## 3 Results  
As energetic particles strike the sensitive nodes of the transistors, the charge accumulated on the sensitive node reaches a critical state, which may cause soft errors, namely SEUs. Considering \(\alpha\)-particles only in this paper, a double exponential current source is commonly used to simulate the process of \(\alpha\)-particles hitting the sensitive nodes. To model the injection of a particle strike and its associated deposited charge, an injection model from [18] is adopted, which is widely used in relevant research [18; 19; 20; 21; 22]. This behavior of the particle hitting on the sensitive nodes of the CMOS device can be modeled as a double exponential current source, which can be expressed by Equation (2):  
\[I_{inj}(t)=\frac{Q_{inj}}{\tau_{1}-\tau_{2}}\Big{(}e^{-t/\tau_{1}}-e^{-t/\tau_ {2}}\Big{)}, \tag{2}\]  
where \(Q_{inj}\) is the charge injected into a CMOS device with a typical value from \(-2\) to 2 pC (a positive value for NMOS and a negative value for PMOS), \(\tau_{1}\) is the collection time constant \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Values** \\ \hline \(R_{1}\) & Top electrode parasitic resistance & 8.5 \(\Omega\) \\ \(R_{2}\) & Metallic parasitic resistance & 5 \(\Omega\) \\ \(R_{3}\) & Bottom electrode parasitic resistance & 73 \(\Omega\) \\ \(R_{\rm P}\) & P state resistance & 3.5 \(\Omega\) \\ \(R_{\rm AP}\) & AP state resistance & 6.47 k\(\Omega\) \\ \(C_{1}\) & Parasitic capacitance & 0.268 fF \\ \(C_{2}\) & Film capacitance & 73.2 fF \\ \(L_{1}\) & Top electrode parasitic inductance & 2.72 nH \\ \(L_{2}\) & Bottom electrode parasitic inductance & 2.09 nH \\ \(R_{\rm sub}\) & Substrate coupling resistance & 156 \(\Omega\) \\ \(C_{\rm sub}\) & Substrate coupling capacitance & 653 fF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters used in the equivalent circuit model for the MTJ device simulation. Figure 3: Schematic of an equivalent circuit of the MTJ device used in simulation. with a typical value of 150 ps, and \(\tau_{2}\) is the establishment time constant with a typical value of 50 ps. As radiation particles hit the sensitive nodes, different particle energy levels lead to diverse linear energy transfer (LET). Figure 4 shows the transient response of the double exponential current source with different values of \(Q_{inj}\). It is seen from the figure that a relatively low-charge pC level is able to induce a harmful leakage of current, of which the peak value reaches the mA level and the duration lasts for up to 0.4 ns. In addition, the peak value increases linearly with the injected charge. This transient response was used as the stimulation in the following simulations of the designed circuits. A spintronic TMR design based on STT-MTJ devices, which can be used to significantly decrease the impact of radiation, was developed to elevate the robustness of CMOS circuits. Focusing on maximizing the immunity to soft errors caused by SEUs, the proposed TMR circuits successfully optimized the traditional CMOS-based TMR circuits, as numerically shown in this section. Figure 5 shows the schematic of the proposed TMR circuit based on STT-MTJ devices. It is an optimization technique to increase robustness against SEUs. The STT-MTJ devices show excellent anti-radiation properties. In Figure 5a, the MTJ device can be regarded as a register. First, the input is divided into three data paths. Then, the data are written into the STT-MTJ devices, in which the devices are connected in series by the peripheral circuit. Afterwards, a pre-charge sense amplifier (PCSA) circuit is used for the amplification of the output logic signal. Figure 5b shows the schematic of the PCSA used in the novel majority voter circuit. As shown in Figure 5a, the proposed circuit includes the STT-MTJ devices and the corresponding transmission gates (TGs). The operations of the circuit can be classified into two modes, namely the writing and reading modes. In writing mode, the writing operation occurs when the clock (CLK) signal is low.