SPICE Modeling of STT-RAM for Resilient Design. Zihan Xu, Ketul Sutaria, Chengen Yang, Chaitali Chakrabarti, Yu (Kevin) Cao School of ECEE, ASU

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1 SPICE odeling of STT-RA for Resilient Design Zihan Xu, Ketul Sutaria, Chengen Yang, Chaitali Chakrabarti, Yu (Kevin) Cao School of ECEE, ASU

2 OUTLINE Heterogeneous emory Design A Promising Candidate: STT-RA Fundamentals of STT-RA Previous approaches Hierarchical odeling Solution SPICE odel of STT-RA Equivalent Circuit odel Device Parameter odel STT-RA Single Cell Simulation Summary and Future Work

3 Trend of Technology Scaling Bulk/SOI OSFET Strained OSFET HKG OSFET G OSFET SRA Flash PC STT DRA FRA RRA Tremendous variety in memory physics, materials, structures, and devices! - 3 -

4 Read + Write Time Tremendous Diversity Performance STT-RA Advantages: Access time comparable to SRA Density comparable to DRA Low standby power High endurance (>10 16 ) STT-RA Cell Size (F 2 ) [R. Venkatesan, ISLPED 2012] Scalable to lower technology nodes Can be used for logic design - 4 -

5 STT-RA Fundamental emory Cell agnetic Tunnel Junction Bit Line TJ Word Line Source Line Parallel Low R => bit 0 Anti-Parallel High R => bit 1 agnetic Tunnel Junction (TJ) consists of thin insulating layer (Dielectric-gO) about ~1nm thick, sandwiched between two layers of ferromagnetic material. agnetization of one layer is fixed while that of other layer is free. Direction of magnetization angle in free layer governs the resistance of TJ. Resistance is translated to logical value of the data that is stored. Parallel state corresponds to bit 0 being stored and anti-parallel state corresponds to bit

6 LLG Equation d dt H d ( u ) ( u 0 2 ea ea s dt s K ) Zeeman (external) Zeeman energy tends to align the magnetization field with the applied field. Damping energy is the energy loss of the precession of magnetization. Anisotropic energy is responsible for self-alignment of magnetization along easy axis. u ea Damping (internal) γ rad s 1 T 1 gyromagnetic ratio μ 0 = 4π 10 7 N A 2 permeability constant K is anisotropy constant dependent on material Anisotropic (internal)

7 Numerical ethod Numerically solve 3D LLG equation Capture both static and transient behavior of magnetization Difficult implementation and low efficiency [J. B. Kammerer, TED 2010] - 7 -

8 acro odel Based on calculated switching (threshold) current J C0 = αγe st FL μ B g H ext ± H ani ± H d 2 J C = J C0 1 k BT E ln τ τ 0 Capture the relation of switching current amplitude and pulse width Cannot capture transient behavior and variation issues [J. D. Harms, TED 2010] - 8 -

9 Hierarchical emory odel ulti-level modeling for design analysis, optimization and path-finding / inverse path-finding Behavioral Structural/ Circuit Device Finite State achine Equivalent Circuit Compact odel (nominal) Process/ aterials Variations Temporal Shift - 9 -

10 SPICE odel cos sin sin 0 K dt d H dt d s s s ) ( ) ( 2 0 ea ea s s u u K dt d H dt d 3D 1D θ Equivalent Circuit

11 Equivalent Circuit odel 0 s H sin 180 θ (Degrees) 90 K sin cos 0 I decreasing 10.0n 15.0n 20.0n 25.0n Be able to simulate transient behavior Time (s) Easy implementation with SPICE components and Verilog-A models Differential equation is solved by SPICE simulator reducing computation time

12 Saturation agnetization ( s ) dθ s dt = γ μ dθ 0 s H sin θ + α s dt aterial and geometry dependent s D = S b 1 exp 3 s0 2D ch 1 3R 2D ch 1 D: diameter of TJ layer s0 : s of bulk ferromagnetic material c: a constant (0<c 1) depends on the interface h: atomic diameter S b : bulk solid-vapour transition entropy + γ K sin θ cos θ R: ideal gas constant [H.. Lu, J. Phys. D 2007]

13 agnetic Field (H) dθ s dt = γ μ dθ 0 s H sin θ + α s dt H = H ex + H 0 H ex is the external magnetic field generated by input current H 0 captures the asymmetric switching threshold + γ K sin θ cos θ H ex Ir 2r I 2r 2 0 r r r r 0 0 Ιr 2 2πr 0 Ι 2πr

14 agnetic Angle to Resistance (Degrees) R () R R P R AP n 15.0n 20.0n 25.0n Time (s) R = R P [ TR(1 cos θ)] R P = t ox F φa exp 1.025t ox φ [J. C. Slonczewski, Phys. Rev. B 2005, Y. Zhang, TED 2012] As θ approaches 180 o, R = R AP t ox Oxide thickness 0.85 nm F aterial parameter φ Potential barrier 0.4 ev A Area 3318 nm

15 Resistance () Voltage Dependence of TR Tunnel agnetoresistance (TR) is the resistance difference ratio of TJ of the two states. TR = R AP R P R P TR depends on the voltage across the TJ. TR TR V Vh 5000 SPICE odel acro odel [Y. Zhang, TED 2012] TR 0 is the TR ratio with 0 voltage. V h is the voltage as TR = 0.5 TR Voltage (mv)

16 odel Summary Equivalent Circuit: 0 s H sin K sin cos θ dθ s dt = γ μ dθ 0 s H sin θ + α s + γ K sin θ cos θ dt Device odels and Parameter Values (65nm) : s D = S b 1 exp 3 s0 2D ch 1 3R 2D ch 1 H 2 Ιr πr 2 0 H 0 R = R P [ TR(1 cos θ)] s0 D 4.94x10 5 A/m 65 nm c 1 h 0.24 nm S b /R 13 r 0 H nm 49 A/m TR TR V h R P TR V Vh 0.5 V 1.2 kω

17 Resistance () Resistance () Geometry Dependence t ox = 0.85nm, 1nm, 1.15nm 1500 r = 30nm, 32.5nm, 35nm Time (ns) Time (ns) This model captures the transition behavior under process variation

18 Temperature Dependence Resistance sin (λt) R T = R(0) λt R(0) is the resistance at T=0K λ = πt oxk ћ 2m e e t ox is oxide thickness, k is Boltzmann constant, ћ is reduced plank constant, m e is electron mass. [. El Baraji, J. Appl. Phys. 2009] agnetic field Thermal fluctuating field H fluc [Y. Zhang, ICCAD 2011]

19 Finite Element ethod agnetic field being function of radius r, the field is nonuniform across TJ causing different switching of magnetization angle. Finite element method helps to capture the non-uniform distribution of magnetic field

20 Resistance () Finite Element Simulations 2500 Simulation time Elements 1.72 s 8 Elements 4.01 s Finite Elements Time (ns) 8 Finite Elements Time (ns) For accurate and fast simulation, we choose 8 elements in the simulation. Increasing number of finite element for simulation increases simulation time with marginal improvement in accuracy

21 Normalized Resistance odel Validation µ µ µ µ 400.0µ 600.0µ Current (A) [Z. Diao, J. Phys. 2007] Hysteresis effect predicted by model validated by experimental data for two different TJs

22 Simulation Setup Bit Line 0 s H sin θ Word Line K sin cos Source Line 8X Finite Elements Read operation: current lower than critical value is applied to TJ to determine its resistance state. During write operation, BL and SL are charged to opposite values depending on bit value that is to be stored. For write-0, BL=V dd, SL=0V; write-1, BL=0V and SL=V dd

23 Simulation Results Evaluation of STT-RA performance with proposed model using 10ns pulse. Write energy for single cell 0 -> pj 1 -> pj Based on the proposed SPICE model, cell level parameters such as resistance, current and geometry dependent variables can be obtained. Using above parameters, a system level memory simulator (CACTI) evaluates memory access time, cycle time, area, leakage, and dynamic power for entire architecture

24 Summary and Future Work SPICE model of STT-RA Hierarchical modeling approach Equivalent circuit model Geometry dependence of model parameters Next step: Validation with silicon data Variability and reliability effects Implementation into multi-level memory design tools Adaptive design techniques: R/W, ECC, etc. Integration of heterogeneous memory devices