A0076958H_Karnati Penchal Rohith Chowdary EE5202 Project

8/7/2019 A0076958H_Karnati Penchal Rohith Chowdary EE5202 Project

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4) The work on magnetic tunnel junctions has been dominated by the use

of aluminum oxide based barriers. However, since 2004 there has been a

quantum leap in the tunnel magnetoresistance (MR) ratio due to the

introduction of crystalline MgO barriers. Do a literature study on the latest

status of MgO-based tunnel junctions by focusing on understanding of themechanism that leads to very high MR ratios. For theoretical work, you may

refer to Butler WH et al., Phys. Rev. B63, 054416 (2001).

Magnetic Tunnel Junctions

LITERATURE REVIEW:

Submitted By: Karnati Penchala Rohith CHowdary

Student Id: A0076958H


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TABLE OF CONTENTS PAGE NO

1.1 Introduction................................................................................. ..................................31.2 Structure................................................................................... .......................................31.3 Background............................................................................ ........................................31.4 Basics of Tunnelling............................................................. .......................................42.1 Julliere Modell........................................................................ .......................................62.2 Mooderas experiment..................................................... ..........................................82.3 De Teresas experiment................................................... ........................................ 83.1 AlOx and MgO based MTJ sensor.................................................. ........................83.2 Tunnelling conductance and magnetoconductance....... ...........................103.3 Structure of MgO........................................................................ ...............................103.4 Electronic Structure................................................................. ................................114.1

Tunnelling Conductance...................................................... ..................................12

4.2 Tunnelling through interface states..................................... ............................174.3 Conductance for anti-parallel alignment............................... .........................174.4 Thickness dependence......................... ...................................................................184.5 Conclusion...................................................... ..............................................................18


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ABSTRACT:

____________________________________________________________________________

The magneto-tunnel junctions (MTJ) are devices which consist of thin insulating layer

between two ferro-magnetic electrodes that exhibits magneto resistance (TMR) phenomenon at room temperature. This type of phenomenon is used in developing

magneto resistive random access memory (MRAM). MTJs made using Al2O3 as insulating

layer over the past few decades showed relatively low MR ratios. This has been replaced by

MgO junctions which is capable of improving the magneto -resistance in the range of 1000

% at room temperature. The Fe(001)/MgO(001)/Fe(001) MTJs are gainin g very good MR

ratios for past few years. The great leap in TMR is due to coherent spin tunnelling of 1

block states in Fe for K||=0. Also the evanescent states in the band of MgO(001) show low

decay for 1 state thus helping the tunnelling process. Also since the Fe 1 states are fully

polarised for K||=0 it couples with the MgO-1 states properly and yields high TMR effects.

1.1 INTRODUCTION:

Magnetism based non-volatile memories have been a core area of research for some

ages now. Thin magnetic films developed, though non-volatile suffered from deep creep

walls, low boundaries which has different magnetisation resulting in data damage.

After that, the position of magnetic memories was taken over by stable and faster

semiconductor memories. After the development of lithography, now we can define

small magnetic elements which can negate the domain wall problem issues faced by the

earlier techniques.

1.2 STRUCTURE:

The figure 1 shows a basic MTJ. It is composed of two parallel layers of conducting

ferromagnetic material separated by an insulator layer of less thickness. The total

resistance between the upper and the lower layers depends upon the relative

magnetism of the two ferromagnetic layers. The tunnelling thickness is about 1nm and

the ferromagnetic layers thickness is around 10nm.


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Figure 1: Basic diagram of Magnetic tunnel junction structure.

1.3 BACKGROUND:

First report on magneto resistance was from julliere from Co/Ge/Fe tunnelling junctionin 1975. The conductance he could achieve was about 14 % at 4.2K [1]. After this in

1995 Moodera could get a magneto resistance of around 11.8 % in CoFe/Al 2O3/Co MTJ.

The figure 2 shows a general road map of tunnelling magneto resistance from 1995[2].

Figure 2: Roadmap of MTJ, showing magneto resistance and barrier oxide used

versus the year.

In 1999, De Teresa, found out that insulator plays an important role for determining the

magnetoresistance. Since then in 2008m Ikeda was able to get magnetoresistance of the

order of 604 % at 300K and around 1140 % at 5K [3].


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1.4 BASICS OF TUNNELING:

Quantum Tunnelling can be described with the transmission probability decreasing

with the thickness of the insulator layer. When a voltage is applied to the tunnelling

junction there will be voltage dependence on the tunnelling probability. A simple fermis

golden rule will be the below formula [4]:

(1)

Where M(U) is the transition matrix element, D1(EF) is the density of states of the FM1, I

representing the current tunnelling through. Stoner Modell is used to explain the

ferromagnetism by explaining the spin degeneracy of band structures in ferromagnetic

materials. The energy of electrons will be energy of electrons without spin interactions

and exchange interaction energy with I as coupling constant.

(2)

And will be the number of electrons with corresponding spin and N is the total

number of atoms. When we align spins per atom, then energy corresponding to

exchange interaction is given by the difference of above two equations.

(3)

(4)

EF is the Fermi energy, the kinetic energy lost is given by:

(5)

Now adding (212) to (214) the total energy change is given as :

(6)

For FM materials this equation has to be negative, so the only way will be.

(7)

This criterion is fulfilled by Co, Fe and Ni. The fictitious density of states seen in a FM is

shown in the figure 3. The arrows indicate the spin direction. The behaviour of FM

materials can e seen in the figure 4, where we can see one of the bands of Ni has higher


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occupation than the other, and the shift is downwards. In Cu and Zn both the spins are

equally occurred so they are not FM.

Figure 3: Fictitious density of states seen in ferromagnetic material.

Figure 4: bands showing Ni having higher occupancy.

2.1 JULLIERE MODELL

The change in resistance due to the change in the magnetisation was first given by

julliere in 1975[1]. The assumption he was that the spin of electrons remains same

during tunnelling. The current I through the tunnelling was first given as :

(8)

G is the conductivity. Another constant he assumed was ai given as :


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(9)

ai is the fraction of the density of states whos spins are parallel to the magnetisation. (1-

ai) is the fraction whose spin are antiparallel. From the equation (eqn (4)) we can get

that G is proportional to the a1 in the first FM times the a2 in the second plus the same

for spin down. So :

(10)

The Tunnelling magnetic resistance is given by:

(11)

The conduction electron polarisation introduced by Julliere is:

(12)

So Now the net change of the resistance relating to the electron polarisation is given as :

(13)

Figure 5: Schematic tunnellling mechanism between two FMs of different

magnetisation configuration.


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R is the resistance of the parallel magnetism of the two FM. The expression (13) is

known as the Jullieres formula for TMR.

2.2 MOODERAS EXPERIMENT:

He was able to obtain resistance change in the range of 11.8 % at room temperature.

The resistance he discovered was based on the angle difference between the direction

of current and the magnetisation [2].

2.3 DE TERESAS EXPERIMENT:

De Teresa in 1999, discovered that the insulator has the main effect on the TMR. The

figures below shows the TMR effects . The figure A and B shows the reverse

Magnetisation , whereas the Figure C and D shows normal magnetisation where the

resistance of the parallel case is smaller than the anti-parallel case[3].


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Figure 6: A and B shows reverse magnetism & C and D show forward

magetism.

3.1 ALOx AND MgO BASED MTJ SENSORS:

From 1995 Al2O3 based insulating layers have been prominent. They are very simple to

fabricate and can allow magnetoresistance of the order of 35 % . In 2001, some of the

theoretical work issued a high magnetoresistance when we use MgO as a insulating

layer. When Al2O3 was being used as a insulating layer over a decade earlier the

magnetoresistance obtained was only around 70 % at room temperature, which is only

very less value compared to the spintronics devices. The difference of the tunnelling

magnetoresistance can be accounted because of the fact that Al2O3 is a Amorphous

material and MgO is a crystalline material.

Figure 7: Schematic diagram of Al 2O3 and MgO based MTJs.

The detailed expanation of the tunnelling magnetoreisistance is explained using

evanescent states and bloch states. The high TMR is due to

1) the spin-dependent coherent tunnelling of1 block states of Fe for k ||=0. Thiscan be seen in figure 7 above, where spin dept coherent tunnelling of1 is shown

with maximum probability.

2) Also another contributing factor will be the evanescent state1 in the MgO(001)which shows slower decay in density of states, thus bringing more probability of

tunnelling.


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Thus the 1 block states of Fe(001) couples with the 1 evanescent states of

MgO(001), giving maximum tunnelling probability. More detailed expalanation of

the phenomenon will be provided in the following pages.

3.2 TUNNELLING CONDUCTANCE AND MAGNETOCONDUCTANCE :

So far the previous theories of tunnelling conducatnce and magnetoconductances were

related to the density of states of the electrodes and not much on the tunnelling matrix

elements. The main factor contributing towards tunnelling is the nature of states in the

both electrodes and the states inside the barrier layers. There can be multiple states

with complex wave form vectors in the insulating barrier which may lead to strong

interface effects in tunnelling. Even the resonance states in the interface can strongly

affect the tunnelling.

The dominant tunnelling mechanism is different for both the majority and minority

channels. For the majority channel case the conductance is through Bloch electrons with

little transverse momentum. A particular symmetry state with 1 is able to effectively

couple from Fe into the MgO and also out of MgO into the Fe electrode. In the case of

minority channel the conductance is mainly through the interface resonance states,

mainly seen in thinner layers. As the tunnelling barrier get increased majority channel

conductance movement dominates the conductance, due to the decaay of1 state in

MgO. Thus this leads to an increase of magnetoresistance with barrier thickness.

3.3 STRUCTURE OF MgO :

The structure of MgO is shown in the figure 8. The Low energy electron diffraction

shows that the Iron atoms lie over the larger oxygen atoms. While Depositing the

Fe[100] lies parallel to the MgO[110]. A separation of only around 2 A was suggested.

Actual deposition was through deposition of several atomic layers of MgO over the

Fe(100), over which the Fe(100) is again deposited[5].


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Figure 8: Structure of MgO.

3.4 ELECTRONIC STRUCTURE :

For determining the electronic structure, we will take into account of the transmission

and reflection amplitude of the bloch wave in Fe on the MgO in the Fe(100) lattice. Four

layers of MgO was attached to the Fe (100) lattice. The atomic potentials of the atomic

sphere was calculated with spherical radii of 1.022 A and 1.427 A for Mg and O. An

empty sphere of radius 0.947 A was inserted in order to correctly calculate the volume

of each layer. The calculations proceed for calculations of bulk Fe.

The density of states (DOS) was calculated and the majority and minority spin channels

for each layer was determined . It was shown that the density of states at theinterfacewas different to that to bulk and this was opposite to the two spin channels as

given in figure 9 and 10.


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Figure 9: Majority and minority DOS.


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Figure 10: majority and minority DOS

Near the interface the majority DOS is strongly reduced in the vicinity where minority

channel fermi energy falls near a sharp peak in DOS. The Final result is that the majorityfermi energy DOS is quite less near the interface and minority DOS has a large peak

above the DOS. Such a kind of effect is quite relevent in the interface between Fe (100)

and insulator or semiconductor. Some of such examples are in Fe(100)| Ge, Fe (100) |

GaAs, Fe(100)|ZnSe.

In the figure 10, the density of states for MgO in the vicinity of fermi level is shown. It is

shown that there are a wide gap in the density of states in the interior MgO

approximately 5.5eV in width from 0.244 hartree to 0.446 hartree.

4.1 TUNNELING CONDUCTANCE :

The tunnelling conductance is calculated using Landauer equation which relates the

conductance to the probability of bloch electron in one of the electrode transmitted

through the MgO to the opposite electrode. The landauer conductance can be best


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understood using the figure 11. The sample here will be MgO tunnel barrier surround

Figure 11: Schematic figure showing the Landauers conductance.

By two Fe electrodes Let the left one be Mu1, which is the emitter of the electrons. Then

the current density of the electrons which leave the Mu1 and enter the reservior on the

right is given as :

Where,

After integral through z direction over kz we get:

And finally the current expression as :

Similarly the expression for the current of electrons in -z direction which enter the

reservior on the left through the resorvior on the right is given as [5] :


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The net current is given as :

Leads to the Landauer conductance formula :

Primitive transmission and reflection amplitudes which the Layer KKR technique use

to propagate plane waves between layers can be used to calculate the transmission and

reflected amplitudes for bloch waves. The equations of waves reflecting and transmittedthrough a barrier can be used to descreibe the transmission and reflection of bloch

waves.

1) MAJORITY TRANSMISSION PROBABILITY :The transmission proabaility is calculated as a function of k for the majority spin

channel. The fugure 12 shows the transmission probability calculated for MgO

thickness of 4,8,and 12. The transmission proability on K || is best understood for

majority channel than for minority channel than for antiparallel. For the case of

majority channel the caonductance has braod peak near centered at K|| = 0. The

figure 12 shows the case for transmission porbability as a function of kx & ky=0. An

important feature to note from the figure 12, is that the transmission probability is


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increased around K|| = 0 when the thickness of MgO is increased.

Figure 12: Transmission probability for MgO for thicknesses 4,8,12.

2) Symmetry near K|| = 0 :To understand the conductance correctly we can examine the tunnelling DOS for

K||=0 for each individual bands. Let us consider the tunnelling density of states to be

the desity of states subjected to following boundary conditions:

(i) There is an incoming Bloch state on the left hand side with unit flux andcorressponding reflected block states too.

(ii) On the right hand side will be the corresponding transmitted block statesThe fig 13 shows the diagram of density of states associated with each Fe(100) block

states with K||=0. The tunnelling density of states plots are shown here, which relates to

the symmettry. In Fe(100) both the minority and majority channels have 4 block states

for K||=0. In the majority channel there are:

I) 1 state ,II) doubly degenerated state called5state and III) final2 state.


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From the figure 14 it shows that the1 states show the slowest decay for the states with

symmetry. The next slowest decay is for states5symmetry followed by2.

Bloch states(majority) with 1 symmetry in Fe decays as evanescent states with1

symmetry in MgO. Also the bloch states 5 with majority and minority in Fe decays as

evanescent states inside the MgO. This is all shown in the figure 13. Only the majority

channel has slow decaying 1 state. Next highest is for 5 state for majority and

minority channels. There is also minority Fe 2 state which couples with 2 state in

MgO and decays faster than the 5 state. These information of the band structures

determined through photoemmission should lead to accurate values of decay rates

inside the barriers.

4.2 TUNNELLING THROUGH INTERFERENCE STATES:

The interfacial resonant states cna yield high wave function amplitude at interference.

For lower values of the K|| the DOS of the interfacial is the highest. Also the symmetry of

the wave function determines the transmission. The large difference arise from thedifference in DOS. Another important factor will be because of the interface resonant

states which occur near the Ky=0 line and also kx>0.154, and also the variation will be

that of an oscillatory function which varies with thickness.

4.3 CONDUCTANCE FOR ANTIPARALLEL ALIGNMENT:

Figure 15: Density of states associated with each Fe(100) block.

From the analysis of transmission functions and combination of majority and minority

channels it is seen that for thinner layers the highest transmission occurs at the line

ky=0.When the layers become thicker the largest transmission will be near closer toorigitn of 2-Ds due to the decay of MgO states from Fe 1 bands. Even for the thicker

MgO layers the antiparallel alignment doesnt occur exactly at the K||=0. This is also

shown in figure 15 at the bottom two line which shows the lines for the antiparallel

alignment. Consider the majority of the 1 energy states on the left hand side of the

barrier. The 1 can propogate through the MgO where it decay readily, on the right

hand side of the barrier it cannot go because there are no minority 1 propogating

states in fermi energy. They also lead to total reflection of1 states. The 5 states


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rapidly decay in MgO but are able to go enter easily because of the states which can

accept them easily.2 states rapidly decay inside the MgO as discussed earlier.

In the right side figure 15 minority2 states decay within MgO also within the majority

Fe, because of no 2 state at fermi in majority Fe. But5 electrons decay rapidly but

enter minority Fe whereas the minority Fe2 decay rapidly.

4.4 THICKNESS DEPENDENCE:

Figure 16: Conductance dependence of majority-parallel etc with MgO layers.

The conducatance dependence on the majority parallel minority parallel and also

both of them anti-parallel is shown in the figure 16. We can see that the majority

conducatnce always over powers the others. This is mainly due to the interficaial

resonant states which is particularly important for very thin barriers. We can also put it

in a way that from out magneto-conductances analysis the magneto-conductance

should increase with thickness because the conductances will be dominated by majority

channels.

4.5 CONCLUSION:

Initially we started with the basic structure of the MTJ and dealed with the basic

physiscs asssociated with the Magnetic tunnel junctions. We also dealt with the basic

equations which relate to the occurance of such phenomenon. Then was new discovery

made when cryastalline MgO replaced amorphous Al2O3 as a insulating material. The

physics involed in the actual mechanism was further studied. Some of the summarised

results will be because of the tunnelling through the epitaxial insulators in the Fe. (1)-

the majority channel tunnelling is through the 1 states (2) minority channel tunnelling,


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though smaller is strongly enhanced for values for K|| near the resonanace states. (3)

another importance observation was the increase of magnetoresistance with the

thickness due to the increaase in the number of states.

The general observation is that the analysis of higher tunnelling was observed when

there are similar or identialc states on the either sides of the barrier. So the tunnelling

electrons need not only go through the barrier, there is a need for a identical state of

symmetry on either side of the barrier to achieve this. This is also a kind of reason for

the decrease in magnetoresistance when there is a bias applied to the device. As there is

a bias increase the opposite sides of the barriers differe leading to lower

magnetoresistance.

REFERENCES:

[1]-M. Julliere, Tunneling Between Ferromagnetic Films; Physics Letters; September

1975.

[2]- J. S. Moodera; Large Magnetoresistance at Room Temperature in Ferromagnetic

Thin Film Tunnel Junctions; PRL April 1995.

[3]- ; J. M. DeTeresa, et al.; Role of Metal-Oxide Interface in Determining the Spin

Polarization of Magnetic Tunnel Junctions Science 286.

[4]- Festkrperphyik script; WS 04/05; Gross, Marx.

[5]-W. H. Butler, X.-G. Zhang, et al. Spin-dependent tunneling conductance of Fe MgO

Fe sandwiches PHYSICAL REVIEW B, VOLUME 63, 054416 .

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A0076958H_Karnati Penchal Rohith Chowdary EE5202 Project