IMPROVED INTRINSIC STRESS MODELS FOR THIN FILMS BASED ON SURFACE STRESS
Study of stress evolution in thin films has been an area of rigorous research for the past few decades. In spite of these research efforts, understanding stress generation and relaxation remains incomplete. In this study, a modified surface stress based approach for modeling intrinsic stresses in thin film using dome-shaped islands and hexagonal shaped grains is proposed. Equations that describe stress evolution at the precoalescence, coalescence and postcoalescence growth stages were derived. The results of the models were then compared to some previous models and validated with experimentally obtained values for copper and silver films at various growth stages. For Cu films deposited on silicon substrates, intrinsic stresses of -200, 140 to 230 and -260 to -80 MPa were obtained for precoalescence, coalescence and steady state postcoalescence stages, respectively while the current models gave -261, 102 and -115MPa. For continuous film, the current model gave -115 MPa which is comparable to -140 MPa obtained from an experimental study conducted on Cu thin films. Furthermore, parametric studies showed that the directions of growth for both intrinsic and steady state stress are converse. Thus, the results obtained indicate that the current models are reliably and can be used for accurate stress prediction. The predictions of the current models are closer to the experimental values than any of the previous models.