Extension of the Equivalent Thickness Concept to the Bifurcation of Large Semiconductor Front Side Metal Taiko Wafer investigated by ANSYS Finite Element Analysis Methods

Scaling up the production of power devices involves, in the semiconductor industry, the use of large semiconductor 8” and 12” wafers of Si or SiC. Their use implicates a successful an effective monitoring and control of wafer warpage, as the geometrical size of the substrate increases, as well as a command control on the degeneration of non-linear warpage into critical phenomena known as bifurcation or buckling. To mitigate the warpage, the use of taiko wafers, which consists of wafers having a thicker region on the edge perimeter region of the wafer, has been generally adopted in the production lines. In a previous work [1] we investigated the warpage of taiko wafers by introducing the concept of equivalent thickness, in the linear approximation, for the case of a front side metalized taiko wafer. However, as the thickness of the central semiconductor substrate region decreases the possibility that also the taiko wafer bifurcates emerges. For this reason, in this work we have investigated the occurrence of bifurcation or buckling in a taiko wafer. In particular, we implemented a finite element analysis method by using ANSYS Mechanical Enterprise 2023/R2 to investigate the phenomenon of bifurcation in a taiko wafer. The investigated system consisted of a 200 mm Si (001) front side metalized (FSM) taiko wafer, having a substrate thickness ranging from $100 \mu \mathrm{m}$ to $400 \mu \mathrm{m}$, with a step height fixed to $450 \mu \mathrm{m}$. The FSM layer consisted of an Al layer of $4.5 \mu \mathrm{m}$ thin. The system was subjected to a thermal load such that, getting cooled from a nominal temperature T to $25^{\circ}\mathrm{C}$, the metal layer can develop a residual stress. To investigate the bifurcation, an asymmetry was induced in the system by applying a slight force on a point of the circumferential region perpendicularly to the substrate. The temperature investigated ranged from $30^{\circ}\mathrm{C}$ to $170^{\circ}\mathrm{C}$. From this investigation, it results that also the bifurcation is mitigated by the taiko structure. Indeed, the bifurcation emerges at higher values of the stresses with respect to the case of flat wafers having the same size and thickness of the substrate. Moreover, the concept of equivalent thickness needs to be reformulated by taking into account of the bifurcation phenomenon. Indeed, from the warpage at the bifurcation point $Warpage_{bif}$ of the taiko wafer, we can determine an overall equivalent thickness of the taiko wafer, such that the taiko wafer act as with a thickness of $h_{tot,eq}\,= h_{s,eq}\,+ h_{m,eq}\,= 2Warpage_{bif} /\sqrt{1+v_{s}}$ of an equivalent flat wafer.