Numerical simulation of bearing balls in the plasma immersion ion implantation process

The process of bearing balls in the plasma immersion ion implantation (PIII) is simulated using a 2-dimensional particle-in-cell (PIC) model. The distributions of normalized potential and dose are studied. In order to avoid overlap of sheaths between different balls in batch process, the minimum distance between two neighboring balls is calculated. When the voltage is -40 kV, plasma density is 4.8 × 10⁹ cm^-3 and pulse width is 10 μs, the minimum distance between two balls should be 34. 18 cm. In addition, the dose distribution along the circumference of the ball is non-uniform. Consequently, a revolving substrate is used to improve the uniformity. Furthermore, to evaluate the model, the expansion process of sheath is measured using a Langmuir probe. Experimental results agree with the calculated value, and the maximum relative error is less than 8.4%.