On the modulation of electron energy distribution function in radiofrequency SiH₄, SiH₄−H₂ bulk plasmas

Abstract

Electron energy distribution functions (EDF) in SiH₄, SiH₄−H₂ radiofrequency discharges have been calculated by solving the time-dependent Boltzmann equation in the presence of a sinusoidal field. Particular emphasis is given to the modulation of EDF as a function of the applied frequency (π·10⁶≤ω/p ₀ ≤π·10⁸ sec⁻¹ torr⁻¹) and of gas composition. The results show that at ω/p ₀ = π·10⁶ sec⁻¹ torr⁻¹ EDF follows in a quasistationary mode the variation of the field with the exception of a small range of electric field near to the zero crossing. Still, at the higher considered frequency (ω/p ₀ =π·10⁸ sec⁻¹ torr⁻¹), we observe some modulation of EDF. The necessity of using a time-dependent approach is tested by comparing the present results with the corresponding ones obtained by using the effective field approximation (i.e., the approximation which solves instead of the time-dependent Boltzmann equation the corresponding stationary one at the effective values$E = E_o /\sqrt 2$ of the rf field). The two sets of results can differ by orders of magnitude in the tail of EDF, the differences decreasing with increasing molar fraction of H₂ and increasing field frequency. The role of excited states (second-kind collisions) is studied by inserting in the Boltzmann equation given concentrations of vibrational and electronic states. The results show that second-kind collisions strongly affect EDF especially in pure silane. Finally a satisfactory agreement has been found between theoretical and experimental results concerning the modulation of electrons of given energy in pure silane discharges.