U.S. patent application number 13/833104 was filed with the patent office on 2014-09-18 for method and apparatus for providing metric relating two or more process parameters to yield.
This patent application is currently assigned to GLOBALFOUNDRIES Inc.. The applicant listed for this patent is Azat LATYPOV. Invention is credited to Azat LATYPOV.
Application Number | 20140282307 13/833104 |
Document ID | / |
Family ID | 51534580 |
Filed Date | 2014-09-18 |
United States Patent
Application |
20140282307 |
Kind Code |
A1 |
LATYPOV; Azat |
September 18, 2014 |
METHOD AND APPARATUS FOR PROVIDING METRIC RELATING TWO OR MORE
PROCESS PARAMETERS TO YIELD
Abstract
A process and apparatus are provided for generating and
evaluating one or more metrics for analyzing the design and
manufacture of semiconductor devices. Embodiments include scanning
a drawn semiconductor design layout to determine a
difficult-to-manufacture pattern within the drawn semiconductor
design layout based on a match with a pre-characterized
difficult-to-manufacture pattern determining a corrected pattern
based on a pre-determined correlation between the corrected pattern
and the pre-characterized difficult-to-manufacture pattern, and
replacing the difficult-to-manufacture pattern with the corrected
pattern within the drawn semiconductor design layout.
Inventors: |
LATYPOV; Azat; (San Jose,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LATYPOV; Azat |
San Jose |
CA |
US |
|
|
Assignee: |
GLOBALFOUNDRIES Inc.
Grand Cayman
KY
|
Family ID: |
51534580 |
Appl. No.: |
13/833104 |
Filed: |
March 15, 2013 |
Current U.S.
Class: |
716/56 |
Current CPC
Class: |
Y02P 90/02 20151101;
G06F 30/39 20200101; Y02P 90/265 20151101; G06F 2119/18
20200101 |
Class at
Publication: |
716/56 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Claims
1. A method comprising: determining two or more parameters
associated with designing a semiconductor device; determining a
process window associated with acceptable limits of the two or more
parameters; and applying a probability density function to the
process window to generate a yield metric that relates the two or
more parameters to yield.
2. The method according to claim 1, further comprising: optimizing
the two or more parameters to generate two or more optimal
parameters; and applying the probability density function based on
the two or more optimal parameters.
3. The method according to claim 1, comprising: applying the
probability density function according to uncorrelated normal
distributions for the two or more parameters.
4. The method according to claim 1, comprising: applying the
probability density function according to at least one of
correlated distributions and spatially varying distributions for
the two or more parameters.
5. The method according to claim 1, further comprising: determining
two or more layers associated with designing the semiconductor
device; and correlating distributions of the two or more parameters
between the two or more layers.
6. The method according to claim 1, further comprising: evaluating
the yield metric with respect to at least one of an optical
proximity correction (OPC) model and a source mask optimization
(SMO) model.
7. The method according to claim 6, further comprising: maximizing
a value associated with the yield metric with respect to the at
least one of the OPC model and the SMO model.
8. The method according to claim 1, wherein the two or more
parameters are exposure focus and exposure dosage.
9. The method according to claim 1, wherein the probability density
function is a Gaussian probability density function.
10. An apparatus comprising: at least one processor; and at least
one memory including computer program code for one or more
programs, the at least one memory and the computer program code
configured to, with the at least one processor, cause the apparatus
to perform at least the following, determine two or more parameters
associated with designing a semiconductor device; determine a
process window associated with acceptable limits of the two or more
parameters; and apply a probability density function to the process
window to generate a yield metric that relates the two or more
parameters to yield.
11. The apparatus according to claim 10, wherein the apparatus is
further caused to: optimize the two or more parameters to generate
two or more optimal parameters; and apply the probability density
function based on the two or more optimal parameters.
12. The apparatus according to claim 10, wherein the apparatus is
further caused to: apply the probability density function according
to uncorrelated normal distributions for the two or more
parameters.
13. The apparatus according to claim 10, wherein the apparatus is
further caused to: apply the probability density function according
to at least one of correlated distributions and spatially varying
distributions for the two or more parameters.
14. The apparatus according to claim 10, wherein the apparatus is
further caused to: determine two or more layers associated with
designing the semiconductor device; and correlate distributions of
the two or more parameters between the two or more layers.
15. The apparatus according to claim 10, wherein the apparatus is
further caused to: evaluate the yield metric with respect to at
least one of an optical proximity correction (OPC) model and a
source mask optimization (SMO) model.
16. The apparatus according to claim 15, wherein the apparatus is
further caused to: maximize a value associated with the yield
metric with respect to the at least one of the OPC model and the
SMO model.
17. The apparatus according to claim 10, wherein the two or more
parameters are exposure focus and exposure dosage.
18. The apparatus according to claim 10, wherein the probability
density function is a Gaussian probability density function.
19. A method comprising: determining one or more layers associated
with designing the semiconductor device; determining two or more
parameters, including exposure dosage and exposure focus,
associated with designing a semiconductor device, wherein one or
more of the parameters are associated with one or more of the
layers; determining one or more process windows associated with
acceptable limits of the two or more parameters; and applying a
Gaussian probability density function according to the one or more
process windows to generate a yield metric that relates the two or
more parameters to yield.
20. The method according to claim 19, further comprising:
evaluating the yield metric with respect to at least one of an
optical proximity correction (OPC) model and a source mask
optimization (SMO) model; and maximizing a value associated with
the yield metric with respect to the at least one of the OPC model
and the SMO model to maximize a cost function.
Description
TECHNICAL FIELD
[0001] The present disclosure relates to the design and manufacture
of semiconductor devices and particularly to evaluating yield with
respect to designing and manufacturing semiconductor devices. The
present disclosure is applicable to all technology nodes, including
20 nanometer (nm) technology nodes and beyond.
BACKGROUND
[0002] For designing and manufacturing semiconductor devices, it is
desirable to relate process parameters to yield. However, there are
currently no metrics that allow for a direct comparison between
process parameters and yield. Currently used metrics require
inscribing an ellipse into a given process window, which is
computationally expensive, requires iterations, and may result in
multiple candidate solutions. It is desirable to develop metrics
without such complicated calculations. Even further, it is
desirable to develop metrics that relate maximizing yield to
minimizing cost associated with the manufacture of semiconductor
devices, such as cost associated with lithography process
steps.
[0003] A need therefore exists for a method and apparatus for
providing a metric that directly relates lithography process
parameters to yield.
SUMMARY
[0004] An aspect of the present disclosure is generating and
evaluating one or more metrics for analyzing the design and
manufacture of semiconductor devices.
[0005] Another aspect of the present disclosure is a device for
generating and evaluating one or more metrics for analyzing the
design and manufacture of semiconductor devices.
[0006] Additional aspects and other features of the present
disclosure will be set forth in the description which follows and
in part will be apparent to those having ordinary skill in the art
upon examination of the following or may be learned from the
practice of the present disclosure. The advantages of the present
disclosure may be realized and obtained as particularly pointed out
in the appended claims.
[0007] According to the present disclosure, some technical effects
may be achieved in part by a method including: determining two or
more parameters associated with designing a semiconductor device;
determining a process window associated with acceptable limits of
the two or more parameters; and applying a probability density
function to the process window to generate a yield metric that
relates the two or more parameters to yield.
[0008] Aspects of the present disclosure include optimizing the two
or more parameters to generate two or more optimal parameters; and
applying the probability density function based on the two or more
optimal parameters. Another aspect includes applying the
probability density function according to uncorrelated normal
distributions for the two or more parameters. Yet another aspect
includes applying the probability density function according to at
least one of correlated distributions and spatially varying
distributions for the two or more parameters. Additional aspects
include determining two or more layers associated with designing
the semiconductor device; and correlating distributions of the two
or more parameters between the two or more layers. An additional
aspect includes evaluating the yield metric with respect to at
least one of an optical proximity correction (OPC) model and a
source mask optimization (SMO) model. Another aspect includes
maximizing a value associated with the yield metric with respect to
the at least one of the OPC model and the SMO model. A further
aspect includes the two or more parameters being exposure focus and
exposure dosage. Yet another aspect includes the probability
density function being a Gaussian probability density function.
[0009] Another aspect of the present disclosure is a device
including: at least one processor; and at least one memory
including computer program code for one or more programs, the at
least one memory and the computer program code configured to, with
the at least one processor, cause the apparatus to perform at least
the following, determine two or more parameters associated with
designing a semiconductor device; determine a process window
associated with acceptable limits of the two or more parameters;
and apply a probability density function to the process window to
generate a yield metric that relates the two or more parameters to
yield.
[0010] Aspects include the apparatus being further caused to:
optimize the two or more parameters to generate two or more optimal
parameters; and apply the probability density function based on the
two or more optimal parameters. Another aspect includes the
apparatus being further caused to: apply the probability density
function according to uncorrelated normal distributions for the two
or more parameters. Yet another aspect includes the apparatus being
further caused to: apply the probability density function according
to at least one of correlated distributions and spatially varying
distributions for the two or more parameters. Still further aspects
include the apparatus being further caused to: determine two or
more layers associated with designing the semiconductor device; and
correlate distributions of the two or more parameters between the
two or more layers. An additional aspect includes the apparatus
being further caused to: evaluate the yield metric with respect to
at least one of an OPC model and a SMO model. Another aspect
includes the apparatus being further caused to: maximize a value
associated with the yield metric with respect to the at least one
of the OPC model and the SMO model. Yet another aspect includes the
two or more parameters being exposure focus and exposure dosage.
Still another aspect includes the probability density function
being a Gaussian probability density function.
[0011] Another aspect of the present disclosure is a method
including: determining one or more layers associated with designing
the semiconductor device; determining two or more parameters,
including exposure dosage and exposure focus, associated with
designing a semiconductor device, wherein one or more of the
parameters are associated with one or more of the layers;
determining one or more process windows associated with acceptable
limits of the two or more parameters; and applying a Gaussian
probability density function according to the one or more process
windows to generate a yield metric that relates the two or more
parameters to yield. Further aspects include evaluating the yield
metric with respect to at least one of an OPC model and a SMO
model; and maximizing a value associated with the yield metric with
respect to the at least one of the OPC model and the SMO model to
maximize a cost function.
[0012] Additional aspects and technical effects of the present
disclosure will become readily apparent to those skilled in the art
from the following detailed description wherein embodiments of the
present disclosure are described simply by way of illustration of
the best mode contemplated to carry out the present disclosure. As
will be realized, the present disclosure is capable of other and
different embodiments, and its several details are capable of
modifications in various obvious respects, all without departing
from the present disclosure. Accordingly, the drawings and
description are to be regarded as illustrative in nature, and not
as restrictive.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The present disclosure is illustrated by way of example, and
not by way of limitation, in the figures of the accompanying
drawings and in which like reference numerals refer to similar
elements and in which:
[0014] FIG. 1 illustrates a process window for two lithography
process parameters, according to an exemplary embodiment;
[0015] FIG. 2 schematically illustrates an overall system for
generating and evaluating one or more metrics for analyzing the
design and manufacture of semiconductor devices, according to an
exemplary embodiment;
[0016] FIG. 3 is a flowchart of a process for generating and
evaluating one or more metrics for analyzing the design and
manufacture of semiconductor devices, according to an exemplary
embodiment;
[0017] FIG. 4 is a flowchart of a process for generating a best
yield metric, according to an exemplary embodiment;
[0018] FIG. 5 is a flowchart of a process for applying a yield
metric as a cost function, according to an exemplary embodiment;
and
[0019] FIG. 6 schematically illustrates a computer system for
implementing the processes of FIGS. 3 through 5, according to an
exemplary embodiment.
DETAILED DESCRIPTION
[0020] In the following description, for the purposes of
explanation, numerous specific details are set forth in order to
provide a thorough understanding of exemplary embodiments. It
should be apparent, however, that exemplary embodiments may be
practiced without these specific details or with an equivalent
arrangement. In other instances, well-known structures and devices
are shown in block diagram form in order to avoid unnecessarily
obscuring exemplary embodiments. In addition, unless otherwise
indicated, all numbers expressing quantities, ratios, and numerical
properties of ingredients, reaction conditions, and so forth used
in the specification and claims are to be understood as being
modified in all instances by the term "about."
[0021] A process window (PW) is the area in the space of the
process parameters corresponding to the values of these parameters
yielding a process result satisfying certain success criteria. For
example, a PW may be composed of the exposure dose and exposure
focus pairs (e.g., E and F, respectively) that will result in the
dimensions (e.g., line widths) of certain features being within 10
percent (e.g., +/-10%) of their target values. Another example of a
practically useful process window is a PW of (E, F) pairs that
result in no bridging occurring between the exposed features or
spaces between them.
[0022] FIG. 1 illustrates a typical PW 105 in a plane defined by
exposure dose 101a along the vertical axis and exposure focus 101b
along the horizontal axis. Curves 103a and 103b correspond to the
exposure conditions (E, F) resulting in the width of the exposed
features deviating +10% and -10%, respectively, off their target
values. The area between the curves 103a and 103b corresponds to
the exposure conditions where the width of the exposed features is
within +/-10% or their target values. Furthermore, the area between
curve 103c and the horizontal axis corresponds to the exposure
conditions that would result in an acceptable level of the resist
loss during the development process, following the exposure. The
intersection of these two areas is the PW 105 with the exposure
conditions (E, F) resulting in the widths of the exposed features
varying within +/-10% of their target values and the acceptable
resist loss during the development step of the process.
[0023] Although the above example shows a PW in the plane of
exposure dose and exposure focus only, any number of these and
other process parameters can be used to compute PWs of higher
dimensions, such as mask bias parameters in addition to exposure
dose and exposure focus to result in a three-dimensional process
window.
[0024] Further, lithography processes usually have random
variations of associated parameters--such as exposure dose and
exposure focus randomly varying around their nominal values because
of, for example, imperfections in the illuminator or imperfections
of the wafer stage, respectively. The random variations of exposure
dose and exposure focus can be described by uncorrelated normal
distributions for both quantities, with the Equation 1 representing
the probability density function for this distribution:
f E 0 , F 0 , .sigma. E , .sigma. F ( E , F ) = 1 2 .pi..sigma. E
.sigma. F exp ( - ( E - E 0 ) 2 2 .sigma. E 2 ) exp ( - ( F - F 0 )
2 2 .sigma. F 2 ) ( 1 ) ##EQU00001##
where E.sub.0 and F.sub.0 are the nominal (e.g., intended/target)
values of the exposure dose and exposure focus, and .sigma..sub.E
and .sigma..sub.F are the standard deviations of these two
parameters, respectively. The error distribution can be based on a
Gaussian distribution.
[0025] While Equation 1 provides acceptable distribution in
general, lithography process errors may alternatively be
characterized by random distributions other than normal or uniform
distributions. The correlation between the errors of different
natures may be present. Furthermore, the error distribution may
vary depending on the spatial location on the wafer, and
correlations between the errors at the neighboring spatial
locations may be present.
[0026] Further, the errors may be in more than just two parameters
(e.g., exposure dose, exposure focus and a mask bias). For cases
with more than two parameters, Equation 1 can be written more
generally. If the process is characterized by, for example, k
parameters x=[x.sub.1, x.sub.2, . . . , x.sub.k], one can write the
generic probability density function simply as f(x) or f(x.sub.1,
x.sub.2, . . . , x.sub.k), subject to the normalization requirement
.intg.f(x)dx=1. In particular, for the same k process parameters,
if the distributions of process parameters x are assumed to be
normal with respective mean (e.g., target or nominal) values of
.mu.=[.mu..sub.1, .mu..sub.2, . . . , .mu..sub.k] and the symmetric
and positive definite k-by-k covariance matrix E, Equation 1 can be
generalized as:
f ( x 1 , , x k ) = 1 ( 2 .pi. ) k / 2 1 / 2 exp ( - 1 2 ( x - .mu.
) T - 1 ( x - .mu. ) ) ( 1 ' ) ##EQU00002##
where |.SIGMA.| is the determinant of .SIGMA..
[0027] Conventionally, for processes with normally distributed
exposure dose and exposure focus errors, the metrics of the PW are
calculated based on a procedure of inscribing a "3 sigma" ellipse
into the PW. Under this approach, a maximal allowable depth of
focus (DOF) assuming a given value of exposure latitude (EL) can be
calculated for various values of EL. However, as discussed above,
such a metric is not directly related to yield. Further, such
metrics are computationally demanding, generally require
iterations, and may result in multiple candidate solutions for
complex-shaped PWs. As more dimensions are added, this conventional
procedure is even more computationally demanding.
[0028] The present disclosure addresses and solves current problems
of an inability to directly relate process parameters to yield and
complex calculations, iterations, and multiple solutions attendant
upon conventional processes involving inscribing a "3 sigma"
ellipse in a PW. In accordance with embodiments of the present
disclosure, a method and apparatus are described for generating
metrics that directly relate two or more process parameters to
yield.
[0029] Methodology in accordance with an embodiment of the present
disclosure includes determining two or more parameters associated
with designing or manufacturing a semiconductor device, such as
exposure dose and exposure focus. Next, a PW is determined
associated with acceptable limits of the two or more parameters.
Then, a probability density function is applied to the PW to
generate a yield metric that relates the two or more parameters to
yield. Such a metric allows for selecting best possible lithography
results directly related to yield rather than basing such decisions
on other metrics that only directly relate to yield.
[0030] FIG. 2 illustrates a metric platform 201 that may generate
and evaluate one or more metrics for analyzing the design and
manufacture of semiconductor devices, in accordance with an
exemplary embodiment. The metric platform 201 may be connected to
or in communication with a process parameter database 207. The
process parameter database 207 may be any type of database that
includes information pertaining to parameters associated with the
design and manufacture of semiconductor devices. Such parameters
may include, for example, exposure dose and exposure focus for a
lithography layer used in manufacturing a semiconductor device, as
well as other parameters discussed herein. Although illustrated and
described as a database, the process parameter database 207 may
instead be any element that provides information to the metric
platform 201 with respect to parameters used in the manufacture of
semiconductor devices.
[0031] The metric platform 201 may further be connected to or in
communication with a yield/cost database 209. The metric platform
201 may provide one or more outputs to the yield/cost database 209,
such as one or more metrics used to evaluate the design and/or
manufacture of a semiconductor device, such as a lithography step
associated with the manufacture of a semiconductor device. The
metric platform 201 may further output yields, such as optimized
yields, based on a PW defined by two or more parameters evaluated
based on the one or more generated metrics, as well as
yield-to-cost analysis with respect to maximizing the yield while
minimizing cost. Although the yield/cost database 209 is
illustrated and described with respect to constituting a database,
the metric platform 201 may provide the metrics or other outputs to
any element or system that requests such information.
[0032] The metric platform 201 may include a process window module
203. The process window module 203 may determine PWs for two or
more parameters that are being evaluated with respect yield and/or
cost. As described above with respect to FIG. 1, the process window
module 203 may determine the PW 105 with respect to two or more
parameters, such as exposure dose and exposure focus of FIG. 1. The
process window module 203 may then provide this information to the
metric platform 201 for use in determining the metrics and other
evaluations with respect to the two or more parameters.
Alternatively, the metric platform 201 may not include a process
window module 203 and, instead, may receive information regarding
PWs from an external source, such as the process parameter database
207.
[0033] The metric platform 201 may also include an error
distribution module 205 that may determine the error distributions
with respect to the two or more parameters. The error distribution
module 205 may determine the error distributions based on
information from the process parameter database 207, such as error
distribution information that is associated with the inputted
process parameters, or may determine error distribution information
from one or more other inputs, such as a technician or operator
selecting one or more error distributions. As discussed, the error
distributions may be normal distributions, distributions other than
normal, correlated distributions, random errors with spatially
varying distributions, random errors with correlations between
neighboring spatial positions, or error distributions accounting
for lithographic processes for more than a single layer (e.g., for
an assemblage of multiple layers for an integrated circuit).
[0034] The metric platform 201 generates and evaluates one or more
metrics for analyzing the design and manufacture of semiconductor
devices. Using notations and definitions introduced above, and
applying Equation 1 to generate an estimated yield metric for a
process with a PW, targeted exposure dose E.sub.0, targeted focus
F.sub.0, and standard deviations of the exposure dose and exposure
focus variations of .sigma..sub.E and .sigma..sub.F, respectively,
the metric platform 201 can generate a metric according to Equation
2:
Y ( W , E 0 , F 0 , .sigma. E , .sigma. F ) = .intg. .intg. W f E 0
, F 0 , .sigma. E , .sigma. F ( E , F ) E F ( 2 ) ##EQU00003##
where f(E,F) is Equation 1 above of the random dose and exposure
errors. Thus, the estimated yield is the probability that the
result of the process will be within specification by satisfying
the process success criteria, as defined by the PW. This
probability is the estimate of the yield of a lithographic process
for a specific layer associated with the exposure dose and exposure
focus parameters.
[0035] Further, Equation 2 can be generalized. For any k number of
parameters x, distributed with a probability density function
f.sub..mu.,.SIGMA.(x), where .mu. are the mean (e.g., nominal or
target) values of the parameters and .SIGMA. is a set of other
parameters of this distribution (not necessarily a covariance
matrix), Equation 2 becomes:
Y ( W , .mu. , ) = .intg. f .mu. , ( x ) x ( 2 ' ) ##EQU00004##
Thus, Equation 2' can be used for determining a yield metric for
more than two parameters.
[0036] For many lithographic processes, the targeted exposure dose
E.sub.0 and exposure focus F.sub.0 are usually optimized and set to
their optimal values, such as optimal exposure dose and optimal
exposure focus. Accordingly, a best estimated yield metric can be
determined according to:
Y max ( W , .sigma. E , .sigma. F ) = max E 0 , F 0 Y ( W , E 0 , F
0 , .sigma. E , .sigma. F ) ( 3 ) ##EQU00005##
This best estimated yield is the highest possible estimated yield
achievable for a process with a given PW defined by the selected
parameters and standard deviations, represented in this case by
.sigma..sub.E and .sigma..sub.F.
[0037] Further, Equation 3 can be generalized. For any k number of
parameters x, distributed with a probability density function
f.sub..mu.,.SIGMA.(x), where .mu. are the mean (e.g., nominal or
target) values of the parameters and .SIGMA. is a set of other
parameters of this distribution (not necessarily a covariance
matrix), Equation 3 becomes:
Y max ( W , ) = max .mu. Y ( W , .mu. , ) ( 3 ' ) ##EQU00006##
As discussed for Equation 2', Equation 3' can be used for
determining a best yield metric for more than two parameters.
[0038] Equations 2 and 3 are examples of PW metrics that do not
require inscribing an ellipse into the PW. Computations using one
or more of the above two equations are straightforward. For
Equation 2, one needs to use one of the well-known numerical
integration formulae to evaluate the integral. For Equation 3, one
needs to numerically compute the convolution of Equation 1 with the
function equal to 1 everywhere inside the PW and equal to 0
everywhere outside the PW. The value of the convolution at point
(E.sub.0, F.sub.0) is equal to the value of Equation 1 with the
target exposure dose and exposure focus equal to (E.sub.0,
F.sub.0). Further, the maximum value attained by this convolution
of the (E, F) plane gives the value of Equation 2.
[0039] As described above, although Equations 1 through 3 are
provided for two-dimensional PWs within the exposure dose and
exposure focus plane with the assumption of normally distributed
process errors, Equations 1 through 3 can be generalized for more
generic and/or higher dimensions. For example, PWs may include a
larger number of process parameters than two, error distributions
may be other than normal distributions, the errors may be
correlated, random errors may vary with spatially varying
distributions, random errors may have correlations between
neighboring spatial positions, and lithographic processes for more
than a single layer may be correlated.
[0040] Further, for a case considering more than just a single
layer, each layer is fabricated with its own process and has its
own errors with their own probability density functions. When the
results of two or more layer processes are combined, the
correlations between the process errors can be accounted for. For
example, residual wafer non-planarity, such as after chemical
mechanical polishing (CMP), may result in correlated exposure focus
errors for layers. The errors of the combined process will
generally be distributed according to a probability density
function taking into account possible correlations between
different layers. By way of another example, the success criteria
for a fabrication process involving multiple layers can take into
account mutual alignment of features on different layers, such as
vertical interconnect accesses (VIAs) on a VIA layer being
positioned properly to provide sufficient overlap with the features
on another layer, to which these VIAs need to be connected. As a
result, a PW for a combined multi-layer fabrication process can be
defined by these mutual alignment requirements, in addition to
other requirements for the sizes of the printed features to be
within a certain specification of their target values. Taking these
two examples into account, generalization of Equations 2 and 3 for
the multi-layer combined process can be accomplished using the
probability density functions with a larger number of parameters
and a possible correlation between parameter errors, as discussed
above.
[0041] With respect to random errors with spatially varying
distributions, or random errors with correlations between the
neighboring spatial positions, one way to generalize Equations 2
and 3 to these situations is to divide the exposure area into
non-overlapping areas (e.g., cells) that are small enough to
neglect the variation of the error distributions within each cell.
These non-overlapping areas may be formed by a regular square grid
with small enough grid cells such that each of these cells will
have its own process parameter errors, and the process parameter
errors for the whole layer will be composed out of the process
parameter errors for these cells. The probability density function
for these errors will be a probability density function depending
on parameter errors in all cells. If correlations between
neighboring positions are present, this probability density
function will be reflecting these correlations. Calculation of
Equations 2 and 3 then can be done in the same way as described
suggested above for the case of a large number parameters,
distributions other than normal and a presence of correlations.
[0042] Still further, using the methodology presented above also
allows for using currently used PW metrics without having to
inscribe ellipses within the PW. As discussed above, one commonly
used metric is DOF for a given EL. A conventional way of
calculating this metric is by considering all ellipses with an
exposure dose semi-axis equal to the EL value and finding the
maximum possible exposure focus semi-axis that would allow such an
ellipse to be inscribed in the PW. The value of the maximum
exposure focus semi-axis is the DOF corresponding to the given EL
value. Such a procedure is justified by interpreting the values of
EL and DOF as "3 sigma" values for the exposure dose and the
exposure focus errors (e.g., three times their standard
deviations). For normally distributed random errors (e.g., Equation
1), the probability that the exposure dose and exposure focus will
be within the ellipse with semi-axes equal to an EL of
3.sigma..sub.E and to a DOF of 3.sigma..sub.F is 99.73%. Therefore,
if the exposure with the standard deviations of errors given by
.sigma..sub.E=EL/3 and .sigma..sub.F=DOF/3 is used, the best
estimated layer yield will be close to 99.73%.
[0043] The above procedure based on finding a maximum ellipse that
can be inscribed into the PW is approximate. Such a procedure
neglects exposures that can happen outside the 3 sigma ellipse but
still fall inside the PW. Accordingly, the following procedure can
calculate the same DOF for a given EL exactly and in a more
computationally efficient way by using the above methodology.
[0044] Given an EL of 5%, the best estimated layer yield
Y.sub.max.sup.(0) of 0.9973, and the PW, a maximal DOF can be found
ensuring the best estimated layer yield according to the following.
Initially, the standard deviation .sigma..sub.E of the exposure
dose variation from the given EL is determined. If the EL and DOF
are both 3 sigma values, then .sigma..sub.E.sup.(0)=EL/3. Further,
for the given PW and the determined value of .sigma..sub.E.sup.(0),
Equation 3 becomes a function of only .sigma..sub.F. Then, the
value of the exposure focus standard deviation .sigma..sub.F
resulting in the highest possible best estimated layer yield is
determined according to Equation 4.
.sigma. F ( 0 ) = argmax .sigma. F Y max ( W , .sigma. E ( 0 ) ,
.sigma. F ) ( 4 ) ##EQU00007##
[0045] The value of
Y.sub.max(W,.sigma..sub.E.sup.(0),.sigma..sub.F) of Equation 4 is
evaluated and compared to the given value of Y.sub.max.sup.(0) of
0.9973. If
Y.sub.max(W,.sigma..sub.E.sup.(0),.sigma..sub.F).gtoreq.Y.sub.max.sup.(0)-
, the exposure with the best estimated layer yield of at least
Y.sub.max.sup.(0) is possible, and the highest standard deviation
of exposure focus ensuring such an exposure is
.sigma..sub.F.sup.(0). If
Y.sub.max(W,.sigma..sub.E.sup.(0),.sigma..sub.F)<Y.sub.max.sup.(0),
the exposure with the best estimated layer yield of
Y.sub.max.sup.(0) is not possible with the given value of EL.
Compared to the conventional way of determined DOF at the given EL
by inscribing ellipses into a PW, described above, the latter
corresponds to a situation when no ellipse of the given dose
semi-axis EL can be inscribed into a PW.
[0046] If an exposure ensuring the best estimated layer yield of at
least Y.sub.max.sup.(0) is possible and the exposure focus standard
deviation .sigma..sub.F.sup.(0) has been determined with respect to
the previous step, the exposure focus standard deviation
.sigma..sub.F.sup.(0) is then used to calculate the DOF, such as
calculating DOF as equal to 3.sigma..sub.F.sup.(0), where DOF
corresponds to a 3 sigma value of the exposure focus variation.
[0047] Computational evaluation of .sigma..sub.F.sup.(0) using
Equation 4 involves evaluating
Y.sub.max(W,.sigma..sub.E.sup.(0),.sigma..sub.F) for a set of
values of .sigma..sub.F, spanning a certain range and then
selecting .sigma..sub.F corresponding to the maximum value of
evaluated Y.sub.max(W,.sigma..sub.E.sup.(0),.sigma..sub.F). Each
evaluation of Y.sub.max(W,.sigma..sub.E.sup.(0),.sigma..sub.F)
involves calculating a convolution of Equation 1 with the PW and
determining the maximum value of the convolution. These
computational procedures are straightforward, deterministic and
non-iterative, unlike the conventional procedure of inscribing a
maximum ellipse into a PW.
[0048] Equations 2 and 3 also can be used as cost functions
associated with modeling the results of the lithography process for
the selected process parameters needed to characterize the PW.
Equation 2 can be evaluated for the given target exposure dose
E.sub.0 and exposure focus F.sub.0 and also given standard
deviations of the exposure dose errors cr and exposure focus errors
.sigma..sub.E, a cost function can be set equal to Equation 2, and
models representing the OPC or SMO valuations can be run so that
the value of the cost function is maximized. Similarly, OPC or SMO
problems can be solved by maximizing the best estimated yield
metric according to Equation 3.
[0049] To evaluate the PW metrics for a given source and mask
combination during the OPC or SMO iterations, (i) the PW in the
space of the selected process parameters (e.g., exposure dose and
exposure focus) for the given source and mask on the current
iteration can be determined, and (ii) a numerical calculation of
the integrals is performed. Step (i) involves applying the OPC/SMO
model for multiple combinations of the process conditions in order
to determine the PW. For most process parameters, application of
the OPC/SMO model for each combination of parameters involves the
same time as it takes to apply this OPC/SMO model once (e.g., each
time all calculations need to be performed with a new set of
parameters from the very beginning).
[0050] For the case of a PW in exposure dose and exposure focus
space (e.g., two parameters only), finding the PW on each OPC/SMO
iteration involves applying the OPC/SMO model at multiple
locations. To sample the shape of the PW, one can estimate that one
will need N.sub.d steps in exposure dose and N.sub.f steps in
exposure focus. This amounts to evaluation of the OPC/SMO model for
N.sub.d*N.sub.f process conditions (e.g., N.sub.d=N.sub.f=10). For
a simple resist model (or no resist models) the exposure
dose/exposure focus pair differing only in a exposure dose value
will involve a single application of the OPC/SMO model and then
re-scaling its result for each dose value. Overall, determining the
PW involves applying the OPC/SMO model N.sub.f times.
[0051] Adverting to FIG. 3, FIG. 3 is a flowchart of a process for
generating and evaluating one or more metrics for analyzing the
design and manufacture of semiconductor devices, according to an
exemplary embodiment. For the process of FIG. 3, the metric
platform 201 performs the process and is implemented in, for
instance, a chip set including a processor and a memory as shown in
FIG. 6.
[0052] At step 301, the metric platform 201 determines two or more
parameters associated with designing a semiconductor device. The
parameters may be associated with the design and/or manufacture of
a semiconductor device, such as, for example, exposure dose;
exposure focus; mask bias; wafer film thickness, stack film
thickness, and spin speeds to deposit such films; optical constants
of the materials used in the wafer film stack; mask film stack
thicknesses; optical constants of the mask film stack materials
(e.g., molybdenum-silicon alloy (MoSi)); exposure wavelength; as
well as other parameters. The determination of the two or more
parameters may be based on an automatic selection by the metric
platform 201 according to the parameters that are input to the
metric platform 201. The determination alternatively may be based
on a manual selection of the two or more parameters, such as by an
operator or technician using the metric platform 201.
[0053] Upon determining the two or more parameters, at step 303,
the metric platform 201 determines a PW associated with acceptable
limits of the two or more parameters. Such as determination may
based on the acceptable limits being provided to the metric
platform 201, or the acceptable limits may be determined by the
metric platform 201 based on one or more analyses associated with
the parameters. As discussed above, as an example, a PW may be
based on acceptable limits of exposure conditions where the width
of the exposed features is within +/-10% of their target values, as
well as exposure conditions that would result in an acceptable
level of the resist loss during the development process, following
the exposure. The intersection of these two areas constitutes the
PW.
[0054] At step 305, the metric platform 201 applies a probability
density function to the PW to generate a yield metric that relates
the two or more parameters to the yield. The probability density
function may be based on a Gaussian probability density function.
According to the above disclosure, the probability density function
can be applied to the PW according to uncorrelated normal
distributions of errors for the two or more parameters, may be
applied according to correlated distributions and spatially varying
distributions for the two or more parameters, or may be applied
according to any other distributions as discussed above. One
example of the disclosed yield metric is described above with
respect to Equation 2. The process disclosed with respect to FIG. 3
may be further modified by correlating distributions between the
two or more parameters across two or more layers associated with
the design and manufacture of a semiconductor device. Upon
determining the yield metric, the metric can be used to relate the
two or more parameters to the yield with respect to the design
and/or manufacture of a semiconductor device.
[0055] Adverting to FIG. 4, FIG. 4 is a flowchart of a process for
generating a best yield metric, according to an exemplary
embodiment. For the process of FIG. 4, the metric platform 201
performs the process and is implemented in, for instance, a chip
set including a processor and a memory as shown in FIG. 6.
[0056] In step 401, the metric platform 201 optimizes the two or
more parameters to generate two or more optimal parameters. The
optimization may be to obtain the optimal values of the two or more
parameters. For the case of exposure dose and exposure focus, the
optimization may generate the optimal exposure dose and the optimal
exposure focus. The optimization may be based on one or more models
for optimizing the parameters. Alternatively, the metric platform
201 may receive the optimal parameters, such as receiving the
optimal parameters from the process parameter database 207.
[0057] At step 403, the metric platform 201 applies the probability
density function based on the two or more optimal parameters. For
example, the targeted exposure dose E.sub.0 and exposure focus
F.sub.0 may be optimized and set to their optimal values, such as
optimal exposure dose and optimal exposure focus. Subsequently,
this best estimated layer yield is the highest possible estimated
layer yield achievable for a process with a given PW defined by the
selected optimal parameters. One example of the resulting best
yield metric is disclosed above with respect to Equation 3.
[0058] Adverting to FIG. 5, FIG. 5 is a flowchart of a process for
applying a yield metric as a cost function, according to an
exemplary embodiment. For the process of FIG. 5, the metric
platform 201 performs the process and is implemented in, for
instance, a chip set including a processor and a memory as shown in
FIG. 6.
[0059] In step 501, the metric platform 501 may evaluate a yield
metric with respect to a process model, such as associated with
evaluating correction and/or optimization of the design and/or
manufacture of the semiconductor device. Examples of such a process
model may be models associated with OPC and SMO. A model that
evaluates the results of a lithography process for the two or more
parameters can be further evaluated with respect to the yield
metric.
[0060] In step 503, a value associated with the yield metric may
maximized with respect to the process model to generate a cost
function associated with yield. Maximizing the yield while
minimizing the cost function allows for the generation of the best
yield at the lowest cost. For example, the yield metric can be
evaluated for a given target of exposure dose and exposure focus,
and also standard deviations of the exposure dose and exposure
focus errors. A cost function can then be set equal to the metric
and an OPC or SMO model can be run so that the value of the cost
function is maximized. According to this process, the layer yield
can be maximized directly instead of relying on optimizing, for
example, a weighted sum of squares of edge placement errors
evaluated at several process conditions and hoping that such an
optimization will also help to increase yield.
[0061] The processes of FIGS. 3 through 5 described herein may be
implemented via software, hardware, firmware, or a combination
thereof. Exemplary hardware (e.g., computing hardware) is
schematically illustrated in FIG. 6. As shown, computer system 600
includes at least one processor 601, at least one memory 603, and
at least one storage 605. Computer system 600 may be coupled to
display 607 and one or more input devices 609, such as a keyboard
and a pointing device. Display 607 may be utilized to provide one
or more GUI interfaces. Input devices 609 may be utilized by users
of computer system 600 to interact with, for instance, the GUI
interfaces. Storage 605 may store applications 611, layout data (or
information) or parameters 613, design plus rules 615, and at least
one shape database (or repository) 617. Applications 611 may
include instructions (or computer program code) that when executed
by processor 601 cause computer system 600 to perform one or more
processes, such as one or more of the processes described herein.
In exemplary embodiments, applications 611 may include one or more
manufacturability analysis and/or yield enhancement tools.
[0062] The embodiments of the present disclosure achieve several
technical effects, including using the above-discussed metrics to
select the best OPC or SMO results rather than basing such
decisions on other metrics that do not directly relate to yield,
evaluating PW metrics in a computationally efficient and
non-iterative and deterministic way that are better suited for OPC
and SMO models, and using OPC or SMO cost functions based on
Equations 2 or 3 to directly maximize yield. The present disclosure
enjoys industrial applicability associated with the designing and
manufacturing of any of various types of highly integrated
semiconductor devices used in microprocessors, smart phones, mobile
phones, cellular handsets, set-top boxes, DVD recorders and
players, automotive navigation, printers and peripherals,
networking and telecom equipment, gaming systems, and digital
cameras.
[0063] In the preceding description, the present disclosure is
described with reference to specifically exemplary embodiments
thereof. It will, however, be evident that various modifications
and changes may be made thereto without departing from the broader
spirit and scope of the present disclosure, as set forth in the
claims. The specification and drawings are, accordingly, to be
regarded as illustrative and not as restrictive. It is understood
that the present disclosure is capable of using various other
combinations and embodiments and is capable of any changes or
modifications within the scope of the inventive concept as
expressed herein.
* * * * *