Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas

The widely used Child-Langmuir law for sheath thickness evaluation in semi- infinite collisionless plasmas makes the assumptions of quasi-neutrality (n (e) = n(i)) and zero electric held intensity E = 0 at the sheath edge, as w ell as applying the Bohm criterion for ions entering the sheath. However, t hrough a whole region fluid model, Poisson's equation has been solved numer ically for the steady-state solution through the sheath and presheath witho ut these assumptions. With the sheath edge defined, as in the Child-Langmui r law, at the place where the ion velocity is equal to the Bohm velocity, t he sheath thickness of a bounded collisionless or weakly collisional plasma has been found with this model in some cases to be much larger than that o btained with the Child-Langmuir Law. The sheath thickness discrepancy is si gnificant under conditions found in low pressure high density plasma (HDP) tools for plasma processing, Results presented indicate that the sheath thi ckness is very sensitive to the electric field and space charge density at the sheath edge. The electric field and space charge density can be success fully estimated by an intermediate scale matching method [1]-[5], and are u sed to derive a modified expression for the potential in the sheath that ca n be solved numerically for sheath thickness, With these results, the match ing problem, arising when sheath and plasma are modeled separately, can be overcome.