Program Interference in
MLC NAND Flash Memory:
Characterization, Modeling, and Mitigation
Yu Cai1 Onur Mutlu1 Erich F. Haratsch2 Ken Mai1
Carnegie Mellon University
2 LSI Corporation
1
Flash Challenges: Reliability and Endurance
§  P/E cycles
(provided)
A few thousand
§  P/E cycles
(required)
Writing
the full capacity
of the drive
10 times per day
for 5 years
(STEC)
E. Grochowski et al., “Future technology challenges for NAND flash and HDD products”,
Flash Memory Summit 2012
> 50k P/E cycles
2
NAND Flash Memory is Increasingly Noisy
Write
Noisy NAND
Read
3
Future NAND Flash-based Storage Architecture
Noisy
Memory
Signal
Processing
Raw Bit
Error Rate
Lower
High
Error
Correction
Uncorrectable
BER < 10-15
Our Goals:
Model NAND Flash as a digital communication channel
Design efficient reliability mechanisms based on the model
4
NAND Flash Channel Model
Write
(Tx Information)
Noisy NAND
Read
(Rx Information)
Simplified NAND Flash channel model based on dominant errors
Write
Additive White
Gaussian Noise
§  Erase operation
§  Program page operation
Cell-to-Cell
Interference
§  Neighbor page
program
Cai et al., “Threshold voltage distribution in MLC NAND
Flash Memory: Characterization, Analysis, and Modeling”,
DATE 2013
?
Time Variant
Retention
Read
§  Retention
Cai et al., “Flash Correct-and-Refresh:
Retention-aware error management for
increased flash memory lifetime”, ICCD 2012
5
Outline
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n
n
n
Background on Program Interference
Characterization of Program Interference
Modeling and Predicting Program Interference
Mitigation of Program Interference
q
n
Read Reference Voltage Prediction
Conclusions
6
How Current Flash Cells are Programmed
n
Programming 2-bit MLC NAND flash memory in two steps
ER
(11)
ER
(11)
1
LSB
Program
Temp
(0x)
0
0
ER
(11)
Vth
0
1
P1
(10)
Vth
1
P2
(00)
P3
(01)
MSB
Program
Vth
7
Basics of Program Interference
(n+1,j-1) (n+1,j) (n+1,j+1)
WL<2>
∆Vxy ∆Vy ∆Vxy
MSB:6
WL<1>
Victim
Cell
MSB:4
∆Vx
∆Vx
(n,j)
WL<0>
∆Vxy ∆Vy ∆Vxy
(n-1,j-1)
n
LSB:3
LSB:1
MSB:2
LSB:0
(n-1,j) (n-1,j+1)
Traditional model of victim cell threshold voltage changes
when neighbor cells are programmed
ΔVvictim = (2C x ΔVx + C y ΔV y + 2C xy ΔVxy ) / Ctotal
8
Previous Work Summary
n
n
No previous work experimentally characterized and
modeled threshold voltage distributions under program
interference
Previous modeling work
q
q
q
q
Assumes linear correlation between the program interference
induced threshold voltage change of the victim cell and the
threshold voltage changes of the aggressor cells
Coupling capacitance and total capacitance of each flash cell
are the key coefficients of the model, which are process and
design dependent random variables
Their exact capacitance values are difficult to determine
Previously proposed model cannot be realistically applied in
flash controller
9
Outline
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n
n
n
Background on Program Interference
Characterization of Program Interference
Modeling and Predicting Program Interference
Mitigation of Program Interference
q
n
Read Reference Voltage Prediction
Conclusions
10
Characterization Hardware Platform
Cai et al., “FPGA-Based Solid-State Drive Prototyping Platform”, FCCM 2011
11
Characterization Studies
n
n
Bitline to bitline program interference
Wordline to wordline program interference
q
q
Program in page order
Program out of page order
12
Bitline to Bitline Program Interference
Victim Cell
P1 State
Wordline
( N+1 )
P2 State
P3 State
Wordline
(N)
Wordline
( N-1 )
L
X
R
L= { P0, P1, P2, P3 }
R= { P0, P1, P2, P3 }
n
n
Vth distributions of victim cells under 16 ( 4 x 4) different neighbor values
{L, R} almost overlap
Bitline to bitline program interferences are small
13
WL to WL Interference with In-Page-Order Programming
Wordline
( N+1 )
Wordline
(N)
Wordline
( N-1 )
Victim Word-line
n
n
Program interference increases the threshold voltage of victim cells and causes
threshold voltage distributions shift to the right and become wider
Program interference depends on the locations of aggressor cells in a block
q  Direct neighbor wordline program interference is the dominant source of
interference
q  Neighbor bitline and far-neighbor wordline interference are orders of magnitude
lower
14
WL to WL Interference with Out-of-Page-Order Programming
Wordline
( N+1 )
Wordline
(N)
Wordline
( N-1 )
Victim Word-line
n
The amount of program interference depends on the programming order of
pages in a block
q
q
In-page-order programming likely causes the least amount of interference
Out-of-page-order programming causes much more interference
15
Comparison under Various Program Interference
n
Signal-to-noise ratio comparison
Out-of-page-order Programming
16
Data Value Dependence of Program Interference
80
MSB Page programmed in aggressor cell
Victim <10>
Victim <00>
Victim <01>
Victim Vth Increase
60
40
20
0
aggressor <11> aggressor<10> aggressor<00> aggressor <01>
n
The amount of program interference depends on the values of both the
aggressor cells and the victim cells
17
Outline
n
n
n
n
Background on Program Interference
Characterization of Program Interference
Modeling and Predicting Program Interference
Mitigation of Program Interference
q
n
Read Reference Voltage Prediction
Conclusions
18
Linear Regression Model
n
Feature extraction for Vth changes based on characterization
q
q
n
Threshold voltage changes on aggressor cell
Original state of victim cell
Enhanced linear regression model
ΔVvictim (n, j ) =
j+K
∑
n=M
before
α
(
x
,
y
)
Δ
V
(
x
,
y
)
+
α
V
∑
neighbor
0 victim ( n, j )
y = j − K x =n +1
Y = Xα + ε
n
(vector expression)
Maximum likelihood estimation of the model coefficients
arg min( X × α − Y
α
2
2
+ λ α 1)
19
Model Coefficient Analysis
n
n
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n
Direct above cell dominance
Direct diagonal neighbor second
Far neighbor interference exists
Victim cell’s Vth has negative affect
20
Model Accuracy Evaluation
(x,y)=(measured before interference, measured after interference)
Ideal if no interference
With Systematic Deviation
(x,y)=(measured before interference, predicted with model)
Ideal if prediction is 100% accurate
Without Systematic Deviation
21
Distribution of Program Interference Noise
n
Program interference noise follows multi-modal Gaussian-mixture
distribution
22
Program Interference vs P/E Cycles
n
Program interference noise distribution does not change significantly
with P/E cycles
23
Outline
n
n
n
n
Background on Program Interference
Characterization of Program Interference
Modeling and Predicting Program Interference
Mitigation of Program Interference
q
n
Read Reference Voltage Prediction
Conclusions
24
Optimum Read Reference for Flash Memory
n
Read reference voltage can affect the raw bit error rate
f(x)
g(x)
f(x)
State-A
State-B
g(x)
State-A
State-B
Vth
v0
BER1 = ∫
+∞
vref
n
vref
Vth
v1
v0 v’ref v1
f ( x)dx + ∫
vref
−∞
g ( x)dx
BER 2 = ∫
+∞
v 'ref
f ( x)dx + ∫
v 'ref
−∞
g ( x)dx
There exists an optimal read reference voltage
q
Predictable if the statistics (i.e. mean, variance) of threshold
voltage distributions are characterized and modeled
25
Optimum Read Reference Voltage Prediction
n
Learning function (periodically, every ~1k P/E cycles)
q
q
n
Program known data pattern and test Vth
Program aggressor neighbor cells and test victim Vth after interference
Optimum read reference voltage prediction
q
Default read reference voltage + Program interference noise mean
Raw bit error rate
Evaluation Results
30% lifetime improvement
32k-bit BCH Code
(acceptable BER = 2x10-3)
No read reference voltage prediction
With read reference voltage prediction
n
Read reference voltage prediction can reduce raw BER and
increase the P/E cycle lifetime
Outline
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n
Background of Program Interference
Program Interference Characterization
Modeling and Predicting Program Interference
Read Reference Voltage Prediction to Mitigate Program
Interference
Conclusions
28
Key Findings and Contributions
n
n
Methodology: Extensive experimentation with real 2Y-nm
MLC NAND Flash chips
Amount of program interference is dependent on
q
q
q
n
n
Location of cells (programmed and victim)
Data values of cells (programmed and victim)
Programming order of pages
Our new model can predict the amount of program
interference with 96.8% prediction accuracy
Our new read reference voltage prediction technique can
improve flash lifetime by 30%
29
Program Interference in
MLC NAND Flash Memory:
Characterization, Modeling, and Mitigation
Yu Cai1 Onur Mutlu1 Erich F. Haratsch2 Ken Mai1
Carnegie Mellon University
2 LSI Corporation
1