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Statistical Analysis of SRAM Cell Stability

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(NoiseL) Node L. Node R. 9. Loop Gain ... is subjected to positive DC noise (NoiseL) at node L and negative noise (NoiseR) at node R ... – PowerPoint PPT presentation

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Title: Statistical Analysis of SRAM Cell Stability


1
Statistical Analysis of SRAM Cell Stability
  • Kanak Agarwal, Sani Nassif
  • IBM Corporation, Austin

2
The Problem
  • Growing importance of systematic and random
    variability
  • Random variation can cause large mismatch in the
    neighboring devices
  • Random device mismatch has most significant
    impact on yield of SRAM arrays
  • Many failure mechanisms such as read stability,
    write fail, performance, and data retention
    failures

3
SRAM A Highly Susceptible Design
  • Data stored in cross coupled inverters
  • Conflicting read and write requirements in cell
    design
  • Retain cell contents during read access and
    change them during write operation
  • Proper cell functionality relies on relative
    strengths of various devices in the cell

4
SRAM A Highly Susceptible Design
  • SRAM cells use the smallest devices
  • Small sized devices are more susceptible to
    variation due to random dopant fluctuation
  • SRAM arrays are ubiquitous and contain large
    number of cells
  • A typical 4 MB cache contains 38 million cells
  • One failure in the cache requires correct
    operation up to 5.44 sigma

R Heald, P. Wang, ICCAD 2004
5
Outline of This Talk
  • SRAM cell stability analysis theory, models and
    simulation results
  • DC noise margin
  • Read stability failures
  • Write failures
  • Read access failures

Cell failure mechanisms
6
Static Noise Margin (SNM)
  • SNM is the most popular metric for characterizing
    cell stability
  • Graphical method
  • Assumes equal and opposite DC offsets at storage
    nodes
  • How do we interpret SNM for checking cell
    stability under read noise, alpha particle
    strikes etc. ?

7
The Loop Gain Concept
  • Cross-coupled inverters form a positive feedback
    loop system
  • Cell is on the verge of instability if its loop
    gain in unity
  • Cell stability can be verified by computing loop
    gain

G2
Cell is unstable if G1G2 gt 1
G1
J Lohstroh et al, JSSC 1983
8
DC Noise Margin Analysis
  • Lets assume cell stores a zero at node L
  • Positive DC offset at node Lcauses VL to rise
    above zero
  • Find minimum DC noise that causes cell to lose
    its state
  • Gains of individual inverter stages depend on
    corresponding inputs
  • Express loop gain as function of VL
  • Find VL at which loop gain 1

DC noise(NoiseL)
VLg (VR)
Node R
Node L
(VR 1)
(VL 0)
VRf (VL)
9
Loop Gain
Forward and feedback stage gain and loop gain as
function of VL
VL(flip) is the minimum DC potential at node L
that flips the cell
10
VL(flip) on Butterfly Curves
DC noise margin at node L
11
DC Disturbance at Node R
  • Negative DC offset (NoiseR) at node R pulls VR
    below one
  • Find minimum DC offset at nodeR that causes cell
    to lose its state
  • Express loop gain asfunction of VR
  • Find minimum DC potential at node R that flips
    the cell (VR(flip))

VLg (VR)
DC noise(NoiseR)
Node L
Node R
(VL 0)
(VR 1)
VRf (VL)
12
DC Disturbance at Node R
DC noise margin at node R
13
DC Disturbance at Both Nodes
  • Cell is subjected to positive DC noise (NoiseL)
    at node L and negative noise (NoiseR) at node R
  • Express loop gain as function of VL and VR
  • Find unity loop gain contour

14
DC Disturbance at Both Nodes
  • Loop gain 1 contour intersects butterfly curves
    at VL(flip) and VR(flip)
  • Model unity loop gain criteria
  • Coefficients a and b canbe computed from
    VL(flip) and VR(flip) values
  • Cell stability verified by checking above
    constraint

15
DC Disturbance at Both Nodes
16
Read Stability Failure
  • Read operation (Node L stores zero)
  • Resistive voltage division between access (AL)
    and pull down device (NL)
  • Disturbance at node L
  • If read disturbance is large,cell state can be
    flipped
  • Read stability failure

BR
BL
VL
VR1
PL
NL
AR
AL
PR
NR
WL1
17
Read Stability Analysis

  • Read operation injects a positive noise at node L
  • Analyze read stability by the loop gain method
  • Compute noise margin during read operation (RNM)

VL at which loop gain 1
Forward stage
Feedback stage
18
Read Noise Margin (RNM)

  • RNM is a useful metric in analyzing read
    stability
  • Negative RNM represents a cell flip during read

19
Read Stability Failure Probability

  • Model RNM distribution as Gaussian
  • Linear function of random threshold voltage
    variation in all six transistors
  • Read stability fail probability

20
Write Failures
  • Write operation
  • Resistive voltage division between access (AR)
    and pull up device (PR) pullsnode R low
  • If write disturbance is small,cell state may not
    flip
  • Write failure

21
Write Failure Analysis
  • Write fails if the time required to pull node R
    low (TW) is more than the word line duration
    (TWL)
  • TW is non-Gaussian
  • Transform TW to obtain linearity
  • For (a 1), (1/TW) can be modeled as Gaussian

22
Write Failure Probability
  • Write fail probability
  • (1/Tw) can be modeled as linear function of
    change in thresholdvoltages

23
Read Access Failures
  • Contents of the cell cannot be read during word
    line duration (TWL)
  • Not enough bitline differential to trigger sense
    amplifier
  • Different from read stability failures as cell
    retains state
  • Can be modeled like write failures
  • Transform access time (TA) to (1/TA)
  • Model (1/TA) as linear function of VT variation
    in all six transistors

24
Read Access Failures
Read access fail probability
25
Cell Failure Probability Results
  • Find sensitivities of the stability metrics (RNM,
    1/TW, 1/TA) to VT variations in all six
    transistors
  • Find individual failure probabilities
  • Joint failure probability can also be easily
    computed

Sensitivities of Stability Metrics (V-1)
26
Summary
  • SRAMs are failing...
  • Accurate prediction of cell stability and SRAM
    array yield is very important
  • Discussed many cell failure mechanisms
  • Hold failures, read stability, writability, and
    read access time failures
  • Proposed new robustness metrics to analyze cell
    stability in the presence of random VT variation
  • Methodology to enable efficient estimation of the
    cell failure probability
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