Threshold Voltage Distribution in MLC NAND Flash: Characterization, Analysis, and Modeling

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Threshold Voltage Distribution in MLC NAND Flash
Characterization, Analysis, and Modeling
Yu Cai1, Erich F. Haratsch2, Onur Mutlu1, and Ken
Mai1

1. DSSC, ECE Department, Carnegie Mellon University
2. LSI Corporation

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Evolution of NAND Flash Memory

• Aggressive scaling
• MLC technology

Increasing capacity
Acceptable low cost
High speed
Low power consumption
Compact physical size
E. Grochowski et al., Future technology
challenges for NAND flash and HDD products,
Flash Memory Summit 2012
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Challenges Reliability and Endurance

• P/E cycles (required)

Complete write of drive 10 times per day for 5
years (STEC)
gt 50k P/E cycles

• P/E cycles (provided)

A few thousand
E. Grochowski et al., Future technology
challenges for NAND flash and HDD products,
Flash Memory Summit 2012
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Solutions Future NAND Flash-based Storage
Architecture
Raw Bit Error Rate
Noisy

• BCH codes
• Reed-Solomon codes
• LDPC codes
• Other Flash friendly codes

• Read voltage adjusting
• Data scrambler
• Data recovery
• Shadow program

Need to understand NAND Flash Error
Patterns/Channel Model
Need to design efficient DSP/ECC and smart error
management
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NAND Flash Channel Modeling
Write (Tx)
Read (Rx)
Noisy NAND
Simplified NAND Flash channel model based on
dominant errors
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Testing Platform
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Characterizing Cell Threshold w/ Read Retry
Erased State
Programmed States
cells
REF1
REF2
REF3
P1
P2
P3
Vth
i
i-1
i1
i-2
i2
0V
Read Retry

• Read-retry feature of new NAND flash
• Tune read reference voltage and check which Vth
  region of cells
• Characterize the threshold voltage distribution
  of flash cells in programmed states through
  Monte-Carlo emulation

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Programmed State Analysis
P3 State
P2 State
P1 State
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Parametric Distribution Learning

• Parametric distribution
• Closed-form formula, only a few number of
  parameters to be stored
• Exponential distribution family
• Maximum likelihood estimation (MLE) to learn
  parameters

Distribution parameter vector
Observed testing data
Likelihood Function
Goal of MLE Find distribution parameters to
maximize likelihood function
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Selected Distributions
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Distribution Exploration
P1 State
P2 State
P3 State
Beta Gamma Gaussian Log-normal Weibull
RMSE 19.5 20.3 22.1 24.8 28.6

• Distribution can be approx. modeled as Gaussian
  distribution

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Noise Analysis

• Signal and additive noise decoupling
• Power spectral density analysis of P/E noise
• Auto-correlation analysis of P/E noise

Flat in frequency domain
Approximately can be modeled as white noise
Spike at 0-lag point in time domain
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Independence Analysis over Space

• Correlations among cells in different locations
  are low (lt5)
• P/E operation can be modeled as memory-less
  channel
• Assuming ideal wear-leveling

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Independence Analysis over P/E cycles

• High correlation btw threshold in same location
  under P/E cycles
• Programming to same location modeled as channel
  w/ memory

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Cycling Noise Analysis

• As P/E cycles increase ...
• Distribution shifts to the right
• Distribution becomes wider

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Cycling Noise Modeling
Mean value (µ) increases with P/E cycles
Exponential model
Standard deviation value (s) increases with P/E
cycles
Linear model
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SNR Analysis

• SNR decreases linearly with P/E cycles
• Degrades at 0.13dB/1000 P/E cycles

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Conclusion Future Work

• P/E operations modeled as signal passing thru
  AWGN channel
• Approximately Gaussian with 22 distortion
• P/E noise is white noise
• P/E cycling noise affects threshold voltage
  distributions
• Distribution shifts to the right and widens
  around the mean value
• Statistics (mean/variance) can be modeled as
  exponential correlation with P/E cycles with 95
  accuracy
• Future work
• Characterization and models for retention noise
• Characterization and models for program
  interference noise

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Backup Slides
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Hard Data Decoding

• Read reference voltage can affect the raw bit
  error rate
• There exists an optimal read reference voltage
• Optimal read reference voltage is predictable
• Distribution sufficient statistics are
  predictable (e.g. mean, variance)

v0
v1
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Soft Data Decoding

• Estimate soft information for soft decoding (e.g.
  LDPC codes)
• Closed-form soft information for AWGN channel
• Assume same variance to show a simple case

log likelihood ratio (LLR)
Sensed threshold voltage range
High Confidence
High Confidence
Low Confidence
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Non-Parametric Distribution Learning

• Non-parametric distribution
• Histogram estimation
• Kernel density estimation
• Summary
• Pros Accurate model with good predictive
  performance
• Cons Too complex, too many parameters need to
  be stored

Kernel Function
Count the number of K of points falling within
the h region
Volume of a hypercube of side h in D dimensions
Smooth Gaussian Kernel Function
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Probability Density Function (PDF)
P1 State
P2 State
P3 State

• Probability density function (PDF) of NAND flash
  memory estimation using non-parametric kernel
  density methodology