## 2 Materials and Methods  
TMR is widely used for reducing device failure, as it rapidly detects and corrects SEUs [12; 13; 14; 15; 16]. A diagram of a traditional TMR is shown in Figure 1. It consists of four majority voters and multiple data paths. Each data path has an independent input to avoid voting errors due to the propagation of the previous error inputs. Under normal working conditions, the three modules offer three identical outputs at the same time. The core principle of TMR is an operation called majority voting on the output of the three data paths. Thus, in a traditional TMR circuit, each majority voter is critical because it is required to tolerate the errors caused by unexpected radiation. If there is an SEU error in one of the three channels of data, the system will determine the correct output through the majority voting operation to achieve SEU error correction. Therefore, a majority voting circuit based on STT-MTJ is proposed here to improve robustness against radiation. To increase the robustness of the TMR module itself, MTJ devices were used in a TMR system for the first time. A perpendicular-anisotropy MTJ is preferred for use in STT-MTJ due to its adequate storage retention and good scalability. The MTJ is a three-layered stack which is composed of two ferromagnetic (FM) layers and a thin MgO barrier layer in between them. Its schematic structure is shown in Figure 2. Due to the effect of giant magnetoresistance (GMR), the resistance of the MTJ is determined by the relative magnetic orientation of the two FM layers, namely the free layer and the reference layer. The parallel (P) state means that the two FM layers of the MTJ share the same magnetic direction, resulting in a low resistance to currents passing through the device, and is therefore represented by the binary data value \"0\". In the figure, \(R_{P}\) is used to denote the low resistance value. In contrast, the anti-parallel (AP) state indicates that the magnetic directions of the two FM layers are opposites, corresponding to a high resistance, and is represented by the binary data value \"1\". The high resistance value is denoted by \(R_{AP}\) in the figure. The value of the tunnel magnetoresistance ratio (_TMRa_) is used to characterize the resistance variation, as shown in Equation (1). \[TMRa=\frac{R_{AP}-R_{P}}{R_{P}}\times 100\%, \tag{1}\]  
The magnetic orientation of the free layer can be changed according to the STT mechanism. Specifically, the state of the STT-MTJ can be manipulated by injecting it with spin-polarized current. The STT-MTJ switches from the P to AP state when spin-polarized current \(I_{\text{P->AP}}\) flows through the STT-MTJ from the free layer to the reference layer, and from the AP to P state when spin-polarized current \(I_{\text{AP->P}}\) is injected in the opposite direction, as shown in Figure 2.  
Based on the STT-MTJ mechanisms, an equivalent circuit for the MTJ device used for simulation purposes is illustrated in Figure 3. Given the fact that digital behaviors are high-frequency, RC networks derived from substrate coupling are necessarily attached to the input and output ports to improve simulation accuracy. In this model, \(R_{1}\) and \(R_{3}\) are the parasitic resistance of the top and bottom electrodes, respectively. \(R_{2}\) is the total parasitic resistance of both the metallic FM layers. \(C_{1}\) is the parasitic capacitance between the two  
Figure 1: Traditional TMR system with four majority voters. Figure 2: Schematic of an STT-MTJ device corresponding to two states, namely the P and AP states. FM layers across the peripheral oxide layer. \(C_{2}\) is the film capacitance of the core oxide layer, which acts a functional tunneling barrier. Similar to \(R_{1}\) and \(R_{3}\), \(L_{1}\) and \(L_{2}\) are the parasitic inductances induced by the top and bottom electrodes. The key trait of the GMR effect is dynamic resistance \(R_{\rm v}\), which is simulated with a switch circuit, as highlighted in the figure.