Understanding residual stress in thin films: Analyzing wafer curvature measurements for Ag, Cu, Ni, Fe, Ti, and Cr with a kinetic model

Abstract

An analytical model for the evolution of residual stress in polycrystalline thin films is used to analyze numerous previously reported wafer curvature measurements obtained for a variety of materials and processing conditions. The model, which has been described in previous publications, considers stress-generating mechanisms that occur at the grain boundary as it forms between adjacent grains and stress due to the subsurface grain growth in layers that have already been deposited. Current work extends the model to include different types of microstructural evolutions. A set of parameters for each dataset is obtained by non-linear least square fitting. Model parameters that are not expected to depend on the processing conditions are constrained to have a common value when fitting the multiple datasets for each material. The dependence of the fitting parameters on the material and process conditions is evaluated and compared with the physical mechanisms implemented in the model.

Effect of processing conditions on residual stress in sputtered transition metal nitrides (TiN, ZrN and TaN): Experiments and modeling

“…The data are consistent with the Hoffman model, although the range of measurements is too small to confirm the predicted dependence. For comparison, a linear correlation was also observed between σ T and ̅̅̅̅̅̅̅̅̅̅̅̅ M f T M √ for evaporated metals [44]. The results for the metal-nitrides are smaller than what would be expected from extrapolation of the evaporated metal results.…”

“…The model parameters are described in Section 4.1. During the fitting, the parameters σ c , σ T , βD, D i are assumed to be independent of processing conditions so that a single value of each was used to fit all the stress data in each material [44]. A 0 , B 0 , l can be different for different values of the pressure and gas flow rate ratios.…”

“…As discussed in ref. [44], the fitting produces a reasonable set of values for the parameters, but their values should not be taken as unique, absolute minima of the mean-squared difference. This is because of several effects including physical approximations that make the model imperfect, experimental errors in the data and the broad minimum in parameter space.…”

“…L is the grain size in the film which is assumed to remain constant for steady-state conditions. The mechanisms in this model, with the addition of stress from grain growth, have been used to analyze stress in metal films deposited by electrodeposition [35,[39][40][41][42] and evaporation [43,44].…”

Polymer-Regulated Electrochemical Reduction of CO2 on Ag

“…The high HER selectivity observed for the (111)-textured Ag ≥ −1.1 V is congruent with previous reports. , The textured evaporated film in this work demonstrates even higher selectivity for the HER compared to an epitaxially grown Ag(111) thin film (86% vs ≈ 50% around −1 V, respectively), which could result from the increased H binding energy due to differences in stress that result from the evaporation process. − Other reports have investigated the production of single-crystal-like surfaces using thin film fabrication procedures and obtained eCO 2 RR results more in line with pure single-crystal counterparts . Another possibility, besides stress induced by evaporation, could be the influence of ambient adventitious carbon on the surface.…”