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Threshold Voltage Distribution in MLC NAND Flash: Characterization, Analysis, and Modeling. Yu Cai 1 , Erich F. Haratsch 2 , Onur Mutlu 1 , and Ken Mai 1. DSSC, ECE Department, Carnegie Mellon University LSI Corporation. Evolution of NAND Flash Memory. Aggressive scaling MLC technology. - PowerPoint PPT Presentation
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3/20/2013
Threshold Voltage Distribution in MLC NAND Flash: Characterization, Analysis, and Modeling
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 University2. LSI Corporation
2
Evolution of NAND Flash Memory
E. Grochowski et al., “Future technology challenges for NAND flash and HDD products”, Flash Memory Summit 2012
Aggressive scaling MLC technology
Increasing capacity
Acceptable low cost
High speed
Low power consumption
Compact physical size
3
Challenges: Reliability and Endurance
E. Grochowski et al., “Future technology challenges for NAND flash and HDD products”, Flash Memory Summit 2012
P/E cycles (provided)
P/E cycles (required)
A few thousand
Complete write of drive 10 times per day for 5 years(STEC)
> 50k P/E cycles
4
Solutions: Future NAND Flash-based Storage Architecture
MemorySignal
Processing
ErrorCorrection
Raw Bit Error Rate
• BCH codes • Reed-Solomon codes• LDPC codes• Other Flash friendly codes
BER < 10-15
Need to understand NAND Flash Error Patterns/Channel Model
• Read voltage adjusting• Data scrambler• Data recovery• Shadow program
Noisy
Need to design efficient DSP/ECC and smart error management
5
NAND Flash Channel Modeling
Noisy NANDWrite(Tx)
Read(Rx)
Simplified NAND Flash channel model based on dominant errors
Erase operation Program page operation
Neighbor page program Retention
Cell-to-CellInterference
Time-variantRetention
Additive WhiteGaussian Noise
Write Read
6
Testing Platform
Virtex-5 FPGA(NAND Controllers)
HAPS-52 Motherboard
USB Board
PCI-e Board
Flash Board Flash Chip
7
Characterizing Cell Threshold w/ 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
Vth11
#cells
10 00 01
REF1 REF2 REF3
0V
Erased State Programmed States
Read Retry
P1 P2 P3
ii-1 i+1i-2 i+2
0100
8
Programmed State Analysis
P3 State
P2 State
P1 State
9
Parametric distribution Closed-form formula, only a few number of parameters to be stored
Exponential distribution family
Maximum likelihood estimation (MLE) to learn parameters
Parametric Distribution Learning
Distribution parameter vector
Likelihood Function
Observed testing data
Goal of MLE: Find distribution parameters to maximize likelihood function
10
Selected Distributions
11
Distribution Exploration
Distribution can be approx. modeled as Gaussian distribution
Beta Gamma Gaussian Log-normal Weibull
RMSE 19.5% 20.3% 22.1% 24.8% 28.6%
P1 State P2 State P3 State
12
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
Spike at 0-lag point in time domain
Approximately can be modeled as white noise
13
Independence Analysis over Space
Correlations among cells in different locations are low (<5%) P/E operation can be modeled as memory-less channel
Assuming ideal wear-leveling
14
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
15
Cycling Noise Analysis
As P/E cycles increase ...Distribution shifts to the right Distribution becomes wider
P1 State P2 State P3 State
16
Cycling Noise Modeling
Mean value (µ) increases with P/E cycles
Standard deviation value (σ) increases with P/E cycles
Exponential model
Linear model
17
SNR Analysis
SNR decreases linearly with P/E cycles Degrades at ~ 0.13dB/1000 P/E cycles
18
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
19
Backup Slides
20
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)
Vth
f(x) g(x)
v0 v1vref
ref
ref
v
vdxxgdxxfBER )()(1
ref
ref
v
vdxxgdxxfBER
'
')()(2
Vth
f(x) g(x)
v’refv0 v1
21
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
Vth
f(x) g(x)
v0 v1vref
))|0(
)|1(log()(
yxp
yxpyLLR
log likelihood ratio(LLR)
Sensed threshold voltage range
Low Confidence
HighConfidence
HighConfidence
22
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
Non-Parametric Distribution Learning
Count the number of K of points falling within the h region
Volume of a hypercube of side h in D dimensions
Kernel Function
Smooth GaussianKernel Function
23
Probability Density Function (PDF)
Probability density function (PDF) of NAND flash memory estimation using non-parametric kernel density methodology
P1 State P2 State P3 State