(Invited) Thermodynamics of Deposition Flux Dependent Intrinsic Film Stress

The growth of polycrystalline films at temperatures above ~0.2 of the melting temperature is accompanied by compressive stress development after film closure.
Mysteriously, a significant part of this stress has a reversible nature: it disappears when the deposition is stopped and re-emerges upon resumption. Chason [1] even showed the corresponding inverse behavior during electrochemical etching

All these observations clearly point towards a steady-state, flux (etching rate) dependent equilibrium phenomenon, which should, therefore, be treated properly by thermodynamics.

It has been suggested that the variation of the surface chemical potential upon starting/stopping of the deposition may cause adatoms to diffuse in/out of the grain boundaries leading to the development/relaxation of the intrinsic compressive film stress.
However, film growth involves a myriad of atomic processes such that the mystery is not yet solved and new mechanisms and ideas are still published frequently.

Here we present an analytical derivation, in which we address, for the first time, the reason why additional atoms want to get incorporated in the grain boundaries. This background delivers the required driving force independently of the precise way the atoms get incorporated. In this sense we are not proposing a new model, but delivering the basis for all different models proposed.

To derive the driving force, we calculate the variation of the chemical potential of the surface, the grain boundaries, and the film. Surprisingly, using pure thermodynamic arguments, our results fully agree with the magnitude of the reversible compressive stress:
the tremendous stress levels observed in the experiments can indeed be explained by the flux induced density variations in the extremely dilute adatom gas on the surface!

[1] Shin and Chason, Phys. Rev. Lett. 103, 056102 (2009)

E-mail:rost@physics.leidenuniv.nl
Web: www.physics.leidenuniv.nl/rost