Electron energy probability function and L-p similarity in low pressure inductively coupled bounded plasma

Particle-In-Cell (PIC) simulations are carried out to investigate the effect of discharge length (L) and pressure (p) on Electron Energy Probability Function (EEPF) in a low pressure radio frequency (rf) inductively coupled plasma (ICP) at 13.56MHz. It is found that for both cases of varying L (0.1-0.5 m) and p (1-10 mTorr), the EEPF is a bi-Maxwellian with a step in the bounded direction (x) and non-Maxwellian with a hot tail in the symmetric unbounded directions (y, z). The plasma space potential decreases with increase in both L and p, the trapped electrons having energies in the range 0-20 eV. In a conventional discharge bounded in all directions, we infer that L and p are similarity parameters for low energy electrons trapped in the bulk plasma that have energies below the plasma space potential (eV(p)). The simulation results are consistent with a particle balance model.