New Method to Recover Activation Energy: Application to Copper Oxidation

Abstract

The calculation of the activation energy helps to understand and to identify the underlying phenomenon of oxidation. We propose a new method without any a priori hypothesis on the oxidation law, to retrieve the activation energy of partially and totally oxidized samples subject to successive annealing. The method handles the uncertainties on the measurement of metal and oxide thicknesses, at the beginning and at the end of the annealing process. The possible change in oxidation law during annealing is included in the model. By using an adapted Particle Swarm Optimization method to solve the inverse problem, we also calculate the time of final oxidation during the last annealing. We apply the method to successive annealings of three samples with initial nanometric layers of copper, at ambient pressure, in the open air. One, two and three successive laws are recovered from experimental data. We found activation energy values about 105–108 kJ mol−1 at the beginning of the oxidation, 76–87 kJ mol−1 at the second step, and finally 47–59 kJ mol−1 in a third step. We also show that the time evolution of copper and oxide thicknesses can also be retrieved with their uncertainties.

Keywords

• metallic thin films
• activation energy
• copper
• copper oxide
• oxidation law
• Arrhenius law