Study of sheath thickness in weakly ionized plasmas and its dependence on the electric potential and position of the probe

Abstract

This paper studies the sheath in front of a plane probe immersed in an electropositive/electronegative plasma in the low ionization regime. We analyze the dependence of the model on the electric potential and the position of the probe. As will be shown, this relationship is a necessary condition to form the sheath and allows us to determine the thickness of the sheath. The above-mentioned relationship provides the mathematical structure of the boundary layer for the sheath in a two-scale formalism as it is well known. It also shows that the Bohm criterion unambiguously determines the potential at the sheath edge in electronegative plasmas even when the electronegativity of the plasma corresponds to values for which the electric potential has an oscillatory behavior, against the commonly accepted view.

Mass spectrometry diagnosis of ion species in low-pressure plasmas

“…Moreover, the DEPA is provided with a 50 µm radius orifice, r o , through which molecules and ions enter the PSM. This radius is lower than the Debye length of the plasma, λ D , and thus, from the point of view of the plasma, the irregularities in the electric field due to the orifice are shielded by the sheath surrounding the DEPA, since the sheath thickness, s, is about 2.6λ D , [12] or even higher [13], so, under our discharge conditions s/r o > 8. Obviously, these irregularities will be lower as r o decreases; nevertheless, no differences are observed when a 25 µm radius orifice is used, so the 50 µm radius orifice is used to increase the signal-to-noise ratio in the PSM measurements.…”

Cold plasma chemistry and diagnostics

“…New calorimetric probes allow estimations of energy fluxes on substrates [52]. In all these cases, special care should be taken to minimize perturbations of the plasma [53][54][55]. Electron temperatures can be deduced alternatively from optical emission measurements assisted by collisional radiative models [56,57].…”

Study of the electropositive to electronegative sheath transition in weakly ionized plasmas

“…This oscillatory structure is related to the Bohm criterion [15] when extended to electronegative plasmas due to its multivalued character [16]. The ratios of negative ion and electron density and temperature, for which oscillations occur, can be affected by the presence of ionization, collisions and/or positive ion thermal motion [6,[17][18][19][20].…”

“…For these purposes, it is important to know what is the relationship between some easily measurable parameters such as the probe size or the electric potential of the probe and other parameters related to the plasma characteristics through the sheath (i.e. positive ion current collected by the probe or the ionization rate) [4][5][6][7]. Several authors have studied positive sheaths in both electropositive and electronegative plasmas.…”

“…In this way, this paper analyzes the thickness of the sheath for a plane probe immersed in weakly ionized plasma and its transition from electropositive to electronegative behavior. This analysis has been done according to the Bohm criterion which has been extensively studied by several authors [12,14,15,17,18] Nevertheless, this analysis uses the formulation of the Bohm criterion provided by the authors in a recent work [6], which is based on the two-scale length formalism that characterizes sheath models. As we show, for the case of electronegative plasmas, the Bohm criterion is not multi-valued but the presheath solution.…”