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VARIUS: A Model of Process
Variation and Resulting Timing
Errors for Microarchitects
Sarangi et al
Prateeksha Satyamoorthy
CS 8501
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Parameter Variation
• Deviation of process, voltage and temperature values from
specifications
• Technology scaling beyond 90nm => higher levels of device
parameter variations => design problem from deterministic to
probabilistic
• Key process parameters: Vth and Leff
▫ Determine transistor and gate speeds
• Vth variation impacts:
▫ Frequency , leakage power
• Variation => some sections of chip are slower than others =>
corresponding circuits suffer timing errors
• Lose benefits from scaling to a technology generation
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Cross-section of a MOSFET
• The clock cycle of a chip is determined by the delay of its
longest path, usually referred to as the critical path
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Impact of Vth and Leff
Source: www.ocw.mit.edu
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Impact of process variation on processor frequency
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Varius
• To study parameter variation affects timing
errors in high-performance processors
▫ A novel model for process variation
 Within-die parameter variation (WID)
▫ A novel model for timing errors
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Process Variation Model
• Systematic variation
▫ Exhibits spatial correlation
▫ Assumptions:
 position independence, isotropy
▫ Spherical model
- initially linear
- then tapers off
to zero
[range] - no correlation
at this distance
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They finally assume phi = 0.5
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• Random variation
▫ Level of individual transistors
▫ Assumption: Vth and Leff normally distributed with
zero mean, uncorrelated
• Final σ and
▫ Total WID variation is normally distributed, so
=½
Assumptions
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VATS - Model for variation-induced timing
errors in processor pipelines
Pdf – probability density function
All paths that have become
longer than 1 generate errors
PE – probability of error
Cdf – cumulative density function
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Timing errors in logic
Dvarlogic distribution
Cdfvarlogic
Error rate
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Timing errors in SRAM Memory
More errors as
paths fail
First path
fails
Distribution
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Validation
180 nm process
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Validation
1. Generate Vth and Leff variation map
2. Apply timing error model to get error rate vs. frequency
for each pipeline stage
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How Varius is used
• Variation-Aware Dynamic Voltage/Frequency Scaling - Herbert et al :
Vth and Leff are generated and the values are used to determine the
maximum frequency and subthreshold leakage of each core across Vdd
and temperature. Variability-aware schemes maintain significant
improvement of power/throughput over the variability-unaware ones,
upto 9.9%
• Maestro: Orchestrating Lifetime Reliability in Chip Multiprocessors Feng et al : Showed that for CMPs without damage profiles, temperature
sensors and performance counters are inadequate in environment with
significant process variations, so they propose low-level damage sensors
• EVAL: Utilizing Processors with Variation-Induced Timing Errors –
Sarangi et al : design for closer to nominal values, and provide some
transistor budget to tolerate unavoidable variation induced errors
• Facelift: Hiding and Slowing Down Aging in Multicores - Tiwari et al :
determine how variation impacts the delay of each gate of each critical
path. The slowest of the critical paths in a processor determines the
processor frequency.
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Related Work, Contribution
• Delay of an inverter from Vth and Leff
• Mukhopadhyay et al. proposed models for timing errors in SRAM memory
due to random Vth variation. The VATS model, is extension of their model
of access time errors by
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▫
▫
▫
including systematic variation effects,
considering variation in Leff,
modeling the maximum access time of a line of SRAM rather than a single cell
using the alpha-power model that uses an [alpha] equal to 1.3
• Memik et al. modeled errors in SRAM memory due to cross-talk noise as
they overclock circuits. They use high degrees of overclocking — twice the
nominal frequency and more. In the less than 25% overclocking regime that
we consider, such cross-talk errors are negligible. For very small feature-size
technologies, however, the situation may change.
• Ernst et al. and Karl et al. measured the error rate of a multiplier and an
SRAM circuit, respectively, by reducing the voltage beyond safe limits to
save power. They plot curves for error rate versus voltage. In this paper, we
outlined a procedure to extract the distribution of path delays from these
curves, and validated parts of our model by comparing it against their
curves.