CN103793557B - The gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity and system - Google Patents
The gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity and system Download PDFInfo
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Abstract
A kind of gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity and system, for the gauze comprising more than one piece of conductor, realize carrying out the process of random walk sampling on the Gauss surface surrounding this gauze, the method is not really geometrically constructing gauze Gauss surface, but in the intersection of the Gauss surface of composition each conductor block of gauze, carry out stochastical sampling, the effect of direct-on-line net Gauss surface up-sampling is then reached by refusal sampling (rejection sampling).Compared to the method being obtained the envelope of all pieces of Gauss surfaces by geometric operation thus obtain gauze Gauss surface, computing of the present invention is simple, efficiency is high, and adapts to the quick random walk method about subtracted based on variance.Avoiding the envelope being sought all pieces of Gauss surfaces by complicated three-dimensional geometry computing, efficiency is high and is easily achieved.
Description
Technical field
The present invention relates to super large-scale integration (Very Large Scale Integrated
Circuits, VLSI) physical Design with checking field, be towards integrated circuit interconnection electric capacity extract
The gauze Gauss surface method of sampling and system.
Background technology
The design cycle of integrated circuit first has to propose function describe, be then passed through logical design,
Layout design obtains describing semiconductor processing dimensions, the domain of structure, finally carries out layout verification,
I.e. simulated by computer software and verify whether above-mentioned design meets requirement.If meeting requirement, then
Carry out next step the manufacturing.Otherwise, if being unsatisfactory for requirement, then return logical design, domain
Design carries out the correction of necessity.In layout verification, an important link is that " interconnection parasitic is joined
Number extracts ".
Along with the development of ic manufacturing technology, circuit scale constantly increases, characteristic size is continuous
Reducing, current a lot of chips have contained 10,000,000 or even more device.But, in integrated circuit
The ghost effect of interconnection line causes interconnection line that the impact of circuit delay has been exceeded device to prolong circuit
Time impact.Accordingly, it would be desirable to the parameters such as the electric capacity of interconnection line, resistance are calculated accurately,
To ensure the correct effectiveness of breadboardin and checking.In order to improve computational accuracy, between interconnection line
Capacitance extraction need to use three-dimensional extracting method, i.e. utilize three dimensional field solver to ask
Solve.The calculating of solver is the most more, to the optimization of its algorithm with Study on Acceleration meaning very
Greatly.
In the field solver method of IC capacitor parameter extraction, random walk electric capacity extracts to be calculated
Method is a kind of popular method.The method is different from the finite difference calculus of routine, FInite Element
And boundary element method, it is without system of linear equations to be solved, having main steps that in space in calculating
Take point (its process obtaining series of points is referred to as " random walk " visually) at random.Such as Fig. 1
Shown in, each random walk is all from the beginning of on the Gauss surface of conductor, in then with current point being
The cube (referred to as " transfer cube ") that the heart constructs a maximum, do not intersects with conductor, next
Secondary taking a little falls the most randomly in the cubical surface of transfer (S (1) in such as Fig. 1 and S (2)).
This process repeats, until taking position a little at random to reach conductive surface, now terminates once
Random walk.Calculate a certain conductor (the conductor i) in such as Fig. 1 and other all conductors it
Between capacitance, need to carry out random walks the most up to ten thousand time.
Applicant 2013 is at International Periodicals IEEE Transactions on Computer-Aided
Paper " the RWCap:A delivered on Design of Integrated Circuits and Systems
floating random walk solver for3-D capacitance extraction of VLSI
Interconnects " (the 3rd phase) and " Efficient space management techniques for
large-scale interconnect capacitance extraction with floating random
Walks " in (the 10th phase), disclose a kind of quick random walk method about subtracted based on variance
With a kind of space management technology.The former by importance sampling (importance sampling) and
Stratified sampling (stratified sampling) technology changes to be entered at Gauss surface and transfer cube face
Probability distribution needed for row stochastical sampling, thus reduce the side calculating the weights sequence used by capacitance
Difference so that the less several times of the number of times of random walk under identical accuracy requirement, reaches to improve calculating
The purpose of speed.The latter includes according to the geological information (position of conductor block in calculated three dimensional structure
With size) the space management data structure set up, use it can extract at random walk electric capacity
The conductor that in journey, the current walking position of judging distance is nearest rapidly, thus accelerate to shift cubical
Structure and overall calculation speed.
Although existing work can accelerate the calculating speed of random walk electric capacity extraction algorithm, but they
All can only calculate between single separation conductor block (three-dimensional single cuboid) and other conductors
Electric capacity.In actual VLSI interconnection structure, polylith conductor is connected and forms a letter
Number path (commonly referred to as " gauze "), needs to calculate the electric capacity between whole piece gauze and other conductors
(referred to as " net capacitance extraction "), then could analyze delay when signal transmits on this gauze
Time.Fig. 2 shows the three-dimensional interconnection structure considered in IC capacitor extraction problem,
Including single three-dimensional conductor block, also include the gauze that polylith conductor is in turn connected to form.
In order to carry out net capacitance extraction, need first to construct a Gauss surface surrounding gauze, and
Point (i.e. " sampling ") is taken at random on it.But, a gauze in a z-direction may
Spanning multilayer, including dozens of conductor block, how to construct one surround the overall Gauss surface of gauze,
And carry out thereon taking and a little become a difficult problem.
Summary of the invention
In view of the foregoing, it is necessary to a kind of gauze extracted towards integrated circuit interconnection electric capacity is provided
The Gauss surface method of sampling and system, its computing is simple, efficiency is high, and adapts to about subtract based on variance
Quick random walk method, it is to avoid seek all pieces of Gauss surfaces by complicated three-dimensional geometry computing
Envelope, efficiency is high and is easily achieved.
A kind of gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity, is applied to meter
Calculating in device, the method includes: select step one, being uniformly distributed between generating 0～1
Random number R1, according to random number R1And accumulation area vector M selects block Gauss surface Gk, described
Block Gauss surface GkFor conductor block BkGauss surface, described conductor block BkFor described gauze one
Conductor block, described gauze includes NbIndividual conductor block Bi, the three-dimensional body that described gauze is corresponding is institute
State conductor block BiUnion, each conductor block B of AiA corresponding block Gauss surface Gi, wherein
I=1,2 ..., Nb,NbRepresent the quantity of conductor block included by described gauze；Select step
Two, at block Gauss surface GkOn randomly select 1 r by being uniformly distributed；Check step, examine successively
Make an inventory of r and other blocks Gauss surface GiRelation do not fall within adopting on gauze Gauss surface to have abandoned
Sampling point, and obtain ncValue, wherein i=1,2 ..., Nb, i ≠ k, ncIf that represent is r
Point falls on gauze Gauss surface, then r point is simultaneously at ncOn individual block Gauss surface；Generation step one,
Uniform random number R between generating one 0～12；Judge step one, it is judged that R2The biggest
In 1/nc, work as R2More than 1/nc, return and perform to select step one；Generation step two, works as R2No
More than 1/ncTime, the uniform random number R between generating 0～13；Judge step 2,
Judge R3Whether more than p (r)/U, work as R3More than p (r)/U, return and perform to select step one；Obtain
Take step, work as R3Being not more than p (r)/U, obtain on the Gauss surface that a r is described gauze is effective
Sampled point, wherein p (r) is the sampled probability density function on the Gauss surface of described gauze.
A kind of gauze Gauss surface sampling system extracted towards integrated circuit interconnection electric capacity, runs on meter
Calculating in device, this system includes: select module, uniform point between generating 0～1
Cloth random number R1, according to random number R1And accumulation area vector M selects block Gauss surface Gk, institute
State block Gauss surface GkFor conductor block BkGauss surface, described conductor block BkFor described gauze one
Individual conductor block, described gauze includes NbIndividual conductor block Bi, the three-dimensional body that described gauze is corresponding is
Described conductor block BiUnion, each conductor block B of described gauzeiA corresponding block Gauss surface
Gi, wherein i=1,2 ..., Nb,NbRepresent the quantity of conductor block included by described gauze；Institute
State selection module, at block Gauss surface GkOn randomly select 1 r by being uniformly distributed；Check
Module, is used for being examined in a r and other blocks Gauss surface GiRelation do not fall within to have abandoned
Sampled point on gauze Gauss surface, and obtain ncValue, wherein i=1,2 ..., Nb,
I ≠ k, ncIf represent is that r point falls on gauze Gauss surface, then r point is simultaneously at ncIndividual block Gauss
On face；Generation module, the uniform random number R between generating 0～12；Judge
Module, is used for judging R2Whether more than 1/nc, work as R2More than 1/nc, described selection module generates
Uniform random number R between one 0～11；Described generation module, for working as R2It is not more than
1/ncTime, the uniform random number R between generating 0～13；Described judge module, uses
In judging R3Whether more than p (r)/U, work as R3More than p (r)/U, described selection module generates one
Uniform random number R between 0～11；Acquisition module, for working as R3It is not more than p (r)/U,
Obtaining the effective sampling points on the Gauss surface that a r is described gauze, wherein p (r) is described gauze
Sampled probability density function on Gauss surface.
Compared to prior art, the virtual Gauss surface that the present invention extracts towards designated critical net electric capacity
The method of sampling and system, particular for the gauze comprising more than one piece of conductor, it is achieved surrounding this line
The process of random walk sampling is carried out on the Gauss surface (referred to as " gauze Gauss surface ") of net.The method
Really geometrically do not constructing gauze Gauss surface, but in the Gauss of composition each conductor block of gauze
Carry out stochastical sampling in the intersection in face (referred to as " block Gauss surface "), then sampled by refusal
(rejection sampling) reaches the effect of direct-on-line net Gauss surface up-sampling.Compared to logical
Cross geometric operation and obtain the envelope of all pieces of Gauss surfaces thus the method that obtains gauze Gauss surface, this
Invention computing is simple, efficiency is high, and adapts to the quick random walk method about subtracted based on variance.
Avoiding the envelope being sought all pieces of Gauss surfaces by complicated three-dimensional geometry computing, efficiency is high and is prone to
Realize.
Accompanying drawing explanation
Fig. 1 is the two-dimensional representation that random walk electric capacity extracts process.
Fig. 2 is the three-dimensional conductor block and gauze concentrating circuit interconnection capacitance to consider in extracting.
The gauze Gauss surface sampling system that Fig. 3 is the present invention to be extracted towards integrated circuit interconnection electric capacity is relatively
The running environment schematic diagram of good embodiment.
Fig. 4 is the gauze Gauss surface sampling that invention extracts towards integrated circuit interconnection electric capacity
The functional block diagram of system preferred embodiment.
The gauze Gauss surface method of sampling that Fig. 5 is the present invention to be extracted towards integrated circuit interconnection electric capacity is relatively
The flow chart of good embodiment.
Fig. 6 is the side view of a gauze including three pieces of conductors.
Main element symbol description
Following detailed description of the invention will further illustrate the present invention in conjunction with above-mentioned accompanying drawing.
Detailed description of the invention
Refering to shown in Fig. 3, it it is the gauze Gauss surface that extracts towards integrated circuit interconnection electric capacity of the present invention
The running environment schematic diagram of sampling system preferred embodiment.Described carry towards integrated circuit interconnection electric capacity
The gauze Gauss surface sampling system 10 taken runs in calculating device 1.This calculating device 1 also wraps
Include storage device 11 and processing equipment 12.Described storage device 11 stores integrated circuit diagram,
This integrated circuit diagram describes the conductor (including leading body and environment conductor) of integrated circuit in space
Distribution situation.Described processing equipment 12 includes CPU(Central Processing Unit, in
Central processor) and GPU(Graphic Processing Unit, graphic process unit) etc..
Described storage device 11 also stores the Green's function database and weight vector pre-build.Described
Green's function database describes the transfering probability distribution of transport zone during random walk, described weights to
The weights that amount storage walking starting point is corresponding.Described Green's function database can describe Single Medium transfer
The transfering probability distribution in region, is used for extracting IC capacitor parameter under the conditions of Single Medium.Institute
State Green's function database and can also describe the transfering probability distribution of multilayer dielectricity transport zone, be used for extracting
IC capacitor parameter under the conditions of multilayer dielectricity.Green's function database and the method for building up of weight vector
Refer to applicant at the 17th international conference Asia and South Pacific Design
Paper " the Fast Floating Random Walk that Automation Conference2012 delivers
Algorithm for Capacitance Extraction with Numerical Characterization
Of Green's Function " (hereinafter referred to as ASP-DAC2012).Described storage device 11 is also deposited
Store up towards integrated circuit interconnection electric capacity extract gauze Gauss surface sampling system 10 program code and
Data required in running.Described processing equipment 12 performs towards integrated circuit interconnection electric capacity
The program code of the gauze Gauss surface sampling system 10 extracted, main quickly to calculate in integrated circuit
Capacitance parameter between conductor and each environment conductor.
The gauze assuming the present invention is A, and gauze A includes NbIndividual conductor block Bi, (i=1,
2 ..., Nb), three-dimensional body corresponding for A is described conductor block Bi, (i=1,2 ..., Nb)
Union.Assume each conductor block B to Ai, established BiGauss surface Gi(block Gauss
Face) method of row stochastical sampling.Assume considered GiComprise Bi, and GiNot with gauze A with
Other outer conductor intersects.Calculate each G simultaneouslyiArea Si, structure accumulation area vector
M, its i-th component is:I=1,2 ..., Nb, and M [0]=0, it is noted that
Last element M [N of vector Mb] it is all GiArea summation.
The Gauss surface of gauze A carries out random sampling site, r table by sampled probability density function p (r)
Show position a little.And pre-set U certain constant for the maximum not less than function p (r)
Value, then the idiographic flow obtaining a sampled point describes in detail at Fig. 5.
Refering to shown in Fig. 4, it it is the gauze Gauss surface that extracts towards integrated circuit interconnection electric capacity of the present invention
The functional block diagram of sampling system preferred embodiment.The gauze extracted towards integrated circuit interconnection electric capacity
Gauss surface sampling system 10 include select module 100, check module 101, generation module 102,
Judge module 103 and acquisition module 104.Functional module 100-104 will be retouched by Fig. 5 in detail
State.
Refering to shown in Fig. 5, it it is the gauze Gauss surface that extracts towards integrated circuit interconnection electric capacity of the present invention
The flow chart of method of sampling preferred embodiment.
Step S701, selects module 100 to generate the uniform random number between 0～1
R1, according to random number R1And accumulation area vector M selects block Gauss surface Gk。
In the present embodiment, module 100 is selected to press lookup algorithm by R1With accumulation area vector M
Element compare, if R1Meet M [k-1]≤R1·M[Nb] < M [k], then it represents that according to each
The area of block Gauss surface have selected G at randomk。
Step S702, selects module 100 at block Gauss surface GkOn randomly select one by being uniformly distributed
Point r.
Subsequent step S703 to step S710 for check module 101 be examined in a r and other
Block Gauss surface Gi, (i=1,2 ..., Nb, i ≠ k) relation to have abandoned, not fall within gauze high
Sampled point on this face, and obtain ncValue, ncMeaning be: if r point falls high at gauze
On this face, then r point is simultaneously at ncOn individual block Gauss surface.Detailed process is as follows:
Step S703, checks that module 101 arranges ncInitial value and cyclic variable i initial
Value, ncMeaning be: if r point falls on gauze Gauss surface, then r point is simultaneously at ncIndividual block Gauss
On face.In the present embodiment, ncInitial value be 1, the initial value of i is 1.Cyclic variable i is
In order to make inspection module 101 be examined in a r and other blocks Gauss surface Gi, (i=1,2 ...,
Nb, i ≠ k) relation.The corresponding Gauss surface G of the most each cyclic variable ii。
Step S704, checks that module 101 judges that whether the value of i is more than Nb, NbRepresent gauze
The quantity of the conductor block included by A, i.e. Bi, (i=1,2 ..., Nb).When the value of i is more than
NbTime, perform step S711；When the value of i is not more than NbTime, perform step S705.
Step S705, checks that module 101 checks that whether the value of i is equal to k.When the value of i is
During equal to k, performing step S710, the value of i adds one automatically, i.e. i=i+1 is then back to hold
Row step S704, until making NbIndividual block Gauss surface is (except GkThe most tested with the relation of some r outward)
Look into；When the value of i is not equal to k, perform step S706.
Step S706, checks that module 101 judges whether some r fall at GiThe interior volume surrounded.
When a r falls at GiDuring the interior volume surrounded, return and perform step S701；When r does not falls within
GiDuring the interior volume surrounded, perform step S707.
Step S707, checks that module 101 judges that whether some r are at GiSurface.When a r is at Gi
Surface time, perform step S708；When a r is not at GiSurface time, perform step S710,
The value of i adds one automatically, i.e. i=i+1, is then back to perform step S704, until making NbIndividual block
Gauss surface is (except GkThe most examined with the relation of some r outward).
Step S708, checks that module 101 judges G at riOuter normal direction and GkOuter normal direction
Direction is the most identical.As G at riOuter normal direction and GkOuter normal orientation identical time, perform
Step S709；As G at riOuter normal direction and GkOuter normal orientation when differing, return
Perform step S701.
Step S709, checks that module 101 is by ncValue add 1.
Step S710, checks that the value of i is added one by module 101 automatically, i.e. i=i+1.
Step S711, generation module 102 generates the uniform random number between 0～1
R2。
Step S712, it is judged that module 103 judges R2Whether more than 1/nc.Work as R2More than 1/nc
Time, return and perform step S701；Work as R2It is not more than 1/ncTime, perform step S713.
Step S713, generation module 102 generates the uniform random number between 0～1
R3。
Step S714, it is judged that module 103 judges R3Whether more than p (r)/U.Work as R3It is more than
During p (r)/U, return and perform step S701；Work as R3When being not more than p (r)/U, perform step
S715。
Step S715, acquisition module 104 obtains effectively adopting on the Gauss surface that a r is gauze A
Sampling point, this flow process terminates.
A random number R is created in above-mentioned steps S7011, it is noted that often perform once
Step S701, all can produce a different random number R1.In step step S711 and step
It S713 is also similar situation.
Above-mentioned steps S703～S710 have abandoned the sampled point not fallen within gauze Gauss surface, step
The point fallen on gauze Gauss surface is then done further by rapid S711～S714 according to stochastical sampling rule
Screening.Illustrate that these abandon and screening rule by a two-dimensional representation below.As Fig. 6 shows
The side view of one gauze containing 3 pieces of conductors, and the block Gauss surface of each of which is depicted with dotted line
G1, G2, G3, some P on block Gauss surface1, P2, P3All fall on gauze Gauss surface, and point
P4, P5Not fall on gauze Gauss surface, wherein P4At G3(by step in the space surrounded
Rapid S706 judges), and P5Simultaneously at G1And G3Surface, but G1And G3At P5Point
The outer normal orientation at place contrary (walked by step S707 and step S708 and judge), therefore
P4, P5The most not on gauze Gauss surface.For P1, P2, P3For, P3At G1And G2's
Surface, the n of its correspondencec=2, understand should accept P by the probability of 50% by step S7123,
P1, P2Only on a block Gauss surface, therefore by step S712 understand can by 100% general
Rate accepts P1, P2.Next the most uniformly adopt in view of Gauss surface sampling to be carried out
Sample, the most also needs to pass through step S714 to P according to sampled probability density function p (r)1, P2And P3
Point is further screened, and the sampled point finally given just can be made to meet probability on gauze Gauss surface
Density Distribution p (r).
The present invention uses C language programming realization.On the work station using (SuSE) Linux OS
Run.Utilize the present invention " the gauze Gauss surface sampling side extracted towards integrated circuit interconnection electric capacity
Method " to carry out the algorithm of net capacitance extraction based on random walk method as follows:
The input of algorithm of net capacitance extraction is carried out for describing integrated circuit based on random walk method
The conductor geometry of middle gauze, need to extract gauze numbering j of electric capacity, and random walk algorithm terminates
Condition.Be output as gauze j and other conductor block (or gauze) i couples electric capacity Cji,
Algorithm 1 net capacitance based on random walk method extracts flow process and comprises the steps:
1: be loaded into the Green's function database needed for random walk and weight vector；
2: generate space management data according to conductor distribution situation, in order to the transfer in step 9
Cube physical ability constructs rapidly；
3: each conductor block of gauze j is constructed its block Gauss surface；
4: electric capacity initial value is set:Random walk number of times initial value npath:=0 is set;
5: repeat the 6th step to the 13rd step;
6:npath:=npath+1;
7: on the Gauss surface of gauze j, take a r at random(0), with r(0)Centered by generate transfer cube
Body, then takes a little according to the probability distribution represented by Green's function database at random at this cube face
r(1), with the help of the weight vector being loaded into, calculate r(1)Corresponding weights ω；
8:While random point r(1)Not at conductive surface do
9: with r(1)Centered by structure is maximum, the transfer cube that do not intersects with conductor；
10: on transfer cube, take one according to the probability distribution represented by Green's function database at random
Point, is assigned to r by this random point(1)；
11:End
12: if r(1)On the surface of conductor i, then Cji:=Cji+ω；
13: until meeting end condition
14:Cji:=Cji/npath,
1st step of above-mentioned algorithm 1, Green's function database can describe turning of Single Medium transport zone
Move probability distribution, be used for extracting IC capacitor parameter under the conditions of Single Medium, it is also possible to describe
The transfering probability distribution of multilayer dielectricity transport zone, is used for extracting integrated circuit under the conditions of multilayer dielectricity
Capacitance parameter.The method for building up of Green's function database and weight vector refers to inventor 2013 and exists
International Periodicals IEEE Transactions on Computer-Aided Design of Integrated
Paper " the RWCap:A floating random walk delivered on Circuits and Systems
solver for3-D capacitance extraction of VLSI interconnects”。
2nd step of algorithm 1, specific practice refers to inventor 2013 at International Periodicals IEEE
Transactions on Computer-Aided Design of Integrated Circuits and
Paper " the Efficient space management techniques for delivered on Systems
large-scale interconnect capacitance extraction with floating random
Walks ", and the application for a patent for invention 201310388975.1 submitted to.
3rd step of algorithm 1 is an innovative point of the present invention, the most not to gauze entirety actual configuration
Gauss surface, the most not actual configuration gauze Gauss surface.
7th step of algorithm 1 comprises the emphasis of the present invention, and it is " random on the Gauss surface of gauze j
Take a r(0)" it is the gauze Gauss surface sampling using the present invention to extract towards integrated circuit interconnection electric capacity
Method (i.e. step S701 to S715) obtains the method for gauze Gauss surface up-sampling point.
Other steps of algorithm 1 are all prior aries, with the electric capacity extraction algorithm carrying out single conductor
Equally, details can be found in inventor 2013 at International Periodicals IEEE Transactions on
The opinion delivered on Computer-Aided Design of Integrated Circuits and Systems
Literary composition " RWCap:A floating random walk solver for3-D capacitance
extraction of VLSI interconnects”。
The virtual Gauss surface method of sampling that the present invention extracts towards designated critical net electric capacity and system,
Particular for the gauze comprising more than one piece of conductor, it is achieved surrounding the Gauss surface of this gauze (referred to as
" gauze Gauss surface ") on carry out the process of random walk sampling.The method is not real geometrically
Structure gauze Gauss surface, but in Gauss surface (referred to as " the block Gauss of composition each conductor block of gauze
Face ") intersection on carry out stochastical sampling, then by refusal sampling (rejection
Sampling) effect of direct-on-line net Gauss surface up-sampling is reached.Compared to passing through geometric operation
The method obtaining the envelope of all pieces of Gauss surfaces thus obtain gauze Gauss surface, this method computing letter
Single, efficiency height, and adapt to the quick random walk method about subtracted based on variance.Avoid and pass through
The envelope of all pieces of Gauss surfaces is sought in complicated three-dimensional geometry computing, and efficiency is high and is easily achieved.
Claims (8)
1. the gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity, is applied to calculate in device, it is characterised in that the method includes:
Select step one, the uniform random number R between generating 0～11, according to random number R1And accumulation area vector M selects block Gauss surface Gk, described piece of Gauss surface GkFor conductor block BkGauss surface, described conductor block BkFor a conductor block of gauze, described gauze includes NbIndividual conductor block Bi, the three-dimensional body that described gauze is corresponding is described conductor block BiUnion, each conductor block B of described gauzeiA corresponding block Gauss surface Gi, wherein i=1,2 ..., Nb,NbRepresent the quantity of conductor block included by described gauze；
Select step 2, at block Gauss surface GkOn randomly select 1 r by being uniformly distributed；
Check step, be examined in a r and other blocks Gauss surface GiRelation to have abandoned the sampled point not fallen within gauze Gauss surface, and obtain ncValue, wherein i=1,2 ..., Nb, i ≠ k, ncIf represent is that r point falls on gauze Gauss surface, then r point is simultaneously at ncOn individual block Gauss surface；
Generation step one, the uniform random number R between generating 0～12；
Judge step one, it is judged that R2Whether more than 1/nc, work as R2More than 1/nc, return and perform to select step one；
Generation step two, works as R2It is not more than 1/ncTime, the uniform random number R between generating 0～13；
Judge step 2, it is judged that R3Whether being more than p (r)/U, described U is the constant value pre-set, and works as R3More than p (r)/U, return and perform to select step one；
Obtaining step, works as R3Being not more than p (r)/U, obtain the effective sampling points on the Gauss surface that a r is described gauze, wherein p (r) is the sampled probability density function on the Gauss surface of described gauze.
2. the gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity as claimed in claim 1, it is characterised in that GiComprise Bi, and GiDo not intersect with other conductor beyond described gauze, calculate each GiArea Si, structure accumulation area vector M, its i-th component is:M [0]=0, last element M [N of vector Mb] it is all GiArea summation.
3. the gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity as claimed in claim 1, it is characterised in that described inspection step includes:
A () arranges ncInitial value and the initial value of cyclic variable i；
B () judges that whether the value of i is more than Nb, when the value of i is more than NbTime, perform described generation step one；
C () is not more than N when the value of ibTime, check that the value of i, whether equal to k, when the value of i is equal to k, performs (h)；
D () is when the value of i is not equal to k, it is judged that whether some r falls at GiThe interior volume surrounded, when a r falls at GiDuring the interior volume surrounded, return and perform described selection step one；
E () does not falls within G as riDuring the interior volume surrounded, it is judged that whether some r is at GiSurface, when a r is not at GiSurface time, perform (h)；
F () is when a r is at GiSurface time, it is judged that G at riOuter normal direction and GkOuter normal orientation the most identical, as G at riOuter normal direction and GkOuter normal orientation when differing, return and perform described selection step one；
G () is as G at riOuter normal direction and GkOuter normal orientation identical time, by ncValue add 1；
H the value of i is added one by () automatically, i.e. i=i+1.
4. the gauze Gauss surface method of sampling extracted towards integrated circuit interconnection electric capacity as claimed in claim 1, it is characterised in that described U is not less than the maximum of function p (r).
5. the gauze Gauss surface sampling system extracted towards integrated circuit interconnection electric capacity, runs in calculating device, it is characterised in that this system includes:
Select module, the uniform random number R between generating 0～11, according to random number R1And accumulation area vector M selects block Gauss surface Gk, described piece of Gauss surface GkFor conductor block BkGauss surface, described conductor block BkFor a conductor block of described gauze, described gauze includes NbIndividual conductor block Bi, the three-dimensional body that described gauze is corresponding is described conductor block BiUnion, each conductor block B of described gauzeiA corresponding block Gauss surface Gi, wherein i=1,2 ..., Nb,NbRepresent the quantity of conductor block included by described gauze；
Described selection module, at block Gauss surface GkOn randomly select 1 r by being uniformly distributed；
Check module, be used for being examined in a r and other blocks Gauss surface GiRelation to have abandoned the sampled point not fallen within gauze Gauss surface, and obtain ncValue, wherein i=1,2 ..., Nb, i ≠ k, ncIf represent is that r point falls on gauze Gauss surface, then r point is simultaneously at ncOn individual block Gauss surface；
Generation module, the uniform random number R between generating 0～12；
Judge module, is used for judging R2Whether more than 1/nc, work as R2More than 1/nc, described selection module generates the uniform random number R between 0～11；
Described generation module, for working as R2It is not more than 1/ncTime, the uniform random number R between generating 0～13；
Described judge module, is used for judging R3Whether being more than p (r)/U, described U is the constant value pre-set, and works as R3More than p (r)/U, the uniform random number R between described selection module generation one 0～11；
Acquisition module, for working as R3Being not more than p (r)/U, obtain the effective sampling points on the Gauss surface that a r is described gauze, wherein p (r) is the sampled probability density function on the Gauss surface of described gauze.
6. the gauze Gauss surface sampling system extracted towards integrated circuit interconnection electric capacity as claimed in claim 5, it is characterised in that GiComprise Bi, and GiDo not intersect with other conductor beyond described gauze, calculate each GiArea Si, structure accumulation area vector M, its i-th component is:M [0]=0, last element M [N of vector Mb] it is all GiArea summation.
7. the gauze Gauss surface sampling system extracted towards integrated circuit interconnection electric capacity as claimed in claim 5, it is characterised in that described inspection module specifically for:
A () arranges ncInitial value and the initial value of cyclic variable i；
B () judges that whether the value of i is more than Nb, when the value of i is more than NbTime, perform described generation module, the uniform random number R between generating 0～12；
C () is not more than N when the value of ibTime, check that the value of i, whether equal to k, when the value of i is equal to k, performs (h)；
D () is when the value of i is not equal to k, it is judged that whether some r falls at GiThe interior volume surrounded, when a r falls at GiDuring the interior volume surrounded, perform described selection module, the uniform random number R between generating 0～11；
E () does not falls within G as riDuring the interior volume surrounded, it is judged that whether some r is at GiSurface, when a r is not at GiSurface time, perform (h)；
F () is when a r is at GiSurface time, it is judged that G at riOuter normal direction and GkOuter normal orientation the most identical, as G at riOuter normal direction and GkOuter normal orientation when differing, perform described selection module, the uniform random number R between generating 0～11；
G () is as G at riOuter normal direction and GkOuter normal orientation identical time, by ncValue add 1；
H the value of i is added one by () automatically, i.e. i=i+1.
8. the gauze Gauss surface sampling system extracted towards integrated circuit interconnection electric capacity as claimed in claim 5, it is characterised in that described U is not less than the maximum of function p (r).
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| CN105095567B (en) * | 2015-07-01 | 2018-02-16 | 清华大学 | Capacitance extraction method |
| CN105335567B (en) * | 2015-11-05 | 2018-08-03 | 清华大学 | Adapt to the random walk Capacitance extraction method and system of non-Manhattan body |
| CN106844798A (en) * | 2015-12-03 | 2017-06-13 | 北京华大九天软件有限公司 | A kind of full panel domain electric capacity rapid extracting method based on array |
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| CN114662445B (en) * | 2022-05-25 | 2022-09-06 | 杭州行芯科技有限公司 | Random walking method and device for parasitic capacitance extraction and electronic device |
| CN116842895B (en) * | 2023-08-31 | 2023-11-21 | 青岛展诚科技有限公司 | Fine granularity parallel processing method for randomly walking in capacitor extraction |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102651047A (en) * | 2012-04-11 | 2012-08-29 | 清华大学 | Method for extracting and calculating capacitance parameter based on random walk in integrated circuit design |
| CN103198177A (en) * | 2013-03-11 | 2013-07-10 | 清华大学 | GPU-based system and method for extracting capacitance parameter of integrated circuit |
| CN103473402A (en) * | 2013-08-30 | 2013-12-25 | 清华大学 | Space management data generation method oriented to integrated circuit interconnection capacitance parameter extraction |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8122419B2 (en) * | 2008-11-09 | 2012-02-21 | International Business Machines Corporation | System and method for three-dimensional variational capacitance calculation |
| US20100122223A1 (en) * | 2008-11-09 | 2010-05-13 | International Business Machines Corporation | Techniques for Computing Capacitances in a Medium With Three-Dimensional Conformal Dielectrics |
-
2014
- 2014-01-14 CN CN201410016439.3A patent/CN103793557B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102651047A (en) * | 2012-04-11 | 2012-08-29 | 清华大学 | Method for extracting and calculating capacitance parameter based on random walk in integrated circuit design |
| CN103198177A (en) * | 2013-03-11 | 2013-07-10 | 清华大学 | GPU-based system and method for extracting capacitance parameter of integrated circuit |
| CN103473402A (en) * | 2013-08-30 | 2013-12-25 | 清华大学 | Space management data generation method oriented to integrated circuit interconnection capacitance parameter extraction |
Non-Patent Citations (3)
| Title |
|---|
| 《A hierarchical floating random walk algorithm for fabric-aware 3D capacitance extraction》;El-Moselhy T. A et al;《Proceedings of the 2009 International Conference on Computer-Aided Design. ACM》;20091102;全文 * |
| 《Accelerated floating random walk algorithm for the electrostatic computation with 3-D rectilinear-shaped conductors》;Yu W et al;《Simulation Modelling Practice and Theory》;20130530;第34卷;全文 * |
| 《RWCap: A Floating Random Walk Solver for 3-D Capacitance Extraction of Very-Large-Scale Integration Interconnects》;W. Yu et al;《IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems》;20130331;第32卷(第3期);全文 * |
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