Three dimensional wiring inductance calculation system

A three dimensional wiring inductance calculating system taking the wiring as analyzing space expressed as three-dimensional configuration and make discrete the analyzing space into a finite number of partial elements. By solving a Poisson's equation with respect to an electrical potential in the discrete analyzing space, a current value and a current density vector distribution within the wiring are derived. Also, by solving an integral equation of a vector potential including the current density vector at each of points of partial elements within the wiring by making discrete, the vector potential as a boundary condition at a boundary of the wiring is derived. Then, the vector potential is derived by solving a vector potential equation in the discretized analyzing space with taking the vector potential value at the boundary as the boundary condition. A product of the obtained vector potential and the current density vector per unit current value is normalized for deriving an integral sum of the produce within the analyzing space and calculating an inductance of the wiring.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method for deriving a parasitic 
parameter of a wiring. More specifically, the invention relates to a 
method for calculating an inductance of a three-dimensional wiring for 
calculating a self inductance and a mutual inductance of a wiring in a 
large scale integrated circuit (LSI) or so forth. 
2. Description of the Related Art 
When a configuration of wiring and a relative arrangement of wirings are 
determined, it is required to accurately derive parasitic parameters, such 
as a resistance, a capacitance, an inductance and so forth through 
arithmetic operation without performing actual measurement. For instance, 
in recent years, speeding of the LSIs and complication of the wiring 
structure within the LSIs are progressing. Associated with this, signal 
delay, fluctuation of power source voltage, generation of signal noise and 
so forth due to inductance component in the wiring structure becomes 
significant. 
Therefore, in designing of an LSI, it is becoming necessary to accurately 
estimate the parasitic parameter of the wiring to increase process steps 
in estimating of the parasitic parameter in the designing operation. 
Similarly, it is also required to arithmetically derive the parasitic 
parameter with respect to the lead portion of the package of the LSI, and 
the wiring on a printed circuit board or wiring in a transition for 
microwave or integration circuit. When the inductance of the wiring is 
derived through arithmetic operation, the inductance is expressed as a sum 
or difference of coefficients having substantially the same size to a self 
inductance of individual wiring and a mutual inductance with respect to 
several adjacent wirings. Therefore, it is required to precisely perform 
calculation for respective of inductances. Also, it is required to perform 
calculation at high speed. 
In order to satisfy such demands, it becomes necessary to accurately 
calculate the inductance on the basis of a basic equation. The accurate 
basic equation of the inductance can be expressed as follow, as recited in 
C. Hoer et al., Journal of Research of NBS, 1965, Vol. 69C, page 127 
(which publication will be hereinafter referred to as publication 1). 
Namely, an inductance L.sub.12 is expressed by a volume integrating 
equation of a local electromagnetic energy per unit current with a current 
density vector J(X.sub.j) at a coordinate x.sub.j of the wiring 2 and a 
vector potential A.sub.1 (x.sub.j) at the coordinate x.sub.j generated by 
the current of the wiring 1. 
##EQU1## 
Here, I.sub.1, and I.sub.2 are current values respectively flowing in 
wirings 1 and 2, and dv.sub.j is a volume factor of the wiring 1. Also, 
A.sub.1 (x.sub.j) is a vector potential expressed by: 
##EQU2## 
Accordingly, the inductance L.sub.1,2 is derived from sextuple integration 
as expressed in the following equation, since double integration of the 
volume factor is to be performed from the foregoing equations (1) and (2). 
##EQU3## 
In the special occasion where the uniform current flows in the straight 
wire with a rectangular cross section, the equation (3) may be 
analytically derived by employing a sum of complicated trigonometric 
functions and exponential functions. 
However, when the wiring is bent or when the wiring configuration includes 
an oblique portion, the current within the wiring becomes non-uniform and 
thus, calculation of a current density vector becomes necessary. 
For calculation of the current density vector, an Ohm's law expressed in 
the following equation (4), in which the current density vector is 
expressed by a conductivity and an electric field vector is assumed. 
EQU J=.rho.(-.gradient..psi.) (4) 
Then, in the continuous equation of the current density vector, assuming a 
quasi-static condition in which a charge density vector is held unchanged 
in the elapsed time, Poisson's equation as in the following equation (5) 
can be derived. Here, .rho. is a conductivity and .psi. is an electric 
potential. 
EQU .gradient..multidot.(.rho..gradient..psi.)=0 (5) 
Namely, similarly to the case of calculation of capacity, by solving the 
Poisson's equation, a potential is derived. From the gradient of electric 
potential, the current density can be derived. 
For solving the foregoing equation (5) to derive the current density 
vector, by dividing the wiring into a several filaments, stepwise 
approximation may be performed. Namely, there is a method wherein a 
current distribution is assumed to be uniform in the filament, and the 
overall inductance coefficient is derived by adding the inductance 
coefficient by the current density of the respective filaments. 
The method wherein a current distribution is assumed to be uniform in the 
filament, and the overall inductance coefficient is derived by adding the 
inductance coefficient by the current density of the respective filaments, 
has been disclosed in P. A. Brennan et al IBM J. Res. Develop., Vol. 23, 
pp 661 to 668, and known as partial element equipment circuit (PEEC) 
method. This publication will be hereinafter referred to as publication 2. 
However, when an attempt is made to actually divide the wiring into the 
rectangular parallelepiped elements, and if the wiring is bent, if the 
configuration of the wiring contains the oblique portion, or if the 
current path within the wiring is not uniform, a large number of elements 
becomes necessary for obtaining necessary accuracy. The analytical formula 
for inductance is complicated one including trigonometric and exponential 
functions. Therefore, when number of partial element is large, a long CPU 
time is required only for the analytical calculation of the elements. 
Furthermore, as an approximating method for inductance calculation, a 
filament approximation (linear), a panel approximation (two-dimension) and 
so forth are present. 
These approximating methods are basically the PEEC method. In the filament 
approximation, the current is expressed by a certain line current 
component. On the other hand, in the panel approximation, the current is 
expressed by a panel form plain current component. These approximating 
methods are simplified and advantageous in the viewpoint of calculation 
speed. However, due to incompleteness of integration of dimension, it is 
possible to cause overflow of the self inductance in the limit of scaling 
down of the element. 
On the otherhand, as a more flexible method than the PEEC method, there is 
a method to directly derive the inductance utilizing the equation (1) with 
solving a differential equation relating to the current density vector and 
the vector potential. 
Namely, initially by solving the Poisson's equation (5) in the wiring, the 
current density vector is derived. Then, by solving a following vector 
potential equation (6), which is obtained from a Maxwell's equation, a 
vector potential A can be obtained for deriving the inductance. 
EQU .DELTA.A=-.mu.J (6) 
Here, .mu. is a magnetic permeability for the vacuum. 
As a boundary condition for the equation (6), a method is taken to set an 
analyzing region sufficiently wide, in which the magnetic field is zero at 
a sufficiently distanced position from the wiring conductor. However, in 
this method, setting for analyzing region becomes quite difficult. Namely, 
it causes a problem in precision. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a three dimensional 
wiring inductance calculating system capable of improving making discrete 
error or lack of analyzing precision in calculation of an inductance 
coefficient of wiring, and thereby shortening CPU time. 
According to the first aspect of the invention, a three dimensional wiring 
inductance calculating system comprises: 
wiring structure inputting means for inputting a three dimensional wiring 
structure of an object for analysis expressed by a three dimensional 
configuration: 
an analyzing space making discrete means for taking the wiring as analyzing 
space and making discrete the analyzing space into a finite number of 
partial elements; 
current density deriving means for solving a Poisson's equation with 
respect to an electrical potential in the discretized analyzing space and 
deriving a current value flowing within the wiring and a current density 
vector distribution; 
boundary condition setting means for solving an integral equation of a 
vector potential including the current density vector at each of points of 
partial elements within the wiring by making discrete and deriving the 
vector potential as a boundary condition at a boundary of the wiring; 
vector potential calculating means for deriving the vector potential by 
solving a vector potential equation in the discretized analyzing space by 
using the vector potential value at the boundary as the boundary 
condition; and 
inductance calculating means for normalizing a product of the obtained 
vector potential and the current density vector per unit current value, 
deriving an integral sum of the produce within the analyzing space and 
calculating an inductance of the wiring. 
In the preferred construction, the analyzing space making discrete means 
divides the analyzing space into quadrangular partial elements. The 
boundary condition setting means may derive the vector potential on the 
surface of the wiring as the vector potential at the boundary of wiring. 
For obtaining an inductance between a first wiring and a second wiring, the 
process comprises, in the preferred process: 
inputting three dimensional wiring structures of the first wiring and the 
second wiring by the wiring structure inputting means; 
dividing the analyzing space of the first wiring and the second wiring into 
finite number of partial elements by making discrete by the analyzing 
space making discrete means; 
deriving the current value and the current density vector distribution 
within the wiring by solving the Poisson's equation with respect to the 
electric potential in the analyzing space of the first wiring and the 
second wiring by the current density calculating means; 
deriving a vector potential at the node with respect to each node on the 
surface of one of the wiring by the boundary condition setting means; 
solving the vector potential equation in the analyzing space with taking 
the vector potential at the node as the boundary condition by making 
discrete by the vector potential calculating means; and 
deriving the inductance between the first wiring and second wiring from an 
integral equation of the produces of the vector potential standardized per 
unit current value and the current density vector by the inductance 
calculating means. 
The boundary condition setting means may derive the vector potential at 
each node utilizing a distance between the contact point of one of the 
wiring and a typical pint of the partial element of the other wiring, and 
the current density vector when the vector potential at each node on the 
surface of the one of the wiring is calculated. The boundary condition 
setting means may use a value of a distance function variable depending 
upon a distance from the contact point to the closest peak of the partial 
element and the distance from the node to the gravity center of the 
partial element as a distance from the node of the wiring to the typical 
point of the partial element when the vector potential at the node of the 
wiring is calculated. 
According to a second aspect of the invention, a three dimensional wiring 
inductance calculating system comprises: 
current density vector calculating means for solving a Poisson's equation 
with respect to an electric potential in an analyzing space and deriving a 
distribution of current density vectors flowing within a wiring with 
taking an analyzing space expressed as three-dimensional configuration as 
the analyzing space; 
boundary condition setting means for calculating a vector operation at a 
boundary of the wiring as a boundary condition by an integral equation of 
a vector potential including the current density vector; 
vector potential calculating means for deriving the vector potential by 
solving a vector potential equation in the analyzing space with taking the 
vector potential as the boundary condition; and 
inductance calculating means for calculating an inductance of the wiring by 
performing integration of products of the vector potential obtained from 
the vector potential equation and the current density vector in the 
analyzing space. 
According to the third aspect of the invention, a method for calculating an 
inductance of a three dimensional wiring comprises the steps of: 
inputting a three dimensional wiring structure of an object for analysis 
expressed by a three dimensional configuration; 
taking the wiring as analyzing space and making discrete the analyzing 
space into a finite number of partial elements; 
solving a Poisson's equation with respect to an electrical potential in the 
discrete analyzing space and deriving a current value flowing within the 
wiring and a current density vector distribution; 
solving an integral equation of a vector potential including the current 
density vector at each of points of partial elements within the wiring by 
making discrete and deriving the vector potential as a boundary condition 
at a boundary of the wiring; 
deriving the vector potential by solving a vector potential equation in the 
analyzing space by making discrete with taking the vector potential value 
at the boundary as the boundary condition; and 
normalizing a product of the obtained vector potential and the current 
density vector per unit currant value, deriving an integral sum of the 
produce within the analyzing space and calculating an inductance of the 
wiring. 
According to the fourth aspect of the invention, a three dimensional wiring 
inductance calculating method comprises the steps of: 
solving a Poisson's equation with respect to an electric potential in an 
analyzing space and deriving a distribution of current density vectors 
flowing within a wiring with taking an analyzing space expressed as 
three-dimensional configuration as the analyzing space; 
calculating a vector operation at a boundary of the wiring as a boundary 
condition by an integral equation of a vector potential including the 
current density vector; 
deriving the vector potential by solving a vector potential equation in the 
analyzing space with taking the vector potential as the boundary 
condition; and 
calculating an inductance of the wiring by performing integration of 
products of the vector potential obtained from the vector potential 
equation and the current density vector in the analyzing space.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The preferred embodiment of the present invention will be discussed with 
reference to the accompanying drawings. In the following description, 
numerous specific details are set forth in order to provide a thorough 
understanding of the present invention. It will be obvious, however, to 
those skilled in the art that the present invention may be practiced 
without these specific details. In other instance, well-known structures 
are not shown in detail in order to unnecessary obscure the present 
invention. 
In the present invention, as a boundary condition with respect to the 
equation (1), a vector potential value is used on the surface of the 
wiring (boundary of the wiring). Namely, by employing the following 
integral equation derived from the foregoing equation (6), the vector 
potential on the surface of the wiring can be obtained. 
##EQU4## 
According to the present invention, since the value of the vector potential 
should be defined only at the surface of wiring as the boundary condition, 
an analyzing space can be limited within the wiring. Thus, the number of 
divided elements can be reduced. Although CPU time for integration of the 
equation (1) is required, the overall calculation period can be shortened 
and a solution with high precision can be obtained. 
FIG. 1 is a block diagram showing a construction of the three dimensional 
wiring inductance calculating system according to the present invention. 
The shown embodiment of a three dimensional wiring inductance calculating 
system is constructed with a wiring structure inputting portion 101, a 
analyzing space discretizing portion 102, a current density vector 
calculating portion 103, a boundary condition setting portion 104, a 
vector potential calculating portion 105 and an inductance coefficient 
calculating portion 106. 
Here, the wiring structure inputting portion 101 performs inputting of a 
three dimensional configuration of the wiring as an object for wiring 
inductance calculation. The analyzing space discretizing portion 102 takes 
a region within the wiring structure as the analyzing space to perform 
element division for the analyzing space. The current density vector 
calculating portion 103 derives a distribution of a current value flowing 
within the wiring and a current density vector. 
The boundary condition setting portion 104 sets a boundary condition with 
respect to a vector potential equation when a current flowing within the 
wiring structure is given. 
A vector potential calculating portion 105 discretizes the vector potential 
equation by taking the inside of the wiring as the analyzing space for 
solving, and derives the vector potential for each divided element. 
An inductance coefficient calculating portion 106 derives a product of a 
current density vector and the vector potential per each divided element 
to standarize the value per unit current value, and derives a sum of the 
products within the wiring. Thus, an inductance coefficient of a three 
dimensional wiring is calculated. The inductance coefficient calculating 
portion 106 outputs the resultant inductance coefficient of the three 
dimensional wiring. 
FIG. 2 is a flowchart showing a first arithmetic processing procedure in 
the shown embodiment of the three dimensional wiring inductance 
calculating system. 
At first, the three dimensional configuration of the wiring as an object of 
the wiring inductance calculation is input (step 201). Here, a wiring 
structure of an LSI is taken as an object for analysis. For example, an 
L-shaped aluminum conductor as shown in FIG. 3, or a memory cell wiring 
structure as shown in FIG. 4, may be the object for analysis. 
FIG. 3 shows the L-shaped wiring conductor. In FIG. 3, it is assumed that 
the current I flows in a direction as indicated by the arrow. On the other 
hand, the memory cell wiring structure of FIG. 4 is constructed with gates 
(word lines) 41, 42 formed on a substrate and extending in one direction, 
and bit lines 43 to 45 intersecting perpendicularly to the gate line 41, 
42 via an insulation layer. The gates 41, 42 and the bit lines 43 to 45 
are formed by a conductor, such as aluminum, polycrystalline silicon or so 
forth, and etching process employing a mask is utilized to obtain a 
predetermined wiring pattern. 
Next,by taking a region within the wiring structure as an analyzing space, 
element division is performed for the analyzing space (step 202). Namely, 
analyzing space discretization is performed. 
FIGS. 3 and 4 show examples of element division with respect to the wiring 
structure. In the drawings, the results of division are shown in wiring 
surface configuration. For example, as shown in FIG. 3, in case of the 
L-shaped wiring conductor, the current I flows to be bent obliquely at the 
L-shaped corner. Here, tetrahedral element division is employed. 
Next, in the discrete analyzing space, a electric potential is obtained by 
solving a Poisson's equation (5) with respect to the electric potential. 
From the obtained electric potential, a gradient of electric potential is 
calculated to obtain current value as well as distribution of the current 
density vector within the wiring (step 203). 
Subsequently, when a current flowing within the wiring is given, the 
boundary condition with respect to the vector potential equation is set 
(step 204). Namely, in the boundary of wiring on the surface of the 
wiring, the vector potential value is calculated. 
In concrete, terms, by using the previous integral equation (7), namely the 
integral equation including the current density electric potential at each 
element position, the vector potential value is calculated (step 210). By 
using these vector potential values at the boundary of wiring as the 
boundary condition, the vector potential equation (6) is solved in the 
discretized analyzing space in the wiring. Thus, the vector potential at 
each divided element position is obtained (step 205). 
Subsequently, at each divided element, the product of the current density 
vector and the vector potential in the divided element is calculated per 
unit current, in the numerical integral procedure for the previous 
equation (1) (step 206). By executing the step 206, the inductance 
coefficient of the three dimensional wiring is obtained. 
Finally, the obtained three dimensional wiring inductance coefficient is 
outputted (step 207), and the process is terminated. 
While the explanation is given for the first arithmetic process according 
to the present invention, a difference between the embodiment and the 
conventional method will be discussed. 
In the conventional method, with respect to the steps corresponding to the 
steps 202 to 205,by taking the space including outside of the wiring as an 
analyzing space, the electric potential and the vector potential are 
obtained. In the alternative, instead of obtaining the electric potential 
and the vector potential, the electrical field and the magnetic field are 
obtained directly in the analyzing space. As the boundary condition in the 
conventional method, it is frequently employed a condition where the 
magnetic field at the end of the analyzing space is sufficiently spaced 
from the wiring. However, in the conventional method, it is required to 
execute calculation with taking a substantially large region in comparison 
with wiring per se as an object for analysis. When a distance from the 
wiring and the end of the analyzing space is made excessively large, pitch 
of the grids established within the analyzing space for element division 
becomes too rough,so as to cause lowering of precision. Conversely, the 
distance to the end of the analyzing region is made excessively small, the 
boundary condition that the magnetic field is zero cannot be established. 
Thus, precision is inherently lowered. 
With respect to this, in the shown embodiment,in which the analyzing space 
is only for region for the wiring per se, the vector potential value on 
the surface of the wiring is obtained by employing the equation (7), and 
the equation (6) is solved by taking the obtained value as the boundary 
condition. Thus, the vector potential at the inside of the wiring is 
obtained. 
With the shown embodiment, the element division should be performed within 
the wiring. Therefore, a number of nodes in the grid required for element 
division can be significantly reduced in comparison with the conventional 
method. 
As a practical example, in case of the L-shaped wiring conductor shown in 
FIG. 3, the number of nodes is 1500. Then, the error of the calculated 
inductance coefficient becomes less than or equal to 1%, and sufficient 
precision of calculation can be obtained. With respect to this, in the 
conventional method, the nodal point in such extent, correct value cannot 
be obtained at all. On the other hand, in the prior art, even when the 
number of nodes is increased in the extent of 10000 to spend a substantial 
analyzing period, sufficient precision, in which an error is in the extent 
of less than or equal to 1%, cannot be obtained. 
Next, FIG. 5 is a flowchart showing a second processing procedure by the 
three dimensional wiring inductance calculating system. 
In the second embodiment, the three dimensional wiring inductance 
coefficient L.sub.1,2 is obtained between the wiring 1 and 2. 
At first, similar to the first arithmetic procedure, the three dimensional 
configuration is input as taking the region in the wiring 1 and 2 as 
object for calculation of wiring inductance (step 501). Then, by taking 
the regions of the wiring 1 and 2 as an analyzing space, the analyzing 
space is divided into tetrahedral elements (step 502). Then, with respect 
to the analyzing space for which the element division is performed, 
Poisson's equation for the electric potential is solved to obtain the 
electric potential. Then, from the electric potential thus obtained, a 
gradient of the electric potential is calculated to obtain the current 
values and the current density vector distributions within the wiring 1 
and 2 (step 503). 
Subsequently, with respect to each node on the surface of the wiring 1, the 
vector potential at the relevant node x.sub.i is calculated (step 504). 
Here, the manner of calculation of the vector potential at the node 
x.sub.i on the surface of the wiring 1 will be discussed in detail. 
At first, the vector potential equation shown in the equation (7) is 
discretized as in the following equation, (step 511). In the following 
equation r.sub.ij is a distance between the node x.sub.i of the wiring 1 
and the typical point of the tetrahedral element j of the wiring 2, and is 
defined as follows. 
##EQU5## 
Next, with respect to each tetrahedral element, a distance r.sub.g from the 
node X.sub.i of the wiring 1 to the gravity center of the tetrahedral 
element j is calculated (step 512). Then, a distance r.sub.m from the node 
x.sub.i to the closest peak of each tetrahedral element j is calculated 
(step 513). Using these distances r.sub.g and r.sub.m, a distance r.sub.ij 
from the node X.sub.i to the typical point of the quadrangular element j 
is calculated by the following algorithm (step 514). 
##EQU6## 
Here, w is a weight coefficient. When the tetrahedral wiring is taken as 
the object for analysis, the weight coefficient is preliminarily 
determined at a reasonable value from a result obtained through comparison 
of precise solution obtained through division into the tetrahedral 
elements and the exact solution by the method of the shown embodiment. In 
the shown embodiment, a value greater than or equal to 0.6 and less than 1 
is used as the weight coefficient. 
Then, using the distance r.sub.ij and the current density vector j(x.sub.i) 
of the tetrahedral element i, the value of the vector potential at the 
node on the surface of wiring is calculated through the following equation 
(step 515). 
##EQU7## 
As set forth above, once the vector potential value at the node on the 
surface of the wiring is obtained, the overall vector potential of the 
inside of the wiring is calculated by a discretizing method of the 
foregoing equation (6) (step 505). Then, from an integral equation (1) of 
the product of the vector potential normalized per unit current value and 
the current density vector, the three dimensional inductance coefficient 
L.sub.1,2 can be obtained (step 506). Finally, the process is terminated 
after outputting the three dimensional inductance coefficient L.sub.12 of 
the wirings 1 and 2 thus obtained. 
In the foregoing second arithmetic process, even when the structures of the 
wirings 1 and 2 are the same, the three dimensional inductance coefficient 
L.sub.1,2 can be obtained accurately. On the other hand, in the foregoing 
calculation, even for the relationship between the wirings 1 and 2, the 
three dimensional wiring inductance coefficient can be similarly obtained. 
FIG. 6 is a graph showing a relationship between a calculation error of the 
inductance in the shown embodiment and the number of nodes per each weight 
coefficient value, by taking the L-shaped conductor shown in FIG. 3 as the 
object for calculation. In the graph, the vertical axis represents an 
error from a numerically exact value L.sub.o of the calculated value L of 
the inductance, and the horizontal axis represents number of nodes in 
element division. 
In the shown embodiment, the calculation error of the inductance is 
primarily caused by an error in discretizing of the foregoing equation 
(8). Therefore, by increasing of the number of nodes, the calculation 
error can be reduced. 
It should be noted that the similar method for discretizing of the integral 
equation of the vector potential shown in FIG. 6, is the method for 
calculation of an electrostatic capacity. Such method has been disclosed 
in K. Nabors et al., IEEE Transactions on Microwave Theory and Techniques, 
Vol. 40, pp 1496 to 1506, 1992. This publication will be referred 
hereinafter as the publication 3. In the method disclosed in the 
publication 3, in the surface integration of a solid body, the integrating 
region is divided into a plurality of panel elements, contribution of each 
panel element is then calculated by expressing with multipole development 
at respective center points of respective panel elements. Thus, the 
electrostatic potential for calculating the capacitance of the wiring is 
obtained. In concrete terms, in the method disclosed in the publication 3, 
when a diameter of the range where the elements are present is less than 
or equal to a distance r to the center of the element, multipole 
development cannot be performed (the contribution of the element is 
represented only by the distance r as first approximation). Otherwise, the 
divided element is further divided. 
In contrast to this, in the shown embodiment, the contribution of each 
element is calculated in consideration of not only the simple distance to 
the center of the element, but also the distance r.sub.m to the closest 
contact point of the element, and further depending on a ratio r.sub.m 
/r.sub.g of the distance r.sub.g to the gravity center of the element and 
the distance r.sub.m to the closest contact point. 
The present invention is directed to calculation of the inductance and the 
publication 3 is directed to calculation of the electrostatic capacity. 
Therefore, it is not possible to simply compare both. However, when 
attempt is made to improve precision in the method of the publication 3, 
the number of divided elements is abruptly increased to require 
significantly long CPU time. In contrast to this, in the method of the 
present invention, precise calculation can be performed with lesser number 
of divided elements. 
In FIG. 6, the case where the weight coefficient value is 1, corresponds to 
the simple approximation in the publication 3 (considering only distance 
r). In the present invention, by setting the weight value less than 1, and 
more typically to 0.7 to 0.8, the distance r.sub.m to the closest contact 
point can be reflected in the contribution as calculated. As a result, by 
setting the number of dividing contact points in the order of 1000, the 
precision in calculation can become less than or equal to 1%. Therefore, 
remarkable improvement of the precision in calculation can be achieved. In 
general, the calculation period of the inductance is increased to be 
proportional to 1.5 power or square of the number of nodes n. Therefore, 
in order to achieve the precision of 1%, the number of nodes in the order 
of 4000 is required in the conventional method. In contrast, the present 
invention can achieve such precision by merely about 1000 of nodes. As a 
result, the required calculation period becomes approximately one tenth in 
comparison with the conventional method. 
On the other hand, even for the memory cell wiring structure including the 
oblique pattern as shown in FIG. 4, the shown embodiment may obtain the 
inductance coefficient at lesser number of nodes (about 5000 to 6000) in 
comparison with the conventional method. 
While the present invention has been discussed in terms of the shown 
embodiment, the process may be applicable for integral calculation of the 
electrostatic potential. Then, even with respect to calculation of 
capacitance of the wiring, the present invention may contribute for 
shortening the CPU time. 
As set forth above, the present invention is effective to make it possible 
to derive the inductance value with high precision in a short CPU time by 
deriving the vector potential value at the surface of the wiring, by 
taking the vector potential value as the boundary condition, and by 
deriving the vector potential within the wiring. Thus, the analyzing space 
can be limited to only to the inside of the analyzing space. Therefore, 
the inductance value can be derived at high speed with high precision. 
Although the invention has been illustrated and described with respect to 
exemplary embodiment thereof, it should be understood by those skilled in 
the art that the foregoing and various other changes, omissions and 
additions may be made therein and thereto, without departing from the 
spirit and scope of the present invention. Therefore, the present 
invention should not be understood as limited to the specific embodiment 
set out above, but to include all possible embodiments which can be 
embodied within a scope encompassed and equivalents thereof with respect 
to the features set out in the appended claims.