Method and system for design and modeling of transmission lines

A method and system for design and modeling of transmission lines are provided. The method includes providing a set of models of core structures (211) of transmission line cells and expanding each of the models of core structures (211) to include different neighboring elements. The parameter characteristics of the expanded core structures (214a-214c) are compared to determine a model having a minimal sufficiently closed neighborhood environment. A closed neighborhood environment complies with design rules to ensure desired transmission line behaviour in a real design environment. A model having a closed neighborhood environment can be used as a stand-alone model of the core structure describing the transmission line behaviour in the actual design environment.

FIELD OF THE INVENTION

This invention relates to the field of design and modeling of transmission lines. In particular, the invention relates to on-chip transmission line design and modeling in dense VLSI design environment.

BACKGROUND OF THE INVENTION

In multi-GHz chip design domains, interconnects are becoming the limiting factor in the performance, energy dissipation, and signal integrity. The demanding requirements from on-chip wiring pose a serious problem, both from the design and the modeling aspects.

Previous solutions for considering on-chip interconnects have focused on analysis of given designs. These include RC(L) extraction methods and analysis tools based on field solvers.

The attempts to develop post-layout RCL extraction methods usually fail to correctly determine the wire inductances, due to the inability to determine the correct current return paths. In addition, existing RC(L) extraction tools do not take into account several physical effects, such as substrate effects, which are expected to have a significant impact on the design performance.

The field solver based analysis tools require the user to define the relevant solution domain including the interconnect to be analyzed, as well as the boundary conditions, for which a deep electromagnetic understanding is needed. As a result, the solution domain can be either redundant or insufficient, or both, which leads to errors that are almost impossible to track.

SUMMARY OF THE INVENTION

It is an aim of the present invention to design on-chip transmission lines (T-lines) so that they ensure the desired T-line performance in an actual VLSI design neighborhood. It is a further aim to define a closed environment of a T-line to be considered in its model so that the model becomes self-contained.

According to a first aspect of the present invention there is provided a method for design and modeling of transmission lines, comprising: providing a set of models of core structures of transmission line cells; expanding each of the models of core structures to include different neighboring elements; comparing the parameter characteristics of the expanded core structures to determine a model having a minimal sufficiently closed neighborhood environment.

The method may include selecting the model having the minimal sufficiently closed neighborhood environment to model a transmission line. A closed neighborhood environment may comply with design rules to ensure desired transmission line behaviour in a real design environment.

A model having a closed neighborhood environment may be a stand-alone model of the core structure describing the transmission line behaviour in the actual design environment.

The parameter characteristics may be one of: time domain characteristics, frequency domain characteristics, or equivalent transmission line characteristics.

The method may include carrying out small circuit simulations using the expanded core structures.

The models of transmission line core structures may be single or coupled transmission lines with dedicated shields serving as current return paths. Each model of a transmission line core structure may be modeled for a set of parameters with optimized geometry to minimize sensitivity to the design neighborhood of the transmission line.

Comparing the parameter characteristics may be carried out by computing parameters by an electromagnetic solver.

The transmission lines may be in dense VLSI design environments.

The neighborhood elements may include crossover and crossunder lines above and below a signal wire, parallel lines exactly above and/or below a signal wire, the silicon substrate, and parallel coplanar lines outside the core structure (coplanar neighbors).

According to a second aspect of the present invention there is provided a method for design and modeling of transmission lines, comprising: identifying a critical path; formulating design requirements for the critical path; choosing a transmission line core structure from a set of models of core structures; identifying the neighboring elements of the transmission line; and choosing the transmission line geometry parameters based on the design requirements and on simulations using expanded core structure models.

The design requirements may be electrical and geometrical requirements.

The expanded core structure models may include different neighboring elements and the parameter characteristics of the expanded core structures may be compared to determine a model having a minimal sufficiently closed neighborhood environment.

According to a third aspect of the present invention there is provided a system for design and modeling of transmission lines, comprising: means for providing a set of models of core structures of transmission line cells; means for selecting a model of a core structure; means for providing a set of expanded models for each of the models of core structures, the expanded models including different neighboring elements of the core structure; and means for comparing the parameter characteristics of the expanded core structures to determine a model having a minimal sufficiently closed neighborhood environment.

The system may include means for carrying out small circuit simulations using the expanded core structures. The system may include an electromagnetic solver for computing and comparing the parameter characteristics.

According to a fourth aspect of the present invention there is provided a computer program product stored on a computer readable storage medium for design and modeling of transmission lines, comprising computer readable program code means for performing the steps of: providing a set of models of core structures of transmission line cells; expanding each of the models of core structures to include different neighboring elements; comparing the parameter characteristics of the expanded core structures to determine a model having a minimal sufficiently closed neighborhood environment.

According to a fifth aspect of the present invention there is provided a computer program product stored on a computer readable storage medium for design and modeling of transmission lines, comprising computer readable program code means for performing the steps of: identifying a critical path; formulating design requirements for the critical path; choosing a transmission line core structure from a set of models of core structures; identifying the neighboring elements of the transmission line; and choosing the transmission line geometry parameters based on the design requirements and on simulations using expanded core structure models.

The suggested solution is based on a suggested concept of “closed design environment”. The “closed environment” of a given interconnect structure is defined as a design fragment including the structure itself (“core structure”) and some other design elements which affect its behavior (“closed neighborhood”), such that the whole fragment can be accurately represented by a self-contained model of the core structure in the actual design environment.

The T-line “closed environment” concept has two interdependent aspects: proper design and proper modeling.

Proper design refers to compliance with certain design rules which ensure the desired T-line behavior in a real design environment. These rules may specify ranges of wires widths and spacings, require excluding parallel wires right above or below the signal line, etc.

Proper modeling refers to the ability of stand-alone models to describe the properly designed T-lines behavior in a real design environment.

DETAILED DESCRIPTION OF THE INVENTION

Interconnect-aware design and modeling methodology provides a comprehensive solution for on-chip wiring design and modeling. Further information is provided in references: Goren, D. et al., “An Interconnect-Aware Methodology for Analog and Mixed Signal Design, Based on High Bandwidth (Over 40 GHz) On-chip Transmission Line Approach” IEEE DATE'02 Conference, Paris March 2002, pp. 804-811 and Goren, D. et al., “On-chip Interconnect-Aware Design and Modeling Methodology, Based on High Bandwidth Transmission Line Devices”, IEEE DAC'03 Conference, CA, June 2003, pp. 724-727.

The basis of this methodology is that the wires in which transmission line effects are pronounced (“critical wires”) are identified already at the pre-layout design stages. The critical wires are then designed differently, using a unique set of transmission line devices, called “on-chip T-lines”, which contain their own dedicated shields serving as the current return paths. For these T-lines, semi-analytical models have been developed which predict their full frequency dependent behavior from DC up to the cut-off frequency of the transistors in the given technology. For non-critical wires, which usually go through multiple changes during the design process, post-layout RC extraction is used.

A central point of the described design and modeling methodology is the concept of “closed environment”. The “closed environment” of a given interconnect structure is defined as a design fragment including the structure itself (“core structure”) and some other design elements which affect its behavior (“closed neighborhood”), such that the whole fragment can be accurately represented by a stand-alone, independent model of the core structure in the actual design environment.

The T-line “closed environment” concept has two interdependent aspects: proper design and proper modeling. Proper design refers to compliance with certain design rules which ensure the desired T-line behavior in a real design environment (these rules may specify ranges of wires widths and spacings, require excluding parallel wires right above or below the signal line, etc.). Proper modeling refers to the ability of stand-alone models to describe the properly designed T-lines behavior in a real design environment.

The behavior of coplanar T-lines in dense VLSI Manhattan designs is strongly affected by their neighbor wires and/or by the silicon substrate, so that in this case, a coplanar on-chip T-line closed environment is never confined to its core structure. The described methodology finds practical criteria for a minimal “sufficiently closed” environment of the coplanar on-chip T-lines in dense VLSI design environments.

FIGS. 1A and 1Bshow the coplanar single110and coupled120T-lines core structures, surrounded by neighborhoods typical for the VLSI Manhattan design.

The coplanar single T-lines core structure110has a single signal line111and two side shield lines114,115. The width of the signal111and side shield lines114,115is defined as “w” and the spacing between the signal line111and a side shield line112,113is defined as “s”.

The coplanar coupled T-lines core structure120has two signal lines S1121, S2122and side shield lines124,125. The width of the signal lines121,122and side shield lines124,125is defined as “w” and the spacing between a signal line121,122and a side shield line124,125is defined as “s”. The spacing between the two signal lines121,122is defined as “d”.

For both the coplanar single and coupled T-line core structures110,120, a T-line neighborhood may include parallel wires in the T-line layer (X1, X2)101,102, crossing (orthogonal) wires right above and below (crossover, crossunder)103,104, parallel wires above and below the orthogonal wires (Y1, Y2)105,106, and the silicon substrate107. Xi, Yi may stand for multiple wires. In a Manhattan environment, a T-line core structure is located either above an adjacent crossunder, or right above the silicon substrate.

In order to define the closed environment of a given T-line, the models of different structures, built by combining the T-line core structure with different groups of elements from its neighborhood, need to be compared. The comparison between the models can be performed using various criteria: time domain characteristics (delay, rise time, signal integrity parameters) and frequency domain characteristics (S-parameters, equivalent transmission line characteristics γ-Z0, equivalent frequency dependent circuit parameters RLCG).

In VLSI design analysis, time domain characterization is the common practice. However, time domain parameters describe the behavior of the critical wiring as a part of specific drivers/receivers setup rather than a stand-alone entity. Frequency domain characteristics allow for a compact and complete representation of the wire characteristics in a given bandwidth. This is why these characteristics are used both by EM solvers and by all broadband measurement equipment.

The described method of design and modeling includes the step of analyzing the frequency dependent circuit parameters of different structures including the same coplanar T-line core structure. This analysis is necessary for obtaining proper T-line design rules and for building their correct models. Then, different structures including the same T-line core structure, are compared using their frequency domain characteristics computed by an EM solver, in order to verify that the suggested T-line environments are sufficiently closed.

T-line structures used to design critical wiring are “long” in a sense that they are featured by a small ratio of their cross-section characteristic dimension to wire length (usually less than 2%). Therefore, both the theoretical and the numerical analysis are performed using the 2D approach.

FIG. 2Ais a flow diagram200of a method of design and modeling. The method includes defining201a T-line parametric cell (Pcell) in which parameters of the cell are defined. For each T-line Pcell, the geometry is optimized202to minimize the sensitivity of the cell to the design environment. For example, as shown further below, for a single coplanar T-line Pcell, the geometry is set so wsignal≦wshield≦2*wsignal. For each T-line Pcell, the broadband model of the core structure is expanded203by including consideration of the closed environment.

FIG. 2Billustrates the method ofFIG. 2Aschematically. A parametric core structure model211for each T-line is defined as an electric circuit having fixed topology (which may differ from T-line to T-line) whose RLC parameters are defined as functions of geometrical parameters of the core structure and technology parameters. The core structure model211is optimized geometrically to provide a geometrically optimized T-line Pcell model213. The geometrically optimized T-line Pcell model213is expanded to include multiple different neighborhoods which provide a closed environment. For each neighborhood, this results in a model214a,214b,214cof the closed environment for the original core structure211, which has the same circuit topology as the original core structure, but differs by functions defining RLC parameters, expanded to include the impact of the respective neighborhood. The diagram shows three models214a,214b,214c, however this is for illustration purposes only and a set may contain any number of models.

Closed Environment Conditions

The conditions which ensure that a given T-line structure can be represented by a stand-alone model are considered, these are referred to as the closed environment conditions. In order to better understand the physics behind the close environment conditions, they are expressed in terms of frequency dependent circuit parameters R(f), C(f), G(f), L(f).

R(f): The computational model of a stand-alone T-line structure yields the DC resistance, RDC, as the sum of the signal wire resistance Rsignaland resistance of the shields Rshield. However, in the actual VLSI design environment, the DC current return path of the T-line structure is not confined to its shields, e.g. it includes the power grid, so that the resistance of the actual DC current return path is negligible relative to Rsignal. Therefore, in an actual design environment, RDCof a T-line structure is equal to Rsignal, and a stand-alone T-line model should be modified by setting RDC=Rsignal.

The theoretical and numeric study of wideband behavior of coplanar T-lines above the lossy substrate given in Goren, D. et al., “Modeling Methodology of On-Chip Coplanar Transmission Lines over the Lossy Silicon Substrate”, SPI'03, Siena, May 2003, supported by comprehensive measurements on a specially designed test site, has shown that the return current in the silicon substrate is small for practical silicon resistivities up to 100 GHz. Hence, the presence of the substrate right below the T-lines does not influence their resistance in the whole bandwidth of interest.

The frequency dependence of the T-line resistance is caused by the skin-effect, so this dependence starts at skin-effect initial frequency fi. First consider the case when there are no parallel wires exactly above and/or below the signal wire. Then, due to the proximity effect, the dedicated T-line shields become the preferred current return path at frequency fretwhich is lower than the skin-effect initial frequency (fret<fi). Hence, in the absence of parallel wires exactly above and/or below the signal wire, the stand-alone model of the T-line frequency dependent resistance developed for its core structure will be correct also in the actual design environment. If there are parallel wires exactly above and/or below the signal wire, they become a part of the preferred current return path, which may affect the frequency dependent resistance.

C(f) and G(f): In a dense VLSI Manhattan design, a T-line neighborhood includes either two adjacent crossings above and below, or an adjacent crossover and the silicon substrate right below. In such a neighborhood, the capacitance of a T-line structure significantly differs from the capacitance of its core structure.

In the presence of silicon substrate right below the T-lines, due to the substrate losses, their conductance G may becomes considerable, and both capacitance and conductance vary significantly over the bandwidth of interest. The impact of the parallel wires (X1, X2, Y1ofFIGS. 1A and 1B) on the T-lines capacitance is insignificant. Therefore, in this case, a stand-alone model of the T-line capacitance should take into account the adjacent crossover, as well as the lossy substrate.

In the presence of a dense crossunder, the silicon substrate influence on the T-line capacitance and conductance can be neglected. In this case, the capacitance is frequency independent, and the conductance is negligible. The impact of the parallel wires (X1, X2, Y1, Y2ofFIGS. 1A and 1B) is still insignificant, so the crossings are the main factor which affects the T-lines capacitance. Therefore, a stand-alone model of the T-line capacitance should take into account both adjacent crossings.

L(f): The fact that the return current in the silicon substrate is small, also implies that the presence of the silicon substrate does not influence the T-lines inductance. Therefore, a stand-alone model of the T-line inductance does not need to consider the silicon substrate.

The wires which can affect the T-line inductance include the coplanar neighbors (X1, X2) and parallel wires (Y1, Y2). The frequency at which the inductance effects become significant is denoted by find. If at frequency findmost of the return current flows through the T-line dedicated return path (i.e. fretis close to find), then the presence of parallel wires does not affect the T-line inductance. The extent this happens in practice has been considered.

Since fret<fi, the ratio fret/findis bounded from above by fi/find. The expression for findcan be obtained based on the trise:
2√(L∞C)=trise=1/(2find),
which gives
1/find=4√(L∞C).
The skin-effect initial frequency fican be estimated as
fi=(1/2π)RDC/(L0−L∞), hence,
fi/find=(2/π)(RDC/√(L∞/C))/(L0/L∞−1).

The inductance effects are negligible if RDC>2√(L∞/C). Since the inductance impact is studied, the case of interest is RDC≦2√(L∞/C), for which
fret/find<fi/find<(4/π)/(L0/L∞−1).

The last estimation helps to understand when fretand findcan be considered as close to each other in terms of the impact on inductance. The skin depth is proportional to √f, and the effective distance from the signal line to the return current (proximity effect) changes even slower than this. The inductance is a logarithmic function of this effective distance. In case of the T-line core structures with w=wshield(as shown inFIGS. 1A and 1B), this gives L0/L28>√2, so fret/find<3. The ratio of the corresponding skin depth values is <3, and the effective distance varies by less than that. Such a change in the effective distance results in a very small variation of the inductance. Moreover, the sensitivity of the signal waveforms to the exact value of the inductance is low. Therefore, in this case, a stand-alone model of the T-line inductance does not need to consider parallel wires (X1, X2, Y1, Y2inFIGS. 1A and 1B).

The geometry of the coplanar T-lines core structures is indicated inFIGS. 1A and 1B. A designer can choose the metal layer (which defines the surrounding dielectric structure and the wires thickness t), the distances between the wires (d and s), and the wires width w.

The shield width wshieldis normally set equal to w. There are several reasons for keeping the same signal and shield width. First, as seen in the previous section, at frequencies where inductance effects and/or skin-effect are significant, such dedicated shields practically turn into the preferred current return path. Second, in the range w≦wshield≦2w, the low frequency inductance is close to its minimum and virtually insensitive to the shield width variation.

FIGS. 3A and 3Bshow the impact of shields on the single T-line low frequency inductance.FIG. 3Ashows the impact of dedicated shields on the core structure inductance (no coplanar neighbors), L0*=L0(wshield=w=s), andFIG. 3Bshows the impact of coplanar neighbors X1-2, L0core-inductance of the core structure with wshield=w=s=2 um. The graphs show that in the range w≦wshield≦2w, the low frequency inductance is close to its minimum and virtually insensitive to the shield width variation for a single coplanar T-line structure. This illustrates the meaning of “geometry optimization”.

Lastly, the shields' width cannot be too large due to design area constraints. For wshield=w, a T-line core structure occupies a minimal area on silicon while still keeping its behavior well predictable.

Impact of a T-Line Neighborhood on its Frequency Domain Parameters

The theoretical and numerical study of the silicon substrate has been presented in Goren, D. et al., “Modeling Methodology of On-Chip Coplanar Transmission Lines over the Lossy Silicon Substrate”, SPI'03, Siena, May 2003. Therefore, the impact of other parts of the T-line typical VLSI neighborhood is now considered.

FIGS. 4A to 4Dshow four different design neighborhoods for a T-line core structure which were investigated as an example. The core structure410is the same as that ofFIG. 1Awith a single signal line411with two side shield lines414,415.

InFIG. 4A, the neighborhood includes a crossover line403and a crossunder line404. InFIG. 4B, the neighborhood includes a crossover line403and a crossunder line404and additional side signal lines431,432. InFIG. 4C, the neighborhood includes the lines ofFIG. 4B, with additional shield lines441-448above and below the crossover and crossunder lines403,404. InFIG. 4D, the neighborhood includes a crossover line403and a crossunder line404, a shield line451above the crossover line403and directly above the signal line411, and a shield line452below the crossunder line404and directly below the signal line411.

Since the T-line models include the power grid influence and therefore assume RDC=Rsignal, Rshieldhas been subtracted from all the EM solver results presented.

FIGS. 5A,5B,6A,6B,7A and7B, show frequency domain characteristics of the test structures ofFIGS. 4A to 4Dfor a practical case of single coplanar T-line core structure with w=s=2 um, t=0.35 um, and the actual non-uniform dielectric.

FIGS. 5A and 5Bshow the impact of neighborhood on the T-line core structure behavior of the test structures ofFIGS. 4A to 4C.FIG. 5Ashows the S-parameters and

The graphs clearly show that for such structures, the crossing wires are the dominant factor which determines the T-line behavior. Therefore, in the absence of parallel wires exactly above and/or below the signal wire, the structure ofFIG. 4Acan be considered as a sufficiently closed environment of the coplanar T-line.

FIGS. 6A and 6Bshow the impact of the width of coplanar neighbors as shown in the test structure ofFIG. 4B.FIG. 6Ashows the S-parameters, andFIG. 6Bshows the γ-Z0characteristics. In the presence of crossings, the impact of the width of coplanar neighbors is quite small.

FIGS. 7A and 7Bshow the influence of parallel wires located exactly above and below the signal in the presence of crossings.FIG. 7Ashows the S-parameters, andFIG. 7Bshows the γ-Z0characteristics for the test structures ofFIG. 4AandFIG. 4D. This influence is pronounced mainly in the signal attenuation and depends on the width of these parallel wires. In cases where the attenuation in the critical wires is important, such parallel wires are best avoided, or considered as a part of the closed environment.

It has been shown here that a stand-alone model for a critical line in a VLSI Manhattan environment is possible in most common cases, provided that the model is modified and expanded to include some environment elements, such as the crossing lines, the silicon substrate, and the correction of the DC resistance due to the power grid.

Referring toFIG. 8, a flow diagram800is provided of a method carried out for each critical path. A critical path is identified801and the design requirements are formulated802for the critical path, such as the electrical and geometric requirements. A T-line core structure is chosen803from a set of pre-optimized T-line Pcells. For example, this set may be as provided in step202ofFIG. 2A.

The closed environment of the T-line is then identified804and the T-line geometry parameters are chosen805based on design requirements and small circuit simulations using the expanded broadband T-line models. For example, this set may be as provided in step203ofFIG. 2A.

It is then determined806if the design requirements are met. If not, then the method loops807to choose805other values of the T-line parameters. If the design requirements are met, it is then determined808is there are more critical paths. If so, the method loops809and repeats for the next critical path801. If not, the method proceeds to larger circuit simulations810.

An integrated circuit design system for implementing a design process including modeling T-lines may be provided. The design system is implemented by specialized CAD software running on a computer processor providing an interface with a designer. The designer controls the design process by appropriate inputs to the system.

The IC design system includes means for modeling T-lines including the methods described inFIGS. 2A and 8. The means for modeling T-lines may be provided in the form of a computer program product. An IC design flow which employs modeling of the critical on-chip wires is disclosed in detail in U.S. Pat. No. 7,080,340 for “Interconnect-Aware Integrated Circuit Design”, filed Nov. 26, 2003, and issued Jul. 18, 2006.

Referring toFIG. 9, an exemplary system for implementing an IC design system includes a data processing system900suitable for storing and/or executing program code including at least one processor901coupled directly or indirectly to memory elements through a bus system903. The memory elements can include local memory employed during actual execution of the program code, bulk storage, and cache memories which provide temporary storage of at least some program code in order to reduce the number of times code must be retrieved from bulk storage during execution.

The memory elements may include system memory902in the form of read only memory (ROM)904and random access memory (RAM)905. A basic input/output system (BIOS)906may be stored in ROM904. System software907may be stored in RAM905including operating system software908. Software applications910may also be stored in RAM905.

The system900may also include a primary storage means911such as a magnetic hard disk drive and secondary storage means912such as a magnetic disc drive and an optical disc drive. The drives and their associated computer-readable media provide non-volatile storage of computer-executable instructions, data structures, program modules and other data for the system900. Software applications may be stored on the primary and secondary storage means911,912as well as the system memory902.

The computing system900may operate in a networked environment using logical connections to one or more remote computers via a network adapter916.

Input/output devices913can be coupled to the system either directly or through intervening I/O controllers. A user may enter commands and information into the system900through input devices such as a keyboard, pointing device, or other input devices (for example, microphone, joy stick, game pad, satellite dish, scanner, or the like). Output devices may include speakers, printers, etc. A display device914is also connected to system bus903via an interface, such as video adapter915.

The described method and system of design and modeling T-lines includes rules for proper design suggested for each type of on-chip T-lines, defining a minimal “sufficiently closed” environment for properly designed T-lines in dense VLSI design neigborhoods, and suggests a methodology for building self-contained models of properly designed T-lines in dense VLSI design neigborhoods.

The method as described above is used in the fabrication of integrated circuit chips. A design and modeling system may be provided as a service to a customer over a network.