# A compact model for magnetic tunnel junction (MTJ) switched by thermally assisted Spin transfer torque (TAS + STT)

- Weisheng Zhao
^{1, 2}Email author, - Julien Duval
^{1, 2}, - Jacques-Olivier Klein
^{1, 2}and - Claude Chappert
^{1, 2}

**6**:368

**DOI: **10.1186/1556-276X-6-368

© Zhao et al; licensee Springer. 2011

**Received: **2 November 2010

**Accepted: **28 April 2011

**Published: **28 April 2011

## Abstract

Thermally assisted spin transfer torque [TAS + STT] is a new switching approach for magnetic tunnel junction [MTJ] nanopillars that represents the best trade-off between data reliability, power efficiency and density. In this paper, we present a compact model for MTJ switched by this approach, which integrates a number of physical models such as temperature evaluation and STT dynamic switching models. Many experimental parameters are included directly to improve the simulation accuracy. It is programmed in the Verilog-A language and compatible with the standard IC CAD tools, providing an easy parameter configuration interface and allowing high-speed co-simulation of hybrid MTJ/CMOS circuits.

## Background

_{P}and R

_{AP}corresponding to the parallel or anti-parallel configuration of the relative magnetization orientations of the two FM layers, respectively. For practical applications, the magnetization direction of one FM layer is pinned as reference and that of the other FM layer is free to store the binary state (see Figure 1a). Recently, TMR = R

_{AP}-R

_{P}/R

_{P}ratio was found to be more than 604% by using the MgO oxide barrier [4] and this allows MTJ to present excellent sensing performance.

Today, most of the R&D efforts in MTJ are focused on its switching approaches, which are expected to be scalable, energy efficient, reliable and fast. A number of approaches have been investigated since 2002, such as thermally assisted switching [TAS] [5] and spin transfer torque [STT] [6, 7]. However all of them suffer from either high power or stability issue and cannot meet the requirements for wide applications. Thermally assisted spin transfer torque [TAS + STT] is an emerging approach [8, 9], which is based on the temperature dependence of exchange bias storage principle [10], as used in TAS [5]. This switching mechanism involves applying a low current through STT to raise the MTJ temperature above the blocking temperature (*T*
_{
b
}) of the antiferromagnetic layer associated to the storage layer, resulting in a hysteresis loop centred about zero (see Figure 1). *T*
_{
b
}depends mainly on the material composition (e.g. ~423K for IrMn and ~573K for PtMn). This method combines the advantages of both TAS and STT technologies, giving the best trade-off among data reliability, power efficiency, speed and density. Unlike other nanodevices [11], MTJ can be easily integrated with CMOS circuits [12]. Based on hybrid MTJ/CMOS [13], innovative memory and logic circuits are expected to provide high performance or new functionalities beyond CMOS. A Spice-compatible efficient compact model for MTJ is an essential requirement for the hybrid MTJ/CMOS design and simulation.

## Physical model integration

This compact model is based on our previous STT MTJ model, which is composed of two sub-modules representing respectively the sensing and switching operations [14]. For sensing, the MTJ resistance and TMR ratio are calculated to obtain respectively *R*
_{
P
}and *R*
_{
AP
}[15]. For switching, the STT critical current, *I*
_{
C
}, calculation model was implemented to obtain the hysteresis loop margin of storage layer [5]. The present model offers an improvement over the previous work [14–17] as it integrates the temperature evaluation and STT dynamic switching models to describe the TAS + STT switching approach. In order to optimise the simulation speed, one of the most important performances for logic and memory designs, some physical phenomena like the oscillating effects during switching are omitted.

### Temperature evaluation model

*M*

_{ 0 }) and an adder (

*A*

_{ 0 }), the temperature

*T*can be observed in real time through the voltage node

*V*

_{ temp }(i.e. 1V = 1K). The values of

*R*

_{ 0 }and

*C*

_{ 0 }are set as constant to obtain τ

_{ th }calculated by Equation 2,

*V*is the voltage across MTJ nanopillar,

*λ*is thermal conductivity of the thermal barrier,

*C*

_{ V }is heat capacity per unit volume,

*j*is current density,

*T*

_{ R }is room temperature, thick_b is the thickness of thermal barrier, thick_s is the total thickness of MTJ nanopillar and

*τ*

_{ th }is the characteristic heating/cooling time. This leads to

*D*

_{ heat }is the heating current pulse duration,

*D*

_{ cool }is the cooling duration, and

*T*

_{ heat }and

*T*

_{ cool }present respectively temperature of MTJ during heating/cooling operations.

### Spin Transfer Torque (STT) dynamic switching model

_{0}between the magnetization of the storage layer and its easy axis [19], which is approximated by Equation 6. High temperature increases Θ

_{0}and then reduces the STT switching duration,

*D*

_{ switch }. STT state reversal depends on switching current value,

*I*

_{ switch }, which should be higher than the critical current,

*I*

_{ C }.

*D*

_{ switch }can be linearly reduced down to according to nanosecond range with high

*I*

_{ switch }[20]. This property is useful for the design and simulation of hybrid MTJ/CMOS circuits dedicated to logic applications, which require very high speed (e.g. approximately gigahertz).

where *H*
_{
ani
}is in-plane uniaxial magnetic anisotropy field, *μ*
_{
0
}
*M*
_{
s
}is saturation field in the storage layer, *α* is Gilbert damping coefficient, *γ*
_{
0
}is the gyromagnetic constant, *Vol* is the volume of storage layer and *k*
_{
B
}is the Boltzmann constant.

## Compact model simulation and validation

### Co-simulation of Hybrid MTJ/CMOS circuit

_{switch}begins to heat the MTJ from ambient temperature. As its temperature reaches up to T

_{b2}after ~11.22 ns, the model compares the

*I*

_{ switch }(approx 462.9 uA) with the STT critical current I

_{C}(~150 uA) and switches the state of MTJ from parallel [P] to anti-parallel [AP] state in about 6 ns according to the STT dynamic model. As "Vg1" is deactivated, MTJ begins to cool down to ambient temperature. The state can be reversed from AP to P by activating the control signal "Vg2", which generates

*I*

_{ switc }

_{h}(approx-375.6uA). The

*I*

_{ switch }values are asymmetric as a constant voltage supply is used in the simulation (e.g. 1V) and the resistance of MTJ changes between two states (

*R*

_{ P }and

*R*

_{ AP }). It is important to note that the voltage pulse width should be longer than

*D*

_{ heat }

*+D*

_{ switch }to ensure the reliable switching operation [5].

### Power and die area estimation

The silicon area of this hybrid circuit is ~9.8 um^{2} as the width of NMOS transistors is set to 1 μm to provide *I*
_{
switch
}much higher than *I*
_{
C
}and reduce the duration down to some nanoseconds. The whole switching operation of TAS + STT between the P and AP states dissipates ~2.7pJ of energy.

## Conclusions

In this paper, we present the first compact model for MTJ nanopillar switching using the TAS+STT approach. Transient simulations of a hybrid MTJ/CMOS circuit validate its functionalities and demonstrate that it can be useful to calculate the critical circuit performances like speed, power and die area. The easy parameter interface of the Verilog-A language allows us to analyse the characteristics of MTJ with different materials, area and thin film thickness etc. By using this model, a number of hybrid MTJ/CMOS complex circuits are under investigation in our laboratory.

## Declarations

### Acknowledgements

The authors wish to acknowledge support from the French national projects CILOMAG, ANR-SPIN and NANO2012 project with STMicroelectronics.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.