During air-gap formation in interconnects, decomposition process of the sacrificial layer induces deformation of a low-k dielectric cap layer. For analysis of ensuing structural instability, a logistic kinetics model is introduced to describe the removal process of the sacrificial layer, and finite difference method (FDM) is applied to evaluate the deformation behavior of the cap layer. The instability of the cap layer depends on its span length and the degree of adhesion between the cap layer and sacrificial layer. During decomposition, strong adhesion causes the collapse of the cap layer, while the cap deformation remains small and stable with weak adhesion. For intermediate adhesion, a snap-back instability is predicted as the cap layer suddenly detaches from the sacrificial layer at a critical deflection. The critical adhesion energy is predicted as a function of the air gap width.