1 Introduction
2 Background
2.1 Logic-in-memory structure
3 Hybrid MTJ/CMOS LIM-based logic gates
3.1 Selection and working of MTJ reading circuit
3.2 SHE+STT MTJ writing circuit for LIM structure
Input signals | Intermediate signals | MTJ status | ||||||
---|---|---|---|---|---|---|---|---|
EnW | EnSHE | Data | STTP | STTN | SHEP | SHEN | MTJ0 | MTJ1 |
0 | X | X | 1 | 0 | 1 | 0 | X | X |
1 | 1 | 1 | 1 | 1 | 0 | 1 | Metastable | |
1 | 0 | 1 | 1 | 1 | 0 | 0 | P | AP |
1 | 1 | 0 | 0 | 0 | 0 | 1 | Metastable | |
1 | 0 | 0 | 0 | 0 | 1 | 1 | AP | P |
3.3 Hybrid MTJ/CMOS LIM-based logic gates
Gate type | Inputs | LB resistance | RB resistance | Resistance | OUT | \(\overline{\text {OUT}}\) | |
---|---|---|---|---|---|---|---|
A | B | For I1(\(R_{LB}\)) | for I2 (\(R_{RB}\)) | Comparison | |||
NOR/OR | 0 | 0 | \(R_{ON}+R_{AP}\) | \(R_{ON}+R_P\) | \(R_{LB}>R_{RB}\) | 0 | 1 |
0 | 1 | \(R_{ON}+R_P\) | \(R_{ON}+R_{AP}\) | \(R_{LB}<R_{RB}\) | 1 | 0 | |
1 | 0 | \(R_{ON}+R_{AP}\) | \(R_{OFF}+R_P\) | \(R_{LB}<R_{RB}\) | 1 | 0 | |
1 | 1 | \(R_{ON}+R_P\) | \(R_{OFF}+R_{AP}\) | \(R_{LB}<R_{RB}\) | 1 | 0 | |
NAND/AND | 0 | 0 | \(R_{OFF}+R_{AP}\) | \(R_{ON}+R_P\) | \(R_{LB}>R_{RB}\) | 0 | 1 |
0 | 1 | \(R_{OFF}+R_P\) | \(R_{ON}+R_{AP}\) | \(R_{LB}>R_{RB}\) | 0 | 1 | |
1 | 0 | \(R_{ON}+R_{AP}\) | \(R_{ON}+R_P\) | \(R_{LB}>R_{RB}\) | 0 | 1 | |
1 | 1 | \(R_{ON}+R_P\) | \(R_{ON}+R_{AP}\) | \(R_{LB}<R_{RB}\) | 1 | 0 | |
XNOR/XOR | 0 | 0 | \(R_{ON}+R_{AP}\) | \(R_{ON}+R_P\) | \(R_{LB}>R_{RB}\) | 0 | 1 |
0 | 1 | \(R_{ON}+R_P\) | \(R_{ON}+R_{AP}\) | \(R_{LB}<R_{RB}\) | 1 | 0 | |
1 | 0 | \(R_{ON}+R_{P}\) | \(R_{ON}+R_{AP}\) | \(R_{LB}<R_{RB}\) | 1 | 0 | |
1 | 1 | \(R_{ON}+R_{AP}\) | \(R_{ON}+R_{P}\) | \(R_{LB}>R_{RB}\) | 0 | 1 |
4 Simulation results and discussion
4.1 Model verification of SHE-assisted STT MTJ model
Parameter | Description | Value |
---|---|---|
\(t_{sl}\) | Free layer thickness | 0.7 nm |
\(t_{ox}\) | MgO barrier thickness | 0.85 nm |
TMR | TMR ratio under zero bias voltage | 200\(\%\) |
Shape | MTJ Surface shape | Circle |
\(\mathrm {a}\) | MTJ Surface length | 32 nm |
\(\mathrm {b}\) | MTJ Surface width | 32 nm |
\(\mathrm {r}\) | MTJ Surface radius | 16 nm |
\(\mathrm {w}\) | Heavy-metal width | 40 nm |
\(\mathrm {d}\) | Heavy-metal thickness | 3 nm |
\(\mathrm {l}\) | Heavy-metal length | 60 nm |
\(\sigma _{TMR}\) | Standard deviation of TMR | 3% of TMR |
\(\sigma _{t_{sl}}\) | Standard deviation of \(t_{sl}\) | 3% of \(t_{sl}\) |
\(\sigma _{t_{ox}}\) | Standard deviation of \(t_{ox}\) | 3% of \(t_{ox}\) |
Particulars | SHE+STT | STT only | No. of devices | |
---|---|---|---|---|
Write 0 | 819.7f | 812.4f | 8MOS+2MTJ | |
Writing core | Write 1 | 819.3f | 812.3f | |
Energy/bit (J) | Redundant | |||
Write | 819.3f | 812.2f | ||
Averagex | 819.4f | 812.3f | ||
Write 0 | 3.23f | 817.9a | 38MOS | |
Control circuit | Write 1 | 2.74f | 986.9a | |
Energy/bit (J) | Redundant | |||
Write | 2.67f | 822.4a | ||
Averagey | 2.88f | 875.7a | ||
Totalx+y | 822.28fJ | 813.17fJ | 46MOS+2MTJ | |
Worst-case delay (ps) | 386.82 | 900 |
4.2 Performance analysis of hybrid MTJ/CMOS logic gates
Gate | HG1 | HG2 | DPTL-\(\text {C}^\text {2}\text {MOS}\) | HG1 | HG2 | DPTL-\(\text {C}^\text {2}\text {MOS}\) | HG1 | HG2 | DPTL-\(\text {C}^\text {2}\text {MOS}\) |
---|---|---|---|---|---|---|---|---|---|
type | NOR/OR | NOR/OR | NOR/OR | NAND/AND | NAND/AND | NAND/AND | XNOR/XOR | XNOR/XOR | XNOR/XOR |
Read | |||||||||
type | PCSA1 | PCSA2 | DPTL-\(\text {C}^\text {2}\text {MOS}\) | PCSA1 | PCSA2 | DPTL-\(\text {C}^\text {2}\text {MOS}\) | PCSA1 | PCSA2 | DPTL-\(\text {C}^\text {2}\text {MOS}\) |
Static | 0a | 0a | 231.8c | 0a | 0a | 240.2c | 0a | 0a | 264.6c |
Power (nW) | (321.15b) | (312.35b) | (274.6b) | (285.35b) | (324.4b) | (311.1b) | |||
Dynamic | |||||||||
Power (nW) | 234.8 | 113.4 | 334.7 | 219.5 | 98.53 | 291.8 | 303.2 | 141.8 | 373.5 |
Total | |||||||||
Power (nW) | 555.95d | 425.75d | 566.5d | 494.1d | 383.88d | 532 d | 627.6d | 452.9d | 638.1d |
Worst case | |||||||||
Delay (ps) | 91.55 | 89.3 | 72.96 | 70.35 | 67.52 | 74.03 | 75.48 | 74.74 | 74.04 |
PDP (aJ) | 50.89 | 38.01 | 41.33 | 34.75 | 25.91 | 39.38 | 47.37 | 33.84 | 47.24 |
Device | 12MOS | 11MOS | 19MOS | 12MOS | 11MOS | 19MOS | 13MOS | 12MOS | 22MOS |
Count | + 2MTJ | + 2MTJ | + 2MTJ | + 2MTJ | + 2MTJ | + 2 MTJ |
Gate type | N3 Width (nm) | 120 | 240 | 480 | 720 | 960 | 1200 |
---|---|---|---|---|---|---|---|
Power (nW) | 425.75 | 436.85 | 457.2 | 475.65 | 492.6 | 508.45 | |
NOR/OR | Delay (ps) | 89.3 | 83.37 | 80.05 | 78.64 | 77.97 | 77.58 |
Power (nW) | 383.88 | 397.85 | 422.8 | 444.55 | 464.1 | 482 | |
NAND/AND | Delay (ps) | 67.52 | 65.03 | 64.2 | 64 | 63.95 | 63.89 |
Power (nW) | 452.9 | 463.3 | 483 | 501.1 | 517.9 | 533.7 | |
XNOR/XOR | Delay (ps) | 74.74 | 67.42 | 63.23 | 61.68 | 60.98 | 60.62 |
Design type | Gate type | Min | Max | Mean | Median | SD |
---|---|---|---|---|---|---|
(nW) | (nW) | (nW) | (nW) | (nW) | ||
HG1 | NOR/OR | 515.25 | 596.55 | 554.35 | 554.65 | 13.63 |
NAND/AND | 456.6 | 529 | 493.05 | 493.8 | 12.13 | |
XNOR/XOR | 580.8 | 670.3 | 625.75 | 626.7 | 16.45 | |
HG2 | NOR/OR | 399.35 | 458.6 | 426.9 | 427.35 | 9.72 |
NAND/AND | 361 | 407.7 | 384.55 | 384.8 | 7.52 | |
XNOR/XOR | 422.3 | 496.9 | 455.3 | 454.8 | 13.33 | |
DPTL-\(\text {C}^\text {2}\text {MOS}\) | NOR/OR | 456.8 | 592.1 | 559.6 | 563.5 | 24.73 |
NAND/AND | 501.7 | 562.9 | 532 | 532.7 | 10.6 | |
XNOR/XOR | 598.9 | 768.1 | 640.3 | 635.2 | 27.42 |