Plasma density determination from ion current to cylindrical Langmuir probe with validation on hairpin probe measurements

Abstract

Numerical and analytical approaches to plasma density determination from the ion current to cylindrical Langmuir probe are validated on hairpin probe measurements. An argon inductively coupled plasma discharge in a pressure range from 4.5 mTorr to 27 mTorr is studied. The discharge input power is varied in the range from 200 to 800 W, giving a plasma density in the range from 109 to 1011 cm−3. The approaches used for plasma density determination are analytical collisionless orbital motion limit theory, fluid semianalytical model of ion radial motion with ion collisions and particle-in-cell with a Monte Carlo collisions model of ion current collection by the cylindrical Langmuir probe. The relative error of different models is shown. The ion collisions should be taken into account, even at relatively low pressures, in order to get a reliable plasma density value from the ion current to the Langmuir probe.