A New Approach To Resistance Extraction For Unconventional Geometries

How 2D fracturing can provide accurate results in a timely manner.


Unconventional metal structures have begun popping up in integrated circuits (ICs) with increasing regularity, for a number of reasons. The growing demand for integrated cameras and image recognition capabilities has fueled the need for components such as high-quality CMOS image sensors with low noise, high dynamic range, and low power. Technology scaling has also contributed to an increase in the use of non-traditional structures as designers attempt to maximize design area.

So what, exactly, is an unconventional structure? The term is generally used to refer to large metal structures that are wider or more square in shape when compared to the relatively narrow metal typically used in signal routing.

Historically, designers used a field solver to extract resistance in such large wide metal structures, but field solvers are often not well integrated within the IC design flow, and require long runtimes that are not suitable for full chip verification. With the use of these geometries growing steadily, designers are looking for more efficient resistance extraction processes and tools that provide accurate results in a timely manner for these unconventional structures.

A brief guide to resistance measurement
Measuring interconnect resistance in an IC design is an essential verification parameter used to ensure circuit reliability. During the IC layout and physical verification, designers must measure resistance values between different physical (probe) points in the layout. These point-to-point (P2P) resistance values are used both to verify that the layout meets electrical design criteria and to optimize the physical design layout where practical. These resistance parameters are also used to evaluate design reliability conditions, such as current flow and electrostatic discharge (ESD) paths, to ensure that the product life and performance meet design and market expectations (Figure 1).

Figure 1. Validating a low resistance path used to avoid an ESD charge device model (CDM) failure.

The following steps represent the basic process used to determine the P2P resistance of interconnect metal:

  • extract physical parameters (height, width, length) for each metal layer
  • fracture (segment) large structures in the layout into simpler polygons
  • extract resistance value for each segment
  • create a resistor network between segments from which the P2P total resistance is calculated

Let’s take a closer look at the fracturing step, because that is where the process breaks down for unconventional metal structures.

Fracturing is the process in which the extraction engine breaks down a complex layout shape into smaller segments (following the flow of the current), and assigns a resistance value to each segment based on the fractured length, width, and sheet resistance of the metal layer. Each assigned resistance value is referred to as a resistor body (r-body). The resistor network is often referred to as an r-bodies chain, since it contains the small fractured geometries that will be presented by a resistor.

One-dimensional (1D) fracturing is the most common technique used in resistance extraction, as it is efficient for regular layout polygons, returning accurate results without creating too many r-bodies in both directions. 1D fracturing divides a polygon in one dimension to create a chain of segments (r-bodies) in which each r-body has one primary width (Figure 2).

Figure 2: A resistor network containing four r-bodies is created to extract P2P resistance between points A and B.

However, for layouts that contain the unconventional large/wide metal structures, multiple P2P resistance measurements between different probing points are required for the accurate extraction of resistance. Because 1D fracturing simplifies the fracturing to improve performance, it is inadequate for measuring resistance in these unconventional geometries. While field solvers can do the work, the increase in the use of these structures means design companies typically can’t invest the time and resources required for field solver calculations if they want to have any hope of meeting their tapeout schedules.

The answer? Why, two-dimensional (2D) fracturing, of course. A relatively new approach, 2D fracturing fractures the metal structure in both directions to create a mesh of r-bodies. 2D fracturing provides accuracy for these unconventional structures that is similar to the results obtained from a field solver, but with much faster runtimes. Figure 3 shows two examples of 2D fracturing across an unconventional geometry. In Figure 3(a), both 1D and 2D fracturing are used to extract the point-to-point resistance between A-B, A-C, and A-D. Figure 3(b) only requires 2D fracturing to create a resistor mesh for accurate extraction of point-to-point resistance values.

Figure 3: 2D fracturing creates a resistor mesh to accurately measure P2P resistance in unconventional metal structures. Layout (a) uses both 1D and 2D fracturing, while (b) uses 2D fracturing exclusively.

Electronic design automation (EDA) tools such as Mentor’s Calibre PERC reliability platform are now available with enhanced capabilities that enable automated selection of the appropriate fracturing technique based on the selected metal structures and the specified probe points. Using an automated fracturing process not only helps ensure more accurate P2P resistance measurements and simulation, but it also minimizes runtimes.

Accurately measuring the interconnect resistance within your IC design is fundamental for ensuring circuit performance and reliability. If you find yourself working more and more with layouts that use unconventional metal structures and multiple probe points, enhanced resistance measurement techniques like 2D fracturing can help you extract P2P resistance quickly and accurately across your entire layout. With applications now ranging from automotive to security to medicine to space, getting your designs to market quickly, with confidence, is an essential element of success.

To learn more, read our whitepaper “Accurate, Fast P2P Resistance Extraction for Unconventional Geometries.”

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