CN1403966A - Generating process of optimal cutting number in virtual multi-medium capacitor extraction - Google Patents

Abstract

The present invention belongs to the field of 3D interconnected capacitor extraction technology in computer-aided IC design. The method generates the optical cutting number and optimizes capacitor extracting speed. The method includes the following successively executed computer steps: determining optional cutting numbers (m, n) to constitute a number set based on the geometric parameters of the simulating structure; calculating Z parameter with the numbers (m, n) successively to obtain set Z (s); and determining the optimal cutting number based on the optional cutting number set and Z (s). The said method can shorten capacitor extracting period in certain calculation accuracy.

Description

A kind of generation method that is used for virtual multi-medium capacitor extraction optimal cutting number

Technical field

A kind of generation method that is used for virtual multi-medium capacitor extraction optimal cutting number belongs to the three-dimensional interconnection electric capacity extractive technique field in the integrated circuit CAD (IC-CAD).

Background technology

(Integrated Circuit IC) is the foundation stone of current electronics industry and even information industry to integrated circuit.Along with the development of SIC (semiconductor integrated circuit) manufacturing technology, metal interconnecting wires more and more narrow (reaching below 0.13 micron) in the circuit, the spacing of line and line is also more and more littler.This makes the electromagnetic field ghost effect between the interconnection line become the principal element of circuit performances such as influence such as delay, power consumption and reliability.Therefore, in integrated circuit (IC) design, must consider the interconnection ghost effect.

The design cycle of current integrated circuit as shown in Figure 1.Design chip piece, at first will propose functional description, obtain describing the domain of semiconductor technology structure then through logical design, layout design.At this moment need to carry out the step of " layout verification ", come the proof scheme design whether can reach the performance requirement of setting originally, just can manufacture if meet the demands, otherwise also will get back to logical design correction, repeat the process of an iteration.In layout verification, an important link is called " parasitic parameter extraction ", and it comprises parameters such as the dead resistance calculated between the metal interconnecting wires, electric capacity, inductance.After only obtaining these interconnection parasitic parameters, just can carry out breadboardin and whether reach performance requirement with decision circuitry.

Stray capacitance between interconnection line (being called for short " interconnection capacitance ") is more extensive to the influence of circuit performance; and the coupling of the substrate of interconnection resistance, Digital Analog Hybrid Circuits and microelectromechanical systems (Micro-Electro-Mechanical Systems, MEMS) etc. the research in field is also very similar with it.The extraction of interconnection capacitance (calculating) is subjected to the concern of academia and industry member most.Under current technology characteristics, extract for carrying out accurate electric capacity, need carry out numerical simulation to the three-dimensional model of integrated circuit diagram, its main method comprise domain type solution (finite difference method and Finite Element Method), DIRECT BOUNDARY ELEMENT method (Boundary ElementMethod, BEM), Element BEM etc. indirectly.Compare with the domain type solution, the advantage of boundary element method is the precision height, less discrete variable and than the ability of strength reason complex boundary shape.

Interconnection structure from actual domain is defined in the limited area usually, and wherein the electromotive force of electrostatic field can be described by Laplce (Laplace) equation of band mixed boundary condition.Because the boundary integral equation that the DIRECT BOUNDARY ELEMENT method is dispersed comprises electromotive force and two variablees of normal electric field intensity, it is more suitable for the simulation of this Galois field, multimedium parasitic capacitance structure than Indirect Boundary Element Technique.Though the DIRECT BOUNDARY ELEMENT method has above-mentioned advantage, because computation requirement three-dimensional structures more and more, that wherein consider are also increasing in the industrial reality, the computing velocity that how to improve the three-dimensional capacitance extracting method has just become the task of top priority.

" the analogy literary composition is strong; Wang Zeyi; Hou Jingsong; ' a kind of three-dimensional fast VLSI interconnection capacitance extracting method: virtual multi-medium method '; electronic letters, vol; the 29th volume at document for I, o. 11th, pp.1526-1529, calendar year 2001 " and " Wenjian Yu andZeyi Wang, ' An efficient quasi-multiple medium algorithm for the capacitance extraction of actual3-D VLSI interconnects ', in Proc.IEEE ASP-DAC 2001, Yokohama, Japan, Jan.2001, pp.366-371. " in virtual multi-medium (Quasi-Multiple Medium; QMM) method and be used for the calculating that three-dimensional multi-medium capacitor extracts, it has become a kind of important quick three-dimensional interconnection capacitance extracting method is proposed.

The input (being generally the text of following certain format) that QMM electric capacity extracts is data of describing three-dimensional multimedium interconnection structure, comprising geometrical body data and electrical parameter (voltage on the conductor, the specific inductive capacity of medium etc.).Interconnection structure integral body is a rectangular parallelepiped zone, as shown in Figure 2, its medium 3 hierarchal arrangement, some metallic conductors are embedded in some dielectric layer.In calculating, suppose that wherein the voltage of interconnective one or more conductor is 1 volt, be called leading body 1, and other conductor voltages are 0 volt, be called environment conductor 2.Metal substrate 4 is pasted mutually with the 1st layer of medium bottom surface, and bias voltage is 0 volt.

By calculating the electric weight to obtain on each conductor, establish that electric weight is Q on the leading body _m, electric weight is Q on other j piece conductors _j, then the coupling capacitance of conductor j and leading body is: C _Jm=-Q _j/ V _Mj

Because voltage difference V _MjIt is 1 volt, so coupling capacitance numerically is-Q between conductor j and leading body _jIn addition, the electric weight Q on the leading body _mBe numerically equal to the total capacitance between itself and environment conductor.Total capacitance and coupling capacitance are exactly that electric capacity extracts the output result who calculates.

The QMM method has increased the step of " virtual cutting " in the process that DIRECT BOUNDARY ELEMENT electric capacity extracts, be about to layered media and be cut into m * n piece equably perpendicular to the bottom surface, as shown in Figure 3.The m here, n are two positive integers, and we claim the binary integer to (m n) is virtual cutting number.

For studying conveniently, carry out multilayered medium interconnection structure that electric capacity extracts a rectangular shape that cuts out the integrated circuit diagram that calculates as a model configuration from needs, wherein comprise multilayered medium and embed wherein plurality of conductors.In the virtual multi-medium capacitor extracting method, at first to each layer medium of model configuration be cut, these areas of dielectric that obtain through this " virtual cutting " are called the virtual medium zone.To carry out discretize (being divided into boundary element) to the border surface of each areas of dielectric (being the virtual medium zone) then.What the boundary element was here divided employing is non-homogeneous boundary element division methods, and the type of promptly distinguishing various border surfaces adopts the boundary elements of different sizes to divide the interval.After the border carried out discretize, just can in each areas of dielectric, list the boundary integral equation of series of discrete, electromotive force and normal electric field intensive variable on each boundary element have wherein been comprised, (electromotive force is known on the conductor border to bring boundary condition into, normal electric field intensity is zero on the model configuration outer boundary), by electromotive force and electric displacement continuity equation on the areas of dielectric interface, above-mentioned all divergent boundary integral equations can be coupled into an overall linear system of equations again.Find the solution the normal electric field intensity that this system of equations obtains each boundary element of conductive surface, and then can calculate the carried charge of each conductor, also promptly obtain required interconnection capacitance value.

As shown in Figure 4, virtual multi-medium capacitor extracts and specifically comprises following six steps:

1. handle the model configuration of input, divide for the virtual cutting in back and non-homogeneous boundary element and carry out data and prepare.At first the model configuration that will calculate (rectangular shape) places a three-dimensional cartesian coordinate system, and makes the bar limit of rectangular parallelepiped all be parallel to three axles of x, y, z of coordinate system accordingly.The information of input comprises position coordinates and geometrical length, the relative dielectric constant of each medium and the numbering of " leading body " of each medium and conductor block.Handle above-mentioned geological information, can obtain the space relation of inclusion (be used to judge the border of each areas of dielectric) of medium to conductor, the conductor of contiguous leading body (is called for short " proximity conductor ", expression is nearer apart from leading body, and and leading body between do not have the conductor of other conductor barrier), and the parameter that is used for non-homogeneous boundary element division methods, they comprise: the boundary element division interval MG that is used to contain " endoporus " surface (also claiming perforated surface) _x, MG _y, MG _zAnd EG _x, EG _y, EG _zAnd the reference boundary element of each body (medium, conductor block and metal substrate) is divided umber ES _x, ES _y, ES _z(because the numerical value possibility that each body is calculated is different, so each body is needed these three parameters of storage separately).

" endoporus " refers to conductor block embedding medium surface, " hole " of causing for original complete dielectric surface.As shown in Figure 2, comprise some conductor block in the 3rd layer of medium, the bottom surface of these conductor block pastes mutually with the bottom surface of the 3rd layer of medium, is equivalent to be embedded in the bottom surface of the 3rd layer of medium.Fig. 5 has shown the bottom surface of the 3rd layer of medium, when this face is carried out the boundary element division, should remove the endoporus 5 that these conductor block form, and with remainder, promptly effectively dielectric surface 6 is divided into boundary element.

The microtomy of perforated surface being divided boundary element is disclosed in document (Gu Jiangchun, Wang Zeyi, Hong Xianlong, " the quick boundary element on porous plane is divided ", computer-aided design (CAD) and graphics journal, Vol.12, No.3, pp.211-215,2000).Microtomy at first is divided into perforated surface female unit, and its key step is:

At first, make sweep trace along the x direction of principal axis, if a sweep trace on same straight line, can only be done, as shown in Figure 6 in a plurality of summits through each summit of this face and the polygonal summit of each endoporus.The part of zone outside endoporus between the every pair of adjacent scanning lines is divided into that several are trapezoidal, wherein, and each trapezoidal section unit 7 that is called; Then, consider to be close to a plurality of sections unit, it is trapezoidal to judge whether they can merge one of formation, if can just merge; At last, as shown in Figure 7, lip-deep section unit is through after judging, merging, and the new section unit area that can not further merge that obtains is called " female unit ".

Female unit can be divided into main (Master) female unit and two kinds in general female unit again.Main female unit be on the porose medium outside surface or porose dielectric interface on female unit of adjacent leading body, the female unit of other of perforated surface be exactly general female first.Fig. 7 is for dividing the result after female unit to the perforated surface of Fig. 5, the endoporus 8 that adjacent leading body the forms main female unit 9～14 that distributing.

MG _x, MG _y, MG _zBe respectively and be used to divide dividing at interval of main female unit along x, y, the axial boundary element of z,

EG _x, EG _y, EG _zBe respectively and be used to divide dividing at interval of general female unit along x, y, the axial boundary element of z,

Their computing formula is as follows: ${\mathrm{MG}}_x=\mathrm{Min}\left\{\mathrm{Max}\right\{\frac{{\mathrm{MstLength}}_x}{4\ln ({\mathrm{MstLength}}_x+0.8)},\frac{{\mathrm{MstLength}}_x}{20}\},{\mathrm{MstLength}}_x\},$ ${\mathrm{MG}}_y=\mathrm{Min}\left\{\mathrm{Max}\right\{\frac{{\mathrm{MstLength}}_y}{4\ln ({\mathrm{MstLength}}_y+0.8)},\frac{{\mathrm{MstLength}}_y}{20}\},{\mathrm{MstLength}}_y\},$ ${\mathrm{MG}}_z=\mathrm{Max}\{\frac{{\mathrm{MstLength}}_z}{6},0.25\},$ ${\mathrm{EG}}_x=\mathrm{Max}\{\frac{x_{\mathrm{len}}}{10},2\·{\mathrm{MG}}_x\},-----\left(a\right)$ ${\mathrm{EG}}_y=\mathrm{Max}\{\frac{y_{\mathrm{len}}}{10},2\·{\mathrm{MG}}_y\},$ ${\mathrm{EG}}_z=\mathrm{Max}\{\frac{\mathrm{MaxMedZ}}{6},2\·{\mathrm{MG}}_z\}.$

Wherein, x in the above-mentioned formula _LenBe model configuration x direction length, y _LenBe model configuration y direction length, unit is micron (down together).Because leading body may be made up of a plurality of conductor block that overlap, so establish MstLength _x, MstLength _y, MstLength _zThe maximal value of each conductor block of leading body along x, y, z direction of principal axis length formed in expression respectively;

MaxMedZ is the maximal value of dielectric layer height (along the z direction of principal axis);

Min{} gets minimum value function, and Max{} gets max function, and ln () is for taking from right logarithmic function.

ES _x, ES _y, ES _zRepresent that respectively body divides umber along x, y, z are axial with reference to boundary element, described body can be conductor block according to the difference of analytic target, and a kind of in three kinds of bodies of metal substrate or medium distinguishes not homomorphs below, introduces ES _x, ES _y, ES _zCalculating:

Medium:

If this medium place layer comprises the adjacent layer of leading body or leading body, then works as ES _zGot 3 at＜3 o'clock.

Wherein, Length _x, Length _y, Length _zBe respectively this body along x, y, the axial length of z, described body can be conductor block according to the difference of analytic target, a kind of (down together) in three kinds of bodies of metal substrate or medium.

Each conductor block of forming leading body:

The proximity conductor piece:

If whole leading body is MasterLength along x direction of principal axis length _x, be MasterLength along y direction of principal axis length _y

If MasterLength _x/ MasterLength _y＞4, then

If MasterLength _y/ MasterLength _x＞4, then

If MasterLength _x/ MasterLength _yAnd MasterLength _y/ MasterLength _xAll be not more than 4, then

If this conductor block and leading body belong to a dielectric layer together, then

, otherwise

Metal substrate:

If it is adjacent with leading body place dielectric layer,

If it is not adjacent with leading body place dielectric layer,

To metal substrate, ESz is nonsensical.

Other conductor block:

In the above-mentioned formula " Be " on round " symbol, promptly

Expression is more than or equal to the smallest positive integral of a.

2. definite virtual cutting number (m, n).Need the artificial virtual cutting number of specifying, perhaps obtain according to certain experimental formula.Experimental formula is:

3. virtual cutting process.Perpendicular to the xoy coordinate plane, whole model configuration evenly is cut into m * n piece virtual medium zone, the conductor block that is embedded in the medium also may be cut into plurality of small blocks, generate the data of the body of these new generations of expression, simultaneously, obtain the information that each virtual medium piece comprises the information of conductor block and describes each areas of dielectric efficiency frontier surface.

4. boundary element is divided.The efficiency frontier surface of each areas of dielectric (virtual medium piece) is divided into the quadrilateral boundary element, and the information of boundary element comprises the numbering of each apex coordinate of quadrilateral, boundary element type (medium outside surface, conductive surface or dielectric interface), affiliated areas of dielectric.This step adopts a kind of non-homogeneous boundary element division methods, distinguishes different situations and divides the surface with different boundary element density, thereby reduce the quantity of boundary element.An effective border surface is divided boundary element specifically comprises following a few step:

Judge whether this face contains endoporus, if need earlier it to be divided into " female unit ".

If this surface is medium non-porous outer surface or medium atresia interface or conductive surface (comprising metal substrate), profit

Divide umber ES with the reference boundary element and (comprise ES _x, ES _y, ES _z) determine that this surface divides G at interval along the boundary element on two orthogonal directionss (if be parallel to the surface of xoy coordinate plane, then be along x axle, y direction of principal axis, and the like) ₁And G ₂If this surface is porose outside surface of medium or the porose interface of medium, the boundary element that utilizes boundary element to divide on two orthogonal directionss that MG, EG at interval determine each female unit of this surface is divided G at interval ₁And G ₂

According to G ₁And G ₂With this surface or should the surface on all female units generate the data of boundary element.

5. formation equation.According to the information of boundary element, with borderline certain the boundary element Г of medium i _kCentral point is as collocation point, but row divergent boundary integral equation: $\frac{{\mathrm{<figure-callout\; id="2"\; label="u\; k"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">u</figure-callout>}}_k}{2}+\underset{j=1}{\overset{N_j}{\mathrm{\&Sigma;}}}\left({\&Integral;}_{{\mathrm{\&Gamma;}}_j}{q}_{\left(k\right)}^{*}\mathrm{d\&Gamma;}\right)u_j=\underset{j=1}{\overset{N_j}{\mathrm{\&Sigma;}}}\left({\&Integral;}_{{\mathrm{\&Gamma;}}_j}{u}_{\left(k\right)}^{*}\mathrm{d\&Gamma;}\right)q_j--------\left(2\right)$

Wherein: N _iBe the sum of medium i border coboundary unit, Г _j(j=1 ..., N _i) represent j boundary element, u _j(j=1 ..., N _i) be the electromotive force of putting on the j boundary element (supposing that electromotive force, electric field intensity are constant on each boundary element), q _j(j=1 ..., N _i) be outer normal direction (outer) component of the electric field intensity put on the j boundary element by pointing in this areas of dielectric.In addition, two function expressions in the sign of integration are: $u_{\left(k\right)}^{*}=\frac{1}{{4\mathrm{\&pi;r}}_{\left(k\right)}},q_{\left(k\right)}^{*}=\frac{-(n,r_{\left(k\right)})}{{4\mathrm{\&pi;r}}_{\left(k\right)}^3},------\left(3\right)$

In the formula, r _(k)For boundary element k central point to boundary element Γ _jThe distance of upper integral point d Г, n is boundary element Γ _jNormal vector outside the last unit, r _(k)For from boundary element k central point to boundary element Γ _jThe vector of upper integral point d Γ, " () " is that two vectors are asked interior product code.

Equation (2) is about discrete variable u _j, q _j(j=1 ..., N _i) linear equation.Then, get, i.e. the Г of coboundary, medium i border unit all over all collocation points _kCentral point (i=1 ..., M, k=1 ..., N _i), wherein M is total number of areas of dielectric, can obtain a complete system of linear equations.The discrete variable of this system of linear equations is electromotive force and the normal electric field intensity on each boundary element, brings known boundary condition (electromotive force is given bias voltage on the conductor border, and normal electric field is zero on the medium outer boundary) into, can get following form after the arrangement:

Ax＝f?????????????????????????????????????????(4)

Wherein x is the electromotive force unknown on each boundary element and the vector of normal electric field intensity composition.

6. solving equation.Find the solution system of linear equations (4) with pre-condition GMRES algorithm, electromotive force and normal electric field intensity all can obtain on all boundary elements.Use following formula to calculate each conductor institute carried charge at last: $Q_i={\&Integral;}_{{\mathrm{\&Gamma;}}_{\mathrm{ci}}}\mathrm{\&epsiv;}\&CenterDot;\mathrm{qd\&Gamma;}=\underset{j=1}{\overset{N_{\mathrm{ci}}}{\mathrm{\&Sigma;}}}\left({\mathrm{\&epsiv;}\&CenterDot;q}_j\right)-----\left(5\right)$

Г wherein _CiBe the surface of conductor i, N _CiBe the boundary element number on conductor i surface, q _j(j=1 ..., N _Ci) be the normal electric field intensity on each boundary element, ε is the specific inductive capacity that comprises the medium of conductor.

In the 2nd step of above-mentioned virtual multi-medium capacitor extracting method, need artificial given cut parameter m and n (perhaps adopting certain experimental formula), this overall computational performance that makes QMM electric capacity extract depends on user's experience to a great extent, and the computing velocity that electric capacity extracts is slower.

Summary of the invention

The objective of the invention is in the virtual multi-medium capacitor extracting method, (m, n), the computing velocity that virtual multi-medium capacitor is extracted reaches optimum or near-optimization, thereby can the high efficiency extraction three-dimensional capacitance to adopt a kind of new method to generate QMM cutting number automatically.

The invention discloses a kind of generation method that virtual multi-medium capacitor extracts optimal cutting number that is used for, this method is called " optimum solution of minimum Z value " (OSMZ:optimal selection with minimal Z-value) method again, and the Z parameter is the number of non-zero entry in the coefficient matrices A; It is characterized in that the method comprises the following steps of being carried out successively by computing machine:

The multilayered medium interconnection structure of a rectangular shape that 1) will cut out from integrated circuit diagram is as model configuration, and according to the geometric parameter of model configuration, getting m is closed interval [m _Min, m _Max] interior arbitrary integer, n is closed interval [n _Min, n _Max] interior arbitrary integer, all integers that obtain like this are to (m, n) initial value of formation S set; Set and judge the dividing value R whether model configuration xoy cross section length breadth ratio lacks of proper care _L, utilize R _LFurther screen the element in the S set;

Wherein, m: from the xoy cross section of model configuration, it is along the cutting umber of y direction virtual medium piece;

N: from the xoy cross section of model configuration, it is along the cutting umber of x direction virtual medium piece;

2) choose each integer in the S set after the screening to cut number (m as the candidate, n), calculate the value of Z parameter when adopting this cutting number to carry out the virtual multi-medium capacitor extraction respectively, wherein the Z parameter is a non-zero entry number in the coefficient matrices A, finally obtain cutting the set Z (S) that manifold is closed the corresponding non-zero entry number of S with the candidate, its steps in sequence is as follows:

2.1) candidate who takes out is cut number, and (m n), calculates the sum M of its virtual areas of dielectric i that cuts out, M=m * n * L, i=1,2 ... M;

Wherein, L is the number of the dielectric layer in the model configuration;

2.2) border surface on the areas of dielectric is divided into two classes: the first kind is conductive surface, metal substrate, medium non-porous outer surface and the porose outside surface of medium, and second class is medium atresia interface and the porose interface of medium; To all areas of dielectric, adopt non-homogeneous boundary element division methods to calculate boundary element number on its all border surfaces respectively, using array location a[i] storage medium zone i goes up the boundary element number on all first kind border surfaces, using array location b[i] storage medium zone i goes up the boundary element number on the second all class border surfaces, i=1,2 ..., M;

2.3) according to formula $Z\left(s\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\left(a\right[i]+b[i\left]\right)\&CenterDot;\left(a\right[i]+2b[i\left]\right)$ , the candidate who takes out in calculating and the S set cuts number (m, n) corresponding Z value;

2.4) execution in step 2.1 repeatedly) to 2.3), each candidate in pair set S cuts number and has carried out corresponding processing;

3) determine threshold value Z according to the minimum value of the Z value of respectively cutting the number correspondence in the S set _gIf (m, n) Dui Ying Z value is less than threshold value Z for certain element in the S set _g, and compare with other element in the S set, the m of this element and n product minimum, then this element is optimal cutting number.

In the method, described m _MinRecommendation be 3, m _MaxRecommendation be n _MinRecommendation be 3, n _MaxRecommendation be

Wherein, x _LenBe model configuration x direction length, y _LenBe model configuration y direction length, unit is micron;

"

Be " on round " symbol, Min{} gets minimum value function.

At this method step 1) in utilize R _LIt is as follows further to screen in the S set method of element:

If x a. _Len/ y _LenGreater than R _L, then keep the element that satisfies " n＞m " in the S set, delete other elements; Otherwise carry out step b;

Wherein, judge the dividing value R whether model configuration xoy cross section length breadth ratio lacks of proper care _LGreater than 1;

If y b. _Len/ x _LenGreater than R _L, then keep the element that satisfies " m＞n " in the S set, delete other elements; Otherwise satisfy the element of " | n-m|＜D " in the reservation S set, delete other elements, wherein, the model configuration of D for not lacking of proper care, the upper limit of the difference of m and n two number values for length breadth ratio.

R described in this method _LRecommendation be 1.4.

The recommendation of the upper limit D of the difference of m described in this method and n two number values is 2.

This method step 3) method of choosing optimal cutting number in is as follows:

At first, ask the minimum value among the set Z (S), be designated as Z ₀

Secondly, with Z ₀Multiply by coefficients R greater than 1 _zObtain a threshold value Z _g, i.e. Z _g=Z ₀* R _z

Once more, initialization Q is infinitely great integer;

At last, the given element among the pair set S (m, n), if its respective value Z (m, n)＜Z _gAnd m * n＜Q, then m _O=m, n _O=n, Q=m * n; (m n) carries out aforesaid operations to elements all among the pair set S, finally obtains the optimal cutting number (m in the S set _O, n _O).

Coefficients R described in this method _zRecommendation be 1.25.

The number e of the non-homogeneous boundary element division methods of employing described in this method calculating conductor surface coboundary unit _A1Method as follows:

At first, the known reference boundary element that does not carry out the conductor block before the virtual cutting is divided umber be assigned on the corresponding sub-conductor that virtual cutting obtains, obtain sub-conductor block and divide umber E along x, y, the axial actual boundary of z unit by length ratio _x, E _y, E _z: $E_x=[{\mathrm{ES}}_x\&CenterDot;\frac{{\mathrm{Length}}_x^{\&prime;}}{{\mathrm{Length}}_x}],$ $E_y=[{\mathrm{ES}}_y\&CenterDot;\frac{{\mathrm{Length}}_y^{\&prime;}}{{\mathrm{Length}}_y}],$ E _z＝ES _z；

Wherein, " [] " rounds symbol in being, for example, [a] is near the integer of a, if less than 1, then value 1;

ES _x, ES _y, ES _z: when under the front surface do not carry out before the virtual cutting body along x, y, z is axial to divide umber with reference to boundary element, described body can be conductor block according to the difference of analytic target, a kind of in three kinds of bodies of metal substrate or medium, their concrete numerical value is calculated by the model configuration parameter preparation process of preorder;

Because the virtual multi-medium cutting may make an original conductor be cut into the sub-conductor of polylith, so establish:

Length _x', Length _y' represent respectively to carry out sub-conductor block after the virtual cutting along the length of x, y direction under this face;

Length _x, Length _yRepresent the length of the affiliated conductor block of this face respectively along x, y direction;

Then, distinguish the situation of this face, respectively the number e of computation bound unit _A1:

If this face is parallel to xoy plane, e _A1=E _x* E _y

If this face is parallel to yoz plane, e _A1=E _y* E _z

If this face is parallel to zox plane, e _A1=E _z* E _x

The method that the non-homogeneous boundary element division methods of employing described in this method is calculated metal substrate surface coboundary unit number is as follows:

The metal substrate surface is the special conductive surface on a kind of xoy of being parallel to plane, metal substrate before the virtual cutting becomes m * n piece substrate after virtual cutting, each sub-substrate is along x, the axial boundary element of y is divided umber and is divided umber and the decision of cutting number by the reference boundary element of virgin metal substrate, and its coboundary unit number is $e_{a2}=\left[\frac{{\mathrm{ES}}_x}{n}\right]\&CenterDot;\left[\frac{{\mathrm{ES}}_y}{m}\right].$

The method of the non-homogeneous boundary element division methods of the employing described in this method calculation medium non-porous outer surface coboundary unit number is as follows:

At first, along x, y is axial to be evenly distributed on the virtual medium piece with reference to boundary element division umber with known medium, and medium remains unchanged along the axial division umber of z, obtains the virtual medium piece and divides umber E along x, y, the axial actual boundary of z unit _x, E _y, E _z: $E_x=\left[\frac{{\mathrm{ES}}_x}{n}\right],$ $E_y=\left[\frac{{\mathrm{ES}}_y}{m}\right],$ E _z＝ES _z；

Then, distinguish the situation on this nonporous medium surface on the virtual medium piece, respectively the number e of computation bound unit _A3:

If this face is parallel to xoy plane, ea ₃=E _x* E _y

If this face is parallel to yoz plane: ea ₃=E _y* E _z

If this face is parallel to zox plane: e _A3=E _z* E _x

When adopting the porose outside surface of non-homogeneous boundary element division methods calculation medium coboundary unit number in this method, use microtomy that this perforated surface is divided female unit, calculate boundary element number of each female unit respectively, they and i.e. boundary element number e on the porose for this reason outside surface _A4, its method of calculating female first boundary element number is as follows:

At first, establish when father's former wife unit and be respectively G at interval along the division of x, y, z direction _x, G _y, G _z

When father's former wife unit is main female unit, then G _x=MG _x, G _y=MG _y, G _z=MG _z

Otherwise work as father's former wife unit is general female unit, G _x=EG _x, G _y=EG _y, G _z=EG _z

MG _x, MG _y, MG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of main female unit, the model configuration parameter preparation process by preorder calculates;

EG _x, EG _y, EG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of general female unit, the model configuration parameter preparation process by preorder calculates;

Then, establish Length _Mx, Length _My, Length _MzBe the length of this mother unit, then obtain boundary element division umber E actual in this mother unit divided by working as father's former wife unit at interval along x, y, the axial division of z respectively with them along x, y, z direction _x, E _y, E _z:

At last, distinguish the situation of this mother unit, calculate the boundary element number e of female unit _m:

If this mother unit is parallel to xoy plane, e _m=E _x* E _y

If this mother unit is parallel to yoz plane, e _m=E _y* E _z

If this mother unit is parallel to zox plane, e _m=E _z* E _x

The method of the non-homogeneous boundary element division methods of the employing described in this method calculation medium atresia interface coboundary unit number is as follows:

At first, along x, y is axial to be evenly distributed on the virtual medium piece with reference to boundary element division umber with known medium, and medium remains unchanged along the axial division umber of z, obtains the virtual medium piece and divides umber E along x, y, the axial actual boundary of z unit _x, E _y, E _z: $E_x=\left[\frac{{\mathrm{ES}}_x}{n}\right],$ $E_y=\left[\frac{{\mathrm{ES}}_y}{m}\right],$ E _z＝ES _z；

Distinguish the situation of this atresia interface then, respectively the number e of computation bound unit _B1Value:

If this face is parallel to xoy plane, e _B1=E _x* E _y

Boundary element for the virtual medium interface on parallel yoz plane or zox plane is divided, and also needs distinguish according to its distance from leading body, and far away more from leading body, its coboundary unit just divides fewly more, and concrete formula is as follows:

If this face is parallel to the yoz plane:

If dielectric layer is taken body place layer, e as the leading factor under this face _B1=E _y* E _z

If dielectric layer is taken the upper and lower adjacent layer of body place layer as the leading factor under this face, ${\mathrm{<figure-callout\; id="1"\; label="e\; b"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">e</figure-callout>}}_b=\left[\frac{{\mathrm{<figure-callout\; id="2"\; label="ES\; y"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">ES</figure-callout>}}_y}{2\&CenterDot;m}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{2}\right];$

If dielectric layer is not leading body place layer and adjacent layer thereof under this face, ${\mathrm{<figure-callout\; id="1"\; label="e\; b"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">e</figure-callout>}}_b=\left[\frac{{\mathrm{ES}}_y}{8\&CenterDot;m}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{8}\right];$

If this face is parallel to the zox plane:

If dielectric layer is taken body place layer, e as the leading factor under this face _B1=E _z* E _x

If dielectric layer is taken the upper and lower adjacent layer of body place layer as the leading factor under this face, ${\mathrm{<figure-callout\; id="1"\; label="e\; b"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">e</figure-callout>}}_b=\left[\frac{{\mathrm{ES}}_x}{2\&CenterDot;n}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{2}\right];$

If dielectric layer is not leading body place layer and adjacent layer thereof under this face, ${\mathrm{<figure-callout\; id="1"\; label="e\; b"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">e</figure-callout>}}_b=\left[\frac{{\mathrm{ES}}_x}{8\&CenterDot;n}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{8}\right].$

When adopting the porose interface of non-homogeneous boundary element division methods calculation medium coboundary unit number in this method, use microtomy that this perforated surface is divided female unit, calculate boundary element number of each female unit respectively, they and i.e. boundary element number e on the porose for this reason interface _B2, its method of calculating female first boundary element number is as follows:

At first, establish when father's former wife unit and be respectively G at interval along the division of x, y, z direction _x, G _y, G _z

When father's former wife unit is main female unit, then G _x=MG _x, G _y=MG _y, G _z=MG _z

Otherwise work as father's former wife unit is general female unit, G _x=EG _x, G _y=EG _y, G _z=EG _z

MG _x, MG _y, MG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of main female unit, the model configuration parameter preparation process by preorder calculates;

EG _x, EG _y, EG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of general female unit, the model configuration parameter preparation process by preorder calculates;

Then, establish Length _Mx, Length _My, Length _MzBe the length of this mother unit, then obtain boundary element division umber E actual in this mother unit divided by working as father's former wife unit at interval along x, y, the axial division of z respectively with them along x, y, z direction _x, E _y, E _z:

At last, distinguish the situation of this mother unit, calculate the boundary element number e of female unit _m:

If this mother unit is parallel to xoy plane, e _m=E _x* E _y

If this mother unit is parallel to yoz plane, e _m=E _y* E _y

If this mother unit is parallel to zox plane, e _m=E _z* E _x

In the virtual multi-medium capacitor extracting method, adopt the OSMZ method can be under the situation that keeps computational accuracy and less internal memory consumption, the time that virtual multi-medium is calculated is approximate to reach the shortest, and less depends on user experience, makes the automaticity height.

Description of drawings

Fig. 1 is the integrated circuit (IC) design flow process.

Fig. 2 is the three-dimensional interconnection model configuration synoptic diagram of embodiment.

Fig. 3 is cut into each dielectric layer among Fig. 2 the synoptic diagram of 3 * 2 structures for adopting the virtual multi-medium method.

Fig. 4 extracts process flow diagram for QMM electric capacity.

Fig. 5 is the 3rd a layer of medium bottom surface of model configuration shown in Figure 2.

Fig. 6 utilizes microtomy to divide the synoptic diagram of perforated surface shown in Figure 5.

Fig. 7 is a perforated surface shown in Figure 5 after microtomy is divided, and merges the synoptic diagram of the female unit that generates.

Fig. 8 is the FB(flow block) of OSMZ method.

Fig. 9 is for determining the process flow diagram of cutting number span S step.

Figure 10 is the process flow diagram of design factor matrix non-zero entry number Z step.

Figure 11 is a process flow diagram of asking the optimal cutting number step.

Figure 12 is the front view of the embodiment of the invention.

Figure 13 is the vertical view of the 3rd layer of medium of the embodiment of the invention.

Figure 14 is the vertical view of embodiment of the invention second layer medium.

Figure 15 is the numbering synoptic diagram (vertical view) in each virtual medium zone of ground floor medium.

Figure 16 a is the front view in the virtual medium zone 1 in the ground floor medium.

Figure 16 b is the vertical view in the virtual medium zone 1 in the ground floor medium.

Embodiment

The implementation that the virtual multi-medium capacitor that contains the OSMZ method below in conjunction with an instantiation explanation extracts.

Operation has embedded the QMM electric capacity that contains the OSMZ method and has extracted software on Sun Ultra Enterprise 450 workstations, extracts the coupling capacitance between the total capacitance of leading body in the present embodiment and it and other conductors.

QMM electric capacity extracting method step is as follows:

Information processing before the OSMZ method and parameter are prepared:

At first the interconnect simulation structure is placed three-dimensional cartesian coordinate system, and make every limit in model configuration zone all be parallel to three axles of x, y, z of coordinate system accordingly.

Figure 12 has shown the front elevation of present embodiment, this be contain 5 layers of medium (D1, D2, D3, D4, model configuration D5), the size of model configuration is 11 * 9 * 5.8 (unit is micron, down with), each dielectric layer height is 0.3,0.9,1 from top to bottom, 4,1.2,2.0.The relative dielectric constant of each layer medium is respectively 3.2,3.9, and 3.2,3.9,3.2.Comprise conductor block in several from bottom to top second and third layer medium, paste mutually with the dielectric layer bottom surface conductor block bottom surface, and the height of this two-layer conductor block is respectively 0.5,0.8, and their position and size are seen Figure 13 and Figure 14.

Black box is represented leading body m7 (1V bias voltage) among Figure 12, and grey block represents that environment conductor (0V bias voltage) is layer of metal substrate plane (being equivalent to earth conductor, the 0V bias voltage) the most beneath of total, represents with thick line.

Figure 13 is the vertical view of several from the bottom up the 3rd layer of medium, has wherein shown 5 size and the positions of conductor on the xoy plane.The size of conductor m1, m2, m3 is 1.5 * 0.7, and conductor m4 is of a size of 0.5 * 1.5, and conductor m5 is of a size of 11 * 1.5, and other physical dimensions mark in the drawings.

Figure 14 is a vertical view of counting second layer medium from the bottom up, has wherein shown 4 size and the positions of conductor on the xoy plane.Four conductor m6, m7, m8 and m9 width on the x direction is 0.3, length difference 2,4,1 and 1 on the y direction, other physical dimensions mark in the drawings.

Calculate parameters such as MG, EG and ES:

In this example, leading body m7 along three direction length is: MstLength _x=0.3, MstLength _y=4, MstLength _z=0.5; The length of x, y direction model configuration is respectively x _Len=11, y _Len=9; Dielectric layer height maximal value MaxMedZ=2.According to formula (a), obtain:

MG _x＝0.3，MG _y＝0.638，MG _z＝0.25；

EG _x＝1.1，EG _y＝1.275，EG _z＝0.5；

Proximity conductor is m2, m5, m6, m8 in this example.According to the method for describing in the size of each body and the virtual multi-medium capacitor extraction step 1, obtain the corresponding ES parameter of each body (comprising medium, conductor and metal substrate), as shown in table 1.

The corresponding ES parameter of table 1 embodiment medium, conductor and metal substrate

	?D1	?D2	?D3	?D4	?D5	?m1	?m2	?m3	?m4	?m3	?m6	?m7	?m8	?m9	Substrate
																?ES x	?10	?10	?10	?10	?10	?2	?6	?2	?1	?20	?1	?4	?2	?1	?17
?ES y	?9	?9	?9	?9	?9	?1	?1	?1	?2	?2	?2	?8	?1	?1	?14
																?ES z	?3	?3	?3	?2	?2	?1	?2	?1	?1	?2	?3	?3	?3	?1	?/

Utilize the OSMZ method to determine optimum virtual cutting number (m _O, n _O), Fig. 8 is the FB(flow block) of OSMZ method, divides following three steps to carry out:

Step 1) is determined the span S of optimum virtual cutting number, and flow process as shown in Figure 9;

1.1) by the length x of x, y direction model configuration _Len=11, y _Len=9, can calculate:

m _Min, n _MinAll get recommendation 3, then S={ (m, n) | m, n are integer, and 3≤m≤7,3≤n≤8}

1.2) R _LGet recommendation 1.4; Because x _Len/ y _Len＜1.4, carry out step 1.3);

1.3) again because y _Len/ x _Len＜1.4, so the length breadth ratio of model configuration is not lacked of proper care.D gets recommendation 2, thus get S={ (m, n) | m, n are integer, 3≤m≤7,3≤n≤8, and | n-m|＜2}, promptly S={ (3,3) (3,4) (4,3) (4,4) (4,5) (5,4) (5,5) (5,6) (6,5) (6,6) (6,7) (7,6) (7,7) (7,8) }, totally 14 (m, n) values.

Step 2) each candidate among the pair set S cuts number (m n), calculates the Z value, and flow process as shown in figure 10;

Situation when getting (3,3) with the cutting number is an example,

2.1) areas of dielectric counts M=m * n * L=3 * 3 * 5=45.

2.2) areas of dielectric is numbered by 1 to 45, the medium of the bottom is cut into 9 areas of dielectric, and their numbering is as shown in figure 15.Order is numbered the areas of dielectric of each layer from the bottom up then.Initialization array a[], b[] 45 unit, each location contents zero clearing are all arranged.

2.3), 2.4) be example with the virtual medium zone in the ground floor medium 1, consider its each surface, calculate.

Shown in Figure 16 a and Figure 16 b, this areas of dielectric comprises 7 efficiency frontier surfaces altogether, is respectively:

◆ medium non-porous outer surface (x=0)

As shown in table 1, the ES value of dielectric layer D1 is: ES _x=10, ES _y=9, ES _z=3; The reference number of partitions of this corresponding virtual medium piece is $E_x=\left[\frac{{\mathrm{ES}}_x}{n}\right]=3,$ $E_y=\left[\frac{{\mathrm{ES}}_y}{m}\right]=3,$ E _z=ES _z=3. (also useful) to the several faces in back.

This face is parallel to the yoz plane, boundary element number e _A3=E _y* E _z=9, be first kind boundary element, a[1]=a[1]+e _A3=9.

◆ medium non-porous outer surface (y=0)

This face is parallel to the zox plane, boundary element number e _A3=E _z* E _x=9, be first kind boundary element, a[1]=a[1]+e _A3=18.

◆ medium atresia interface (x=3.67)

This face is parallel to the adjacent layer that yoz plane and this areas of dielectric are taken body place layer as the leading factor, then:

The boundary element number of this face $e_b$ $1_{}=\left[\frac{{\mathrm{<figure-callout\; id="2"\; label="ES\; y"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">ES</figure-callout>}}_y}{2\&CenterDot;m}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{2}\right]=4,$ Be the second class boundary element, b[1]=b[1]+e _B1=4.

◆ medium atresia interface (y=3)

This face is parallel to the zox plane, the boundary element number $e_b$ $1_{}=\left[\frac{{\mathrm{<figure-callout\; id="2"\; label="ES\; y"\; filenames="A0213085000262.png,A0213085000272.png"\; state="\{\{state\}\}">ES</figure-callout>}}_y}{2\&CenterDot;n}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{2}\right]=4,$ Be the second class boundary element, b[1]=b[1]+e _B1=8.

◆ metal substrate surface (z=0)

As shown in table 1, the ES value of metal substrate is: ESx=17, ESy=14;

The boundary element number of this face $e_{a2}=\left[\frac{{\mathrm{ES}}_x}{n}\right]\&CenterDot;\left[\frac{{\mathrm{ES}}_y}{m}\right]=30,$ Be first kind boundary element, a[1]=a[1]+e _A2=48.

◆ conductive surface (bottom surface of m6, z=0.3)

As shown in table 1, the ES value of conductor block m6 is: ES _x=1, ES _y=2, ES _z=3; Calculate again:

$E_x=[{\mathrm{ES}}_x\&CenterDot;\frac{{\mathrm{Length}}_x^{\&prime;}}{{\mathrm{Length}}_x}]=1,$ $E_y=[{\mathrm{ES}}_y\&CenterDot;\frac{{\mathrm{Length}}_y^{\&prime;}}{{\mathrm{Length}}_y}]=2,$ E _z=ES _z=3. Length wherein _x=Length _x'=0.3, Length _y=Length _y'=2.0.

This face is parallel to the xoy plane, boundary element number e _A1=E _x* E _y=2, be first kind boundary element, a[1]=a[1]+e _A1=50.

◆ the porose interface of medium (z=0.3)

With microtomy this face is divided into three first me1 of mother, me2, me3, shown in Figure 16 b, they are general female unit, and division is spaced apart: G _x=EG _x=1.1, G _y=EG _y=1.275, G _z=EG _z=0.5; These female units all are parallel to the xoy plane, and the process of calculating its boundary element number is as follows:

Female first me1:

Female first me2:

Female first me3:

This porose interface has boundary element e _B2=12, be the second class boundary element, b[1]=b[1]+e _B2=20.

At last, the two class boundary element numbers that obtain areas of dielectric 1 are a[1]=50, b[1]=20.

2.5) carry out 2.3 repeatedly) and 2.4), obtain two class boundary element numbers of all 45 areas of dielectric, use array a[], b[] storage, as shown in table 2.

Table 2 array a[], b[] content

????i	1	?2	?3	??4	?5	??6	?7	?8	?9	?10	?11	??12	??13	?14	??15
																??a[i]	50	?63	?51	??39	?38	??39	?48	?39	?48	?51	?120	??56	??9	?32	??9
??b[i]	20	?58	?21	??21	?74	??21	?17	?21	?17	?37	?108	??39	??45	?132	??45
																????i	16	?17	?18	??19	?2a	??21	?22	?23	?24	?25	?26	??27	??28	?29	??30
??a[i]	18	?9	?18	??57	?69	??63	?23	?14	?23	?18	?9	??18	??12	?6	??12
																??b[i]	36	?45	?36	??21	?23	??22	?28	?32	?28	?26	?30	??26	??20	?21	??20
????i	31	?32	?33	??34	?35	??36	?37	?38	?39	?40	?41	??42	??43	?44	??45
																??a[i]	6	?0	?6	??12	?6	??12	?21	?15	?21	?15	?9	??15	??21	?15	??21
??b[i]	21	?22	?21	??20	?21	??20	?11	?12	?11	?12	?13	??12	??11	?12	??11

2.6) calculating corresponding Z value, $Z=\underset{i=1}{\overset{45}{\mathrm{\&Sigma;}}}\left(a\right[i]+b[i\left]\right)\&CenterDot;\left(a\right[i]+2b[i\left]\right),$ The result is 326555, that is: Z (3,3)=326555.

2.7) carry out 2.1 repeatedly)-2.6) step, obtain cutting the set Z (S) that manifold is closed the corresponding non-zero entry number of S with the candidate, the result is as follows:

Z(3，3)＝326555；????Z(3，4)＝259006；????Z(4，3)＝286184；

Z(4，4)＝230010；????Z(4，5)＝270737；????Z(5，4)＝184303；

Z(5，5)＝215074；????Z(5，6)＝208758；????Z(6，5)＝216683；

Z(6，6)＝215788；????Z(6，7)＝180822；????Z(7，6)＝149421；

Z(7，7)＝134335；????Z(8，7)＝126451；

Step 3) is selected optimal cutting number according to the Z value size of respectively cutting the number correspondence in the S set, and flow process as shown in figure 11;

3.1) obtain minimum value Z ₀=126451;

3.2) threshold value Z _g=126451 * 1.25=158063.75;

3.3) initialization Q is infinitely great, value successively from S set judges whether to satisfy condition: Z (m, n)＜Z _gAnd m * n＜Q; What first satisfied condition is (7,6), upgrades Q=42; m _O=7, n _O=6; Other elements all do not satisfy condition among the S, finally obtain optimal cutting number and are (7,6).

Processing after the OSMZ method:

Perpendicular to the xoy coordinate plane, whole model configuration evenly is cut into 7 * 6 virtual medium zones, the conductor that is embedded in the medium also may be cut into plurality of small blocks, generate the data of the body of these new generations of expression, simultaneously, obtain the information that each virtual medium piece comprises the information of conductor and describes each areas of dielectric efficiency frontier surface.

The efficiency frontier surface of each areas of dielectric (virtual medium piece) is divided into the quadrilateral boundary element, obtains 2355 boundary elements at last, the system of linear equations that draws " Ax=f " contains 3500 variablees, has the element of 149421 non-zeros in the matrix A.Use is found the solution system of linear equations " Ax=f " with the GMRES method of pre-condition, convergence after the iteration 17 times.Electric weight (unit is the 10-18 coulomb) is on final each conductor:

Substrate :-415.720237

Conductor m6:-6.069719

Conductor m8:-0.699613

Conductor m9:-0.035718

Conductor m1-1.335993

Conductor m2-68.465130

Conductor m3-12.096716

Conductor m4-0.119530

Conductor m5-202.377256

Conductor m7 (leading body): 718.467608

Just calculate the situation of present embodiment below,, illustrate and use the OSMZ method to carry out the advantage that QMM electric capacity extracts by comparing with the QMM electric capacity extracting method that generates the cutting number with existing experimental formula.Following table has shown the relevant data of two kinds of QMM electric capacity extracting method calculating present embodiments:

The comparison of two kinds of extracting method of table 3

	Experimental formula generates the cutting number	The OSMZ method
			The cutting number rise time (second)	????0	????0.20
The virtual cutting number that obtains	????(3，3)	????(7，6)
			Matrix of coefficients non-zero entry number (Z parameter)	????326555	????149421
Virtual multi-medium capacitor extracts T.T. (second)	????3.28	????2.68
			Total capacitance value (10 -18Farad)	????706.0	????718.5
Total internal memory consumption (megabyte)	????2.38	????4.56

As seen from Table 3, the working time of the method for experimental formula generation cutting number is almost nil, and the OSMZ method needs certain CPU time owing to will calculate the Z value of various situation correspondences, is 0.20 second as this example.But the virtual cutting number that both obtain is different, and the efficient that also causes whole virtual multi-medium capacitor to extract has very big difference.Adopted the OSMZ method, integral capacitor extraction time is 2.68 seconds, than adopting the experimental formula method to shorten 0.6 second (speed improves about 22%).And from result of calculation (total capacitance), both difference illustrate and adopt the OSMZ method to guarantee computational accuracy (difference 5% is the zone of reasonableness of precision usually) in 2%.And be used for from making of internal memory, use the electric capacity extraction of OSMZ method to use more internal memory, but 4.56 million size is still much smaller than a lot of other electric capacity extraction softwares, influence is little in actual applications.

Compare with adopting the experimental formula method, though adopt OSMZ method itself will increase some computing times, the optimal cutting number that is obtained by it makes the raising that whole virtual multi-medium capacitor extracts to be had than computation speed.According to the principle of OSMZ method, it is higher than experimental formula method automaticity in addition, can all produce good calculating effect to various structures widely.

Claims (13)

1. one kind is used for the generation method that virtual multi-medium capacitor extracts optimal cutting number, it is characterized in that the method comprises the following steps of being carried out successively by computing machine:

The multilayered medium interconnection structure of a rectangular shape that 1) will cut out from integrated circuit diagram is as model configuration, and according to the geometric parameter of model configuration, getting m is closed interval [m _Min, m _Max] interior arbitrary integer, n is closed interval [n _Min, n _Max] interior arbitrary integer, all integers that obtain like this are to (m, n) initial value of formation S set; Set and judge the dividing value R whether model configuration xoy cross section length breadth ratio lacks of proper care _L, utilize R _LFurther screen the element in the S set;

Wherein, m: from the xoy cross section of model configuration, it is along the cutting umber of y direction virtual medium piece;

N: from the xoy cross section of model configuration, it is along the cutting umber of x direction virtual medium piece;

2) choose each integer in the S set after the screening to cut number (m as the candidate, n), calculate the value of Z parameter when adopting this cutting number to carry out the virtual multi-medium capacitor extraction respectively, wherein the Z parameter is a non-zero entry number in the coefficient matrices A, finally obtain cutting the set Z (S) that manifold is closed the corresponding non-zero entry number of S with the candidate, its steps in sequence is as follows:

2.1) candidate who takes out is cut number, and (m n), calculates the sum M of its virtual areas of dielectric i that cuts out, M=m * n * L, i=1,2 ... M;

Wherein, upward be the number of the dielectric layer in the model configuration;

2.2) border surface on the areas of dielectric is divided into two classes: the first kind is conductive surface, metal substrate, medium non-porous outer surface and the porose outside surface of medium, and second class is medium atresia interface and the porose interface of medium; To all areas of dielectric, adopt non-homogeneous boundary element division methods to calculate boundary element number on its all border surfaces respectively, using array location a[i] storage medium zone i goes up the boundary element number on all first kind border surfaces, using array location b[i] storage medium zone i goes up the boundary element number on the second all class border surfaces, i=1,2 ..., M;

2.3) according to formula $Z\left(s\right)=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\left(a\right[i]+b[i\left]\right)\&CenterDot;\left(a\right[i]+2b[i\left]\right)$ , the candidate who takes out in calculating and the S set cuts number (m, n) corresponding Z value;

2.4) execution in step 2.1 repeatedly) to 2.3), each candidate in pair set S cuts number and has carried out corresponding processing;

3) determine threshold value Z according to the minimum value of the Z value of respectively cutting the number correspondence in the S set _gIf (m, n) Dui Ying Z value is less than threshold value Z for certain element in the S set _g, and compare with other element in the S set, the m of this element and n product minimum, then this element is optimal cutting number.

2. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that described m _MinRecommendation be 3, m _MaxRecommendation be

, n _MinRecommendation be 3, n _MaxRecommendation be

Wherein, x _LenBe model configuration x direction length, y _LenBe model configuration y direction length, unit is micron; "

Be " on round " symbol, Min{} gets minimum value function.

3. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that the R that utilizes in the described step 1) _LIt is as follows further to screen in the S set method of element:

If x a. _Len/ y _LenGreater than R _L, then keep the element that satisfies " n＞m " in the S set, delete other elements; Otherwise carry out step b;

Wherein, judge the dividing value R whether model configuration xoy cross section length breadth ratio lacks of proper care _LGreater than 1;

If y b. _Len/ x _LenGreater than R _L, then keep the element that satisfies " m＞n " in the S set, delete other elements; Otherwise satisfy the element of " | n-m|＜D " in the reservation S set, delete other elements, wherein, the model configuration of D for not lacking of proper care, the upper limit of the difference of m and n two number values for length breadth ratio.

4. according to claim 1 or the 3 described generation methods that are used for virtual multi-medium capacitor extraction optimal cutting number, it is characterized in that: described R _LRecommendation be 1.4.

5. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 3 is characterized in that: the recommendation of the upper limit D of the difference of described m and n two number values is 2.

6. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that the method for choosing optimal cutting number in the described step 3) is as follows:

At first, ask the minimum value among the set Z (S), be designated as Z ₀

Secondly, with Z ₀Multiply by coefficients R greater than 1 _zObtain a threshold value Z _g, i.e. Z _g=Z ₀* R _z

Once more, initialization Q is infinitely great integer;

At last, the given element among the pair set S (m, n), if its respective value Z (m, n)＜Z _gAnd m * n＜Q, then m _O=m, n _O=n, Q=m * n; (m n) carries out aforesaid operations to elements all among the pair set S, finally obtains the optimal cutting number (m in the S set _O, n _O).

7. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 6 is characterized in that: described coefficients R _zRecommendation be 1.25.

8. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that the number e of the non-homogeneous boundary element division methods of described employing calculating conductor surface coboundary unit _A1Method as follows:

At first, the known reference boundary element that does not carry out the conductor block before the virtual cutting is divided umber be assigned on the corresponding sub-conductor that virtual cutting obtains, obtain sub-conductor block and divide umber E along x, y, the axial actual boundary of z unit by length ratio _x, E _y, E _z: $E_x=[{\mathrm{ES}}_x\&CenterDot;\frac{{\mathrm{Length}}_x^{\&prime;}}{{\mathrm{Length}}_x}],$ $E_y=[{\mathrm{ES}}_y\&CenterDot;\frac{{\mathrm{Length}}_y^{\&prime;}}{{\mathrm{Length}}_y}],$ E _z＝ES _z；

Wherein, " [] " rounds symbol in being, for example, [a] is near the integer of a, if less than 1, then value 1;

ES _x, ES _y, ES _z: when under the front surface do not carry out before the virtual cutting body along x, y, z is axial to divide umber with reference to boundary element, described body can be conductor block according to the difference of analytic target, a kind of in three kinds of bodies of metal substrate or medium, their concrete numerical value is calculated by the model configuration parameter preparation process of preorder;

Because the virtual multi-medium cutting may make an original conductor be cut into the sub-conductor of polylith, so establish:

Length _x', Length _y' represent respectively to carry out sub-conductor block after the virtual cutting along the length of x, y direction under this face;

Length _x, Length _yRepresent the length of the affiliated conductor block of this face respectively along x, y direction;

Then, distinguish the situation of this face, respectively the number e of computation bound unit _A1:

If this face is parallel to xoy plane, e _A1=E _x* E _y

If this face is parallel to yoz plane, e _A1=E _y* E _z

If this face is parallel to zox plane, e _A1=E _z* E _x

9. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that the method for the non-homogeneous boundary element division methods calculating of described employing metal substrate surface coboundary unit number is as follows:

The metal substrate surface is the special conductive surface on a kind of xoy of being parallel to plane, metal substrate before the virtual cutting becomes m * n piece substrate after virtual cutting, each sub-substrate is along x, the axial boundary element of y is divided umber and is divided umber and the decision of cutting number by the reference boundary element of virgin metal substrate, and its coboundary unit number is $e_{a2}=\left[\frac{{\mathrm{ES}}_x}{n}\right]\&CenterDot;\left[\frac{{\mathrm{ES}}_y}{m}\right].$

10. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that the method for the non-homogeneous boundary element division methods of described employing calculation medium non-porous outer surface coboundary unit number is as follows:

At first, along x, y is axial to be evenly distributed on the virtual medium piece with reference to boundary element division umber with known medium, and medium remains unchanged along the axial division umber of z, obtains the virtual medium piece and divides umber E along x, y, the axial actual boundary of z unit _x, E _y, E _z: $E_x=\left[\frac{{\mathrm{ES}}_x}{n}\right],$ $E_y=\left[\frac{{\mathrm{ES}}_y}{m}\right],$ E _z＝ES _z；

Then, distinguish the situation on this nonporous medium surface on the virtual medium piece, respectively the number e of computation bound unit _A3:

If this face is parallel to xoy plane, e _A3=E _x* E _y

If this face is parallel to yoz plane: e _A3=E _y* E _z

If this face is parallel to zox plane: e _A3=E _z* E _x

11. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1, when it is characterized in that adopting the porose outside surface of non-homogeneous boundary element division methods calculation medium coboundary unit number, use microtomy that this perforated surface is divided female unit, calculate boundary element number of each female unit respectively, they and i.e. boundary element number e on the porose for this reason outside surface _A4, its method of calculating female first boundary element number is as follows:

At first, establish when father's former wife unit and be respectively G at interval along the division of x, y, z direction _x, G _y, G _z

When father's former wife unit is main female unit, then G _x=MG _x, G _y=MG _y, G _z=MG _z

Otherwise work as father's former wife unit is general female unit, G _x=EG _x, G _y=EG _y, G _z=EG _z

MG _x, MG _y, MG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of main female unit, the model configuration parameter preparation process by preorder calculates;

EG _x, EG _y, EG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of general female unit, the model configuration parameter preparation process by preorder calculates;

Then, establish Length _Mx, Length _My, Length _MzBe the length of this mother unit, then obtain boundary element division umber E actual in this mother unit divided by working as father's former wife unit at interval along x, y, the axial division of z respectively with them along x, y, z direction _x, E _y, E _z:

At last, distinguish the situation of this mother unit, calculate the boundary element number e of female unit _m:

If this mother unit is parallel to xoy plane, e _m=E _x* E _y

If this mother unit is parallel to yoz plane, e _m=E _y* E _z

If this mother unit is parallel to zox plane, e _m=E _z* E _x

12. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1 is characterized in that the method for the non-homogeneous boundary element division methods of described employing calculation medium atresia interface coboundary unit number is as follows:

At first, along x, y is axial to be evenly distributed on the virtual medium piece with reference to boundary element division umber with known medium, and medium remains unchanged along the axial division umber of z, obtains the virtual medium piece and divides umber E along x, y, the axial actual boundary of z unit _x, E _y, E _z: $E_x=\left[\frac{{\mathrm{ES}}_x}{n}\right],$ $E_y=\left[\frac{{\mathrm{ES}}_y}{m}\right],$ E _z＝ES _z；

Distinguish the situation of this atresia interface then, respectively the number e of computation bound unit _B1Value:

If this face is parallel to xoy plane, e _B1=E _x* E _y

Boundary element for the virtual medium interface on parallel yoz plane or zox plane is divided, and also needs distinguish according to its distance from leading body, and far away more from leading body, its coboundary unit just divides fewly more, and concrete formula is as follows:

If this face is parallel to the yoz plane:

If dielectric layer is taken body place layer, e as the leading factor under this face _B1=E _y* E _z

If dielectric layer is taken the upper and lower adjacent layer of body place layer as the leading factor under this face, $e_{b1}=\left[\frac{{\mathrm{ES}}_y}{2\&CenterDot;m}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{2}\right];$

If dielectric layer is not leading body place layer and adjacent layer thereof under this face, $e_{b1}=\left[\frac{{\mathrm{ES}}_y}{8\&CenterDot;m}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{8}\right];$

If this face is parallel to the zox plane:

If dielectric layer is taken body place layer, e as the leading factor under this face _B1=E _z* E _x

If dielectric layer is taken the upper and lower adjacent layer of body place layer as the leading factor under this face, $e_{b1}=\left[\frac{{\mathrm{ES}}_x}{2\&CenterDot;n}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{2}\right];$

If dielectric layer is not leading body place layer and adjacent layer thereof under this face, $e_{b1}=\left[\frac{{\mathrm{ES}}_x}{8\&CenterDot;n}\right]\&times;\left[\frac{{\mathrm{ES}}_z}{8}\right].$

13. the generation method that is used for virtual multi-medium capacitor extraction optimal cutting number according to claim 1, when it is characterized in that adopting the porose interface of non-homogeneous boundary element division methods calculation medium coboundary unit number, use microtomy that this perforated surface is divided female unit, calculate boundary element number of each female unit respectively, they and i.e. boundary element number e on the porose for this reason interface _B2, its method of calculating female first boundary element number is as follows:

At first, establish when father's former wife unit and be respectively G at interval along the division of x, y, z direction _x, G _y, G _z

When father's former wife unit is main female unit, then G _x=MG _x, G _y=MG _y, G _z=MG _z

Otherwise work as father's former wife unit is general female unit, G _x=EG _x, G _y=EG _y, G _z=EG _z

MG _x, MG _y, MG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of main female unit, the model configuration parameter preparation process by preorder calculates;

EG _x, EG _y, EG _z: be respectively and be used to divide dividing at interval along x, y, the axial boundary element of z of general female unit, the model configuration parameter preparation process by preorder calculates;

Then, establish Length _Mx, Length _My, Legth _MzBe the length of this mother unit, then obtain boundary element division umber E actual in this mother unit divided by working as father's former wife unit at interval along x, y, the axial division of z respectively with them along x, y, z direction _x, E _y, E _z:

At last, distinguish the situation of this mother unit, calculate the boundary element number e of female unit _m:

If this mother unit is parallel to xoy plane, e _m=E _x* E _y

If this mother unit is parallel to yoz plane, e _m=E _y* E _z

If this mother unit is parallel to zox plane, e _m=E _z* E _x

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