## 2 Materials and Methods
### Local Protective Structure of Electronic Devices  
Electronics are more focused on TID than on transient disturbances, which have been previously mentioned in regard to photon-counting detectors. A protective box is designed specifically for use with electronics in space, as illustrated in Figure 3. The box is composed of two separate boxes that enclose the sensitive electronic components and extend horizontally from the side walls, creating a finite boundary. Due to the design of the box, the equivalent thickness of the shield increases quickly when the incident angle is nearly parallel to the PCB, thus increasing the range of particles that can enter the PCB. Figure 4 shows the geometrical dimensions of the outer edge of the protective box after optimization. The width of the edge is represented by \(D_{E}\), and its thickness is indicated by \(D_{T}\). The wall thickness of two local protective boxes on and off the PCB is denoted by \(D_{K}\). Whether the material is single or multi-layered, its equivalent density can be given by \(\rho_{eff}\). The thickness of the PCB is marked as \(D_{P}\), and its equivalent density is described as \(\rho_{p}\). To ensure a uniform thickness in all directions, the width and thickness of the outer edge should abide by the following limits:  
\[\left(D_{E}+D_{K}\right)^{2}+\left(D_{P}\right)^{2}\geq\left(\frac{\rho_{eff} }{\rho_{p}}\right)^{2}\times\left(D_{K}\right)^{2}, \tag{2}\]  
\[D_{T}\geq D_{K}-\frac{\rho_{p}}{\rho_{eff}}\times D_{P}, \tag{3}\]  
Here, the equivalent thickness of the PCB is noted as \(\frac{\rho_{p}}{\rho_{eff}}\times D_{P}\). For any position on the top surface of the PCB, the width of the outer edge \(D_{E}\) must be true in order for Equation (2) to be fulfilled. This ensures that the equivalent Al thickness of the path A length in the PCB is always greater than or equal to the side wall \(D_{K}\), as illustrated in Figure 4a. When the thickness of the outer edge \(D_{T}\) is increased in order for Equation (3) to be true, then for any position on the top surface of the PCB, the equivalent Al thickness corresponding to the path B length from incident particles is always greater or equal to the side wall \(D_{K}\), as depicted in Figure 4b. Since radiation can come from any angle, particles enter the substance from all directions at a \(4\pi\) solid angle. The ray-tracing method was used to introduce multiple rays into the omnidirectional space from position O in order to be analyzed. As illustrated in Figure 5, the omnidirectional area is divided into several rooms with a small enough solid angle. The arrow on the ray OP marks the small space. The angle between the OP projection and the positive X axis in the XOY plane is denoted as \(\varphi\) (ranging from \(0^{\circ}\) to \(360^{\circ}\)), while the angle between the OP and XOY plane is defined as \(\theta\) (\(-90^{\circ}\) to \(+90^{\circ}\)). With this information, the omnidirectional space radiation dose at point O of the device can be expressed as:  
Figure 3: Model of local protective structure with finite boundary. (**a**) Overall view of the box; (**b**) sectional view of the box. \[D_{O}=\int_{-90^{\circ}}^{90^{\circ}}\int_{0^{\circ}}^{360^{\circ}}D(T(\varphi, \theta))d\varphi d\theta,\ \ \varphi e(0^{\circ},360^{\circ})\ \theta e(-90^{\circ},90^{\circ}), \tag{4}\]  
where \(T(\varphi,\theta)\) represents the thickness of the shielding material penetrated by the ray. \(D(T(\varphi,\theta))\) indicates the radiation dose of the space corresponding to the ray OP through the shielding substance \(T(\varphi,\theta)\). When the ray passes through the multilayer materials, the total shielding strength at this position can be given as follows:  
\[S_{O}=\sum_{i=1}^{n}\rho_{(\varphi,\theta)}(i)\times d_{(\varphi,\theta)}(i), \ \ \varphi e(0^{\circ},360^{\circ})\ \theta e(-90^{\circ},90^{\circ}), \tag{5}\]  
where \(\rho_{(\varphi,\theta)}(i)\) is the density of the i-layer shielding material experienced in the range of \((\varphi,\theta)\) rays.