# High Performance MRAM with Spin-Transfer-Torque and Voltage-Controlled Magnetic Anisotropy Effects
## 2 MTJ Fundamental and Physical Modeling
### VCMA-Assisted Switching  
Figure 2 illustrates a typical structure of VCMA-MTJ which is similar to that of PMA-STT-MTJ [25]. It is composed of two ferromagnetic layers sandwiched by an insulator as the oxide barrier. As the same as STT-MTJ, the resistance of the device is determined by magnetization orientations of the two ferromagnetic layers. In PMA-MTJ, the magnetization direction of one layer can be changed by sufficient current density (precessional switching) or sufficient pulse width (thermally-assisted switching) flowing through it while that of the other is fixed. By using the VCMA mechanism, the external voltage (or electric field) can modulate the interfacial PMA of CoFeB/MgO stacks [20]. With this effect, a positive (negative) voltage can reduce (increase) interfacial PMA. Figure 2 illustrates a typical structure of VCMA-MTJ which is similar to that of PMA-STT-MTJ [25]. It is composed of two ferromagnetic layers sandwiched by an insulator as the oxide barrier. As is also the case for STT-MTJ, the resistance of the device is determined by the magnetization orientations of the two ferromagnetic layers. In PMA-MTJ, the magnetization direction of one layer can be changed by a sufficient current density (precessional switching) or sufficient pulse width (thermally-assisted switching) flowing through it, while that of the other is fixed. By using the VCMA mechanism, the external voltage (or electric field) can modulate the interfacial PMA of CoFeB/MgO stacks [20]. With this effect, a positive (negative) voltage can reduce (increase) interfacial PMA. As shown in Figure 2, the impact of voltage amplitude (V\({}_{\text{b}}\)) on the VCMA-MTJ is explained as follows: thermally assisted switching is realized with low positive voltage (0 \(<\) V\({}_{\text{b}}\) \(<\) V\({}_{\text{c}}\)) and a reduced energy barrier. Alternatively, precessional VCMA switching is achieved by way of a high positive V\({}_{\text{b}}\), which is greater than V\({}_{\text{c}}\), to eliminate the energy barrier (E\({}_{\text{b}}\)). When V\({}_{\text{b}}\) is lower than 0 V, the negative voltages can be used to strengthen the E\({}_{\text{b}}\). From the aspect of energy levels, the stable magnetization states of the free layer in a PMA-MTJ device are divided by E\({}_{\text{b}}\) which is modeled as a function of the applied voltage [23]. The voltage dependent \(\Delta(\text{V}_{\text{b}})\) is obtained:  
\[\Delta(\text{V}_{\text{b}})=\text{E}_{\text{b}}(\text{V}_{\text{b}})/\text{k} _{\text{B}}\text{T}=\Delta(0)-\xi\Delta\text{V}_{\text{b}}/\text{k}_{\text{B }}\text{T}_{\text{tor}} \tag{5}\]  
where \(\Delta(0)\) is the thermal stability (zero voltage), \(\xi\), is the coefficient to weigh the PMA at V\({}_{\text{b}}\), t\({}_{\text{ox}}\) is MTJ oxide layer thickness, A is the MTJ sectional area, k\({}_{\text{B}}\) and T are the Boltzmann constant and temperature respectively. As demonstrated in Figure 2, by setting \(\Delta(\text{V}_{\text{b}})=0\), V\({}_{\text{c}}\) as the minimum voltage of VCMA effect can be estimated by:  
\[\text{V}_{\text{c}}=\Delta(0)\text{k}_{\text{B}}\text{T}_{\text{tor}}/\xi\text {A} \tag{6}\]  
Figure 2: Typical structure of the voltage-controlled magnetic anisotropy (VCMA)-MTJ device. The applied voltage amplitude (V\({}_{\text{b}}\)) and critical voltage (V\({}_{\text{c}}\)) determine the operation regimes of VCMA-MTJ: thermally assisted, precessional switching and STT-assisted precessional switching. which is used to entirely eliminate the energy barrier of the MTJ. When a \(\rm V_{b}\) (positive) is greater than \(\rm V_{c}\), \(\rm E_{b}\) can be entirely eliminated so that the magnetization of the free layer becomes unstable and precessionally oscillates between the two stable states (referred as precessional switching regime). Alternatively, with the amplitude of the voltage inferior to \(\rm V_{c}\), the energy barrier is lowered, where the thermally-activated switching regime can be realized in this domain.