Temperature-Dependent Sheet Resistance and Surface Characterization of Thin Copper Films Bonded to FR4 Composite under Mechanical Vibrations  
[PERSON]  
1 Mechanical Engineering Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia;  
[EMAIL_ADDRESS] (S.M.); [EMAIL_ADDRESS] (M.K.H.)  
[PERSON]  
1 Mechanical Engineering Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia;  
[EMAIL_ADDRESS] (S.M.); [EMAIL_ADDRESS] (M.K.H.)  
[PERSON]  
1 Mechanical Engineering Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia;  
[EMAIL_ADDRESS] (S.M.); [EMAIL_ADDRESS] (M.K.H.)  
[PERSON]  
2  
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\) (Figure 13a) and the presence of rolling traces of crystalline domains was probably due to the mode of fabrication of the samples (Figures 14a and 15a).  
Figure 13: ESEM images (back-scatter mode) of samples S0 (**a**), S11 (**b**), and S31 (**c**) at 50\(\times\) magnification.
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Figure 14: ESEM images (back-scatter mode) of samples S0 (a), S11 (b), and S31 (c) at 500\(\times\) magnification.  
Figure 15: ESEM images (back-scatter mode) of samples S0 (**a**), S11 (**b**), and S31 (**c**) at 3000\(\times\) magnification.  
After 200 k and 800 k vibration cycles, the surfaces clearly developed cracks, as evidenced in panels (b) and (c) of Figures 13-15. These cracks were perpendicular to the longitudinal axis of the samples and were the result of the plastic deformation undergone by the samples after vibration stress. The apparent density of cracks increased with the number of cycles from ~3 cracks per mm at 200 k cycles to ~8 cracks per mm at 800 k cycles, indicating a dependence of the overall damage on the number of cycles. These cracks were ~1 \(\upmu\)m in width and several millimeters in length and seemed to follow dislocation lines perpendicular to the longitudinal axis, as shown in Figure 16.  
This type of crack development has been observed in other fatigue studies of copper thin films and is attributed to the presence of dislocations [34; 35] and favored by surface roughness [36].  
Interestingly, the surface composition (100% copper) was not altered even upon a high number of vibration cycles, indicating that the vibration stress only produced physical damage and not chemical processes such as oxidation, as shown in Figure 17. The samples were also analyzed by measuring the water droplet contact angle. This technique is useful in assessing hydrophilicity/hydrophobicity changes on surfaces and is widely used in adsorption and surface modification studies [37]. Figures 18 and 19 show the contact angle measurements for samples before and after vibrations, respectively.  
Figure 16: ESEM images corresponding to Figure 15b,c, respectively, showing crack dimensions (at 3000\(\times\) magnification).  
Figure 17: Surface elemental composition of samples corresponding to: (**a**) Figure 14a (before vibrations); (**b**) Figure 14c (after vibrations).  
The observed contact angles for untreated samples ranged from 78 to 95 degrees, similar to those observed for pure copper, indicating a hydrophilicity similar to that of aluminum [38]. After vibration damage, the contact angle increased to 117-119 degrees, typical of a hydrophobic surface such as PTFE (polytetrafluoroethylene). This marked change in contact angle could be attributed to increased surface roughness [39] and also to  
Figure 19: Contact angle measurements of sample S31 at different locations. The grey area indicates a higher density of cracks in the sample. Zones A, B, and C correspond to Figure 1.  
Figure 18: Contact angle measurements of sample S0 at different locations. Zones A, B, and C correspond to Figure 1.  
the accumulation of very small air bubbles on the cracks that hindered water contact with the surface.