Modeling Parasitics in Sub-Micron IC Designs: Extract Them Before They Cost You a Re-Spin
I.Â Â Â Â Â Â Summary
IC designers who work at the deep sub-micron level know that smaller process size means lower per-unit costs, higher performance, and lower power consumption, not an end-run on the laws of physics.
As nets get closer together, parasitic capacitance becomes a design consideration. While designers have long made estimates as to where on the chip these effects might arise between layers, they are turning their attention to lateral effects within layers as they design below .25Âµm, where nodes become taller, thinner and denser. The best way to manage these effects is to use a parasitic extraction (PX) tool to model them in the design; the worst way is to send a chip to fabrication and have it come back faulty due to unintended influences.
This paper explains why designers must devote more attention to such parasitic effects as capacitance and resistance as process size shrinks. It describes the shortcomings of current approaches to dealing with these effects and the characteristics of a comprehensive parasitic extraction tool. Finally, it introduces HiPer PX from Tanner EDA, a high-performance, 2D/3D tool that enables designers to model parasitic effects and address them while still in the layout phase.
II.Â Â Â Â The Nature of Parasitic Effects
The push to pack more transistors and functionality into integrated circuits (ICs) has driven ever-smaller process sizes. Regular bulletins with foundry data compiled by the Semiconductor Industry Association (SIA) since 2005 demonstrate dramatic year-upon-year increases in production at 120nm and 90nm feature sizes, reaffirming the trend that confronts most IC designers at their desks each day: â€œMake it smaller.â€
Shrinking process-size exacerbates certain problems on ICs, though. Sub-micron designs comprise more devices, and the devices are smaller, leading to more congested interconnect and more difficulty in isolating wires. As wires in an IC get narrower, resistance along them increases. Foundries compensate for this by making the metal layers thicker, as depicted in the blue and grey metal layers in Figure 1.
Figure 1 - SRAM Cell
With this change in the aspect ratio of the metal, interconnect coupling increases relative to device performance. Lateral capacitance can build up, as indicated by the Clateral term between the taller, thinner Metal 2 wires shown in Error! Reference source not found.. Vertical capacitance between Metals 1 and 2 and between Metals 2 and 3 (shown as Cvat, Cvft, Cvab and Cvfb) has long figured in the calculations of IC designers, and has been easy to identify in larger-process sizes using common extraction tools, but intra-layer capacitance becomes of greater importance than inter-layer capacitance as process size shrinks below .25Âµm. Higher operating frequencies and lower voltages also intensify this effect.
Figure 2 - As process feature size decreases, metal thickness and vertical spacing does not significantly decrease, but lateral spacing decreases significantly.
While some capacitance is natural and limited, lateral capacitance often brings unintended consequences in high-density chip layouts. For example, with more capacitance comes more crosstalk. A change in state in a very noisy Metal 2 node may result in an unexpected state change in a sensitive Neighbor Metal 2 node. Also, capacitance of any type loads down the node, requiring more time and power for the node to change state. Thus, the amount of parasitic capacitance on the node can have significant effects on events that are sensitive to time constants, such as signal propagation.
Designers need to allow for these consequences by including them in their simulations and accurately calculating delay and circuit behavior; otherwise, they run the risk of going through layout and tapeout to first sample back from the foundry before discovering that their chip does not work â€“ a costly oversight.
III.Â Current Approaches to Extracting Parasitic Effects
To extract circuit parasitics and deliver a correct design the first time, IC designers have come up with several approaches for avoiding or identifying interconnect parasitics.
A.Â Â Â Prevention
Experienced designers route sensitive nodes separately from noisy nodes, keeping them far apart from one another or placing shields between them. In larger process sizes, the area of influence is relatively small, so careful prevention is often sufficient.
However, at smaller process size, it is risky to rely solely on this approach because nodes are so much closer to one another and may influence one another so much more. Also, the process of keeping noisy nodes separate from sensitive ones may be unnecessarily conservative, costing space in the design and time in the layout.
B.Â Â Â Extraction and simulation
Lumped capacitance to ground extraction â€“ Several tools allow designers to extract vertical capacitance to ground from the layout, essentially a process of extracting the area and perimeter of the net and estimating a load capacitance based on that. This simple, low-cost process simulates some of the parasitic effects and results in a basic loading amount that protects against simulating faster than the circuit will actually perform; however, it does not account for shielding, crosstalk, lateral capacitance or interconnect resistance.
Informal, â€œback of envelopeâ€ interconnect resistance estimation â€“ Designers may also estimate very roughly the resistance in a potentially troublesome interconnect: â€œIt runs 500Âµm and is .5Âµm wide, so thatâ€™s about x ohms.â€ They manually update the netlist with the resistance, then re-run the simulation to ensure it still works. The process is similar for roughly estimating crosstalk or any other effects not covered by extracting lumped capacitance to ground. However, the disadvantages of this time-consuming and often subjective technique are manifold, from relying on the designerâ€™s ability to anticipate all of the problem areas in the IC, to overlooking a sensitive net next to a noisy one, to underestimating the parasitic load between them, to the risk of sending an error-filled design to the foundry. It can suffice for a few, relevant parasitic interactions, but if nets are interacting in a widespread manner, then the â€œback of the envelopeâ€ approach becomes untenable.
At their best, then, these approaches may help extract parasitics, but at a potential cost in chip performance, silicon size and power consumption. How, then, can IC designers model interconnects and extract parasitics from a layout with maximum accuracy?
IV. Tools for Extracting Parasitics â€“ Considerations
A well-rounded parasitic extraction tool should:
- integrate smoothly with layout, verification and simulation workflow;
- reduce the amount of guesswork and estimation in finding problematic parasitic effects;
- extract netlists of devices and parasitics, including vertical and lateral coupling capacitance and interconnect resistance;
- enable the designer to run a simulation with confidence that parasitics are accurately modeled; and
- allow the designer to optimize the mix of speed and accuracy in modeling.
A.Â Â Â Resistance-Capacitance (RC) extraction using finite-element interconnect network models
This technique applies a set of advanced algorithms to represent the nodes in the network as finite elements. Â Then, when the circuit is extracted, instead of having the transistors connected with ideal, zero-resistance lines, they will be connected through a series of resistors and capacitors comprising that network, thereby modeling the parasitic effects of the interconnect.
B.Â Â Â Resistance or capacitance in isolation
The tool should also allow the designer the option of seeing either interconnect resistance or total nodal capacitance for simple extracts of one or the other in isolation. The advantage in extracting only interconnect resistance is that it helps in the identification and diagnosis of resistance-related problems.Â For example, resistance extraction allows the designer to identify narrow traces in the power distribution network that might affect the power integrity of the chip.
C.Â Â Implementation
A parasitic extractor automates the task of discovering and modeling parasitics on any cell at frequent points during layout rather than waiting until the end of the project, when it becomes expensive to address problems. Since the tool is run at all levels of design, different operating modes are required for detailed analysis of small cells than for bulk extraction of an entire chip.
|The option of 2D or 3D modeling addresses the trade-off between the accuracy of the model and the amount of time needed to generate it. 3D modeling is more accurate and better suited to small circuit blocks (<5000 transistors); 2D modeling takes less time and affords reasonably accurate interconnect models
in large circuit blocks.
2D extraction algorithms are used for faster modeling, especially when speed of extraction is a factor. A 2D algoritym employs a finite element method to extract interconnect resistance, and an interpolation method to extract vertical and lateral coupling capacitance by looking up values in a table.
3D capacitance extraction algorithms provide greater accuracy, but have much higher computation cost. Typically, a boundary-element method is employed, where the field solver captures all relevant crosstalk, shielding, and fringing capacitance.
|Figure 3- Reduction of the IC Network
Netlist reduction is a critical part of the RC parasitic extraction process, since the number of nodes in the resulting netlist can slow simulation unacceptably. Designers can specify the maximum frequency of interest for the circuit, and the tool will simplify the model while guaranteeing accuracy in the simulation up to that frequency. For example, Figure 3(a) depicts an original layout in a circuit and Figure 3(b) the parasitics in the circuit modeled as resistors and capacitors. Figure 3(c) shows the resulting network after reduction.
D. Workflow Example
Take the following example design â€“ a nine-stage ring oscillator shown in Figure 4. The design consists of 18 transistors configured into nine inverters. When the layout is extracted without parasitics, only the 18 transistors are modeled. A SPICE simulation of this netlist yields an oscillation frequency of 1.5 GHz (upper half of Figure 5).
However, this simulation does not take interconnect parasitics into account. A second run â€“ this time using extracted interconnect parasitics as a finite element RC network â€“ results in a netlist showing the 18 transistors plus 350 parasitic resistors and capacitors.
Figure 4 - Nine-Stage Ring Oscillator (Example)
A second simulation yields the new estimated operating frequency of 680 MHz, a difference of more than
50% (lower half of Figure 5).
Figure 5 - Operating Frequencies Without and With Parasitic Modeling
It is not surprising that the interconnect parasitics should slow down the frequency of oscillation; however,
the designer may need the oscillator to run faster. Armed with the parasitic netlist, he can find the nodes most
responsible and fix them. From the extracted data, he can see that nodes st5 and st9 in Figure 4 have
excessive resistance compared to the others, due to the long routes on narrow polysilicon, and modify the
As widely-used feature sizes in analog designs drop below .25#m, design problems caused by interconnect
parasitics become more common. Designers must use software tools to model and extract these parasitic
effects, or run the risk of chips that function in simulation but fail in silicon and require a re-spin.