A semi-analytical method to study the temperature evolutions of a slab and a semi-infinite target for plasma immersion ion implantation

The problems of heating a slab of finite thickness and a semi-infinite target with repetitive high negative bias voltage pulses in contact with a plasma are solved by using the two-dimensional Laplace integral transform technique. The plasma is composed of a collisionless presheath and sheath on an electrically negative biased wall, which partially reflects and secondarily emits ions and electrons. The heating of the workpiece from the plasma accounting for the presheath and sheath is determined by kinetic analysis. This work proposes a semi-analytical model to calculate the temperature evolutions and the melting times of the front surface of a slab and a semi-infinite target, and provides quantitative results applicable to control the temperature evolutions and the melting times. The predicted surface temperature of the slab as a function of time is found to agree well with experimental data. The effects of dimensionless pulse parameters, including the pulse duty cycle and pulse bias voltage, on the melting time and heating rate of the front surface are obtained. The results show that the temperatures and heating rates of the front surface of the slab and target increase with pulse parameters. The melting times to initiate the melting at the front surface are strongly dependent on the pulse parameters. The heat flux transport to workpiece from plasma is important to increase the surface temperature of the workpiece when the bias voltage is switched-off for low pulse duty cycle and low pulse bias voltage. The temperature of the workpiece is underestimated when not accounting for the heating effects during the pulse-off duration for low value of pulse parameters.