Structure-dependent mechanical behavior of copper thin films

The mechanical properties of copper foils electroplated with (200) and (220) preferred orientations and thicknesses of 8-24 μm were assessed at various temperatures. It was found that the yield strength and elastic modulus both decrease with increasing temperature to 150 °C, and that the greater susceptibility of a columnar structure to defects makes it more sensitive to temperature than an equiaxed structure. Thus, for a given grain size, a columnar structure has a lower yield strength. A modified Hall-Petch relation was subsequently developed to take into account the effect of micro-structure on material strength by introducing a structure factor (S) : σy = σ0 + kd− 1/2 + S. As the slope (k) of this equation is constant, it can be used for copper thin films of any thickness, provided they are at room temperature and above the micro-level in scale. This structure factor concept, however, is only valid at room temperature. In the modified Hall-Petch relation, the new variable related to the equiaxed and columnar structures in the copper thin films was abstracted from the Hall-Petch relation. Then, if the materials are the same, the k value and the σ0 value are constant regardless of the scale, and the relationship between the grain size and the yield strength can be shown by only changing the structure factor.