STT-RAM Circuit Design
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Transcript of STT-RAM Circuit Design
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STT-RAM Circuit Design
MTJ Specs (Update),MTJ Sharing
I-STT MTJ Specs (Jianping)
UPDATED SPECS– RP ≈ 744Ω
– TMR ≈ 136%– AP→P:
● 630μA Max (breakdown current)● 387μA for 3ns switching● 330μA for 5ns switching
– P→AP:● 1.5mA Max (breakdown current)● Need more device measurements
– IWRITE(P→AP)/IWRITE(AP→P): 1.5-2
– 1ns read pulse (P→AP) with 1% chance of write: 220μA● AP→P might be better
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Maximum Write Currents (Thick Oxide)
Thin Oxide: 1.25nm– Max VDD = 1.0V
– LMIN = 50nm
Medium Oxide: 2.2nm– Max VDD = 1.5V
– LMIN = 100nm
– Per μm width: IMAX,MEDIUM/IMAX,LVT = 93%
Thick Oxide: 5.2nm– Max VDD = 3.3V
– LMIN = 230nm
– Per μm width: IMAX,THICK/IMAX,LVT = 73%3
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MTJ Sharing
TMR Degradation(Reading)
TMR Degradation
Parallel Resistance (R||)
degrades TMR
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MTJ1,1
WL<1>
MTJ1,2
MTJ1,M
SL
BL<1>
BL<2>
BL<M>
MTJ2,1
WL<2>
MTJ2,2
MTJ2,M
MTJN,1
WL<N>
MTJN,2
MTJN,M
Parasitic Parallel Resistance
||
1, all P
1 1
11 , all AP
1 1
P
P
N MR
N MR
N MTMR R
N M
Effective RP and RAP
Worst case TMR’: largest RP’ and smallest RAP’
Largest RP’:
Smallest RAP’
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||
1 1' || || 1 1
1 1 1P P P P P
N M N MR R R R TMR R TMR R
N M NM N M TMR
||
1 1' || 1 || 1
1 1 1 1AP AP P P P
N M N MR R R TMR R R TMR R
N M NM N M TMR
Effective TMR
Putting it all together:
Example 1kbit Arrays: TMR = 120%, M = 2, N = 16, 32-bit words: TMR’ = 4.8% TMR = 120%, M = 2, N = 8, 64-bit words: TMR’ = 9.8% TMR = 120%, M = 2, N = 4, 128-bit words: TMR’ =
20.7%7
' ''
'
1 11 1
1 1 11
11
2 1
1 1
AP P
P
P P
P
R RTMR
R
N M N MTMR R TMR R
NM N M TMR NM N M TMRN M
TMR RNM N M TMR
N M NMTMR
NM N M TMR
Monte Carlo Simulations (M = 2, 3)
ERROR IN MATLAB CODE used to generate last week’s Monte Carlo plots → Not simulating the intended cases!– Fixed and reran simulations → results not so good
Ran multiple simulations with and w/o random variations in RP and TMR (based on worst case from Jianping)
– Extracted worst case TMR’ and TMR’ for 10% read error
For 128-bit words, with bit read error = 10.0%:– # error correcting bits = 36 (1/5 word)
● Probability of a word error: 1 in 6,788 reads
– # error correcting bits = 32 (1/4 word)● Probability of a word error: 1 in 3.59x106 reads
– # error correcting bits = 43 (1/3 word)● Probability of a word error: 1 in 13.2x1012 reads 8
TMR’ vs. N for 1T-2MTJ (M = 2)
9
2 4 6 8 10 12 14 160
10
20
30
40
50
60
70T
MR
[%
]
N
TMR = 50%TMR = 100%TMR = 150%TMR = 200%
Monte Carlo Simulations: M = 2, N = 4
TMR = 120% RP = 500Ω 25k Simulations TMR’
– Worst Case = 20.7%– ~10% Read Error = 30.0%
TMR = 120%, 3σ = ±12% RP = 500Ω, 3σ = ±50Ω 25k Simulations TMR’
– Worst Case = 3.7%– ~10% Read Error = 25.4%
10
200 300 400 500 600 700 8000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Resistance [ ]
PR
OB
RP
RAP
200 300 400 500 600 700 8000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Resistance [ ]
PR
OB
RP
RAP
Monte Carlo Simulations: M = 2, N = 8
TMR = 120% RP = 500Ω 25k Simulations TMR’
– Worst Case = 9.8%– ~10% Read Error = 14.6%
TMR = 120%, 3σ = ±12% RP = 500Ω, 3σ = ±50Ω 25k Simulations TMR’
– Worst Case = -4.1%– ~10% Read Error =
12.4%
11
200 250 300 350 400 450 500 550 600 650 7000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Resistance [ ]
PR
OB
RP
RAP
200 250 300 350 400 450 500 550 600 650 7000
0.02
0.04
0.06
0.08
0.1
0.12
Resistance [ ]
PR
OB
RP
RAP
Monte Carlo Simulations: M = 2, N = 16
TMR = 120% RP = 500Ω 25k Simulations TMR’
– Worst Case = 5.1%– ~10% Read Error =
8.5%
TMR = 120%, 3σ = ±12% RP = 500Ω, 3σ = ±50Ω 25k Simulations TMR’
– Worst Case = -10.3%– ~10% Read Error =
4.7%12
200 250 300 350 400 450 500 550 600 650 7000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Resistance [ ]
PR
OB
RP
RAP
200 250 300 350 400 450 500 550 600 650 7000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Resistance [ ]
PR
OB
RP
RAP
TMR’ vs. N for 1T-3MTJ (M = 3)
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2 4 6 8 10 12 14 16-30
-20
-10
0
10
20
30
40T
MR
[%
]
N
TMR = 50%TMR = 100%TMR = 150%TMR = 200%
Monte Carlo Simulations: M = 3, N = 4
TMR = 120% RP = 500Ω 25k Simulations TMR’
– Worst Case = 0.0%– ~10% Read Error =
15.6%
TMR = 120%, 3σ = ±12% RP = 500Ω, 3σ = ±50Ω 25k Simulations TMR’
– Worst Case = -10.1%– ~10% Read Error =
15.9%
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200 250 300 350 400 450 500 550 6000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Resistance [ ]
PR
OB
RP
RAP
200 250 300 350 400 450 500 550 6000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Resistance [ ]
PR
OB
RP
RAP
Monte Carlo Simulations: M = 3, N = 8
TMR = 120% RP = 500Ω 25k Simulations TMR’
– Worst Case = -11.2%– ~10% Read Error = -0.6%
TMR = 120%, 3σ = ±12% RP = 500Ω, 3σ = ±50Ω 25k Simulations TMR’
– Worst Case = -16.7%– ~10% Read Error = -
1.0%
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200 250 300 350 400 450 5000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Resistance [ ]
PR
OB
RP
RAP
200 250 300 350 400 450 5000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Resistance [ ]
PR
OB
RP
RAP
Monte Carlo Simulations: M = 3, N = 16
TMR = 120% RP = 500Ω 25k Simulations TMR’
– Worst Case = -15.9%– ~10% Read Error = -11.2%
TMR = 120%, 3σ = ±12% RP = 500Ω, 3σ = ±50Ω 25k Simulations TMR’
– Worst Case = -23.4%– ~10% Read Error = -11.4%
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100 150 200 250 300 350 400 450 5000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Resistance [ ]
PR
OB
RP
RAP
100 150 200 250 300 350 400 450 5000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Resistance [ ]
PR
OB
RP
RAP
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MTJ Sharing
Device IREAD/IWRITE Requirements(Writing)
Defining IREAD,MAX & IWRITE,MIN
IREAD,MAX: The maximum read current such that the probability of flipping the MTJ is less than some ε (i.e. ε = 0.1% → IREAD,MAX = 200μA)
IWRITE,MIN: The minimum write current such that the probability of failing to flip the MTJ is less than some ξ (i.e. ξ = 0.1% → IWRITE,MIN = 600μA)
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
PR
OB
(WR
ITE
)
IWRITE
,READ AP P MAXI
,WRITE AP P MINI
,READ P AP MAXI
,WRITE P AP MINI
IREAD/IWRITE for 1T-2MTJ & 1T-3MTJ
Example: 1T-2MTJ architecture
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WL<1> WL<2>
BL<1>
BL<2>
IWRITE,MIN
α∙IREAD,MAX
, ,
, ,
READ P AP MAX WRITE P AP MIN
READ AP P MAX WRITE AP P MIN
I I
I I
IREAD/IWRITE for 1T-2MTJ
RP Case 1: RAP Case 1:
RP Case 2: RAP Case 2:
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“1” “0”RP RP
RP RP
“1” “0”RAP RP
RAP RP
“1” “0”RAP RAP
RAP RP
“1” “0”RP RP
RP RAP
, , ,
,
,
2
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P P PWRITE MIN P AP READ MAX P AP READ MAX P AP
READ MAX P AP
WRITE MIN P AP
R I R I R I
I
I
, , , ,
, , , ,
,
,
1
1
11
1
P WRITE MIN P AP P READ MAX P AP P READ MAX P AP P READ MAX AP P
P WRITE MIN P AP P READ MAX P AP P READ MAX P AP P READ MAX P AP
READ MAX P AP
WRITE MIN P AP
R I R I R I R TMR I
TMRR I R I R I R I
I
I TMR
, , , ,
, , , ,
,
,
1 1 1
1 1 1
1
1
P WRITE MIN AP P P READ MAX AP P P READ MAX P AP P READ MAX AP P
P WRITE MIN AP P P READ MAX AP P P READ MAX AP P P READ MAX AP P
READ MAX P AP
WRITE MIN P AP
R TMR I R TMR I R I R TMR I
R TMR I R TMR I R I R TMR I
I
I
1
TMR
, , ,
, , ,
,
,
1 1 2
1 1 2
1
21
P WRITE MIN AP P P READ MAX AP P P READ MAX P AP
P WRITE MIN AP P P READ MAX AP P P READ MAX AP P
READ MAX P AP
WRITE MIN P AP
R TMR I R TMR I R I
R TMR I R TMR I R I
I
ITMR
IREAD/IWRITE vs. TMR for 1T-2MTJ
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0 50 100 150 200 2500.25
0.3
0.35
0.4
0.45
0.5
0.55
I RE
AD/I W
RIT
E
TMR [%]
= 1.5 (P AP) = 1.5 (AP P) = 2.0 (P AP) = 2.0 (AP P)
IREAD/IWRITE for 1T-3MTJ
RP Case 1: RAP Case 1:
RP Case 2: RAP Case 1:
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, , ,
,
,
1.5
11.5
P P PWRITE MIN P AP READ MAX P AP READ MAX P AP
READ MAX P AP
WRITE MIN P AP
R I R I R I
I
I
, , , ,
, , , ,
,
,
11
2
1 1
2
1111
2
P WRITE MIN P AP P READ MAX P AP P READ MAX P AP P READ MAX AP P
P WRITE MIN P AP P READ MAX P AP P READ MAX P AP P READ MAX P AP
READ MAX P AP
WRITE MIN P AP
R I R I R I R TMR I
TMRR I R I R I R I
I
I TMR
, , , ,
, , , ,
,
,
11 1 1
2
11 1 1
2
P WRITE MIN AP P P READ MAX AP P P READ MAX P AP P READ MAX AP P
P WRITE MIN AP P P READ MAX AP P P READ MAX AP P P READ MAX AP P
READ MAX P AP
WRITE MIN P AP
R TMR I R TMR I R I R TMR I
R TMR I R TMR I R I R TMR I
I
I
10.5
11 TMR
, , ,
, , ,
,
,
1 1 1.5
1 1 1.5
1
1.51
P WRITE MIN AP P P READ MAX AP P P READ MAX P AP
P WRITE MIN AP P P READ MAX AP P P READ MAX AP P
READ MAX P AP
WRITE MIN P AP
R TMR I R TMR I R I
R TMR I R TMR I R I
I
ITMR
“1” “0”RP RP
RP RP RP
“1” “0”RP RP
RP RAP RAP
“1” “0”RAP RP
RAP RP RP
“1” “0”RAP RAP
RAP RP RP
IREAD/IWRITE vs. TMR for 1T-3MTJ
23
0 50 100 150 200 2500.25
0.3
0.35
0.4
0.45
0.5
0.55
I RE
AD/I W
RIT
E
TMR [%]
= 1.5 (P AP) = 1.5 (AP P) = 2.0 (P AP) = 2.0 (AP P)
SUMMARY
TMR Degradation (READING)– M = 2:
● Not as good as previously thought● Read circuit need to work for 25-30% TMR
– 10-12% for more wordlines
– M = 3: not really possible (negative TMR)
IREAD/IWRITE (WRITING)
– For TMR = 120%, χ = 1.5-2:● M = 2: IREAD/IWRITE > 0.36-0.43
● M = 3: IREAD/IWRITE > 0.42-0.49
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