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 rim 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 µm to 400 µm, with a step height fixed to 450 µm. The FSM layer consisted of an Al layer of 4.5 µm thin. The system was subjected to a thermal load such that, getting cooled from a nominal temperature T to 25°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 °C to 170 °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 of the taiko wafer, we can determine an overall equivalent thickness of the taiko wafer.

In this work, the analytical Lagrange-Kirchhoff model for the deformation for a taiko plate silicon is proposed. Under the conditions of validity of the linear theory of thin plates, the model is in agreement with the experimental data.

The successful handling of large semiconductor wafers is crucial for scaling up their production. Early-stage warpage control allows to prevent undesirable asymmetric warpage, known as wafer bifurcation or buckling. Indeed, even in a gravity-free environment, thinning an 8" or 12" semiconductor wafer can result in warpage and bifurcation. To mitigate this issue, the taiko method, which involves creating a thicker ring region around the rim of the wafer, has been widely used. Previous research has focused on the theoretical factors affecting the warpage of a backside metalized taiko wafer. This work extends the case to a front-side metalized taiko wafer and introduces the concept of the equivalent thickness of a taiko wafer. The equivalent thickness of a taiko wafer, influenced by the ring region, lies in between the thickness of the central region and that of the annular region. Because of the limited number of taiko wafers that can be produced on a production line, modelling can be beneficial. In this work we compared the results of a developed analytical model with those obtained from a finite element analysis (FEA) approach with ANSYSY® software to model the equivalent thickness of a taiko wafer. We investigated the curvature as a function of the stress of the metal layer, considering key design factors such as the substrate region thickness, the thickness of the thin metal film, the step height, and the width of the ring region. By systematically varying the thickness of the central region of the taiko wafer, we explored the curvature as a function of stress induced by thermal load in the linear regime and determined the slopes in the linear region of the curvature vs. stress curves. The aim of this study is to identify regularities and similarities with the Stoney equation and investigate the validity of the analytical approach for the case of a taiko substrate. It results that there is a good agreement between the analytical model of a taiko wafer and the numerical analysis gained by the FEA methods.

An extension of the Stoney formula for the case of a back side metallized 8” silicon taiko wafer has been developed, in the elastic regime, within the frame of the theory of elasticity. A good correlation between the calculated warpage, determined by the stress released by a given back side metallization (BSM), and the corresponding experimental warpages of the same thick metal layers deposited on an 8” silicon taiko wafer provides evidences of the correctness of the developed theory. This development suggests the possibility to extend this approach to the case of 8” taiko wafers based on a wide band gap semiconductor such as silicon carbide (SiC).