Method for controlling growth of a silicon crystal

System and method for determining the diameter of a silicon crystal being pulled from a silicon melt for controlling a silicon crystal growing apparatus. The melt has a surface with a meniscus which is visible as a bright ring adjacent the crystal. A camera generates an image pattern of a portion of the bright ring adjacent the crystal. Image processing circuitry detects a characteristic of the image pattern and defines an edge of the bright ring as a function of the detected characteristic. The image processing circuitry further defines a generally circular shape including the defined edge of the bright ring. The diameter of the crystal is then determined based on the diameter of the defined shape for use in controlling the crystal growing apparatus.

NOTICE 
Copyright.COPYRGT. 1995 MEMC Electronic Materials, Inc. A portion of the 
disclosure of this patent document contains material which is subject to 
copyright protection. The copyright owner has no objection to the 
facsimile reproduction by anyone of the patent document or the patent 
disclosure, as it appears in the Patent and Trademark Office patent files 
or records, but otherwise reserves all copyright rights whatsoever. 
BACKGROUND OF THE INVENTION 
This invention relates to an improved system and method for measuring the 
diameter of silicon crystals grown by the Czochralski process and, in 
particular, a system or method for use in controlling an apparatus or 
method employing the Czochralski process. 
The substantial majority of monocrystalline silicon used to make silicon 
wafers for the microelectronics industry is produced by crystal pulling 
machines employing the Czochralski process. Briefly described, the 
Czochralski process involves melting chunks of high-purity polycrystalline 
silicon in a quartz crucible located in a specifically designed furnace to 
form a silicon melt. A relatively small seed crystal is mounted above the 
crucible on the lower end of a pull wire hanging from a crystal lifting 
mechanism for raising and lowering the seed crystal. The crystal lifting 
mechanism lowers the seed crystal into contact with the molten silicon in 
the crucible. When the seed begins to melt, the mechanism slowly withdraws 
it from the silicon melt. As the seed is withdrawn, it grows drawing 
silicon from the melt. During the growth process, the crucible is rotated 
in one direction and the crystal lifting mechanism, wire, seed, and 
crystal are rotated in an opposite direction. 
As crystal growth is initiated, the thermal shock of contacting the seed 
with the melt may cause dislocations in the crystal. The dislocations are 
propagated throughout the growing crystal and multiplied unless they are 
eliminated in the neck region between the seed crystal and the main body 
of the crystal. The known methods of eliminating dislocations within 
silicon single crystal involve growing a neck having a small diameter at a 
relatively high crystal pull rate to completely eliminate dislocations 
before growing the body of the crystal. After dislocations are eliminated 
in the neck, its diameter is enlarged until the desired diameter of the 
main crystal body is reached. When the neck, which is the weakest part of 
the crystal, has too small of a diameter, it can fracture during crystal 
growth, causing the body of the crystal to drop into the crucible. The 
impact of the crystal ingot and splashing molten silicon can cause damage 
to the crystal growing apparatus as well as present a serious safety 
hazard. 
As is known in the art, the Czochralski process is controlled, in part, as 
a function of the diameter of the crystal being grown. Thus, for both 
control and safety reasons, an accurate and reliable system for measuring 
crystal diameter, including neck diameter, is needed. 
Several technologies are known for providing crystal diameter measurements 
including methods of measuring the width of the bright ring. The bright 
ring is a characteristic of the reflection of the crucible wall in the 
meniscus which is formed at the solid-liquid interface. Conventional 
bright ring and meniscus sensors employ optical pyrometers, photocells, 
rotating mirrors with photocells, light sources with photocells, line-scan 
cameras, and two-dimensional array cameras. U.S. Pat. Nos. 3,740,563, 
5,138,179 and 5,240,684, the entire disclosures of which are incorporated 
herein by reference, disclose methods and apparatus for determining the 
diameter of a crystal during the crystal growth process. 
Unfortunately, conventional apparatus for automatically measuring crystal 
width are not sufficiently accurate or reliable for use during the 
different phases of crystal growth or for large diameter crystals in which 
the true maximum of the bright ring may be obscured from view by the solid 
body of the crystal itself. In an effort to correct this problem, 
conventional apparatus for measuring crystal width attempt to measure the 
meniscus at a chord or at a single point along the meniscus. However, such 
apparatus require precise mechanical positioning of the scanning device 
and are highly sensitive to fluctuations in melt level. Further, 
conventional measuring apparatus require frequent calibration by the 
operator of the crystal growing apparatus to ensure that the diameter 
remains within specification. 
In addition to the problems described above, conventional apparatus for 
automatically measuring crystal diameter fail to provide accurate 
measurements when the crystal orbits, or moves in a pendular manner, as it 
is pulled from the melt. Known measurement apparatus are also unable to 
discriminate between the bright ring and reflections on the melt surface 
or on the growing crystal itself, resulting in unreliable measurements. 
Further, such apparatus are often unable to provide measurements when the 
viewport window is blocked by, for example, splashes of silicon. 
Another disadvantage with conventional systems and methods for measuring 
crystal diameter is that they are unable to provide additional information 
regarding the crystal growth process, such as a measure of melt level and 
an indication of a loss of zero dislocation growth. 
For these reasons, conventional apparatus fail to provide an accurate and 
reliable system of automatically determining crystal diameter for 
controlling the crystal growth process. 
SUMMARY OF THE INVENTION 
Among the objects and features of the present invention may be noted the 
provision of an improved system and method of control and operation which 
overcome at least some of the disadvantageous conditions described above; 
the provision of such system and method which provide accurate and 
reliable measurements of crystal diameter during the growth process; the 
provision of such system and method which compensate for errors caused by 
distortion due to camera angle; the provision of such system and method 
which is not affected by movement of the crystal during the growth 
process; the provision of such system and method which provide accurate 
and reliable measurements of melt level; the provision of such system and 
method which provide an indication of a loss of zero dislocation growth; 
and the provision of such system which is economically feasible and 
commercially practical and such method which can be carried out 
efficiently and relatively inexpensively. 
Briefly described, a system embodying aspects of the present invention is 
for use in combination with an apparatus for growing a silicon crystal 
from a silicon melt. The system determines a dimension of the crystal 
being pulled from the melt wherein melt has a surface with a meniscus 
which is visible as a bright area adjacent the crystal. The system 
includes a camera for generating an image pattern of a portion of the 
bright area adjacent the silicon crystal and a detection circuit for 
detecting a characteristic of the image pattern. The system also includes 
a defining circuit for defining an edge of the bright area as a function 
of the detected characteristic and for defining a shape including the 
defined edge of the bright area. A measurement circuit determines a 
dimension of the defined shape whereby the dimension of the silicon 
crystal is determined as a function of the determined dimension of the 
defined shape. 
Generally, another form of the invention is a method for use in combination 
with an apparatus for growing a silicon crystal from a silicon melt. The 
method determines a dimension of the crystal being pulled from the melt 
wherein melt has a surface with a meniscus which is visible as a bright 
area adjacent the crystal. The method includes the steps of generating an 
image pattern of a portion of the bright area adjacent the silicon crystal 
and detecting a characteristic of the image pattern. The method also 
includes defining an edge of the bright area as a function of the detected 
characteristic and defining a shape including the defined edge of the 
bright area. The method further includes the step of determining a 
dimension of the defined shape whereby the dimension of the silicon 
crystal is determined as a function of the determined dimension of the 
defined shape. 
Alternatively, the invention may comprise various other systems and 
methods. 
Other objects and features will be in part apparent and in part pointed out 
hereinafter.

Corresponding reference characters indicate corresponding parts throughout 
the drawings. 
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
Referring now to FIG. 1, a system 21 is illustrated for use with a 
Czochralski crystal growing apparatus 23 in accordance with the present 
invention. In the illustrated embodiment, the crystal growing apparatus 23 
includes a vacuum chamber 25 enclosing a crucible 27 which is surrounded 
by a resistance heater 29 or other heating means. Generally, a crucible 
drive unit 31 rotates the crucible 27 in the clockwise direction, as 
indicated by the arrow, and raises and lowers crucible 27 as desired 
during the growth process. Crucible 27 contains a silicon melt 33 from 
which a single crystal 35 is pulled, starting with a seed crystal 37 
attached to a pull shaft or cable 39. As shown in FIG. 1, the melt 33 has 
a melt level 41, and crucible 27 and the single crystal 35 have a common 
vertical axis of symmetry 43. 
According to the Czochralski crystal growth process, a crystal drive unit 
45 rotates the cable 39 in the opposite direction that crucible drive unit 
31 rotates crucible 27. The crystal drive unit 45 also raises and lowers 
crystal 35 as desired during the growth process. A heater power supply 47 
energizes the resistance heater 29 and insulation 49 lines the inner wall 
of the vacuum chamber 25. An inert atmosphere of argon gas is preferably 
fed into vacuum chamber 25 as gas is removed from within vacuum chamber 25 
by a vacuum pump (not shown). In one embodiment, a chamber cooling jacket 
(not shown) fed with cooling water may surround vacuum chamber 25. 
Preferably, a temperature sensor 51, such as a photo cell, measures the 
melt surface temperature. 
In a preferred embodiment of the invention, at least one two-dimensional 
camera 53 is for use with a control unit 55 to determine the diameter of 
single crystal 35. The control unit 55 processes signals from the 
temperature sensor 51 as well as the camera 53. As shown in FIG. 2, 
control unit 55 includes a programmed digital or analog computer for use 
in controlling, among other things, crucible drive unit 31, single crystal 
drive unit 45 and the heater power supply 47. 
Referring further to FIG. 1, according to a general silicon single crystal 
growth process, a quantity of polycrystalline silicon is charged to 
crucible 27. Heater power supply 47 provides electric current through 
heater 29 to melt the charge. Crystal drive unit 45 lowers the seed 
crystal 37 via cable 39 into contact with the molten silicon of melt 33 
contained by crucible 27. When seed crystal 37 begins to melt, crystal 
drive unit 45 slowly withdraws, or pulls, it from melt 33. Seed crystal 37 
draws silicon from melt 33 to produce a growth of silicon single crystal 
35 as it is pulled from melt 33. Before seed crystal 37 contacts melt 33, 
it may first be necessary to lower seed crystal 37 nearly in contact with 
melt 33 for preheating seed crystal 37. 
Crystal drive unit 45 rotates crystal 35 at a predetermined reference rate 
as it is pulled from melt 33. Crucible drive unit 31 similarly rotates 
crucible 27 at a second predetermined reference rate, but usually in the 
opposite direction relative to crystal 35. Control unit 55 initially 
controls the withdrawal, or pull, rate and the power supplied to heater 29 
by power supply 47 to cause a neck down of crystal 35. Preferably, control 
unit 55 then adjusts these parameters to cause the diameter of crystal 35 
to increase in a cone-shaped manner until a predetermined desired crystal 
diameter is reached. Once the desired crystal diameter is reached, control 
unit 55 controls the pull rate and heating to maintain constant diameter 
as measured by system 21 until the process approaches its end. At that 
point, the pull rate and heating are increased so that the diameter 
decreases to form a tapered portion at the end of single crystal 35. 
As described above, accurate and reliable control is desired during the 
crystal growth process, particularly in the neck portion of crystal 35. 
The neck is preferably grown at a substantially constant diameter as seed 
crystal 37 is drawn from melt 33. For example, control unit 55 causes a 
substantially constant neck diameter to be maintained so that the neck 
diameter remains within fifteen percent of the desired diameter. As is 
known in the art, the top portion of the neck adjacent seed crystal 37 may 
contain dislocations (not shown) first introduced by the thermal shock 
associated with bringing the dislocation-free seed crystal 37 into contact 
with silicon melt 33. As is known in the art, excessive fluctuations in 
neck diameter may also cause dislocations to form. 
Commonly assigned U.S. Pat. No. 5,178,720, the entire disclosure of which 
is incorporated herein by reference, discloses a preferred method for 
controlling crystal and crucible rotation rates as a function of the 
crystal diameter. 
FIG. 2 illustrates a preferred embodiment of control unit 55 in block 
diagram form. According to the present invention, camera 53 is preferably 
a monochrome charge coupled device (CCD) camera, such as a Sony XC-75 CCD 
video camera having a resolution of 768.times.494 pixels. Camera 53 is 
mounted in a viewport (not shown) of chamber 25 at an angle of 
approximately 34.degree. with respect to the vertical axis 43 and is aimed 
generally at the intersection of axis 43 and melt 33 at the melt level 41 
(see FIG. 3). 
Camera 53 generates a video image of the width of crystal 35 as it is 
pulled from melt 33 including an image of a portion of the meniscus (see 
FIG. 3) at the interface between melt 33 and crystal 35. Preferably, the 
lens of camera 53 is a 16 mm lens providing a field of view of at least 
approximately 300 mm. Camera 53 communicates the video image via line 57 
(e.g., RS-170 video cable) to a vision system 59. As shown in FIG. 2, the 
vision system 59 includes a video image frame buffer 61 and an image 
processor 63. As an example, vision system 59 is a Cognex CVS-400 vision 
system. In turn, vision system 59 communicates with a programmable logic 
controller (PLC) 65 via line 67. In one preferred embodiment, the PLC 65 
is a Model 575 PLC manufactured by Siemens and line 67 represents a VME 
backplane interface. 
Referring further to FIG. 2, vision system 59 also communicates with a 
video display 69 via line 71 (e.g., RS-170 RGB video cable) and with a 
personal computer 73 via line 75 (e.g., RS-232 cable). In a preferred 
embodiment, the video display 69 displays the video image generated by 
camera 53 and the computer 73 is used to program vision system 59. 
In the illustrated embodiment, PLC 65 communicates with an operator 
interface computer 77 via line 79 (e.g., RS-232 cable) and with one or 
more process input/output modules 81 via line 83 (e.g., RS-485 cable). The 
operator interface computer 77 permits the operator of crystal growing 
apparatus 23 to input a set of desired parameters for the particular 
crystal being grown. The process input/output module 81 provides a path to 
and from crystal growing apparatus 23 for controlling the growth process. 
As an example, PLC 65 receives information regarding the melt temperature 
from temperature sensor 51 and outputs a control signal to heater power 
supply 47 via process input/output module 81 for controlling the melt 
temperature thereby controlling the growth process. 
FIG. 3 is a fragmentary view of silicon crystal 35 being pulled from melt 
33. Crystal 35 constitutes a generally cylindrical body of crystalline 
silicon and is preferably an ingot of crystalline silicon having vertical 
axis 43 and a diameter D. It should be understood that an as-grown 
crystal, such as crystal 35, may not have a uniform diameter, although it 
is generally cylindrical. For this reason, diameter D may vary slightly at 
different axial positions along axis 43. Further, diameter D will vary in 
the different phases of crystal growth (e.g., seed, neck, crown, shoulder, 
body and end cone). FIG. 3 also illustrates a surface 85 of melt 33 having 
a liquid meniscus 87 formed at the interface between crystal 35 and melt 
33. As is known in the art, the reflection of crucible 27 on the meniscus 
87 is typically visible as a bright ring adjacent crystal 35. 
As described above, camera 53 is preferably mounted in a viewport (not 
shown) of chamber 25 aimed generally at the intersection of axis 43 and 
melt 33. In other words, camera 53 has an optical axis 89 that is at an 
acute angle .THETA. with respect to vertical axis 43. As an example, 
.THETA. is approximately 34.degree.. Further, the lens of camera 53 
preferably provides a field of view including the width of crystal 35 and 
including at least a portion of the bright ring of meniscus 87. In a 
preferred embodiment, proper lens selection provides both telephoto 
viewing for high resolution of small seeds and necks as well as wide angle 
viewing for the larger body portion of crystal 35. 
Referring now to FIG. 4, an exemplary view of crystal 35, including 
meniscus 87, is shown as viewed through the viewport of chamber 25 by 
camera 53. According to a preferred embodiment of the invention, the frame 
buffer 61 of vision system 59 receives the video image signal from camera 
53 and captures an image pattern for processing by the image processor 63. 
In general, image processor 63 performs digital edge-detection to locate 
the coordinates of at least three points around the inside or outside of 
the bright ring of meniscus 87. Since the cross-section of crystal 35 and 
meniscus 87 is known to be generally circular, the bright ring edge 
coordinates detected by image processor 63 are assumed to be elliptical, 
transformed and mapped into a circular shape. In the alternative, the edge 
coordinates can be mapped into a circular shape by compensating for the 
distortion caused by the angle at which camera 53 is mounted. Gonzalez and 
Wintz, Digital Image Processing, 1987, pages 36-52, incorporated herein by 
reference, disclose mathematical transformations for compensating for 
perspective distortion caused by the position of a camera with respect to 
a three-dimensional object. Such transformations may be used to extract a 
circular shape from a distorted elliptical shape. 
In one preferred embodiment of the invention, image processor 63 defines at 
least three, and preferably five or more, regions of interest 91 on the 
image generated by camera 53 which is captured by frame buffer 61. Image 
processor 63 examines the regions of interest 91, also referred to as edge 
tools or window regions, for a characteristic of the image pattern, such 
as the intensity or gradient of the intensity of the pixels included in 
each region 91. Based on the detected characteristic of the image pattern, 
image processor 63 determines edge coordinates along the outside of the 
bright ring of meniscus 87. Preferably, regions 91 are defined at 
preselected positions that generally correspond to positions along a curve 
matching the expected shape of the bright ring as viewed by camera 53. In 
other words, regions 91 are positioned radially with respect to a defined 
center point along the bottom half of an ellipse or circle to approximate 
the shape of the bright ring. By defining regions 91 at preselected 
positions approximating the shape of a portion of the bright ring, regions 
91 avoid known or expected reflections on the surface 85 of melt 33 that 
might cause spurious measurements. Also, since image processor 63 defines 
a number of regions 91, if part of the viewport of chamber 25 is blocked, 
image processor 63 is still able to detect the edges of the bright ring. 
It is to be understood that other characteristics of the image pattern, 
such as color or contrast, may be detected for finding edge coordinates of 
the bright ring of meniscus 87 in addition to intensity or intensity 
gradient. 
FIG. 4 illustrates a set of preferred positions at which regions 91 are 
defined. As shown, the left-most and right-most regions 91 are preferably 
located below the y coordinate of the center point C. Thus, system 21 
operating in accordance with the present invention is not subject to 
errors caused when the body of crystal 35 obscures the maximum width of 
the bright ring as it is viewed through the viewport of chamber 25. 
Advantageously, the present invention overcomes this problem caused by 
perspective distortion which is particularly troublesome for large 
diameter crystals (e.g., 200 mm and larger). 
As described above, crystal 35 is pulled from melt 33 generally along 
vertical axis 43 which is generally perpendicular to melt surface 85. 
During pulling, crystal 35 may move relative to vertical axis 43. 
Advantageously, regions 91 are large enough so that edge coordinates of 
the bright ring may be defined within regions 91 even though crystal 35 is 
moving. Image processor 63 further dynamically moves the preselected 
positions of regions 91 so that they are adjacent the imaged portion of 
the bright ring to follow the crystal diameter throughout all phases of 
growth (e.g., seed, neck, crown, shoulder, body and end cone). In other 
words, regions91 track crystal diameters from approximately 4 mm to 320 
mm. As is known in the art, however, the bright ring is not always visible 
during all phases of growth. For example, during growth of the crown 
portion of crystal 35, the bright ring may be relatively small or not 
visible. For this reason, system 21 preferably detects the perimeter of 
the crown which appears as a bright area relative to the intensity of the 
background of the image pattern. In this instance, the background of the 
image pattern is representative of melt surface 85. Thus, in the 
alternative to detecting the bright ring, system 21 detects the bright 
area associated with the crown of crystal 35. 
In a preferred embodiment, the coordinates of the edges of the bright ring 
detected within regions 91 are mathematically transformed to compensate 
for perspective distortion and then input into a best-fit circle 
measurement. For example, image processor 63 uses a Hough transform or 
least-squares fit to define a circular shape corresponding to the detected 
edges. According to the invention, image processor 63 defines a generally 
circular shape 93 having a circle diameter D' and a center point C based 
on the detected coordinates. Practically, at least three edge coordinates 
are needed to define circle 93. 
In order to obtain an accurate measurement of the diameter D of crystal 35 
for use by PLC 65 in controlling the crystal growth process, image 
processor 63 first digitally processes the diameter D' of defined circle 
93. In this manner, image processor 63 uses the dimensions of circle 93 to 
determine crystal diameter D, a measure of the quality of fit relative to 
an exact circle, and melt level 41. For purposes of this application, melt 
level 41 is defined as the distance from the top of heater 29 to surface 
85 of melt 33 and may be determined as a function of the coordinates of 
center point C. 
In operation, image processor 63 defines regions 91 adjacent the portion of 
the bright ring and detects an intensity gradient characteristic of the 
image pattern within regions 91. Image processor 63 further defines the 
coordinates of an edge of the bright ring within each region 91 as a 
function of the detected characteristic and defines generally circular 
shape 93 including the defined edge coordinates. The diameter D of crystal 
35 is then determined based on defined circular shape 93 for use in 
controlling the crystal growth process. PLC 65 of control unit 55 is 
responsive to the determined diameter D of silicon crystal 35 for 
controlling the rates at which crucible 27 and crystal 35 are rotated 
and/or the rate at which crystal 35 is pulled from melt 33 and/or the 
temperature of melt 33 and is responsive to the determination of melt 
level 41 for controlling the level of crucible 27 thereby to control 
crystal growth apparatus 23. Thus, image processor 63 constitutes a 
detection circuit, a defining circuit and a measurement circuit and PLC 65 
constitutes a control circuit. 
In one preferred embodiment of the invention, the diameter D' is measured 
in terms of radius pixels. As an example, crystal diameter D 
(mm)=CF(radius pixels)-3.02 mm where CF is a calibration factor between 
0.95 and 1.05 and 3.02 mm compensates for the width of the bright ring. 
The value of 3.02 mm is determined by analyzing data from grown necks and 
the calibration factor CF is an operator-entered value based on a measured 
value. According to the invention, the operator of crystal growth 
apparatus 23 measures the growing crystal 35 with a telescope that slides 
on a calibrated track and then inputs a value of CF via computer 77 so 
that the determined diameter D equals the measured value. In this manner, 
CF compensates for variability in the diameter measurement. Such 
variability is due primarily to changes in the distance between camera 53 
and crystal 35 which affect the magnification of the optics. Increasing 
the distance causes crystal 35 to appear smaller which may result in the 
actual crystal 35 being grown oversized. These changes in distance can 
occur from one crystal growth apparatus 23 to another, from one run to 
another, and even within a single run because of variability in melt level 
41. 
With respect to melt level 41, image processor 63 determines center point C 
which is indicative of melt level 41. According to the invention, the 
difference between the y coordinate of center point C and a reference 
value is used to determine melt level 41. Alternatively, commercially 
available optical methods (e.g., a light beam/detector apparatus mounted 
on the cover plate of chamber 25) may be used to determine melt level 41. 
The determination of melt level 41 may be used to reduce variability of 
diameter measurements by the calculation of a correction factor and by 
reducing melt level variation through lift control of crucible 27. 
Another primary source of variability in the diameter measurements is that 
the width of the bright ring changes depending on the height of the hot 
wall of crucible 27 which is exposed and reflected by liquid meniscus 87. 
As melt 33 is depleted, the width of the bright ring increases which 
causes crystal 35 to appear larger and may result in the actual crystal 35 
being grown undersized. As an alternative to using the 3.02 mm constant, 
the bright ring width can be calculated by using additional vision tools 
or mathematical modeling. For example, detecting the edge between crystal 
35 and the bright ring, in addition to detecting the edge between melt 33 
and the bright ring, provides a measure of bright ring width. Further, 
mathematical modeling of liquid meniscus 87 taking into account its 
reflective characteristics with respect to crucible wall height, provides 
a measure of bright ring width. 
In an alternative embodiment, the five edge coordinates of the bright ring 
defined within regions 91 of the image pattern are used to detect periodic 
deviations in crystal diameter with respect to the rate at which crystal 
drive unit 45 rotates crystal 35. As is known in the art, &lt;100&gt; zero 
dislocation growth is indicated by facets, or growth lines, generally 
parallel to vertical axis 43 and spaced apart along the body of crystal 
35. These growth lines appear as dimple-like features on the perimeter of 
a cross-section of crystal 35. For this reason, as crystal 35 rotates at a 
known rate, growth lines are expected within a particular region 91 at a 
rate of four times, for example, the rate of rotation. As such, image 
processor 63 confirms zero dislocation growth of crystal 35 and 
constitutes means for detacting periodic deviation in the determined 
diameter of defined circular shape 93. 
Further, it is to be understood that vision system 59 of the present 
invention may be used to determine other crystal growth parameters, such 
as purge tube gap or melt gap, complete meltdown, ice, convection currents 
and temperature, in addition to crystal diameter, melt level and loss of 
zero dislocation growth. 
FIG. 5 illustrates the operation of system 21 according to one preferred 
embodiment of the invention in the form of a flow diagram 95. After 
beginning at step 97, frame buffer 61 acquires an image pattern from 
camera 53 at step 99. Image processor 63 receives the captured image and 
adjusts its pixel values to compensate for distortion of the image pattern 
caused by the camera angle. This is accomplished by scaling the y values 
of the image pattern (y.sub.pixel) by a factor of 1.2, as derived from 
cos.THETA., at step 101 to define y values. Preferably, x=x.sub.pixel. 
Thus, image processor 63, performing step 101, constitutes means for 
adjusting the image pattern so that the portion of the bright area 
adjacent crystal 35 is generally arcuate. 
At step 103, image processor 63 of vision system 59 performs edge detection 
by examining the gradient of the intensity of the pixels within each 
region of interest 91. The gradient is obtained by taking the derivative 
of the relative intensity of the image pattern within each region 91. 
Thus, image processor 63 identifies the coordinates of the greatest change 
in intensity within each region 91 which is indicative of an edge of the 
bright ring. At step 105, if five edge coordinates are defined, image 
processor 63 proceeds to step 107 for fitting the defined edge coordinates 
to a generally circular shape by means of a circle-fitting algorithm, such 
as the Hough transform or least-squares fit. For example, the Hough 
transform uses sorting routines to develop clusters of data points that 
can be used to find circles and then finds the best cluster of data points 
for the desired object. The data is then averaged to find the center and 
radius of a fitted circle. 
At step 109, vision system 59 determines the quality of the circle-fit by 
comparing the defined circular shape 93 to an exact circle. This 
determination provides an indication of the validity of the measurements. 
If the defined shape is sufficiently circular, vision system 59 
communicates information representative of the diameter D' of defined 
circle 93 and the x-y coordinates of its center point C to PLC 65 of 
control unit 55 for use in controlling the crystal growth process. In the 
embodiment of flow diagram 95, vision system 59 reports the radius of 
circle 93. Thus, image processor 63 performing step 111, in cooperation 
with PLC 65, constitute means for determining the center of defined 
circular shape 93 with respect to a reference x-y coordinate system. 
Operation of system 21 then proceeds to step 113 where a counter N is set 
to zero. Image processor 63 then re-positions regions 91 based on the 
determined center point and radius. According to one preferred embodiment 
of the invention, each of regions 91 is defined at a preselected radial 
position along the lower half of the defined circle (shown generally in 
FIG. 4). In this manner, regions 91 are essentially centered on the 
detected edge of the bright ring of meniscus 87 after each iteration of 
flow diagram 95, and image processor 63 responds to movement of crystal 35 
during pulling as well as changes in diameter. 
If the edge coordinates of the bright ring are not defined within regions 
91 at step 105, image processor increments the counter N at step 117. 
Image processor 63 then repeats steps 99, 101, 103, 105 and 117 until N=10 
at step 119, or until image processor 63 defines five edge coordinates. 
After ten unsuccessful attempts at defining the edge of the bright ring, 
image processor 63 searches for the general position of the bright ring by 
performing a scanning routine at step 121 (shown in greater detail in 
FIGS. 6A-6C). The scanning routine of step 121 finds the approximate 
location of meniscus 87 on the image pattern based on the intensity of the 
bright ring relative to the intensity of the background of the image 
pattern which, in this instance, is representative of melt surface 85. 
Image processor 83 determines an approximate center point and radius for 
defining the preselected positions of regions 91. Thus, image processor 63 
performing steps 105, 113, 115, 117, 119 and 121 constitutes means for 
moving window regions 91 as a function of the detected characteristic and 
means for adjusting the preselected positions of window regions 91. 
FIGS. 6A-6C illustrate a preferred scanning routine of step 121 of FIG. 5 
in the form of a flow diagram 123. After beginning at step 125, frame 
buffer 61 acquires an image pattern from camera 53 at step 127. Image 
processor 63 receives the captured image and adjusts its pixel values to 
compensate for distortion of the image pattern caused by the camera angle 
at step 129. Proceeding to steps 131, 133 and 35, image processor 63 
positions additional regions of interest, referred to as ROI.sub.1, 
ROI.sub.2 and ROI.sub.3, at the left, right and bottom edges of the image 
pattern. These additional regions of interest, ROI.sub.1, ROI.sub.2 and 
ROI.sub.3, are relatively larger than regions 91 and are also referred to 
as light meter tools. At step 137, the number of detected edges is set to 
zero and, at step 139, a parameter LAST.sub.MAX, representative of the 
last maximum intensity reading, is set to a relatively high value (e.g., 
1000). 
In one preferred embodiment, a subroutine 141 is used to find the left edge 
of meniscus 87 by comparing the maximum intensity of the image pattern 
within ROI.sub.1, i.e., MAX.sub.PIXEL, to a threshold, such as 100. If 
MAX.sub.PIXEL exceeds 100 at step 143, image processor 63 proceeds to step 
145 where the ratio MAX.sub.PIXEL :LAST.sub.MAX is compared to 1.1. If the 
ratio exceeds 1.1, image processor 63 considers a left edge to be found 
within ROI.sub.1 and increments the edge counter at step 147. The x 
coordinate of ROI.sub.1 is then stored at step 149 for identifying the 
left edge of the bright ring. If MAX.sub.PIXEL is 100 or less at step 143, 
or if the ratio MAX.sub.PIXEL :LAST.sub.MAX is 1.1 or less at step 145, 
LAST.sub.MAX is reset to equal MAX.sub.PIXEL at step 151. Image processor 
63 then moves ROI.sub.1 to the right by a predetermined amount. For 
example, at step 153, image processor re-positions ROI.sub.1 five x 
coordinates to the right. So long as ROI.sub.1 has not reached the right 
border of the image pattern, as determined at step 155, image processor 63 
repeats subroutine 141. 
Referring now to FIG. 6B, after image processor 63 detects the left edge of 
the bright ring within ROI.sub.1 or after ROI.sub.1 reaches the right 
border of the image pattern, image processor 63 resets LAST.sub.MAX to 
1000 at step 157 and performs a subroutine 159 which is essentially 
identical to subroutine 141 but opposite in direction. The subroutine 159 
is used to find the right edge of meniscus 87 by comparing the maximum 
intensity of the image pattern within ROI.sub.2, i.e., MAX.sub.PIXEL, to a 
threshold, such as 100. If MAX.sub.PIXEL exceeds 100 at step 161, image 
processor 63 proceeds to step 163 where the ratio MAX.sub.PIXEL 
:LAST.sub.MAX is compared to 1.1. If the ratio exceeds 1.1, image 
processor 63 considers a right edge to be found within ROI.sub.2 and 
increments the edge counter by two at step 165. The x coordinate of 
ROI.sub.2 is then stored at step 167 for identifying the right edge of the 
bright ring. If MAX.sub.PIXEL is 100 or less at step 161, or if the ratio 
MAX.sub.PIXEL :LAST.sub.MAX is 1.1 or less at step 159, LAST.sub.MAX is 
reset to equal MAX.sub.PIXEL at step 169. Image processor 63 then moves 
ROI.sub.2 to the left by a predetermined amount. For example, at step 171, 
image processor re-positions ROI.sub.2 five x coordinates to the left. So 
long as ROI.sub.2 has not reached the left border of the image pattern, as 
determined at step 173, image processor 63 repeats subroutine 159. 
Referring now to FIG. 6C, after image processor 63 detects the right edge 
of the bright ring within ROI.sub.2 or after ROI.sub.2 reaches the left 
border of the image pattern, image processor 63 resets LAST.sub.MAX to 
1000 at step 175 and performs a subroutine 177 which is essentially 
identical to subroutines 141 and 159 but in the y direction. The 
subroutine 177 is used to find the bottom edge of meniscus 87 by comparing 
the maximum intensity of the image pattern within ROI.sub.3, i.e., 
MAX.sub.PIXEL, to a threshold, such as 100. If MAX.sub.PIXEL exceeds 100 
at step 179, image processor 63 proceeds to step 181 where the ratio 
MAX.sub.PIXEL :LAST.sub.MAX is compared to 1.1. If the ratio exceeds 1.1, 
image processor 63 considers a bottom edge to be found within ROI.sub.3 
and increments the edge counter by four at step 183. The y coordinate of 
ROI.sub.3 is then stored at step 185 for identifying the bottom edge of 
the bright ring. If MAX.sub.PIXEL is 100 or less at step 179, or if the 
ratio MAX.sub.PIXEL :LAST.sub.MAX is 1.1 or less at step 181, LAST.sub.MAX 
is reset to equal MAX.sub.PIXEL at step 187. Image processor 63 then moves 
ROI.sub.3 toward the top of the image pattern by a predetermined amount. 
For example, at step 189, image processor re-positions ROI.sub.3 6.6 y 
coordinates toward the top. So long as ROI.sub.3 has not reached the top 
border of the image pattern, as determined at step 191, image processor 63 
repeats subroutine 177. 
After the left, right and bottom edges of meniscus 87 have been found, as 
determined at step 193, image processor 63 proceeds to calculate an 
approximate circle radius at step 195 by dividing the difference in the x 
coordinates by two and proceeds to calculate the coordinates of the circle 
center at step 197 by finding the midpoint between the x coordinates and 
by adding the circle radius to the y coordinate of the bottom edge. At 
step 199, image processor 63 preferably calculates the coordinates of a 
point approximately on the right edge of the bright ring. According to the 
illustrated embodiment of the invention, the calculated radius, center 
point and edge point are used to position regions 91 approximately at the 
bright ring of meniscus 87 before processor 63 returns to operation 
according to flow diagram 95 of FIG. 5. On the other hand, if all of the 
edges are not found, as determined at step 193, image processor 63 returns 
to step 131 of flow diagram 123. At step 201, flow diagram 123 ends. 
In an alternative embodiment of the invention, vision system 59 may be 
embodied as a computer having a frame grabber (e.g., Creative Technology's 
VideoBlaster.RTM.) for capturing the video image generated by camera 53. 
The computer, functioning as image processor 63, scans the image pattern 
and analyzes the individual intensity values of each scan line. Starting 
at the left and right edges of the image pattern and moving toward its 
center, the background (i.e., melt surface 85) intensities are measured 
and averaged. The scan continues until an abrupt increase in intensity is 
found or a predetermined number of samples have been taken. Binary 
thresholding is performed to identify the edges of the bright ring where 
the threshold consists of the average intensity value plus an empirical 
offset. A pair of window regions are defined for each scan line at 
positions generally symmetrical about the previously determined circle 
center's x coordinate to prevent extraneous reflections from being 
identified as valid edges. The windows apply a tolerance of .+-.n pixels 
from the reported edges of the previous scan line. In this manner, 
changing crystal diameters and movement of crystal 35 during pulling are 
accommodated. By searching the image pattern from top to bottom, the left 
and right window regions are re-positioned at an equal rate toward the 
center from their respective borders until two valid edges are located. 
The window regions are then re-positioned with their centers on the edge. 
Each edge detected in subsequent scan lines are preferably within the 
window region from the previous scan line, thus, ensuring that the edges 
are connected. If a scan line fails tolerance checks, it is simply 
ignored, or if a predetermined number of lines fail, the search is 
restarted. Again, perspective distortion caused by the angle at which 
camera 53 is mounted may be compensated for by means such as the Gonzalez 
transformation. The validated edges are then fit to a circle for 
calculating the circle center point and circle diameter. 
The following examples are presented to describe preferred embodiments and 
utilities of the present invention and are not meant to limit the present 
invention unless otherwise stated in the claims appended hereto. 
EXAMPLES 
1. FIG. 7 graphically illustrates diameter measurements in pixels versus 
diameter D in millimeters for the crown portion of crystal 35. As 
described above, vision system 59 determines the diameter of crystal 59 
based on the width of defined circle 93 in terms of x.sub.pixel values 
which may be converted to millimeters. As shown in FIG. 7, approximately 
1.8 x.sub.pixel values corresponds to one millimeter as measured by, for 
example, calipers. 
2. FIGS. 8A-8B illustrate measurements taken in the neck portion of crystal 
35 in graphical form. FIG. 8A shows the diameter in millimeters as 
measured with calipers and the diameter in millimeters as measured by 
vision system 59 versus the length of the neck. As shown, fine-tuning may 
be necessary on the scaling (e.g., bias and gain) to minimize the error 
between the two measurements. Further, the curve showing the measurements 
determined by vision system 59 is based on a sampling rate of one sample 
per minute which might miss certain peaks and valleys of the neck diameter 
since the neck portion of crystal 35 grows as much as five millimeters in 
one minute. Improvements in scaling have yielded results with an accuracy 
of .+-.0.5 mm in the 4.5 mm to 7.0 mm range of diameters. FIG. 8B shows 
the diameter in millimeters as measured by vision system 59 versus the 
diameter in millimeters as measured with calipers. 
3. FIGS. 9A-9B illustrate measurements taken over the length of crystal 35 
in graphical form. For purposes of FIGS. 9A-9B, crystal length is measured 
from a reference point on the body portion of crystal 35 where crystal 35 
has a relatively uniform diameter and does not include the neck and crown 
portions of crystal 35. FIG. 9A shows the diameter in millimeters as 
measured by vision system 59 and the y coordinate of the center point C in 
corrected pixels versus the length of crystal 35. As described above, the 
y coordinate of the center point C is calculated by: y=1.2(y.sub.pixel) 
where y is in terms of corrected pixels. FIG. 9B shows the corrected y 
coordinate of center point C in corrected pixels versus the crystal length 
in millimeters. As described above, the value of the y coordinate 
interacts with the diameter of crystal 35 due to the perspective 
distortion caused by the angle at which camera 53 is mounted and the 
assumption of an elliptically-shaped bright ring. Although multiplying 
y.sub.pixel by a scaling factor of 1.2 partially compensates for this 
distortion, further correction is desirable. The further correction 
attempts to isolate the predicted drop in melt level 41 caused by the 
reduced diameter of crucible 27 as melt 33 is depleted to approximately 40 
kg remaining. With the lift ratio of crucible 27 fixed, melt 33 tends to 
be depleted faster than crucible drive unit 31 raises crucible 27. In this 
instance, the corrected y coordinate is determined by: y.sub.corrected 
=y-C.sub.1 (crystal length)+C.sub.2 (diameter D-C.sub.3) where C.sub.1 
=0.0033, C.sub.2 =0.35 and C.sub.3 =209. In other words, the y coordinate 
of the center point C is adjusted by subtracting the long-term, apparently 
linear, increase in melt level 41 from 0 to approximately 750 mm in length 
and by adding a delta diameter multiplied by a scale factor. 
In view of the above, it will be seen that the several objects of the 
invention are achieved and other advantageous results attained. 
As various changes could be made in the above constructions and methods 
without departing from the scope of the invention, it is intended that all 
matter contained in the above description or shown in the accompanying 
drawings shall be interpreted as illustrative and not in a limiting sense.