## 3 Results and Discussion
### Performance of Cu-AAO Interposer  
According to the X-ray diffraction (XRD) analysis results, only the (220) crystal plane could be observed when the electrodeposition current density was 5 A/dm2 (as shown in Figure 7a), which indicated that the CNPs have formed a single crystal structure, and <220> is the preferred crystal orientation. When the current density increased to 10 A/dm2 and 15 A/dm2, the crystal planes with crystal planes of (111), (200), and (220) were observed (as shown in Figure 7b), which revealed the CNPs are the polycrystalline structure. In fact, CNPs with a single-crystal is beneficial to fabricating the unidirectional microbumps in the subsequent Cu/Sn bumping process, which can suppress the vacancy formation and improve the interconnection reliability [23]. It is reported that lower current density resulted in lower overpotential, and further resulted in lower nucleation rates. The observations in this study are consist with the references [12; 18]. During the crystallization process, there are two ways for crystal formation to occur. One is the continuing growth on the preexisting crystal nuclei and the other is the formation of new grains [21; 22; 23; 24; 25; 26]. According to the above-mentioned discussion, low current density and low overpotential will suppress the nucleation rate. Therefore, the copper pillars will prefer to grow along initial crystal orientation and newly formed grains will be greatly suppressed. Preferred forming of the (220) crystal plane was caused by the dehydration reduction process. During the growing process of CNPs, copper ions in electrolyte need to obtain electrons to form copper atoms. Therefore, the CNPs will choose the crystal structure that is most favorable for receiving electrons [22]. As the copper crystal is face-centered and cubic, three crystal planes could be chosen to form nano-pillars in this study, which include (200), (111), and (220) planes. The schematics of atoms arrangement with three crystal orientations were shown in Figure 7b. The atoms on (111) and (200) planes have six and four nearest neighboring atoms, respectively, which are arranged very tightly. Therefore, it is difficult for electrons to pass in the narrow space. However, in the case of (220), each Cu atom merely has two nearest neighboring atoms. The arrangement gaps between atoms provide sufficient space for the movement of electrons. As a result, <220> will be the preferred  
Figure 6: Potential vs. time curve for the galvanostatic electrodeposition of CNPs (\(i\) = 5 A/dm2) into pores of an AAO film. The scheme displays three different stages of the growth process: in region (**a**) growth on the ITO glass; (**b**) growth in the nano-pores; in region (**c**), growth on the surface. orientation. Furthermore, the pore size also has an influence on the growth of crystal. Due to the restriction of nanoscale pore size, only one critical nuclei with <220> orientation could form in it. Moreover, low current density could not provide enough energy for the <220>-oriented grain to rotate in the narrow space. Hence, a <220>-oriented grain is difficult to rotate into the grain with other orientations. And then, subsequent copper atoms can be stacked along previously <220>-oriented nuclei. Ultimately, a pillar with a <220>-oriented grain was formed. High thermal conductivity is necessary for interposer material. The thermal conductivities were respectively calculated in horizontal and vertical directions by the following equations:  
\[\lambda_{\mathrm{v}}{}^{\mathrm{c}}=V_{\mathrm{Cu}}\lambda_{\mathrm{Cu}}+V_{ \mathrm{AAO}}\lambda_{\mathrm{AAO}} \tag{4}\]  
\[\lambda_{\mathrm{h}}{}^{\mathrm{c}}=\lambda_{\mathrm{Cu}}\lambda_{\mathrm{AAO} }/(V_{\mathrm{Cu}}\lambda_{\mathrm{AAO}}+V_{\mathrm{AAO}}\lambda_{\mathrm{Cu}}) \tag{5}\]  
In which, \(\lambda_{\mathrm{v}}{}^{\mathrm{c}}\) and \(\lambda_{\mathrm{h}}{}^{\mathrm{c}}\) are the calculated value of thermal conductivities in vertical and horizontal directions, respectively.