Evaluation of polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation for thinned silicon wafers

Abstract

Polishing is widely used to obtain smooth thinned wafer surfaces and the process-induced subsurface damage is often evaluated by scanning electron microscope or transmission electron microscope images. However, the difference of microscope images is very slight and subtle between wafers and affected by the location selection of the measured points. In this study, we explored the method of evaluating the polishing-induced subsurface damage based on residual stress distribution via measured global surface deformation. The surface deformation was first measured and then the polishing-induced residual stress distribution was calculated from the surface topography data by solving the system of linear equations. The polishing-induced subsurface damage could be evaluated independent of the dimension of the silicon wafer by the proposed method. How the thinned silicon wafer was supported during measurement process greatly affected polishing-induced wafer deformation and gravity-induced deformation should be separated from the measured data. Regularization method should be introduced in the calculation of residual stress to reduce the errors caused by the multi-collinearity of the system of linear equations. The calculated residual stress distribution was found to be an obvious centrosymmetric figure and exhibited a quasi-axisymmetric pattern with the axis of symmetry correlated with certain crystalline directions, indicating the effect of anisotropy of monocrystalline silicon in the polishing process. The proposed method could also be used in the evaluation of polishing-induced subsurface damage of other large and thin substrate plates.

Obtainment of Residual Stress Distribution from Surface Deformation under Continuity Constraints for Thinned Silicon Wafers

“…The residual stress could be obtained using the proposed regularization method with continuity constraints by the wafer deformation and used to assess the machining process The Tikhonov matrix L could also be an Identify matrix I to improve the solution result [18]. However, the effect of the positional relationship between different x i s is neglected and the improvement of the continuity of the residual stress distribution across the wafer is limited.…”

“…means that the differentiation of the wafer surface is enough to character the true status of residual stress distribution. The Tikhonov matrix L could also be an Identify matrix I to improve the solution result [18]. However, the effect of the positional relationship between different xis is neglected and the improvement of the continuity of the residual stress distribution across the wafer is limited.…”

“…Therefore, it could be simplified and the residual stress in the subsurface damage layer in Figure 2 represented the residual stresses of both sides. The details of the finite element model of silicon wafers could be found in our previous study [18]. The total wafer deformation was simulated using the calculated x and compared with the measurement result to verify the method.…”

“…The authors have engaged in research on the deformation measurement of silicon wafers and found that the deformation of thinned silicon wafers could be obtained accurately after eliminating the effect of gravity [17,18]. Unlike the cross-section observation methods which are focused on the microstructure changes, the deformations of silicon wafers are the overall effects of all the residual stresses across the wafer surface and show the potential for the evaluation of processing quality.…”

“…The conventional regularization method using an Identify matrix as the Tikhonov matrix was used in our previous research. The overfitting phenomenon was improved and the calculated largest residual stress value was reduced [18]. However, the continuity problem of the residual stress distribution across the wafer was not directly addressed since the positional relationship of different subareas was not taken into consideration.…”