The effects of plasma characteristics on the melting time at the front surface of a film on a substrate: An exact solution

Plasma heating of a film on a substrate is solved by using the Laplace transform method. The plasma is composed of a collisionless presheath and sheath on an electrically negative bias film partially reflecting and secondly emitting ions and electrons. The heating of the film from the plasma accounting for the presheath and sheath is determined from the kinetic analysis. This work proposes an analytical model to calculate the melting time and heating rate of the front surface of a film on the substrate, and provides quantitative results applicable to control the temperature evolution and the melting time in the film. The predicted surface temperature of the film on the substrate as a function of time is found to agree well with experimental data. The effects of dimensionless bias voltage, reflectivities of the ions and electrons on the wall, electron-to-ion source temperature ratio at the presheath edge, ion-to-electron mass ratio, charge number, plasma flow work-to-heat conduction ratios, substrate-to-film solid thermal conductivity ratios, and film-to-substrate solid specific heat ratios on the melting time and heating rate of the front surface are obtained. The contact Biot number between the film and substrate to simulate the heat conduction into substrate is also discussed. The results show that the melting time is strongly dependent on the plasma parameters and thermal properties of the material.