CacheEM: For Reliability Analysis on Cache Memory Aging Due to Electromigration

Full citation

R. Zhang, T. Liu, K. Yang, and L. Milor, “CacheEM: For Reliability Analysis on Cache Memory Aging Due to Electromigration,” *IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*, vol. 41, no. 9, pp. 3078–3091, Sept. 2022, doi: 10.1109/TCAD.2021.3121636.

Plain-language overview

This paper presents CacheEM, a simulation framework for predicting how SRAM cache memories age because of electromigration, or EM. Electromigration is the gradual movement of metal atoms caused by electrical current. Over time, this movement can create voids in on-chip copper interconnects, increase their resistance, slow memory operations, and eventually cause circuit failure.

The central idea is that cache reliability cannot be predicted accurately from wire geometry and nominal current density alone. The actual stress experienced by a cache depends on the programs running on the processor, because different workloads read and write different memory cells at different rates. CacheEM therefore connects application-level behavior to circuit activity, interconnect current, physics-based stress evolution, resistance degradation, and statistical lifetime prediction.

The framework combines processor emulation, cache simulation, current modeling, a physics-based electromigration solver, and Monte Carlo analysis into one workflow. Its purpose is to help designers evaluate how cache architecture and operating conditions influence electromigration reliability under realistic usage.

What problem does the paper address?

Modern processors contain large SRAM caches with long metal lines used for bit lines, power delivery, and signal propagation. These lines can be vulnerable to electromigration because they carry repeated current pulses during cache reads and writes.

Traditional electromigration analysis often uses Black’s equation, an empirical relationship between current density, temperature, and mean time to failure. Such methods are fast, but they commonly treat wire segments independently. They may therefore neglect atomic transport and stress interaction across connected interconnect branches.

The paper argues that these simplified methods can be overly pessimistic. It instead adopts an extended Korhonen model, which describes the time-dependent evolution of mechanical stress and atomic flux along a metal line. Previous physics-based studies had largely focused on power grids or isolated SRAM structures; they generally did not connect EM degradation to realistic processor workloads and cache-access patterns.

The paper therefore addresses two related gaps:

1. A **physics gap**: conventional segment-by-segment lifetime models do not fully represent stress evolution in connected interconnect trees.
2. A **system-use gap**: prior EM studies often do not account for the actual read and write activity generated by applications running on a processor.

Questions the paper answers

1. How can realistic processor workloads be translated into electromigration stress in an SRAM cache?

CacheEM records memory accesses generated by programs, determines how often each SRAM cell is read or written, maps those events to current pulses, and calculates the equivalent current density in every long interconnect segment.

2. How can bidirectional and pulsed cache currents be incorporated into EM analysis?

Read and write currents may flow in opposite directions. CacheEM uses a pulse-averaged effective current-density approximation so that opposite current directions can partially offset one another.

3. How does electromigration stress evolve over time in a complex cache interconnect?

The framework solves a physics-based stress equation derived from the Korhonen model and calculates void nucleation, incubation, growth, and resistance increase.

4. How should cache lifetime be defined at the circuit level?

The paper defines the lifetime of an interconnect as the time at which its resistance rises by 10%. The lifetime of an entire cache sample is then the minimum lifetime among all of its analyzed interconnects.

5. How do cache-architecture parameters affect EM reliability?

The paper studies cache-line size, cache size, replacement policy, set associativity, and cache latency.

6. Which architectural parameters matter most for EM reliability?

The results indicate that cache-line size and cache size can significantly affect EM lifetime, while replacement policy, associativity, and latency have comparatively small effects in the studied design and workloads.

Key technical terms

SRAM. Static random-access memory, the technology commonly used for processor caches. Each SRAM cell stores one binary value using a small transistor circuit, typically a six-transistor, or 6T, cell.

Cache memory. A small, fast memory located close to a processor core. It stores recently or frequently used instructions and data.

L1 instruction cache. The first-level cache storing machine instructions near the processor core.

Interconnect. A metal wire used to carry electrical current or signals. Important long SRAM interconnects include BL, BLB, VDD, and GND.

Electromigration. The movement of metal atoms under sustained electrical-current stress, driven largely by momentum transfer from conducting electrons.

Atomic flux. The rate and direction at which atoms move through the conductor.

Hydrostatic stress. Mechanical pressure within the metal. Electromigration creates compressive stress in some regions and tensile stress in others.

Void nucleation. Formation of a small atom-depleted region inside or at the boundary of a metal line.

Activation energy. A parameter controlling how strongly atomic diffusivity depends on temperature.

Critical stress. The stress threshold at which a void is assumed to nucleate.

Monte Carlo simulation. Repeated evaluation using randomly varied physical parameters to obtain a lifetime distribution.

Process variation. Manufacturing-induced differences among nominally identical wires or devices.

Current density. Current divided by conductor cross-sectional area, usually represented by j.

Cache hit rate. The fraction of memory requests served by the cache.

Set associativity. The number of cache locations available for a particular memory block.

Replacement policy. The rule used to remove a cache entry when a set is full.

CacheEM workflow

CacheEM contains five major components.

1. Microprocessor emulation

The processor and cache hierarchy are modeled with gem5. Programs are executed, and accesses to the target cache are recorded.

2. Cache-cell activity extraction

A custom cache simulator processes the memory traces. It counts read-0, read-1, write-0, and write-1 operations for each cache cell.

3. Current extraction and prediction

Current pulses associated with each operation are initially obtained through HSPICE circuit simulations. To avoid running a new simulation for every voltage, temperature, geometry, and capacitance combination, the authors train regression models.

The model inputs include gate length, bit-line unit capacitance, number of SRAM rows, supply voltage, and temperature. The output consists of effective current magnitude and duration. More than 10,000 HSPICE-generated data points are used, with a reported target of R² greater than 99%.

4. Equivalent interconnect-current calculation

Cell activity and current models determine the current in each BL, BLB, VDD, and GND segment. Because currents are pulsed and may reverse direction, CacheEM calculates an effective pulse-averaged current density.

5. Physics-based EM lifetime analysis

The extended Korhonen equation is solved using a finite-difference method. The model calculates time-dependent hydrostatic stress, atomic flux, void nucleation, void incubation, void growth, resistance change, and time to failure. Monte Carlo analysis produces an EM lifetime distribution.

Electromigration degradation phases

Phase I: Nucleation

Stress develops inside the metal line. Resistance remains approximately unchanged until maximum tensile stress reaches the critical threshold.

Phase II: Incubation

A void has nucleated and begins to grow but is still too small to obstruct the entire conductor cross-section.

Phase III: Growth

The void reaches a critical size and forces current through a higher-resistivity liner. Resistance then rises significantly.

Experimental configuration

The demonstration uses a single-core ARMv8 processor operating at 2 GHz and executing `sjeng`, `specrand`, and `patricia`.

The default L1 cache configuration is:

• Cache size: 16 kB
• Cache line: 16 bytes
• Associativity: two-way
• Replacement policy: LRU
• Latency: one cycle

Power is estimated with McPAT and temperature with HotSpot. The average instruction-cache temperature is approximately 345 K, or about 72°C.

Main findings

1. Cache-line size significantly affects EM lifetime

The authors compare 8-, 16-, and 32-byte cache lines. The 32-byte configuration provides the best lifetime distribution because its interconnects are shorter and its most vulnerable wires experience lower current density.

The 8-byte configuration performs worse than the 16-byte configuration because it causes more cache accesses and activity is unevenly concentrated in one bank.

The reported access counts are approximately:

• 256.277 million for 8-byte lines
• 192.292 million for 16-byte lines
• 156.353 million for 32-byte lines

Cache-line size has only a small effect on hit rate in these experiments.

2. Replacement policy has little effect

FIFO, LFU, LRU, MRU, and random replacement produce very similar EM lifetime distributions. MRU gives a somewhat lower hit rate, but lifetime differences are minor.

3. Associativity has only a minor and non-monotonic effect

Direct-mapped, two-way, four-way, eight-way, and fully associative configurations are examined. Hit rate generally improves through eight-way associativity, but EM lifetime does not follow a consistent trend.

4. Cache latency has little effect

Increasing latency from one to four cycles produces only small changes in hit rate and lifetime distribution. The authors conclude that latency, associativity, and replacement policy should mainly be selected for architectural performance.

5. Cache size has a significant but non-simple effect

The authors examine 8-, 16-, 32-, and 64-kB caches. Hit rates are approximately:

• 89.2% for 8 kB
• 93.7% for 16 kB
• 97.4% for 32 kB
• 99.2% for 64 kB

The 8-kB cache has the best lifetime distribution because its interconnects are shortest and carry lower current density. Among 16, 32, and 64 kB, increasing cache size improves lifetime because activity is distributed across more banks and cells.

The relationship between cache size and EM lifetime is therefore not monotonic. It depends on wire length, current density, bank organization, access distribution, and effective stress duration.

Technical significance

The paper is technically significant because it links multiple abstraction levels:

• Application workloads
• Processor execution
• Cache architecture
• SRAM-cell activity
• Circuit-level currents
• Interconnect geometry
• Material physics
• Statistical lifetime

It replaces nominal activity assumptions with spatially resolved cell activity, handles connected interconnect structures, includes bidirectional current, predicts lifetime distributions rather than one lifetime value, and enables architectural reliability tradeoffs.

Potential industrial impact

The paper does not report deployment in a commercial product, so its industrial implications are potential applications:

• Early reliability-aware cache design
• Reduction of unnecessary design margin
• Identification and reinforcement of vulnerable interconnects
• Workload-specific qualification
• Advanced-node design support
• Architecture-circuit-technology co-optimization
• Integration into electronic design automation flows

Why the paper matters

The paper matters because it demonstrates that electromigration reliability is not solely a property of the metal wire. It is also a property of how the system uses the wire.

Two physically identical caches may age differently if they execute different workloads. Two architectures with similar hit rates may have different EM lifetimes because their physical organizations produce different wire lengths and activity concentrations.

The central question shifts from:

How much current does this wire carry?

to:

How do workload, cache architecture, circuit behavior, physical layout, and material variability combine to determine this wire’s stress history and lifetime?

Limitations and scope

The conclusions are based on one ARMv8 processor configuration, one L1 instruction-cache organization, three benchmarks, a selected SRAM and interconnect model, a fixed average temperature near 345 K, a 10% resistance-rise failure criterion, and selected distributions for activation energy and critical stress.

The numerical ranking of cache configurations should not be assumed to hold for every processor, workload, layout, or technology.

Concise technical abstract

CacheEM is a cross-layer, workload-aware reliability-analysis framework for predicting electromigration-induced aging in SRAM-cache interconnects. It combines gem5 processor emulation, cache-cell activity extraction, HSPICE-derived regression models for read/write currents, effective current-density calculation, an extended Korhonen stress-evolution model, finite-difference numerical analysis, resistance-shift modeling, and Monte Carlo lifetime estimation. The framework evaluates BL, BLB, VDD, and GND interconnects and defines cache failure by the earliest interconnect reaching a 10% resistance increase. Application to an ARMv8 L1 instruction cache shows that cache-line size and cache size can substantially affect EM lifetime through changes in wire length, current density, bank organization, access count, and stress duration. Replacement policy, associativity, and latency have comparatively small effects for the workloads studied.