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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 at 13.56 MHz. 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 in the symmetric unbounded directions (y, z) the EEPF are a Maxwellian with a hot tail. The plasma space potential decreases with increase in both L and p, the trapped electrons having energies in the range 0 to 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 (eVp). The simulation results are consistent with a particle balance model.