Langmuir probe analysis for high density plasmas

Abstract

High-density, radio-frequency plasmas used in semiconductor processing have progressed to densities ${\text{n⩾5×10}}^{11} {\mathrm{cm}}^{\text{−3}},$ where the methods used to interpret Langmuir probe characteristics in low-density ${\text{(10}}^{\text{9–11}} {\mathrm{cm}}^{\text{−3}})$ plasma reactors are no longer valid. Though theory and computations for arbitrarily dense collisionless plasmas exist, they are difficult to apply in real time. A new parametrization and iteration scheme is given which permits rapid analysis of Langmuir probe data using these theories. However, at high n, measured ion saturation curves are shown which do not agree in shape with the “correct” theory, yielding anomalously high values of n. The discrepancy with independent measures of n, which can exceed a factor of 2, is believed to be caused by charge-exchange collisions well outside the sheath. Probe designs for avoiding this discrepancy are suggested.