High-Performance, High-Precision Memory Characterization

By Federico Politi, Altos Design Automation, Inc

Introduction

It is a very rare IC design that does not include some form of on-chip memory, with embedded ROM, RAM, and multi-port register files consuming as much as half the die area. There may be as many as a few hundred unique memory instances on a highly-integrated programmable System-on-Chip (SoC). Some of the most critical paths will start, end or pass through memory instances, and therefore these memory elements must precisely model a comprehensive range of nanometer effects in order to enable the highest integrity SoC verification and subsequent silicon success. Many of the current approaches to memory characterization however are ad-hoc and do not accurately model the detailed timing, noise and power data needed for electrical signoff, forcing re-spins, delaying schedules and increasing the total cost of design. Furthermore, existing memory characterization methods cannot be scaled towards statistical timing (SSTA) model generation.

Memory characterization is of increasing concern to SoC designers, who require accurate and efficient models at all stages of design. Compounding this problem are the number and magnitude of the challenges faced. The number of memory instances per chip is increasing rapidly, with some forecasts pointing to greater than 90% of the die area being taken up by memories and other large macros within 5 years. In addition, to support the full range of process, voltage and temperature corners (PVTs) and the sensitivity to process variation, the number of characterization runs and the number of data points per characterization run is growing exponentially.

Existing Approaches to Memory Characterization

There are currently two main approaches to creating memory models 1) memory compiler generated and 2) instance-based characterization.

Memory compilers are tools that can automate the creation of many different memory instances by abutted placement of pre-designed leaf cells (for example, bit cells, word and bit line drivers, decoders, multiplexers and sense amplifiers, etc) and routing cells together where direct abutment is not possible. The compiler also generates a power ring appropriate in width and number of taps to the frequency of operation; defines signal and power pin locations; and creates the different electrical views, netlists and side files required for downstream verification and integration tasks. Memory compilers can very quickly generate hundreds or thousands of unique memories, differing in address length, data length, column multiplexing, density, performance and power etc.

Memory compilers do not do explicit characterization but instead create models by fitting timing data to polynomial equations whose coefficients are derived from characterizing a small sample of memory instances (perhaps the largest, smallest and one or two selected intermediate sizes). The advantage of this approach is that the model generation is very fast but the drawback is that the accuracy is poor. To safeguard against chip failure due to inaccurate models, the memory compiler will typically add guard bands. These additional margins however can lead to more timing closure iterations, increased power and larger chip area. In addition, the fitting approach doesn’t work well for advanced current based models that are commonly used from timing, power and noise at 40nm and below.

To overcome the inaccuracies of compiler generated models, design teams will resort to instance-specific characterization of each memory instance used over a range of PVTs. This is a much more time-consuming process that should yield more accurate results. However, oftentimes due to limitations in the characterization approach and available resources, the accuracy improvement is not as much as it could be, while the cost is high.

There are a couple of common approaches to instance-based characterization. One method is to treat the entire memory as a single block and characterize the complete instance using a large capacity “fast-spice” simulator. The advantage of this approach is that the complete circuit is simulated as one, essential for example for accurate power and leakage modeling. It can also be distributed across a number of machines to improve turn-around time if there are enough available high capacity simulation licenses available. The disadvantage to this approach is that the “fast-spice” simulators are less accurate than “true-spice” simulators particularly when used with lower accuracy settings required to get reasonable turn-around time. Accuracy and characterization performance are also further compromised when there is significant coupling between the signal lines in the memory, very common below 90nm. The transistor models used by “fast-spice” methods also are less capable at modeling stress effects than “true-spice” simulators. Stress effects are prominent at 40nm and below. Finally, this block-based approach still requires users to identify probes points within the circuit for characterizing timing constraints. For a custom memory block, the characterization engineer can get this information from the memory designer but this information will not be available for a memory generated from a 3rd party compiler. Other drawbacks for this method is that it doesn’t work well for generating some of the newer model formats such as noise models and cannot be scaled to generate process variation models needed for statistical static timing analysis (SSTA).

Another approach to memory characterization is to divide and conquer by breaking the memory into a set of critical paths, characterizing each of these paths using a “true-spice” simulator and integrating the electrical data from each of these components back into a complete memory model. Typically the critical paths fall into the following categories a) input data to probe, b) clock signal to probe, and c) input signal to output pin. The probe points are internal nodes in the memory where the clock and data signals meet, typically at a latch.

The critical paths are either created by the designer for a custom memory instance or by use of a path-tracing and cutting tool. The advantage with this approach is that the accuracy comes from “true-spice” silicon calibrated models. It can also be distributed across a computer network with each critical path being simulated independently. The disadvantage is that for advanced memories where there is significant coupling or virtual power supply network the circuitry making up the critical path grows to be too large for “true-spice” simulators to complete in a reasonable time such that “fast-spice” simulators may need to be used. In addition, SSTA model generation, especially for mismatch parameters, becomes prohibitively expensive in turnaround time with such a large circuit.

Other challenges of this “static cutting” approach include ensuring correct identification of clock circuitry, memory elements and the tracing of critical paths through analog circuitry such as sense amps for many different memory architectures using many different circuit design styles. Because of the variation in the memory's architecture and usage (multiple ports, synchronous or asynchronous, scan, bypass, write-through, power-down etc), a significant amount of effort is required by the characterization engineer, manually guiding the process to completion by creating stimulus files, simulation decks and other needed data. This makes the characterization process even slower and even more prone to error, and these unintentional user-injected errors and delays become a huge thorn in the side of model consumers. With an increasing number of delayed and failing chips, many requiring some level of re-design or a re-spin, the situation requires a substantial rethink.

Memories now contain greater functionality, particularly adding structures and techniques with a view to minimizing power consumption, both static and dynamic; for example, adding header and footer cells, power-off modes and in some cases dynamic voltage and frequency scaling for multi-domain power management. In addition, fine-line process geometries require more comprehensive characterization in order to acquire the complete data needed to capture coupling impact; the abstracted models must faithfully incorporate the effects of signal integrity and noise analysis. This in turn requires more extracted parasitic data to remain in the netlist for SPICE simulation, increasing run-times during data acquisition and further sapping productivity.

Both the newer architectures and increased coupling inhibit the applicability of this “static cutting” approach; simulation performance during data acquisition slows down to a crawl when users try to retain the precision they so desperately need. Modeling errors continue to increase, impacting design and verification. There's a clear and pressing need for a new approach in the area of memory characterization, with the following requirements:

1. First, the new solution must offer high productivity, even for large memory arrays, in order to accelerate the availability of models to design and verification teams. The characterization must be straightforward to configure and control, as well as offer high throughput.
2. The generated models should be of the utmost precision – the impact on parametric timing, noise and power data from the characterization process must be minimized, and certainly under 0.5%.
3. In addition, the models must be comprehensive, supporting all the latest features in the intended target tools included in corner-based and statistical methodologies; they must be reliable and robust in their support of the all necessary verification features.
4. Finally, the models must be consistent with other characterized components, such as standard cells, I/O buffers, and other large macros, in the selection of switching points, characterization methodologies, and general look and feel.

Memory Characterization for 40nm and below

Figure 1 - Memory Characterization Architecture with Dynamic Partitioning

The existing methods of memory characterization, both block-based or “static cutting”, can be augmented to address today’s challenges via the use of “dynamic partitioning.” (see Error! Reference source not found. figure 1.) Rather than relying on static path tracing, ”dynamic partitioning” leverages a full-instance transistor-level simulation, using acquisition data specific vectors, to derive a record of circuit activity. The critical paths for each timing arc, such as from the clock to output bus or from the data or address buses and clock to each probe point, can be derived from the simulation results. The probe points where the clock and data paths intersect can be automatically derived from a graph traversal of the circuit without requiring design dependent transistor pattern matching. A “dynamic partition” can then be created for each path including all the necessary circuitry along with any “active” side-paths such as coupling aggressors. This technique is particularly effective for extracting critical paths through circuitry that contain embedded analog; for example, sense amplifiers along the clock to output path.

Another benefit of “dynamic partitioning” is that memories – like many analog blocks – exhibit the characteristic that partition boundaries can adjust during operation. A”read” operation following a write to a distinct location exercises quite different parts of the instance. Dynamic partitioning, in offering a more flexible and general purpose solution, gives superior results in these situations.

Figure 2 - Dynamic Partition Simulation results for a Memory Path from Clock to Output

Once this comprehensive partitioning is complete, accurate SPICE simulations are performed independently on decomposed partitions, with the assembled results faithfully representing the timing behavior of the original, larger instance. This "bi-modal view" uses the full-instance simulation to determine large-scale characteristics, like power and partition connectivity, while the much smaller individual partitions, each containing typically only a few hundred transistors, are simulated using a ”true-spice” simulator to ensure the highest levels of precision. Communication between the full-block and partitioned sub-block simulations ensures identical initial conditions and DC solutions, essential for obtaining precise and consistent data. This analysis and partitioning technology can be coupled to sophisticated job control for parallel execution and distribution across the network. In addition, the partitions can be represented as super-cells to cell characterization systems to: enable the generation of current sources models (CCS and ECSM) for timing, noise and power analysis; and even the generation of statistical timing models using the same proven statistical characterization methods for standard cells. Consistent application of a library-wide characterization approach ensures interoperability between all instances in the design, serving to eliminate hard to find timing errors due to library element incompatibilities.

As each “dynamic partition” is simulated using “true-spice,” the generated timing models are nearly identical to simulating the complete block using “true-spice” which is impractical for all but the smallest memory instances. The only source of error is related to tying off in-active gates and wires. The table in Figure 3 shows a comparison between a golden result (small memory simulated entirely in “true-spice”), the results from dynamic partitioning and the result from simulating the entire block in “fast-spice.” The accuracy loss due to “dynamic partitioning” is less than 1% for delay, transition and constraints while using “fast-spice” results in up to 6% difference.

Accuracy Vs “true-spice”	Delay	Transition	Constraints
“fast-spice”	5.98%	3.17%	2.61%
Dynamic partitioning	0.82%	0.41%	0.50%

Figure 3 – Accuracy of Dynamic partitioning Vs “true-spice”

As well as delivering accuracy, dynamic partitioning greatly improves both the CPU time and total turn-around time for memory characterization by an order of magnitude or more. Figure 4 shows the total CPU time comparison using a block-based memory characterization approach with “fast-spice” versus using dynamic partitioning with “true-spice.” For the more complex dual port RAM, the run-time improvement is over 60X. This differential grows with the size of the memory as the runtime for the simulations of dynamic partitions remains constant unlike the block-based runtime which grows super linearly.

Memory Type	Speedup
288 Kb single port SRAM	10.4X
36 Kb dual port, dual clock SRAM with scan, bypass	67.7X

Figure 4 - Speed Improvement from Dynamic Partitioning

The “dynamic partitioning” approach can be quickly deployed either for instance-based characterization of integrated into a memory compiler. The additional information required is minor; either stimulus or functional truth-tables derived from the memory datasheet. It is applicable to all flavors of embedded memory such as SRAM, ROM, CAM and registers files and also for custom macro blocks such as SERDES and PHY.

Conclusion

Applying “dynamic partitioning” to large memory instances eliminates the errors seen in solutions that employ only static SPICE netlist-cutting or rely totally on “fast-spice” simulators. This new technology provides the most precise and comprehensive models for design, verification and analysis available today while enabling very fast runtimes, often an order of magnitude faster for large macros. This superior level of precision enables designers to be much more selective in the application of timing margins during design and verification resulting in higher performance designs, optimal die area, and closer correlation with manufactured silicon.

When coupled to a proven cell characterization platform, a consistent characterization methodology can be used for cells and macros, critical for electrical sign-off and analysis of large and complex SoC designs.

Effective and efficient characterization certainly helps get models promptly into the hands of designers and into the flow, but precision and accuracy are everything. Utilizing “dynamic partitioning” designers can benefit from the comprehensive, accurate and efficient models it generates, with time-to-market and die-size improvements the result.