Constrained Flash Memory Programming - Semantic Scholar
Constrained Flash Memory Programming Amit Berman and Yitzhak Birk {bermanam@tx, birk@ee}.technion.ac.il
Technion – Israel Institute of Technology
International Symposium on Information Theory, August, 2011
Contributions • Characterization and formulation of Inter-Cell Interference in Flash Memory • Proposing constrained coding for ICI mitigation • Examples: Capacity and codes for “Breadth-First” and “Even-Odd” ICI channels
2
Flash Memory • Non-Volatile Solid-State Memory Device • Widely used in consumer and industrial electronics
3
Floating-Gate (FG) Cell • Conductive FG layer surrounded by dielectrics • Write: Inject charge from substrate to FG layer • Erase: Release charge from FG layer to substrate VERS
VPGM
Float
Float
-
-
-
-
-
-
-
VERS
Write 4
Erase
-
Vt Distributions • Stored data = amount of charge in FG •
The amount of charge determines Vt , the minimum gate voltage that causes the transistor to conduct
• Observed Vt is inaccurate • • •
Cell programming with limited resolution + …. Interference from other cells (~40 % and growing!) Result: must allocate a Vt range to each stored value Log2(#cells) 11
Vt Range 00
01
10
Safety margin
5
Vt
Inter-Cell Coupling • FG-FG inter-cell coupling causes the charge in one cell to affect a neighboring cell’s threshold voltage. BLi 1
BLi
BLi 1
FG
6
WL j 1
Nd
Ny
Nd
WL j
Nx
C
Nx
WL j 1
Nd
Ny
Nd
FG
CFGXY
FG
CFGY
CFGX FG
FG
FG
FG
FG
FG
Vt Distribution Widening • When considering each cell in isolation, the observed phenomenon is a “widening” of the threshold voltage distributions. Log2(#cells) 01
11
00
10
Width multiplied by up to 4x Vt Log2(#cells) 11
7
01
00
10
Vt
ICI experiment (program pulse) [Lee et-al.] • Neglecting CFGXY and assuming QFG=0, the floating gate voltage due to ICC is: VFG
CONOVCG CFGX V1 V2 CFGY V3 V4 VFGCG V5 V6 CTUN CONO 2CFGX 2CFGY 2CFGCG V3 FG
FG
CFGXY V1
CTUN, CONO are the FG dialectics cap., V5, V6 are gate voltages in neighbor vertical cells (do not appear in the Figure) 8
FG
CFGY V2
CFGX
FG
FG
FG
FG
FG
FG
V4
Insights
9
ICI with Program & Verify • Program & Verify: – Charge is added to a cell in small increments – Vt is checked after each addition – Programming ceases upon reaching the desired Vt • Therefore, Vt of any given cell is affected only by charge added to its neighbors after its own charging has been completed. The effect of inter-cell interference depends on the coupling, data and the programming scheme 10
Existing Interference-Mitigation Schemes • Proportional programming [Trinh et-al., USP 6,996,004] Concurrent, “proportional” programming of same-row cells near-simultaneous completion. Pros: insensitive to coupling parameters, simple read. Cons: complicated, possibly slow programming, can’t account for next line.
• Intelligent read decoding [Li et-al., USP 7,301,839] Based on programming order, decode w. successive interference cancellation. Pros: simple programming. Cons: Must know coupling parameters, no variation allowed, requires fine-resolution read complex and slow 11
Our Approach: Constrained Coding • Forbid certain adjacent-cell level combinations: – Criterion depends on programming order – Threshold is a design trade-off • Programming: use only permissible combinations (legal code words) • Decoding: use inverse mapping
12
Constrained Coding – Main Features • Pros: – Limits the effect of inter-cell coupling → narrow distributions → many levels or higher reliability – Fairly simply encoding and decoding – Only need to know an upper bound on coupling coefficients • Cons: – Code rate 1 cells programmed to level 2 • … • Sequence eligibility criterion:
NL, C, NR: respective target levels
WL j
D C max N L C,0 max N R C,0 T • T represents a trade-off: • Large T: efficient coding, but wider distributions and fewer levels • Small T: opposite pros and cons 17
BLi 1
BLi
BLi 1
NL
C
NR
Breadth 1st programming order - demonstration • {0,…,3} levels per cell
18
Breadth 1st” programming order - demonstration
19
Breadth 1st” programming order - demonstration Target values:
20
3
2
1
3
3
3
2
2
2
1
1
1
Breadth 1st” programming order - demonstration Target values:
21
3
2
1
Program pulse
3
3
3
• • •
2
2
2
1
1
1
Applied to all - Charge injection - Inter-Cell Interference
Breadth 1st” programming order - demonstration Target values:
22
3
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Non reached desired value
Breadth 1st” programming order - demonstration Target values:
23
3
2
1
Program pulse
3
3
3
• • • •
2
2
2
1
1
1
Applied to all - Charge injection - Inter-Cell Interference - Accounted-for ICI
Breadth 1st” programming order - demonstration Target values:
24
3
2
1
Verify
3
3
3
• Right cell reached target (no more program pulses for it)
2
2
2
1
1
1
Breadth 1st” programming order - demonstration Target values:
25
3
2
1
Program pulse
3
3
3
• • • • •
2
2
2
1
1
1
Applied left and center - Charge injection - Inter-Cell Interference - Accounted-for ICI - Post-programming ICI
Breadth 1st” programming order - demonstration Target values:
26
3
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Centered cell reached target
Breadth 1st” programming order - demonstration Target values:
27
3
2
1
Program pulse
3
3
3
• • • • •
2
2
2
1
1
1
Applied left and center - Charge injection - Inter-Cell Interference - Accounted-for ICI - ICI after verified
Breadth 1st” programming order - demonstration Target values:
28
3
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Non verified
Breadth 1st” programming order - demonstration Target values:
29
3
2
1
Program pulse
3
3
3
• • • • •
2
2
2
1
1
1
Applied to left cell - Charge injection - Inter-Cell Interference - Accounted-for ICI - ICI after verified
Breadth 1st” programming order - demonstration Target values:
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Left cell verified
Program Ends
30
3
Breadth 1st” programming order - demonstration Target values: Centered cell is erroneous
3
2
1
3
3
3
2
2
2
1
1
1
D C max N L C,0 max N R C,0 T 31
2) Set T and determine code rate
32
Example: T=2, L={0,1} two levels per cell • D(c)
Technion – Israel Institute of Technology
International Symposium on Information Theory, August, 2011
Contributions • Characterization and formulation of Inter-Cell Interference in Flash Memory • Proposing constrained coding for ICI mitigation • Examples: Capacity and codes for “Breadth-First” and “Even-Odd” ICI channels
2
Flash Memory • Non-Volatile Solid-State Memory Device • Widely used in consumer and industrial electronics
3
Floating-Gate (FG) Cell • Conductive FG layer surrounded by dielectrics • Write: Inject charge from substrate to FG layer • Erase: Release charge from FG layer to substrate VERS
VPGM
Float
Float
-
-
-
-
-
-
-
VERS
Write 4
Erase
-
Vt Distributions • Stored data = amount of charge in FG •
The amount of charge determines Vt , the minimum gate voltage that causes the transistor to conduct
• Observed Vt is inaccurate • • •
Cell programming with limited resolution + …. Interference from other cells (~40 % and growing!) Result: must allocate a Vt range to each stored value Log2(#cells) 11
Vt Range 00
01
10
Safety margin
5
Vt
Inter-Cell Coupling • FG-FG inter-cell coupling causes the charge in one cell to affect a neighboring cell’s threshold voltage. BLi 1
BLi
BLi 1
FG
6
WL j 1
Nd
Ny
Nd
WL j
Nx
C
Nx
WL j 1
Nd
Ny
Nd
FG
CFGXY
FG
CFGY
CFGX FG
FG
FG
FG
FG
FG
Vt Distribution Widening • When considering each cell in isolation, the observed phenomenon is a “widening” of the threshold voltage distributions. Log2(#cells) 01
11
00
10
Width multiplied by up to 4x Vt Log2(#cells) 11
7
01
00
10
Vt
ICI experiment (program pulse) [Lee et-al.] • Neglecting CFGXY and assuming QFG=0, the floating gate voltage due to ICC is: VFG
CONOVCG CFGX V1 V2 CFGY V3 V4 VFGCG V5 V6 CTUN CONO 2CFGX 2CFGY 2CFGCG V3 FG
FG
CFGXY V1
CTUN, CONO are the FG dialectics cap., V5, V6 are gate voltages in neighbor vertical cells (do not appear in the Figure) 8
FG
CFGY V2
CFGX
FG
FG
FG
FG
FG
FG
V4
Insights
9
ICI with Program & Verify • Program & Verify: – Charge is added to a cell in small increments – Vt is checked after each addition – Programming ceases upon reaching the desired Vt • Therefore, Vt of any given cell is affected only by charge added to its neighbors after its own charging has been completed. The effect of inter-cell interference depends on the coupling, data and the programming scheme 10
Existing Interference-Mitigation Schemes • Proportional programming [Trinh et-al., USP 6,996,004] Concurrent, “proportional” programming of same-row cells near-simultaneous completion. Pros: insensitive to coupling parameters, simple read. Cons: complicated, possibly slow programming, can’t account for next line.
• Intelligent read decoding [Li et-al., USP 7,301,839] Based on programming order, decode w. successive interference cancellation. Pros: simple programming. Cons: Must know coupling parameters, no variation allowed, requires fine-resolution read complex and slow 11
Our Approach: Constrained Coding • Forbid certain adjacent-cell level combinations: – Criterion depends on programming order – Threshold is a design trade-off • Programming: use only permissible combinations (legal code words) • Decoding: use inverse mapping
12
Constrained Coding – Main Features • Pros: – Limits the effect of inter-cell coupling → narrow distributions → many levels or higher reliability – Fairly simply encoding and decoding – Only need to know an upper bound on coupling coefficients • Cons: – Code rate 1 cells programmed to level 2 • … • Sequence eligibility criterion:
NL, C, NR: respective target levels
WL j
D C max N L C,0 max N R C,0 T • T represents a trade-off: • Large T: efficient coding, but wider distributions and fewer levels • Small T: opposite pros and cons 17
BLi 1
BLi
BLi 1
NL
C
NR
Breadth 1st programming order - demonstration • {0,…,3} levels per cell
18
Breadth 1st” programming order - demonstration
19
Breadth 1st” programming order - demonstration Target values:
20
3
2
1
3
3
3
2
2
2
1
1
1
Breadth 1st” programming order - demonstration Target values:
21
3
2
1
Program pulse
3
3
3
• • •
2
2
2
1
1
1
Applied to all - Charge injection - Inter-Cell Interference
Breadth 1st” programming order - demonstration Target values:
22
3
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Non reached desired value
Breadth 1st” programming order - demonstration Target values:
23
3
2
1
Program pulse
3
3
3
• • • •
2
2
2
1
1
1
Applied to all - Charge injection - Inter-Cell Interference - Accounted-for ICI
Breadth 1st” programming order - demonstration Target values:
24
3
2
1
Verify
3
3
3
• Right cell reached target (no more program pulses for it)
2
2
2
1
1
1
Breadth 1st” programming order - demonstration Target values:
25
3
2
1
Program pulse
3
3
3
• • • • •
2
2
2
1
1
1
Applied left and center - Charge injection - Inter-Cell Interference - Accounted-for ICI - Post-programming ICI
Breadth 1st” programming order - demonstration Target values:
26
3
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Centered cell reached target
Breadth 1st” programming order - demonstration Target values:
27
3
2
1
Program pulse
3
3
3
• • • • •
2
2
2
1
1
1
Applied left and center - Charge injection - Inter-Cell Interference - Accounted-for ICI - ICI after verified
Breadth 1st” programming order - demonstration Target values:
28
3
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Non verified
Breadth 1st” programming order - demonstration Target values:
29
3
2
1
Program pulse
3
3
3
• • • • •
2
2
2
1
1
1
Applied to left cell - Charge injection - Inter-Cell Interference - Accounted-for ICI - ICI after verified
Breadth 1st” programming order - demonstration Target values:
2
1
Verify
3
3
3
•
2
2
2
1
1
1
Left cell verified
Program Ends
30
3
Breadth 1st” programming order - demonstration Target values: Centered cell is erroneous
3
2
1
3
3
3
2
2
2
1
1
1
D C max N L C,0 max N R C,0 T 31
2) Set T and determine code rate
32
Example: T=2, L={0,1} two levels per cell • D(c)
