# Engineering of Voltage-Controlled Magnetic Tunnel Junctions at Cryogenic Temperatures

Pedro Brandao Veiga, Ricardo C. Sousa, L. D. Buda-Prejbeanu, Ioan Lucian

Prejbeanu, Bernard Diény

► To cite this version:

Pedro Brandao Veiga, Ricardo C. Sousa, L. D. Buda-Prejbeanu, Ioan Lucian Prejbeanu, Bernard Diény. Engineering of Voltage-Controlled Magnetic Tunnel Junctions at Cryogenic Temperatures. INTERMAG 2023, May 2023, Sendai, Japan. [hal-04679334](https://hal.science/hal-04679334v1)

HAL Id: hal-04679334

https://hal.science/hal-04679334v1

Submitted on 27 Aug 2024

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## ABSTRACT

* A VCMA system is modeled to expand on how its precessional nature exhibits a deterministic switching regime at low temperatures [1];

* MRAM devices are fabricated with high resistance-area product (RA) to measure their VCMA magnitude for different compositions, given by $\xi$ with a maximum of 35 fJ/Vm at 10K;

* The measured VCMA dependence with the storage layer thickness deviates from the expected trends [2] and shows correlation with the quality of the MgO/FeCoB interface of the devices.

## Motivation

### MRAM magnetic hysteresis loop

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### Energy barrier at low temperatures

$$ \Delta_{300K} \sim 50 \rightarrow E_B \sim 15000k_B $$

$$ \Delta_{3K} \sim 50 \rightarrow E_B \sim 150k_B $$

$$ E_B: 1 \rightarrow \frac{1}{100} $$

### Energy barrier definition

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### Stability Factor
$\Delta$ at low temperatures

$$ \Delta = \frac{E_B}{k_B T} \quad T: 300K \rightarrow 3K $$

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$$ E_B \propto V_C \propto E_{bit} $$

### Writing energy consumption per bit $E_{bit}$

### Capacitive

$$ E_C = \frac{\varepsilon_0 \varepsilon_{MgO} A}{t_{MgO}} V_C^2 $$

### Dissipative

$$ E_{diss} = \int_{0}^{t_{on}} \frac{V_C^2}{R_P} dt $$

In STT-MRAM operating at RT,
$E_{bit} \sim 100fJ$

In VCMA-MRAM operating at low-T,
$E_{bit} \sim 10aj$

## System Modeling

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Storage Layer

High RA Insulator

Polarizer/Reference Layer

$$ K_{1s}(V_{app}) = K_{1s}(0) - \xi \frac{V_{app}}{t_{MgO}} \quad \text{VCMA influence on anisotropy} $$

$$ V_C = \frac{1}{\xi} \left[ \frac{\mu_0 M_S H_{app} (1 - \sin \theta_{eq})}{\cos^2 \theta_{eq}} - K_2 \cos \theta_{eq} - K_{1eff} \right] \quad \text{Critical voltage} $$

Model description by Landau-Lifshitz-Gilbert-Slonzewski equation

$$ \frac{d\vec{m}}{dt} = -\gamma_0(\vec{m} \times \vec{H}_{eff}) + \alpha \left(\vec{m} \times \frac{d\vec{m}}{dt}\right) - a/V_{app}\vec{m} \times (\vec{m} \times \vec{p}) $$

Energy density description of the storage layer in easy-cone configuration

$$ \epsilon = -K_1 m_z^2 - K_2 m_z^4 - \mu_0 M_S (H_{IP} m_x + H_{OOP} m_z) + \frac{1}{2} \mu_0 M_S^2 \vec{m} \cdot \vec{N} $$

Energy landscape of an easy-cone anisotropy

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## Deterministic VCMA Switching

Deterministic switching occurs when the two stable states are still present under applied voltage.

3D trace of $\vec{m}$ with deterministic switching

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$t_0$ - Pulse on
$t_{off}$ - Pulse off
$t_f$ - Simulation end

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The switching diagram shows features that are only stable at very low temperatures (<50K), which can be exploited for cryogenic applications.

## VCMA Extraction – Material and Temperature Dependence

### MRAM schematics of magnetic pillar

<figure><img src="image_14.png" /></figure>

Cross-section of double-wedge
deposition of MTJ

<figure><img src="image_15.png" /></figure>

### DC phase diagram and boundary fitting from $H_{sw}$ equation

<figure><img src="image_16.png" /></figure>

Switching field $H_{sw}$ fitting function
for DC phase diagrams [3]

$$ H_{sw}^{P \rightarrow AP} = H_{c0} + H_{RL} + \frac{\tau V_b}{\alpha R A} + \epsilon V_b - \zeta \frac{V_b^2}{R A'} $$

Contributions for

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Extraction of VCMA coefficient $\xi$ from DC phase diagrams:

$$ \frac{\partial H_K}{\partial V_G} = \epsilon * \left( 1 - \frac{1}{2} \sqrt{\frac{\ln(\frac{\tau}{\tau_0})}{\Delta}} \right)^{-1} $$

$$ \xi = \frac{M_S * t_{FeCoB} * t_{MgO}}{2} \frac{\partial H_K}{\partial V_G} $$

$H_{sw}$ plot for different temperatures

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$\xi$ dependence with MgO and FeCoB thickness

<figure><img src="image_22.png" /></figure>

TMR and coercivity dependence with $\xi$

## CONCLUSIONS

* VCMA is a promising write approach for MRAM operating in cryogenic environment.

* Conditions are predicted to exist for VCMA to reach a deterministic regime rather than precessional.

* The method used to extract $\xi$ is a reliable way to acquire statistics for VCMA characterization.

* The magnitude of VCMA may be closely related to the quality of the MgO/FeCoB interface as it is proportional to TMR.

## REFERENCES

1. One, RA., et al. Sci Rep 11, 8801 (2021).

2. Y.C.Lau et al., Appl. Phys. Letters, 110, 2, 022405 (2017)

3. G. Mihajlović et al., Phys. Rev. Applied, 13, 024004 (2020).

## ACKNOWLEDGEMENTS

This work was partially supported by the French National Agency (ANR) under the CRYMCO project (ANR-20-CE24-0009) and in part by the European Research Council via grant MAGICAL ERC Adv 669204 and PEPR project PRESQUILE

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