U.S. patent application number 11/029052 was filed with the patent office on 2006-07-06 for ion beam scanning control methods and systems for ion implantation uniformity.
This patent application is currently assigned to Axcelis Technologies, Inc.. Invention is credited to Victor M. Benveniste, William F. DiVergilio, Peter L. Kellerman.
Application Number | 20060145096 11/029052 |
Document ID | / |
Family ID | 36579155 |
Filed Date | 2006-07-06 |
United States Patent
Application |
20060145096 |
Kind Code |
A1 |
Benveniste; Victor M. ; et
al. |
July 6, 2006 |
ION BEAM SCANNING CONTROL METHODS AND SYSTEMS FOR ION IMPLANTATION
UNIFORMITY
Abstract
Methods are provided for calibrating an ion beam scanner in an
ion implantation system, comprising measuring a plurality of
initial current density values at a plurality of locations along a
scan direction, where the values individually correspond to one of
a plurality of initial voltage scan intervals and one of a
corresponding plurality of initial scan time values, creating a
system of linear equations based on the measured initial current
density values and the initial voltage scan intervals, and
determining a set of scan time values that correspond to a solution
to the system of linear equations that reduces current density
profile deviations. A calibration system is provided for
calibrating an ion beam scanner in an ion implantation system,
comprising a dosimetry system and a control system.
Inventors: |
Benveniste; Victor M.;
(Gloucester, MA) ; Kellerman; Peter L.; (Essex,
MA) ; DiVergilio; William F.; (Brookline,
MA) |
Correspondence
Address: |
ESCHWEILER & ASSOCIATES, LLC;NATIONAL CITY BANK BUILDING
629 EUCLID AVE., SUITE 1210
CLEVELAND
OH
44114
US
|
Assignee: |
Axcelis Technologies, Inc.
|
Family ID: |
36579155 |
Appl. No.: |
11/029052 |
Filed: |
January 4, 2005 |
Current U.S.
Class: |
250/492.21 |
Current CPC
Class: |
H01J 2237/31703
20130101; H01J 37/3171 20130101 |
Class at
Publication: |
250/492.21 |
International
Class: |
H01J 37/08 20060101
H01J037/08 |
Claims
1. A method for calibrating an ion beam scanner in an ion
implantation system, the method comprising: measuring a plurality
of initial current density values at a plurality of locations along
a scan direction, the initial current density values individually
corresponding to one of a plurality of initial voltage scan
intervals and one of a corresponding plurality of initial scan time
values; creating a system of linear equations based on the measured
initial current density values and the initial scan time values;
and determining a set of scan time values for the voltage scan
intervals corresponding to a solution to the system of linear
equations that reduces current density profile deviations.
2. The method of claim 1, wherein the initial current density
values are measured at an integer number m locations, wherein the
individual current density values correspond to one of an integer
number n initial voltage scan intervals, and wherein m is greater
than n.
3. The method of claim 2, wherein the m locations and the n initial
voltage scan intervals do not correspond with one another.
4. The method of claim 2, wherein creating the system of linear
equations comprises: forming a matrix A of the measured initial
current density values with m rows corresponding to the m locations
along the scan direction and n columns corresponding to the n
initial voltage scan intervals and time values; forming an initial
time vector T.sub.0 comprising the n initial scan time values; and
computing an initial profile vector P.sub.0 comprising m initial
current density profile values, wherein the initial profile vector
P.sub.0=A*T.sub.0.
5. The method of claim 4, wherein determining a set of scan time
values comprises: computing a profile average value P.sub.AVG as
the average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.01+P.sub.02+ . . . +P.sub.0m); computing a
profile deviation vector .DELTA.P comprising m profile deviation
values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1 through
m; computing an inverse matrix A.sup.-1; multiplying the inverse
matrix A.sup.-1 and the profile deviation vector .DELTA.P to obtain
a time deviation solution vector .DELTA.T.sub.SOLUTION comprising n
scan time deviation values, wherein
.DELTA.T.sub.SOLUTION=A.sup.-1*.DELTA.P; and computing a scan time
solution vector T.sub.SOLUTION as the sum of the time deviation
solution vector .DELTA.T.sub.SOLUTION and the initial time vector
T.sub.0, the scan time solution vector T.sub.SOLUTION comprising
the set of scan time values corresponding to the solution to the
system of linear equations that reduces current density profile
deviations, wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0.
6. The method of claim 5, wherein the inverse matrix A.sup.-1 is
computed using singular value decomposition (SVD).
7. The method of claim 6, further comprising: selectively
truncating the matrix A by eliminating one or more columns having
no non-zero entries to form a truncated matrix A.sub.T having m
rows corresponding to the m locations along the scan direction and
n' columns corresponding to the n' remaining initial voltage scan
intervals and time values, wherein n' is less than n; and
selectively truncating the initial time vector T.sub.0 to form a
truncated initial time vector T.sub.0T comprising n' initial scan
time values; wherein the initial profile vector P.sub.0 is computed
as P.sub.0=A.sub.T*T.sub.0T; and wherein determining the set of
scan time values comprises: computing the profile average value
P.sub.AVG as the average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.01+P.sub.02+ . . . +P.sub.0m); computing a
profile deviation vector .DELTA.P comprising m profile deviation
values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1 through
m; computing an inverse matrix A.sub.T.sup.-1; multiplying the
inverse matrix A.sub.T.sup.-1 and the profile deviation vector
.DELTA.P to obtain a time deviation solution vector
.DELTA.T.sub.SOLUTION comprising n' scan time deviation values,
wherein .DELTA.T.sub.SOLUTION=A.sub.T.sup.-1*.DELTA.P; and
computing a scan time solution vector T.sub.SOLUTION as the sum of
the time deviation solution vector .DELTA.T.sub.SOLUTION and the
truncated initial time vector T.sub.0T, the scan time solution
vector T.sub.SOLUTION comprising the set of scan time values
corresponding to the solution to the system of linear equations
that reduces current density profile deviations, wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0T.
8. The method of claim 4, further comprising: selectively
truncating the matrix A by eliminating one or more columns having
no non-zero entries to form a truncated matrix A.sub.T having m
rows corresponding to the m locations along the scan direction and
n' columns corresponding to the n' remaining initial voltage scan
intervals and time values, wherein n' is less than n; and
selectively truncating the initial time vector T.sub.0 to form a
truncated initial time vector T.sub.0T comprising n' initial scan
time values; wherein the initial profile vector P.sub.0 is computed
as P.sub.0=A.sub.T*T.sub.0T.
9. The method of claim 1, wherein creating the system of linear
equations comprises: forming a matrix A of the measured initial
current density values with an integer number m rows corresponding
to the m locations along the scan direction and an integer number n
columns corresponding to n initial voltage scan intervals and time
values; forming an initial time vector T.sub.0 comprising the n
initial scan time values; and computing an initial profile vector
P.sub.0 comprising m initial profile values, wherein the initial
profile vector P.sub.0=A*T.sub.0.
10. The method of claim 9, wherein determining a set of scan time
values comprises: computing a profile average value P.sub.AVG as
the average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.01+P.sub.02+ . . . +P.sub.0m); computing a
profile deviation vector .DELTA.P comprising m profile deviation
values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1 through
m; computing an inverse matrix A.sup.-1; multiplying the inverse
matrix A.sup.-1 and the profile deviation vector .DELTA.P to obtain
a time deviation solution vector .DELTA.T.sub.SOLUTION comprising n
scan time deviation values, wherein
.DELTA.T.sub.SOLUTION=A.sup.-1*.DELTA.P; and computing a scan time
solution vector T.sub.SOLUTION as the sum of the time deviation
solution vector .DELTA.T.sub.SOLUTION and the initial time vector
T.sub.0, the scan time solution vector T.sub.SOLUTION comprising
the set of scan time values corresponding to the solution to the
system of linear equations that reduces current density profile
deviations, wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0.
11. The method of claim 10, wherein the inverse matrix A.sup.-1 is
computed using singular value decomposition (SVD).
12. The method of claim 11, further comprising: selectively
truncating the matrix A by eliminating one or more columns having
no non-zero entries to form a truncated matrix A.sub.T having m
rows corresponding to the m locations along the scan direction and
n' columns corresponding to the n' remaining initial voltage scan
intervals and time values, wherein n' is less than n; and
selectively truncating the initial time vector T.sub.0 to form a
truncated initial time vector T.sub.0T comprising n' initial scan
time values; wherein the initial profile vector P.sub.0 is computed
as P.sub.0=A.sub.T*T.sub.0T; and wherein determining the set of
scan time values comprises: computing the profile average value
P.sub.AVG as the average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.01+P.sub.02+ . . . +P.sub.0m); computing a
profile deviation vector .DELTA.P comprising m profile deviation
values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1 through
m; computing an inverse matrix A.sub.T.sup.-1; multiplying the
inverse matrix A.sub.T.sup.-1 and the profile deviation vector
.DELTA.P to obtain a time deviation solution vector
.DELTA.T.sub.SOLUTION comprising n' scan time deviation values,
wherein .DELTA.T.sub.SOLUTION=A.sub.T.sup.-1*.DELTA.P; and
computing a scan time solution vector T.sub.SOLUTION as the sum of
the time deviation solution vector .DELTA.T.sub.SOLUTION and the
truncated initial time vector T.sub.0T, the scan time solution
vector T.sub.SOLUTION comprising the set of scan time values
corresponding to the solution to the system of linear equations
that reduces current density profile deviations, wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0T.
13. The method of claim 9, further comprising: selectively
truncating the matrix A by eliminating one or more columns having
no non-zero entries to form a truncated matrix A.sub.T having m
rows corresponding to the m locations along the scan direction and
n' columns corresponding to the n' remaining initial voltage scan
intervals and time values, wherein n' is less than n; and
selectively truncating the initial time vector T.sub.0 to form a
truncated initial time vector T.sub.0T comprising n' initial scan
time values; wherein the initial profile vector P.sub.0 is computed
as P.sub.0=A.sub.T*T.sub.0T.
14. The method of claim 1, wherein the plurality of locations along
the scan direction are spaced from one another by a profile
interval distance that is less than a lateral dimension of an ion
beam.
15. A calibration system for calibrating an ion beam scanner in an
ion implantation system, the calibration system comprising: a
dosimetry system operable to measure a plurality of initial current
density values at a corresponding plurality of locations along a
scan direction in a workpiece location of an ion implantation
system; and a control system operably coupled with the dosimetry
system and a power supply associated with a beam scanner of the ion
implantation system, the control system being operable to cause the
scanner to scan an ion beam across the workpiece location of the
ion implantation system in the scan direction one or more times
according to a plurality of initial voltage scan intervals and a
corresponding plurality of initial voltage scan time values such
that the dosimetry system can measure a plurality of initial
current density values at a plurality of locations along a scan
direction in a workpiece location of an ion implantation system;
wherein the initial current density values individually correspond
to one of the plurality of initial voltage scan intervals and to
one of the corresponding plurality of initial scan time values; and
wherein the control system is further operable to create a system
of linear equations based on the measured initial current density
values and the initial scan time values, and to determine a set of
scan time values for the voltage scan intervals corresponding to a
solution to the system of linear equations that reduces current
density profile deviations.
16. The calibration system of claim 15, wherein the control system
is operable to form a matrix A of the measured initial current
density values with an integer number m rows corresponding to the m
locations along the scan direction and an integer number n columns
corresponding to n initial voltage scan intervals and time values,
to form an initial time vector T.sub.0 comprising the n initial
scan time values, and to compute an initial profile vector P.sub.0
comprising m initial profile values, wherein the initial profile
vector P.sub.0=A*T.sub.0.
17. The calibration system of claim 16, wherein the control system
is operable to compute a profile average value P.sub.AVG as the
average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.0130 P.sub.02+ . . . +P.sub.0m), to compute
a profile deviation vector .DELTA.P comprising m profile deviation
values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1 through
m, to compute an inverse matrix A.sup.-1, to multiply the inverse
matrix A.sup.-1 and the profile deviation vector .DELTA.P to obtain
a time deviation solution vector .DELTA.T.sub.SOLUTION comprising n
scan time deviation values, wherein
.DELTA.T.sub.SOLUTION=A.sup.-1*.DELTA.P, and to compute a scan time
solution vector T.sub.SOLUTION as the sum of the time deviation
solution vector .DELTA.T.sub.SOLUTION and the initial time vector
T.sub.0, the scan time solution vector T.sub.SOLUTION comprising
the set of scan time values corresponding to the solution to the
system of linear equations that reduces current density profile
deviations, wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0.
18. The calibration system of claim 17, wherein the control system
is operable to compute inverse matrix A.sup.-1 using singular value
decomposition (SVD).
19. The calibration system of claim 18, wherein the control system
is further operable to selectively truncate the matrix A by
eliminating one or more columns having no non-zero entries to form
a truncated matrix A.sub.T having m rows corresponding to the m
locations along the scan direction and n' columns corresponding to
the n' remaining initial voltage scan intervals and time values,
wherein n' is less than n, and to selectively truncate the initial
time vector T.sub.0 to form a truncated initial time vector
T.sub.0T comprising n' initial scan time values; wherein the
control system computes the initial profile vector P.sub.0 as
P.sub.0=A.sub.T*T.sub.0T; and wherein the control system determines
the set of scan time values by computing the profile average value
P.sub.AVG as the average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.01+P.sub.02+ . . . +P.sub.0m), computing a
profile deviation vector .DELTA.P comprising m profile deviation
values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1 through
m, computing an inverse matrix A.sub.T.sup.-1, multiplying the
inverse matrix A.sub.T.sup.-1 and the profile deviation vector
.DELTA.P to obtain a time deviation solution vector
.DELTA.T.sub.SOLUTION comprising n' scan time deviation values,
wherein .DELTA.T.sub.SOLUTION=A.sub.T.sup.-1*.DELTA.P, and
computing a scan time solution vector T.sub.SOLUTION as the sum of
the time deviation solution vector .DELTA.T.sub.SOLUTION and the
truncated initial time vector T.sub.0T, the scan time solution
vector T.sub.SOLUTION comprising the set of scan time values
corresponding to the solution to the system of linear equations
that reduces current density profile deviations, wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0T.
20. The calibration system of claim 16, wherein the control system
is further operable to selectively truncate the matrix A by
eliminating one or more columns having no non-zero entries to form
a truncated matrix A.sub.T having m rows corresponding to the m
locations along the scan direction and n' columns corresponding to
the n' remaining initial voltage scan intervals and time values,
wherein n' is less than n; wherein the control system selectively
truncates the initial time vector T.sub.0 to form a truncated
initial time vector T.sub.0T comprising n' initial scan time
values; and wherein the control system computes the initial profile
vector P.sub.0 as P.sub.0=A.sub.T*T.sub.0T.
Description
FIELD OF THE INVENTION
[0001] The present invention relates generally to ion implantation
systems, and more specifically to improved systems and methods for
uniformly scanning ion beams across a workpiece.
BACKGROUND OF THE INVENTION
[0002] In the manufacture of semiconductor devices and other
products, ion implantation is used to dope semiconductor wafers,
display panels, or other workpieces with impurities. Ion implanters
or ion implantation systems treat a workpiece with an ion beam, to
produce n or p-type doped regions or to form passivation layers in
the workpiece. When used for doping semiconductors, the ion
implantation system injects a selected ion species to produce the
desired extrinsic material, wherein implanting ions generated from
source materials such as antimony, arsenic or phosphorus results in
n-type extrinsic material wafers, and implanting materials such as
boron, gallium or indium creates p-type extrinsic material portions
in a semiconductor wafer.
[0003] FIG. 1A illustrates an exemplary ion implantation system 10
having a terminal 12, a beamline assembly 14, and an end station
16. The terminal 12 includes an ion source 20 powered by a high
voltage power supply 22 that produces and directs an ion beam 24 to
the beamline assembly 14. The beamline assembly 14 has a beamguide
32 and a mass analyzer 26 in which a dipole magnetic field is
established to pass only ions of appropriate charge-to-mass ratio
through a resolving aperture 34 at an exit end of the beamguide 32
to a workpiece 30 (e.g., a semiconductor wafer, display panel,
etc.) in the end station 16. The ion source 20 generates charged
ions that are extracted from the source 20 and formed into the ion
beam 24, which is directed along a beam path in the beamline
assembly 14 to the end station 16. The ion implantation system 10
may include beam forming and shaping structures extending between
the ion source 20 and the end station 16, which maintain the ion
beam 24 and bound an elongated interior cavity or passageway
through which the beam 24 is transported to the workpiece 30
supported in the end station 16. The ion beam transport passageway
is typically evacuated to reduce the probability of ions being
deflected from the beam path through collisions with air
molecules.
[0004] Low energy implanters are typically designed to provide ion
beams of a few thousand electron volts (keV) up to around 80-100
keV, whereas high energy implanters can employ linear acceleration
(linac) apparatus (not shown) between the mass analyzer 26 and the
end station 16 to accelerate the mass analyzed beam 24 to higher
energies, typically several hundred keV, wherein DC acceleration is
also possible. High energy ion implantation is commonly employed
for deeper implants in the workpiece 30. Conversely, high current,
low energy ion beams 24 are typically employed for high dose,
shallow depth ion implantation, in which case the lower energy of
the ions commonly causes difficulties in maintaining convergence of
the ion beam 24.
[0005] In the manufacture of integrated circuit devices, display
panels, and other products, it is desirable to uniformly implant
the dopant species across the entire surface of the workpiece 30.
Different forms of end stations 16 are found in conventional
implanters. "Batch" type end stations can simultaneously support
multiple workpieces 30 on a rotating support structure, wherein the
workpieces 30 are rotated through the path of the ion beam until
all the workpieces 30 are completely implanted. A "serial" type end
station, on the other hand, supports a single workpiece 30 along
the beam path for implantation, wherein multiple workpieces 30 are
implanted one at a time in serial fashion, with each workpiece 30
being completely implanted before implantation of the next
workpiece 30 begins.
[0006] The implantation system 10 includes a serial end station 16,
wherein the beamline assembly 14 includes a beam scanner 36 that
receives the ion beam 24 having a relatively narrow profile (e.g.,
a "pencil" beam), and scans the beam 24 back and forth in the X
direction to spread the beam 24 out into an elongated "ribbon"
profile, having an effective X direction width that is at least as
wide as the workpiece 30. The ribbon beam 24 is then passed through
a parallelizer 38 that directs the ribbon beam toward the workpiece
30 generally parallel to the Z direction (e.g., generally
perpendicular to the workpiece surface).
[0007] Referring also to FIGS. 1B-1J, the beam scanner 36 is
further illustrated in FIG. 1B, having a pair of scan plates or
electrodes 36a and 36b on either lateral side of the beam path, and
a voltage source 50 that provides alternating voltages to the
electrodes 36a and 36b, as illustrated in a waveform diagram 60 in
FIG. 1C. The time-varying voltage potential between the scan
electrodes 36a and 36b creates a time varying electric field across
the beam path therebetween, by which the beam 24 is bent or
deflected (e.g., scanned) along a scan direction (e.g., the X
direction in FIGS. 1A, 1B, and 1F-1J). When the scanner electric
field is in the direction from the electrode 36a to the electrode
36b (e.g., the potential of electrode 36a is more positive than the
potential of electrode 36b, such as at times "a" and "c" in FIG.
1C), the positively charged ions of the beam 24 are subjected to a
lateral force in the negative X direction (e.g., toward the
electrode 36b). When the electrodes 36a and 36b are at the same
potential (e.g., zero electric field in the scanner 36, such as at
time "e" in FIG. 1C), the beam 24 passes through the scanner 36
unmodified. When the field is in the direction from the electrode
36b to the electrode 36a (e.g., times "g" and "i" in FIG. 1C), the
positively charged ions of the beam 24 are subjected to a lateral
force in the positive X direction (e.g., toward the electrode
36a).
[0008] FIG. 1B shows the scanned beam 24 deflection as it passes
through the scanner 36 at several exemplary discrete points in time
during scanning prior to entering the parallelizer 38 and FIG. 1D
illustrates the scanned and parallelized beam 24 impacting the
workpiece 30 at the corresponding times indicated in FIG. 1C. The
scanned and parallelized ion beam 24a in FIG. 1D corresponds to the
applied electrode voltages at the time "a" in FIG. 1C, and
subsequently, the beam 24b-24i is illustrated in FIG. 1D for scan
voltages at corresponding times "c", "e", "g", and "i" of FIG. 1C
for a single generally horizontal scan across the workpiece 30 in
the X direction. FIG. 1E illustrates a simplified scanning of the
beam 24 across the workpiece 30, wherein mechanical actuation (not
shown) translates the workpiece 30 in the positive Y (slow scan)
direction during X (fast scan) direction scanning by the scanner
36, whereby the beam 24 is imparted on the entire exposed surface
of the workpiece 30.
[0009] Prior to entering the scanner 36, the ion beam 24 typically
has a width and height profile of non-zero X and Y dimensions,
respectively, wherein one or both of the X and Y dimensions of the
beam typically vary during transport due to space charge and other
effects. For example, as the beam 24 is transported along the beam
path toward the workpiece 30, the beam 24 encounters various
electric and/or magnetic fields and devices that may alter the beam
width and/or height or the ratio thereof. In addition, space charge
effects, including mutual repulsion of positively charged beam
ions, tend to diverge the beam (e.g., increased X and Y
dimensions), absent countermeasures.
[0010] Also, the geometry and operating voltages of the scanner 36
provide certain focusing properties with respect to the beam 24
that is actually provided to the workpiece 30. Thus, even assuming
a perfectly symmetrical beam 24 (e.g., a pencil beam) entering the
scanner 36, the bending of the beam 24 by the scanner 36 changes
the beam focusing, wherein the incident beam typically is focused
more at the lateral edges in the X direction (e.g., 24a and 24i in
FIG. 1D), and will be focused less (e.g., wider or more divergent)
in the X dimension for points between the lateral edges (e.g., 24c,
24e, and 24g in FIG. 1D).
[0011] FIGS. 1F-1J illustrate the incident beam 24 corresponding to
the scanned instances 24a, 24c, 24e, 24g, and 24i, respectively. As
the beam 24 is scanned across the wafer 30 in the X direction, the
X direction focusing of the scanner 36 varies, leading to increased
lateral defocusing of the incident beam 24 as it moves toward the
center, and then improved focusing as the beam 24 again reaches the
other lateral edge. For no scanning, the beam 24e proceeds directly
to the center of the workpiece 30, at which the incident beam 24e
has an X direction width W.sub.c, as shown in FIG. 1H. As the beam
24 is scanned laterally in either direction away from the center,
however, the time varying focusing properties of the scanner 36
lead to stronger and stronger lateral focusing of the incident
beam. For instance, at the outermost edges of the workpiece 30, the
incident beam 24a in FIG. 1F has a first left side width W.sub.L1,
and on the right side, the incident beam 24i in FIG. 1J has a first
right side width W.sub.R1. FIGS. 1G and 1I illustrate two
intermediate beams 24c and 24g having incident beam widths W.sub.L2
and W.sub.R2, respectively, showing X direction focal variation
between the edges and the center of the workpiece 30.
[0012] In general, it is desirable to provide uniform implantation
of the surface of the workpiece 30, regardless of the particular
focal properties of the beam transport and scanning system.
Accordingly, conventional systems often undergo a calibration
operation to adjust the voltage waveform of the beam scanner 36 to
counteract the focal variation of the beam 24 along the scan
direction and/or to compensate for other beam irregularities. This
is typically done in a point-to-point fashion by measuring a
current density profile in a region at or near the workpiece
location that results from a beam set to the region. The profile
region and the scanner voltage range are subdivided into
corresponding intervals. For a given scanner voltage interval, a
measurement sensor is located at the position corresponding to the
center of the interval, and the beam is directed at the region
being measured. Such measurements are then repeated for each of the
voltage intervals, and the final scan waveform is adjusted to
compensate for profile non-uniformities.
[0013] Although the conventional point-to-point scanner calibration
techniques may be adequate where the width of the ion beam 24 is
narrow and the beam width is relatively constant across the target
area, these techniques are less suitable in the case of wider beams
24 and/or in situations where the beam width varies along the scan
direction, as in the example of FIGS. 1F-1J. In particular, if the
beam 24 is wide and/or variable across the target area, the
point-to-point technique fails to account for the workpiece dose
produced by the beam some distance from the beam center. This
situation is particularly problematic with low energy ion beams 24
that experience space charge expansion (e.g., lateral divergence in
the scan or X direction).
[0014] Another consideration is the amount of beam overscan, which
includes the extent to which the ion beam 24 is scanned past the
edges of the workpiece 30, as illustrated in FIG. 1E. In most
applications, the beam 24 must be scanned beyond the target by an
amount related to the width of the beam 24 in order to achieve
uniform implantation of the entire workpiece surface. However, the
time that the scanned beam 24 spends outside the target area is
essentially wasted, and detracts from the system scan efficiency,
defined as the time spent on the target workpiece 30 divided by the
total scan time.
[0015] Accordingly there is a need for improved ion beam scanner
calibration techniques by which uniform implantation can be
facilitated, and which facilitates improved scan efficiency by
determining the minimum overscan required to achieve uniform
implantation of a workpiece.
SUMMARY OF THE INVENTION
[0016] The following presents a simplified summary of the invention
in order to provide a basic understanding of some aspects of the
invention. This summary is not an extensive overview of the
invention, and is neither intended to identify key or critical
elements of the invention nor to delineate the scope of the
invention. Rather, the purpose of the summary is to present some
concepts of the invention in a simplified form as a prelude to the
more detailed description that is presented later.
[0017] The present invention relates to systems and methods for
calibrating an ion beam scanner in an ion implantation system, in
which the current density contributions of multiple scanner voltage
intervals are individually measured for multiple profile points
along a beam scan direction to generate a system of linear
equations, and a set of scan time values are computed for the
voltage scan intervals corresponding to a solution that reduces
current density profile deviations. Unlike conventional
point-to-point calibration techniques, the invention provides
compensation for implant contributions produced by the beam some
distance from the beam center, and is thus particularly suitable
for use in low energy ion implanters having relatively wide beams
and/or in situations where the lateral beam width varies along the
scan direction to provide uniform implantation across a workpiece
surface. In addition, the invention may be employed to reduce
excess overscan, thereby improving system scan efficiency without
sacrificing implant uniformity.
[0018] One aspect of the invention provides a method for
calibrating an ion beam scanner in an ion implantation system,
comprising measuring a plurality of initial current density values
at a plurality of locations along a scan direction, where the
initial current density values individually correspond to one of a
plurality of initial voltage scan intervals and to one of a
corresponding plurality of initial scan time values. The method
further comprises creating a system of linear equations based on
the measured initial current density values and initial scan time
values, and determining a set of scan time values for the voltage
scan intervals that correspond to a solution to the system of
linear equations that reduces current density profile
deviations.
[0019] Another aspect of the invention provides a calibration
system for calibrating an ion beam scanner in an ion implantation
system. The calibration system comprises a dosimetry system and a
control system operably coupled with the dosimetry system and a
power supply associated with a beam scanner, where the dosimetry
system measures a plurality of initial current density values at a
plurality of locations along a scan direction in a workpiece
location of an ion implantation system. The control system causes
the scanner to scan an ion beam across the workpiece location of
the ion implantation system in the scan direction according to an
initial set of voltage scan intervals and corresponding scan time
values so that the dosimetry system can measure a plurality of
initial current density values at the plurality of locations along
the scan direction in a workpiece location of an ion implantation
system, where the initial current density values individually
correspond to one of the plurality of initial voltage scan
intervals and to one of the corresponding plurality of initial scan
time values. The control system is further operable to create a
system of linear equations based on the measured initial current
density values and the initial scan time values, and to determine a
set of scan time values for the voltage scan intervals
corresponding to a solution to the system of linear equations that
reduces current density profile deviations.
[0020] The following description and annexed drawings set forth in
detail certain illustrative aspects and implementations of the
invention. These are indicative of but a few of the various ways in
which the principles of the invention may be employed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] FIG. 1A is a schematic diagram illustrating an ion
implantation system with a conventional scanner and
parallelizer;
[0022] FIG. 1B is a partial top plan view illustrating the scanner
of FIG. 1B and several exemplary scanned ion beams;
[0023] FIG. 1C is a graph illustrating an exemplary triangular
scanning plate voltage waveform in the scanner of FIGS. 1A and
1B;
[0024] FIG. 1D is a perspective view illustrating a scanned ion
beam striking a workpiece in the system of FIGS. 1A and 1B at
several discrete points in time;
[0025] FIG. 1E is an end elevation view illustrating scanning of an
ion beam across a workpiece;
[0026] FIGS. 1F-1J are partial front elevation views illustrating
variation in the ion beam width upon striking the workpiece in the
ion implantation system of FIGS. 1A and 1B;
[0027] FIG. 2 is a flow diagram illustrating an exemplary beam
scanner calibration method in accordance with one or more aspects
of the present invention;
[0028] FIG. 3A is a flow diagram illustrating an exemplary
measurement sequence that may be employed in the method of FIG. 2
in accordance with one aspect of the invention;
[0029] FIG. 3B is a flow diagram illustrating an exemplary
measurement sequence that may be employed in the method of FIG. 2
in accordance with another aspect of the invention;
[0030] FIG. 4A is a schematic diagram illustrating an ion
implantation system with a calibration system comprising a control
system and a dosimetry system in accordance with the invention;
[0031] FIG. 4B is an end elevation view illustrating an exemplary
plurality of profile point locations along a lateral beam scan
direction at a workpiece location in the exemplary implantation
system of FIG. 4A in accordance with the invention;
[0032] FIG. 4C is a graph illustrating partitioning of an initial
triangular scanner voltage waveform into a plurality of initial
voltage scan intervals with a plurality of corresponding scan time
values in accordance with the invention;
[0033] FIG. 4D is a schematic diagram illustrating an exemplary
matrix of measured current density values in accordance with the
invention;
[0034] FIG. 5 is a flow diagram illustrating an exemplary
computation sequence that may be employed in the method of FIG. 2
in accordance with the invention;
[0035] FIG. 6A is a schematic diagram illustrating an exemplary set
of linear equations in accordance with the invention;
[0036] FIG. 6B is a schematic diagram illustrating an exemplary
profile deviation vector in accordance with the invention;
[0037] FIG. 6C is a schematic diagram illustrating an exemplary
time deviation vector in accordance with the invention;
[0038] FIG. 6D is a schematic diagram illustrating an exemplary set
of linear equations relating the profile deviation vector of FIG.
6B to the time deviation vector of FIG. 6C using the matrix of FIG.
4D;
[0039] FIG. 6E is a schematic diagram illustrating a solution to
the set of equations of FIG. 6D relating a time deviation solution
vector to the profile deviation vector of FIG. 6B using an inverse
of the matrix of FIG. 4D in accordance with the invention;
[0040] FIG. 6F is a schematic diagram illustrating computation of
an exemplary scan time solution vector comprising the set of scan
time values corresponding to the solution to the system of linear
equations that reduces current density profile deviations in
accordance with the invention;
[0041] FIG. 6G is a graph illustrating an exemplary piecewise
linear calibrated scanner voltage waveform created using the
initially defined scan voltage intervals and the computed scan time
solution vector of FIG. 6F to improve implant uniformity in
accordance with the invention; and
[0042] FIGS. 7A and 7B are schematic diagrams illustrating
selective truncation of the matrix and scan time vector to
eliminate excess overscan in accordance with the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
[0043] The present invention will now be described with reference
to the drawings wherein like reference numerals are used to refer
to like elements throughout, and wherein the illustrated structures
are not necessarily drawn to scale. The invention provides methods
and systems for calibrating an ion beam scanner in an ion
implantation system, which may be employed to improve implant
uniformity and to improve system scan efficiency by reducing excess
overscan.
[0044] FIG. 2 illustrates an exemplary beam scanner calibration
method 200 in accordance with one or more aspects of the present
invention, in which measurements are taken and computations are
performed to determine a set of scan times for constructing a
piecewise linear scanner voltage waveform to improve implant
uniformity and to reduce excess overscan in an ion implantation
system. FIGS. 3A and 5 illustrate exemplary measurement and
computation sequences, respectively, that may be employed in the
method 200, as described further below. While the exemplary method
200 and the exemplary measurement and computation sequences are
illustrated and described hereinafter as a series of acts or
events, it will be appreciated that the present invention is not
limited by the illustrated ordering of such acts or events. For
example, some acts may occur in different orders and/or
concurrently with other acts or events apart from those illustrated
and/or described herein, in accordance with the invention. In
addition, not all illustrated steps may be required to implement a
methodology in accordance with the present invention. Furthermore,
the methods according to the present invention may be implemented
in association with the implantation and scanner calibration
systems which are illustrated and described herein as well as in
association with other systems and devices not illustrated.
[0045] The method 200 begins at 202 in FIG. 2, wherein a plurality
of initial current density profile measurements are taken at 300 at
a plurality of locations along a scan direction, where the measured
values individually correspond to one of a plurality of initial
voltage scan intervals and to one of a corresponding plurality of
initial scan time values. The measurements at 300 may be taken
using any suitable dosimetry equipment or other measurement system,
which may include one or multiple measurement sensors (e.g.,
dosimetry cups, etc.), wherein the measurements may be taken
concurrently or individually in any order, wherein all such
implementations are contemplated as falling within the scope of the
invention and the appended claims. One exemplary measurement
sequence 300 is illustrated and described further below with
respect to FIG. 3A in accordance with the invention.
[0046] Computations are then performed at 400 in FIG. 2 to
determine a set of scan time values according to the measured
current density values obtained at 300. At 404, a system of linear
equations is created based on the measured initial current density
values and the initial scan time values. A set of scan time values
is then determined at 406 for the voltage scan intervals, where the
determined time values correspond to a solution to the system of
linear equations that reduces current density profile deviations,
and the method 200 ends at 204. The set of scan time values
determined at 406 may then be used to create a beam scanner voltage
waveform for use in implanting workpieces as illustrated and
described further below with respect to FIG. 6G. Alternatively, one
or more iterations may be undertaken to refine the set of time
values determined at 406, which may, but need not involve
redefining the number, size, or spacing of the voltage scan
intervals.
[0047] Referring also to FIGS. 3A-4D, FIG. 3A illustrates one
example of a measurement sequence 300 that may be employed in the
method 200, FIG. 4A illustrates an ion implantation system 110 with
a calibration system comprising a control system 154 and a
dosimetry system 152 in accordance with the invention. In order to
further illustrate the exemplary measurement technique 300 of FIG.
3A, FIG. 4B illustrates an exemplary plurality of profile point
locations along a lateral beam scan direction at a workpiece
location in the implantation system 110, FIG. 4C illustrates an
initial triangular scanner voltage waveform segmented into a
plurality of initial voltage scan intervals with a plurality of
corresponding scan time values, and FIG. 4D illustrates a matrix of
measured current density values in accordance with the
invention.
[0048] As shown in FIG. 4A, the exemplary ion implantation system
110 is a low-energy ion implanter with no linear accelerator
(linac) components. However, the invention may alternatively be
employed in high or medium energy ion implanters, which may include
acceleration components. The implantation system 110 comprises a
terminal 112, a beamline assembly 114, and an end station 116,
wherein an ion source 120 in the terminal 112 is powered by a power
supply 122 to provide an extracted ion beam 124 to the beamline
assembly 114, where the source 120 includes one or more extraction
electrodes (not shown) to extract ions from the source chamber and
thereby to provide the extracted ion beam 124 to the beamline
assembly 114.
[0049] The beamline assembly 114 comprises a beamguide 132 having
an entrance near the source 120 and an exit with an exit aperture
134, as well as a mass analyzer 126 that receives the extracted ion
beam 124 and creates a dipole magnetic field to pass only ions of
appropriate charge-to-mass ratio or range thereof (e.g., a mass
analyzed ion beam 124 having ions of a desired mass range) through
the resolving aperture 134 to a workpiece location in the end
station 116. Various beam forming and shaping structures (not
shown) may be provided in the beamline assembly to maintain the ion
beam 124 and which bound an elongated interior cavity or passageway
through which the beam 124 is transported along a beam path to the
end station 116. The illustrated end station 116 is a "serial" type
end station that supports a single workpiece (not shown) along the
beam path for implantation (e.g., a semiconductor wafer, display
panel, or other workpiece to be implanted with ions from the beam
124), wherein a dosimetry system 152 is situated at the workpiece
location in FIG. 4A for calibration measurements prior to
implantation operations.
[0050] The beamline assembly 114 further comprises a scanning
system with a scanner 136 and a power supply 150 coupled to scanner
plates or electrodes 136a and 136b, where the scanner 136 receives
a mass analyzed ion beam 124 along the beam path from the mass
analyzer 126 and provides a scanned beam 124 along the beam path to
a parallelizer 138. The parallelizer 138 then directs the scanned
beam 124 to the end station 116 such that the beam 124 strikes
measurement sensor(s) of the dosimetry system 152 at a generally
constant angle of incidence. The scanner 136 receives a mass
analyzed ion beam 124 having a relatively narrow profile (e.g., a
"pencil" beam in the illustrated system 110), and a voltage
waveform applied by the power supply 150 to the scanner plates 136a
and 136b operates to scan the beam 124 back and forth in the X
direction (the scan direction) to spread the beam 124 out into an
elongated "ribbon" profile (e.g., a scanned beam 124), having an
effective X direction width that may be at least as wide as or
wider than the workpieces of interest. The scanned beam 124 is then
passed through the parallelizer 138 that directs the beam toward
the workpiece 130 generally parallel to the Z direction (e.g.,
generally perpendicular to the workpiece surface).
[0051] Referring also to FIG. 4B, the dosimetry system 152
comprises one or more current density sensors (not shown), such as
multiple conventional Faraday cups located at predetermined
locations 160 along the scan direction, or a single sensor which
may be positioned at the various locations 160 for successive
measurements of the amount of ions (current density) imparted by a
scanned ion beam 124 at a given location 160. U.S. Pat. No.
6,677,598, assigned to the assignee of the present invention,
illustrates measurement apparatus that may be employed in measuring
current density values in accordance with the present invention,
the entirety of which is hereby incorporated by reference as if
fully set forth herein. The dosimetry system 152 is operatively
coupled to the control system 154 to receive command signals
therefrom and to provide measurement values thereto to implement
the measurement aspects of the calibration techniques of the
invention as described further hereinafter.
[0052] During initial setup or calibration of the system 110, the
dosimetry system 152 is positioned at the workpiece location of the
end station 116, as shown in FIG. 4A, and a workpiece width
dimension 158 is partitioned in FIG. 4B into an initial set of
profile intervals, within which an integer number m measurement
locations (profile points) 160 are determined for initial
measurement of current density values during scanning of the ion
beam 124. In the illustrated example, the locations 160 along the
scan direction are spaced from one another by a profile interval
distance that is less than a lateral dimension of an ion beam 124,
although other spacings are possible. In addition, the exemplary
selection of the measurement locations 160 in FIG. 4B provides for
generally even spacing, although the profile intervals need not be
of equal lateral dimensions.
[0053] Referring also to FIG. 4C, an initial voltage scan range 159
is selected, which provides some measure of beam overscan beyond
the ends of the workpiece width 158 (e.g., the scan range 159 is
sufficiently wide to cause the scanned ion beam 124 to extend past
the lateral edges of the workpiece). The voltage scan range 159 is
divided into an integer number n voltage intervals, as shown in
FIG. 4C, wherein each interval extends between a first voltage
V.sub.i-1 to a second voltage V.sub.i for i=1 through n. FIG. 4C
illustrates an initial triangle waveform for the scanner voltage
(V.sub.136a-V.sub.136b), wherein the exemplary scan voltage
intervals V.sub.i-1 to V.sub.i are equal, and wherein a
corresponding set of n initial scan time values T.sub.01, T.sub.02,
. . . , T.sub.0n are equal. Any initial range selection 159 and
segmentation of the range 159 is possible within the scope of the
invention, wherein the voltage intervals V.sub.i-1 to V.sub.i need
not be equal and the scan time values T.sub.0i need not be equal.
Furthermore, as discussed below, the intervals may be changed or
redefined following an initial measurement (e.g., to reduce excess
overscan and/or to improve uniformity), and the time values used in
implanting workpieces in the system 110 are determined or solved
according to computations following the initial measurements (e.g.,
so as to improve implant uniformity) in accordance with the present
invention.
[0054] In a measurement operation during system calibration, the
control system 152 of FIG. 4A controls the voltage of the power
supply 150 such that the scanner voltage (e.g., the voltage
difference between the scanner plates 136a and 136b) varies
linearly between the voltage interval endpoints over the initial
scan time values, and the dosimetry system 152 takes corresponding
current density measurements to construct a matrix A, as shown in
FIG. 4D. The control system 154 then performs various computations
(e.g., at 404 and 406 in the method 200 of FIG. 2 above) to
determine a set of scan time values that correspond to a solution
to the system of linear equations that reduces current density
profile deviations. The dosimetry system 152 is then removed from
the workpiece location and the determined set of scan time values
may then be used to create a beam scanner voltage waveform for
workpiece implantation, for example, as shown in FIG. 6G below.
[0055] Referring to FIG. 3A, the exemplary measurement sequence 300
of the method 200 is hereinafter described with respect to an
implementation using the calibration system 152, 154 in the
implanter 110 of FIG. 4A, the initial measurement locations 160 of
FIG. 4B, and the initial voltage range segmentation of FIG. 4C. The
measurements 300 begin at 302, with the voltage span being defined
at 304 (e.g., the initial scanner voltage range 159 of FIGS. 4B and
4C, which extends beyond the voltages associated with the lateral
edges of the workpiece width 158 to provide some amount of initial
overscan). The voltage range 159 is then divided or segmented at
306 into an integer number n voltage intervals (a plurality of n
intervals V.sub.i-1 to V.sub.i for i=1 through n as shown in FIG.
4C). The partitioning of the voltage range 159 at 306 and the
assumed initial triangular scan waveform of FIG. 4C define the
corresponding set of n initial scan time values T.sub.01 through
T.sub.0n, which are equal, and which together form a vector T.sub.0
of dimension n. However, any initial scan waveform may be used,
wherein the voltage partitioning and the waveform selection define
the initial set of time values T.sub.0 used in the measurements
300, wherein the initial time entries of the vector T.sub.0 need
not be equal. The lateral scan direction range (e.g., the workpiece
width 158 in FIGS. 4B and 4C) is then divided into multiple profile
intervals, thereby defining an integer number m measurement
locations along the scan direction (e.g., the locations 160.sub.1
through 160.sub.m in FIG. 4B).
[0056] With the initial segmentation of the measurement range 158
and the voltage range 159, the control system 154 provides
appropriate control signals to the power supply 150 to cause the
scanner 136 to scan an ion beam 124 across the workpiece location
in the scan direction X one or more times according to the n
initial voltage scan intervals (V.sub.i-1 to V.sub.i for i=1
through n) and the corresponding n scan time values (T.sub.0), and
also controls the dosimetry system 152 to measure a plurality of
initial current density values A.sub.j,i at the locations 160,
where the initial current density values A.sub.j,i individually
correspond to one of the n voltage intervals (V.sub.i-1 to V.sub.i)
and the corresponding scan time value T.sub.0i. In this regard, the
illustrated measurement sequence 300 of FIG. 3A is shown for the
case of a single measurement sensor in the dosimetry system 152
that is moved from location to location, wherein the beam 124 is
scanned an integer number m times. However, fewer beam scans may be
needed where the dosimetry system 152 includes multiple sensors,
for example, where a single calibration measurement scan may be
used if m sensors are provided at the locations 160.
[0057] For the single sensor case in FIG. 3A, a measurement counter
j is set to a value of 1 at 310, and a voltage scan interval
counter i is set to a value of 1 at 312. The calibration system
152, 154 then obtains a first current density value A.sub.j,i at
314, 316 representing the first entry in to the matrix A of FIG.
4D. For this first value A.sub.j,i, the control system 154 directs
the power supply 150 at 314 to scan the voltage (e.g.,
(V.sub.136a-V.sub.136b)) linearly from V.sub.i-1 to V.sub.i over
the corresponding initial scan interval time T.sub.0i, and also
directs the dosimetry system 152 to measure the resultant current
density A.sub.j,i at 316 at the measurement location j (e.g., at
location 160.sub.1 in FIG. 4B). This first measurement A.sub.1,1
represents the current density contribution at the first location
160.sub.1 resulting from scanning the beam 124 from V.sub.0 to
V.sub.1 over the time T.sub.01, and is placed in the first row,
first column position in the matrix A of FIG. 4D.
[0058] A determination is made at 318 as to whether i=n (e.g.,
whether the entire voltage scan range 159 has been scanned). If not
(NO at 318), the measurement sequence 300 proceeds to 320 where the
voltage counter i is incremented. Thereafter, the scanner voltage
is scanned across the next scan interval at 314 with i=2 (e.g.,
from V.sub.1 to V.sub.2 over the second initial time value
T.sub.02), and another measurement is taken at 316. This second
value A.sub.1,2 is placed in the first row, second column position
of the matrix A, representing the current density contribution at
the first location 160, resulting from scanning the beam 124 from
V.sub.1 to V.sub.2 over the time T.sub.02.
[0059] Interval scanning and single position measurements continue
in this fashion (at 314, 316, 318, and 320) until i=n (e.g., at
which point the first row of the matrix A in FIG. 4D has been
filled with values measured at the first profile location
160.sub.1, which individually reflect the current density
contributions at the location 160.sub.1 corresponding to scanning
the beam 124 through one of the n initial voltage scan intervals
V.sub.i-1 to V.sub.i over the corresponding initial time value
T.sub.0i. It is noted at this point that the summation of the
values A.sub.1,i represents the total current density seen at the
location 160.sub.1 resulting from scanning the beam 124 across the
entire voltage scan range 159. This summation is therefore a better
measure of the amount of ions implanted at the location 160.sub.1
during actual implantation than was the measurement obtained using
the conventional point-by-point technique, in which the measurement
at a given point was taken only for current density resulting from
the time when the beam was at that point.
[0060] When i becomes equal to n in FIG. 3A (YES at 318), a
determination is made at 322 as to whether the measurement counter
j is equal to m. If not (NO at 322), the measurement counter j is
incremented at 324, and the process 300 returns to again set the
voltage counter i to a value of 1. In the case of a single
measurement sensor in the dosimetry system 152, the sensor would be
moved at this time to the next location 160.sub.j. Thus, for
example, when j is incremented at 324 after measurements at the
first location 160.sub.1, the dosimetry system 152 is then
configured to take measurements at the second location 160.sub.2.
With i=1 and j=2, the process 300 proceeds to 314 and 316, wherein
the voltage is scanned at 314 from V.sub.0 to V.sub.1 over the
corresponding time T.sub.01, and a current density value A.sub.2,1
is measured at 316 and placed in the second row, first column
position of the matrix A, representing the current density
contribution at the second location 160.sub.2 resulting from
scanning the beam 124 from V.sub.0 to V.sub.1 over the time
T.sub.01. The process 300 is then repeated in this fashion until
the counter j=m (YES at 322), indicating that the m rows of the
matrix A have been filled, and the measurements 300 end at 326 in
FIG. 3A.
[0061] Referring to FIG. 4D, the exemplary measurement sequence 300
of FIG. 3A provides for m scans of the beam 124 across the voltage
range 150 (FIG. 4C) to obtain n.times.m measurements A.sub.j,i,
using a single sensor in the dosimetry system 152, wherein the
matrix A is filled on a row-by-row basis. Alternatively, if m
sensors are provided and positioned at the locations
160.sub.1-160.sub.m in FIG. 4B, a single scan of the beam 124 may
be used, where the scanner voltage (V.sub.136a-V.sub.136b) may be
transitioned linearly from V.sub.0 through V.sub.n according to the
time values T.sub.01 through T.sub.0n, with the dosimetry system
152 obtaining m measurement values A.sub.j,i during each time
interval T.sub.0i, wherein a column of the matrix A is filled at
the conclusion of each time value T.sub.0i. Any suitable
measurement approach may be employed at 300 within the scope of the
invention, by which the matrix A is filled with the corresponding
entry values A.sub.j,i, or otherwise by which a set of linear
equations may be derived based on measured current density values
A.sub.j,i that individually corresponding to one of a plurality of
initial voltage scan intervals V.sub.i-1 to V.sub.i and one of a
corresponding plurality of initial scan time values T.sub.0i.
[0062] In an alternative aspect of the present invention, the data
may be collected in accordance with the method 300' of FIG. 3B,
wherein for each scan voltage interval i, an entire profile
measurement is taken (e.g., wherein j is incremented from 1 to m).
For example, as illustrated in FIG. 3B, for a give scan voltage
interval I (set at 312 or 320, the current density is measured
across the entire measurement range at 316, 322 and 324. When j=m
(YES at 322), the measurements have been taken across the entire
measurement range, and the scan voltage interval is incremented in
accordance with 318, 320 and the next scan voltage interval takes
place at 314, wherein current density is again measured across the
entire measurement range at 316, 322 and 324. The process then
continues until the entire scan interval range has been traversed
(YES at 318), wherein the measurement method 300' concludes at
326.
[0063] Referring now to FIGS. 2, 4A, and 5-6G, the control system
154 is further operable to create a system of linear equations
based on the measured initial current density values A.sub.j,i and
the initial scan time values T.sub.0i, and to determine a set of
scan time values T.sub.SOLUTION for the voltage scan intervals
V.sub.i-1 to V.sub.i, where the values T.sub.SOLUTION correspond to
a solution to the system of linear equations that reduces current
density profile deviations. This set of interval scan times
T.sub.SOLUTION may then be employed by the control system 154 to
create a scanner voltage waveform during implantation of workpieces
in the system 110. Moreover, the control system may determine the
vector of solution time values T.sub.SOLUTION based on the full set
of equations according to the full matrix A of FIG. 4D, or may
selectively truncate the matrix A and the time value vector T if
one or more columns of the matrix A are all zero values (e.g., no
non-zero values), as illustrated and described below with respect
to FIGS. 7A and 7B. Furthermore, one or more iterations may be
employed after obtaining the initial matrix A, for example, wherein
the definitions of the voltage scan intervals V.sub.i-1 to V.sub.i
and/or the set of locations 160.sub.j are refined, where the
numbers (n, m) of these may be adjusted as well, wherein all such
variant implementations are contemplated as falling within the
scope of the present invention and the appended claims.
[0064] FIG. 5 illustrates one possible implementation of the
computations 400 in the method 200 of FIG. 2 above, and FIGS. 6A-6G
illustrate the various corresponding mathematical computations and
matrix equations, as well as a resulting voltage scan waveform. The
exemplary computations 400 begin at 402 in FIG. 5, wherein a system
of linear equations is constructed at 404 using the measurement
matrix A of FIG. 4D, the corresponding initial time value vector
T.sub.0, and a current density profile vector P, where P=A*T in
matrix notation. As illustrated in FIG. 6A, the set of linear
equations are constructed as an initial profile vector P.sub.0 of
vertical dimension m being equal to the matrix A (m.times.n) times
the initial time vector T.sub.0 of dimension n. This equation set
includes m individual equations with n unknowns, where m is
preferably larger than n. Each individual equation characterizes
the cumulative current density contribution at the corresponding
measurement location 160 with the scanning of the beam 124 through
the voltage scan intervals according to the interval times
T.sub.0.
[0065] The control system 154 then determines a set of scan time
values at 406 for the voltage scan intervals, where the determined
time values correspond to a solution to the system of linear
equations that reduces current density profile deviations. In this
regard, the set of equations may be solved using any suitable
techniques, including but not limited to the computations
illustrated and described hereinafter.
[0066] At 407 in FIG. 5, the matrix A and the vector T may be
selectively truncated to eliminate zero matrix columns and the
corresponding time entries, as illustrated and described below with
respect to FIGS. 7A and 7B.
[0067] After any such truncation, the computations 400 proceed to
408, where a deviation vector .DELTA.P is constructed for the
profiles and scan times, respectively. As shown in FIG. 6B, a
profile average value P.sub.AVG is computed from the profile vector
P.sub.0 as the average of the m initial profile values, wherein
P.sub.AVG=(1/m)*(P.sub.01+P.sub.02+ . . . +P.sub.0m), and a profile
deviation vector .DELTA.P is computed, which comprises m profile
deviation values, wherein .DELTA.P.sub.j=P.sub.0j-P.sub.AVG for j=1
through m. The resulting profile deviation vector .DELTA.P thus
represents the deviation of the current density at each measurement
location 160 from the average current density across the entire
profile P.sub.0. As illustrated in FIG. 6C, a time value deviation
vector .DELTA.T is then defined, wherein the entries .DELTA.T.sub.i
thereof represent the difference between a corresponding solution
set value T.sub.SOLUTIONi and the initial value T.sub.01 (e.g.,
.DELTA.T.sub.i=T.sub.SOLUTIONi-T.sub.0i, for i-1 through n).
[0068] Referring also to FIGS. 6D and 6E, the equations may be
restated in terms of the deviation vectors .DELTA.P and .DELTA.T,
wherein .DELTA.P=A*.DELTA.T. In this regard, it is noted that it is
desirable to minimize deviations in the current density profile
across an implanted workpiece. The expression of FIG. 6D in terms
of the deviation vectors .DELTA.P and .DELTA.T allows the equations
to be solved for a solution set of time values that will optimize
uniformity by minimizing the profile deviations, wherein the
expression of FIG. 6D may be solved for the time value deviation
vector .DELTA.T, for example, by inverting the matrix A and
multiplying the inverse A.sup.-1 by the profile deviation vector
.DELTA.P, as illustrated in FIG. 6E, wherein
.DELTA.T=A.sup.-1*.DELTA.P.
[0069] At 410, an inverse matrix is computed from the initial
matrix A, where the inverse A.sup.-1 may be computed using any
suitable techniques. For example, if m>n, the system of
equations is over determined, and the inverse matrix A.sup.-1 may
be computed using singular value decomposition (SVD). Other
techniques are available, particularly if m=n. However, it is noted
that the voltage scan intervals and the profile intervals
(measurement locations 160) can be defined independent of one
another, wherein it may be preferable to include a large number of
measurement locations 160 to provide a better optimization, with
relatively few voltage scan segments to facilitate timely
calibration.
[0070] At 412 in FIG. 5, a time deviation solution vector
.DELTA.T.sub.SOLUTION is computed (e.g., the set of equations is
solved) by multiplying the inverse matrix A.sup.-1 and the profile
deviation vector .DELTA.P to obtain the deviation solution vector
.DELTA.T.sub.SOLUTION comprising n scan time deviation values,
wherein .DELTA.T.sub.SOLUTION=A.sup.-1*.DELTA.P, as shown in FIG.
6E. Because the scan time deviation vector .DELTA.T was defined in
FIG. 6C as .DELTA.T=T.sub.SOLUTION-T.sub.0, a scan time solution
vector T.sub.SOLUTION is then computed at 414 by adding the scan
time deviation vector .DELTA.T.sub.SOLUTION and the initial scan
time vector T.sub.0, where the scan time solution vector
T.sub.SOLUTION comprises the set of scan time values corresponding
to the solution to the system of linear equations that reduces
current density profile deviations, and wherein
T.sub.SOLUTION=.DELTA.T.sub.SOLUTION+T.sub.0, as illustrated in
FIG. 6F, after which the computations 400 end at 416.
[0071] Referring also to FIG. 6G, the solution set of scan time
values T.sub.SOLUTION may then be used to create a piecewise linear
beam scanner voltage waveform for use in implanting workpieces. In
operation of the system 110 (FIG. 4A) to implant workpieces, the
control system 154 controls the power supply 150 to provide the
waveform of FIG. 6G, wherein the scanner plate voltage
(V.sub.136a-V.sub.136b) transition linearly in each voltage
interval (e.g., from V.sub.i-1 to V.sub.i) in the time
T.sub.SOLUTIONi for each fast scan across the lateral scan
direction (the X direction), as the workpiece is translated along
the slow scan direction (the Y direction), to achieve scanning of
the workpiece surface, where the employment of the solution set of
time values T.sub.SOLUTION provides the best fit to achieve proper
implant uniformity.
[0072] Referring now to FIGS. 4A, 4B, 7A, and 7B, as discussed
above, another aspect of the invention facilitates improved system
scan efficiency by eliminating unnecessary overscan of the beam 124
past the edges of the workpiece during implantation. In this
regard, it is noted that the initial voltage scan range 159 of
FIGS. 4B and 4C was selected to provides some degree of beam
overscan beyond the ends of the workpiece width 158. If one or more
voltage scan intervals of this wide initial scan range 159 do not
contribute any current density to any of the profile intervals as
measured at the locations 160, the corresponding column or columns
in the matrix A will have no non-zero entries as shown in the
example of FIG. 7A, thus indicating that there is no need to scan
the beam 124 in those voltage intervals.
[0073] Accordingly, such superfluous columns can be truncated from
the matrix A, and the corresponding time entries in the initial
time vector T.sub.0 can be truncated (e.g., at 407 in FIG. 5). This
selective truncation, if performed, leaves a truncated matrix
A.sub.T having m rows corresponding to the m locations along the
scan direction and n' columns corresponding to the n' remaining
initial voltage scan intervals and time values, as well as a
corresponding truncated time vector T.sub.0T of length n', wherein
n' is less than n, as illustrated in FIG. 7B. It is noted that this
truncation effectively reduces the spatial range across which the
beam 124 is scanned in subsequent implantation operations, thereby
saving time and improving system scan efficiency.
[0074] In this case, the initial profile vector P.sub.0 is computed
as P.sub.0=A.sub.T*T.sub.0T for use in computing P.sub.AVG and the
profile deviation vector .DELTA.P (FIG. 6B above). In addition, the
inverse matrix A.sub.T.sup.-1 is computed from the truncated matrix
A.sub.T, and is then multiplied by the profile deviation vector
.DELTA.P to obtain a time deviation solution vector
.DELTA.T.sub.SOLUTION comprising n' scan time deviation values,
wherein .DELTA.T.sub.SOLUTION=A.sub.T.sup.-1*.DELTA.P (FIG. 6E
above). Thereafter, the scan time solution vector T.sub.SOLUTION is
determined as the sum of the time deviation solution vector
.DELTA.T.sub.SOLUTION and the truncated initial time vector
T.sub.0T, where T.sub.SOLUTION Will include n' values.
[0075] Alternatively, the voltage scan intervals may be redefined
to include the original number n intervals spread out over a
smaller range to exclude the unneeded overscan, and the calibration
process may be repeated. Other iterative approaches may be employed
as well, such as redefining the measurement locations (profile
intervals) to include more measurements in areas experiencing the
largest deviations, or according to other criteria, wherein all
such alternative approaches are contemplated as falling within the
scope of the invention and the appended claims.
[0076] Although the invention has been illustrated and described
with respect to one or more implementations, alterations and/or
modifications may be made to the illustrated examples without
departing from the spirit and scope of the appended claims. In
particular regard to the various functions performed by the above
described components or structures (blocks, units, engines,
assemblies, devices, circuits, systems, etc.), the terms (including
a reference to a "means") used to describe such components are
intended to correspond, unless otherwise indicated, to any
component or structure which performs the specified function of the
described component (e.g., that is functionally equivalent), even
though not structurally equivalent to the disclosed structure which
performs the function in the herein illustrated exemplary
implementations of the invention. In addition, while a particular
feature of the invention may have been disclosed with respect to
only one of several implementations, such feature may be combined
with one or more other features of the other implementations as may
be desired and advantageous for any given or particular
application. Furthermore, to the extent that the terms "including",
"includes", "having", "has", "with", or variants thereof are used
in either the detailed description and the claims, such terms are
intended to be inclusive in a manner similar to the term
"comprising".
* * * * *