Magnetoresistive Random Access Memory (MRAM)

2.1.1 Magnetoresistance Effect

In this section, we will discussion the magnetoresistance, include pseudo spin valve effect and tunneling magnetoresistance effect.

The pseudo spin valve is composed of a hard magnetic layer, HM, and a soft magnetic layer, SM, magnetically separated with a nonmagnetic layer, NM. The HM has a larger coercivity than the SM. A prototype pseudo spin valve film proposed by Shinjo et al. is [NiFe(3)/Cu(5)/Co(3)/Cu(5)]¹⁵ multilayered film [1]. NiFe is used for the SM and Co is used for the HM. This multilayered film showed a MR ratio of ~8%. The magnetocrystalline anisotropy energy, Ea, for the films having cubic symmetry is given as

Ea=K1/8(1-cos4θ)+…

Fig. 2.1. (a) Magnetization curve and (b) MR curve of the pseudo-spin-valve, where the magnetization directions of the SM and the HM are denoted with gray and black arrows, respectively.

When the magnetization rotates in the (100) plane, where θ is the angle between the magnetization direction and the [010] axis. The K1 is the negative for fcc NiFe and Co.

Therefore, the NiFe and Co layers have the easy axis along the [011] direction. This is the reason why the magnetization reversal of the NiFe and Co layers take place. These characteristics are suitable for the application of pseudo-spin-valve to MRAM devices, as the magnetization reversal of the HM(=Co) layers is used for the data writing and that of SM(=NiFe) layers is used for data reading, The switching field of SM is lower than that of the HM layers. The schematic magnetization curve and the MR curve of the pseudo-spin-valve are shown in Fig. 2.1(a) and (b). With the application of a small magnetic field that causes magnetization reversal of the SM, but not of the HM, the magnetization directions of the SM and the HM take an antiparallel configuration. Then, the pseudo-spin-valve shows high resistance. With the application of a large magnetic field that causes magnetization reversal of the HM, the magnetization directions of the SM and HM take a parallel configuration and the pseudo-spin-valve shows low resistance. Pseudo-spin-valve shows a symmetric MR curve with the magnetic field direction, while the exchange-biased spin valves show a nonsymmetric one as shown in Fig. 2.2, as the HM in the pseudo-spin-valve has uniaxial anisotropy, while the pinned magnetic layer (PL)/ antiferromagnetic (AF) in the exchange-bias spin valve has unidirectional anisotropy.

Fig. 2.2. MR curve for the single spin valve, where the magnetization directions of the FM and the PL are denoted with gray and black arrows, respectively.

The exchange-biased spin valve shows a reversible MR curve with the magnetic field. But the pseudo-spin-valve shows an irreversible one. This is a disadvantage of pseudo-spin-valve for application to MR heads. However, pseudo-spin-valves are studied for application to MRAM (magnetic random access memory) devices [2,3].

Tunneling magnetoresistance (TMR) is observed for ferromagnetic spin tunneling junctions (MTJ) consisting of ferromagnetic-insulator- ferromagnetic layers [4-6]. When the insulating layer, usually referred to as the barrier layer, is very thin (the order of 1nm), electrons can tunnel through this forbidden region as a result of the wave-like nature of electrons for a voltage applied between the two electrodes, and can only be described in terms of quantum mechanics. The basic principle of TMR is the dependence of the tunneling probability on the relative orientation of magnetization in the two ferromagnetic electrodes.

The tunneling conductance is spin dependent due to the spin dependent density of states (DOS) at the Fermi level for ferromagnets. When the applied voltage is small enough for electrons near the Fermi level to tunnel, the tunneling conductance G in the MTJ can be written as (2.1.1)-(2.1.2) by neglecting the spin dependency of the tunneling probability [7],

( ) ( )

where R, T, Diσ(EF) are the junction resistance, tunneling probability, DOS at the Fermi level for spin σ band of the i-th ferromagnet, respectively, andφ,s, χand h are the barrier height and thickness, electron wave vector in the barrier and the Planck constant, respectively. The TMR is defined as

(

)

TMR= − / ………..…………(2.1.4)

where RP and RAP are the resistance for parallel and antiparallel spin configurations of two ferromagnetic electrodes, respectively. If we assume that spin is conserved during tunneling as shown Fig. 2.3, (2.1.1)-(2.1.4) lead to Julliere’s model [4],

(

)

2

1 /1

2PP PP

TMR= − ………..…..(2.1.5)

Fig. 2.3. A schematic model for spin dependent tunneling

Fig. 2.4. Probing the spin polarization of tunneling electrons from the ferromagnet to the superconductor

Pi is the spin polarization of tunneling electrons of ferromagnet i and given by the effect will become infinitely large corresponding to a value of 1 in (2.1.5). Unfortunately, determining the spin polarization at the Fermi energy of a ferromagnet is not easy. A typical transition metal ferromagnet has two components to its electronic structure; narrow d-bands that may be fully or partially spin polarized and broad s-bands with a lesser degree of spin polarization due to hybridization with the d-bonds. The value of P is controlled by extending to which these s- and d-bonds cross the Fermi energy. If the orbital character at the Fermi surface of the ferromagnetic metal is primarily d-like, then the spin polarization will be high. If the orbital character, however, is s-like or s-d hybridized, then the spin polarization can be low or high depending on the detail of the electronic structure. The magnetization of a material may show that all the electronic spins associated with the d orbits are aligned but the spin polarization at E_F can de depressed. On the other hand, metallic oxide ferromagnets, for example, have a greater opportunity for high spin polarization because of the predominance of the d orbital character at E_F.

Measuring the spin polarization requires a spectroscopic technique that can discriminate between the spin-up and spin-down electrons near E_F spin polarized photoemission spectroscopy is technically capable of providing the most direct measurement of P, but lacks the necessary energy resolution (~1meV). An effective alternative to photoemission is the use of spin polarized tunneling in a planar junction geometry which does allow the electronic spectrum near EF to be probe with sub-meV energy resolution.

Tedrow and Meservey pioneered this technique by marking superconductor/insulator/ferromagnet junctions and Zeeman splitting the superconductor’s strongly peaked single-particle excitation spectrum by the application of a magnetic field [8].

The spin-splitting of the quasiparticle density of states in a superconductor by the application of a magnetic field allows probing the spin polarization of tunneling electrons from the ferromagnet, which is schematically shown in Fig. 2.4. The resulting spectrum of the superconductor roughly corresponds to two fully spin polarized peaks (neglecting spin-orbit

coupling effects) that can be used to detect the spin polarization of a current from the ferromagnetic film. Another method of measuring spin polarization of a metal was developed recently [9], which is a metallic point contact between the point contact measures the conversion between superconducting pairs and the single particle charge carriers of the metal.

The conversion of normal current to supercurrent at a metallic interface is called Andreev reflection.

The values of P measured are shown in Table 2.1.1 for various ferromagnets except for the theoretically expected values for half metals with P=1, which have an energy gap in the minority spin (down spin) band as shown schematically in Fig. 2.5, thus only majority spin (up spin) electrons at the Fermi level. The spin polarization of tunneling electrons seems to be nearly proportional to the magnetic moment µ of the electrode as shown for Ni-Fe alloys in Fig.

2.6 [8], while it is not always proportional to µ of the ferromagnetic electrode as shown in Fig.

2.7 [10], which exhibits TMR and µ² as a function of the composition of Fe-Co alloy electrodes used for the junctions.

Table 2.1.1 Spin polarization of various magnetic materials

Magnetic material Spin polarization Magnetic materials Spin polarization

Fe 0.44 NiMnSb 1,0.58 tunneling barrier height for the MTJ using CoFe electrodes. The TMR is larger for the higher barrier height. The barrier height can be estimated by Simmons’ expressions (2.1.7)-(2.1.10)

(

)

for lower bias voltage, where J, φ and s are current density [A/cm²], barrier height [eV] and barrier thickness [cm], respectively.

Fig. 2.5. Schematic energy band structure for a half metal

Fig. 2.6. Spin polarization of tunneling electrons versus the magnetic moment µ of the electrode.

Fig. 2.7. TMR and µ² as function of the composition of Fe-Co alloy electrodes used for the junctions.

2.1.2 Magneto Impedance Theory

Magneto impedance, MI = M|Z|e^iθ = MR +iMX, in which X = XL-XC, originates mainly from the inductance and capacitance of the magneto device. Z is the impedance, θ is the phase angle, R is the real part of magneto impedance, and X is the imaginary part of magneto impedance.

In 1999, X.Q. Xiao [11] shows giant magnetoimpedance (GMI) effect in films with a sandwiched structure [12]. As compared to single layered films, the sandwiched films have much higher GMI ratio at relatively low frequencies. This is because of the separation of the ac current path from the magnetic flux path. The inner highly conductive metal reduces the entire resistance of the sandwiched film, and the outer magnetic layers form a magnetic alloy closed-loop structure. Therefore, less power is dissipated in the films to generate the ac transverse field. In the FeNiCrSiB/Cu/FeNiCrSiB structure, GMI ratios of 63% and 77% have been obtained at 13 MHz in longitudinal and transverse fields, respectively as shown in Fig.

2.8. These values are almost twice as large as those obtained in single layered FeNiCrSiB films.

Fig. 2.8. Field dependence of △∣Z∣/∣Zs∣ at 13 MHz in longitudinal (filled symbols) and transverse (hollowed symbols) field.

In 2000, M.F. Gillies [13] further proposed the magneto impedance effect for magneto tunneling junctions [14]. The structure is the Si/SiO2/Co/AlOx /Co. Due to differing conductivities charge collects at the interface between the dielectrics as well as on the capacitor plates (Maxwell Wagner capacitor model). This results in two contributions to the impedance.

In the case of the magnetic tunnel junctions studied, they extend this simple analysis to more than two layers in order to provide a model with which the complicated results of the impedance measurements as shown in Fig. 2.9 (a) and (b). By this AC analysis, the oxide/Co multilayer proved a very useful way of determining the total oxide thickness as a function of oxidation time and allowed a rough check of what was determined from the impedance measurements. The strength of the impedance measurements is that they provide a

“fingerprint'' of the oxide, rather than definitive fit parameters, and in so doing help to characterize the oxide.

Fig. 2.9. (a) Real and (b) imaginary parts of impedance for junctions with different oxidation times (in seconds). In both figures the dots show the measured results and the solid lines are fits.

2.1.3 Field Driven Magnetization Switching Designs

In most of today’s MRAM designs, the memory element is a magnetic tunnel junction (MTJ) that consists of two magnetic electrodes sandwiching an insulative tunnel barrier, as shown in Fig. 2.10 [15-18]. The resistance of these magnetic tunnel junctions depends on the relative orientation of the magnetic moments in the two magnetic electrodes interfacing with the tunnel barrier [19-22]. When the magnetic moments of the two magnetic layers are antiparallel, the resistance of the tunnel junction is significantly higher than when they are in parallel. The magnetic electrodes are shaped like an ellipse to create a shape-defined magnetic anisotropy. The magnetic moment will always be resting along the long axis of the element, referred to as the magnetic easy axis, as shown in Fig. 2.11 [23]. Assuming we can “fix” or

“pin” the direction of the magnetic moment of the bottom layer, referred to as the reference layer, along the easy axis, the magnetic moment orientation of the storage layer along the easy axis will give rise to two states with distinctively different resistance values, thereby, the two states in binary bit. The magnetization of the reference layer is “fixed” via a multilayer structure, which includes an antiferromagnetic layer at the bottom. The reference layer is part of a trilayer known as synthetic antiferromagnet (SAF) that is free of stray field. A good example is CoFe/Ru/CoFe with Ru of thickness around 8A˚. The antiferromagnetic layer yields an interfacial exchange field that “pins” the magnetic moment of the bottom SAF layer (pinned layer).

In a memory element array, each memory element is connected to a transistor, which performs the read addressing for reading back the memory state of an individual cell. The memory state writing of an individual memory element in the array is performed by a x-y grid of conducting wires, referred to as word lines and digital lines, placed over and below the memory elements with a memory element located at each cross, as shown in Fig. 2.12.

A current flowing through a selected word line (running in the y-direction in the figure) generates a magnetic field along the easy axis Hx while a current flowing through a selected

digital line (running in the x-direction) generates a field H_y in a direction transverse to the easy axis. A simple theoretical analysis shows that the field threshold for resulting in a magnetic switching is given by H_x^2/3+H_y^2/3=H_k^2/3 often referred to as the Stoner–Wohlfarth switching astroid, where Hk is the anisotropy field of the element [24]. According to the above equation, the switching field threshold is the lowest when both field components are equal in magnitude:

The memory state of the element at the cross of the activated word line and digital line can be changed. Whereas the rest of the elements along the selected word or digital lines, known as the half-selected elements, shall not be affected since they only experience one of the two fields, provided each field component is below H_k.

Fig. 2.10. Schematic drawing of a typical magnetic tunnel junction memory element and corresponding memory states that have two distinctive resistance values due to the magnetoresistive effect.

Fig. 2.11. Simulated magnetic switching of an eye-shaped magnetic element. The magnetization reversal starts at the center of the element with quasi-coherent magnetization rotation. The reversed region expands towards the ends as the reversal completes.

Fig. 2.12. Schematic drawing of the memory element array. Each memory element is connected to a field effect transistor for read addressing. A grid of x-y conducting wires, known as the digital lines (wires along the x-direction) and word lines (wires along the y-direction), is placed over and below the memory elements for providing the magnetic field for the write operation. Each memory element is located at a cross in the x-y wire grid. The lower bottom shows the switching field threshold contour, known as the Stoner–Wohlfarth switching astroid. The magnetization of the storage layer will remain unchanged if the field applied is located within the enclosed region of the astroid. Otherwise, the magnetic moment will irreversibly switch to the direction of the word line field.

2.1.4 Spin Torque Transfer Driven Switching Designs

Right before the turn of the century, researchers demonstrated magnetic switching of a patterned magnetic element at deep submicrometer dimension by direct perpendicular current injection [25-28], a phenomenon previously predicted by theorists Berger and Slonczewski, known as spin torque transfer [29,30]. When current is injected normally through a uniformly and firmly magnetized ferromagnetic layer, i.e., the reference layer, acts as a “spin filter”: the injected electrons with spin parallel to the magnetization direction of the ferromagnetic layer get transmitted and the electrons with antiparallel spins get, partially, reflected. The current becomes spin polarized in the vicinity of the reference layer. If another magnetic layer, i.e., the free layer, is placed within the range of the spin polarization, the spin polarized current would result in a torque, referred to as spin torque that is, to rotate the local magnetic moment away from the equilibrium orientation direction causing the magnetic moment to precess around the local effective magnetic field. This spin torque will be present until the local magnetization becomes parallel to the spin polarization direction. The current spin polarization is opposite in sign at the opposite side of the reference layer with respect to the direction of injection.

Reversing current direction, thus, reverses the sign of the spin torque, as illustrated in Fig.2.13.

If the spin torque, proportional to the injected current density, in the free layer exceeds the restrain torque caused by local magnetic anisotropy, magnetization rotation occurs. The critical current density to irreversibly reverse the magnetic moment of the free layer is given by the following [20]:

where M_S, t_F, and H_k are the saturation magnetization, the thickness, and the anisotropy field of the free layer, respectively. Also in the above equation, α, known as the Gilbert damping constant, is a phenomenological parameter measuring the magnitude of the damping torque that yields a natural dissipation of the magnetic energy into other nonmagnetic energy form(s),

Fig. 2.13. Illustration of spin torque transfer. Injecting a current through a ferromagnetic layer of a ‘‘fixed’’ magnetization, the current will be spin polarized. Placing a free layer nearby, the spin polarized current will result in a torque that will act to rotate free-layer magnetization away from the equilibrium orientation. The sign of spin polarization direction outside of the

‘‘fix’’ layer reverses with reversing direction of current.

such as heat. The most commonly recognized energy dissipation channel is the coupling between spin waves and lattice vibration, known as magnon–phonon interaction. With a slight manipulation, above equation can be rewritten as

where A, V, and Ku are the surface area, the volume, and the anisotropy energy constant of a free layer, respectively, and I_C0 is the critical current amplitude. The term K_uV on the right-hand side is the anisotropy energy of the free layer, namely, the magnetic energy stored in the memory element or the energy barrier between the two memory states. It is important to note that the volume V in the above equation should be the activation volume, which could be smaller than the actual volume of a memory element. The term arises from the surface demagnetizing energy due to the out-of-plane precession of the magnetization during the switching. It is important to note that the surface demagnetizing energy is typically greater than the energy stored in the bit. The fact that the Gilbert damping constant appears in above equation reflects the nature of spin torque transfer driven magnetization reversal.

In a free layer at equilibrium absent spin torque transfer, the magnetization is always parallel to the local effective magnetic field, a direct result of the existed damping torque due to energy dissipation. When free-layer magnetization is in the opposite direction of the current spin polarization, the spin torque is effectively antidamping: its direction is exactly opposite to that of the damping torque. When the magnitude of spin torque becomes greater than that of the damping torque, the energy of the local magnetic moment increases with time and an irreversible magnetization reversal could eventually occur. A smaller damping torque will yield a smaller critical current for irreversible magnetization reversal. When the energy barrier between the two memory states becomes comparable to the thermal activation energy, k_T where k is the Boltzmann constant and T is the absolute temperature, memory state switching can occur at a current level below switching threshold, as illustrated in Fig.2.14. The probability per unit time for a transition between the memory states to occur is given as

where f₀ is known as the attempt frequency and its value is believed to be on the order of 10⁹ to 10¹⁰ Hz. With an injected current pulse at a density and a pulse duration, the memory state switching probability is [31.32]

The above relationship is often used for quantitative determination of the energy barrier [32].

The above relationship is often used for quantitative determination of the energy barrier [32].