Method and apparatus for characterizing a plasma using broadband microwave spectroscopic measurements

Abstract

A method and apparatus for accurately characterizing the electron density and distribution of a confined plasma on the basis of high-frequency, broadband electromagnetic measurements is disclosed herein. The technique involves noninvasive, broadband measurement of electromagnetic transmission through a plasma. In one implementation, multivariate analysis techniques are employed to correlate features of the resultant spectra with plasma characteristics such as electron density or electron distribution. Alternately, such techniques are used to correlate the resultant spectra with parameters relating to conditions under which the plasma is generated. More specifically, the quantitative plasma characterization technique involves generating a set of broadband calibration spectra by measuring transmission of electromagnetic energy through a calibration plasma. Each broadband calibration spectrum is obtained using a different set of reference parameters being related to predefined quantitative characteristics. The reference parameters may comprise known values of quantitative characteristics of the calibration plasma including, for example, electron distribution or electron density. Alternately, the reference parameters may comprise known values of operating conditions within the chamber bearing a predetermined empirical relationship to particular plasma quantitative characteristics. A reference parameter transformation, which relates measured spectra of electromagnetic energy transmitted through the calibration plasma to values of the reference parameters, is derived on the basis of the broadband calibration spectra. A test spectrum is then obtained by measuring transmission of electromagnetic energy through a subject plasma. Values of the predefined quantitative characteristics of the subject plasma are then determined by analyzing the test spectrum using the reference parameter transformation.

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