A Method for Obtaining Stress - Depth Profiles by Absorption Constrained Profile Fitting of Diffraction Peaks

A new absorption constrained profile fitting method has been developed for use in depth profile analysis of residual stress using x-ray diffraction data at a series of fixed incidence angles. By explicitly accounting for absorption of x-rays during the peak fitting process this method establishes a direct association between a chosen layer depth and resulting fit data. While peak positions are still converted to stress values via conventional methods the method yields plots of average values of stress for layers whose thickness and depth can be independently chosen, rather than plots of stress as a function of 1/e penetration depth. An example of the application of the method to the determination of the residual stress versus depth profile in a 600 nm sputtered W film is presented. Introduction Historically, various methods for extracting depth profiles of residual stress from x-ray diffraction peaks have been reported in the literature. The earliest method (which is still used in some applications) involved collecting a series of diffraction peaks with a layer of material being removed after each pattern was collected. More recently developed depth profiling methods used a series of fixed incidence diffraction profiles to investigate residual stress as a function of depth. In each case, the peak positions obtained from the diffraction data were associated with the 1/e penetration depth, τ. Subsequently, τ-profiles of residual stress were converted to z-profiles using either a LaPlace transformation technique or numerical methods. Although these more recent depth profiling methods have the advantage over the layer removal method in that they are non-destructive, they are not ideal. In particular, these depth profiling methods are subject to the following limitations: 1. It is difficult to establish the uniqueness of the solution. 2. The LaPlace transformation method can only be used in cases where the profiling depth is much less than the film thickness. 3. Since the conventional definition of an expression for τ assumes a semi-infinite diffracting medium, τ characterization of diffraction data from thin films does not represent a consistent fraction of the diffracted intensity (the fraction of intensity associated with each τ value depends upon the film thickness, incidence angle and hkl considered). 4. There is insufficient constraint for unique profile fits to be obtained when peaks from different layers are close together in 2θ. 5. If the structure or the stress state is layered, absorption of the beam with depth is not properly accounted for in the subsurface layers. Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 1