The theory of Langmuir probes has been reexamined for use in high-density plasma tools with plasmas in the N = 10@super 11-13@ cm@super -3@ range. The most accurate computations for collisionless plasmas have been done by Laframboise,@footnote 1@ but the results are difficult to apply to data because of the normalized units used. Up to now, for densities in the 10@super 9-11@ cm@-3@ range, the simpler Orbital Motion Limited (OML) theory has sufficed. The two theories agree at low densities. To make the Laframboise curves accessible for real-time I - V analysis of probe data at higher N, we have found analytic approximations to the curves by a double parametrization technique. Furthermore, an iterative procedure permits separating the ion and electron currents in their overlap region, thus yielding an accurate fit to the shape of the ion characteristic and hence accurate values of N and KT@sub e@ regardless of the density range. Comparison with experiment, however, gives surprising results. For N such that the ratio of probe radius to Debye length exceeds 3 (thin sheaths), the OML theory is expected to fail, but it fits the SHAPE of the ion characteristics better than the Laframboise theory, which gives N values 2-3 times higher. The latter seems to agree better with independent measurements of N using microwaves or plasma oscillation probes. We have also parametrized an intermediate theory, that of Allen, Boyd, and Reynolds,@footnote 2@ but this gives unreasonably low N values. A possible cause of the paradox is the effect of charge-exchange collisions.
@FootnoteText@
@Footnote 1@ Laframboise, J.G., Univ. Toronto Inst. Aerospace Studies Rept. 100 (June, 1966). @Footnote 2@ Allen, J.E., Boyd, R.L.F., and Reynolds, P., Proc. Phys. Soc. (London) B70, 297 (1957).