Method to determine tool paths for thinning and correcting errors in thickness profiles of films

A method to determine the tool path of a material removal tool which is part of a system to shape the surface of a substrate is disclosed. The method conditions initial metrology data of the substrate into a dwell time versus position on the surface for the removal tool. The dwell time array is subsequently converted into a velocity versus position array so that a position controller means may be utilized to guide the movement of the substrate with respect to the removal tool to perform precise material removal on the surface of the substrate.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a system to shape the surface of a 
substrate, namely, to thin and modify films, and more particularly, to a 
method for determining the path for a plasma assisted chemical etching 
material removal tool to thin and modify the thickness profile of an 
existing substrate layer. The present invention provides a means to obtain 
a layer of uniform and specified thickness from a layer having a measured, 
but non-uniform thickness profile. 
2. Description of the Prior Art 
Substrate materials with thin solid layers, such as silicon-on-insulator 
(SOI) wafers, and films are used extensively in the fabrication of 
electronic, optical, magnetic, superconducting and other important 
technological devices. Such substrates are often subjected to figuring and 
thinning processes which remove some of the material from the surface. 
Along with describing conventional material removal processes, a system 
for removing material from the surface of an SOI wafer is described in a 
related patent application entitled "System for Removing Material from a 
Wafer", U.S. patent application Ser. No. 07/696,897, filed on May 7, 1991. 
The system disclosed therein includes a means for determining thickness 
profile data for a surface of a wafer, means for converting the thickness 
profile data to a dwell time versus position map stored in a system 
controller and a means for removing material from the surface of the wafer 
in accordance with the map such that the wafer has a preselected thickness 
profile. 
The present invention is directed toward a method used to determine the 
paths that the removal tool must make over the wafer to thin the wafer to 
a uniform thickness or a desired profile. 
SUMMARY OF THE INVENTION 
The present invention relates to a system to shape the surface of a 
substrate, and more particularly, to a method to thin and modify 
semiconductor films for the production of silicon-on-insulator (SOI) 
wafers. The present invention provides a method to determine the path a 
localized material removal tool comprising a plasma assisted chemical 
etching apparatus must make over the surface of the wafer to thin and 
modify the thickness profile of an existing layer, where the profile of 
the layer may be arbitrary but measurable, to another desired profile. The 
final thickness profile of the layer after processing by the removal tool 
utilizing the method of the present invention is independent of the 
overall surface shape (shape of the substrate to layer). 
The present invention provides a means to specify the tool material removal 
shape, the tool removal dependence with tool velocity, and the amount of 
tool overlap necessary to construct a tool velocity versus position map 
for guiding the local material removal over the surface of the wafer to 
achieve the desired change in the film thickness profile. It performs this 
function using measured initial thickness profile data, desired film 
thickness profile data and the spatial material removal rate of the 
removal tool. 
One objective of the present invention is to provide a method to thin and 
modify films by plasma assisted chemical etching apparatus. 
Another objective of the present invention is to provide a method by which 
material removal paths can be determined to produce layers of material 
with desired thickness profiles more accurately and more rapidly. 
Another objective of the present invention is to provide a method to obtain 
a layer of uniform and specified thickness from a layer having a measured, 
but non-uniform, thickness profile. 
Other objects and advantages of the present invention will become apparent 
to those skilled in the art from the following detailed description read 
in conjunction with the attached drawings and claims appended hereto.

DETAILED DESCRIPTION OF THE PRESENT INVENTION 
A system to modify the thickness profile of a layer by plasma assisted 
chemical etching is generally described in U.S. patent application Ser. 
No. 07/696,897 referenced above in the Description of the Prior Art. A 
flow diagram of the simplified process steps of the system to modify the 
thickness profile of a wafer is illustrated in FIG. 1. The process steps 
of the system invention generally comprise a metrology step 10 to measure 
and map the initial thickness layer profile of the substrate, a step 12 to 
compute a map relating plasma removal tool velocity to the position of the 
removal tool, and a step 14 to modify a substrate layer thickness profile 
by moving the removal tool means with respect to a substrate surface. The 
removal tool generally comprises a computer controlled plasma assisted 
chemical etching reactor (not shown) constructed so as to facilitate local 
material removal. The shape and characteristics of the plasma (the removal 
tool) produced by the apparatus is controllable by varying a number of 
parameters such as radio frequency power input, reactive gas compositions, 
flow rates and pressures, and the physical apparatus itself. 
The present invention is directed to the system step 12 to determine the 
map relating the plasma removal tool velocity to the position of the tool 
required before performing the actual removal process. FIG. 2 shows a flow 
diagram of associated inputs, processing steps and outputs needed for the 
determination step 12. Referring to FIG. 2, the method of the present 
invention generally comprises the substeps of processing previously 
measured metrology data 16 in the form of a film thickness error map 17, 
generating a dwell time array 18 from the processed data, and generating a 
tool velocity map 20 from the array 18 for each position of the removal 
tool. Thus, by performing the above steps, the removal tool can be 
accurately guided and dynamically moved about the surface of the wafer to 
precisely excise material from the surface and fabricate a wafer with a 
uniform layer on it. 
The processing metrology data step 16 generally comprises the substeps of 
extending film edge data 22, interpolating metrology data points 24 and 
smoothing spurious metrology data 26. The substep to extend the film edge 
data permits the system to avoid edge effects and allows the attainment of 
the desired target film thickness profile over the maximum possible area 
of the film. 
Accurate thickness correction at the edge of the substrate is accomplished 
by commanding controlled continuous movement of the removal tool off the 
substrate as if the film being corrected is actually extended beyond the 
area over which thickness data is measured. Thus, to maintain controlled 
continuous motion off of the substrate, the film position/thickness data 
array constructed by the measurement step 10 must be extended a distance 
beyond the actual measured edge of the film. The distance must be at least 
the radius of a tool removal footprint and the extended data must fit the 
actual measured data smoothly. Otherwise, the resulting motion of the tool 
is discontinuous, although centered off of the film, and will feed back 
errors onto the corrected film through material removal of the trailing 
edge of the removal footprint which is still on the film. Continuous 
motion off the edge can be achieved by assuring that the extended data 
matches the magnitude and slopeof the film thickness error to be removed. 
FIGS. 3a and 3b are interference fringe pictures of thinned silicon films 
taken in monochromatic light. The substrate in each figure is a 1 micron 
silicon dioxide layer on a 100 mm diameter silicon wafer. Each line 
represents a thickness change of 650 .ANG. in the silicon film. Prior to 
thinning, each wafer's starting film thickness was about 4.+-.1.5 microns 
which is nearly a 50 fringe variation. FIG. 3a shows a film thinned to 
about 0.3 microns without using an algorithm of the present invention for 
continuously extending the data at the edge of the film. The resulting 
velocity map did not command the tool to move smoothly off the film and 
the trailing part of the tool introduced thickness variations up to a tool 
radius in from the film edge as the center of the tool moved off the film 
edge. 
FIG. 3b shows a film thinned using the algorithm of the present invention 
to extend the measured thickness data over the film area by radially 
extending the measured thickness values around the edge. FIG. 3b shows a 
number of concentric fringes along film. A the edge which indicate that 
there are much lower errors near the edge of the further improvement in 
the error at the edge may be gained by including provisions for matching 
the slope of the film thickness. 
The step of generating a dwell time array 18, as discussed more fully 
below, requires a greater number of data points than are supplied by the 
metrology step 10 even though the resolution of the film thickness 
measurement points sufficiently samples the surface. Thus, the processing 
of the metrology data step of the present invention additionally comprises 
the use of an interpolation substep 24 to fill in film thickness values 
between measured points. Various interpolations methods may be used to 
fill in the values. For example, the simplest interpolation method which 
can be used with the present invention is a 2-dimensional linear 
interpolation. More representative interpolated values are obtained by 
performing a polynomial spline fit of the slope of the surface at each 
measured point. The film thickness profile corrections shown in FIGS. 3a 
and 3b were made from an error map 17 having data measurements of film 
thickness points spaced on a 5 mm grid spacing. The number of data points 
was subsequently increased five fold by interpolation so as to reduce the 
spacing between data points to 1 mm. 
The film thickness error map 17 may have spurious data or actual thickness 
data that represents film thickness errors that are beyond the capability 
of the system to accurately correct due to limitations in the removal tool 
with respect to the surface. For example, such errors may result from 
discontinuous edges of the substrate. The data from the map 17 is smoothed 
and filtered by a smoothing substep 26. Smoothing is accomplished by 
eliminating the effects of spurious data and/or limiting the change in the 
slope of the thickness to be corrected. The effects of spurious data may 
be eliminated by averaging multiple measurements and additionally, 
throwing out data which differs from the average at a given point by more 
than a predetermined value. Change in the slope of the film thickness, as 
given by the measured data, can be limited by imposing a maximum value to 
the difference value between the thickness at a given point and the 
average of the surrounding measured thickness values. The smoothing 
substep insures that when the correction to the film profile is performed, 
the removal tool accurately responds to motion commands from a controller 
supplied with tool velocity data. Also, such smoothing methods insure that 
secondary errors are not introduced into the film to correct false errors 
or errors with a spatial frequency content too high for the material 
removal tool to correct (i.e. spatial errors within an area much smaller 
than the tool removal footprint size). 
As stated above, after the metrology data has been processed, the processed 
data is used to generate a dwell time array in substep 18. The dwell time 
calculation made by this substep uses the processed film thickness data, 
the inputs of a material removal footprint shape and a target film 
thickness profile to calculate a map of dwell times for the material 
removal tool as a function of removal tool position. The calculation of 
the dwell time map is necessary for building a velocity map to provide 
guidance to a means for moving the substrate with respect to the removal 
tool when making the corrections to the thickness of the film. 
As stated above the calculated dwell time data points are spaced closer 
than the footprint size of the material removal tool. This spacing 
arrangement reduces the sensitivity of the removal tool footprint to the 
exact shape of the material removal footprint and allows a more accurate 
prediction of the material removal dwell time obtained by continuous tool 
velocity. A 1 mm grid spacing for the dwell time map was used for the 
thinned silicon films in FIGS. 3a and 3b. The removal tool footprint 
defined by the plasma shape was 13 mm wide at half the maximum removal 
depth. 
When the tool footprint size is much smaller than a representative 
dimension of the size of the film thickness errors to be corrected, an 
accurate dwell time map is obtained by allowing the dwell time to be 
proportional to the error itself. When correcting for errors having 
characteristic dimensions on the order of the footprint size, an accurate 
dwell time is obtained by explicitly accounting for the footprint shape. 
A dwell time map which accounts for the footprint shape can be calculated 
by a number of methods. However, whatever the method used for calculation, 
the method must take into account computational speed and accuracy 
tradeoffs. One method starts with a dwell time approximation proportional 
to the film thickness error and then makes corrections to the 
approximation based on the footprint shape. This method, where the initial 
dwell time is proportional to the film thickness error, can be viewed as a 
method that enhances the error map by exaggerating the higher spatial 
frequency errors so as to efficiently correct the errors with the removal 
tool. The solution to this method can be implemented in several ways. 
An iterative solution starts with a dwell time proportional to the error at 
any point. The solution simulates the thickness profile that would be 
obtained with a dwell time map represented by T0(x,y), where T0(x,y) is 
the dwell time at point x,y, derived by convolving T0(x,y) with the foot 
print shape using techniques known to those skilled in the art. Next, the 
residual error after simulation, Er(x,y), where Er(x,y) is the error at 
point (x,y), is computed by subtracting the simulated thickness profile 
from the starting measured film thickness error. Following the residual 
error computation, the starting dwell time is scaled by the calculated 
residual error to give a corrected dwell time map, T1(x,y) where T1 is the 
corrected dwell time at point x,y. The corrected dwell time for a point, 
T1(x,y), is obtained by solving the equation: 
EQU T1(x,y)=T0(x,y)[1+Er(x,y)]. 
The scaling procedure inherently accounts for the footprint shape in the 
convolution of the measured footprint shape with the initial dwell time 
estimate, T0(x,y), to obtain a correction, Er(x,y). Additional simulated 
iterations and dwell time rescaling can be done to obtain greater accuracy 
for the dwell time map while the number of iterations actually used is 
dictated by computer speed limitations and overall time constraints. 
A local surface error correction solution to the method for determining 
dwell time adjusts T0(x,y) based on the local film thickness error. 
However, the higher the spatial frequency of the film thickness error in 
the region of point (x,y), the larger the adjustment to T0(x,y). The 
adjustment is calculated from the shape of the film thickness error over a 
region characteristic of the footprint area. It should be recognized that 
the footprint shape needs to be accounted for only when the film thickness 
error has a spatial curvature, and, thus, simple piston (cylindrically 
shaped substrates surface discontinuities) or tilt errors in the film 
thickness are corrected exactly by T0(x,y). A more accurate dwell time, 
T'1(x,y) is obtained by adding a term C(x,y) which is subject to the 
local, spatial dependence on the film thickness error. Thus, the more 
accurate dwell time, T'1, is determined by solving the equations 
T'1(x,y)=T0(x,y)+C(x,y) and C(x,y)=k[E(x,y)-Eave(s;x,y)], where k is a 
proportionality constant determined from the footprint shape and which can 
be further refined from the measured accuracy of film thickness profiles 
after correction, E(x,y) is the film thickness error value at point (x,y) 
and Eave(s;x,y) is an average value of the thickness error at a 
surrounding characteristic distance, s. To reflect the footprint shape, s 
is of the order of the footprint size (the width at half of maximum 
removal). 
Generally, dwell times may be calculated in real, physical space or Fourier 
space (spatial frequency domain). Calculations with Fourier transforms add 
the advantage of increasing computation speed when array sizes are large 
since integrations can be performed as multiplications. 
Referring to FIG. 2, once the dwell time map has been generated by substep 
18 a tool path must be determined to satisfy the map. To satisfy the tool 
path determination, a substep 22 must be performed to calculate a tool 
velocity map. Similar to the calculation for the dwell map, using a 
spacing between calculated data points much smaller than the footprint 
size reduces the sensitivity to the exact shape of the material removal 
footprint when correcting the error in the film thickness. Tool scans of 
the surface of the substrate must overlap. Correspondingly, the increment 
between overlapping tool scans as determined by the tool path calculation 
should be much less than the diameter of the tool foot print shown in FIG. 
4a. By keeping the increment small, "ripple" effects introduced into the 
film thickness from overlapping tool scans can be made arbitrarily small 
(&lt;1 .ANG. ). For a small increment between scans, the summed removal 
depth, D, is related to the increment step dx by 
EQU D=A/dx 
where A is a constant that depends on the volume removed by the tool. Thus, 
referring to FIGS. 4a, 4b, and 4c, programmed control of the depth of 
removal when scanning the removal tool over the surface of the substrate 
can be obtained by varying the tool velocity. Utilizing a uniform tool 
velocity with a small step increment between tool scans yields a uniform 
removal from the surface. Referring to FIG. 4d, by varying the tool 
velocity to meet the calculated dwell time map conditions, an arbitrary 
correction to the film thickness profile is achieved. 
The wafers shown in FIGS. 3a and 3b were thinned using an x-y scan. Other 
tool paths such as circular paths or spiral paths could be used provided 
the calculated velocity map is consistent with the dwell time map. Film 
thickness can be more precisely controlled if the tool is allowed to move 
continuously off of the film as described above. The path chosen for the 
removal tool should extend at least one tool radius off of the edge of the 
film. 
The material removal must be calibrated to the calculated dwell time units 
to satisfy the dwell time map. The calibration must include the dependence 
of the material removal on tool velocity and the magnitude of the 
calculated dwell time units must be correlated to the actual removal by 
the tool. 
Because tool velocity is used to provide a dwell time or conversely dwell 
time is used to provide tool velocity, the dependence of material removal 
is expressed as an inverse of tool velocity. Generally the dependence 
relationship is non-linear. FIGS. 5a and 5b show material removal 
dependencies on plasma etching tool velocity for silicon and fused silica. 
Referring to FIG. 5a, the measured dependencies under set plasma 
parameters for silicon are plotted. FIG. 5a shows that the dependence for 
silicon is linear. FIG. 5b shows that the dependence for fused silica is 
non-linear as is the case for most materials. The removal depth data can 
be fit to measured points over the velocity range to analytically describe 
the dependence. 
As stated above, the magnitude of the calculated dwell time units must be 
correlated to the actual tool removal. This can be accomplished by 
comparing the predicted volume removal in the calculated dwell time units 
to the actual, measured tool volume removal. Tool volume removal can be 
experimentally derived from a uniform removal with closely overlapped tool 
scans at a uniform velocity. The dwell time calculation can give a volume 
removal prediction by integrating the static tool removal shape over its 
area. 
When making a correction to the film thickness profile, the tool velocity 
required must be achievable by the actual hardware. Velocities specified 
by the tool velocity map to meet the calculated dwell times must be within 
the dynamic range of apparatus controlling the tool to substrate velocity. 
The velocity range required by the dwell time map can be shifted to be 
within the dynamic range of the hardware by changing the increment, dx, 
between scans. For example, reducing dx by a factor of two decreases the 
tool velocity by a factor of two (assuming removal is linear with tool 
velocity), thus changing the velocity range required. The velocity range 
can be shifted to be within the dynamic range of the hardware by changing 
the process volume removal rate. This is accomplished by changing the tool 
removal rate parameters (i.e., rf power, gas pressure, gas mixture). For 
example, doubling the volume removal rate decreases the tool velocity 
required by a factor of two. 
To meet calculated dwell time requirements, other parameters may be 
programmed to vary the instantaneous tool removal depth provided the 
removal rate has a rapid, controllable response to the changing parameter. 
For example, varying the rf power gives a rapid and well defined removal 
rate response. Programmed control of the rf power provides a means to 
correct film thickness, and when used in conjunction with the tool 
velocity is a means to extend the dynamic range of the tool. 
Thus what has been described is a method for determining the tool path for 
a material removal tool so as to provide a means to make corrections to 
the surface of a substrate. The method disclosed herein provides the 
required information to drive the stage controller providing a means to 
guide the removal tool over the substrate surface so that precise material 
removal can be made and a uniform layer on a wafer can be obtained.