transformed 
into corresponding spatial deviations at the location of the wafer W. 
These calculations were carried out separately for the collecting lenses 
L1 and L2 and, following these calculations, the results were added to 
determine a secure upper boundary for the effect of the grid openings. The 
results of these calculations are summarized in the following table. 
TABLE 
______________________________________ 
ARRANGE- ARRANGE- 
MENT MENT 
A B 
______________________________________ 
Design Field of Mask M 
60 .times. 60 mm.sup.2 
60 .times. 60 mm.sup.2 
Voltage Ratio of Collecting 
5.90 5.57 
Lens L1 
Scaling.sup.1) of Collecting Lens L1 
1.50 1.04 
Voltage Ratio of Collecting 
0.1713 6.07 
Lens L2 
Scaling.sup.1) of Collecting Lens L2 
0.50 0.93 
Distance Mask M - Wafer W 
3.15 m 3.00 m 
Reduction Factor 3.0 3.0 
(Ion Energy).sub.Wafer /(Ion Energy).sub.Mask 
1.01 33.8 
Maximum Distortion.sup.2) (within the 
0.015 .mu.m 
0.030 .mu.m 
20 .times. 20 mm.sup.2 illumination field of 
Wafer W) 
Maximum Chromatic Blurring 
0.019 .mu.m 
0.035 .mu.m 
(based on the energy spread.sup.3)) 
Maximum Blurring Based on Lens 
0.020 .mu.m 
0.037 .mu.m 
Effect of the Grid Openings.sup.4) 
______________________________________ 
.sup.1) Similar enlargement or reduction relative to FIG. 3. 
.sup.2) Maximum deviation of an image point from the ideal image. 
.sup.3) For energy spread of the ions at ion source output of .DELTA.E = 
.+-. 3 Ev, where E is the energy of the ions at the output of the ion 
source. 
.sup.4) For grid openings of 5 .mu.m diameter. 
It was found that a structure of a mask field of 60 .mu.mm.times.60 mm 
could be imaged on a wafer with a reduction by a factor of 3 and that 
simultaneously a minimum of the image distortion and blurring of the image 
as a result of chromatic aberration caused by lack of sharpness of the ion 
energy could be achieved at the location of the image. The maximum 
distortion at the location of the image as a result of fifth-order image 
distortion in the total field was less than 0.015 .mu.m (case A) and less 
than 0.03 .mu.m in case B. The blurring of the image was less than 0.04 
.mu.m (case A) and less than 0.07 .mu.m (case B) for a mask-wafer distance 
of about 3 meters. 
If one compares these results with the values in U.S. Pat. No. 4,985,634, 
the improvement obtained with the use of three electrode grid lenses as 
collecting lenses between the mask and wafer will be apparent. 
The machine in U.S. Pat. No. 4,985,634, with a machine length (mask-wafer 
spacing) of 2.1 m and an image field of 10 mm.times.10 mm had a maximum 
distortion of less than 0.2 .mu.m. For a comparison of the two systems, 
the distortion values must be normalized to the same image field sizes. By 
such normalization, it can be found that in an ion projection lithographic 
system according to this United States Patent for an image field of 20 
mm.times.20 mm when a maximum distortion of 0.4 .mu.m is to be reached, 
the machine length must be increased to 4.2 m (an increase in the system 
factor by a factor of 2) with the use of three electrode grid lenses 
according to the invention the length of the ion projection system can be 
reduced by approximately 15% (of 4.2 m) and simultaneously the distortion 
reduced by a factor of 10-20. This difference greatly increases the 
applicability of ion projection lithographic systems with three electrode 
grid lenses. 
With three electrode grid lenses of the invention, moreover, the depth of 
field can be significantly increased since the image distortions of the 
collecting lens L1 and L2 are so small that compensation of aberration is 
less critical. 
In the use of three electrode grid lenses in an ion beam lithographic 
system according to the invention, the illumination of the mask M by an 
ion source Q with very small virtual source size (approximately 10 .mu.m) 
requires the following observations: 
With previously used ion sources of limited virtual source size, a highly 
inhomogeneous intensity developed within the illumination field. In this 
case, from a mask point, a beam ion is trained on the location of the grid 
with a size which could be of the same order of magnitude as that of the 
grid opening. The mask-wafer transmission would vary strongly with the 
periodicity of the grid if such a grid was used. This can be overcome by 
wobbling of the grid by using a more extended virtual ion source or by 
periodic (wobbling) of the virtual source. 
Since it is important that ions on wobbling of the grid reach the wafer 
from every point of the structure of the mask., the grid is so moved that 
within the illumination time, each point on the grid plane is transverse 
to the same fraction of the total ion flux. This is achieved by shifting 
the grid in two mutually perpendicular directions in the grid plane with 
two different frequencies and with an amplitude corresponding to several 
grid opening diameters. This means an oscillation amplitude in each 
direction of several 10 .mu.m and frequencies in the range of 100 to 1000 
Hz, preferably utilizing a piezoelectric driver which has been found to be 
free from problems. 
In earlier ion lithographic systems, ion sources with virtual source size 
were required which were so small that the opening angle of the beam cone 
could be minimized and the aberrations at the lens L1 and L2 should have 
no significant effect with respect to the resolution. These requirements 
meant that the source diameter had to be approximately 10 .mu.m. With the 
present invention, therefore, while such sources can still be used, the 
image distortions are so much smaller that significantly larger opening 
angles and ion source sizes can be used. 
Numerical calculations have indicated that in arrangements like those of 
the table, a virtual source size of 60 .mu.m in diameter will only 
contribute 7 nm to the resolution in case A and 14 nm to the resolution in 
case B. This effect is extremely small compared to other effects on 
resolution. With such large virtual sources, as can also be demonstrated 
by calculation, the spread of the beam bundle from a mask point at each of 
the two grids of the lens L1 and L2 is about 30 .mu.m, covering a region 
of 20 grid openings, thereby ensuring a practically uniform transmission 
from the mask to the wafer. This can easily be achieved in the system of 
the invention and has the further advantage that the space charge at the 
location of the crossover C (FIG. 6) is significantly smaller so that 
undesired space charge effects can be avoided. With a 60 .mu.m source Q, a 
significantly higher beam current can be achieved. 
An enlarged ion source can also be simulated by electrostatically wobbling 
the ion beam illuminating the mask. This corresponds to a periodic shift 
of the source transverse to the ion optical axis. This can be achieved 
also by providing at an appropriate location between the ion source and 
the illumination lens BL, the electrostatic multipole as has been 
described and varying as a function of time the dipole fields in the X and 
Y directions. The directions in which the beam impinges on the mask is 
thereby varied also as a function of time, corresponding thereto a shift 
in the virtual source in the X and Y directions and therefore to a 
spreading of the ion source.