Method for astigmatism correction in charged particle beam systems

A method for calculating and correcting an astigmatism error in a charged particle beam system. Images are collected during a single focus sweep of the charged particle beam system. Different orientations of image features, such as lines on a stigmation target, are analyzed. Optimum sharpness or best focus values are obtained as a function of the objective lens settings. Appropriate changes to the settings of the astigmatism correctors are computed by taking a linear combination of optimum sharpness values associated with the different orientations of image features. Proper settings of the objective lens and the astigmatism correctors result in focusing of the beam into a "small" spot. In a scanning electron microscope, for example, two sets of quadrupole compensation coils are typically used as astigmatism correctors.

TECHNICAL FIELD 
The present invention relates generally to charged particle beam systems 
and, more specifically, to a method which enhances the focusing properties 
of the charged particle beam system through astigmatism correction. 
BACKGROUND OF THE INVENTION 
A typical goal of charged particle systems is to focus a particle beam into 
a small spot. This goal is accomplished using a column of magnetic and 
electrostatic lenses that set the focal properties of the beam. A 
cross-section of an exemplary column of magnetic and electrostatic lenses 
is shown in FIG. 7. Such a column includes an objective lens 706, a double 
deflection coil 702, a stigmator 704, and a beam limiting aperture 708. 
The column is disposed along a longitudinal axis a-a; the beam travels 
along this axis. 
There are many imperfections in tools that use charged particle beams. 
These imperfections cause, in turn, imperfections in the focusing 
properties of the tool. One imperfection that prevents sharp focus is 
referred to as astigmatism. The causes of astigmatism may be traced to 
many sources: lens aberrations, mechanical misalignments, and particle 
contaminants, to name just a few. Specifically, astigmatism results in the 
focal length in some direction transverse to the direction of the charged 
beam to be different from the focal length in the orthogonal transverse 
direction. Simultaneous best focus in the two transverse directions (best 
focus) is thereby prevented. An example of the effects of astigmatism is 
shown in FIG. 8. FIG. 8(a) shows a gray scale image of a sample contact 
hole in optimal focus; FIGS. 8(b), 8(c), 8(d), and 8(e) show stigmated 
images of the same contact hole. FIG. 8(b) shows blurring of the contact 
hole image in the -45.degree. direction transverse to the direction of the 
charged beam. FIG. 8(c) shows blurring of the contact hole image in the 
+45.degree. direction transverse to the direction of the charged beam. 
FIG. 8(d) shows blurring of the contact hole image in the vertical 
direction transverse to the direction of the charged beam. FIG. 8(e) shows 
blurring of the contact hole image in the horizontal direction transverse 
to the direction of the charged beam. 
To combat the problem of astigmatism, many charged particle beam systems 
are fitted with adjustable stigmator coils. These compensation coils are 
used to correct the accumulated effects of astigmatism along the path of 
the beam. For unknown reasons, however, the correct compensator settings 
tend to change a periodically. 
In particular, modern scanning electron microscopes (SEMs) are equipped 
with two sets of quadrupole compensation coils. FIG. 9 shows a schematic 
cross-section of a SEM 900. The SEM 900 includes: an electron gun 902, 
condenser lenses 904, scan coils 906, an objective lens 907, a cathode ray 
tube (CRT) 908, a scan generator 910, and an amplifier 912. 
FIG. 10(a) shows a cross-section view of an eight-pole iron yoke that may 
be configured to produce two compensators. FIGS. 10(b) and 10(c) 
illustrate wiring schematics for the eight-pole iron yoke shown in FIG. 
10(a). In many applications, such as semiconductor manufacturing, 
limitations in focusing properties or astigmatism in metrology tools is a 
major stumbling block. For example, as semiconductor manufacturing 
advances into the sub 0.18 .mu.m domain, the requirements for focusing and 
astigmatism correction of critical dimension-SEMs (CD-SEMs) metrology 
tools have become so severe that human operators can no longer make these 
adjustments with sufficient accuracy and repeatability. Therefore, the 
development of sound and consistent methodologies for determining proper 
compensator coil settings is crucial. 
The difficulty with using quadrupole lenses, which is a consequence of 
Maxwell's laws, is that adjustment of the focusing properties in one 
direction causes defocusing in an orthogonal direction. In order to 
properly focus the beam, the settings of the quadrupole compensation coils 
should be adjusted in at least two directions simultaneously with an 
optimization of the main objective lens excitation. 
Adjustments to corrector quadrupole lenses are often performed by human 
operators. Human operators use subjective criteria to determine the 
optimal quadrupole compensation settings. This presents serious 
difficulties: two different measurements performed by the same tool on the 
same specimen, each time having been adjusted by a different operator, 
yield two different results. Discrepancies between such measurement 
results may be intolerable with respect to an error budget. Error budgets 
are constantly narrowing, as pointed out above, to meet the new demands of 
semiconductor circuit technologies. Therefore, it is desirable to 
determine correct astigmation corrector settings by automated means, and 
by using objective, well-defined focusing or sharpness criteria. 
Many charged particle beam systems are already equipped with an automated 
focusing routine for the objective lens. A block diagram outlining the 
steps involved in such an automated focusing routine is displayed in FIG. 
11. In step 1102 a focus sweep is initiated. In step 1104 the focus 
setting of an objective lens is determined. In step 1106 a target is 
scanned and an image containing information about the target is obtained. 
In step 1108 the information contained in the image obtained is analyzed 
to determine certain sharpness measures. In step 1109 a test is performed 
to determine whether sufficient sharpness measure information has been 
obtained in order to detect a sharpness maximum. If so, the objective lens 
is set for maximum sharpness in step 1110. If the information obtained 
thus far in the focus sweep is insufficient, then the focus setting of the 
objective lens must be varied and the process of steps 1104-1110 repeated. 
A block diagram illustrating the steps involved in a conventional 
astigmatism correction method is displayed in FIG. 12. In step 1202 the 
astigmatism algorithm is initiated. In step 1204 the setting of the 
X-astigmatism corrector is determined. In step 1206 a focus sweep such as, 
for example, the focus sweep of FIG. 11 is initiated. In step 1208 a test 
is performed to determine whether sufficient sharpness measure information 
has been obtained in order to set the X-astigmatism corrector properly. If 
the information obtained thus far is insufficient, then steps 1204, 1206, 
and 1208 are repeated. The function of steps 1210, 1212, and 1214 
performed for the Y-astigmatism corrector are analogous to the function of 
steps 1204, 1206, and 1208 performed for the X-astigmatism corrector. 
Conventional astigmatism correction methods systematically step through a 
range of magnet currents for one of the astigmation correctors. At each 
setting of the corrector magnet current, a best focus is determined for 
the tool, e.g. a SEM, using the automated focus routine of the tool. The 
automated focus routine may work according to a number of different 
principles each corresponding to a sharpness measure such as, for example, 
contrast maximizing, maximizing high spatial frequency signal content, or 
the like. 
Central to its application, however, is the systematic stepping through the 
objective lens current (OLC) as well as other steps taken to ensure that a 
sharpness measure curve with a clear maximum is obtained. At each setting, 
the equivalent of an image of a sample is obtained from the tool for 
analysis. Best focus corresponds to a maximum in the sharpness measure 
curve. Best astigmation corrector (magnet current) setting is then 
determined by finding the maximum best focus sharpness measure as a 
function of corrector magnet current. The process can then be repeated for 
the second astigmation corrector. For this process to succeed, it is 
important for the sample to contain edges along the principal axes of the 
two astigmation correctors. It is also important that the focus routine be 
sensitive to the sharpness of those edges. 
Conventional astigmation correction methods may involve many applications 
of the automated focus routine of the tool (see FIG. 12); this repetition 
detracts from the efficiency of the method and may cause sample damage. In 
addition, astigmation correction by human operators may no longer be 
sufficiently accurate for current and future industrial applications. 
Proprietary automated astigmation correction routines may not, by their 
nature, provide the user of the tool with the precise criteria and 
methodology used in the computation of the astigmatism error and its 
correction. The effectiveness and appropriateness of use of such 
proprietary routines is hence difficult to evaluate. 
These deficiencies of conventional and proprietary methodologies, and of 
human operators, invoke a need to determine efficiently proper astigmation 
corrector settings by automated means using objective, well-defined 
focusing or sharpness criteria. An object of the present invention is to 
provide a methodology for computing and correcting astigmatism by 
automated means in a charged particle beam system based on sharpness 
criteria. Another object of the present invention is to provide users of 
charged particle beam systems with objective means for comparison of 
astigmatism error measurement and correction made by, for example, 
proprietary routines or the like. 
SUMMARY OF THE INVENTION 
To achieve these and other objects, and in view of its purposes, the 
present invention provides a method for determining and correcting an 
astigmatism error in a charged particle beam system. The method includes 
the steps of choosing a plurality of objective lens settings, collecting a 
plurality of images each corresponding to at least one of the plurality of 
objective lens settings, determining a plurality of sharpness measure 
values each associated with at least one of the plurality of images, 
finding a plurality of optimum sharpness values based on the plurality of 
sharpness measure values, computing the astigmatism error of the charged 
particle beam system based on the plurality of optimum sharpness values, 
and correcting the astigmatism error of the charged particle beam system 
by adjusting an astigmatism corrector. 
It is to be understood that both the foregoing general description and the 
following detailed description are exemplary, but are not restrictive, of 
the invention. Although both the foregoing general description and the 
following detailed description focus on SEMs, the method of the present 
invention is also applicable to other charged particle beam systems such 
as microprobe machines and focused ion beam tools.

DETAILED DESCRIPTION OF THE INVENTION 
A flow diagram illustrating the method for determining an astigmatism error 
in a charged particle beam system according to the present invention is 
shown in FIG. 1. The algorithm begins at step 102. A focus sweep of the 
objective lens current is performed in the loop comprising steps 106, 110, 
114, and 118. In step 106, the focus or objective lens current is set or 
incremented, then in steps 110 and 114 image data is collected and 
analyzed for each increment. A half-dozen saved images are a typical 
example of data from a single focus sweep of the objective lens current. 
For each of the images obtained at each of the settings of the objective 
lens current, several sharpness measure values are determined in step 114. 
Each image may be analyzed, for example, for sharpness measure values 
along the four directions corresponding to the principal axes of the two 
astigmation correctors. In step 118, optimum sharpness values (best focus) 
over all the objective lens current settings are found. For example, for 
each of the four directions, the best focus as a function of OLC may be 
determined. Finally, in step 122 the astigmatism error of the charged 
particle beam system is computed from the optimum sharpness values and 
from known rigid properties of the system. It should be emphasized that 
the method outlined above for computing the astigmatism error may be 
completed using image data from a single focus sweep. 
The astigmatism error and optimal sharpness value (best focus) information 
thus deduced can in turn be used to compute the proper settings for the 
astigmatism correctors, as indicated in step 126. For example, based on 
the best focus settings in each of the four directions, as a function of 
OLC, the proper current settings for the two corrector magnets and 
simultaneously for the objective lens may be calculated. 
In a first exemplary embodiment of the present invention, the correct 
astigmation coil compensation settings are computed by using an auto-focus 
algorithm of a SEM on four neighbor lines patterned on a wafer with 
different orientations: vertical, horizontal, plus forty-five degrees, and 
minus forty-five degrees. If all four best focus values result in the same 
corrector current setting, then astigmatism compensation has been 
correctly set. If the best focus values differ then, after a single focus 
sweep, the correct current settings for the two quadrupole correctors may 
be computed from the four best focus value determinations. 
Each astigmation corrector distorts the electron beam spot into an ellipse. 
For a SEM in which one of the astigmation correctors produces an ellipse 
with major and minor axes in the vertical and horizontal directions, often 
called the Y-astigmation corrector, the correct change in corrector 
current setting is proportional to the difference between the best focus 
value associated with the vertical and horizontal orientations. Typical 
quadrupole correctors have a second corrector rotated by forty-five 
degrees with respect to the first. In the present embodiment, the second 
corrector, often called the X-astigmation corrector, distorts the electron 
beam spot into an ellipse with major and minor axes along the plus and 
minus forty-five degree directions. The correct change in corrector 
current setting for the X-astigmation corrector is proportional to the 
difference between the optimum focus measure values associated with the 
plus and minus forty-five degree orientations. 
The constants of proportionality may be determined by plotting the best 
focus values for the four line orientations as each of the two corrector 
settings is systematically changed. These will be straight line trends. In 
the present embodiment, the lines associated with the plus and minus 
forty-five degree orientations will remain flat as a function of 
Y-astigmation corrector current change, while the vertical and horizontal 
best focus trends will have equal but opposite slopes, say "m." The 
Y-astigmation corrector proportionality constant is then 1/(2 m). 
Similarly, the lines associated with the vertical and horizontal 
orientations will remain flat as a function of X-astigmation corrector 
current change, while the plus and minus forty-five degree best focus 
trends will have equal but opposite slopes, say "n." The X-astigmation 
corrector proportionality constant is then 1/(2 n). 
FIGS. 2(a) and 2(b) are graphs of an exemplary relationship between the 
best focus value and the X- and Y-astigmatism corrector current settings, 
respectively, for each of the four above-mentioned orientation lines. It 
should be noted that the graphs show rigid properties of the SEM. That is, 
the properties displayed in FIGS. 2(a) and 2(b) may be, for example, 
provided by the manufacturer of the SEM. The graphs displayed in FIGS. 
2(a) and 2(b) show how the best focus values may vary around the ideal 
operating point in the case where the quadrupole principal axes are 
aligned with the four line orientations. The ideal operating point is 
found by keeping the X-astigmatism corrector current setting at its proper 
value for compensation while the Y-astigmatism setting is changed and vice 
versa. In FIG. 2(a), the correct setting for the X-astigmatism corrector 
current is given by the point of intersection of the lines associated with 
the plus forty-five degree and minus forty-five degree orientations. 
Similarly, in FIG. 2(b), the correct setting for the Y-astigmatism 
corrector current is given by the point of intersection of the lines 
associated with the vertical and horizontal orientations. 
FIGS. 3(a) and 3(b) show how the best focus for the various line 
orientations varies around an arbitrary operating point such that the 
X-astigmatism corrector current setting is not ideal as the Y-astigmatism 
corrector current is varied, and vice versa. The quadrupole axes are 
aligned in this case, however, with the various line orientations. 
A second embodiment of the present invention addresses the more general but 
less common case in which the quadrupole corrector axes are not aligned 
with the vertical, horizontal, plus and minus forty-five degree 
orientations. The best focus trend slopes will all be non-zero. In order 
to find and correct the astigmatism error, the desired change in X- and 
Y-astigmatism corrector current is computed. The proper Y-astigmation 
corrector current change is equal to the difference between vertical and 
horizontal best focus values times a first constant plus the difference 
between plus forty-five degree and minus forty-five degree best focus 
values times a second constant. The proper X-astigmation corrector current 
change is equal to the difference between vertical and horizontal best 
focus values times a third constant plus the difference between plus 
forty-five degree and minus forty-five degree best focus values times a 
fourth constant. 
FIGS. 4(a) and 4(b) show how the best focus for the four line orientations 
varies around the ideal operating point for the case when the quadrupole 
principal axes are not aligned with the four line orientations. The 
symmetry of the orientation pairs should be noted. That is, best focus 
lines associated with orthogonal orientations have equal but opposite 
slopes. The focus trends illustrated in FIGS. 4(a) and 4(b) may be used to 
determine the first through fourth constants of proportionality. A linear 
algebraic calculation may be performed to provide the four constants of 
proportionality. 
FIGS. 5(a) and 5(b) show the case in which the quadrupole axes are not 
aligned with the four line orientations and the variation of each 
astigmatism corrector current value is performed while the other 
astigmatism corrector current value is not at the ideal value for 
compensation. FIGS. 5(a) and 5(b) illustrate that the phenomenon of 
astigmatism associated with the present invention could be difficult to 
interpret. The method of the present invention may be used for rapid 
astigmatism correction based on such graphs. 
The constants of proportionality in the general case may be determined as 
follows: the SEM best focus is measured and graphed as a function of X- 
and Y-astigmatism corrector setting for the four line orientations as 
shown, for example, in FIGS. 4(a) and 4(b). For X-astigmatism, denote the 
slopes of the vertical and horizontal line trends by p and -p, 
respectively, and the slopes of the plus and minus forty-five degree line 
trends by q and -q, respectively. For Y-astigmatism, denote the slopes of 
the vertical and horizontal line trends by r and -r, respectively, and the 
slopes of the plus and minus forty-five degree line trends by -s and s, 
respectively. When the corrector coils are wound with the same number of 
windings and are located at the same position, then the high symmetry of 
the configuration implies p=s and q=r. These assumptions regarding coil 
windings and positioning are not, however, made in the following. Denote 
the best focus values for the horizontal, vertical, plus forty-five 
degrees, and minus forty-five degrees line orientations, respectively, by 
BF.sub.h, BF.sub.v, BF.sub.+45, BF.sub.-45. The best focus values may be 
computed by 
EQU BF.sub.v =p*.DELTA.X.sub.astigm +r*.DELTA.Y.sub.astigm +BF.sub.o 
EQU BF.sub.h =-p*.DELTA.X.sub.astigm -r*.DELTA.Y.sub.astigm +BF.sub.o 
EQU BF.sub.+45 =q*.DELTA.X.sub.astigm -s*.DELTA.Y.sub.astigm +BF.sub.o 
EQU BF.sub.-45 =-q*.DELTA.X.sub.astigm +s*.DELTA.Y.sub.astigm +BF.sub.o, 
where BF.sub.o is the common best focus value at optimal astigmatism 
correction, .DELTA.X.sub.astigm and .DELTA.Y.sub.astigm are the respective 
X-astigmation and Y-astigmation setting differences from optimal 
compensation. The proper change in corrector settings for the two 
astigmatism correctors, .DELTA.X.sub.astigm and .DELTA.Y.sub.astigm may be 
determined by solving an equation of the following form: 
EQU .DELTA.Y.sub.astigm =K.sub.1 *(BF.sub.v -BF.sub.h)+K.sub.2 *(BF.sub.+45 
-BF.sub.-45) 
EQU .DELTA.X.sub.astigm =k.sub.3 *(BF.sub.v -BF.sub.h)+K.sub.4 *(BF.sub.+45 
-BF.sub.-45), 
where 
##EQU1## 
The most sensitive determinations of the correct astigmatism corrector 
current values are performed when the line orientations patterned on a 
target are aligned with the quadrupole axes. When such alignment is 
achieved, only one difference measurement is involved for each astigmatism 
corrector. The corrector axes orientation yielding alignment may be 
determined from the trend lines on a stigmation target by finding the 
rotation transformation that reduces each corrector current value change, 
.DELTA.Y.sub.astigm and .DELTA.X.sub.astigm, to depend on only one rotated 
set of orthogonal line orientations. 
Because many modern SEMs provide a readout of their best focus setting, for 
example, the method of the present invention may be applied immediately 
regardless of the best focus algorithm used. For charged particle beam 
systems that determine a best focus setting along a specific direction, 
which can be rotated, a variation of the method of the present invention 
may be applied. For a wafer geometry with edges in all directions, such as 
a contact hole, the best focus is determined along all four of the 
astigmation corrector axes. The corrector current value changes can then 
be calculated as above. This methodology may be implemented in a CD-SEM, 
in software for example, to provide a fully automatic astigmation 
correction routine. 
If the line orientations on a target are sufficiently close, so that they 
are at the same SEM working distance, then only three focus measurement 
may be needed to determine the two corrector current value changes, 
.DELTA.Y.sub.astigm and .DELTA.X.sub.astigm. In practice, a fourth 
measurement is useful as a consistency check. If a contact hole geometry 
may be used, then the closeness condition is generally guaranteed. 
When performing measurements on semiconductor wafers, a special stigmation 
target (sometimes referred to as a kerf target) would generally guarantee 
the ability to measure the astigmatism error regardless of chip patterns. 
An important property of the stigmation target is that the straight line 
orientations appear in equal proportions. An example of a stigmation 
target is shown in FIG. 6. Such a target may be used on different types of 
SEMs. For example, for a SEM in which the focus algorithm is not known, a 
field of view is chosen such that one line orientation is visible, then 
the visible line is scanned. Different directions are scanned by changing 
the field of view for each of the line orientations. The images obtained 
may be used to determine the best focus settings. For a SEM in which the 
direction along which best focus is determined may be specified, a field 
of view including the whole target may be considered. 
Many conventional auto-stigmation techniques rely on specialized non-wafer 
targets or proprietary analyses, where the relationship to actual line 
width measurements is not quantitatively clear. The method of the present 
invention provides a quantitative way to judge other astigmation 
correction techniques. In the present invention the astigmatism error is 
determined by measurements in terms of the actual focus errors. 
Although illustrated and described herein with reference to certain 
specific embodiments, the present invention is nevertheless not intended 
to be limited to the details shown. Rather, various modifications may be 
made in the details within the scope and range of equivalents of the 
claims and without departing from the spirit of the invention.