A model for pressurized hydrogen induced thin film blisters

TL;DR

This paper presents a theoretical model for hydrogen-induced blister formation in nanometer-thick films, calculating critical parameters like adhesion energy, internal pressure, and blister growth conditions, validated with experiments on Mo/Si multilayers.

Contribution

The paper introduces a novel model for blister formation that combines energy and flux balances, enabling estimation of key physical parameters from experimental data.

Findings

Adhesion energy of blister cap ~1.05 J/m²

Internal pressure in blisters 175-280 MPa

Minimum ion dose for blister formation ~4.2×10^18 ions/cm²

Abstract

We introduce a model for hydrogen induced blister formation in nanometer thick thin films. The model assumes that molecular hydrogen gets trapped under a circular blister cap causing it to deflect elastically outward until a stable blister is formed. In the first part, the energy balance required for a stable blister is calculated. From this model, the adhesion energy of the blister cap, the internal pressure and the critical H-dose for blister formation can be calculated. In the second part, the flux balance required for a blister to grow to a stable size is calculated. The model is applied to blisters formed in a Mo/Si multilayer after being exposed to hydrogen ions. From the model the adhesion energy of the Mo/Si blister cap was calculated to be around 1.05 J/m2 with internal pressures in the range of 175-280 MPa. Based on the model a minimum ion dose for the onset of blister formation was calculated to be d = 4.2*10^18 ions/cm2. From the flux balance equations the diffusion constant for the Mo/Si blister cap was estimated to be D_H2 = (10+-1) *10^18 cm2/s.