Nonparametric estimation of SiC film residual stress from the wafer surface profile

Abstract

Thin film residual stress is proportional to substrate curvature change after film deposition, based on Stoney’s equation. Curvature is approximately equal to the second derivative of substrate deflection. It is common to apply Stoney’s equation locally, where the residual stress at a selected point and direction is estimated from the local substrate curvature. The locally weighted least squares regression method (LowLSR) is adapted for estimating the substrate curvature in the radial directions across the wafer from the corresponding deflection profiles measured by a profilometer. LowLSR is implemented in the R package npregderiv developed by the authors. The changing film thickness profiles in the radial directions are estimated using the local linear estimator and plugged into Stoney’s equation. Thus, this research is the first attempt of using nonparametric statistical methods to estimate the residual stress in SiC films with non-uniform thickness.