Dual mechanical behaviour of hydrogen in stressed silicon nitride thin films

Abstract

In the present article, we report a study on the mechanical behaviour displayed by hydrogen atoms and pores in silicon nitride (SiN) films. A simple three-phase model is proposed to relate the physical properties (stiffness, film stress, mass density, etc.) of hydrogenated nanoporous SiN thin films to the volume fractions of hydrogen and pores. This model is then applied to experimental data extracted from films deposited by plasma enhanced chemical vapour deposition, where hydrogen content, stress, and mass densities range widely from 11% to 30%, −2.8 to 1.5 GPa, and 2.0 to 2.8 g/cm3, respectively. Starting from the conventional plotting of film's Young's modulus against film porosity, we first propose to correct the conventional calculation of porosity volume fraction with the hydrogen content, thus taking into account both hydrogen mass and concentration. The weight of this hydrogen-correction is found to evolve linearly with hydrogen concentration in tensile films (in accordance with a simple “mass correction” of the film density calculation), but a clear discontinuity is observed toward compressive stresses. Then, the effective volume occupied by hydrogen atoms is calculated taking account of the bond type (N-H or Si-H bonds), thus allowing a precise extraction of the hydrogen volume fraction. These calculations applied to tensile films show that both volume fractions of hydrogen and porosity are similar in magnitude and randomly distributed against Young's modulus. However, the expected linear dependence of the Young's modulus is clearly observed when both volume fractions are added. Finally, we show that the stiffer behaviour of compressive films cannot be only explained on the basis of this (hydrogen + porosity) volume fraction. Indeed this stiffness difference relies on a dual mechanical behaviour displayed by hydrogen atoms against the film stress state: while they participate to the stiffness in compressive films, hydrogen atoms mainly behave like pores in tensile films where they do not participate to the film stiffness.