Crystallite coalescence during film growth based on improved contact mechanics adhesion models

Abstract

Intrinsic tensile stress, which can lead to problems in deposited thin films such as cracking, peeling, and delamination, often develops during the early stages of thin film growth. Many attempts have been made to estimate the tensile stress during crystallite coalescence, both experimentally and analytically. Most recently, using a combination of Hertzian contact mechanics and elasticity theory, Freund and Chason applied the Johnson-Kendall-Roberts (JKR) theory to account for adhesion between crystallites under specific conditions. Other existing contact mechanics models that naturally account for adhesion include the improved Derjaguin-Muller-Toporotov and Maugis-Dugdale theories. The objective of this study is to provide useful analytical and numerical techniques based on these contact mechanics theories for a wide range of conditions that accurately approximate the intrinsic tensile stress that develops during crystallite coalescence. As an analytical method, the Maugis-Dugdale model is proposed as a more general alternative to the JKR model. Parameters such as the contact radius and “net” adhesive force are computed as a function of the relative separation between two adjacent crystallites in a thin gold film. Another useful parameter known as the “jump-to-contact” separation is also calculated by the Maugis-Dugdale and JKR models. For comparison to the analytical models, a finite element method is used to simulate the crystallite coalescence problem. The numerical technique is based on a nonlinear surface interaction element developed to approximate van der Waals adhesion, and allows for full-field analysis of stress and displacement in crystallites. Two different boundary conditions are used, for which corresponding contact radius and tensile stress are computed and compared to the analytical results. As a further study, the length scale effect is also investigated by varying the radius of individual crystallites from 20nm to 300nm. It is concluded that in order to estimate the average tensile stress accurately using analytical models, the radius of individual crystallites must be large compared to the contact radius. For small length scales, the finite element approach is more appropriate.