## Doctoral Dissertations

Fall 1997

Dissertation

Engineering

#### Degree Name

Doctor of Philosophy

A new technique to estimate the out-of-plane thermal expansion coefficient (CTE) of several 1 $\mu$m thick, spin-coated polyimides is introduced. Arrays of parallel copper and polyimide lines of various aspect ratios on Si substrate were imaged in air at room temperature and at 97$\sp\circ$C using an atomic force microscope (AFM). The out-of-plane CTE of the polyimides was estimated by matching the experimental results with the predictions of finite element models with different out-of-plane parameters. For FPI-135 (6FCDA-TMOB) polyimide the out-of-plane CTE was found to be $\approx$260 ppm/$\sp\circ$C, for FPI-136 (PMDA-6FDA-TFMOB) polyimide $\approx$120 ppm/$\sp\circ$C. Polyimide lines with widths equal to or less than the film thickness of 1 $\mu$m showed less thermal expansion than wider lines. This was attributed to change of polyimide properties at the Cu/polyimide interface as a result of the reactive ion etching step of the structure manufacturing process.
High density interconnect structures are subjected to 350$\sp\circ$C during manufacturing. The mismatch between the Cu and the polyimide out-of-plane CTE leads to high shear stresses at the interfaces normal to the film plane during heating. The experimental observation of thermally induced deformation of Cu/Ta/polyimide line arrays as a result of RT-350$\sp\circ$C-RT thermal cycle is discussed. In addition to "classical" high temperature deformation mechanisms (grain boundary sliding, grain elevation and Coble creep on the Cu surface), sliding at the Cu/Ta interface was observed using the AFM. It was found that the Cu/Ta interfacial sliding is a strong function of the Cu line width. 10 $\mu$m wide Cu lines were found to exhibit less Cu/Ta sliding compared to 1 $\mu$m wide Cu lines. This was attributed to ability of wide Cu lines relax the stresses using other mechanisms. A finite element model was constructed to analyze the Cu/Ta interfacial sliding.