## 3 Results and Discussion
### The Test Results  
The bridge areas with the same size of 0.5 mm (L) \(\times\) 0.5 mm (W) \(\times\) 4 \(\mu\)m (d) were obtained by etching the three Cu foils above. The physical photographs are shown in Figure 6.  
Using the test system in Figure 1, the flyer speed of the three samples in Figure 6 is tested under the condition of different driving voltages. The same discharge device was used in the test. The discharge capacitance was 0.2 \(\mu\)F and the driving voltage was 1.1 kV, 1.3 kV, 1.5 kV, 1.8 kV, and 2.0 kV, respectively. When the loading voltage is 2.0 kV, the original frequency spectrum waveform of the collected flyer speed is shown in Figure 7a. The flyer speed history obtained in the test is shown in Figure 7b-d. The effective measured time is about 2 \(\mu\)s.  
Figure 6: The photographs of (**a**) Sample A, (**b**) Sample B, and (**c**) Sample C with a 5-mm diameter. Figure 7: (**a**) The spectrum diagram of the flyer velocity, and the Fourier transform velocity spectrum (2.0 kV) of (**b**) Sample A, (**c**) Sample B, and (**d**) Sample C.  
In Figure 7, it can be observed that for all three samples, the inflection point of the flyer speed appears at about 0.92 \(\upmu\)s. Before that, the flyer speed rises rapidly, reaching 75% of the final speed within about 100 ns. After the inflection point, the speed of the flyer increases relatively slowly. The remaining speed of 25% increases within about 100 ns. The speed history curves of the three samples under the driving voltages of 1.5 kV and 2.0 kV are shown in Figure 8.  
It can be seen from Figure 8 that the flyer speed of Sample A is the smallest under the same driving voltage, followed by that of Samples B and C. It can be obtained from the experimental data that, under the same driving voltage, the compactness and the uniformity of the grain size of the Cu film have a greater influence on the flyer speed. The compactness and grain size of the Cu film are more uniform, and the flyer speed is higher, which is more beneficial for energy conversion. According to the calculation formula of metal resistivity:  
\[\rho=R\frac{\mathrm{t}}{F} \tag{1}\]  
\(\rho\): Resistivity/m\(\Omega\).mm;  
\(R\): Resistance/m\(\Omega\);  
t: Film thickness;  
\(F\): The dimensionless geometric factor, which is related to the thickness, area, position, and interlayer material of the samples. From Formula (1), it can be seen that the relation between the resistivity and resistance of a Cu foil with the same thickness is \(\rho\)\(\propto\)R.  
The resistivity of metals is determined by their purity, density, and grain size. Copper foil has a polycrystalline structure. In addition, the larger the grain size becomes, the more the range of grain boundaries and the resistivity will be reduced. For the copper foil, the number of grain boundaries will greatly affect the resistivity of copper. The grain size of Cu foil is closely related to the sputtering power, and the sputtering rate is directly proportional to the sputtering power. The expression of the sputtering rate is shown in Equation (2). \[S=\frac{3a}{4\pi^{2}}\frac{4m_{i}m_{t}}{m_{i}+m_{t}}\frac{E}{U_{0}} \tag{2}\]  
\(E\): Incident ion energy;  
\(m_{i}\): Mass of incident ion;  
\(m_{t}\): Changed ionic mass;  
\(U_{0}\): Surface building energy of target;  
\(a\): \(a\) = 0.7\(\sim\)1.4. With the change of sputtering conditions, metal particles will show different effects of surface diffusion, bulk diffusion, and atom shielding, thus forming different microstruc  
Figure 8: The displacement curves of the flyer velocity for three samples: (**a**)1.5 kV and (**b**) 2.0 kV. tures. From the different sputtering conditions controlled by the equipment, the diffusion of Cu particles will be affected, and a concave morphology will be formed on the surface of the copper film. At the same time, if the construction conditions are not suitable, the transverse diffusion of Cu atoms will occur too late to diffuse laterally and produce a large number of longitudinal stackings.