U.S. patent application number 12/103804 was filed with the patent office on 2008-08-14 for system and computer program for efficient cell failure rate estimation in cell arrays.
Invention is credited to Rajiv V. Joshi, Rouwaida N. Kanj, Sani R. Nassif.
Application Number | 20080195325 12/103804 |
Document ID | / |
Family ID | 38519466 |
Filed Date | 2008-08-14 |
United States Patent
Application |
20080195325 |
Kind Code |
A1 |
Joshi; Rajiv V. ; et
al. |
August 14, 2008 |
SYSTEM AND COMPUTER PROGRAM FOR EFFICIENT CELL FAILURE RATE
ESTIMATION IN CELL ARRAYS
Abstract
A system and computer program for efficient cell failure rate
estimation in cell arrays provides an efficient mechanism for
raising the performance of memory arrays beyond present
levels/yields. An initial search is performed across cell circuit
parameters to determine failures with respect to a set of
performance variables. For a single failure region the initial
search can be a uniform sampling of the parameter space and when
enough failure points have been accumulated, a mean is chosen from
the mean of the detected failure points. Mixture importance
sampling (MIS) is then performed to efficiently estimate the single
failure region. For multiple failure regions, a particular failure
region is selected by varying the memory circuit cell parameters
along a random set of vectors until failures are detected, thus
identifying the boundary of the failure region of interest as the
closest failure region. A new mean is chosen for MIS in conformity
with the location of the detected boundary.
Inventors: |
Joshi; Rajiv V.; (Yorktown
Heights, NY) ; Kanj; Rouwaida N.; (Round Rock,
TX) ; Nassif; Sani R.; (Austin, TX) |
Correspondence
Address: |
IBM CORPORATION (MH);c/o MITCH HARRIS, ATTORNEY AT LAW, L.L.C.
P.O. BOX 515
LAKEMONT
GA
30552-0515
US
|
Family ID: |
38519466 |
Appl. No.: |
12/103804 |
Filed: |
April 16, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11375477 |
Mar 14, 2006 |
7380225 |
|
|
12103804 |
|
|
|
|
Current U.S.
Class: |
702/19 |
Current CPC
Class: |
G11C 29/028 20130101;
G11C 29/54 20130101; G11C 29/56008 20130101; G06F 30/367 20200101;
G11C 29/56004 20130101; G11C 2029/0403 20130101 |
Class at
Publication: |
702/19 |
International
Class: |
G01N 33/00 20060101
G01N033/00 |
Claims
1. A workstation computer system comprising a processor for
executing program instructions and a memory coupled to said
processor for storing program instructions, said program
instructions including program instructions for efficiently
analyzing a failure rate of a cell in an array of cells, said
program instructions comprising program instructions for:
identifying a failure region of interest corresponding to values of
circuit parameters of said cell from a result of a statistical
performance analysis, wherein the failure region of interest is
determined according to first samples of a performance variable;
selecting a sampling function center in conformity with a position
of said failure region of interest to increase a frequency of
samples of said performance variable in or near said region of
interest; performing a mixture importance analysis in conformity
with said sampling function center to determine effects of
variation of said cell circuit parameters within and near said
failure region of interest on said failure rate, wherein the
mixture importance analysis computes second samples from a mixture
distribution obtained by summing multiple differing distributions
of said performance variable according to weighting coefficients
associated with each of said multiple distributions, whereby said
second samples are generated according to a mixture of said
multiple distributions; and storing a result of said mixture
importance analysis within a memory of said workstation computer
system.
2. The workstation computer system of claim 1, wherein said program
instructions for identifying include program instructions for:
uniformly sampling a cell circuit parameter space to select input
vectors for said performance analysis; and accumulating at least a
threshold number of failure points to define said failure region of
interest.
3. The workstation computer system of claim 2, wherein said program
instructions for selecting compute a center of gravity of said
failure region of interest from input vectors of said accumulated
failure points.
4. The workstation computer system of claim 2, wherein said program
instructions for identifying comprise program instructions for:
varying said cell circuit parameters from a nominal-valued vector
of said cell circuit parameters until a failure point is detected
over a number of randomly generated cell circuit parameter vector
directions; and finding a group of failure points resulting from
said varying and closest to said nominal-valued vector to locate a
boundary of said failure region of interest, whereby said failure
region of interest is identified.
5. The workstation computer system of claim 4, wherein said program
instructions for selecting compute a mean input vector across said
group of failure points, whereby said new sampling center is
selected around said boundary of said failure region of
interest.
6. The workstation computer system of claim 4, wherein said program
instructions for selecting estimate a point within said failure
region of interest from input vectors corresponding to points
within said group of failure points, whereby said new sampling
center is selected within said failure region of interest.
7. The workstation computer system of claim 6, wherein said
estimating estimates the center of said failure region of
interest.
8. The workstation computer system of claim 2, wherein said program
instructions for performing said mixture importance analysis are
executed to determine each of a plurality of performance variables
including writeability, read stability, write delay and read delay
times.
9. The workstation computer system of claim 1, wherein said
multiple distributions comprise at least three distributions, and
wherein said program instructions for performing perform said
mixture importance analysis in conformity with said at least three
distributions.
10. A computer program product comprising a computer-readable
storage media encoding program instructions for execution on a
workstation computer, said program instructions for altering design
parameters of a cell in an array of cells, said program
instructions comprising program instructions for: identifying a
failure region of interest corresponding to values of circuit
parameters of said cell from a result of a statistical performance
analysis, wherein the failure region of interest is determined
according to first samples of a performance variable; selecting a
sampling function center in conformity with a position of said
failure region of interest to increase a frequency of samples of
said performance variable in or near said region of interest;
performing a mixture importance analysis in conformity with said
sampling function center to determine effects of variation of said
cell circuit parameters within and near said failure region of
interest on said failure rate, wherein the mixture importance
analysis computes second samples from a mixture distribution
obtained by summing multiple differing distributions of said
performance variable according to weighting coefficients associated
with each of said multiple distributions, whereby said second
samples are generated according to a mixture of said multiple
distributions; and storing a result of said mixture importance
analysis within a memory of said workstation computer system.
11. The computer program product of claim 10, wherein said program
instructions for identifying include program instructions for:
uniformly sampling a cell circuit parameter space to select input
vectors for said performance analysis; and accumulating at least a
threshold number of failure points to define said failure region of
interest.
12. The computer program product of claim 11, wherein said program
instructions for selecting compute a center of gravity of said
failure region of interest from input vectors of said accumulated
failure points.
13. The computer program product of claim 11, wherein said program
instructions for identifying comprise program instructions for:
varying said cell circuit parameters from a nominal-valued vector
of said cell circuit parameters until a failure point is detected
over a number of randomly generated cell circuit parameter vector
directions; finding a group of failure points resulting from said
varying and closest to said nominal-valued vector to locate a
boundary of said failure region of interest, whereby said failure
region of interest is identified.
14. The computer program product of claim 10, wherein said multiple
distributions comprise at least three distributions, and wherein
said program instructions for performing perform said mixture
importance analysis in conformity with said at least three
distributions.
Description
[0001] This application is a Continuation of U.S. patent
application Ser. No. 11/375,477, filed on Mar. 14, 2006.
BACKGROUND OF THE INVENTION
[0002] 1. Technical Field:
[0003] The present invention relates generally to memory circuit
design methodologies and programs for designing digital memory
circuits, and more particularly to a method and computer program
for estimating cell failure rates in cell arrays.
[0004] 2. Description of the Related Art:
[0005] As memory array architectures are pushed to their practical
limits by increasing requirements for density and speed, accurately
estimating the cell failure rate of a design becomes increasingly
critical. Since a finite number of redundant rows and/or columns is
available to replace those containing defective cells, a number of
failed cells above this level of redundancy will yield a defective
device. The number of defective devices, or device yield is then
directly related to the cell failure rate. The larger arrays being
fabricated today have increasingly stringent failure rate control
requirements. For example, in order to achieve a yield of 90% in a
one-million cell array without redundancy, a failure rate below
5.sigma. must be held.
[0006] Traditional techniques such as Monte-Carlo analysis produce
accurate results at a cost of a large number of iterations, due to
the random sampling of the entire probability space of the
independent variables that are treated in the analysis. As the cell
failure rate decreases, the number of samples and iterations
required for accurate analysis becomes increasingly large, because
of the relatively sparse distribution of samples in the
distribution tail(s) that correspond to failed cells. The effect of
circuit changes on cell read and writeability, as well as minimum
read and write cycle times and margins are difficult to estimate at
very low failure rate levels, so such low failure rates cause
further complications for adjusting designs to achieve the best
result.
[0007] Techniques other than Monte-Carlo analysis have been
implemented for estimating cell failure rates, each with related
drawbacks. Sensitivity analysis is a well-known technique in which
the gradients of the various independent variables are used to
determine the bounds of the non-failure confidence region. However,
accurate estimates of the failure rate are not typically produced
by sensitivity analysis, as sensitivity analysis by its very nature
cannot determine the exact overlapping impact of all independent
variables on the cell failure rate at once. Another technique that
can accurately estimate the failure rate is the grid analysis
approach, in which the grid size can be made arbitrarily small.
However, the number of simulations increases exponentially with the
number of independent variables and typically a large amount of
custom coded program control (scripting) must be employed to direct
the analysis.
[0008] It is therefore desirable to provide a method for accurately
and efficiently determining cell failure rates under extremely low
failure rate conditions.
SUMMARY OF THE INVENTION
[0009] The objective of accurately and efficiently determining
array cell failure rates under extremely low failure rate
conditions is achieved by a statistical analysis method.
[0010] The method may be embodied in program instructions executing
within a workstation computer, and also in a computer program
product comprising media for storing the program instructions for
execution within a workstation computer system.
[0011] An initial search is used in the design parameter variable
space in order to gather information about one or more failure
regions. A failure region of interest is identified from the
initial search result and a new distribution center is chosen for
further analysis using mixture importance sampling (MIS) of the
region of interest.
[0012] The region of interest may be a single failure mode region,
and the new center may be determined as the center of gravity of
cell failures from a uniform sampling performed for the initial
search, so that further analysis is focused on the single failure
mode region. Alternatively, the location of groups of samples from
the uniform sampling can be observed and if multiple regions are
present, either a dominant region of interest can be selected for
further analysis using MIS, or multiple regions can be studied
either independently or via an MIS distribution with multiple
regions of interest.
[0013] Alternatively, in circuits where multiple failure modes (and
thus multiple failure regions) are present, the boundary of the
failure region of interest can be determined by finding the closest
failures to the (non-failing) nominal design parameters and
performing the initial search by generating random vector
directions around the nominal values. The variation is
progressively increased along the vectors away from the nominal
values until failures are detected corresponding to a failure
region boundary. Then, the mixture importance sampling is performed
around a new mean determined in conformity with the detected
boundary, which may be a mean position of the boundary points, or
an estimated point within the region determined from the location
of the boundary.
[0014] The foregoing and other objectives, features, and advantages
of the invention will be apparent from the following, more
particular, description of the preferred embodiment of the
invention, as illustrated in the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] The novel features believed characteristic of the invention
are set forth in the appended claims. The invention itself,
however, as well as a preferred mode of use, further objectives,
and advantages thereof, will best be understood by reference to the
following detailed description of an illustrative embodiment when
read in conjunction with the accompanying drawings, wherein like
reference numerals indicate like components, and:
[0016] FIG. 1 is a schematic diagram of a memory cell within an
array of memory cells that can be modeled in accordance with an
embodiment of the invention.
[0017] FIGS. 2A-2B and 3A-3B are graphs illustrating techniques
employed in embodiments of the present invention.
[0018] FIG. 4 is a flowchart depicting a method in accordance with
an embodiment of the present invention.
[0019] FIG. 5 is a flowchart depicting another method in accordance
with another embodiment of the present invention.
[0020] FIG. 6 is a pictorial diagram depicting a workstation
computer system in which the methods of FIGS. 4-5 can be practiced
by executing program instructions of a computer program product in
accordance with an embodiment of the present invention.
DESCRIPTION OF ILLUSTRATIVE EMBODIMENT
[0021] The present invention concerns techniques for overcoming the
limitations of traditional Monte-Carlo analysis for circuits where
the failure rate of the circuit being analyzed is very low. In
particular, with respect to circuits having large arrays of
identical cells, the cells are generally the determining factor in
the failure rate, but only as a totality of the cells. Since
millions of cells may be incorporated in a memory array, even very
low failure rates contribute significantly to the failure rate of
the individual memory devices or other devices that incorporate
memory such arrays.
[0022] Therefore, it is necessary to analyze the cell design and
process variations at the extreme end of the distribution of actual
cell parameters in order to gain meaningful information that can
accurately predict device yields and permit improvement of the
cells in order to improve device yields. The techniques presently
used either require exhaustive computation and storage, or do not
perform well once there are more than a small number of variable
design and process parameters, such as device areas or lengths and
widths, doping densities, threshold voltages and other measures of
design and process parameters. The present invention provides a
mechanism for using mixture importance sampling (MIS), which is a
known technique, in a manner that effectively models memory
cells.
[0023] MIS uses a mixture of two or more distributions for
generating sample values, with at least one of the distributions
biased to generate samples in a region of interest. In the present
invention the sample values are input vectors of design and
process-dependent electrical circuit parameters that determine the
performance of the memory cell. The performance is measured in
terms of operational performance values such as read and write
delay time, writability (i.e., can the cell value be changed during
a write) and read stability (i.e., will the cell hold its value
during reads), as well as the margins associated with the read and
write times, under the operational and circuit parametric
conditions simulated. Since a priori knowledge about what regions
in N-space might be of interest is not generally easily obtained
(where N is the number of variable parameters), the present
invention provides a front-end mechanism to the MIS analysis that
identifies and quantifies a particular region or regions of
interest for further study via the MIS technique. The result is
that the computational overhead and storage associated with the
analysis is greatly reduced, while yielding the desired accuracy
with respect to the failure mechanism(s) being studied.
[0024] In order to locate a region of interest that provides
information about a particular failure mechanism, a priori
information about the failure mechanisms to expect is useful. If it
is known that a single dominant failure mode is present, such as in
many SRAM cell designs, then the identification of the region of
interest is simplified. If it is known that multiple regions of
interest having statistically significant impact will be present,
then the analysis can proceed until all regions of interest are
identified. If it is not known how many failure mechanisms will be
of interest and/or significant within the probability space to be
explored, then techniques must be employed that can handle either
the single-region or multiple region cases.
[0025] In the multiple region case, there are also two alternatives
for applying the MIS technique. Either the regions of interest can
be studied independently, or the sampling function for the MIS
technique can include multiple sampling centers concentrated on the
approximate centers of the multiple regions. The latter technique
can be used to avoid error in failure rate prediction due to
overlap of the regions of interest in one or more dimensions.
[0026] With reference now to the figures, and in particular with
reference to FIG. 1, an exemplary memory cell that can be modeled
by a method in accordance with an embodiment of the invention is
shown in an array that includes other cells 5. Transistors P10,
N10, P11 and N11 form a cross-coupled static latch that provides
the storage of a value in the cell. Transistors N12 and N13 provide
for access to the value in response to a wordline select signal WL.
Bitlines BLT (true bitline) and BLC (complement bitline) couple all
cells in a column, so that when a row is selected by signal WL,
only one row cell from each column is exposed to the memory logic.
For a write operation, bitlines BLC and BLT are charged to voltages
corresponding to the desired state of the memory cell and WL is
activated (pulsed), setting the state of the latch formed by
transistors P10, N10, P11 and N11. For a read operation, the
bitlines BLC and BLT are previously charged to opposite state
predetermined voltages (generally V.sub.dd and ground), and to
commence the read, WL is pulsed and a sense amplifier coupled to
bitlines BLC and BLT determines the stored state by differential
comparison of bitlines BLC and BLT. Depending on the relative
strengths of the transistors P10-11 and N10-13, the cell will
exhibit varying ability to perform to predetermined read/write
cycle times and may be unstable in that the cell value does not
remain constant after a write or when being read. As operating
frequencies are increased and device sizes correspondingly
decreased, the variations take on a statistically significantly
greater range causing failure of an increasing number of devices in
a lot. The present invention is directed toward an efficient method
for statistically analyzing the design of memory cells so that the
yield of memory cells can be predicted accurately and further so
that yields may be improved by selecting optimized nominal values
for the device parameters and other environmental parameters such
as operating voltages.
[0027] While the illustrated cell is an example of a cell of order
4 that may be analyzed and improved by a method according to an
embodiment of the invention, it should be understood that the
techniques illustrated herein may be applied to memory cells of any
order and design and to circuits other than memory circuits, as
well. (Order as used herein refers to the number of devices that
implement the storage element of the cell exclusive of the bitline
access transistors.)
[0028] Referring now to FIG. 2A, a graph illustrating the purpose
and techniques of the invention is shown. A distribution 10 of
operational performance values, such as the above-mentioned delay
times and writeability/read stability measures, generally following
a Gaussian shape extends past 5 standard deviations (5.sigma.) on
either side of a mean value. The input parameter values are
generated by a similar Gaussian distribution of samples as
generated around a nominal vector of cell parameter values by a
Monte-Carlo algorithm.
[0029] Failure zone 12A in the graph is located past the 5.sigma.
point and is shown as a shaded area. The yield of the cell modeled
by distribution 10 can be predicted from the graph, and thus the
yield of the overall device. However, the accuracy near failure
zone 12A is limited due to the relatively sparse distribution of
samples in the tails of distribution 10. The present invention uses
MIS to concentrate sampling within one or more failure zones, so
that more accurate estimates of yield are produced.
[0030] Referring now to FIG. 2B, a graph showing the operation of
the present invention is shown. Once a region of interest is
identified in the device and process-dependent parameter space, a
mixture 10C of distributions 10, 10A and 10B is employed to improve
the density of samples in zone 12A, while ensuring that gaps are
not left in the distribution that might otherwise miss other
failures. The mixture sampling function distribution 10C can be
expressed by:
g.sub..lamda.(x)=.lamda..sub.1p(x)+.lamda..sub.2U(x)+(1-.lamda..sub.1-.l-
amda..sub.2)p(x-.mu..sub.s),
where .lamda..sub.1 and .lamda..sub.2 are coefficients used to
control the mixture, which can be determined by the position of a
new sampling function center .mu..sub.s 14 that is used to improve
the concentration of samples around .mu..sub.s. Note that
.mu..sub.s is not the center of mixture sampling function
distribution 10C, but rather the center of gaussian distribution
10A forming part of sampling function distribution 10C. Uniform
distribution U(x) 10B is also included in the mixture, which helps
in ensuring that some samples are present for all values within the
interval over which uniform distribution 10B extends. The choice of
coefficients, in combination with the inclusion of the uniform
distribution is made so that the number of samples in the region of
interest is increased, but no "dead spots" are present in the
analysis.
[0031] The result of the mixture sampling function is to generate a
relatively larger number of samples over zone 12A (as compared to
the distribution of FIG. 2A), yielding a much more precise estimate
of the impact of zone 12A on. Results show a more than 10.times.
improvement (or greater, in proportion to the distance of zone 12A
from the nominal mean .mu.) in convergence time for estimates of
the edges of failure zone 12A, which results in a corresponding
improvement in convergence of the calculation of overall device
yield.
[0032] While, generally, the statistical analysis detailed above
will be conducted independently over the operational performance
variables being studied, it is possible to conduct a combined
pass/fail analysis over the parameter space in which no information
about the particular operational performance variables associated
with each failed point is retained, but the overall desirability of
a particular design can be directly observed with respect to
process variations. MIS analysis can then be conducted with one or
more mean-shifting distributions included to precisely predict the
yield.
[0033] Referring now to FIG. 3A, a first technique for locating
sampling function center .mu..sub.s 14, is depicted. Since memory
cell operational performance variable failure regions generally
will extend to the bounds of the analysis range (with respect to
the parameter deviation) from the point at which the failures
occur, failure regions can be ascribed to failure region boundaries
beyond which the probability of failure only increases. The
illustration is two-dimensional but in actual practice, a larger
number of dimensions are actually being evaluated simultaneously. A
number of sample points are generated by uniformly sampling the
variable memory cell parameter space, corresponding to the dots
shown in the Figure. Quasi-random sampling techniques can be used
to improve the spread of the samples across the parameter space. In
the Figure, hollow dots depict non-failing points and solid dots
depict failing points. After a threshold number of failures is
accumulated, which may be qualified by observing their proximity in
the parameter space if multiple failure regions might be present
(in order to group the failures), a particular failure region of
interest 20B is identified and the vector centroid 14 of that
region computed and used as new sampling function center .mu..sub.s
14 for subsequent MIS analysis. The vector centroid is computed
from the vector distances of the points as the vector of average
distance in each parameter space. There may be multiple failure
regions for some applications of the techniques of the present
invention including other failure regions such as 20A, and those
regions can be ignored if not of interest, or may be further
evaluated with independent MIS analysis around their centers.
[0034] The above-described technique is especially applicable to
the study of memory cell designs that have a single dominant
failure region of interest. However, if it is not known in advance
that there will be a single dominant region, the positions of the
failure samples in parameter vector space can be observed and the
samples grouped into one or more groups as mentioned above. If a
group is much more distant from the nominal parameter vector, then
that group may be discarded as being due to a relatively
unimportant failure mechanism. The technique of the present
invention can be used to obtain better information about multiple
failure mechanisms by the above grouping technique or discarding of
groups.
[0035] A threshold number of samples can then be collected for each
group to be studied and either an independent set of MIS analyses
can be conducted for each group, or the above MIS sampling
distribution function can be modified to follow:
g.sub..lamda.(x)=.lamda..sub.1p(x)+.lamda..sub.2U(x)+.lamda..sub.3p(x-.m-
u..sub.s1)+(1-.lamda..sub.1-.lamda..sub.2-.lamda..sub.3)p(x-.mu..sub.s2),
where .lamda..sub.1, .lamda..sub.2 and .lamda..sub.3 are
coefficients used to control the mixture and new sampling function
centers .mu..sub.s1 .mu..sub.s2 are used to improve the
concentration of samples around two regions of interest. If more
than two regions of interest are present, the above sampling
function can be expanded to include other mean shifting values and
their associated sampling function kernels in the above sampling
function.
[0036] Referring now to FIG. 3B, another technique adapted for
treating circuits having multiple dominant failure regions is
depicted, e.g., circuits for which multiple failure mechanisms have
fairly equivalent statistical significance. The technique may also
be used for single failure region analysis, as well. A vector of
nominal memory cell parameter values 16 is used as a starting point
for random generation of a sufficient initial number of vector
directions 18 along which cell failure analysis proceeds until
failure points are detected. A sufficient number of vector is
generated so that failure regions will not be missed by the
analysis. Gaussian latin hypercube sampling can be used to ensure
uniform placement of the vectors in all directions.
[0037] The analysis then proceeds away from nominal vector 16 as
illustrated. The generally monotonic behavior of the circuits as
the parameters vary in one direction away form the nominal ensures
that failing points will only be encountered at and beyond the
boundaries of the failure regions 20A, 20B. The new sampling
function center .mu..sub.s 14 for subsequent MIS analysis is
determined either by the mean vector 14B corresponding to the group
of boundary points 22, or an estimated vector 14A is extrapolated
within failure region of interest 20B from the location of the
boundary points. After a first iteration, if the boundaries of
failure regions 20A, 20B are not sufficiently defined, a local set
of random vectors is generated to enhance the set of samples around
the boundaries. After boundaries 20A, 20B are sufficiently defined
.mu..sub.s 14 is chosen as described above. As in the center of
gravity technique, regions of interest that are more distant from
the nominal vector can be discarded as relatively unimportant
failure mechanisms. The technique illustrated in FIG. 3B also
provides better information about multiple failure mechanisms by
locating the boundaries of the regions of interest. If the
boundaries are not well defined after the above analysis has been
attempted, then the entire process can be repeated with a larger
set of initial random vectors.
[0038] Referring now to FIG. 4, a method according to an embodiment
of the present invention is shown, corresponding to the
centroid-locating technique described above with reference to FIG.
3A. First, a statistical analysis across ranges of memory circuit
parameters is performed for multiple performance variables (step
30) and once a threshold number of failing samples is accumulated
(possibly qualified as being in a single failure region if
required) (step 32) the centroid of the parameters corresponding to
the group of failures is determined (step 34). Finally, a new
distribution of input parameter vectors is selected in conformity
with the determined centroid and the nominal vector (step 36) and
an MIS analysis is performed (step 38) using the new mixture
distribution to gain more accurate results in the region of the
failures and a faster convergence of the overall yield
computation.
[0039] Referring now to FIG. 5, another method according to an
embodiment of the present invention is shown, corresponding to the
random vector technique described above with reference to FIG. 3B.
First, random vector directions are generated around the nominal
value of the memory circuit parameters (step 50). The memory cell
is simulated along the vectors until a failure is detected,
corresponding to a failure region boundary (step 52). Then, a mean
point is computed from multiple failure region boundary points or a
point is estimated within the failure region from the boundary
points (step 54). An MIS distribution function is then selected
(step 56) as a mixture of a distribution around the nominal
parameter values and the mean point computed in step 54 (along with
the uniform distribution), and an MIS analysis is performed (step
58) using the new mixture distribution to gain more accurate
results in the region of the failures and a faster convergence of
the overall yield computation.
[0040] Referring now to FIG. 6, a workstation computer system, in
which the above-described methods according to an embodiment of the
present invention are performed, is depicted. A workstation
computer 112, having a processor 116 coupled to a memory 117, for
executing program instructions from memory 117, wherein the program
instructions include program instructions for executing one or more
methods in accordance with an embodiment of the present invention,
such as the methods described above with respect to FIGS. 4 and
5.
[0041] Workstation computer 112 is coupled to a graphical display
113 for displaying program output such as simulation results and
circuit layout structure input, design and verification programs
implementing embodiments of the present invention. Workstation
computer 112 is further coupled to input devices such as a mouse
115 and a keyboard 114 for receiving user input. Workstation
computer may be coupled to a public network such as the Internet,
or may be a private network such as the various "intra-nets" and
software containing program instructions embodying methods in
accordance with embodiments of the present invention may be located
on remote computers or locally within workstation computer 112. A
computer program product for carrying out the method of the present
invention may be embodied in a file on an internal storage device
118 of computer 112, or stored on a transportable medium such as a
compact disc or flash memory storage device.
[0042] While the invention has been particularly shown and
described with reference to the preferred embodiment thereof, it
will be understood by those skilled in the art that the foregoing
and other changes in form, and details may be made therein without
departing from the spirit and scope of the invention.
* * * * *