Peeling stress analyzed for resistance to delamination - application to multiple thin films on a thick substrate

Timoshenko examined axial stresses and bending in bimetal thermostats; he did not examine interfacial stresses. Research has since proceeded on two fronts - approximate analyses of interfacial peeling and shear in a bimaterial beam or plate, and examination of axial stress and warpage in a multilayer beam. This paper draws on an exact partial solution for peeling at all interfaces in a multilayer beam, and presents a case study of multiple layers on silicon. It is a significant advantage to have a negative peeling stress at the free edge in order to prevent delamination from starting. The sign and magnitude of the peeling moment in a bimaterial beam or plate indicate the sign of the peeling stress at the free edge and a relative measure of its magnitude. These immediately show whether a resistance or a propensity to delamination exists at the free edge of the interface. This paper describes an exact solution for the peeling moments at each interface in a multilayer beam; it also offers a new insight into how peeling stresses arise. The method gives values at all interfaces, irrespective of the temperatures of bonding at each. It is equally applicable to layers of similar thicknesses, and to thin films on a thick substrate. An analysis is made of a silicon substrate with three thin layers applied at different temperatures. The peeling moment and shear force in each interface is determined. A discussion is included on the effects of changes to material properties and thicknesses; this analysis found that for all reasonable variations in layer thickness and properties the interfaces on the Silicon-on-Insulator wafer are inherently resistant to the start of delamination at room temperature.