3/20/2013 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 1.DSSC, ECE Department, Carnegie Mellon University 2.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 Memory Signal Processing Error Correction Raw Bit Error Rate BCH codes Reed-Solomon codes LDPC codes Other Flash friendly codes BER < 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 NAND Write (Tx) Read (Rx) Simplified NAND Flash channel model based on dominant errors  Erase operation  Program page operation  Neighbor page program  Retention Cell-to-Cell Interference Time-variant Retention Additive White Gaussian Noise Write Read

6 Testing Platform Virtex-5 FPGA (NAND Controllers) HAPS-52 Motherboard USB Board PCI-e Board Flash BoardFlash Chip

7 Characterizing Cell Threshold w/ Read Retry  Read-retry feature of new NAND flash  Tune read reference voltage and check which V th region of cells  Characterize the threshold voltage distribution of flash cells in programmed states through Monte-Carlo emulation V th 11 #cells REF1REF2REF3 0V Erased StateProgrammed States Read Retry P1P2P3 ii-1i+1i-2i+2 01  00

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 BetaGammaGaussianLog-normalWeibull RMSE19.5%20.3%22.1%24.8%28.6% P1 StateP2 StateP3 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

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) V th f(x) g(x) v0v0 v1v1 v ref V th f(x) g(x) v’ ref v0v0 v1v1

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 V th f(x) g(x) v0v0 v1v1 v ref log likelihood ratio (LLR) Sensed threshold voltage range Low Confidence High Confidence High Confidence

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 Gaussian Kernel Function

23 Probability Density Function (PDF)  Probability density function (PDF) of NAND flash memory estimation using non-parametric kernel density methodology P1 StateP2 StateP3 State