OPRX(TM): Parametric Anchoring
Anchoring is a process of modifying model-generated correction
rules so the rules correspond more accurately to empirical measurements.
The rules are what determine how edges are moved by the OPRX(TM)
correction program. Our original method for anchoring is in our description
of EmpRule(TM). With
that method, several hundred measurements were required to satisfactorily
anchor a one-dimensional rule set of several thousand points. Our new method
of Parametric Anchoring requires far fewer measurements and
those measurements apply to two-dimensional rule sets as well.
Parametric Anchoring is a methodology in which the SimRule(TM)
model parameters are adjusted so that the models are satisfactory predictors
of measured line/space and line length data. This particular type of data
is chosen because process engineers are already accustomed to acquiring
it. Line/space data in particular can be measured using cross sectional,
top-down SEM and electrical techniques.
Example: Before going into a detailed description, let's first consider
a simple example. Suppose that (1) a conventional binary mask will be used
and (2) the resist is very high contrast so that the developed resist edge
positions are well-described by an aerial imaging model. The stepper's numerical
aperture, NA, and partial coherence, sigma are known, but
the image threshold intensity, IT, which corresponds
to the developed resist edge is not known. A single measurement of a line/space
pattern or an isolated line can determine IT.
Given a description of the reference line/space pattern as it appears on
the mask and a measured line-width value, SimRule(TM) can automatically
determine the correct threshold intensity. Caution--that "single"
measurement may really be an ensemble average over a number of stepper field
positions and over a number of steppers. For the correction process to be
effective, there is a presumption that the measurement ensemble is tightly
distributed.
Figure 1. An example of a measurement test pattern test pattern
for a top-down SEM measurement. The values of L, S and 4 micrometers are
"as designed" values and represent what appears on the mask (at
wafer dimensions). The 4 micrometer value is chosen to be larger than the
proximity effect influence range. The values of A, B and C are measured
values.
Before Getting Started: It is important to understand that Optical
Proximity Correction (OPC) is an important tool in getting the most out
of your process. Its principal benefit is in aligning the process windows
of different types of figure arrangements so that they all print correctly.
As a consequence of process window alignment, OPC can improve the resolution
capabilities of the process. However, for a single type of figure arrangement
OPC, which amounts to moving edges in the mask, cannot make a process print
beyond its intrinsic limits. This is illustrated in the figue below:
Figure 2. A hypothetical process: Without OPC there is a common
process window for both Dense and Isolated patterns at modest critical dimension,
CD1, but not at the smaller critical dimension CD0. With OPC, the CD0 and
CD1 process windows can be aligned, improving the resolution capability
of the process.
Suppose CD0 is the minimum CD for which a process has a satisfactory
exposure-focus window for dense line/space patterns. OPC on its own cannot
reduce CD0. It is common however that the process window for dense patterns
at CD0 does not overlap with the process window for sparce CD0 patterns.
This means that CD0 cannot be used as the minimum CD for the process. The
process engineer must choose a larger value, say CD1, for which the process
windows do overlap satisfactorily. Using OPC allows the process windows
for dense and isolated CD0 patterns to be aligned, so that the process engineer
does not have to retreat to CD1. It is in this practical sense that OPC
provides resolution enhancement.
Getting Started: The first question to answer is whether you are
going to use an existing process, with the intent of using
OPC to increase the overall process window, or whether you are designing
a new process. If it is an existing process then the nominal
exposure and focus condition, E|F is known. If it is a new process,
then the nominal exposure and focus conditions are to be determined.
Nominal Exposure/Focus for a new process:
The process engineer knows how to do this: The engineer prints a variety
of structures (usually isolated and dense) with CD's that extend beyond
the projected process limits over a range of exposure and focus conditions.
Then the minimum CD is identified for which a satisfactory exposure/focus
window exists for which both isolated and dense structures print within
a specified tolerance.
If OPC is going to be used, however, a better overall process window and
smaller CDs are possible if a slightly different analysis is performed.
First the most difficult structure is analysed. Usually it is the dense
structures. A minimum CD, which we will call CD0, is found for which
a satisfactory process window exists for dense structures. A nominal exposure/focus
condition, E0|F0 is found at which the dense structures print correctly.
Now we have an E0|F0 for which a dense equal line/space structure
designed at CD0 prints at CD0. For isolated line or space
structures, we require that there be a design width, CDI0, which
will print as CD0 at E0|F0. This can be determined if there
are a number of isolated line or space test structures with several increments
around CD0. Hopefully one of those design increments is at CDI0.
Unfortunately, CDI0 is not know in advance, but process simulators
may provide an estimate so fewer test structures are required. Note:
The difference CDI0-CD0 is the correction which must be applied to
minimum CD isolated structure. The correction to be applied for the dense
minimum CD structure should be close to zero.
Now the E|F for this process is known: it is E0|F0.
The Principle of Parametric Anchoring:
The basic idea behind Parametric Anchoring is to perform a best fit of model-predicted
linewidth errors to experimental linewidth error measurements by varying
model parameters. For example, suppose the model incorporates a Hopkins
formulation aerial image simulator including a model for post-exposure-bake
resist diffusion. In it simplest form the model has two unknown parameters,
I0, the image intensity threshold and, D, a diffusion parameter.
The model is exercized, varying the two parameters to obtain a cost function
minimization (least squares fit) between the model prediction and measured
linewidth error data.
Since there are two parameters, at least two measurements are required to
fix values for I0 and D. However, it is better to have more
than two measurements. With a number of measurements, measurement noise
is averaged out. In addition, with several measurements, the fitting process
will return a measure of the quality of the fit of the model to the measurements.
The figure below illustrates how the process of fitting the model to measured
data works.
Figure 3. A schematic example of the Parametric Anchoring fitting
process. There are five distinct line/space patterns whose linewidth errors
have been measured (LS0-LS4). Suppose LS0 represents the minimum CD equal
line and space pattern and that the process has been optimized so that this
pattern prints correctly. LS1 - LS4 represent coarser and/or sparser line-space
patterns and exhibit a linewidth error as shown by the heavy dots. The model
has computed linewidth errors for all of these patterns for various combinations
of model parameters. Three model parameter combinations are shown, with
"Model 2" showing the best fit to the measured data.
Collecting
Data for Parametric Anchoring:
The structure in Figure 1 or something similar to it can be used as a basic
data gathering tool. If CD is the minimum critical dimension, then we suggest
both bright and dark field versions of: A sequence of structures with L/CD
= {1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.4, 2.8, 3.2, 3.6, 4.0} with S = L and
with S = infinity (single 4 micrometer lines).
Strictly speaking, the C measurement should not be necessary. So
for the electrical or cross sectional measurements for which a C measurement
is problematic, it can be ignored. However, line end shortening is strongly
affected by the diffusion parameter and the C measurement is a most
sensitive way of getting a good diffusion value.
Presently, the model parameter optimization process for Parametric Anchoring
is a semi-manual process through which Trans Vector Technologies guides
its customers. It will soon be automated in SimRule(TM).
Return to OPRX Product Description Index
This page last updated March 21, 1996.