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Method of calibrating effects of multi-AOI-system for easy changing angles-of-incidence in ellipsometers and the like

  • US 7,265,838 B1
  • Filed: 08/24/2004
  • Issued: 09/04/2007
  • Est. Priority Date: 09/29/1998
  • Status: Expired due to Term
First Claim
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1. A method of accurately evaluating parameters in parameterized equations in a mathematical model of a system of spatially separated input and output electromagnetic beam intercepting angle-of-incidence changing system elements, said parameterized equations enabling, when parameters therein are properly evaluated, independent calculation of retardation entered by each of said input output electromagnetic beam intercepting angle-of-incidence changing system elements between orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output electromagnetic beam intercepting angle-of-incidence changing system elements, at least one of said input and output electromagnetic beam intercepting angle-of-incidence changing system elements being birefringent, said method comprising, in a functional order, the steps of:

  • a. providing spatially separated input and output electromagnetic beam intercepting angle-of-incidence changing system elements, at least one of said input and output electromagnetic beam intercepting angle-of-incidence changing system elements demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a sample system positioned between said input and output electromagnetic beam intercepting angle-of-incidence changing system elements;

    b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said input electromagnetic beam intercepting angle-of-incidence changing system element, interact with a sample system, in a plane of incidence thereto, and exit through said output electromagnetic beam intercepting angle-of-incidence changing system element and enter said detector system;

    c. providing a sample system to said means for supporting a sample system, the composition of said sample system being sufficiently well known so that retardance entered thereby to a polarized beam of electromagnetic radiation of a given wavelength, which is caused to interact with said sample system in a plane of incidence thereto, can be accurately modeled mathematically by a parameterized equation which, when parameters therein are properly evaluated, allows calculation of retardance entered thereby between orthogonal components of a beam of electromagnetic radiation caused to interact therewith in a plane of incidence thereto;

    d. in combination with the other steps, providing a mathematical model for said ellipsometer system and said input and output electromagnetic beam intercepting angle-of-incidence changing system elements, in which electromagnetic radiation is caused to pass through said input and output electromagnetic beam intercepting angle-of-incidence changing system elements, and said sample system, comprising separate parameterized equations for independently calculating retardance entered between orthogonal components of a beam of electromagnetic radiation caused to pass through each of said input and output electromagnetic beam intercepting angle-of-incidence changing system elements, and interact with said sample system in a plane of incidence thereto;

    such that where parameters in said mathematical model are properly evaluated, retardance entered between orthogonal components of a beam of electromagnetic which passes through each of said input and output electromagnetic beam intercepting angle-of-incidence changing system elements, and interacts with said sample system in a plane of incidence thereto can be independently calculated from said parameterized equations;

    e. obtaining a spectroscopic set of ellipsometric data with said parameterizable sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input electromagnetic beam intercepting angle-of-incidence changing system element, interact with said parameterizable sample system in a plane of incidence thereto, and exit through said output electromagnetic beam intercepting angle-of-incidence changing system element and enter said detector system, such that a physical concrete and tangible transformation of said electromagnetic beam from one state to another is caused by interaction thereof with said parameterizable sample system and said input and output electromagnetic beam intercepting angle-of-incidence changing system elements;

    f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independently calculating retardance entered between orthogonal components in a beam of electromagnetic radiation caused to pass through said input electromagnetic beam intercepting angle-of-incidence changing system element, interact with said sample system in a plane of incidence thereto, and exit through said output electromagnetic beam intercepting angle-of-incidence changing system element;

    to the end that application of said parameterized equations for each of said input and output electromagnetic beam intercepting angle-of-incidence changing system elements and sample system for which values of parameters therein have been determined in step f., enables independent calculation of retardance entered between orthogonal components of a beam of electromagnetic radiation by each of said input and output electromagnetic beam intercepting angle-of-incidence changing system elements, and said sample system, at given wavelengths in said spectroscopic set of ellipsometric data, said calculated retardance values for each of said input electromagnetic beam intercepting angle-of-incidence changing system element, output electromagnetic beam intercepting angle-of-incidence changing system element and sample system being essentially uncorrelated;

    said result being useful and the direct result of a physical concrete and tangible transformation of said electromagnetic beam from one state to another caused by interaction thereof with said parameterizable sample system and said input and output electromagnetic beam intercepting angle-of-incidence changing system elements.

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