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