Spin-Transfer Torque Magnetic Random Access Memory (STT-MRAM)

1. Theory

Definition: STT-MRAM stores a bit in a magnetic tunnel junction (MTJ) and writes it with a spin-polarized current passed through the junction.
MTJ structure: A fixed reference layer and a switchable free layer (typically CoFeB) separated by a thin MgO tunnel barrier.
Tunnel magnetoresistance (TMR): The parallel state has low resistance $R_{P}$ and the antiparallel state high resistance $R_{A P} = R_{P} (1 + T M R)$ .
Coherent MgO tunnelling: Symmetry filtering of $Δ_{1}$ states in crystalline MgO gives TMR of several hundred percent, far above the Julliere estimate.
Spin-transfer torque: Spin-polarized electrons transfer angular momentum to the free layer (the Slonczewski term of the LLGS equation).
Perpendicular anisotropy: CoFeB/MgO interfacial anisotropy makes the free layer magnetized out of plane, lowering switching current and allowing round cells.
Thermal stability factor: $Δ = K_{e f f} V / k_{B} T$ (typically about 60 for 10-year retention).

2. Working Principle

Write: A current above the critical current $I_{c 0} \propto (α / η) E_{b}$ switches the free layer; current direction selects parallel or antiparallel.
Stability vs write current: Both scale with the energy barrier, so keeping $Δ$ while lowering $I_{c 0}$ needs lower damping $α$ or higher spin efficiency $η$ .
Thermally activated regime: Pulses longer than about 10 ns switch with help from thermal fluctuations, so the needed current falls slowly with pulse length.
Precessional regime: Nanosecond pulses need currents well above $I_{c 0}$ , with switching time $\propto 1/ (I / I_{c 0} - 1)$ .
Read: A small current senses $Δ V = I_{r} R_{P} T M R$ ; TMR falls with bias, and the read current must stay well below $I_{c 0}$ to avoid read disturb.
Shared read and write path: The same junction carries both currents, so MgO breakdown limits write amplitude.

3. Applications

Embedded non-volatile memory at advanced nodes: Replaces embedded flash in microcontrollers and IoT SoCs at 28–22 nm and below.
Persistent write buffers: Standalone STT-MRAM for SSD and storage-controller caches that must survive power loss.
Last-level cache (emerging): Dense, non-volatile alternative to SRAM for low-standby-power caches.

Name	Formula	Related Formulae	Variables/Constants
Tunnelling magnetoresistance (TMR)	$T M R = \frac{R _{A P} - R _{P}}{R _{P}} = \frac{G _{P} - G _{A P}}{G _{A P}}$	$T M R_{J} = \frac{2 P _{1} P _{2}}{1 - P _{1} P _{2}}$ $T M R^{'} = \frac{R _{A P} - R _{P}}{R _{A P}} = \frac{2 P _{1} P _{2}}{1 + P _{1} P _{2}}$	$T M R : r a t i o o f t h e r es i s t an ce c han g e t o t h e l o w r es i s t an ce, b e tw ee n t h e an t i p a r a l l e l an d p a r a l l e l s t a t es o f t h e ma g n e t i c t u nn e l j u n c t i o n$ $R_{P}, R_{A P} : r es i s t an ce o f t h e j u n c t i o n w i t h p a r a l l e l an d an t i p a r a l l e l ma g n e t i z a t i o n s o f t h e tw o f er r o ma g n e t i c l a y er s$ $G_{P}, G_{A P} : t h e cor r es p o n d in g co n d u c t an ces$ $T M R_{J} : t h e v a l u e g i v e n b y t h e J u l l i er e m o d e l (s p in - p o l a r i z e d t u nn e l l in g w i t h s p in co n ser v e d)$ $P_{1}, P_{2} : s p in p o l a r i z a t i o n s o f t h e tw o f er r o ma g n e t i c e l ec t r o d es$ $T M R^{'} : t h e s am e r a t i o n or ma l i z e d t o R_{A P} (u se d in so m e p a p er s, an d n e v er g r e a t er t han 100%, T M R^{'} = T M R / (1 + T M R))$ $(J u l l i er e m o d e l : M . J u l l i er e, P h y s . L e tt . A 54, 225 (1975); t h e p o l a r i z a t i o n s a r e t r e a t e d a s co n s t an t s o f t h e e l ec t r o d es)$
Conductance against the angle between the magnetizations	$G (θ) = G_{0} (1 + P_{e f f}^{2} cos θ)$	$G (θ) = \frac{G _{P} + G _{A P}}{2} + \frac{G _{P} - G _{A P}}{2} cos θ$	$G (θ) : co n d u c t an ce o f t h e j u n c t i o n w h e n t h e ma g n e t i z a t i o n s o f t h e tw o l a y er s mak e an an g l e θ$ $G_{0} : a v er a g e co n d u c t an ce$ $P_{e f f} : e f f ec t i v e s p in p o l a r i z a t i o n o f t h e t u nn e l l in g (S l o n cz e w s k i m o d e l)$ $G_{P}, G_{A P} : co n d u c t an ces a t θ = 0 an d θ = π$ $(t h e seco n d f or m f o l l o w s f r o m t h e f i r s t w i t h G_{0} = (G_{P} + G_{A P}) /2 an d P_{e f f}^{2} = (G_{P} - G_{A P}) / (G_{P} + G_{A P}), so t ha t T M R = 2 P_{e f f}^{2} / (1 - P_{e f f}^{2}), t h e J u l l i er e f or m w i t h P_{1} = P_{2} = P_{e f f})$ $(J . C . S l o n cz e w s k i, P h y s . R e v . B 39, 6995 (1989))$
Bias dependence of the TMR	$T M R (V) = \frac{T M R ( 0 )}{1 + ( V / V _{h} ) ^{2}}$	$V_{h} : T M R (V_{h}) = \frac{T M R ( 0 )}{2}$	$T M R (V) : T M R a t a bia s v o l t a g e V a cr oss t h e j u n c t i o n$ $T M R (0) : T M R a t a l o w bia s$ $V_{h} : v o l t a g e a t w hi c h t h e T M R i s ha l f o f i t s l o w - bia s v a l u e (an e m p i r i c a l f i t p a r am e t er, so t h e r e a d v o l t a g e m u s t b e k e pt b e l o w V_{h} t o k ee p a g oo d s i g na l)$ $(t h e L or e n t z ian f or m i s o n e o f se v er a l e m p i r i c a l f i t s; V_{h} i s t y p i c a l l y a f e w h u n d r e d mV f or C o F e B / M g O)$
Cell resistance and resistance-area product	$R_{P} = \frac{R A}{A _{ce l l}}$ $R_{A P} = R_{P} (1 + T M R)$	$R A = R A_{0} exp (2 κ t_{b})$ $κ = \frac{2 m ^{*} φ}{ℏ}$ $A_{ce l l} = \frac{π d ^{2}}{4}$	$R_{P}, R_{A P} : ce l l r es i s t an ce in t h e p a r a l l e l an d t h e an t i p a r a l l e l s t a t e$ $R A : r es i s t an ce - a r e a p r o d u c t o f t h e t u nn e l ba r r i er in t h e p a r a l l e l s t a t e$ $A_{ce l l} : a r e a o f t h e j u n c t i o n$ $d : d iam e t er o f t h e c i r c u l a r j u n c t i o n$ $T M R : t u nn e l l in g ma g n e t or es i s t an ce o f t h e f i r s t r o w$ $R A_{0} : p r e f a c t or o f t h e e x p o n e n t ia l t hi c k n ess d e p e n d e n ce$ $t_{b} : t hi c k n ess o f t h e M g O t u nn e l ba r r i er$ $κ : d ec a y co n s t an t o f t h e w a v e f u n c t i o n in t h e ba r r i er$ $m^{*}, φ : t u nn e l l in g e f f ec t i v e ma ss an d ba r r i er h e i g h t$ $(s in g l e - κ W K B es t ima t e; in cr y s t a l l in e M g O t h e d ec a y i s t ha t o f t h e Δ_{1} s t a t e, so κ i s a f i tt e d v a l u e, an d A_{ce l l} = π d^{2} /4 a ss u m es a c i r c u l a r p i l l a r)$
Spin-transfer torque: Landau-Lifshitz-Gilbert-Slonczewski equation	$\frac{d m}{d t} = - γ m \times H_{e f f} + α m \times \frac{d m}{d t} - γ H_{S T T} m \times (m \times p)$	$H_{S T T} = \frac{ℏ η J}{2 e μ _{0} M _{s} t _{F}}$	$m : u ni t v ec t or a l o n g t h e ma g n e t i z a t i o n o f t h e f r ee l a y er$ $γ : g y r o ma g n e t i c r a t i o (d e f in e d f or a f i e l d in A / m)$ $H_{e f f} : e f f ec t i v e ma g n e t i c f i e l d (ani so t r o p y, d e ma g n e t i z in g an d a ppl i e d f i e l d s)$ $α : G i l b er t d am p in g co n s t an t$ $p : u ni t v ec t or a l o n g t h e ma g n e t i z a t i o n o f t h e r e f er e n ce (p o l a r i z in g) l a y er$ $H_{S T T} : e q u i v a l e n t f i e l d o f t h e s p in - t r an s f er t or q u e (in A / m)$ $η : s p in - t r an s f er e f f i c i e n cy (s p in p o l a r i z a t i o n o f t h e c u r r e n t a t t h e f r ee l a y er)$ $J : c u r r e n t d e n s i t y t h r o ug h t h e j u n c t i o n$ $e, ℏ : e l e m e n t a r y c ha r g e an d r e d u ce d P l an c k co n s t an t$ $μ_{0} : v a c uu m p er m e abi l i t y$ $M_{s}, t_{F} : s a t u r a t i o n ma g n e t i z a t i o n an d t hi c k n ess o f t h e f r ee l a y er$ $(o n l y t h e d am p in g - l ik e t or q u e i s k e pt; t h e f i e l d - l ik e t or q u e a dd s a t er m - γ H_{F L} m \times p, s ma l l in M g O j u n c t i o n s a t l o w bia s)$ $(t h e s i g n o f t h e l a s t t er m, w hi c h d ec i d es w h e t h er t h e c u r r e n t f a v o u r s t h e p a r a l l e l or t h e an t i p a r a l l e l s t a t e, d e p e n d s o n t h e d i r ec t i o n o f t h e c u r r e n t an d o n t h e co n v e n t i o n f or p)$
Interfacial perpendicular anisotropy	$K_{e f f} = \frac{K _{i}}{t _{F}} + K_{b} - \frac{μ _{0} M _{s}^{2}}{2}$	$H_{k} = \frac{2 K _{e f f}}{μ _{0} M _{s}}$	$K_{e f f} : e f f ec t i v e p er p e n d i c u l a r ani so t r o p y e n er g y d e n s i t y o f t h e f r ee l a y er (p os i t i v e f or a p er p e n d i c u l a r e a sy a x i s)$ $K_{i} : in t er f a c ia l ani so t r o p y e n er g y p er u ni t a r e a a t t h e C o F e B / M g O in t er f a ce$ $t_{F} : t hi c k n ess o f t h e f r ee l a y er (t h e in t er f a ce t er m f a l l s a s 1/ t_{F}, so t h e l a y er m u s t b e t hin)$ $K_{b} : b u l k ma g n e t ocr y s t a l l in e ani so t r o p y e n er g y d e n s i t y$ $μ_{0} M_{s}^{2} /2 : s ha p e (d e ma g n e t i z in g) ani so t r o p y e n er g y d e n s i t y o f a t hin f i l m$ $H_{k} : e f f ec t i v e ani so t r o p y f i e l d$ $M_{s} : s a t u r a t i o n ma g n e t i z a t i o n$ $(f or a f r ee l a y er b e tw ee n tw o M g O l a y er s, t h e d o u b l e - in t er f a ce d es i g n, K_{i} i s r e pl a ce d b y 2 K_{i}; t y p i c a l C o F e B / M g O v a l u es a r e K_{i} \approx 1.0 - 1.3 m J / m^{2}, M_{s} \approx 1.0 - 1.3 M A / m, t_{F} \approx 1 - 1.5 nm)$
Thermal stability factor	$Δ = \frac{E _{b}}{k _{B} T} = \frac{K _{e f f} V}{k _{B} T} = \frac{μ _{0} M _{s} H _{k} V}{2 k _{B} T}$	$τ = τ_{0} exp (Δ)$	$Δ : t h er ma l s t abi l i t y f a c t or, t h e e n er g y ba r r i er b e tw ee n t h e tw o s t a t es in u ni t s o f k_{B} T$ $E_{b} : e n er g y ba r r i er f or r e v er s a l o f t h e f r ee l a y er (m o n o d o main)$ $K_{e f f} : e f f ec t i v e ani so t r o p y e n er g y d e n s i t y$ $V : v o l u m e o f t h e f r ee l a y er$ $k_{B}, T : B o l t z mann co n s t an t an d t e m p er a t u r e$ $μ_{0}, M_{s}, H_{k} : v a c uu m p er m e abi l i t y, s a t u r a t i o n ma g n e t i z a t i o n an d ani so t r o p y f i e l d$ $τ : m e an t im e f or a t h er ma l l y a c t i v a t e d r e v er s a l (N ee l - B r o w n), w i t h τ_{0} t h e a tt e m pt t im e, t ak e n a s 0.1 - 1 n s$ $(ma cr os p in a ss u m pt i o n : f or d iam e t er s ab o v e a f e w t e n s o f nm t h e r e v er s a l i s b y n u c l e a t i o n an d t h e m e a s u r e d Δ i s b e l o w K_{e f f} V / k_{B} T)$ $(t h e d a t a r e t e n t i o n r e q u i r e m e n t o n Δ i s co v er e d o n t h e r e l iabi l i t y p a g es)$
Critical switching current	$I_{c 0} = \frac{4 e}{ℏ} \frac{α}{η} E_{b}$	$I_{c 0} = \frac{4 e α k _{B} T}{ℏ η} Δ$ $I_{c 0} = \frac{2 e}{ℏ} \frac{α}{η} μ_{0} M_{s} H_{k} V$	$I_{c 0} : cr i t i c a l c u r r e n t f or s w i t c hin g o f a p er p e n d i c u l a r f r ee l a y er a t z er o t e m p er a t u r e (t h e c u r r e n t a t w hi c h t h e t or q u e c an ce l s t h e d am p in g)$ $e, ℏ : e l e m e n t a r y c ha r g e an d r e d u ce d P l an c k co n s t an t$ $α : G i l b er t d am p in g co n s t an t$ $η : s p in - t r an s f er e f f i c i e n cy$ $E_{b} : e n er g y ba r r i er o f t h e f r ee l a y er$ $Δ : t h er ma l s t abi l i t y f a c t or$ $k_{B}, T : B o l t z mann co n s t an t an d t e m p er a t u r e$ $μ_{0}, M_{s}, H_{k}, V : v a c uu m p er m e abi l i t y, s a t u r a t i o n ma g n e t i z a t i o n, ani so t r o p y f i e l d an d v o l u m e o f t h e f r ee l a y er$ $(f or an in - pl an e f r ee l a y er t h e d e ma g n e t i z in g f i e l d a dd s t o H_{k} in t h e l a s t f or m a s H_{k} + M_{s} /2 (S u n), an d t h e c u r r e n t i s l a r g er f or t h e s am e Δ)$ $(η i s d e f in e d so t ha t t h e t or q u e i s η ℏ J /2 e p er u ni t a r e a; f or an M T J S l o n cz e w s k i g i v es η = P / (1 + P^{2} cos θ), w hi c h i s w h y so m e p a p er s w r i t e 2 e /ℏ w i t h a d i f f er e n t e f f i c i e n cy f a c t or)$
Precessional switching time	$\frac{1}{τ _{s w}} = \frac{2}{C + l n ( π /2 θ _{0} )} \frac{μ _{B} P}{e m ( 1 + P ^{2} )} (I - I_{c 0})$	$τ_{s w} \propto \frac{1}{I / I _{c 0} - 1}$ $E_{w} = I^{2} R_{a v g} τ_{s w}$	$τ_{s w} : m e an s w i t c hin g t im e f or a c u r r e n t I ab o v e t h e cr i t i c a l c u r r e n t, in t h e p r ecess i o na l r e g im e$ $C : E u l er co n s t an t (ab o u t 0.577)$ $θ_{0} : ini t ia l an g l e o f t h e ma g n e t i z a t i o n f r o m t h e e a sy a x i s (se t b y t h er ma l f l u c t u a t i o n s)$ $μ_{B} : B o h r ma g n e t o n$ $P : s p in p o l a r i z a t i o n o f t h e c u r r e n t$ $e : e l e m e n t a r y c ha r g e$ $m : t o t a l ma g n e t i c m o m e n t o f t h e f r ee l a y er, m = M_{s} V (so μ_{B} / m i s d im e n s i o n l ess an d I / e g i v es t h e r a t e)$ $(t h er ma l ini t ia l an g l e θ_{0} \approx 1/ 2Δ; t h e f or m i s t h e hi g h - c u r r e n t l imi t o f S u n^{'} s m o d e l, an d E_{w} i s a r o ug h es t ima t e w i t h an a ss u m e d a v er a g e r es i s t an ce)$ $I, I_{c 0} : w r i t e c u r r e n t an d cr i t i c a l c u r r e n t$ $E_{w} : e n er g y o f o n e w r i t e p u l se$ $R_{a v g} : a v er a g e ce l l r es i s t an ce d u r in g t h e p u l se$
Thermally activated switching	$P_{s w} = 1 - exp [- \frac{t _{p}}{τ _{0}} exp (- Δ (1 - \frac{I}{I _{c 0}}))]$	$I_{s w} (t_{p}) = I_{c 0} [1 - \frac{1}{Δ} ln (\frac{t _{p}}{τ _{0}})]$	$P_{s w} : p r o babi l i t y t ha t a c u r r e n t p u l se o f am pl i t u d e I an d d u r a t i o n t_{p} s w i t c h es t h e f r ee l a y er (b e l o w I_{c 0})$ $t_{p} : p u l se d u r a t i o n$ $τ_{0} : a tt e m pt t im e$ $Δ : t h er ma l s t abi l i t y f a c t or$ $I, I_{c 0} : w r i t e c u r r e n t an d z er o - t e m p er a t u r e cr i t i c a l c u r r e n t$ $I_{s w} (t_{p}) : c u r r e n t f or w hi c h t h e s w i t c hin g p r o babi l i t y i s ab o u t o n e ha l f f or a p u l se o f l e n g t h t_{p} (t h e s w i t c hin g c u r r e n t f a l l s w i t h l o n g er p u l ses; e x a c tl y P_{s w} = 1/2 g i v es ln (t_{p} / τ_{0} ln 2) in pl a ce o f ln (t_{p} / τ_{0}))$ $(l in e a r ba r r i er r e d u c t i o n, t h e s im pl es t f or m; so m e p a p er s u se (1 - I / I_{c 0})^{2})$ $(v a l i d f or p u l ses l o n g co m p a r e d w i t h t h e p r ecess i o n t im e, ab o u t 10 n s or m or e)$

Important Questions

Ques: How does an STT-MRAM cell store and write a bit?

The cell is a magnetic tunnel junction (MTJ): a thin MgO tunnel barrier between a reference layer, whose magnetization is fixed, and a free layer, usually CoFeB, whose magnetization can point parallel or antiparallel to it. The parallel state has the low resistance $R_{P}$ and the antiparallel state the high resistance $R_{A P} = R_{P} (1 + T M R)$ . A current through the junction is spin-polarized by the reference layer and exerts a torque on the free layer (the Slonczewski term of the LLGS equation). Above the critical current $I_{c 0}$ this torque overcomes the damping and switches the free layer, and the direction of the current decides the final state. The read is done at a low voltage that does not switch the free layer. Reference: J.C. Slonczewski, “Current-driven excitation of magnetic multilayers,” J. Magn. Magn. Mater. 159, L1 (1996); L. Berger, “Emission of spin waves by a magnetic multilayer traversed by a current,” Phys. Rev. B 54, 9353 (1996); A.V. Khvalkovskiy et al., “Basic principles of STT-MRAM cell operation in memory arrays,” J. Phys. D 46, 074001 (2013).

Ques: Why does an MgO barrier give a TMR much larger than the Julliere formula suggests?

The Julliere formula takes the spin polarization of the electrodes as a material constant and gives a TMR of the order of tens of percent for Fe, Co and CoFe. In a crystalline MgO barrier between bcc electrodes the tunnelling is coherent, and the electron wave functions of different symmetry decay at different rates in the barrier, so the fully symmetric $Δ_{1}$ states, which are spin-polarized at the Fermi level in bcc Fe and CoFe, dominate the current in the parallel state and are blocked in the antiparallel state. The first-principles calculations predicted a TMR of the order of 1000% and experiments reached several hundred percent at room temperature in CoFeB/MgO/CoFeB junctions (604% at 300 K in the best report, Ikeda et al. 2008), while production cells use about 100 to 200%. Reference: W.H. Butler, X.-G. Zhang, T.C. Schulthess and J.M. MacLaren, “Spin-dependent tunneling conductance of Fe|MgO|Fe sandwiches,” Phys. Rev. B 63, 054416 (2001); S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki and K. Ando, “Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions,” Nat. Mater. 3, 868 (2004); S.S.P. Parkin et al., Nat. Mater. 3, 862 (2004); S. Ikeda et al., “Tunnel magnetoresistance of 604% at 300 K by suppression of Ta diffusion in CoFeB/MgO/CoFeB pseudo-spin-valves annealed at high temperature,” Appl. Phys. Lett. 93, 082508 (2008).

Ques: Why are the thermal stability factor and the write current linked?

Both depend on the energy barrier $E_{b} = K_{e f f} V$ . The critical current is $I_{c 0} = (4 e α /ℏ η) E_{b} = (4 e α k_{B} T /ℏ η) Δ$ , so for a chosen retention (a chosen $Δ$ ) the critical current cannot be reduced without lowering the damping $α$ or raising the efficiency $η$ . For an example with $α = 0.01$ , $η = 0.5$ , $Δ = 60$ and $T = 300$ K, $E_{b} \approx 2.5 \times 1 0^{- 19}$ J and $I_{c 0} \approx 30 μ$ A. A smaller cell has a smaller volume, so a higher $K_{e f f}$ is needed to keep $Δ$ , which is why interfacial perpendicular anisotropy is used. Reference: J.Z. Sun, “Spin-current interaction with a monodomain magnetic body: a model study,” Phys. Rev. B 62, 570 (2000); A.V. Khvalkovskiy et al., J. Phys. D 46, 074001 (2013).

Ques: Why are perpendicular MTJs used instead of in-plane ones?

For an in-plane free layer the critical current contains the demagnetizing field, $H_{k} + H_{d} /2$ , which is much larger than the anisotropy field, so for the same $Δ$ the current is about an order of magnitude higher. A perpendicular layer has the easy axis along the normal, the demagnetizing field only subtracts from the anisotropy (the interfacial anisotropy row), and the shape of the cell can be a circle, which scales better. CoFeB/MgO interfaces give a perpendicular anisotropy at a thickness of about 1 nm, and this was shown in 2010 in a junction with a TMR of about 120%. Typical perpendicular CoFeB/MgO parameters are a damping $α \approx 0.005$ to $0.01$ , an RA of a few to about 20 $Ω μ$ m $^{2}$ and $Δ \geq 60$ for long retention (ranges from the reviews cited). Reference: S. Ikeda et al., “A perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction,” Nat. Mater. 9, 721 (2010); A.V. Khvalkovskiy et al., J. Phys. D 46, 074001 (2013).

Ques: What are the switching regimes and how do they set the write pulse?

For pulses longer than about 10 ns the reversal is thermally assisted, and the switching probability follows the thermally activated row, so the required current falls logarithmically as the pulse is lengthened. For short pulses (a few nanoseconds) the reversal is precessional and the switching time falls as $1/ (I / I_{c 0} - 1)$ , so a short pulse needs a current well above $I_{c 0}$ . The energy of a write is $E_{w} = I^{2} R_{a v g} τ_{s w}$ . The write error rate has a tail from the random initial angle of the magnetization, which is why a very low error rate needs a longer or stronger pulse, and the breakdown of the MgO under a stronger pulse limits the amplitude (the reliability pages). Reference: R.H. Koch et al., “Time-resolved reversal of spin-transfer switching in a nanomagnet,” Phys. Rev. Lett. 92, 088302 (2004); Z. Li and S. Zhang, “Thermally assisted magnetization reversal in the presence of a spin-transfer torque,” Phys. Rev. B 69, 134416 (2004); J. Z. Sun, Phys. Rev. B 62, 570 (2000).

Ques: What limits the read signal?

The read signal is the difference between the two resistances at the read current, $Δ V = I_{r} (R_{A P} - R_{P}) = I_{r} R_{P} T M R$ . The TMR falls with the bias as in the bias-dependence row, so a read voltage close to $V_{h}$ is inefficient, and the read current must stay well below the switching current to avoid a read disturb (a thermally activated switching probability, covered on the reliability pages). The resistance-area product sets the cell resistance for a given diameter, so the barrier thickness is chosen to match the resistance to that of the select transistor, and a cell resistance spread from the barrier thickness (the exponential dependence of $R A$ ) reduces the read margin. Reference: A.V. Khvalkovskiy et al., J. Phys. D 46, 074001 (2013); D. Apalkov et al., “Spin-transfer torque magnetic random access memory (STT-MRAM),” ACM J. Emerg. Technol. Comput. Syst. 9, 13 (2013).

Quartz 5

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