Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design
Reexamination Certificate
1998-11-06
2001-11-06
Smith, Matthew (Department: 2825)
Computer-aided design and analysis of circuits and semiconductor
Nanotechnology related integrated circuit design
C716S030000, C716S030000, C703S001000, C703S002000, C703S014000, C345S182000, C345S182000
Reexamination Certificate
active
06314545
ABSTRACT:
FIELD OF INVENTION
This invention is in the field of simulation, or parameter extraction of characteristics of electrical elements used in the design of printed circuit boards, and solid state integrated circuits.
BACKGROUND OF THE INVENTION
Parameter extraction, or simulation, of electronic elements has a significant role in the design of modern integrated circuits (IC) operating increasingly at frequencies in the range of hundreds of megahertz. Increasing IC operating frequencies, coupled with reduced, submicron size structures, have made accurate simulation critical for components created within an IC.
As described in the parent application, U.S. Ser. No. 08/904,488, incorporated herein by reference in its entirety, historically, capacitive elements were computed from the geometry of an IC by using general purpose field solvers based on finite-difference or finite-element tools. Typical of these tools of the prior art is a requirement for volume or surface discretization. For finite-element tools, solutions are computed for large numbers of points descriptive of the electric field of the volume of an element within a device. Using this approach, as frequencies go up, the number of points required for a simulation also goes up resulting in large computation time and memory use for the completion of one simulation.
Another approach of the prior art is the use of integral equation methods. An example of this approach is FastCap: A multipole accelerated 3-D capacitance extraction program
IEEE Transaction on Computer Aided Design
10(10):1447-1459, November 1991, incorporated herein by reference in its entirety.
Integral formulations have certain advantages over finite-difference or finite-element tools. These include good conditioning, reduction in dimensionality and ease in dealing with layered dielectrics. Discretizing an element using integral equations generally leads to a linear system of equations represented conveniently using a “dense” matrix. The inverse of this matrix is required to solve for the parameter being sought. Previous solution methods for this “dense” matrix have discretized the integral equation using a first-order collocation. In these methods, the charge density is assumed to be piecewise constant. With this crude approximation, computing accurate answers mandates large discretizations even for simple problems. That is, the matrix to be solved involves a large number of points thus impacting negatively the time required to arrive at a solution.
SUMMARY OF THE INVENTION
Above listed problems to the solution methods for the simulation of elements within an IC are avoided in accordance with one aspect of the invention by using a discretization technique, which reduces the integral equation to a finite system and by replacing the integral equation with a high-order quadrature. The element to be simulated is divided into regions, and each region is further divided into a plurality of quadrature nodes. Pairs are formed for all the quadrature nodes. Green's functions are computed and stored for the pairs thus obtained. Each of the pairs is allocated to either the far field or the near field for purposes of simulation in accordance with a criterion. The criterion includes the order of the high order quadrature, an accuracy, and the Green's function for each of the pairs. A Gaussian quadrature is computed for the pairs allocated to the far field while a high order quadrature is computed for the pairs of nodes allocated in the near field. The component simulation is arrived after combining information derived from the Gaussian quadrature and the high order quadrature. The information derived from the Gaussian and high order quadratures is generally combined in a matrix. Said matrix is solved to obtain the charge distribution. Summing over the charges yields the capacitance of the element being simulated.
The high order quadrature is computed using a plurality of basis functions. The basis functions, denoted &psgr;
i
k
(r′), are 1, x,y,x
2
,xy,y
2
. The basis functions are used to compute a set of weights v
j
k
. The weights are computed by solving
∑
j
=
1
p
a
ij
v
j
k
=
∫
T
k
G
(
r
,
r
′
)
ψ
i
k
(
r
′
)
ⅆ
r
′
,
where &psgr;
i
k
(r′) are the basis functions, G(r,r′) are the Green's functions for each of the pairs allocated to the near field separated by a distance r-r′, and a
ij
is a matrix satisfying the relationship
a
ij
=G
(
r,r
j
k
)&psgr;
i
(
r
j
k
)
and where index k counts the regions in the near field T
k
, index i counts the number of pairs, and index j counts up to a number p of the quadrature nodes in the near field.
The advantage of this approach is that a fast solution to an integral equation descriptive of the element to be simulated can be achieved in exchange for constructing quadratures.
REFERENCES:
patent: 6051027 (2000-04-01), Kapur et al.
patent: 6064808 (2000-05-01), Kapur et al.
Zhao, J., “Singularity-treated quadrature-evaluated method of moments solver for 3-D capacitance extraction”; IEEE Conference on Design Automation; Jun. 2000; pp. 536-539.*
Pham, H.H; Nathan, A., “Generating Gauss quadratures for Green's function randomized algorithm”, IEEE Canadian Conference on Electrical and Computer Engineering, 1998, vol. 2, 1998.*
Schlemmer, E. et al, “Accuracy improvements using a modified Gauss-quadrature for integrations methods in electromagnetics”, IEEE Transactions on Magnetics, vol.: 28, iss. 2, Mar. 1992.
Kapur Sharad
Long David Esley
Agere Systems Guardian Corporation
Istrate Ionescu
Smith Matthew
Speight Jibreel
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